From eca18f065ee76ffde900b8d1b6d9a994a66987d6 Mon Sep 17 00:00:00 2001 From: Adam Gohs Date: Thu, 15 Oct 2026 13:19:03 -0400 Subject: [PATCH 1/5] Move the Backward Erosion Piping Screening technical reference to the System Response Library Migrates the document from the developer section to web-applications/system-response/backward-erosion-piping-screening as an active draft, with its bibliography and navigation updated for the new location. --- .../v1.0/00-document-info.mdx | 25 + .../v1.0/00-version-history.mdx | 29 ++ .../v1.0/01-preface.mdx | 46 ++ .../v1.0/02-model-overview.mdx | 135 ++++++ .../v1.0/03-input-parameters.mdx | 441 ++++++++++++++++++ .../v1.0/04-flaw-assessment.mdx | 175 +++++++ ...05-hydraulic-loading-and-seepage-paths.mdx | 210 +++++++++ .../v1.0/06-event-tree.mdx | 280 +++++++++++ .../v1.0/07-delegated-models.mdx | 201 ++++++++ .../v1.0/08-assumptions-and-limitations.mdx | 117 +++++ .../v1.0/09-output-and-interpretation.mdx | 199 ++++++++ .../v1.0/_input-needed.md | 245 ++++++++++ src/docConfig.js | 2 +- .../v1.0/bib.json | 50 ++ 14 files changed, 2154 insertions(+), 1 deletion(-) create mode 100644 docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/00-document-info.mdx create mode 100644 docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/00-version-history.mdx create mode 100644 docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/01-preface.mdx create mode 100644 docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/02-model-overview.mdx create mode 100644 docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/03-input-parameters.mdx create mode 100644 docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/04-flaw-assessment.mdx create mode 100644 docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/05-hydraulic-loading-and-seepage-paths.mdx create mode 100644 docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/06-event-tree.mdx create mode 100644 docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/07-delegated-models.mdx create mode 100644 docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/08-assumptions-and-limitations.mdx create mode 100644 docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/09-output-and-interpretation.mdx create mode 100644 docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/_input-needed.md create mode 100644 static/bibliographies/web-applications/system-response/backward-erosion-piping-screening/v1.0/bib.json diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/00-document-info.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/00-document-info.mdx new file mode 100644 index 000000000..2b5cff419 --- /dev/null +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/00-document-info.mdx @@ -0,0 +1,25 @@ +--- +title: Document Info +reportDate: August 2026 +reportType: Technical Reference +reportTitle: BEP Screening Model Technical Reference +reportSubTitle: System Response Library +reportAuthors: ['Adam Gohs, P.E.'] +reportAbstract: Technical reference documenting the Backward Erosion Piping (BEP) screening model in the System Response library. The model computes a system response probability (SRP) for backward erosion piping at each headwater level using a seven-node event tree. The probability of a continuous foundation flaw is estimated by Bayesian updating of a geology-based prior with subsurface and seepage-observation evidence. Unfiltered-exit and initiation probabilities are computed from blanket theory with a companion defect-survival model for the downstream confining layer, and progression is evaluated with the Schmertmann critical-gradient method. The model applies screening-level simplifications appropriate for the Dam Screening Tool. +reportSubjectTerms: ['BEP', 'Backward Erosion Piping', 'Screening', 'Event Tree', 'System Response Probability', 'System Response Curve', 'Blanket Theory', 'Bayesian Updating', 'Dam Screening Tool', 'Monte Carlo'] +citationGuide: 'U.S. Army Corps of Engineers, Risk Management Center, BEP Screening Model Technical Reference, Lakewood, CO: U.S. Army Corps of Engineers, Risk Management Center, 2026.' +--- + +import Link from '@docusaurus/Link'; +import DocumentMetadata from '@site/src/components/DocumentMetadata'; +import NavContainer from '@site/src/components/NavContainer'; + + + +# Document Information + + diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/00-version-history.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/00-version-history.mdx new file mode 100644 index 000000000..19979ae91 --- /dev/null +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/00-version-history.mdx @@ -0,0 +1,29 @@ +--- +title: Version History +--- + +import NavContainer from '@site/src/components/NavContainer'; +import TableVersionHistory from '@site/src/components/TableVersionHistory'; + + + +# Version History + + diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/01-preface.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/01-preface.mdx new file mode 100644 index 000000000..29e139cd1 --- /dev/null +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/01-preface.mdx @@ -0,0 +1,46 @@ +--- +title: Preface +--- + +import NavContainer from '@site/src/components/NavContainer'; + + + +# Preface + +This document provides a technical reference for the Backward Erosion Piping (BEP) screening model in the System Response library. The model +computes a system response probability (SRP) as a function of headwater elevation for the backward erosion piping failure mode. It is designed for +the Dam Screening Tool (DST), where it operates with screening-level simplifications intended to reduce input burden while avoiding false +negatives. + +The intended audience includes dam and levee safety engineers evaluating whether the model is appropriate for their assessment, and peer reviewers +checking the technical basis of screening-level results. Readers are assumed to have a general background in internal-erosion risk analysis — +event trees, seepage mechanics, and probability concepts — but no familiarity with the software implementation is required. + +The document covers the model's complete execution pathway: the evidence-based assessment of a continuous foundation flaw, the resolution of +hydraulic loading and seepage-path geometry from the site inputs, the assembly of the seven-node event tree at each pool level, the assumptions +made along the way with their engineering bases, the inputs the user provides and the options available, and the results the model produces. + +## Document Organization + +- **[Model Overview](./02-model-overview.mdx)** — The model's purpose, its role in the Dam Screening Tool, the overall execution pathway from + inputs to results, the exit pathways evaluated and when each exists, and the relationship to the full toolbox models. +- **[Input Parameters](./03-input-parameters.mdx)** — Every user input: hydraulic loading, embankment geometry, upstream blanket, downstream + seepage berm, confining-layer characterization, flaw-evidence selections, embankment materials, foundation sand properties, unit weights, and + the intervention and breach probabilities, with units, valid ranges, defaults, and guidance for each selectable option. +- **[Flaw Assessment](./04-flaw-assessment.mdx)** — The Bayesian assessment of the probability that a continuous path of fine to medium, uniform + sand exists in the foundation: the geology-based prior, the subsurface-data and seepage-observation evidence updates, and the uncertainty + quantification. +- **[Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx)** — The downstream reference elevations, the treatment of + tailwater, the net driving head, the resolution of the upstream, embankment, and downstream seepage path lengths, and the selection between the + two blanket-theory configurations. +- **[Event Tree](./06-event-tree.mdx)** — The seven event-tree nodes, how each probability is populated at each pool level (including the + composition of the unfiltered-exit node from the defect and blowout pathways), and how the SRP and the governing system response curve are + computed. +- **[Delegated Models](./07-delegated-models.mdx)** — How the screening model invokes the blanket-theory initiation analysis and the Schmertmann + progression analysis: the quantities passed in, the outputs consumed, and each fixed screening-level adjustment relative to the dedicated + toolbox models. +- **[Assumptions and Limitations](./08-assumptions-and-limitations.mdx)** — Each modeling assumption with its engineering basis, its effect on + results, and the conditions under which it may not hold. +- **[Output and Interpretation](./09-output-and-interpretation.mdx)** — The complete result inventory, how to read the system response curve, + which exit pathway tends to govern, sensitivity to key inputs, and the role of screening results relative to detailed analysis. diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/02-model-overview.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/02-model-overview.mdx new file mode 100644 index 000000000..8964d9b46 --- /dev/null +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/02-model-overview.mdx @@ -0,0 +1,135 @@ +--- +title: Model Overview +--- + +import NavContainer from '@site/src/components/NavContainer'; +import TableReference from '@site/src/components/TableReference'; +import TableVertical from '@site/src/components/TableVertical'; + + + +# Model Overview + +## Purpose + +The BEP screening model computes a system response probability (SRP) for the backward erosion piping failure mode as a function of headwater +elevation. The SRP represents the conditional probability of dam or levee breach due to backward erosion piping, given a specific pool level. The +model produces a system response curve — an array of SRP values across a range of headwater elevations — that characterizes the structure's +vulnerability to this failure mode. + +Backward erosion piping is the progressive removal of cohesionless foundation soil by seepage, beginning at an unfiltered downstream exit and +eroding backward (upstream) beneath the embankment until a continuous pipe connects the impounded water to the exit. The failure mode requires a +continuous path of erodible material, an unfiltered exit, sufficient gradient to initiate erosion, a soil roof that keeps the developing pipe +open, and sufficient gradient to advance the pipe to the reservoir. + +## Intended Use + +The model is designed for the Dam Screening Tool (DST), where it serves as a screening-level assessment of backward erosion piping risk. It makes +simplifying and generally conservative assumptions with two goals: + +- **Preventing false negatives** — The model is calibrated to avoid underestimating risk at the screening level, so that structures with + potential BEP concerns are flagged for further analysis. +- **Reducing input burden** — The model requires fewer inputs than the full BEP toolbox models. Qualitative selections (confining layer + thickness category, relative density category, geologic environment) substitute for site-specific distributions, and default distributions + cover material properties that are typically unavailable at the screening stage. Where a site characteristic is genuinely unknown — the + presence of a confining layer, or the extent of that layer beyond the embankment — the model accepts "unknown" as an answer and substitutes a + deliberately wide characterization rather than requiring the user to guess. + +The model is not intended for detailed or semi-quantitative risk assessments. For higher-level analyses, the full +[BEP Initiation (BT Case 1–8)](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-initiation/v1.0/preface) and +[BEP Progression (Schmertmann and Sellmeijer)](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.0/preface) +toolbox models provide the complete methodologies with full parameterization. + +## How the Model Works + +The screening model executes three stages: + +1. **Flaw assessment** — A Bayesian analysis estimates the probability that a continuous path of fine to medium, uniform sand exists in the + foundation. A prior probability based on the geologic depositional environment is updated with subsurface-data evidence and observed-seepage + evidence when available. The mean posterior probability populates the first event-tree node and is independent of pool level + (see [Flaw Assessment](./04-flaw-assessment.mdx)). + +2. **Hydraulic and seepage-geometry resolution** — The model resolves the downstream reference elevations that control net driving head, the + upstream seepage path length $L_1$, the embankment base width $L_2$, and the downstream seepage path length $L_3$ from the site inputs, and + selects the appropriate blanket-theory configuration — Case 2 when an upstream seepage barrier is present, Case 4 otherwise + (see [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx)). + +3. **Event-tree assembly** — At each headwater level, the model composes seven node probabilities and multiplies them to produce the SRP. Two + nodes are evaluated by Monte Carlo simulation delegated to established analysis methods: blanket theory computes the blowout and heave + probabilities feeding the unfiltered-exit and initiation nodes, and the Schmertmann critical-gradient method computes the probability of pipe + progression. A companion defect-survival model contributes the probability that a pre-existing defect already penetrates the confining layer + (see [Event Tree](./06-event-tree.mdx) and [Delegated Models](./07-delegated-models.mdx)). + +## Exit Pathways + +The model evaluates up to two seepage exit pathways: + +- **Toe pathway** — Seepage exits at the downstream toe of the embankment, or at the toe of the downstream seepage berm when one is present. + This pathway is always evaluated. When a confining layer may be present and the toe exit remains beneath it — no berm, or a berm ending + within the layer's known extent — the unfiltered-exit probability at the toe is composed from two mechanisms — a pre-existing defect through + the layer, and hydraulic blowout (rupture) of the layer — and the initiation probability is the blanket-theory heave probability. Where a + berm instead places the exit at or beyond the layer's downstream termination, the exit daylights at the berm toe and the unfiltered-exit + and initiation probabilities are certain there. + +- **Daylight pathway** — Seepage exits at the downstream termination of the confining layer, where the underlying sand daylights at the ground + surface. This pathway is evaluated whenever a confining layer may be present (its presence is confirmed or unknown) *and* the daylighting + exit is distinct from the toe exit. At the daylight exit there is no confining layer to penetrate, so the unfiltered-exit and initiation + probabilities are both certain there, and the pathway is distinguished by its longer seepage path to the exit. When a berm over a confirmed + layer reaches or clears the layer's downstream extent — or overlies a confirmed layer whose extent is unknown — the berm toe is itself the + daylighting exit: the toe pathway then represents that exit directly, so a separate daylight pathway would repeat the same exit and is not + reported. A layer of unknown presence always retains both pathways. + +The governing SRP at each headwater level is the maximum of the two pathway SRPs, so the more critical exit condition controls the screening +result. When no confining layer is present — or the daylighting exit is the berm toe, so the toe pathway already represents it — only the toe +pathway is evaluated and it governs directly. + +## Relationship to Toolbox Models + +The screening model delegates its Monte Carlo computations to the same analysis engines as the standalone toolbox models — the blanket-theory +initiation cases and the Schmertmann progression method — but constructs their configurations internally from the screening inputs, applying +fixed screening-level simplifications. summarizes the differences. + + + +The delegated analysis engines execute identically whether invoked by the screening model or directly — the screening model controls only the +configuration passed to them. [Delegated Models](./07-delegated-models.mdx) documents each fixed choice and its basis. diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/03-input-parameters.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/03-input-parameters.mdx new file mode 100644 index 000000000..13ec2d809 --- /dev/null +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/03-input-parameters.mdx @@ -0,0 +1,441 @@ +--- +title: Input Parameters +--- + +import EquationNoRef from '@site/src/components/EquationNoRef'; +import NavContainer from '@site/src/components/NavContainer'; +import TableReference from '@site/src/components/TableReference'; +import TableVertical from '@site/src/components/TableVertical'; + + + +# Input Parameters + +This chapter documents every user input to the BEP screening model. Inputs are organized into ten groups: hydraulic loading, embankment geometry, +upstream blanket, downstream seepage berm, foundation flaw evidence, confining-layer characterization, observed-seepage refinements, embankment +materials, foundation sand properties and unit weights, and the intervention and breach probabilities. + +Several inputs are statistical distributions that characterize uncertainty in a physical quantity. A distribution input may take any of five +forms: a deterministic (single) value, a uniform distribution between a low and high bound, a normal distribution (mean and standard deviation), +a triangular distribution (low, mode, high), or a PERT distribution (low, mode, high). The Monte Carlo analyses described in +[Delegated Models](./07-delegated-models.mdx) sample these distributions. Geometric seepage-path lengths — the upstream blanket length, the berm +length, and the confining-layer extents — are the exception: a known length is a site measurement entered as a single value. Where such a length +is unknown, the input is omitted and the model substitutes the wide default characterization documented in +[Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx). + +## Hydraulic Loading + +The hydraulic loading is defined by a headwater rating series and an optional companion tailwater series +(). The model evaluates the event tree across a range of pool levels spanning the supplied +headwater values. + + + +## Embankment Geometry + +The embankment cross-section is described by its crest and by slope-segment tables for the upstream and downstream faces +(). Each face is a sequence of one or more segments ordered from the crest down to the toe; +each segment is defined by its bottom elevation and its slope, expressed as horizontal run per unit of vertical rise (H:V). Multiple segments +accommodate compound slopes and intermediate benches. + +c', 'Wc', '—', '—', 'Eday'], + ['ft', 'ft', 'ft, H:V', 'ft, H:V', 'ft'], + [ + 'Required', + '> 0 (required)', + 'At least one segment (required)', + 'At least one segment (required)', + 'Optional', + ], + [ + 'Elevation of the embankment crest.', + 'Width of the embankment crest.', + 'Bottom elevation and slope of each upstream face segment, ordered from the crest to the toe. Every slope must be positive.', + 'Bottom elevation and slope of each downstream face segment, ordered from the crest to the toe. Every slope must be positive. The lowest segment elevation defines the downstream toe, which must lie below the crest.', + 'Ground-surface elevation at the downstream termination of the confining layer — the daylight exit. When omitted, the daylight exit is assumed to share the toe reference elevation (the berm toe when a berm with a specified toe elevation is present, otherwise the downstream embankment toe). When the daylighting exit is the berm toe itself (a berm over a confirmed layer that reaches or clears its downstream extent, or overlies a layer of unknown extent), a supplied value is ignored with a validation warning: the berm-toe reference is the only coherent datum for that exit (see Hydraulic Loading and Seepage Paths).', + ], + ]} +/> + +Three geometric quantities are derived from the cross-section rather than entered directly: + +- **Downstream toe elevation** $E_{toe}$ — the lowest bottom elevation among the downstream face segments. +- **Embankment base width** $L_2$ — the crest width plus the horizontal projections of the upstream and downstream faces from the crest to + their respective toes. This is the embankment component of the seepage path. A downstream seepage berm is *not* part of $L_2$; it extends the + downstream seepage path beyond the toe instead (see [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx)). +- **Embankment height** $H_d = E_c - E_{toe}$ — used to scale the downstream seepage path when the confining layer extent is unknown. + +## Upstream Blanket + +An engineered impervious blanket extending upstream of the embankment lengthens the seepage path and reduces gradients at the downstream exit +(). When an upstream blanket is present, the blowout and heave analyses route to Blanket +Theory Case 2, which represents impervious strata on both sides of the embankment (see +[Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx)). + +1'], + ['—', 'ft'], + ['Yes / No (default No)', '> 0; required when the blanket is present'], + [ + 'Whether an engineered impervious blanket extends upstream of the embankment toe.', + 'Length of the blanket measured from the upstream embankment toe, entered as a single value. It serves directly as the upstream seepage path length L1.', + ], + ]} +/> + +## Downstream Seepage Berm + +A downstream seepage or stability berm adds weight over the exit area and displaces the seepage exit beyond the berm +(). Its consequences for the event tree depend on where the berm ends relative to the +confining layer: a berm ending within a confirmed layer's known extent retains the through-layer exit mechanisms at an exit point beyond the +berm, while a berm that reaches or clears the layer's extent — or overlies a layer of unknown extent or unknown presence — is assumed to +produce a daylighting exit at the berm toe, where the unfiltered exit is certain. Every berm extends the toe progression path. The full rules +are documented in [Event Tree](./06-event-tree.mdx) and [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx). + +b', 'Ebt'], + ['—', 'ft', 'ft'], + ['Yes / No (default No)', '> 0; required when the berm is present', 'Optional'], + [ + 'Whether a downstream seepage or stability berm is present.', + 'Length of the berm measured from the downstream embankment toe.', + 'Ground-surface elevation at the downstream toe of the berm. When provided, this elevation becomes the toe reference for the net head on the toe progression pathway. When omitted, the ground beneath the berm is assumed flat and the berm toe shares the downstream embankment toe elevation.', + ], + ]} +/> + +## Foundation Flaw Evidence + +The probability that a continuous path of fine to medium, uniform sand exists in the foundation is assessed from three categories of evidence +(). The meaning of each selection and the way the evidence combines are documented in +[Flaw Assessment](./04-flaw-assessment.mdx). + + + +## Confining-Layer Characterization + +The downstream confining layer — a fine-grained stratum overlying the foundation sand on the landside — controls whether seepage can exit +unfiltered at the toe. Seven inputs characterize it (). The presence selection is +deliberately tri-state: when the presence of a layer cannot be established, the model runs the full confined-exit machinery with a wide +thickness characterization rather than assuming either extreme. The categorical selections carry no preselected answer in the Dam Screening +Tool: the thickness category, the permeability, and the upstream-extension question start unanswered, and the calculation does not run until +the user has chosen a category — including Unknown — for each one that applies. The defaults noted in the table are the values the model +assumes when a request omits the field; they are not presented to the user as a starting selection. + + 0; required when the layer extends upstream and its thickness category is not Very Thin', + 'Single value, ft; > 0; optional (omitted = unknown)', + ], + [ + 'Whether a confining layer overlies the foundation sand downstream of the embankment. Yes confirms the layer: the defect and blowout analyses run with the selected thickness category, and the layer itself is credited as the roof for pipe progression. No removes the layer: seepage exits unfiltered at the toe with certainty, and only the toe pathway is evaluated. Unknown runs the defect and blowout analyses with the Unknown thickness band and evaluates roof support from the embankment materials, so an unverified layer is neither ignored nor fully credited.', + 'Qualitative thickness of the confining layer. Each category maps to a uniform thickness range per the table below. Select the category supported by borings or geologic mapping; select Custom to supply a site-specific distribution; select Unknown when no thickness information exists. When the layer presence is Unknown, the Unknown band is used regardless of the category selected.', + 'Site-specific thickness distribution used when the thickness category is Custom.', + 'Permeability character of the confining layer. Only a layer characterized as Impervious is credited as an upstream seepage barrier (see Hydraulic Loading and Seepage Paths); a Semi-pervious or Unknown layer contributes no upstream head loss.', + 'Whether the confirmed impervious layer continues upstream beneath the reservoir. The question is asked only when no engineered upstream blanket is present (a blanket takes precedence as the upstream barrier). Yes credits the layer as the upstream seepage barrier and asks for its length; No and Unknown credit no upstream head loss. A Yes answer for a Very Thin layer is recorded but credits a zero-length extension.', + 'Length of the confining layer beyond the upstream embankment toe, entered as a single value. Supplied only when the layer extends upstream; it is credited directly as the upstream seepage path L1. When the extension question is answered No or Unknown, no upstream head loss is credited.', + 'Length of the confining layer beyond the downstream embankment toe, entered as a single value. This is the distance to the daylight exit. Omitted means unknown: with no berm, the downstream seepage path is characterized by a wide default range scaled to the embankment height (see Hydraulic Loading and Seepage Paths); with a berm over a confirmed layer, a daylighting exit is assumed at the berm toe. When a berm is present, the supplied extent also determines whether the berm end remains beneath the layer — retaining the through-layer exit mechanisms at an offset exit point — or reaches and clears the layer, producing a daylighting exit at the berm toe (see Event Tree). As a seepage-path length, a supplied extent is used only when the layer presence is confirmed Yes; when the presence is Unknown, the wide default range applies to the no-berm path regardless, although a supplied extent still determines whether a berm reaches or clears the layer.', + ], + ]} +/> + +Each qualitative thickness category maps to a uniform distribution of confining-layer thickness $z_{bl}$ +(). + + + +:::warning[INPUT NEEDED IN-01 — Engineering Basis] +The thickness ranges assigned to the qualitative confining-layer categories (Very Thin 0–5 ft, Thin 5–10 ft, Moderate 10–20 ft, Thick +20–35 ft, Unknown 0–10 ft) require an engineering basis. Provide a literature citation (to be added to the bibliography) or the +engineering-judgment attribution to state here, including the reasoning for the Unknown band spanning 0–10 ft. +::: + +## Observed-Seepage Refinements + +When sand boils or concentrated seepage have been observed, two additional inputs refine how that observation enters the event tree +(). + + + +## Embankment Materials + + + +## Foundation Sand Properties + +The foundation sand — the erodible aquifer beneath the embankment — is characterized by its thickness, relative density, gradation, and fines +content (). The thickness, the relative density category, and the fines content category +are required selections with no preselected answer; Unknown is offered for the two categories but must be chosen deliberately. The gradation +properties carry screening defaults that the user may override with site-specific distributions. + +r', 'Cu', 'D10', '—'], + ['ft', '%', '—', 'mm', '%'], + [ + 'Required (no default)', + 'Required (no default); Unknown maps to uniform 15–65%', + 'Triangular (1.1, 2.0, 4.0)', + 'Normal (mean 0.25, standard deviation 0.085), values limited to no less than 0.1', + 'Required (no default); Unknown maps to 0.0', + ], + [ + 'Thickness of the pervious foundation (aquifer) layer, as a distribution. Used by both the blanket-theory analysis (seepage path entrance and gradient computations) and the Schmertmann progression analysis (depth correction).', + 'Qualitative relative density of the foundation sand. Each preset category maps to a uniform distribution per the table below; the Custom category instead uses a site-specific distribution supplied by the user. Denser sands resist progression through the Schmertmann density correction.', + 'Coefficient of uniformity of the foundation sand gradation. Controls the base critical gradient in the Schmertmann method — more uniform sands (lower values) are more erodible.', + 'Grain size at 10% passing for the foundation sand. Controls the Schmertmann grain-size correction.', + 'Fines content of the foundation sand, selected as one of three categories: less than 5%, 5% or more, or Unknown. The first two enter the model as deterministic fines contents of 0% and 5%, which place the sand on either side of the step in the screening fines-content correction of the Schmertmann analysis (see Delegated Models). Unknown omits the field, so the model applies its 0% default and takes no fines credit.', + ], + ]} +/> + +:::warning[INPUT NEEDED IN-02 — Engineering Basis] +The default coefficient-of-uniformity distribution (triangular with low 1.1, mode 2.0, high 4.0) requires an engineering basis. Provide a +literature citation or the engineering-judgment attribution to state here. + +Proposed (unconfirmed): representative of the poorly graded, uniform fine to medium sands that are susceptible to backward erosion piping; +confirm or replace. +::: + +:::warning[INPUT NEEDED IN-03 — Engineering Basis] +The default effective-grain-size distribution (normal with mean 0.25 mm and standard deviation 0.085 mm, limited below at 0.1 mm) requires an +engineering basis — both the distribution parameters and the lower limit. Provide a literature citation or the engineering-judgment attribution +to state here. +::: + +Each preset relative density category maps to a uniform distribution of relative density $D_r$ +(). The Unknown category carries a broad band spanning loose to medium-dense conditions; +the model also accepts a legacy Default category with the same band, which the Dam Screening Tool no longer offers. Select the Custom category to supply a site-specific relative-density distribution instead; every value the custom distribution can +produce must lie within the physical range of 0 to 100% (an unbounded form such as a normal distribution therefore requires explicit lower and +upper limits). + + + +:::warning[INPUT NEEDED IN-04 — Engineering Basis] +The relative-density uniform ranges require an engineering basis — the category band boundaries and the choice of the 15–65% band for the +Unknown category. Provide a literature citation or the engineering-judgment attribution to state here. + +Proposed (unconfirmed): the category boundaries (15 / 35 / 65 / 85%) follow the standard qualitative relative-density classification for +granular soils; a uniform distribution over each band takes no position on a most-likely value within the category; and the Unknown +band spans loose to medium-dense as a conservative screening posture. Confirm or replace, and supply the classification source for the +bibliography if the proposal stands. +::: + +## Unit Weights + +Two saturated unit weights enter the blanket-theory critical-gradient computations +(): the confining layer's for blowout (rupture of the layer) and the foundation sand's for +heave through a defect. Both carry screening defaults that may be overridden. + +sand', 'γbl'], + ['pcf', 'pcf'], + ['Normal (mean 122.0, standard deviation 3.0)', 'Normal (mean 118.0, standard deviation 3.0)'], + [ + 'Saturated unit weight of the foundation sand. Sets the critical vertical gradient for heave through a defect in the confining layer.', + 'Saturated unit weight of the confining-layer material. Sets the critical vertical gradient for hydraulic blowout (rupture) of the layer.', + ], + ]} +/> + +:::warning[INPUT NEEDED IN-05 — Engineering Basis] +The default foundation-sand saturated unit weight (normal with mean 122.0 pcf and standard deviation 3.0 pcf) requires an engineering basis. +Provide a literature citation or the engineering-judgment attribution to state here. + +Proposed (unconfirmed): typical of loose to medium-dense saturated alluvial sand; confirm or replace. +::: + +:::warning[INPUT NEEDED IN-06 — Engineering Basis] +The default confining-layer saturated unit weight (normal with mean 118.0 pcf and standard deviation 3.0 pcf) requires an engineering basis. +Provide a literature citation or the engineering-judgment attribution to state here. +::: + +## Intervention and Breach Probabilities + +The final two event-tree nodes are user-specified scalar probabilities (). Both default to +1.0 (certain), which is conservative for screening. + + diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/04-flaw-assessment.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/04-flaw-assessment.mdx new file mode 100644 index 000000000..9efd43f9a --- /dev/null +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/04-flaw-assessment.mdx @@ -0,0 +1,175 @@ +--- +title: Flaw Assessment +--- + +import Equation from '@site/src/components/Equation'; +import EquationReference from '@site/src/components/EquationReference'; +import NavContainer from '@site/src/components/NavContainer'; +import TableReference from '@site/src/components/TableReference'; +import TableVertical from '@site/src/components/TableVertical'; + + + +# Flaw Assessment + +The first event-tree node is the probability that a continuous path of fine to medium, uniform sand exists in the foundation — the flaw that +backward erosion piping requires. The screening model estimates this probability with a Bayesian assessment: a prior probability based on the +geologic depositional environment is updated by the available site evidence. The assessment is independent of pool level; the resulting +probability applies across the entire system response curve. + +## Bayesian Framework + +The assessment combines up to three pieces of information: + +1. **Geologic prior** — The depositional environment of the foundation soils sets the prior probability $p_0$ that a laterally continuous, + uniform fine sand layer was deposited. +2. **Subsurface-data evidence** — When borings, soundings, geophysics, or comparable data inform the judgment, the analyst characterizes the + strength of that evidence for (or against) a continuous flaw, together with the quality of the data behind the judgment. +3. **Seepage-observation evidence** — When seepage has been observed downstream during past loading, the character of the observation serves + as evidence that a continuous transmissive pathway already exists. + +Each evidence source is expressed as a likelihood ratio $LR$ — the ratio of the probability of the observation given that a continuous flaw +exists to its probability given no flaw. Ratios above one make the flaw more probable; ratios below one make it less probable. The update is +performed in log-odds form: + + + + + + + +where: + +> $p_0$ = prior probability of a continuous flaw from the geologic environment +> $\ell_0$, $\ell$ = prior and posterior log-odds +> $LR_{sub}$ = likelihood ratio for the subsurface-data evidence +> $q$ = subsurface data quality factor, which scales the weight given to the subsurface evidence +> $LR_{seep}$ = likelihood ratio for the seepage observation +> $P_{flaw}$ = posterior probability of a continuous flaw + +When subsurface data is not available, the subsurface term drops out of (equivalently, +$LR_{sub} = 1$). When no seepage has been observed, the seepage term drops out ($LR_{seep} = 1$). The quality factor $q$ acts as an exponent on +the subsurface likelihood ratio: high-quality data receives full weight ($q = 1$), while lower-quality data is discounted toward neutral +($q < 1$). + +## Uncertainty Quantification + +Each categorical selection maps to a *range* of values rather than a single number, reflecting the imprecision of the underlying judgments. +The model propagates this uncertainty by Monte Carlo simulation: in each realization, the prior probability and each active likelihood ratio +and quality factor are drawn independently and uniformly from their ranges, and the posterior probability is computed from +. Across realizations this produces a distribution of the posterior flaw probability. + +The **mean posterior probability** populates the event-tree node. The 5th–95th percentile band of the posterior is reported alongside it as a +diagnostic, so the user can see how sharply the evidence constrains the flaw judgment (see +[Output and Interpretation](./09-output-and-interpretation.mdx)). + +## Geologic Environment Priors + + lists the prior probability range for each depositional environment. Environments that +deposit laterally continuous, well-sorted fine sands — glacial outwash foremost — carry the highest priors. The Unknown selection carries a +moderate, deliberately broad prior. + + + +:::warning[INPUT NEEDED IN-07 — Engineering Basis] +The prior probability ranges by geologic depositional environment require an engineering basis. Provide a literature citation (to be added to +the bibliography) or the engineering-judgment attribution to state here — including whether the ranges derive from a published compilation of +depositional-environment characteristics or from elicited expert judgment. +::: + +## Subsurface-Data Evidence + + lists the likelihood-ratio range for each strength-of-evidence selection, and + the quality factor that scales the weight of that evidence. A neutral selection carries a +likelihood ratio of exactly one (no update in either direction). + + + + + +:::warning[INPUT NEEDED IN-08 — Engineering Basis] +The strength-of-evidence likelihood-ratio ranges and the data-quality factor ranges require an engineering basis. Provide a literature +citation or the engineering-judgment attribution to state here — including the reasoning behind the order-of-magnitude bands (0.01–30) and +the quality discounts (0.50–1.00). +::: + +## Seepage-Observation Evidence + + lists the likelihood-ratio range for each observed seepage signature. Localized, +sediment-transporting observations are the strongest evidence of a continuous transmissive flaw; diffuse wet areas that do not respond to pool +level are close to uninformative. + + + +:::warning[INPUT NEEDED IN-09 — Engineering Basis] +The seepage-observation likelihood-ratio ranges require an engineering basis. Provide a literature citation or the engineering-judgment +attribution to state here. +::: + +A sand-boil or concentrated-seepage observation also interacts with the event tree beyond the flaw node: it activates the +seepage-through-confining-layer question and, through the trigger elevation, can force the initiation node to certainty at high pools +(see [Input Parameters](./03-input-parameters.mdx) and [Event Tree](./06-event-tree.mdx)). diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/05-hydraulic-loading-and-seepage-paths.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/05-hydraulic-loading-and-seepage-paths.mdx new file mode 100644 index 000000000..cc7be6d7f --- /dev/null +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/05-hydraulic-loading-and-seepage-paths.mdx @@ -0,0 +1,210 @@ +--- +title: Hydraulic Loading and Seepage Paths +--- + +import Citation from '@site/src/components/Citation'; +import CitationFootnote from '@site/src/components/CitationFootnote'; +import Equation from '@site/src/components/Equation'; +import EquationReference from '@site/src/components/EquationReference'; +import NavContainer from '@site/src/components/NavContainer'; +import TableReference from '@site/src/components/TableReference'; +import TableVertical from '@site/src/components/TableVertical'; + + + +# Hydraulic Loading and Seepage Paths + +Before the event tree is assembled, the model resolves the hydraulic loading and the seepage-path geometry from the site inputs: the downstream +reference elevations that control net driving head, the treatment of tailwater, the three seepage path components $L_1$, $L_2$, and $L_3$, the +selection between the two blanket-theory configurations, and the location of the exit evaluation point. This chapter documents each resolution +rule in calculation order. + +## Downstream Reference Elevations + +Two reference elevations define the downstream boundary of the head computations: + +- **Toe reference elevation** $E_{toe,ref}$ — the controlling ground surface at the downstream limit of the embankment section. When a seepage + berm is present and its toe ground-surface elevation is specified, the berm toe controls; otherwise the downstream embankment toe controls + (the ground beneath a berm is then assumed flat, so the berm toe shares the embankment toe elevation). + +- **Daylight reference elevation** $E_{day,ref}$ — the controlling ground surface at the downstream termination of the confining layer, where + the foundation sand daylights. When the daylight ground-surface elevation is supplied, it controls; otherwise the daylight exit is assumed to + share the toe reference elevation. The daylight ground may sit above or below the embankment toe. One exception applies: when the daylighting + exit is the berm toe itself — a berm over a confirmed layer that reaches or clears its downstream extent, or overlies a layer of unknown + extent — the toe reference is the exit's datum, and a separately supplied daylight ground-surface elevation would describe the same location + a second time. The supplied value is then ignored and the validation reports a warning. + +The blowout and heave analyses and the daylight progression pathway reference the daylight elevation; the toe progression pathway references the +toe elevation. Consequently, once a daylight ground surface is supplied (and the daylighting exit is not the berm toe), the embankment toe +elevation no longer enters the unfiltered-exit and initiation head computations at all — the daylight ground is the exit datum for those nodes. + +## Tailwater and Net Driving Head + +At each pool level, the downstream control level is the higher of the tailwater and the applicable reference elevation. Where no tailwater +exists — the tailwater series was omitted, or an individual stage has no tailwater — the control level falls directly to the reference +elevation. The net driving head is then: + + + +where: + +> $h$ = headwater elevation +> $t$ = tailwater elevation at that pool level (where one exists) +> $E_{ref}$ = the applicable reference elevation ($E_{day,ref}$ for the blowout, heave, and daylight-progression analyses; $E_{toe,ref}$ for +> the toe-progression analysis) + +A pool at or below the exit reference elevation produces zero net head — no water stands against the seepage path above its exit — so the +pool-dependent event-tree nodes contribute no failure probability there. This gate is a deliberate feature of the model. + +The control level is evaluated at the supplied rating points and varies linearly between them. On any rating segment where the raw tailwater +crosses the reference elevation, this linear treatment slightly overstates the control level (and so slightly understates the net head) within +that segment; the effect is bounded by the segment's tailwater change and is noted in +[Assumptions and Limitations](./08-assumptions-and-limitations.mdx). + +## Seepage Path Components + +Blanket theory idealizes the seepage path in three segments: the upstream entry length $L_1$ through or +beneath the upstream top stratum, the path $L_2$ beneath the embankment, and the downstream path $L_3$ from the embankment toe to the seepage +exit. The screening model resolves each from the site inputs. + +### Upstream Path Length L₁ + +The upstream path length is resolved by precedence: + +1. **Engineered upstream blanket present** — $L_1$ equals the supplied blanket length. +2. **Confining layer confirmed and Very Thin** — $L_1 = 0$. A very thin upstream extension is credited with no head loss. +3. **Confining layer confirmed, impervious, with a supplied upstream extension** — $L_1$ equals the supplied upstream confining-layer + length. +4. **Otherwise** — $L_1 = 0$. An upstream extension of unknown length, or a layer that is semi-pervious or of unknown permeability, is + credited with no upstream head loss. + +:::warning[INPUT NEEDED IN-10 — Engineering Basis] +Two judgments in the upstream-path crediting rules require an engineering basis to state here: + +1. A confirmed Very Thin confining layer contributes no upstream path length ($L_1 = 0$), taking precedence over the impervious-extension + credit. Proposed (unconfirmed): a layer thinner than about 5 ft cannot be relied on to remain intact and carry head loss over its upstream + extent; confirm or replace. +2. Only a layer characterized as Impervious is credited; Semi-pervious and Unknown permeability contribute nothing. + +Provide the citation or engineering-judgment attribution for each. +::: + +### Embankment Path Length L₂ + +The embankment path length $L_2$ is the derived base width of the outer shell — the crest width plus the horizontal projections of the +upstream and downstream faces (see [Input Parameters](./03-input-parameters.mdx)). A downstream seepage berm is not part of $L_2$; its length +extends the downstream path instead. + +### Downstream Path Length L₃ + +The downstream path length $L_3$ — from the embankment toe to the seepage exit — is resolved from the berm and confining-layer inputs +(). A supplied downstream extent enters as its single value; the unknown-extent default is +the only downstream-path characterization carried as a distribution. + +d to 5·Hd), sampled per Monte Carlo realization.', + 'The supplied downstream confining-layer length, as a single value.', + ], + ]} +/> + +:::warning[INPUT NEEDED IN-11 — Engineering Basis] +The default downstream path length for an unknown confining-layer extent — uniform between 1 and 5 embankment heights — requires an +engineering basis. Provide a literature citation or the engineering-judgment attribution to state here, including the reasoning for scaling +the range to embankment height. +::: + +## Blanket-Theory Configuration Selection + +The blowout and heave analyses run under one of two blanket-theory configurations, selected from the upstream seepage barrier: + +- **Blanket Theory Case 2** — impervious top strata on both the riverside and the landside + ([dedicated documentation](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-initiation/v1.0/blanket-theory-case-2)). + Selected when an engineered upstream blanket is present, **or** when the confining layer is confirmed, impervious, and has a supplied + upstream extension length. The total seepage path is: + + + +- **Blanket Theory Case 4** — no riverside top stratum, impervious landside top stratum only + ([dedicated documentation](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-initiation/v1.0/blanket-theory-case-4)). + Selected otherwise. With an open seepage entrance, the effective entry length is approximated from the foundation thickness: + + + +where $d$ is the sampled foundation sand thickness. Note that the Case 2 routing does not test the thickness category: a confirmed Very Thin +impervious layer with a supplied upstream extension still routes to Case 2, but carries $L_1 = 0$ per the crediting rules above — the +configuration reflects the presence of an upstream barrier while crediting it with no head loss. + +## Exit Evaluation Point + +The blowout and heave probabilities are evaluated at an exit point along the downstream blanket. By default the evaluation point is the +downstream toe (zero offset), where the excess head is highest. One site condition shifts it: when a berm overlies a confirmed confining layer +whose supplied downstream extent exceeds the berm length — the configuration in which the toe exit remains beneath the layer and the +through-layer defect and blowout mechanisms are retained (see [Event Tree](./06-event-tree.mdx)) — the evaluation point is offset downstream +by + + + +where: + +> $x$ = offset of the exit evaluation point from the embankment toe +> $L_{cl}$ = supplied downstream confining-layer extent +> $L_b$ = berm length + +The excess head available at the offset point follows the linear blanket-theory head profile documented in +[Delegated Models](./07-delegated-models.mdx); the offset therefore reduces the head (and the blowout and heave probabilities) relative to the +toe. When the berm instead reaches or clears the layer's downstream extent, no offset arises — the exit daylights at the berm toe and the +confined-exit nodes are overridden to certainty rather than computed (see [Event Tree](./06-event-tree.mdx)). + +:::warning[INPUT NEEDED IN-12 — Definition] +The physical interpretation of the exit-offset distance requires confirmation. The intended evaluation location is the berm toe — the first +exposed ground beyond the berm. The model computes the offset as the supplied confining-layer extent minus the berm length, measured from the +embankment toe. Under the linear head profile (head decaying from the toe value to zero at the blanket termination), the head fraction +remaining at the computed offset equals the berm length divided by the confining-layer extent — whereas an exit evaluated *at the berm toe* +(a distance of one berm length from the embankment toe) would retain the complementary fraction, the extent minus the berm length divided by +the extent. The two constructions coincide only when the berm covers exactly half the extent; for a berm covering more than half the layer +the computed offset retains more head (conservative), and for a shorter berm it retains less (non-conservative). Confirm which exit location +the offset is intended to represent — if the berm toe, the computation may warrant review. The model's computed behavior is documented as-is +above. +::: + +## Progression Path Lengths + +The Schmertmann progression analysis uses the full geometric path from the upstream limit of the seepage barrier to the exit under evaluation: + + + + + +where the berm length $L_b$ is included only when a berm is present. $L_3$ in the daylight path is sampled per Monte Carlo realization only +when the downstream extent is unknown (the one-to-five-embankment-height default); a supplied extent enters as its single value. A longer path +reduces the average applied gradient and thus the probability of progression. + +## References + + diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/06-event-tree.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/06-event-tree.mdx new file mode 100644 index 000000000..a38aa7837 --- /dev/null +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/06-event-tree.mdx @@ -0,0 +1,280 @@ +--- +title: Event Tree +--- + +import Citation from '@site/src/components/Citation'; +import CitationFootnote from '@site/src/components/CitationFootnote'; +import Equation from '@site/src/components/Equation'; +import EquationReference from '@site/src/components/EquationReference'; +import Figure from '@site/src/components/Figure'; +import NavContainer from '@site/src/components/NavContainer'; +import TableReference from '@site/src/components/TableReference'; +import TableVertical from '@site/src/components/TableVertical'; + + + +# Event Tree + +The BEP screening model computes the system response probability at each headwater level by multiplying probabilities from a seven-node event +tree. The tree follows the structure defined in the +[Typical Event Tree Database](/docs/toolbox-technical-manuals/risk-calculations-suite/typical-event-tree-database/v1.5/Backward-Erosion-Piping) +for the backward erosion piping failure mode; every database node maps one-to-one onto a screening-model node. + +
+ +## Node Summary + + summarizes the seven nodes, the engineering question each answers, and how the screening +model populates each probability. Nodes 2, 3, and 5 vary with pool level and differ between the toe and daylight pathways; the remaining nodes +are pool-independent and shared by both pathways. + + + +## Node 1: Flaw — Continuous Path + +The probability $P_{flaw}$ that a continuous path of erodible foundation sand exists is the mean posterior probability from the Bayesian flaw +assessment documented in [Flaw Assessment](./04-flaw-assessment.mdx). The flaw is a geologic condition, so this probability is constant across +all pool levels and is shared by both exit pathways. + +## Node 2: Flaw — Unfiltered Exit + +### Toe pathway + +When a confining layer may be present and the toe exit remains beneath it — no berm, or a berm ending within the layer's known downstream +extent — seepage can reach the surface unfiltered at the toe through either of two mechanisms: + +- **Pre-existing defect** — a discontinuity that already penetrates the layer (desiccation crack, root channel, animal burrow, or similar). + The probability that a defect passes completely through the layer is evaluated as a survival function on the layer thickness: + + + + where $z_{bl}$ is the confining-layer thickness, $t_c = 3.5$ ft is the characteristic defect penetration depth, and $k = 1.25$ is the shape + parameter. The expression is the probability that a defect's penetration depth equals or exceeds the layer thickness under a Weibull + distribution of defect depths — thinner layers are more likely to be fully penetrated. The probability is evaluated for each sampled layer + thickness and averaged across the Monte Carlo realizations; it does not depend on pool level. + +- **Hydraulic blowout** — rupture of the layer when uplift at its base exceeds its buoyant weight. The blowout probability $P_{blowout}(h)$ at + each pool level is computed by the blanket-theory analysis using the confining layer's saturated unit weight + (see [Delegated Models](./07-delegated-models.mdx)); it increases with pool level. The probability is evaluated at the exit evaluation + point — the toe by default, offset beyond a berm that ends within the layer's known extent + (see [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx)). + +The two mechanisms are combined as the union of independent pathways: + + + +Three site conditions override the composition and force $P_{ue} = 1.0$ at every pool level: + +1. **No confining layer** — with the layer's presence answered No, nothing filters the exit. +2. **The exit daylights at the berm toe** — for a confirmed layer, a berm that reaches or clears the supplied downstream extent, or overlies + a layer of unknown extent: the berm toe then sits at or beyond the layer's termination, so nothing filters the exit there. In these cases + the berm toe is itself the daylighting exit and no separate daylight pathway is evaluated (see Governing SRP below). For a layer of + unknown presence, any berm forces this override — a daylighting exit at the berm toe is assumed rather than established — and both + pathways are retained. +3. **Observed seepage through the layer** — sand boils or concentrated seepage have been observed emerging through the confining layer, + demonstrating that an unfiltered exit already exists. The override applies to any toe exit that remains beneath the layer, with or + without a berm. + +A berm ending within a confirmed layer's known extent triggers none of these overrides: the through-layer composition above is retained, with +the blowout probability evaluated at the offset exit point beyond the berm. + +:::warning[INPUT NEEDED IN-13 — Engineering Basis] +The Weibull defect-survival parameters — characteristic penetration depth $t_c = 3.5$ ft and shape parameter $k = 1.25$ — require an +engineering basis. These are empirical values with no published-literature provenance recorded. Provide the data source, calibration +rationale, or engineering-judgment attribution to state here. +::: + +:::warning[INPUT NEEDED IN-14 — Engineering Basis] +Two judgments in the berm treatment require an engineering basis to state here: + +1. No berm is ever credited with filtering the exit: where the berm end remains beneath the layer, the exit resistance is carried entirely + by the layer's defect and blowout composition (evaluated at the offset exit point), and where the berm daylights the exit, the unfiltered + exit is certain. +2. When the layer's presence is unknown and a berm is present, a daylighting exit at the berm toe is assumed (forcing the unfiltered exit to + certainty) rather than evaluated. + +Proposed (unconfirmed): for (1), seepage and stability berms are not engineered filters, so no filtering credit is taken for any berm; for +(2), with the layer itself unverified, its lateral extent beneath the berm cannot be relied upon, and assuming a daylighting exit at the berm +toe is the conservative screening posture. Confirm or replace. +::: + +:::warning[INPUT NEEDED IN-15 — Engineering Basis] +The union formula treats the defect and blowout mechanisms as statistically independent pathways. Provide the engineering basis or judgment +attribution for the independence treatment to state here. +::: + +### Daylight pathway + +At the daylight exit the confining layer has terminated; there is nothing to filter the seepage. The unfiltered-exit probability on the +daylight pathway is 1.0 at every pool level. The pathway itself is evaluated only when the daylighting exit is distinct from the toe exit +(see Governing SRP below). + +## Node 3: Initiation + +### Toe pathway + +Initiation at a confined exit requires the vertical gradient through the layer (or through a defect in it) to fluidize the underlying sand. +The initiation probability $P_{init}(h)$ at each pool level is the blanket-theory heave probability, computed with the foundation sand's +saturated unit weight (see [Delegated Models](./07-delegated-models.mdx)). Four site conditions override the computed value and force +$P_{init} = 1.0$: + +1. **No confining layer** — with no overburden to resist heave, initiation accompanies the unfiltered exit. +2. **A berm overlies a confirmed layer of unknown downstream extent** — a daylighting exit is assumed at the berm toe, beyond the + characterized layer. +3. **The berm reaches or clears a supplied downstream extent** — the berm is at least as long as the layer's extent, so the exit sits at or + beyond the layer's termination. The override applies whether the layer's presence is confirmed or unknown. +4. **The pool reaches the trigger elevation** — sand boils have historically activated at or above this pool, demonstrating initiation: + + + +where $E_{trigger}$ is the trigger elevation and $P_{heave}(h)$ the blanket-theory heave probability. + +Over a confirmed layer, the second and third conditions are the berm-toe daylighting cases: they force both this node and the unfiltered-exit +node to certainty, and the separate daylight pathway is not evaluated (see Governing SRP below). Under a layer of unknown presence, the third +condition forces this node alone and both pathways remain. + +### Daylight pathway + +At the daylight exit the sand is exposed at the surface with no confining layer to resist heave; the initiation probability is 1.0 at every +pool level. + +## Node 4: Progression — Mechanical Condition + +A pipe can only progress if the material above it sustains a stable roof. When the confining layer's presence is confirmed (answered Yes), the +layer itself provides the roof and the probability is 1.0. Otherwise, the probability is evaluated from the embankment materials: each USCS +class maps to a roof-support probability per , following Fell et +al. (2024), and the minimum across the listed materials governs — every material along the pipe path must +hold a roof, so the least capable material controls. The probability is constant across pool levels. + + + +## Node 5: Progression — Hydraulic Condition + +The probability that the applied gradient is sufficient to advance the pipe from the exit toward the reservoir is the mean probability of +advancement from the Schmertmann analysis, evaluated at each pool level for the pathway's seepage path length +(see [Delegated Models](./07-delegated-models.mdx)). The toe pathway uses the path to the embankment or berm toe; the daylight pathway uses +the longer path to the daylight exit. The resulting probability is constrained to be non-decreasing with pool level, reflecting that a higher +pool cannot make progression less likely. + +## Nodes 6 and 7: Unsuccessful Intervention and Breach + +The final two nodes are the user-specified scalar probabilities documented in [Input Parameters](./03-input-parameters.mdx). Both default to +1.0 — no successful intervention and certain breach — a conservative screening posture. + +## SRP Computation + +The system response probability for each pathway at each pool level is the product of its seven node probabilities: + + + +where: + +> $P_{flaw}$ = probability of a continuous flaw (Node 1) +> $P_{ue}(h)$ = probability of an unfiltered exit (Node 2) +> $P_{init}(h)$ = probability of initiation (Node 3) +> $P_{roof}$ = probability of roof support (Node 4) +> $P_{prog}(h)$ = probability of hydraulic progression (Node 5) +> $P_{int}$ = probability of unsuccessful intervention (Node 6) +> $P_{br}$ = probability of breach (Node 7) + +On the daylight pathway, $P_{ue}$ and $P_{init}$ are both 1.0 and $P_{prog}$ reflects the longer daylight path. + +## Governing SRP + +A daylight pathway is evaluated only where the daylighting exit is distinct from the toe exit. When a berm over a confirmed layer reaches or +clears the layer's downstream extent — or overlies a confirmed layer of unknown extent — the berm toe is itself the daylighting exit: the toe +pathway then carries a certain unfiltered exit and certain initiation over the berm-extended path, which are exactly the daylighting-exit +conditions, so a separate daylight pathway would repeat the same exit node for node and is not evaluated. A layer of unknown presence retains +both pathways even with a berm, because its toe pathway keeps the heave-gated initiation node and the two pathways genuinely differ. + +When both pathways are evaluated, the governing SRP at each pool level is the larger of the two pathway values: + + + +When only the toe pathway exists — no confining layer, or a berm-toe daylighting exit — it governs directly. + +## References + + diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/07-delegated-models.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/07-delegated-models.mdx new file mode 100644 index 000000000..059f55273 --- /dev/null +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/07-delegated-models.mdx @@ -0,0 +1,201 @@ +--- +title: Delegated Models +--- + +import Citation from '@site/src/components/Citation'; +import CitationFootnote from '@site/src/components/CitationFootnote'; +import Equation from '@site/src/components/Equation'; +import EquationReference from '@site/src/components/EquationReference'; +import NavContainer from '@site/src/components/NavContainer'; +import TableReference from '@site/src/components/TableReference'; +import TableVertical from '@site/src/components/TableVertical'; + + + +# Delegated Models + +The screening model delegates its Monte Carlo computations to two established analysis methods, each documented in a dedicated technical +manual: blanket theory for the blowout and heave probabilities +([BEP Initiation](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-initiation/v1.0/preface)) and the Schmertmann +critical-gradient method for progression +([BEP Progression](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.0/schmertmann)). The theory +lives in those manuals; this chapter documents how the screening model invokes each method — the quantities passed in, the outputs consumed, +and every screening-level adjustment relative to the dedicated documentation. + +## Blanket Theory — Blowout and Heave + +Blanket theory computes the excess head beneath the downstream confining layer and the vertical gradient +through it, from which the probability of a gradient-driven failure of the layer follows. The screening model routes the analysis to Case 2 or +Case 4 as documented in [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx), and runs it **twice with +identical sampled realizations** of the foundation thickness, confining-layer thickness, and downstream path length: + +- **Blowout run** — the critical gradient is computed from the *confining layer's* saturated unit weight $\gamma_{bl}$, representing rupture + of the layer's buoyant weight. Its result feeds the unfiltered-exit node. +- **Heave run** — the critical gradient is computed from the *foundation sand's* saturated unit weight $\gamma_{sand}$, representing + fluidization of the sand column at a defect through the layer. Its result feeds the initiation node. + +Because the two runs share their sampled realizations, the blowout and heave probabilities differ only through the unit weight entering the +critical gradient. + +### Governing relationships + +Within each Monte Carlo realization, and at each pool level with net head $H$ (defined in +[Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx)): + + + + + + + + + +where: + +> $h_o$ = excess head above the exit datum at the embankment toe +> $h_x$ = excess head at the exit evaluation point, offset $x$ from the toe +> $L_3$, $L_{total}$ = downstream and total seepage path lengths ($L_3$ sampled per realization when the downstream extent is unknown) +> $i_{cv}$ = critical vertical gradient +> $\gamma_{sat}$ = saturated unit weight ($\gamma_{bl}$ for blowout, $\gamma_{sand}$ for heave) +> $\gamma_w$ = unit weight of water (62.4 pcf) +> $i_v$ = vertical exit gradient through the confining layer +> $z_{bl}$ = sampled confining-layer thickness +> $FS$ = factor of safety against the vertical gradient + +The blowout or heave probability at each pool level is the fraction of Monte Carlo realizations in which $FS < 1$. Realizations with no exit +gradient (zero net head) contribute no failure. + +### Screening-level adjustments + +Relative to the dedicated blanket-theory documentation, the screening model fixes the following: + +- **Finite-blanket head loss always applies** — the excess head at the toe is always reduced by the path-length ratio + (). The idealization of an infinite downstream blanket carrying the full net head at + the toe is not used. +- **Downstream blanket length follows the resolved downstream path** — $L_3$ enters as the supplied downstream extent's single value, or is + drawn per realization from the wide default range when the extent is unknown + (see [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx)). +- **Confining-layer thickness comes from the category band** — the sampled $z_{bl}$ follows the qualitative thickness category (or the custom + distribution) documented in [Input Parameters](./03-input-parameters.mdx). +- **The unit weight is mechanism-specific** — $\gamma_{bl}$ for blowout and $\gamma_{sand}$ for heave, each defaulting per + [Input Parameters](./03-input-parameters.mdx). +- **Foundation permeability does not influence the screening result** — hydraulic conductivity affects only the seepage-quantity outputs of + the blanket-theory analysis, which the screening model does not use; the exit-gradient computations are independent of it. + +## Schmertmann Method — Progression + +The Schmertmann method evaluates whether the average applied gradient along the seepage path exceeds +the critical gradient required to advance an erosion pipe through the foundation sand. The complete method — the laboratory basis and every +correction factor — is documented in the +[BEP Progression manual](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.0/schmertmann); this +section documents the screening invocation. + +### Base gradient and critical gradient + +The base critical gradient derives from laboratory piping-model tests, represented as a family of quantile curves linear in the coefficient of +uniformity: + + + +where $i_{pmt}(q)$ is the laboratory critical gradient at cumulative probability $q$, and $m(q)$ and $b(q)$ are the quantile regression +coefficients from the dedicated documentation. The screening model uses these built-in laboratory relationships without modification. The +field critical gradient scales the laboratory gradient by the correction factors: + + + +In the screening configuration, four factors are fixed at unity and five remain active +(). + +D', 'CL', 'CS', 'Cγ', 'CK', 'CZ', 'Cα', 'CR', 'COF'], + [ + 'Active', + 'Active', + 'Active', + 'Active', + 'Fixed at 1.0', + 'Fixed at 1.0', + 'Fixed at 1.0', + 'Fixed at 1.0', + 'Active (toolbox default)', + ], + [ + 'Depth correction, from the sampled foundation thickness and seepage path length.', + 'Path-length correction, from the seepage path length.', + 'Grain-size correction, from the sampled effective grain size.', + 'Density correction, from the sampled relative density (per the category mapping or custom distribution in Input Parameters).', + 'Anisotropy correction disabled: the horizontal-to-vertical conductivity ratio is treated as 1.0. No anisotropy input is accepted at the screening level.', + 'Underlayer correction disabled: no underlayer beneath the aquifer is characterized at screening level.', + 'Pipe-path inclination fixed horizontal (inclination of 0°), so no inclination correction applies.', + 'Reference correction at its baseline value.', + 'Overall field correction — the product of the fines-content correction and the exit-geometry factor, per the equations below.', + ], + ]} +/> + +### Exit geometry and fines corrections + +The overall field correction is: + + + +The exit-geometry factor $C_{3d}$ distinguishes concentrated (hole-type) exits from distributed (plane-type) exits. Van Beek et +al. (2015) found that three-dimensional flow converging toward a single exit point produces critical +gradients roughly half those of the two-dimensional configuration, so a hole-type exit takes $C_{3d} = 0.5$ and a plane-type exit +$C_{3d} = 1.0$. The screening model assigns the exit type as follows: + +- **Toe pathway** — hole-type ($C_{3d} = 0.5$) when the confining layer is confirmed, *unless* a berm is present and either the layer's + downstream extent is unknown or the berm reaches or clears that extent (the exit then daylights beyond the layer and is plane-type). When + the layer's presence is No or Unknown, the toe exit is plane-type. +- **Daylight pathway** — always plane-type ($C_{3d} = 1.0$); the exit is an exposed sand surface. + +The fines-content correction is a step function of the foundation sand's fines content: + + + +The higher factor applies at exactly 5% fines and above; a fines content below 5% takes no correction. This step is the Schmertmann +analysis engine's built-in fines-content relationship, not a screening-level substitution: the screening model passes no fines override, so +the screening and toolbox analyses apply the same correction. The dedicated Schmertmann documentation does not describe the fines-content +term. + +:::warning[INPUT NEEDED IN-16 — Engineering Basis] +The fines-content correction applied by the Schmertmann analysis engine — a step from 1.0 to 1.4, with the higher factor applying at exactly +5% fines and above — requires an engineering basis. Provide the source or engineering-judgment attribution for the step form, the 5% +threshold, and the 1.4 value, and add the term to the dedicated Schmertmann documentation, which currently omits it. +::: + +### Probability of advancement + +At each pool level, the applied gradient is the net head over the pathway's seepage path length: + + + +where $L_{prog}$ is the toe or daylight progression path length from +[Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx) (sampled per realization on the daylight pathway when the +downstream extent is unknown). Within each realization, the correction factors scale the entire family of laboratory quantile curves +(), and the probability of advancement is the cumulative probability that the corrected +critical gradient is at or below the applied gradient — interpolated from the scaled quantile family, and clamped to 0 and 1 beyond its ends. +A pool producing no positive net head yields no probability of advancement. + +The progression node probability at each pool level is the mean probability of advancement across the Monte Carlo realizations, subsequently +constrained to be non-decreasing with pool level as described in [Event Tree](./06-event-tree.mdx). + +## References + + diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/08-assumptions-and-limitations.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/08-assumptions-and-limitations.mdx new file mode 100644 index 000000000..5f4aa2d01 --- /dev/null +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/08-assumptions-and-limitations.mdx @@ -0,0 +1,117 @@ +--- +title: Assumptions and Limitations +--- + +import NavContainer from '@site/src/components/NavContainer'; +import TableReference from '@site/src/components/TableReference'; +import TableVertical from '@site/src/components/TableVertical'; + + + +# Assumptions and Limitations + +The BEP screening model applies deliberate simplifications relative to the full toolbox models. They reduce input requirements and are designed +to avoid false negatives at the screening level. documents each assumption with its +engineering basis, its effect on results, and the conditions under which it may not hold. Where an engineering basis is still awaiting +confirmation, the table cross-references the input marker at the assumption's primary location in this document. + + + +## Interpretation Cautions + +Three aspects of the screening formulation deserve particular attention when reading results: + +- **Unknown-driven breadth.** The Unknown selections (layer presence, thickness, extent) intentionally substitute wide characterizations. A + high screening SRP at an unknown-heavy site reflects that breadth as much as the site physics; resolving the unknowns with field information + and re-running is the intended response. + +- **Defect-pathway dominance for thin layers.** Because the defect-survival probability rises steeply as the layer thins, the unfiltered-exit + node for Very Thin and Unknown thickness bands is often controlled by the defect pathway rather than blowout, and it does not diminish at + low pools (the defect probability is pool-independent). The pool dependence of the SRP then comes mainly from the initiation and progression + nodes. + +- **No driving head below the exit reference.** Pools at or below the governing exit reference elevation produce zero net head and therefore + effectively zero SRP. The reference elevations — and the daylight ground surface in particular — directly position the low-pool end of the + system response curve. diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/09-output-and-interpretation.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/09-output-and-interpretation.mdx new file mode 100644 index 000000000..246bea989 --- /dev/null +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/09-output-and-interpretation.mdx @@ -0,0 +1,199 @@ +--- +title: Output and Interpretation +--- + +import NavContainer from '@site/src/components/NavContainer'; +import TableReference from '@site/src/components/TableReference'; +import TableVertical from '@site/src/components/TableVertical'; + + + +# Output and Interpretation + +The analysis reports three groups of results: pool-independent probabilities, pool-dependent series, and audit values describing the resolved +analysis configuration. + +## Pool-Independent Results + + + +## Pool-Dependent Series + +Every pool-dependent result is reported as a series over the evaluated pool levels, which span the supplied headwater rating +(). The daylight-pathway series are present only when a confining layer may be present +(its presence is Yes or Unknown) *and* the daylighting exit is distinct from the toe exit. When the berm toe is itself the daylighting exit — +a berm over a confirmed layer that reaches or clears its downstream extent, or overlies a layer of unknown extent — the daylight series are +absent and the toe series carry the governing curve (see [Event Tree](./06-event-tree.mdx)). + + + +## Analysis Audit Record + +Alongside the numerical results, the analysis reports an audit record documenting how the model resolved the analysis configuration, so a +reviewer can verify the routing, geometry, and inputs without re-deriving them. The record is observation-only — assembling it never alters +the numerical results — and contains: + +- **Selected blanket-theory configuration** — Case 2 or Case 4, per the routing rule in + [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx); not reported when no confining layer is present (the + blowout and heave analyses do not run). +- **Effective seepage path lengths** — the upstream path length $L_1$ and embankment base width $L_2$ actually used; the low and high + bounds of the resolved downstream path length $L_3$ (equal when $L_3$ resolved to a single value), together with the resolution rule that + produced each of $L_1$ and $L_3$; and the toe and daylight progression path lengths. +- **Resolved hydraulic geometry** — the toe and daylight reference elevations, the exit-evaluation offset, whether the toe exit was treated + as a concentrated (hole-type) exit, and whether the daylighting exit resolved to the berm toe (collapsing the daylight pathway into the + toe pathway). +- **Resolved inputs with their origins** — every distribution the analysis used, each marked as supplied by the user, filled from a + screening default, derived from a qualitative category, or overridden by the model (for example, the thickness band forced to Unknown when + the layer presence is unverified), with an explanatory note wherever the resolution needs one; and the per-material roof-support + probabilities behind the governing minimum. +- **Delegated-analysis records** — one record per delegated analysis (the flaw assessment, the blowout and heave analyses, the defect + evaluation, and the toe and daylight progression analyses) documenting the exact quantities passed in and a digest of the outputs + consumed, including the net head series and the initiation probabilities at the toe and at the offset exit point. +- **Node provenance** — which rule produced the toe unfiltered-exit and initiation values: computed from the underlying mechanisms, or + forced to certainty by a specific override, with the trigger elevation echoed so per-pool forcing is readable off the series. +- **Request echo and replay** — a verbatim copy of the request as received, and, on each delegated-analysis record, the service endpoint + that reproduces that analysis directly from the recorded quantities, so a reviewer can rerun any single delegated analysis in isolation. +- **Resolution summaries** — the mean of the resolved downstream path length $L_3$ and whether the analysis treated a confining layer as + possibly present (presence Yes or Unknown), alongside the full resolution record above. +- **Sampling health** — the number of degenerate Monte Carlo realizations encountered, in total and split between the progression and + blanket-theory analyses, and the mean Schmertmann factor-of-safety series behind the progression digest; a blanket-theory digest also + carries the engine's own consistency checks. +- **Run metadata** — the wall-clock computation time and the UTC completion timestamp, and any non-fatal validation warnings raised while + resolving the inputs (for example, an ignored daylight ground-surface elevation). + +The audit record is requested with the analysis and is included by default; a caller may omit it, which changes no numerical output. + +### Monte Carlo Controls + +The delegated analyses sample their distributions by Monte Carlo simulation under three controls that the request may override and that +the audit record echoes. The screening defaults are 10,000 realizations, a fixed random seed of 6414, and 50 points in the expanded +headwater analysis grid; the synchronous service rejects more than 20,000 realizations. Because the seed is fixed by default, repeated +analyses of the same inputs reproduce the same results, and the blowout and heave analyses draw identical realizations (see +[Delegated Models](./07-delegated-models.mdx)); supplying no seed draws a fresh seed for each delegated analysis and removes both +properties. The flaw assessment runs its own simulation of 5,000 realizations with the same default seed, independent of the screening +realization count. + +### Provenance + +Every response, including a failed one, carries three provenance values: the model key (`bep-screening`), which identifies the screening +model among the models the service exposes; the engineering model version, which changes whenever a formula, default, lookup value, +sampling order, or seed treatment changes, so a stored result can be tied to the model revision that computed it; and the service build, +a deployment identifier for troubleshooting only, never to be compared when deciding whether a stored result is current. The audit record +repeats the model key and version together with the Monte Carlo controls in effect. + +## Interpreting the System Response Curve + +The governing SRP series is the system response curve — the conditional probability of breach by backward erosion piping as a function of pool +level. The curve is non-decreasing with pool level: the flaw, roof-support, intervention, and breach nodes are constant; the blowout and heave +probabilities rise with net head; and the progression node is explicitly constrained to be non-decreasing. Pools at or below the governing exit +reference elevation carry effectively zero SRP because no net driving head exists there; the reported value is floored at 10−16 +rather than exactly zero, so the curve can be plotted on a logarithmic axis. + +### Which Pathway Governs + +The toe and daylight pathways trade off against each other: + +- The **toe pathway** carries unfiltered-exit and initiation probabilities below one (the confining layer resists both), but its progression + analysis benefits from a shorter seepage path — and, when the layer is confirmed, from the concentrated (hole-type) exit that halves the + Schmertmann critical gradient. +- The **daylight pathway** carries certain unfiltered exit and initiation (nothing confines the exit there), but its progression analysis runs + over the longer path to the layer's termination with a plane-type exit. + +When the confining layer is thick and well characterized, its resistance suppresses the toe pathway and the daylight pathway tends to govern. +When the layer is thin — or its thickness band is wide because it is unknown — the defect pathway drives the toe unfiltered-exit probability +up and the toe pathway tends to govern. When both pathways are evaluated, both are reported, so the trade-off is visible directly in the +results. When the berm toe is itself the daylighting exit, only the toe pathway is reported — it *is* the daylighting exit, carrying certain +unfiltered-exit and initiation probabilities over the berm-extended progression path. + +### Sensitivity to Key Inputs + +The inputs with the greatest influence on the screening SRP are: + +- **Flaw evidence selections** — the flaw probability scales the entire curve. Moving the geologic environment, strength of evidence, or + observed-seepage selections shifts every pool level proportionally. +- **Confining layer thickness category** — thickness controls both the defect probability (steeply, at small thickness) and the vertical exit + gradients in the blowout and heave analyses. +- **Downstream layer extent** — sets the daylight path length and the head remaining at the exit; the unknown-extent default spans a wide + range and widens the result accordingly. +- **Relative density category** — denser sand raises the Schmertmann critical gradient and suppresses progression. +- **Embankment materials** — the minimum roof-support probability governs; a single clean sand or gravel in the list reduces the SRP sharply + when no confining layer is confirmed. +- **Reference elevations** — the toe and daylight ground surfaces position the zero-head threshold and thereby the low-pool end of the curve. + +### Screening Versus Detailed Analysis + +A high screening SRP does not by itself indicate a high risk of failure — it indicates that the structure warrants analysis with the full +toolbox models +([BEP Initiation](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-initiation/v1.0/preface), +[BEP Progression](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.0/preface)), where: + +- the blanket-theory case matching the actual stratigraphy can be selected from all eight configurations; +- site-specific blanket geometry replaces the screening defaults and unknown-value ranges; +- the anisotropy, underlayer, and pipe-inclination corrections can be applied to the Schmertmann analysis; +- the Sellmeijer method is available as an alternative progression formulation; and +- the flaw judgment can be refined by targeted subsurface investigation rather than screening-level evidence categories. + +A low screening SRP provides reasonable confidence that backward erosion piping is not a critical concern at the screening level, subject to +the assumptions and limitations documented in this reference. diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/_input-needed.md b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/_input-needed.md new file mode 100644 index 000000000..c908d850f --- /dev/null +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/_input-needed.md @@ -0,0 +1,245 @@ +# Input Needed — BEP Screening Model (v1.0) + +Answer inline and return this file (or paste its contents into the conversation). Leave an +Answer blank to keep that marker in place. Do not renumber — the IDs tie each entry to its +admonition in the document. (IN-17 was retired in the August 2026 update: the mean-of- +distribution treatment it questioned no longer exists — supplied seepage-path lengths are now +single values by design.) + +--- + +## IN-01 — Engineering Basis — `03-input-parameters.mdx` + +**Regarding:** The thickness ranges assigned to the qualitative confining-layer categories +(Very Thin 0–5 ft, Thin 5–10 ft, Moderate 10–20 ft, Thick 20–35 ft, Unknown 0–10 ft, each as +a uniform distribution). + +**Needed:** Literature citation (full bibliographic details for the bibliography) or the +engineering-judgment attribution to state, including the reasoning for the Unknown band +spanning 0–10 ft. + +**Answer:** + +--- + +## IN-02 — Engineering Basis — `03-input-parameters.mdx` + +**Regarding:** Default coefficient-of-uniformity distribution for the foundation sand +(triangular: low 1.1, mode 2.0, high 4.0). + +**Needed:** Literature citation or engineering-judgment attribution. + +**Proposed (unconfirmed):** Representative of the poorly graded, uniform fine to medium sands +susceptible to backward erosion piping. + +**Answer:** + +--- + +## IN-03 — Engineering Basis — `03-input-parameters.mdx` + +**Regarding:** Default effective-grain-size (D10) distribution for the foundation sand +(normal: mean 0.25 mm, standard deviation 0.085 mm, values limited to no less than 0.1 mm). + +**Needed:** Literature citation or engineering-judgment attribution for both the distribution +parameters and the 0.1 mm lower limit. + +**Answer:** + +--- + +## IN-04 — Engineering Basis — `03-input-parameters.mdx` + +**Regarding:** The relative-density category uniform ranges (Very Loose 0–15%, Loose 15–35%, +Medium Dense 35–65%, Dense 65–85%, Very Dense 85–100%, and the Unknown band 15–65%). + +**Needed:** Literature citation or engineering-judgment attribution for the band boundaries +and for the Unknown selection. + +**Proposed (unconfirmed):** Boundaries follow the standard qualitative relative-density +classification for granular soils; a uniform distribution over each band takes no position on +a most-likely value within the category; Unknown spans loose to medium-dense as a +conservative screening posture. If confirmed, supply the classification source for the +bibliography. + +**Answer:** + +--- + +## IN-05 — Engineering Basis — `03-input-parameters.mdx` + +**Regarding:** Default foundation-sand saturated unit weight (normal: mean 122.0 pcf, +standard deviation 3.0 pcf). + +**Needed:** Literature citation or engineering-judgment attribution. + +**Proposed (unconfirmed):** Typical of loose to medium-dense saturated alluvial sand. + +**Answer:** + +--- + +## IN-06 — Engineering Basis — `03-input-parameters.mdx` + +**Regarding:** Default confining-layer saturated unit weight (normal: mean 118.0 pcf, +standard deviation 3.0 pcf). + +**Needed:** Literature citation or engineering-judgment attribution. + +**Answer:** + +--- + +## IN-07 — Engineering Basis — `04-flaw-assessment.mdx` + +**Regarding:** The prior probability ranges by geologic depositional environment (glacial +outwash 0.500–0.900; high-energy fluvial 0.100–0.500; coastal shoreface/barrier 0.100–0.500; +aeolian dune 0.075–0.500; delta deposits 0.050–0.500; alluvial fans 0.050–0.300; shallow +marine shelf 0.050–0.300; low-energy deltaic/coastal mud 0.010–0.050; residual soils +0.001–0.100; unknown 0.050–0.300). + +**Needed:** Literature citation or engineering-judgment attribution — including whether the +ranges derive from a published compilation of depositional-environment characteristics or +from elicited expert judgment. + +**Answer:** + +--- + +## IN-08 — Engineering Basis — `04-flaw-assessment.mdx` + +**Regarding:** The strength-of-evidence likelihood-ratio ranges (very strong 10–30; strong +3–10; moderate 1–3; neutral 1; weak 0.10–0.30; very weak 0.01–0.10) and the subsurface +data-quality factor ranges (high 1.00; moderate 0.75–0.90; low 0.50–0.75). + +**Needed:** Literature citation or engineering-judgment attribution, including the reasoning +behind the order-of-magnitude likelihood bands and the quality discounts. + +**Answer:** + +--- + +## IN-09 — Engineering Basis — `04-flaw-assessment.mdx` + +**Regarding:** The seepage-observation likelihood-ratio ranges (sand boils 3.50–5.00; +concentrated seepage 2.00–3.50; stage-dependent wet areas 1.25–2.00; stage-independent wet +areas 1.00–1.25). + +**Needed:** Literature citation or engineering-judgment attribution. + +**Answer:** + +--- + +## IN-10 — Engineering Basis — `05-hydraulic-loading-and-seepage-paths.mdx` + +**Regarding:** Two judgments in the upstream seepage-path crediting rules: (1) a confirmed +Very Thin confining layer contributes no upstream path length (L1 = 0), taking precedence +over the impervious-extension credit; (2) only a layer characterized as Impervious is +credited — Semi-pervious and Unknown permeability contribute nothing. + +**Needed:** Citation or engineering-judgment attribution for each judgment. + +**Proposed (unconfirmed):** For (1): a layer thinner than about 5 ft cannot be relied on to +remain intact and carry head loss over its upstream extent. + +**Answer:** + +--- + +## IN-11 — Engineering Basis — `05-hydraulic-loading-and-seepage-paths.mdx` + +**Regarding:** The default downstream seepage path length when the confining-layer extent (or +presence) is unknown: uniform between 1 and 5 embankment heights. + +**Needed:** Literature citation or engineering-judgment attribution, including the reasoning +for scaling the range to embankment height. + +**Answer:** + +--- + +## IN-12 — Definition — `05-hydraulic-loading-and-seepage-paths.mdx` + +**Regarding:** The physical interpretation of the exit-offset distance used when a berm +overlies a confirmed confining layer whose supplied downstream extent exceeds the berm +length — the berm-within-known-extent case in which the through-layer defect/blowout +composition is retained. The model design notes record the intended evaluation location as +the berm toe, but the model computes the offset as (supplied confining-layer extent − berm +length), measured from the embankment toe. Under the linear head profile, the head fraction +remaining at the computed offset equals (berm length ÷ confining-layer extent) — whereas an +exit evaluated at the berm toe (one berm length from the embankment toe) would retain the +complementary fraction, (extent − berm length) ÷ extent. The two coincide only when the berm +covers exactly half the extent; the computed construction is conservative for longer berms +and non-conservative for shorter ones relative to the berm-toe reading. + +**Needed:** Confirmation of which exit location the offset is intended to represent, and the +engineering basis for the chosen construction. (If the intent is the berm toe, the +computation may warrant review — the document currently describes the computed behavior +as-is.) + +**Answer:** + +--- + +## IN-13 — Engineering Basis — `06-event-tree.mdx` + +**Regarding:** The Weibull defect-survival parameters — characteristic defect penetration +depth 3.5 ft and shape parameter 1.25 — in the probability that a pre-existing defect fully +penetrates the confining layer. + +**Needed:** The data source, calibration rationale, or engineering-judgment attribution. +These are recorded as empirical values with no published-literature provenance. + +**Answer:** + +--- + +## IN-14 — Engineering Basis — `06-event-tree.mdx` + +**Regarding:** Two judgments in the revised berm treatment (updated August 2026 — the former +rule that any berm forces the unfiltered exit to certainty no longer exists; the treatment +now follows where the berm ends relative to the confining layer): + +1. No berm is ever credited with filtering the exit — where the berm end remains beneath the + layer, the exit resistance is carried entirely by the layer's defect/blowout composition + (evaluated at the offset exit point), and where the berm daylights the exit, the + unfiltered exit is certain. +2. When the layer's presence is unknown and a berm is present, a daylighting exit at the + berm toe is assumed (forcing the unfiltered exit to certainty) rather than evaluated. + +**Needed:** The engineering basis or judgment attribution for each. + +**Proposed (unconfirmed):** For (1): seepage and stability berms are not engineered filters, +so no filtering credit is taken for any berm. For (2): with the layer itself unverified, its +lateral extent beneath the berm cannot be relied upon, and assuming a daylighting exit at the +berm toe is the conservative screening posture. + +**Answer:** + +--- + +## IN-15 — Engineering Basis — `06-event-tree.mdx` + +**Regarding:** Treating the defect and blowout mechanisms as statistically independent +pathways in the unfiltered-exit union formula. + +**Needed:** Engineering basis or judgment attribution for the independence treatment. + +**Answer:** + +--- + +## IN-16 — Engineering Basis — `07-delegated-models.mdx` + +**Regarding:** The fines-content correction applied by the Schmertmann analysis engine — a +step from 1.0 to 1.4, with the higher factor applying at exactly 5% fines and above. The +screening model passes no override; the dedicated Schmertmann documentation does not describe +the term. + +**Needed:** Source or engineering-judgment attribution for the step form, the 5% threshold, +and the 1.4 value, and an addition to the dedicated Schmertmann documentation. + +**Answer:** + +--- diff --git a/src/docConfig.js b/src/docConfig.js index 12d53e22d..2d6c8d9e4 100644 --- a/src/docConfig.js +++ b/src/docConfig.js @@ -329,7 +329,7 @@ const docs = [ software: 'system-response', doc_location: 'web-applications/system-response/backward-erosion-piping-screening', doc_name: 'Backward Erosion Piping Screening Technical Reference Manual', - active: false, + active: true, draft: true, }, { diff --git a/static/bibliographies/web-applications/system-response/backward-erosion-piping-screening/v1.0/bib.json b/static/bibliographies/web-applications/system-response/backward-erosion-piping-screening/v1.0/bib.json new file mode 100644 index 000000000..776c10912 --- /dev/null +++ b/static/bibliographies/web-applications/system-response/backward-erosion-piping-screening/v1.0/bib.json @@ -0,0 +1,50 @@ +[ + { + "citationKey": "Fell2024", + "entryType": "report", + "author": [ + "R. Fell", + "M.A. Foster", + "J. Cyganiewicz", + "R.R. Davidson", + "G.L. Sills" + ], + "title": "Methods for Estimating Probability of Failure of Embankment Dams by Internal Erosion and Piping (The Piping Toolbox 2024)", + "year": 2024, + "institution": "University of New South Wales, School of Civil and Environmental Engineering", + "report": "Report No. 470" + }, + { + "citationKey": "Schmertmann2000", + "entryType": "incollection", + "author": ["J.H. Schmertmann"], + "year": 2000, + "title": "The no-filter factor of safety against piping through sands", + "booktitle": "Judgment and Innovation: The Heritage and Future of the Geotechnical Engineering Profession (Geotechnical Special Publication No. 111)", + "publisher": "American Society of Civil Engineers", + "pages": "65–132", + "doi": "10.1061/9780784405376.006" + }, + { + "citationKey": "vanBeek2015", + "entryType": "article", + "author": ["V.M. van Beek", "H.M. Van Essen", "K. Vandenboer", "A. Bezuijen"], + "year": 2015, + "title": "Developments in modelling of backward erosion piping", + "journal": "Géotechnique", + "volume": "65", + "edition": "9th", + "pages": "740–754", + "doi": "10.1680/geot.14.P.119" + }, + { + "citationKey": "USACE1956", + "entryType": "report", + "author": ["U.S. Army Corps of Engineers"], + "year": 1956, + "title": "Investigation of underseepage and its control: Lower Mississippi River Levees (Technical Manual [TM] 3-424)", + "institution": "U.S. Army Corps of Engineers, Waterways Experiment Station", + "number": "TM 3-424", + "url": "https://usace.contentdm.oclc.org/digital/collection/p266001coll1/id/2416/" + } +] From edcd0fb2fbd40171844411fd1d5a99c703ab10e0 Mon Sep 17 00:00:00 2001 From: Adam Gohs Date: Thu, 15 Oct 2026 15:17:53 -0400 Subject: [PATCH 2/5] Update BEP Screening documentation to the revised model-documentation rules Restructure the Model Overview to the standard opening, move long table text and option sets into lists, convert the assumptions to a numbered list, and rename Delegated Models to Delegated Methods with node-first sections linking the specific BEP Initiation and Progression chapters. Remove response-record, Monte Carlo control, provenance and numerical-floor content, and replace the input ranking with conditional effects on SRP. --- .../v1.0/00-document-info.mdx | 10 +- .../v1.0/00-version-history.mdx | 13 +- .../v1.0/01-preface.mdx | 25 +- .../v1.0/02-model-overview.mdx | 128 +++-- .../v1.0/03-input-parameters.mdx | 466 ++++++++++-------- .../v1.0/04-flaw-assessment.mdx | 12 +- ...05-hydraulic-loading-and-seepage-paths.mdx | 49 +- .../v1.0/06-event-tree.mdx | 78 +-- .../v1.0/07-delegated-methods.mdx | 244 +++++++++ .../v1.0/07-delegated-models.mdx | 201 -------- .../v1.0/08-assumptions-and-limitations.mdx | 279 +++++++---- .../v1.0/09-output-and-interpretation.mdx | 298 +++++------ .../v1.0/_input-needed.md | 75 ++- 13 files changed, 1071 insertions(+), 807 deletions(-) create mode 100644 docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/07-delegated-methods.mdx delete mode 100644 docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/07-delegated-models.mdx diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/00-document-info.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/00-document-info.mdx index 2b5cff419..e92eecf39 100644 --- a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/00-document-info.mdx +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/00-document-info.mdx @@ -1,13 +1,13 @@ --- title: Document Info -reportDate: August 2026 +reportDate: October 2026 reportType: Technical Reference -reportTitle: BEP Screening Model Technical Reference +reportTitle: Backward Erosion Piping Screening Technical Reference Manual reportSubTitle: System Response Library reportAuthors: ['Adam Gohs, P.E.'] -reportAbstract: Technical reference documenting the Backward Erosion Piping (BEP) screening model in the System Response library. The model computes a system response probability (SRP) for backward erosion piping at each headwater level using a seven-node event tree. The probability of a continuous foundation flaw is estimated by Bayesian updating of a geology-based prior with subsurface and seepage-observation evidence. Unfiltered-exit and initiation probabilities are computed from blanket theory with a companion defect-survival model for the downstream confining layer, and progression is evaluated with the Schmertmann critical-gradient method. The model applies screening-level simplifications appropriate for the Dam Screening Tool. -reportSubjectTerms: ['BEP', 'Backward Erosion Piping', 'Screening', 'Event Tree', 'System Response Probability', 'System Response Curve', 'Blanket Theory', 'Bayesian Updating', 'Dam Screening Tool', 'Monte Carlo'] -citationGuide: 'U.S. Army Corps of Engineers, Risk Management Center, BEP Screening Model Technical Reference, Lakewood, CO: U.S. Army Corps of Engineers, Risk Management Center, 2026.' +reportAbstract: Technical reference documenting the Backward Erosion Piping (BEP) screening model in the System Response library. The model computes a system response probability (SRP) for backward erosion piping at each headwater level using a seven-node event tree. The probability of a continuous foundation flaw is estimated by Bayesian updating of a geology-based prior with subsurface and seepage-observation evidence. Unfiltered-exit and initiation probabilities are computed from blanket theory with a companion defect-survival model for the downstream confining layer, and progression is evaluated with the Schmertmann critical-gradient method. The model applies simplifications appropriate for screening-level risk analysis. +reportSubjectTerms: ['BEP', 'Backward Erosion Piping', 'Screening', 'Event Tree', 'System Response Probability', 'System Response Curve', 'Blanket Theory', 'Bayesian Updating', 'Schmertmann Method', 'Monte Carlo'] +citationGuide: 'U.S. Army Corps of Engineers, Risk Management Center, Backward Erosion Piping Screening Technical Reference Manual, Lakewood, CO: U.S. Army Corps of Engineers, Risk Management Center, 2026.' --- import Link from '@docusaurus/Link'; diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/00-version-history.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/00-version-history.mdx index 19979ae91..89f6b753a 100644 --- a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/00-version-history.mdx +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/00-version-history.mdx @@ -14,16 +14,17 @@ import TableVersionHistory from '@site/src/components/TableVersionHistory'; # Version History diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/01-preface.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/01-preface.mdx index 29e139cd1..b00a40b0c 100644 --- a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/01-preface.mdx +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/01-preface.mdx @@ -9,9 +9,9 @@ import NavContainer from '@site/src/components/NavContainer'; # Preface This document provides a technical reference for the Backward Erosion Piping (BEP) screening model in the System Response library. The model -computes a system response probability (SRP) as a function of headwater elevation for the backward erosion piping failure mode. It is designed for -the Dam Screening Tool (DST), where it operates with screening-level simplifications intended to reduce input burden while avoiding false -negatives. +computes a system response probability (SRP) as a function of headwater elevation for the backward erosion piping failure mode. It is a screening-level +model: it applies simplifications intended to reduce input burden while avoiding false negatives, and any application that performs screening-level +risk analysis can use it. The intended audience includes dam and levee safety engineers evaluating whether the model is appropriate for their assessment, and peer reviewers checking the technical basis of screening-level results. Readers are assumed to have a general background in internal-erosion risk analysis — @@ -23,11 +23,13 @@ made along the way with their engineering bases, the inputs the user provides an ## Document Organization -- **[Model Overview](./02-model-overview.mdx)** — The model's purpose, its role in the Dam Screening Tool, the overall execution pathway from - inputs to results, the exit pathways evaluated and when each exists, and the relationship to the full toolbox models. +- **[Model Overview](./02-model-overview.mdx)** — The model's purpose and intended use, a summary of its execution pathway from inputs to + results, its physics basis, a comparison with the full toolbox models, the exit pathways evaluated and when each exists, and its relationship + to the toolbox models. - **[Input Parameters](./03-input-parameters.mdx)** — Every user input: hydraulic loading, embankment geometry, upstream blanket, downstream - seepage berm, confining-layer characterization, flaw-evidence selections, embankment materials, foundation sand properties, unit weights, and - the intervention and breach probabilities, with units, valid ranges, defaults, and guidance for each selectable option. + seepage berm, flaw-evidence selections, confining-layer characterization, observed-seepage refinements, embankment materials, foundation sand + properties, unit weights, and the intervention and breach probabilities, with units, valid ranges, defaults, and the choices available for + each selection. - **[Flaw Assessment](./04-flaw-assessment.mdx)** — The Bayesian assessment of the probability that a continuous path of fine to medium, uniform sand exists in the foundation: the geology-based prior, the subsurface-data and seepage-observation evidence updates, and the uncertainty quantification. @@ -37,10 +39,9 @@ made along the way with their engineering bases, the inputs the user provides an - **[Event Tree](./06-event-tree.mdx)** — The seven event-tree nodes, how each probability is populated at each pool level (including the composition of the unfiltered-exit node from the defect and blowout pathways), and how the SRP and the governing system response curve are computed. -- **[Delegated Models](./07-delegated-models.mdx)** — How the screening model invokes the blanket-theory initiation analysis and the Schmertmann - progression analysis: the quantities passed in, the outputs consumed, and each fixed screening-level adjustment relative to the dedicated - toolbox models. +- **[Delegated Methods](./07-delegated-methods.mdx)** — For blanket theory and the Schmertmann progression method: the event-tree node each + serves and the question it answers there, the chapter of the dedicated manual that documents it, and each screening-level adjustment. - **[Assumptions and Limitations](./08-assumptions-and-limitations.mdx)** — Each modeling assumption with its engineering basis, its effect on results, and the conditions under which it may not hold. -- **[Output and Interpretation](./09-output-and-interpretation.mdx)** — The complete result inventory, how to read the system response curve, - which exit pathway tends to govern, sensitivity to key inputs, and the role of screening results relative to detailed analysis. +- **[Output and Interpretation](./09-output-and-interpretation.mdx)** — The results the model produces, how to read the system response curve, + how the governing pathway is determined, how key inputs affect the SRP, and the role of screening results relative to detailed analysis. diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/02-model-overview.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/02-model-overview.mdx index 8964d9b46..058d10e04 100644 --- a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/02-model-overview.mdx +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/02-model-overview.mdx @@ -2,6 +2,8 @@ title: Model Overview --- +import Citation from '@site/src/components/Citation'; +import CitationFootnote from '@site/src/components/CitationFootnote'; import NavContainer from '@site/src/components/NavContainer'; import TableReference from '@site/src/components/TableReference'; import TableVertical from '@site/src/components/TableVertical'; @@ -12,10 +14,10 @@ import TableVertical from '@site/src/components/TableVertical'; ## Purpose -The BEP screening model computes a system response probability (SRP) for the backward erosion piping failure mode as a function of headwater -elevation. The SRP represents the conditional probability of dam or levee breach due to backward erosion piping, given a specific pool level. The -model produces a system response curve — an array of SRP values across a range of headwater elevations — that characterizes the structure's -vulnerability to this failure mode. +The BEP screening model computes a system response curve for the backward erosion piping failure mode as a function of headwater elevation. +The system response probability (SRP) at each headwater level represents the conditional probability of dam or levee breach due to backward +erosion piping, given that pool level. The model produces a curve of SRP values across a range of headwater elevations that +characterizes the structure's vulnerability to this failure mode. Backward erosion piping is the progressive removal of cohesionless foundation soil by seepage, beginning at an unfiltered downstream exit and eroding backward (upstream) beneath the embankment until a continuous pipe connects the impounded water to the exit. The failure mode requires a @@ -24,21 +26,20 @@ open, and sufficient gradient to advance the pipe to the reservoir. ## Intended Use -The model is designed for the Dam Screening Tool (DST), where it serves as a screening-level assessment of backward erosion piping risk. It makes -simplifying and generally conservative assumptions with two goals: +The model is a screening-level assessment of backward erosion piping risk. It makes simplifying and generally conservative assumptions with two +goals: -- **Preventing false negatives** — The model is calibrated to avoid underestimating risk at the screening level, so that structures with +- **Preventing false negatives** — The model is designed to avoid underestimating risk at the screening level, so that structures with potential BEP concerns are flagged for further analysis. -- **Reducing input burden** — The model requires fewer inputs than the full BEP toolbox models. Qualitative selections (confining layer +- **Reducing input burden** — The model requires fewer inputs than the full BEP toolbox models. Qualitative selections (confining-layer thickness category, relative density category, geologic environment) substitute for site-specific distributions, and default distributions cover material properties that are typically unavailable at the screening stage. Where a site characteristic is genuinely unknown — the - presence of a confining layer, or the extent of that layer beyond the embankment — the model accepts "unknown" as an answer and substitutes a + presence of a confining layer, or the extent of that layer beyond the embankment — the model accepts Unknown as an answer and substitutes a deliberately wide characterization rather than requiring the user to guess. -The model is not intended for detailed or semi-quantitative risk assessments. For higher-level analyses, the full -[BEP Initiation (BT Case 1–8)](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-initiation/v1.0/preface) and -[BEP Progression (Schmertmann and Sellmeijer)](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.0/preface) -toolbox models provide the complete methodologies with full parameterization. +The model is not intended for detailed or semi-quantitative risk assessments. For higher-level analyses, the full BEP Initiation and BEP +Progression toolbox models provide the complete methodologies with full parameterization (see +[Comparison with Detailed Models](#comparison-with-detailed-models)). ## How the Model Works @@ -51,43 +52,36 @@ The screening model executes three stages: 2. **Hydraulic and seepage-geometry resolution** — The model resolves the downstream reference elevations that control net driving head, the upstream seepage path length $L_1$, the embankment base width $L_2$, and the downstream seepage path length $L_3$ from the site inputs, and - selects the appropriate blanket-theory configuration — Case 2 when an upstream seepage barrier is present, Case 4 otherwise + selects the blanket-theory configuration — Case 2 when an upstream seepage barrier is present, Case 4 otherwise (see [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx)). -3. **Event-tree assembly** — At each headwater level, the model composes seven node probabilities and multiplies them to produce the SRP. Two - nodes are evaluated by Monte Carlo simulation delegated to established analysis methods: blanket theory computes the blowout and heave - probabilities feeding the unfiltered-exit and initiation nodes, and the Schmertmann critical-gradient method computes the probability of pipe - progression. A companion defect-survival model contributes the probability that a pre-existing defect already penetrates the confining layer - (see [Event Tree](./06-event-tree.mdx) and [Delegated Models](./07-delegated-models.mdx)). +3. **Event-tree assembly** — At each headwater level, the model composes seven node probabilities and multiplies them to produce the SRP. Blanket + theory computes the blowout and heave probabilities feeding the unfiltered-exit and initiation nodes, a defect-survival relationship gives the + probability that a pre-existing defect already penetrates the confining layer, and the Schmertmann critical-gradient method computes the + probability of pipe progression. The blanket-theory and Schmertmann analyses are evaluated by Monte Carlo simulation over the uncertain + material and geometric inputs (see [Event Tree](./06-event-tree.mdx) and [Delegated Methods](./07-delegated-methods.mdx)). -## Exit Pathways +## Physics Basis -The model evaluates up to two seepage exit pathways: +The model combines the following engineering methods: -- **Toe pathway** — Seepage exits at the downstream toe of the embankment, or at the toe of the downstream seepage berm when one is present. - This pathway is always evaluated. When a confining layer may be present and the toe exit remains beneath it — no berm, or a berm ending - within the layer's known extent — the unfiltered-exit probability at the toe is composed from two mechanisms — a pre-existing defect through - the layer, and hydraulic blowout (rupture) of the layer — and the initiation probability is the blanket-theory heave probability. Where a - berm instead places the exit at or beyond the layer's downstream termination, the exit daylights at the berm toe and the unfiltered-exit - and initiation probabilities are certain there. +- **Bayesian updating in log-odds form** for the probability of a continuous foundation flaw, combining a geology-based prior with likelihood + ratios for the site evidence (see [Flaw Assessment](./04-flaw-assessment.mdx); the source of the formulation is requested at marker IN-18) +- **Blanket theory** for the excess head beneath the downstream confining layer and the vertical exit gradient through it, from which the + blowout and heave probabilities follow +- **A Weibull defect-survival relationship** for the probability that a pre-existing defect fully penetrates the confining layer (see + [Event Tree](./06-event-tree.mdx)) +- **Roof-support probabilities by soil classification** for the mechanical condition of pipe progression +- **The Schmertmann critical-gradient method** for the hydraulic condition of pipe progression, with + an exit-geometry factor that distinguishes concentrated from distributed exits -- **Daylight pathway** — Seepage exits at the downstream termination of the confining layer, where the underlying sand daylights at the ground - surface. This pathway is evaluated whenever a confining layer may be present (its presence is confirmed or unknown) *and* the daylighting - exit is distinct from the toe exit. At the daylight exit there is no confining layer to penetrate, so the unfiltered-exit and initiation - probabilities are both certain there, and the pathway is distinguished by its longer seepage path to the exit. When a berm over a confirmed - layer reaches or clears the layer's downstream extent — or overlies a confirmed layer whose extent is unknown — the berm toe is itself the - daylighting exit: the toe pathway then represents that exit directly, so a separate daylight pathway would repeat the same exit and is not - reported. A layer of unknown presence always retains both pathways. +## Comparison with Detailed Models -The governing SRP at each headwater level is the maximum of the two pathway SRPs, so the more critical exit condition controls the screening -result. When no confining layer is present — or the daylighting exit is the berm toe, so the toe pathway already represents it — only the toe -pathway is evaluated and it governs directly. - -## Relationship to Toolbox Models - -The screening model delegates its Monte Carlo computations to the same analysis engines as the standalone toolbox models — the blanket-theory -initiation cases and the Schmertmann progression method — but constructs their configurations internally from the screening inputs, applying -fixed screening-level simplifications. summarizes the differences. +The detailed counterparts of the screening model are the full BEP Initiation and BEP Progression toolbox models. The BEP Initiation manual +covers all eight blanket-theory configurations (see its [General Overview](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-initiation/v1.0/general-overview)), of which the screening model uses +[Blanket Theory Case 2](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-initiation/v1.0/blanket-theory-case-2) and [Blanket Theory Case 4](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-initiation/v1.0/blanket-theory-case-4). The BEP Progression manual covers the +[Schmertmann](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.0/schmertmann) method used by the screening model and the alternative [Sellmeijer](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.0/sellmeijer) method. + summarizes the differences. -The delegated analysis engines execute identically whether invoked by the screening model or directly — the screening model controls only the -configuration passed to them. [Delegated Models](./07-delegated-models.mdx) documents each fixed choice and its basis. +## Exit Pathways + +The model evaluates up to two seepage exit pathways: + +- **Toe pathway** — Seepage exits at the downstream toe of the embankment, or at the toe of the downstream seepage berm when one is present. + This pathway is always evaluated. When a confining layer may be present and the toe exit remains beneath it — no berm, or a berm ending + within the layer's known extent — the unfiltered-exit probability at the toe is composed from two mechanisms (a pre-existing defect through + the layer, and hydraulic blowout of the layer), and the initiation probability is the blanket-theory heave probability. Where a berm instead + places the exit at or beyond the layer's downstream termination, the exit daylights at the berm toe and the unfiltered-exit and initiation + probabilities are certain there. + +- **Daylight pathway** — Seepage exits at the downstream termination of the confining layer, where the underlying sand daylights at the ground + surface. This pathway is evaluated whenever a confining layer may be present (its presence is confirmed or unknown) *and* the daylighting + exit is distinct from the toe exit. At the daylight exit there is no confining layer to penetrate, so the unfiltered-exit and initiation + probabilities are both certain. With no berm, or with a berm inside a confirmed layer's known extent, the daylight pathway is also + distinguished by its longer seepage path to the exit. When a berm over a confirmed layer reaches or clears the layer's downstream extent — or + overlies a confirmed layer whose extent is unknown — the berm toe is itself the daylighting exit: the toe pathway then represents that exit + directly, and no separate daylight pathway is evaluated. A layer of unknown presence always retains both pathways; with a berm, both then + share the berm-extended path length and differ in the toe initiation node and the exit datum (see [Event Tree](./06-event-tree.mdx)). + +The governing SRP at each headwater level is the larger of the two pathway SRPs, so the more critical exit condition controls the screening +result. When only the toe pathway is evaluated, it governs directly. + +## Relationship to Toolbox Models + +The screening model uses the same blanket-theory and Schmertmann methods as the standalone toolbox models for its blowout, heave, and +progression computations. The screening model differs only in what it supplies to +them: it builds their geometry and material inputs from the screening selections and fixes several choices that the toolbox models leave to +the analyst (). [Delegated Methods](./07-delegated-methods.mdx) documents each fixed choice +and its basis. + +## References + + diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/03-input-parameters.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/03-input-parameters.mdx index 13ec2d809..422e611e5 100644 --- a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/03-input-parameters.mdx +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/03-input-parameters.mdx @@ -2,7 +2,6 @@ title: Input Parameters --- -import EquationNoRef from '@site/src/components/EquationNoRef'; import NavContainer from '@site/src/components/NavContainer'; import TableReference from '@site/src/components/TableReference'; import TableVertical from '@site/src/components/TableVertical'; @@ -11,42 +10,48 @@ import TableVertical from '@site/src/components/TableVertical'; # Input Parameters -This chapter documents every user input to the BEP screening model. Inputs are organized into ten groups: hydraulic loading, embankment geometry, +This chapter documents every user input to the BEP screening model. Inputs are organized into eleven groups: hydraulic loading, embankment geometry, upstream blanket, downstream seepage berm, foundation flaw evidence, confining-layer characterization, observed-seepage refinements, embankment -materials, foundation sand properties and unit weights, and the intervention and breach probabilities. +materials, foundation sand properties, unit weights, and the intervention and breach probabilities. Each group gives the short facts for its +quantities in a table, followed by a description of each input and, for selections, a list of the available choices and what each implies. Several inputs are statistical distributions that characterize uncertainty in a physical quantity. A distribution input may take any of five forms: a deterministic (single) value, a uniform distribution between a low and high bound, a normal distribution (mean and standard deviation), -a triangular distribution (low, mode, high), or a PERT distribution (low, mode, high). The Monte Carlo analyses described in -[Delegated Models](./07-delegated-models.mdx) sample these distributions. Geometric seepage-path lengths — the upstream blanket length, the berm -length, and the confining-layer extents — are the exception: a known length is a site measurement entered as a single value. Where such a length -is unknown, the input is omitted and the model substitutes the wide default characterization documented in +a triangular distribution (low, mode, high), or a PERT distribution (low, mode, high). Any distribution may also carry a lower limit, an upper +limit, or both; a sampled value beyond a limit is set to that limit. The Monte Carlo analyses described in +[Delegated Methods](./07-delegated-methods.mdx) sample these distributions. Geometric seepage-path lengths — the upstream blanket length, the berm +length, and the confining-layer extents — are the exception: a known length is a site measurement entered as a single value. The blanket +length, berm length, and upstream extent are required where they apply. Only the downstream extent may be left blank when it is unknown, and +the model then substitutes the wide default characterization documented in [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx). ## Hydraulic Loading -The hydraulic loading is defined by a headwater rating series and an optional companion tailwater series -(). The model evaluates the event tree across a range of pool levels spanning the supplied -headwater values. +The hydraulic loading is defined by a headwater series and an optional companion tailwater series +(). The model evaluates the event tree at every supplied headwater value and at additional +pool levels distributed between them, with the tailwater at each additional level interpolated linearly between the supplied pairs. +- **Headwater elevation series** — The pool elevations that define the range of hydraulic loading to be evaluated. A headwater value supplied + more than once is evaluated once, with its first paired tailwater. +- **Tailwater elevation series** — Tailwater elevations paired one-to-one with the headwater series. The entire series may be omitted (no + tailwater at any pool level), or individual stages may be left blank (no tailwater at that pool level). Wherever no tailwater exists, the + downstream ground surface controls the net head, as described in + [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx). + ## Embankment Geometry The embankment cross-section is described by its crest and by slope-segment tables for the upstream and downstream faces @@ -58,47 +63,50 @@ accommodate compound slopes and intermediate benches. tableKey="bep-screening-table-3" alt="Embankment geometry parameters" caption="Embankment geometry parameters." - colWidths={[20, 8, 8, 16, 'minmax(22ch, 1fr)']} - headers={[[{ value: 'Parameter' }, { value: 'Symbol' }, { value: 'Units' }, { value: 'Valid Range / Default' }, { value: 'Description' }]]} + headers={[[{ value: 'Parameter' }, { value: 'Symbol' }, { value: 'Units' }, { value: 'Valid Range' }, { value: 'Default' }]]} columns={[ [ 'Crest elevation', 'Crest width', 'Upstream face slope segments', 'Downstream face slope segments', - 'Daylight ground surface elevation', + 'Daylight ground-surface elevation', ], ['Ec', 'Wc', '—', '—', 'Eday'], ['ft', 'ft', 'ft, H:V', 'ft, H:V', 'ft'], [ - 'Required', - '> 0 (required)', - 'At least one segment (required)', - 'At least one segment (required)', - 'Optional', - ], - [ - 'Elevation of the embankment crest.', - 'Width of the embankment crest.', - 'Bottom elevation and slope of each upstream face segment, ordered from the crest to the toe. Every slope must be positive.', - 'Bottom elevation and slope of each downstream face segment, ordered from the crest to the toe. Every slope must be positive. The lowest segment elevation defines the downstream toe, which must lie below the crest.', - 'Ground-surface elevation at the downstream termination of the confining layer — the daylight exit. When omitted, the daylight exit is assumed to share the toe reference elevation (the berm toe when a berm with a specified toe elevation is present, otherwise the downstream embankment toe). When the daylighting exit is the berm toe itself (a berm over a confirmed layer that reaches or clears its downstream extent, or overlies a layer of unknown extent), a supplied value is ignored with a validation warning: the berm-toe reference is the only coherent datum for that exit (see Hydraulic Loading and Seepage Paths).', + 'Above the downstream toe', + '> 0', + 'One or more segments; slopes > 0', + 'One or more segments; slopes > 0', + 'Any elevation', ], + ['None (required)', 'None (required)', 'None (required)', 'None (required)', 'Toe reference elevation'], ]} /> +- **Crest elevation** $E_c$ — Elevation of the embankment crest. +- **Crest width** $W_c$ — Width of the embankment crest. +- **Upstream face slope segments** — Bottom elevation and slope of each upstream face segment, ordered from the crest to the toe. +- **Downstream face slope segments** — Bottom elevation and slope of each downstream face segment, ordered from the crest to the toe. The + lowest segment elevation defines the downstream toe, which must lie below the crest. +- **Daylight ground-surface elevation** $E_{day}$ — Ground-surface elevation at the downstream termination of the confining layer, where the + foundation sand daylights. It may lie above or below the embankment toe. When it is left blank, the daylight exit is assumed to share the toe + reference elevation (the berm toe when a berm with a specified toe elevation is present, otherwise the downstream embankment toe). When the + daylighting exit is the berm toe itself, a supplied value is not used, because the berm-toe reference elevation is then the exit datum (see [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx)). + Three geometric quantities are derived from the cross-section rather than entered directly: - **Downstream toe elevation** $E_{toe}$ — the lowest bottom elevation among the downstream face segments. - **Embankment base width** $L_2$ — the crest width plus the horizontal projections of the upstream and downstream faces from the crest to their respective toes. This is the embankment component of the seepage path. A downstream seepage berm is *not* part of $L_2$; it extends the downstream seepage path beyond the toe instead (see [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx)). -- **Embankment height** $H_d = E_c - E_{toe}$ — used to scale the downstream seepage path when the confining layer extent is unknown. +- **Embankment height** $H_d = E_c - E_{toe}$ — used to scale the downstream seepage path when no berm is present and the confining-layer extent or presence is unknown. ## Upstream Blanket An engineered impervious blanket extending upstream of the embankment lengthens the seepage path and reduces gradients at the downstream exit -(). When an upstream blanket is present, the blowout and heave analyses route to Blanket +(). When an upstream blanket is present, the blowout and heave analyses use Blanket Theory Case 2, which represents impervious strata on both sides of the embankment (see [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx)). @@ -106,137 +114,168 @@ Theory Case 2, which represents impervious strata on both sides of the embankmen tableKey="bep-screening-table-4" alt="Upstream blanket parameters" caption="Upstream blanket parameters." - colWidths={[18, 8, 8, 16, 'minmax(22ch, 1fr)']} - headers={[[{ value: 'Parameter' }, { value: 'Symbol' }, { value: 'Units' }, { value: 'Valid Range / Default' }, { value: 'Description' }]]} + headers={[[{ value: 'Parameter' }, { value: 'Symbol' }, { value: 'Units' }, { value: 'Valid Range' }, { value: 'Default' }]]} columns={[ ['Upstream blanket present', 'Upstream blanket length'], ['—', 'L1'], ['—', 'ft'], - ['Yes / No (default No)', '> 0; required when the blanket is present'], - [ - 'Whether an engineered impervious blanket extends upstream of the embankment toe.', - 'Length of the blanket measured from the upstream embankment toe, entered as a single value. It serves directly as the upstream seepage path length L1.', - ], + ['—', '> 0'], + ['No', 'None (required when present)'], ]} /> +- **Upstream blanket present** (Yes or No) — Whether an engineered impervious blanket extends upstream of the embankment toe. +- **Upstream blanket length** $L_1$ — Length of the blanket measured from the upstream embankment toe, entered as a single value. It serves + directly as the upstream seepage path length $L_1$. + ## Downstream Seepage Berm -A downstream seepage or stability berm adds weight over the exit area and displaces the seepage exit beyond the berm -(). Its consequences for the event tree depend on where the berm ends relative to the -confining layer: a berm ending within a confirmed layer's known extent retains the through-layer exit mechanisms at an exit point beyond the -berm, while a berm that reaches or clears the layer's extent — or overlies a layer of unknown extent or unknown presence — is assumed to -produce a daylighting exit at the berm toe, where the unfiltered exit is certain. Every berm extends the toe progression path. The full rules -are documented in [Event Tree](./06-event-tree.mdx) and [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx). +A downstream seepage or stability berm moves the seepage exit beyond the berm. The model credits no berm weight in the blowout and heave +factors of safety, which depend on the confining-layer thickness alone +(). Its effect on the event tree depends on where the berm ends relative to the confining +layer: a berm ending within a confirmed layer's known extent retains the through-layer exit mechanisms at an exit point beyond the berm, while a +berm that reaches or clears the layer's extent — or overlies a confirmed layer of unknown extent, or a layer of unknown presence — is assumed to produce a daylighting +exit at the berm toe, where the unfiltered exit is certain. Every berm lengthens the toe progression path. The full rules are documented in +[Event Tree](./06-event-tree.mdx) and [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx). b', 'Ebt'], ['—', 'ft', 'ft'], - ['Yes / No (default No)', '> 0; required when the berm is present', 'Optional'], - [ - 'Whether a downstream seepage or stability berm is present.', - 'Length of the berm measured from the downstream embankment toe.', - 'Ground-surface elevation at the downstream toe of the berm. When provided, this elevation becomes the toe reference for the net head on the toe progression pathway. When omitted, the ground beneath the berm is assumed flat and the berm toe shares the downstream embankment toe elevation.', - ], + ['—', '> 0', 'Any elevation'], + ['No', 'None (required when present)', 'Downstream embankment toe elevation'], ]} /> +- **Berm present** (Yes or No) — Whether a downstream seepage or stability berm is present. +- **Berm length** $L_b$ — Length of the berm measured from the downstream embankment toe. +- **Berm-toe ground-surface elevation** $E_{bt}$ — Ground-surface elevation at the downstream toe of the berm. When provided, it becomes the toe + reference elevation for the net head on the toe progression pathway. When it is left blank, the ground beneath the berm is assumed flat and + the berm toe shares the downstream embankment toe elevation. It is ignored when no berm is present. + ## Foundation Flaw Evidence -The probability that a continuous path of fine to medium, uniform sand exists in the foundation is assessed from three categories of evidence -(). The meaning of each selection and the way the evidence combines are documented in -[Flaw Assessment](./04-flaw-assessment.mdx). +The probability that a continuous path of fine to medium, uniform sand exists in the foundation is assessed from three categories of evidence: +the geologic setting, subsurface data, and seepage observations. The way the evidence combines, and the probability range behind each +choice, are documented in [Flaw Assessment](./04-flaw-assessment.mdx). - +**Geologic depositional environment** (required) — The depositional setting of the foundation soils. It selects the prior probability range for +the continuous-flaw assessment; environments that deposit laterally continuous, uniform fine sands carry higher priors. The choices are: + +- Glacial outwash +- High-energy fluvial systems +- Coastal shoreface and barrier systems +- Aeolian dune systems +- Delta deposits +- Alluvial fans +- Shallow marine shelf +- Low-energy deltaic and coastal mud systems +- Residual soils +- Unknown — the depositional setting has not been established; a moderate, deliberately broad prior applies + +**Subsurface data available** (Yes or No) — Whether borings, cone soundings, geophysics, or comparable subsurface information inform the flaw +judgment. When no subsurface data is available, the two selections below are not used. + +**Strength of evidence** (required when subsurface data is available) — The degree to which the subsurface data supports or refutes the presence +of a continuous fine sand layer. The choices are: + +- Very strong — the data strongly indicates a continuous layer; the flaw probability increases most +- Strong — the data indicates a continuous layer +- Moderate — the data modestly indicates a continuous layer +- Neutral — the data neither supports nor refutes a continuous layer; the flaw probability is unchanged +- Weak — the data tends to indicate that no continuous layer exists; the flaw probability decreases +- Very weak — the data strongly indicates that no continuous layer exists; the flaw probability decreases most + +**Subsurface data quality** (required when subsurface data is available) — The quality of the data behind the strength-of-evidence judgment: +extent of coverage, sampling method, and reliability. The choices are: + +- High — the evidence receives full weight +- Moderate — the evidence is partly discounted toward neutral +- Low — the evidence is discounted most strongly toward neutral + +**Seepage observed** (Yes or No) — Whether seepage has been observed downstream of the embankment during past loading events. + +**Seepage observation type** (required when seepage has been observed) — The character of the observed seepage. More localized, +sediment-carrying signatures are stronger evidence of a continuous transmissive flaw than diffuse wet areas. The choices are: + +- Sand boils — the strongest seepage evidence of a continuous flaw; also enables the observed-seepage refinements below +- Concentrated seepage — the next strongest evidence; also enables the observed-seepage refinements below +- Stage-dependent wet areas — wet areas that respond to pool level; weaker evidence than concentrated seepage +- Stage-independent wet areas — wet areas that do not respond to pool level; close to uninformative ## Confining-Layer Characterization The downstream confining layer — a fine-grained stratum overlying the foundation sand on the landside — controls whether seepage can exit -unfiltered at the toe. Seven inputs characterize it (). The presence selection is -deliberately tri-state: when the presence of a layer cannot be established, the model runs the full confined-exit machinery with a wide -thickness characterization rather than assuming either extreme. The categorical selections carry no preselected answer in the Dam Screening -Tool: the thickness category, the permeability, and the upstream-extension question start unanswered, and the calculation does not run until -the user has chosen a category — including Unknown — for each one that applies. The defaults noted in the table are the values the model -assumes when a request omits the field; they are not presented to the user as a starting selection. +unfiltered at the toe. The presence, the thickness category, the permeability, and the upstream-extension question are each required where they +apply, and Unknown is a valid answer to each. + +**Confining layer presence** (required) — Whether a confining layer overlies the foundation sand downstream of the embankment. The choice is +deliberately three-way, so that a layer whose presence cannot be established is neither ignored nor fully credited: + +- Yes — the layer is confirmed. The defect and blowout analyses run with the selected thickness category, and the layer itself is credited as + the roof for pipe progression. +- No — there is no layer. Seepage exits unfiltered at the toe with certainty, and only the toe pathway is evaluated. +- Unknown — the layer may be present. The Unknown thickness band applies (no thickness category is asked), roof support is evaluated from the + embankment materials, and both exit pathways are evaluated. + +**Confining layer thickness category** (required when the presence is Yes) — The qualitative thickness of the layer, chosen by the analyst +from borings or geologic mapping. The choices are: + +- Very Thin, Thin, Moderate, or Thick — each maps to a uniform thickness range () +- Unknown — no thickness information exists; the broad Unknown band applies +- Custom — the user supplies a site-specific thickness distribution, in feet, that cannot produce negative values + +**Confining layer permeability** (required when the presence is Yes) — The permeability character of the layer, which decides whether it can +act as an upstream seepage barrier (see [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx)). The choices +are: + +- Impervious — the layer can be credited as an upstream seepage barrier +- Semi-pervious — the layer contributes no upstream head loss +- Unknown — the layer contributes no upstream head loss + +**Confining layer extends upstream** (asked when the presence is Yes, the permeability is Impervious, and no upstream blanket is present) — +Whether the confirmed impervious layer continues upstream beneath the reservoir. An engineered upstream blanket takes precedence as the upstream +barrier, so the question is not asked when one is present. The choices are: + +- Yes — the layer is treated as the upstream seepage barrier and its upstream length is entered; a Very Thin layer still selects Blanket + Theory Case 2 but is credited with zero upstream length +- No — no upstream head loss is credited +- Unknown — no upstream head loss is credited + +The two confining-layer extents are entered as single lengths (). 0; required when the layer extends upstream and its thickness category is not Very Thin', - 'Single value, ft; > 0; optional (omitted = unknown)', - ], - [ - 'Whether a confining layer overlies the foundation sand downstream of the embankment. Yes confirms the layer: the defect and blowout analyses run with the selected thickness category, and the layer itself is credited as the roof for pipe progression. No removes the layer: seepage exits unfiltered at the toe with certainty, and only the toe pathway is evaluated. Unknown runs the defect and blowout analyses with the Unknown thickness band and evaluates roof support from the embankment materials, so an unverified layer is neither ignored nor fully credited.', - 'Qualitative thickness of the confining layer. Each category maps to a uniform thickness range per the table below. Select the category supported by borings or geologic mapping; select Custom to supply a site-specific distribution; select Unknown when no thickness information exists. When the layer presence is Unknown, the Unknown band is used regardless of the category selected.', - 'Site-specific thickness distribution used when the thickness category is Custom.', - 'Permeability character of the confining layer. Only a layer characterized as Impervious is credited as an upstream seepage barrier (see Hydraulic Loading and Seepage Paths); a Semi-pervious or Unknown layer contributes no upstream head loss.', - 'Whether the confirmed impervious layer continues upstream beneath the reservoir. The question is asked only when no engineered upstream blanket is present (a blanket takes precedence as the upstream barrier). Yes credits the layer as the upstream seepage barrier and asks for its length; No and Unknown credit no upstream head loss. A Yes answer for a Very Thin layer is recorded but credits a zero-length extension.', - 'Length of the confining layer beyond the upstream embankment toe, entered as a single value. Supplied only when the layer extends upstream; it is credited directly as the upstream seepage path L1. When the extension question is answered No or Unknown, no upstream head loss is credited.', - 'Length of the confining layer beyond the downstream embankment toe, entered as a single value. This is the distance to the daylight exit. Omitted means unknown: with no berm, the downstream seepage path is characterized by a wide default range scaled to the embankment height (see Hydraulic Loading and Seepage Paths); with a berm over a confirmed layer, a daylighting exit is assumed at the berm toe. When a berm is present, the supplied extent also determines whether the berm end remains beneath the layer — retaining the through-layer exit mechanisms at an offset exit point — or reaches and clears the layer, producing a daylighting exit at the berm toe (see Event Tree). As a seepage-path length, a supplied extent is used only when the layer presence is confirmed Yes; when the presence is Unknown, the wide default range applies to the no-berm path regardless, although a supplied extent still determines whether a berm reaches or clears the layer.', - ], + ['Upstream confining layer length', 'Downstream confining layer length'], + ['L1 (when credited)', 'Lcl'], + ['ft', 'ft'], + ['≥ 0', '> 0'], + ['None (required when the layer extends upstream)', 'Unknown'], ]} /> -Each qualitative thickness category maps to a uniform distribution of confining-layer thickness $z_{bl}$ -(). +- **Upstream confining layer length** — Length of the layer beyond the upstream embankment toe. It is required when the layer extends + upstream. It is credited directly as the upstream seepage path $L_1$, except for a Very Thin layer, which is credited with $L_1 = 0$ (see + [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx)). +- **Downstream confining layer length** $L_{cl}$ — Length of the layer beyond the downstream embankment toe, which is the distance to the + daylight exit. Leaving it blank means the extent is unknown: + - With no berm, the downstream seepage path is characterized by a wide default range scaled to the embankment height (see + [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx)). + - With a berm over a confirmed layer, a daylighting exit is assumed at the berm toe. +- When a berm is present, a supplied extent also decides whether the berm end remains beneath the layer (retaining the through-layer exit + mechanisms at an offset exit point) or reaches and clears it (producing a daylighting exit at the berm toe; see + [Event Tree](./06-event-tree.mdx)). +- As a seepage-path length, a supplied downstream extent is used only when the presence is Yes. When the presence is Unknown, the wide default + range applies to the no-berm path regardless, although a supplied extent still decides whether a berm reaches or clears the layer. +Each qualitative thickness category maps to a uniform distribution of confining-layer thickness $z_{bl}$ over the range in +. + :::warning[INPUT NEEDED IN-01 — Engineering Basis] The thickness ranges assigned to the qualitative confining-layer categories (Very Thin 0–5 ft, Thin 5–10 ft, Moderate 10–20 ft, Thick 20–35 ft, Unknown 0–10 ft) require an engineering basis. Provide a literature citation (to be added to the bibliography) or the @@ -266,52 +308,44 @@ When sand boils or concentrated seepage have been observed, two additional input tableKey="bep-screening-table-9" alt="Observed-seepage refinement parameters" caption="Observed-seepage refinement parameters." - colWidths={[22, 8, 20, 'minmax(24ch, 1fr)']} - headers={[[{ value: 'Parameter' }, { value: 'Units' }, { value: 'Valid Range / Default' }, { value: 'Description' }]]} + headers={[[{ value: 'Parameter' }, { value: 'Symbol' }, { value: 'Units' }, { value: 'Valid Range' }, { value: 'Default' }]]} columns={[ ['Seepage through confining layer', 'Trigger elevation'], + ['—', 'Etrigger'], ['—', 'ft'], - [ - 'Yes / No; required exactly when sand boils or concentrated seepage have been observed, and left unanswered otherwise', - 'Optional; positive and at or below the crest elevation', - ], - [ - 'Whether the observed sand boils or concentrated seepage emerged through the confining layer. Yes establishes that an unfiltered exit through the layer already exists, forcing the unfiltered-exit probability to certainty. No records that the observation did not penetrate the layer and has no further effect. The input is deliberately left unanswered when there is no sand-boil or concentrated-seepage observation, keeping "no observation" distinct from "observed, but not through the layer."', - 'Pool elevation at or above which sand boils have historically activated (or are expected to activate). At pool levels at or above the trigger elevation, the initiation probability is set to certainty, reflecting that initiation has been demonstrated at those loads.', - ], + ['—', '> 0 and at or below the crest'], + ['None (required after sand boils or concentrated seepage)', 'No trigger'], ]} /> +- **Seepage through confining layer** (Yes or No) — Whether the observed sand boils or concentrated seepage emerged through the confining layer. Yes + establishes that an unfiltered exit through the layer already exists, forcing the unfiltered-exit probability to certainty; No records that + the observation did not penetrate the layer and has no further effect. The question is asked only after a sand-boil or concentrated-seepage + observation, which keeps "no observation" distinct from "observed, but not through the layer." +- **Trigger elevation** $E_{trigger}$ — Pool elevation at or above which sand boils or concentrated seepage have historically + activated (or are expected to activate). At pool levels at or above it, the initiation probability is set to certainty, because initiation has been demonstrated at those + loads. + ## Embankment Materials - +**Embankment materials** (required unless the confining layer presence is Yes) — One or more Unified Soil Classification System (USCS) +classes describing the materials overlying the developing pipe along the seepage pathway. Each class maps to a probability that it can sustain a +stable pipe roof, and the minimum across the listed materials governs, because every material along the path must hold a roof for the pipe to +remain open. The mapping is given in [Event Tree](./06-event-tree.mdx). When the confining layer presence is Yes, the layer itself is credited as +the roof and the materials are not used. ## Foundation Sand Properties The foundation sand — the erodible aquifer beneath the embankment — is characterized by its thickness, relative density, gradation, and fines content (). The thickness, the relative density category, and the fines content category -are required selections with no preselected answer; Unknown is offered for the two categories but must be chosen deliberately. The gradation +are required; Unknown is a valid answer for the two categories. The gradation properties carry screening defaults that the user may override with site-specific distributions. r', 'Cu', 'D10', '—'], - ['ft', '%', '—', 'mm', '%'], + ['ft', '%', '—', 'mm', '—'], + ['> 0', '0 to 100', '≥ 1', '> 0', '—'], [ - 'Required (no default)', - 'Required (no default); Unknown maps to uniform 15–65%', - 'Triangular (1.1, 2.0, 4.0)', - 'Normal (mean 0.25, standard deviation 0.085), values limited to no less than 0.1', - 'Required (no default); Unknown maps to 0.0', - ], - [ - 'Thickness of the pervious foundation (aquifer) layer, as a distribution. Used by both the blanket-theory analysis (seepage path entrance and gradient computations) and the Schmertmann progression analysis (depth correction).', - 'Qualitative relative density of the foundation sand. Each preset category maps to a uniform distribution per the table below; the Custom category instead uses a site-specific distribution supplied by the user. Denser sands resist progression through the Schmertmann density correction.', - 'Coefficient of uniformity of the foundation sand gradation. Controls the base critical gradient in the Schmertmann method — more uniform sands (lower values) are more erodible.', - 'Grain size at 10% passing for the foundation sand. Controls the Schmertmann grain-size correction.', - 'Fines content of the foundation sand, selected as one of three categories: less than 5%, 5% or more, or Unknown. The first two enter the model as deterministic fines contents of 0% and 5%, which place the sand on either side of the step in the screening fines-content correction of the Schmertmann analysis (see Delegated Models). Unknown omits the field, so the model applies its 0% default and takes no fines credit.', + 'None (required)', + 'None (required)', + 'Triangular: 1.1, 2.0, 4.0', + 'Normal: mean 0.25, standard deviation 0.085, not less than 0.1', + 'None (required)', ], ]} /> +The thickness, coefficient of uniformity, and effective grain size are entered as distributions, and the relative density as a category or a +custom distribution. The valid ranges are the physical ranges of each quantity (the coefficient of uniformity cannot be less than 1 by +definition). Apart from the relative density, the model does not test sampled values against these ranges, so a distribution that could stray +outside them should carry lower or upper limits. + +- **Foundation sand thickness** $d$ — Thickness of the pervious foundation (aquifer) layer, entered as a distribution. It enters both the + blanket-theory analysis (the seepage entrance and gradient computations) and the Schmertmann progression analysis (the depth correction). +- **Relative density category** $D_r$ — Qualitative relative density of the foundation sand. Denser sands resist progression through the + Schmertmann density correction. The choices are: + - Very Loose, Loose, Medium Dense, Dense, or Very Dense — each maps to a uniform distribution of relative density + () + - Unknown — a broad band spanning loose to medium-dense conditions applies + - Custom — the user supplies a site-specific distribution; every value it can produce must lie within the physical range of 0 to 100%, so an + unbounded form such as a normal distribution requires explicit lower and upper limits +- **Coefficient of uniformity** $C_u$ — Coefficient of uniformity of the foundation sand gradation. It sets the base critical gradient in the + Schmertmann method; more uniform sands (lower values) are more erodible. +- **Effective grain size** $D_{10}$ — Grain size at 10% passing for the foundation sand. It sets the Schmertmann grain-size correction. +- **Fines content category** — Fines content of the foundation sand, which places the sand on one side or the other of the step in the + Schmertmann fines-content correction (see [Delegated Methods](./07-delegated-methods.mdx)). The choices are: + - Less than 5% — taken as 0% fines; no fines correction applies + - 5% or more — taken as 5% fines; the higher fines correction applies + - Unknown — taken as 0% fines, so no fines credit is taken + + + :::warning[INPUT NEEDED IN-02 — Engineering Basis] The default coefficient-of-uniformity distribution (triangular with low 1.1, mode 2.0, high 4.0) requires an engineering basis. Provide a literature citation or the engineering-judgment attribution to state here. @@ -353,25 +417,6 @@ engineering basis — both the distribution parameters and the lower limit. Prov to state here. ::: -Each preset relative density category maps to a uniform distribution of relative density $D_r$ -(). The Unknown category carries a broad band spanning loose to medium-dense conditions; -the model also accepts a legacy Default category with the same band, which the Dam Screening Tool no longer offers. Select the Custom category to supply a site-specific relative-density distribution instead; every value the custom distribution can -produce must lie within the physical range of 0 to 100% (an unbounded form such as a normal distribution therefore requires explicit lower and -upper limits). - - - :::warning[INPUT NEEDED IN-04 — Engineering Basis] The relative-density uniform ranges require an engineering basis — the category band boundaries and the choice of the 15–65% band for the Unknown category. Provide a literature citation or the engineering-judgment attribution to state here. @@ -385,27 +430,30 @@ bibliography if the proposal stands. ## Unit Weights Two saturated unit weights enter the blanket-theory critical-gradient computations -(): the confining layer's for blowout (rupture of the layer) and the foundation sand's for -heave through a defect. Both carry screening defaults that may be overridden. +(). Both carry screening defaults that may be overridden. sand', 'γbl'], ['pcf', 'pcf'], - ['Normal (mean 122.0, standard deviation 3.0)', 'Normal (mean 118.0, standard deviation 3.0)'], - [ - 'Saturated unit weight of the foundation sand. Sets the critical vertical gradient for heave through a defect in the confining layer.', - 'Saturated unit weight of the confining-layer material. Sets the critical vertical gradient for hydraulic blowout (rupture) of the layer.', - ], + ['> 62.4', '> 62.4'], + ['Normal: mean 122.0, standard deviation 3.0', 'Normal: mean 118.0, standard deviation 3.0'], ]} /> +Both unit weights are entered as distributions. A saturated unit weight must exceed the unit weight of water (62.4 pcf) for the critical +gradient to be positive; the model does not test sampled values against this limit, so a distribution that could fall below it should carry a +lower limit. + +- **Foundation sand saturated unit weight** $\gamma_{sand}$ — Sets the critical vertical gradient for heave of the sand through a defect in + the confining layer. +- **Confining layer saturated unit weight** $\gamma_{bl}$ — Sets the critical vertical gradient for hydraulic blowout (rupture) of the layer. + :::warning[INPUT NEEDED IN-05 — Engineering Basis] The default foundation-sand saturated unit weight (normal with mean 122.0 pcf and standard deviation 3.0 pcf) requires an engineering basis. Provide a literature citation or the engineering-judgment attribution to state here. @@ -420,22 +468,24 @@ Provide a literature citation or the engineering-judgment attribution to state h ## Intervention and Breach Probabilities -The final two event-tree nodes are user-specified scalar probabilities (). Both default to -1.0 (certain), which is conservative for screening. +The final two event-tree nodes are user-specified probabilities (). Both default to 1.0 +(certain), which is conservative for screening. int', 'Pbr'], ['0 to 1', '0 to 1'], ['1.0', '1.0'], - [ - 'Probability that detection and emergency intervention fail to stop the piping process before breach. The default assumes no successful intervention. Reduce only when documented monitoring, early-warning, and response capabilities support a lower value.', - 'Probability that an uncontrolled release of impounded water occurs given that the pipe has progressed fully and intervention has failed. The default assumes certain breach.', - ], ]} /> + +- **Probability of unsuccessful intervention** $P_{int}$ — Probability that detection and emergency intervention fail to stop the piping + process before breach. The default assumes no successful intervention; a lower value should be used only when documented monitoring, + early-warning, and response capabilities support it. +- **Probability of breach** $P_{br}$ — Probability that an uncontrolled release of impounded water occurs, given that the pipe has progressed + fully and intervention has failed. The default assumes certain breach. diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/04-flaw-assessment.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/04-flaw-assessment.mdx index 9efd43f9a..2210b1237 100644 --- a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/04-flaw-assessment.mdx +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/04-flaw-assessment.mdx @@ -61,6 +61,14 @@ $LR_{sub} = 1$). When no seepage has been observed, the seepage term drops out ( the subsurface likelihood ratio: high-quality data receives full weight ($q = 1$), while lower-quality data is discounted toward neutral ($q < 1$). +:::warning[INPUT NEEDED IN-18 — Bibliography] +The Bayesian formulation of the flaw assessment requires a literature source: expressing each evidence source as a likelihood ratio, updating +the prior in log-odds form ( to ), +and weighting the subsurface likelihood ratio by the quality factor $q$ as an exponent. Provide full bibliographic details for the source of +the formulation (for addition to the bibliography), or the engineering-judgment attribution for the quality-factor weighting if it is specific +to this model. +::: + ## Uncertainty Quantification Each categorical selection maps to a *range* of values rather than a single number, reflecting the imprecision of the underlying judgments. @@ -68,8 +76,8 @@ The model propagates this uncertainty by Monte Carlo simulation: in each realiza and quality factor are drawn independently and uniformly from their ranges, and the posterior probability is computed from . Across realizations this produces a distribution of the posterior flaw probability. -The **mean posterior probability** populates the event-tree node. The 5th–95th percentile band of the posterior is reported alongside it as a -diagnostic, so the user can see how sharply the evidence constrains the flaw judgment (see +The **mean posterior probability** populates the event-tree node. The spread of the posterior, from its 5th to its 95th percentile, is reported +alongside it, so the user can see how sharply the evidence constrains the flaw judgment (see [Output and Interpretation](./09-output-and-interpretation.mdx)). ## Geologic Environment Priors diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/05-hydraulic-loading-and-seepage-paths.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/05-hydraulic-loading-and-seepage-paths.mdx index cc7be6d7f..07f02c7a7 100644 --- a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/05-hydraulic-loading-and-seepage-paths.mdx +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/05-hydraulic-loading-and-seepage-paths.mdx @@ -30,13 +30,15 @@ Two reference elevations define the downstream boundary of the head computations - **Daylight reference elevation** $E_{day,ref}$ — the controlling ground surface at the downstream termination of the confining layer, where the foundation sand daylights. When the daylight ground-surface elevation is supplied, it controls; otherwise the daylight exit is assumed to share the toe reference elevation. The daylight ground may sit above or below the embankment toe. One exception applies: when the daylighting - exit is the berm toe itself — a berm over a confirmed layer that reaches or clears its downstream extent, or overlies a layer of unknown - extent — the toe reference is the exit's datum, and a separately supplied daylight ground-surface elevation would describe the same location - a second time. The supplied value is then ignored and the validation reports a warning. + exit is the berm toe itself — a berm over a confirmed layer that reaches or clears its downstream extent, or overlies a confirmed layer of + unknown extent — the toe reference is the exit's datum, and a separately supplied daylight ground-surface elevation would describe the same location + a second time. The supplied value is then not used. The blowout and heave analyses and the daylight progression pathway reference the daylight elevation; the toe progression pathway references the toe elevation. Consequently, once a daylight ground surface is supplied (and the daylighting exit is not the berm toe), the embankment toe -elevation no longer enters the unfiltered-exit and initiation head computations at all — the daylight ground is the exit datum for those nodes. +elevation no longer enters the unfiltered-exit and initiation head computations at all — the daylight ground is the exit datum for those nodes, +even though the blowout and heave probabilities are evaluated at the toe (assumption 17 in +[Assumptions and Limitations](./08-assumptions-and-limitations.mdx)). ## Tailwater and Net Driving Head @@ -57,11 +59,11 @@ where: > the toe-progression analysis) A pool at or below the exit reference elevation produces zero net head — no water stands against the seepage path above its exit — so the -pool-dependent event-tree nodes contribute no failure probability there. This gate is a deliberate feature of the model. +pool-dependent event-tree nodes contribute no failure probability there. -The control level is evaluated at the supplied rating points and varies linearly between them. On any rating segment where the raw tailwater -crosses the reference elevation, this linear treatment slightly overstates the control level (and so slightly understates the net head) within -that segment; the effect is bounded by the segment's tailwater change and is noted in +The control level is evaluated at each supplied headwater–tailwater pair and varies linearly between successive supplied headwater values. +Within any interval between successive supplied headwater values where the supplied tailwater crosses the reference elevation, this linear treatment slightly overstates the +control level (and so slightly understates the net head); the effect is bounded by the change in tailwater across that interval and is noted in [Assumptions and Limitations](./08-assumptions-and-limitations.mdx). ## Seepage Path Components @@ -78,8 +80,8 @@ The upstream path length is resolved by precedence: 2. **Confining layer confirmed and Very Thin** — $L_1 = 0$. A very thin upstream extension is credited with no head loss. 3. **Confining layer confirmed, impervious, with a supplied upstream extension** — $L_1$ equals the supplied upstream confining-layer length. -4. **Otherwise** — $L_1 = 0$. An upstream extension of unknown length, or a layer that is semi-pervious or of unknown permeability, is - credited with no upstream head loss. +4. **Otherwise** — $L_1 = 0$. A layer whose upstream extension is No or Unknown, or a layer that is semi-pervious or of unknown permeability, + is credited with no upstream head loss. :::warning[INPUT NEEDED IN-10 — Engineering Basis] Two judgments in the upstream-path crediting rules require an engineering basis to state here: @@ -94,15 +96,15 @@ Provide the citation or engineering-judgment attribution for each. ### Embankment Path Length L₂ -The embankment path length $L_2$ is the derived base width of the outer shell — the crest width plus the horizontal projections of the +The embankment path length $L_2$ is the embankment base width — the crest width plus the horizontal projections of the upstream and downstream faces (see [Input Parameters](./03-input-parameters.mdx)). A downstream seepage berm is not part of $L_2$; its length extends the downstream path instead. ### Downstream Path Length L₃ The downstream path length $L_3$ — from the embankment toe to the seepage exit — is resolved from the berm and confining-layer inputs -(). A supplied downstream extent enters as its single value; the unknown-extent default is -the only downstream-path characterization carried as a distribution. +(). A supplied downstream extent enters as its single value; the default for no berm with an +unknown extent or unknown layer presence is the only downstream-path characterization carried as a distribution. -- **Blanket Theory Case 4** — no riverside top stratum, impervious landside top stratum only - ([dedicated documentation](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-initiation/v1.0/blanket-theory-case-4)). +- **Blanket Theory Case 4** — no riverside top stratum, impervious landside top stratum only (see + [Blanket Theory Case 4](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-initiation/v1.0/blanket-theory-case-4) + in the BEP Initiation manual). Selected otherwise. With an open seepage entrance, the effective entry length is approximated from the foundation thickness: -where $d$ is the sampled foundation sand thickness. Note that the Case 2 routing does not test the thickness category: a confirmed Very Thin +where $d$ is the sampled foundation sand thickness. Case 2 is selected regardless of the thickness category: a confirmed Very Thin impervious layer with a supplied upstream extension still routes to Case 2, but carries $L_1 = 0$ per the crediting rules above — the configuration reflects the presence of an upstream barrier while crediting it with no head loss. @@ -177,9 +181,9 @@ where: > $L_b$ = berm length The excess head available at the offset point follows the linear blanket-theory head profile documented in -[Delegated Models](./07-delegated-models.mdx); the offset therefore reduces the head (and the blowout and heave probabilities) relative to the +[Delegated Methods](./07-delegated-methods.mdx); the offset therefore reduces the head (and the blowout and heave probabilities) relative to the toe. When the berm instead reaches or clears the layer's downstream extent, no offset arises — the exit daylights at the berm toe and the -confined-exit nodes are overridden to certainty rather than computed (see [Event Tree](./06-event-tree.mdx)). +confined-exit nodes are set to certainty rather than computed (see [Event Tree](./06-event-tree.mdx)). :::warning[INPUT NEEDED IN-12 — Definition] The physical interpretation of the exit-offset distance requires confirmation. The intended evaluation location is the berm toe — the first @@ -202,8 +206,9 @@ The Schmertmann progression analysis uses the full geometric path from the upstr where the berm length $L_b$ is included only when a berm is present. $L_3$ in the daylight path is sampled per Monte Carlo realization only -when the downstream extent is unknown (the one-to-five-embankment-height default); a supplied extent enters as its single value. A longer path -reduces the average applied gradient and thus the probability of progression. +when no berm is present and the downstream extent or the layer's presence is unknown (the one-to-five-embankment-height default); otherwise it +enters as a single value. A longer path reduces the average applied gradient. When the presence is Unknown and a berm is present, $L_3 = L_b$, +so the two progression paths are equal. ## References diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/06-event-tree.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/06-event-tree.mdx index a38aa7837..42e6bdb3a 100644 --- a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/06-event-tree.mdx +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/06-event-tree.mdx @@ -30,17 +30,16 @@ for the backward erosion piping failure mode; every database node maps one-to-on ## Node Summary - summarizes the seven nodes, the engineering question each answers, and how the screening -model populates each probability. Nodes 2, 3, and 5 vary with pool level and differ between the toe and daylight pathways; the remaining nodes + summarizes the seven nodes and how the screening model populates each probability on each +exit pathway. The sections that follow state the engineering question each node answers and give each node in full. Nodes 2, 3, and 5 vary with pool level and differ between the toe and daylight pathways; the remaining nodes are pool-independent and shared by both pathways. ## Node 1: Flaw — Continuous Path +*Question:* Does a continuous path of fine to medium, uniform sand exist in the foundation? + The probability $P_{flaw}$ that a continuous path of erodible foundation sand exists is the mean posterior probability from the Bayesian flaw assessment documented in [Flaw Assessment](./04-flaw-assessment.mdx). The flaw is a geologic condition, so this probability is constant across all pool levels and is shared by both exit pathways. ## Node 2: Flaw — Unfiltered Exit +*Question:* Does seepage exit unfiltered at the ground surface? + ### Toe pathway When a confining layer may be present and the toe exit remains beneath it — no berm, or a berm ending within the layer's known downstream @@ -98,7 +101,7 @@ extent — seepage can reach the surface unfiltered at the toe through either of - **Hydraulic blowout** — rupture of the layer when uplift at its base exceeds its buoyant weight. The blowout probability $P_{blowout}(h)$ at each pool level is computed by the blanket-theory analysis using the confining layer's saturated unit weight - (see [Delegated Models](./07-delegated-models.mdx)); it increases with pool level. The probability is evaluated at the exit evaluation + (see [Delegated Methods](./07-delegated-methods.mdx)); it increases with net head. The probability is evaluated at the exit evaluation point — the toe by default, offset beyond a berm that ends within the layer's known extent (see [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx)). @@ -157,11 +160,13 @@ daylight pathway is 1.0 at every pool level. The pathway itself is evaluated onl ## Node 3: Initiation +*Question:* Is the exit gradient sufficient to initiate backward erosion at the unfiltered exit? + ### Toe pathway Initiation at a confined exit requires the vertical gradient through the layer (or through a defect in it) to fluidize the underlying sand. The initiation probability $P_{init}(h)$ at each pool level is the blanket-theory heave probability, computed with the foundation sand's -saturated unit weight (see [Delegated Models](./07-delegated-models.mdx)). Four site conditions override the computed value and force +saturated unit weight (see [Delegated Methods](./07-delegated-methods.mdx)). Four site conditions override the computed value and force $P_{init} = 1.0$: 1. **No confining layer** — with no overburden to resist heave, initiation accompanies the unfiltered exit. @@ -169,7 +174,7 @@ $P_{init} = 1.0$: characterized layer. 3. **The berm reaches or clears a supplied downstream extent** — the berm is at least as long as the layer's extent, so the exit sits at or beyond the layer's termination. The override applies whether the layer's presence is confirmed or unknown. -4. **The pool reaches the trigger elevation** — sand boils have historically activated at or above this pool, demonstrating initiation: +4. **The pool reaches the trigger elevation** — sand boils or concentrated seepage have historically activated at or above this pool, demonstrating initiation: , following Fell et @@ -226,15 +234,20 @@ hold a roof, so the least capable material controls. The probability is constant ## Node 5: Progression — Hydraulic Condition +*Question:* Is the applied gradient sufficient to advance the pipe toward the impounded water? + The probability that the applied gradient is sufficient to advance the pipe from the exit toward the reservoir is the mean probability of advancement from the Schmertmann analysis, evaluated at each pool level for the pathway's seepage path length -(see [Delegated Models](./07-delegated-models.mdx)). The toe pathway uses the path to the embankment or berm toe; the daylight pathway uses -the longer path to the daylight exit. The resulting probability is constrained to be non-decreasing with pool level, reflecting that a higher -pool cannot make progression less likely. +(see [Delegated Methods](./07-delegated-methods.mdx)). The toe pathway uses the path to the embankment or berm toe; the daylight pathway uses +the longer path to the daylight exit. The resulting probability is constrained to be non-decreasing with pool level, reflecting that, for a net +head that rises with pool level, a higher pool cannot make progression less likely (see assumption 15 in +[Assumptions and Limitations](./08-assumptions-and-limitations.mdx)). ## Nodes 6 and 7: Unsuccessful Intervention and Breach -The final two nodes are the user-specified scalar probabilities documented in [Input Parameters](./03-input-parameters.mdx). Both default to +*Questions:* Do detection and intervention fail (Node 6)? Does an uncontrolled release of impounded water occur (Node 7)? + +The final two nodes are the user-specified probabilities documented in [Input Parameters](./03-input-parameters.mdx). Both default to 1.0 — no successful intervention and certain breach — a conservative screening posture. ## SRP Computation @@ -256,15 +269,20 @@ where: > $P_{int}$ = probability of unsuccessful intervention (Node 6) > $P_{br}$ = probability of breach (Node 7) -On the daylight pathway, $P_{ue}$ and $P_{init}$ are both 1.0 and $P_{prog}$ reflects the longer daylight path. +On the daylight pathway, $P_{ue}$ and $P_{init}$ are both 1.0 and $P_{prog}$ reflects the daylight path. ## Governing SRP A daylight pathway is evaluated only where the daylighting exit is distinct from the toe exit. When a berm over a confirmed layer reaches or clears the layer's downstream extent — or overlies a confirmed layer of unknown extent — the berm toe is itself the daylighting exit: the toe pathway then carries a certain unfiltered exit and certain initiation over the berm-extended path, which are exactly the daylighting-exit -conditions, so a separate daylight pathway would repeat the same exit node for node and is not evaluated. A layer of unknown presence retains -both pathways even with a berm, because its toe pathway keeps the heave-gated initiation node and the two pathways genuinely differ. +conditions, so a separate daylight pathway would repeat the same exit node for node and is not evaluated. This merging applies only to a +confirmed layer: under a layer of unknown presence the model always evaluates both pathways. With a berm over a layer of unknown presence, the +downstream path resolves to the berm length, so both pathways share the same progression path length and plane-type exit. They then differ only +in two respects: the toe initiation node, which stays at the heave probability unless the berm reaches or clears a supplied downstream extent +(Node 3), and the exit datum, because the toe progression references the toe reference elevation and the daylight progression the daylight +reference elevation. Where the two datums coincide, the daylight SRP is at least the toe SRP, because its unfiltered-exit and initiation nodes +are certain. When both pathways are evaluated, the governing SRP at each pool level is the larger of the two pathway values: diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/07-delegated-methods.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/07-delegated-methods.mdx new file mode 100644 index 000000000..6c35f3739 --- /dev/null +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/07-delegated-methods.mdx @@ -0,0 +1,244 @@ +--- +title: Delegated Methods +--- + +import Citation from '@site/src/components/Citation'; +import CitationFootnote from '@site/src/components/CitationFootnote'; +import Equation from '@site/src/components/Equation'; +import EquationReference from '@site/src/components/EquationReference'; +import NavContainer from '@site/src/components/NavContainer'; +import TableReference from '@site/src/components/TableReference'; +import TableVertical from '@site/src/components/TableVertical'; + + + +# Delegated Methods + +The screening model hands two of its event-tree calculations to established analysis methods, each documented in a dedicated technical manual: + +- **Blanket theory** evaluates the blowout and heave probabilities behind Node 2 (Flaw: Unfiltered Exit) and Node 3 (Initiation) on the toe + pathway. +- **The Schmertmann critical-gradient method** evaluates the probability of pipe advancement behind Node 5 (Progression: Hydraulic Condition) on + both pathways. + +The theory of each method lives in its manual. Each section below states the node the method serves and the question it answers there, links +the chapter of the manual that covers it, and then documents only what the screening model supplies, what it uses from the result, and every +screening-level adjustment relative to the manual. The flaw assessment (Node 1) and the defect-survival relationship (part of Node 2) are the +screening model's own calculations, documented in [Flaw Assessment](./04-flaw-assessment.mdx) and [Event Tree](./06-event-tree.mdx). + +## Blanket Theory — Blowout and Heave + +**Nodes served:** Node 2 (Flaw: Unfiltered Exit) and Node 3 (Initiation), on the toe pathway, wherever a confining layer may be present and the +toe exit remains beneath it. + +**Questions answered:** At Node 2, is the uplift pressure at the base of the confining layer large enough to rupture the layer (blowout), opening +an unfiltered exit? At Node 3, is the vertical gradient through a defect in the layer large enough to fluidize the underlying sand (heave), +starting erosion at the exit? Both questions compare the vertical exit gradient through the layer with a critical gradient set by a saturated +unit weight, which is what blanket theory computes. + +### Blanket-theory configuration + +The model evaluates one of two blanket-theory configurations, selected from the upstream seepage barrier by the rule documented in +[Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx#blanket-theory-configuration-selection): + +- **Case 2** — impervious top strata on both the riverside and the landside, used when an upstream seepage barrier is present. The theory, + including the exit head at the landside toe and at a given distance beyond it, is in + [Blanket Theory Case 2](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-initiation/v1.0/blanket-theory-case-2) + of the BEP Initiation manual. +- **Case 4** — no riverside top stratum and an impervious landside top stratum, used otherwise. The theory, including the effective entrance + length of $0.43\,d$ for an open riverside entrance, is in + [Blanket Theory Case 4](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-initiation/v1.0/blanket-theory-case-4) + of the BEP Initiation manual. + +### Blowout and heave evaluations + +The model evaluates the selected configuration **twice with identical sampled realizations** of the foundation thickness, confining-layer +thickness, and downstream path length: + +- **Blowout** — the critical gradient is computed from the *confining layer's* saturated unit weight $\gamma_{bl}$, representing rupture + of the layer against its buoyant weight. The result feeds Node 2. +- **Heave** — the critical gradient is computed from the *foundation sand's* saturated unit weight $\gamma_{sand}$, representing + fluidization of the sand column at a defect through the layer. The result feeds Node 3. + +Because the two evaluations share their sampled realizations, the blowout and heave probabilities differ only through the unit weight entering +the critical gradient. + +### Governing relationships + +Within each Monte Carlo realization, and at each pool level with net head $H$ (defined in +[Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx)): + + + + + + + + + +where: + +> $h_o$ = excess head above the exit datum at the embankment toe +> $h_x$ = excess head at the exit evaluation point, offset $x$ from the toe +> $L_3$, $L_{total}$ = downstream and total seepage path lengths ($L_3$ sampled per realization when no berm is present and the extent or the layer's presence is unknown) +> $i_{cv}$ = critical vertical gradient +> $\gamma_{sat}$ = saturated unit weight ($\gamma_{bl}$ for blowout, $\gamma_{sand}$ for heave) +> $\gamma_w$ = unit weight of water (62.4 pcf) +> $i_v$ = vertical exit gradient through the confining layer +> $z_{bl}$ = sampled confining-layer thickness +> $FS$ = factor of safety against the vertical gradient + +The blowout or heave probability at each pool level is the fraction of Monte Carlo realizations in which $FS < 1$. Realizations with no exit +gradient (zero net head) contribute no failure. + +### Screening-level adjustments + +Relative to the blanket-theory chapters of the BEP Initiation manual, the screening model fixes the following: + +- **Finite-blanket head loss always applies** — the excess head at the toe is always reduced by the path-length ratio + (). The idealization of an infinite downstream blanket carrying the full net head at + the toe is not used. +- **Downstream blanket length follows the resolved downstream path** — $L_3$ enters as the supplied downstream extent, or is drawn per + realization from the wide default range when no berm is present and the extent or the layer's presence is unknown + (see [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx)). +- **Confining-layer thickness comes from the category band** — the sampled $z_{bl}$ follows the qualitative thickness category (or the custom + distribution) documented in [Input Parameters](./03-input-parameters.mdx). +- **The unit weight is mechanism-specific** — $\gamma_{bl}$ for blowout and $\gamma_{sand}$ for heave, each defaulting per + [Input Parameters](./03-input-parameters.mdx). +- **Foundation permeability does not influence the screening result** — hydraulic conductivity affects only the seepage-quantity results of + blanket theory, which the screening model does not use; the exit-gradient computations are independent of it. + +## Schmertmann Method — Progression + +**Node served:** Node 5 (Progression: Hydraulic Condition), on the toe pathway and, when it is evaluated, the daylight pathway. + +**Question answered:** Once erosion has initiated at the exit and a roof is available, is the average hydraulic gradient along the seepage path +large enough to keep advancing the pipe upstream through the foundation sand until it reaches the reservoir? The Schmertmann +method answers it by comparing the average applied gradient with a field critical gradient derived from +laboratory piping tests and corrected for site conditions. The complete method is documented in the +[Schmertmann](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.0/schmertmann) chapter of the BEP +Progression manual; the subsections below link the part of that chapter each step follows. + +### Base critical gradient + +The base critical gradient derives from laboratory piping-model tests, represented as a family of quantile curves linear in the coefficient of +uniformity (see +[Laboratory Horizontal Critical Gradient](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.0/schmertmann#laboratory-horizontal-critical-gradient)): + + + +where $i_{pmt}(\xi)$ is the laboratory critical gradient at cumulative probability $\xi$, and $m(\xi)$ and $b(\xi)$ are the quantile regression +coefficients from the BEP Progression manual. The screening model uses these laboratory relationships without modification. + +### Field critical gradient and correction factors + +The field critical gradient scales the laboratory gradient by the correction factors (see +[Field Horizontal Critical Gradient](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.0/schmertmann#field-horizontal-critical-gradient)): + + + +In the screening configuration, five factors remain active and four are fixed at unity +(). + +D', 'CL', 'CS', 'Cγ', 'COF', 'CK', 'CZ', 'Cα', 'CR'], + [ + 'Depth', + 'Seepage path length', + 'Grain size', + 'Density', + 'Overall field correction', + 'Anisotropy', + 'Underlayer', + 'Pipe-path inclination', + 'Axis curvature', + ], + ['Active', 'Active', 'Active', 'Active', 'Active', 'Fixed at 1.0', 'Fixed at 1.0', 'Fixed at 1.0', 'Fixed at 1.0'], + ]} +/> + +The active factors take their values from the screening inputs: + +- $C_D$ — from the sampled foundation thickness $d$ and the pathway's seepage path length +- $C_L$ — from the pathway's seepage path length +- $C_S$ — from the sampled effective grain size $D_{10}$ +- $C_\gamma$ — from the sampled relative density $D_r$ (per the category mapping or custom distribution in + [Input Parameters](./03-input-parameters.mdx)) +- $C_{OF}$ — the product of the fines-content correction and the exit-geometry factor, given below + +The fixed factors reflect information that is rarely available at the screening stage: + +- $C_K$ — taken as 1.0, which the BEP Progression manual's anisotropy relationship, $C_K = (1.5/R_{kf})^{0.5}$, gives for a reference + conductivity ratio $R_{kf} = k_h/k_v$ of 1.5; the seepage path length is not transformed for anisotropy (assumption 12 in + [Assumptions and Limitations](./08-assumptions-and-limitations.mdx)) +- $C_Z$ — taken as 1.0, the value for no higher-permeability underlayer; no stratum beneath the aquifer is characterized (assumption 13) +- $C_\alpha$ — the pipe path is fixed horizontal (inclination 0°), so no inclination correction applies (see + [Pipe Path Inclination](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.0/schmertmann#pipe-path-inclination)) +- $C_R$ — the axis is treated as straight, as in the BEP Progression manual + +### Exit geometry and fines corrections + +The overall field correction is: + + + +The exit-geometry factor $C_{3d}$ distinguishes concentrated (hole-type) exits from distributed (plane-type) exits. Van Beek et +al. (2015) found that three-dimensional flow converging toward a single exit point produces critical +gradients roughly half those predicted for the two-dimensional configuration. Their comparison was made against the Dutch (Sellmeijer) piping +model, and the BEP Progression manual notes that the reduction was not developed and calibrated for the Schmertmann method; the screening model +applies it to the Schmertmann critical gradient by engineering judgment, as the manual does, so a hole-type exit takes $C_{3d} = 0.5$ and a +plane-type exit $C_{3d} = 1.0$. The screening model assigns the exit type as follows: + +- **Toe pathway** — hole-type ($C_{3d} = 0.5$) when the confining layer is confirmed, *unless* a berm is present and either the layer's + downstream extent is unknown or the berm reaches or clears that extent (the exit then daylights beyond the layer and is plane-type). When + the layer's presence is No or Unknown, the toe exit is plane-type (assumption 18 in + [Assumptions and Limitations](./08-assumptions-and-limitations.mdx)). +- **Daylight pathway** — always plane-type ($C_{3d} = 1.0$); the exit is an exposed sand surface. + +The fines-content correction is a step function of the foundation sand's fines content: + + + +The higher factor applies at exactly 5% fines and above; a fines content below 5% takes no correction. + +:::warning[INPUT NEEDED IN-16 — Engineering Basis] +The fines-content correction applied in the Schmertmann analysis — a step from 1.0 to 1.4, with the higher factor applying at exactly 5% fines +and above — requires an engineering basis. Provide the source or engineering-judgment attribution for the step form, the 5% threshold, and the +1.4 value, and add the term to the Schmertmann chapter of the BEP Progression manual, which currently omits it. +::: + +### Probability of advancement + +At each pool level, the applied gradient is the net head over the pathway's seepage path length (see +[Likelihood of Backward Erosion Piping Progression](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.0/schmertmann#likelihood-of-backward-erosion-piping-progression)): + + + +where $L_{prog}$ is the toe or daylight progression path length from +[Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx) (sampled per realization on the daylight pathway when no berm is +present and the downstream extent or the layer's presence is unknown). Within each realization, the correction factors scale the entire family of laboratory quantile curves +(), and the probability of advancement is the cumulative probability that the corrected +critical gradient is at or below the applied gradient — interpolated from the scaled quantile family, and limited to 0 and 1 beyond its ends. +A pool producing no positive net head yields no probability of advancement. + +The Node 5 probability at each pool level is the mean probability of advancement across the Monte Carlo realizations, then constrained to be +non-decreasing with pool level as described in [Event Tree](./06-event-tree.mdx). + +## References + + diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/07-delegated-models.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/07-delegated-models.mdx deleted file mode 100644 index 059f55273..000000000 --- a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/07-delegated-models.mdx +++ /dev/null @@ -1,201 +0,0 @@ ---- -title: Delegated Models ---- - -import Citation from '@site/src/components/Citation'; -import CitationFootnote from '@site/src/components/CitationFootnote'; -import Equation from '@site/src/components/Equation'; -import EquationReference from '@site/src/components/EquationReference'; -import NavContainer from '@site/src/components/NavContainer'; -import TableReference from '@site/src/components/TableReference'; -import TableVertical from '@site/src/components/TableVertical'; - - - -# Delegated Models - -The screening model delegates its Monte Carlo computations to two established analysis methods, each documented in a dedicated technical -manual: blanket theory for the blowout and heave probabilities -([BEP Initiation](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-initiation/v1.0/preface)) and the Schmertmann -critical-gradient method for progression -([BEP Progression](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.0/schmertmann)). The theory -lives in those manuals; this chapter documents how the screening model invokes each method — the quantities passed in, the outputs consumed, -and every screening-level adjustment relative to the dedicated documentation. - -## Blanket Theory — Blowout and Heave - -Blanket theory computes the excess head beneath the downstream confining layer and the vertical gradient -through it, from which the probability of a gradient-driven failure of the layer follows. The screening model routes the analysis to Case 2 or -Case 4 as documented in [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx), and runs it **twice with -identical sampled realizations** of the foundation thickness, confining-layer thickness, and downstream path length: - -- **Blowout run** — the critical gradient is computed from the *confining layer's* saturated unit weight $\gamma_{bl}$, representing rupture - of the layer's buoyant weight. Its result feeds the unfiltered-exit node. -- **Heave run** — the critical gradient is computed from the *foundation sand's* saturated unit weight $\gamma_{sand}$, representing - fluidization of the sand column at a defect through the layer. Its result feeds the initiation node. - -Because the two runs share their sampled realizations, the blowout and heave probabilities differ only through the unit weight entering the -critical gradient. - -### Governing relationships - -Within each Monte Carlo realization, and at each pool level with net head $H$ (defined in -[Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx)): - - - - - - - - - -where: - -> $h_o$ = excess head above the exit datum at the embankment toe -> $h_x$ = excess head at the exit evaluation point, offset $x$ from the toe -> $L_3$, $L_{total}$ = downstream and total seepage path lengths ($L_3$ sampled per realization when the downstream extent is unknown) -> $i_{cv}$ = critical vertical gradient -> $\gamma_{sat}$ = saturated unit weight ($\gamma_{bl}$ for blowout, $\gamma_{sand}$ for heave) -> $\gamma_w$ = unit weight of water (62.4 pcf) -> $i_v$ = vertical exit gradient through the confining layer -> $z_{bl}$ = sampled confining-layer thickness -> $FS$ = factor of safety against the vertical gradient - -The blowout or heave probability at each pool level is the fraction of Monte Carlo realizations in which $FS < 1$. Realizations with no exit -gradient (zero net head) contribute no failure. - -### Screening-level adjustments - -Relative to the dedicated blanket-theory documentation, the screening model fixes the following: - -- **Finite-blanket head loss always applies** — the excess head at the toe is always reduced by the path-length ratio - (). The idealization of an infinite downstream blanket carrying the full net head at - the toe is not used. -- **Downstream blanket length follows the resolved downstream path** — $L_3$ enters as the supplied downstream extent's single value, or is - drawn per realization from the wide default range when the extent is unknown - (see [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx)). -- **Confining-layer thickness comes from the category band** — the sampled $z_{bl}$ follows the qualitative thickness category (or the custom - distribution) documented in [Input Parameters](./03-input-parameters.mdx). -- **The unit weight is mechanism-specific** — $\gamma_{bl}$ for blowout and $\gamma_{sand}$ for heave, each defaulting per - [Input Parameters](./03-input-parameters.mdx). -- **Foundation permeability does not influence the screening result** — hydraulic conductivity affects only the seepage-quantity outputs of - the blanket-theory analysis, which the screening model does not use; the exit-gradient computations are independent of it. - -## Schmertmann Method — Progression - -The Schmertmann method evaluates whether the average applied gradient along the seepage path exceeds -the critical gradient required to advance an erosion pipe through the foundation sand. The complete method — the laboratory basis and every -correction factor — is documented in the -[BEP Progression manual](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.0/schmertmann); this -section documents the screening invocation. - -### Base gradient and critical gradient - -The base critical gradient derives from laboratory piping-model tests, represented as a family of quantile curves linear in the coefficient of -uniformity: - - - -where $i_{pmt}(q)$ is the laboratory critical gradient at cumulative probability $q$, and $m(q)$ and $b(q)$ are the quantile regression -coefficients from the dedicated documentation. The screening model uses these built-in laboratory relationships without modification. The -field critical gradient scales the laboratory gradient by the correction factors: - - - -In the screening configuration, four factors are fixed at unity and five remain active -(). - -D', 'CL', 'CS', 'Cγ', 'CK', 'CZ', 'Cα', 'CR', 'COF'], - [ - 'Active', - 'Active', - 'Active', - 'Active', - 'Fixed at 1.0', - 'Fixed at 1.0', - 'Fixed at 1.0', - 'Fixed at 1.0', - 'Active (toolbox default)', - ], - [ - 'Depth correction, from the sampled foundation thickness and seepage path length.', - 'Path-length correction, from the seepage path length.', - 'Grain-size correction, from the sampled effective grain size.', - 'Density correction, from the sampled relative density (per the category mapping or custom distribution in Input Parameters).', - 'Anisotropy correction disabled: the horizontal-to-vertical conductivity ratio is treated as 1.0. No anisotropy input is accepted at the screening level.', - 'Underlayer correction disabled: no underlayer beneath the aquifer is characterized at screening level.', - 'Pipe-path inclination fixed horizontal (inclination of 0°), so no inclination correction applies.', - 'Reference correction at its baseline value.', - 'Overall field correction — the product of the fines-content correction and the exit-geometry factor, per the equations below.', - ], - ]} -/> - -### Exit geometry and fines corrections - -The overall field correction is: - - - -The exit-geometry factor $C_{3d}$ distinguishes concentrated (hole-type) exits from distributed (plane-type) exits. Van Beek et -al. (2015) found that three-dimensional flow converging toward a single exit point produces critical -gradients roughly half those of the two-dimensional configuration, so a hole-type exit takes $C_{3d} = 0.5$ and a plane-type exit -$C_{3d} = 1.0$. The screening model assigns the exit type as follows: - -- **Toe pathway** — hole-type ($C_{3d} = 0.5$) when the confining layer is confirmed, *unless* a berm is present and either the layer's - downstream extent is unknown or the berm reaches or clears that extent (the exit then daylights beyond the layer and is plane-type). When - the layer's presence is No or Unknown, the toe exit is plane-type. -- **Daylight pathway** — always plane-type ($C_{3d} = 1.0$); the exit is an exposed sand surface. - -The fines-content correction is a step function of the foundation sand's fines content: - - - -The higher factor applies at exactly 5% fines and above; a fines content below 5% takes no correction. This step is the Schmertmann -analysis engine's built-in fines-content relationship, not a screening-level substitution: the screening model passes no fines override, so -the screening and toolbox analyses apply the same correction. The dedicated Schmertmann documentation does not describe the fines-content -term. - -:::warning[INPUT NEEDED IN-16 — Engineering Basis] -The fines-content correction applied by the Schmertmann analysis engine — a step from 1.0 to 1.4, with the higher factor applying at exactly -5% fines and above — requires an engineering basis. Provide the source or engineering-judgment attribution for the step form, the 5% -threshold, and the 1.4 value, and add the term to the dedicated Schmertmann documentation, which currently omits it. -::: - -### Probability of advancement - -At each pool level, the applied gradient is the net head over the pathway's seepage path length: - - - -where $L_{prog}$ is the toe or daylight progression path length from -[Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx) (sampled per realization on the daylight pathway when the -downstream extent is unknown). Within each realization, the correction factors scale the entire family of laboratory quantile curves -(), and the probability of advancement is the cumulative probability that the corrected -critical gradient is at or below the applied gradient — interpolated from the scaled quantile family, and clamped to 0 and 1 beyond its ends. -A pool producing no positive net head yields no probability of advancement. - -The progression node probability at each pool level is the mean probability of advancement across the Monte Carlo realizations, subsequently -constrained to be non-decreasing with pool level as described in [Event Tree](./06-event-tree.mdx). - -## References - - diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/08-assumptions-and-limitations.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/08-assumptions-and-limitations.mdx index 5f4aa2d01..adfd450fa 100644 --- a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/08-assumptions-and-limitations.mdx +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/08-assumptions-and-limitations.mdx @@ -2,116 +2,203 @@ title: Assumptions and Limitations --- +import Citation from '@site/src/components/Citation'; +import CitationFootnote from '@site/src/components/CitationFootnote'; import NavContainer from '@site/src/components/NavContainer'; -import TableReference from '@site/src/components/TableReference'; -import TableVertical from '@site/src/components/TableVertical'; # Assumptions and Limitations The BEP screening model applies deliberate simplifications relative to the full toolbox models. They reduce input requirements and are designed -to avoid false negatives at the screening level. documents each assumption with its -engineering basis, its effect on results, and the conditions under which it may not hold. Where an engineering basis is still awaiting -confirmation, the table cross-references the input marker at the assumption's primary location in this document. - - +to avoid false negatives at the screening level. Each assumption below states its engineering basis, its effect on results, and the conditions +under which it may not hold. Where an engineering basis is still awaiting confirmation, the assumption cross-references the input marker at its +primary location in this document. + +## Seepage Geometry and Hydraulics + +1. **The site is idealized as one of two blanket-theory configurations, Case 2 or Case 4.** The configuration is selected from the upstream + seepage barrier (see [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx)). + - *Engineering basis:* Screening design decision (engineering judgment): the two cases bracket the screening-relevant configurations — an + upstream barrier either exists or does not — and automatic selection removes a choice from the user. + - *Effect on results:* Sites whose stratigraphy matches other blanket-theory cases (semi-pervious strata, more complex layering) are + approximated by the nearer of the two configurations. + - *When it may not hold:* Sites with well-characterized semi-pervious strata or geometries that need Cases 1, 3, or 5 through 8; the + toolbox models apply directly to such sites. +2. **The downstream confining layer carries a linear head profile.** The excess head decays from its value at the toe to zero at the layer's + downstream termination. + - *Engineering basis:* Blanket theory. The landside layer is analyzed as an impervious top stratum + whatever permeability is selected; the permeability selection affects only the upstream credit. + - *Effect on results:* Exit heads are reduced by the path-length ratio, which is less conservative than an infinite-blanket idealization. + - *When it may not hold:* Blankets with strong lateral heterogeneity, or relief wells and toe drains that alter the head profile. A + semi-pervious landside layer also departs from it: blanket theory replaces a semi-pervious landside stratum with an equivalent impervious + length that can be shorter or longer than the physical length, depending on the landside boundary condition (see + [Blanket Theory Case 6](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-initiation/v1.0/blanket-theory-case-6)), + so the impervious treatment can overstate or understate the exit head. +3. **When the confining-layer extent or presence is unknown and no berm is present, the downstream seepage path spans 1 to 5 embankment heights.** + - *Engineering basis:* Basis requested — see marker IN-11 in [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx). + - *Effect on results:* The wide range spreads the sampled exit heads, gradients, and daylight path lengths, widening the uncertainty carried + into the blowout, heave, and daylight-progression results. + - *When it may not hold:* Sites where mapping or borings bound the layer extent outside 1 to 5 embankment heights, where the analyst supplies the extent instead. +4. **Supplied seepage-path lengths are single values.** The upstream blanket length and the upstream and downstream confining-layer extents + carry no uncertainty; the default range for an unknown downstream extent is the only seepage-path length treated as a distribution. + - *Engineering basis:* Screening design decision (engineering judgment): a known length is a geometric site measurement entered as one + value, and uncertainty about an unknown downstream extent is represented by the wide default range instead. + - *Effect on results:* The SRP reflects the entered path lengths exactly; uncertainty in a measured length does not spread the result. + - *When it may not hold:* Sites where a supplied seepage-path length is both highly uncertain and influential; the analyst then brackets + that uncertainty by running the analysis at candidate lengths. +5. **The downstream control level is interpolated linearly between successive supplied headwater values.** The control level is the higher of the tailwater + and the exit reference elevation, evaluated at each supplied headwater–tailwater pair. + - *Engineering basis:* Screening simplification (engineering judgment) with a bounded, documented effect (see + [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx)). + - *Effect on results:* Within any interval between successive supplied headwater values where the tailwater crosses the reference elevation, the + interpolated control level slightly overstates the true value, understating the net head there by no more than the change in tailwater + across that interval (slightly non-conservative). + - *When it may not hold:* Tailwater that crosses the exit reference within a wide interval between successive supplied headwater values; + additional headwater–tailwater pairs near the crossing reduce the effect. + +## Unfiltered Exit and Initiation + +6. **A pre-existing defect fully penetrates the confining layer with a probability given by a Weibull survival function of thickness.** The + characteristic depth is 3.5 ft and the shape parameter is 1.25 (see [Event Tree](./06-event-tree.mdx)). + - *Engineering basis:* Basis requested — see marker IN-13 in [Event Tree](./06-event-tree.mdx). + - *Effect on results:* The defect probability sets a pool-independent lower bound on the toe unfiltered-exit probability, because the + unfiltered-exit probability can never be less than the defect probability. Averaged over the thickness bands, the defect probability is + about 0.55 for Very Thin, 0.32 for Unknown, 0.09 for Thin, and below 0.01 for Moderate and Thick, so it controls Node 2 whenever the band + includes thin layers and the blowout probability is lower. + - *When it may not hold:* Sites with a defect survey or verified intact layers (inspection, construction records) that contradict the + generic defect population. +7. **The defect and blowout pathways to an unfiltered exit are statistically independent.** + - *Engineering basis:* Basis requested — see marker IN-15 in [Event Tree](./06-event-tree.mdx). + - *Effect on results:* The combined unfiltered-exit probability is at least as large as either mechanism alone. + - *When it may not hold:* Where the two mechanisms share a common cause (both concentrated at thin spots in the layer), the union may misstate + the combined probability. +8. **A downstream seepage berm is classified by where it ends relative to the confining layer.** A berm within a confirmed layer of known + greater extent retains the through-layer exit mechanisms at an offset exit point. A berm that reaches or clears the extent, or overlies a + layer of unknown extent or unknown presence, produces a daylighting exit at the berm toe with a certain unfiltered exit. No berm is credited + with filtering, and every berm lengthens the toe progression path. + - *Engineering basis:* Basis requested — see marker IN-12 in + [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx) and marker IN-14 in [Event Tree](./06-event-tree.mdx). + - *Effect on results:* A berm within a known layer extent keeps the defect and blowout composition, with the head reduced at the offset exit + point. Over a confirmed layer, a berm that daylights the exit makes the unfiltered-exit and initiation nodes certain, and the toe pathway + then carries the governing curve. Over a layer of unknown presence, a berm makes the unfiltered-exit node certain (and the initiation node + too when it reaches or clears a supplied extent), and both pathways are still evaluated (see [Event Tree](./06-event-tree.mdx)). + - *When it may not hold:* Engineered filter berms designed to filter the exit; sites where the berm length relative to the layer extent is + itself uncertain, since that comparison switches the exit treatment. +9. **A confining layer of unknown presence is evaluated as possibly present.** The defect and blowout analyses run with the Unknown thickness + band, roof support comes from the embankment materials, and both exit pathways are evaluated. + - *Engineering basis:* Screening design objective (engineering judgment): an unverified layer is neither ignored nor fully credited, avoiding false negatives from + either extreme. + - *Effect on results:* Results for unknown-presence sites reflect deliberately wide parameter bands rather than either the confirmed-present + or the confirmed-absent treatment. + - *When it may not hold:* Once field verification confirms the layer present or absent, the analysis is re-run with the confirmed answer. + +## Progression + +10. **A confirmed confining layer provides a certain pipe roof; otherwise the least capable embankment material governs roof support.** + - *Engineering basis:* Roof-support values follow Fell et al. (2024). Layer-as-roof: engineering + judgment adopted in the model design — a fine-grained layer able to confine the foundation also sustains the pipe roof. + - *Effect on results:* With a confirmed layer, no roof-support reduction applies. Otherwise the governing roof-support probability multiplies + the SRP at every pool level, so a single listed clean sand or gravel (roof-support probability 0.01) lowers the whole curve by two orders + of magnitude. + - *When it may not hold:* Layers too thin or brittle to sustain a roof over a growing pipe; heavily fractured or desiccated layers. +11. **The pipe path is horizontal.** No inclination correction is applied. + - *Engineering basis:* Screening design decision (engineering judgment): pipe inclination is rarely known at the screening stage. + - *Effect on results:* Neutral for horizontal paths; conservative for downward-inclined paths and non-conservative for upward-inclined + paths. The size of the effect at shallow angles awaits a basis (marker IN-19 below). + - *When it may not hold:* Steeply inclined pipe paths (the angle beyond which the effect matters awaits a basis; marker IN-19 below). +12. **The anisotropy correction is set to its reference value.** The correction factor $C_K$ is taken as 1.0, the value the Schmertmann + relationship $C_K = (1.5/R_{kf})^{0.5}$ gives for a conductivity ratio $R_{kf} = k_h/k_v$ of 1.5, and the seepage path length is not + transformed for anisotropy (see + [Field Horizontal Critical Gradient](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.0/schmertmann#field-horizontal-critical-gradient)). + - *Engineering basis:* Screening design decision (engineering judgment): the conductivity ratio is rarely characterized at the screening stage. + - *Effect on results:* Relative to applying the full method with the site ratio, the result is conservative for ratios below 1.5 (at equal + conductivity the full method gives $C_K \approx 1.22$, a higher critical gradient). For ratios above 1.5 it can be substantially + non-conservative: at a ratio of 4 the full method gives $C_K \approx 0.61$, partly offset because the full method also shortens the + transformed path length, which raises the path-length and depth corrections. + - *When it may not hold:* Strongly layered or stratified foundations, where horizontal conductivity is well above vertical. +13. **No underlayer correction is applied beneath the aquifer.** The correction factor $C_Z$ is taken as 1.0, the Schmertmann method's value + when no higher-permeability underlayer exists. + - *Engineering basis:* Screening design decision (engineering judgment): underlayer properties are rarely available at the screening stage. + - *Effect on results:* A higher-permeability layer beneath the piping sand increases the flow toward the pipe and lowers the critical + gradient ($C_Z < 1$), so neglecting it is non-conservative where one exists; where none exists, the treatment matches the full method. The + BEP Progression manual notes that $C_Z$ is approximately 1 when the ratio of piping-layer depth to pipe radius exceeds about 80 (see + [Field Horizontal Critical Gradient](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.0/schmertmann#field-horizontal-critical-gradient)). + - *When it may not hold:* A higher-permeability stratum (for example, coarse sand or gravel) beneath a thin piping sand. +14. **An Unknown fines content is taken as 0%, and the fines correction is a step at 5% fines.** The correction factor is 1.0 below 5% fines and + 1.4 at or above 5%. + - *Engineering basis:* Taking an Unknown fines content as 0% is a conservative screening posture (engineering judgment): it forgoes the higher fines correction, which would raise the resistance to progression. Step form: basis + requested — see marker IN-16 in [Delegated Methods](./07-delegated-methods.mdx). + - *Effect on results:* Sands with real fines content receive less progression resistance than the method would assign unless the 5% or + more category is selected. + - *When it may not hold:* Sands with significant fines where gradation data is available, where the analyst selects the matching fines + category. +15. **The progression probability is non-decreasing with pool level.** + - *Engineering basis:* Physical reasoning: for a fixed seepage geometry and a net head that rises with pool level, a higher pool cannot make progression less likely. + - *Effect on results:* Sampling noise cannot produce a locally decreasing progression node. + - *When it may not hold:* Configurations where the net head genuinely falls as the pool rises (tailwater rising faster than headwater); the + constraint then overrides a real decrease. + +:::warning[INPUT NEEDED IN-19 — Engineering Basis] +Assumption 11 (horizontal pipe path) needs a basis for two statements about the size of the neglected inclination effect: that it is small at +shallow angles, and that it becomes significant for paths inclined more than about 10° from horizontal. Provide the literature source (for +example, the pipe-path inclination relationship of the Schmertmann method) with full bibliographic details, or the engineering-judgment +attribution, and confirm or replace the 10° threshold. +::: + +## Exit Datum and Exit Type + +17. **The toe blowout and heave analyses use the daylight datum.** Where a daylight ground-surface elevation is supplied (and the daylighting + exit is not the berm toe), the net head for the blowout and heave analyses is measured to the daylight reference elevation, although the + probabilities are evaluated at the toe. + - *Engineering basis:* Basis requested — see marker IN-20 below. + - *Effect on results:* The difference between the daylight ground and the toe ground is not added to or removed from the uplift at the toe. + Where the daylight ground lies below the toe, the toe uplift is overstated (conservative); where it lies above, the toe uplift is + understated (non-conservative). + - *When it may not hold:* Sites where the daylight ground differs markedly from the toe ground. +18. **The toe exit type follows the presence answer.** The toe exit is hole-type only for a confirmed layer whose exit stays beneath it; for a + layer of unknown presence it is plane-type (see [Delegated Methods](./07-delegated-methods.mdx)). + - *Engineering basis:* Basis requested — see marker IN-21 below. + - *Effect on results:* A plane-type exit takes no exit-geometry reduction, so the toe progression probability under unknown presence is + lower than it would be with a hole-type exit through a possibly present layer (less conservative). + - *When it may not hold:* Sites where a confining layer is in fact present, so that toe seepage would emerge through defects as concentrated + exits. + +:::warning[INPUT NEEDED IN-20 — Engineering Basis] +Assumption 17: where a daylight ground-surface elevation is supplied, the toe blowout and heave analyses measure the net head to the daylight +reference elevation rather than the toe ground, so the elevation difference between them does not enter the uplift at the toe. Provide the +engineering basis or judgment attribution for this datum choice, or confirm whether the toe ground should be the datum for those analyses. +::: + +:::warning[INPUT NEEDED IN-21 — Engineering Basis] +Assumption 18: under a layer of unknown presence, the toe exit is treated as plane-type ($C_{3d} = 1.0$), which is less conservative than the +hole-type treatment ($C_{3d} = 0.5$) applied to a confirmed layer. Provide the engineering basis or judgment attribution for this choice, or +confirm whether a possibly present layer should take the hole-type factor. +::: + +## Flaw + +16. **The flaw probability is independent of pool level.** + - *Engineering basis:* Definitional: the flaw is a geologic condition whose existence does not depend on the pool. + - *Effect on results:* The same flaw probability scales the SRP at every pool level. + - *When it may not hold:* Pool-dependent flaw mechanisms (for example, first-filling collapse features) are outside the model. ## Interpretation Cautions Three aspects of the screening formulation deserve particular attention when reading results: - **Unknown-driven breadth.** The Unknown selections (layer presence, thickness, extent) intentionally substitute wide characterizations. A - high screening SRP at an unknown-heavy site reflects that breadth as much as the site physics; resolving the unknowns with field information - and re-running is the intended response. + high screening SRP at a site with many Unknown answers reflects that breadth as much as the site physics; resolving the unknowns with field + information and re-running the analysis is the intended response. -- **Defect-pathway dominance for thin layers.** Because the defect-survival probability rises steeply as the layer thins, the unfiltered-exit - node for Very Thin and Unknown thickness bands is often controlled by the defect pathway rather than blowout, and it does not diminish at - low pools (the defect probability is pool-independent). The pool dependence of the SRP then comes mainly from the initiation and progression - nodes. +- **Defect floor for thin layers.** Because the defect probability does not depend on pool level and the toe unfiltered-exit probability can + never fall below it (assumption 6), thickness bands that include thin layers keep Node 2 high even at low pools. Where that floor exceeds the + blowout probability, the pool dependence of the toe SRP comes from the initiation and progression nodes instead. - **No driving head below the exit reference.** Pools at or below the governing exit reference elevation produce zero net head and therefore - effectively zero SRP. The reference elevations — and the daylight ground surface in particular — directly position the low-pool end of the + zero SRP. The reference elevations — and the daylight ground surface in particular — directly position the low-pool end of the system response curve. + +## References + + diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/09-output-and-interpretation.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/09-output-and-interpretation.mdx index 246bea989..0ebc8ff86 100644 --- a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/09-output-and-interpretation.mdx +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/09-output-and-interpretation.mdx @@ -3,196 +3,166 @@ title: Output and Interpretation --- import NavContainer from '@site/src/components/NavContainer'; -import TableReference from '@site/src/components/TableReference'; -import TableVertical from '@site/src/components/TableVertical'; # Output and Interpretation -The analysis reports three groups of results: pool-independent probabilities, pool-dependent series, and audit values describing the resolved -analysis configuration. +The model produces two groups of results: probabilities that do not depend on pool level, and series evaluated at each pool level. The +governing SRP series is the system response curve. ## Pool-Independent Results - +- **Flaw probability** — the mean posterior probability of a continuous foundation flaw (Node 1), from the Bayesian assessment in + [Flaw Assessment](./04-flaw-assessment.mdx). +- **Flaw probability spread** — the 5th, 25th, 50th, 75th, and 95th percentiles of the posterior flaw probability, which show how sharply the + evidence constrains the flaw judgment. +- **Defect probability** — the mean probability that a pre-existing defect fully penetrates the confining layer; produced only when a confining + layer may be present. +- **Roof-support probability** — the probability that the material over the developing pipe sustains a roof (Node 4): 1.0 with a confirmed + confining layer, otherwise the minimum across the listed embankment materials. +- **Intervention and breach probabilities** — the user-specified probabilities for Nodes 6 and 7. ## Pool-Dependent Series -Every pool-dependent result is reported as a series over the evaluated pool levels, which span the supplied headwater rating -(). The daylight-pathway series are present only when a confining layer may be present -(its presence is Yes or Unknown) *and* the daylighting exit is distinct from the toe exit. When the berm toe is itself the daylighting exit — -a berm over a confirmed layer that reaches or clears its downstream extent, or overlies a layer of unknown extent — the daylight series are -absent and the toe series carry the governing curve (see [Event Tree](./06-event-tree.mdx)). - - - -## Analysis Audit Record - -Alongside the numerical results, the analysis reports an audit record documenting how the model resolved the analysis configuration, so a -reviewer can verify the routing, geometry, and inputs without re-deriving them. The record is observation-only — assembling it never alters -the numerical results — and contains: - -- **Selected blanket-theory configuration** — Case 2 or Case 4, per the routing rule in - [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx); not reported when no confining layer is present (the - blowout and heave analyses do not run). -- **Effective seepage path lengths** — the upstream path length $L_1$ and embankment base width $L_2$ actually used; the low and high - bounds of the resolved downstream path length $L_3$ (equal when $L_3$ resolved to a single value), together with the resolution rule that - produced each of $L_1$ and $L_3$; and the toe and daylight progression path lengths. -- **Resolved hydraulic geometry** — the toe and daylight reference elevations, the exit-evaluation offset, whether the toe exit was treated - as a concentrated (hole-type) exit, and whether the daylighting exit resolved to the berm toe (collapsing the daylight pathway into the - toe pathway). -- **Resolved inputs with their origins** — every distribution the analysis used, each marked as supplied by the user, filled from a - screening default, derived from a qualitative category, or overridden by the model (for example, the thickness band forced to Unknown when - the layer presence is unverified), with an explanatory note wherever the resolution needs one; and the per-material roof-support - probabilities behind the governing minimum. -- **Delegated-analysis records** — one record per delegated analysis (the flaw assessment, the blowout and heave analyses, the defect - evaluation, and the toe and daylight progression analyses) documenting the exact quantities passed in and a digest of the outputs - consumed, including the net head series and the initiation probabilities at the toe and at the offset exit point. -- **Node provenance** — which rule produced the toe unfiltered-exit and initiation values: computed from the underlying mechanisms, or - forced to certainty by a specific override, with the trigger elevation echoed so per-pool forcing is readable off the series. -- **Request echo and replay** — a verbatim copy of the request as received, and, on each delegated-analysis record, the service endpoint - that reproduces that analysis directly from the recorded quantities, so a reviewer can rerun any single delegated analysis in isolation. -- **Resolution summaries** — the mean of the resolved downstream path length $L_3$ and whether the analysis treated a confining layer as - possibly present (presence Yes or Unknown), alongside the full resolution record above. -- **Sampling health** — the number of degenerate Monte Carlo realizations encountered, in total and split between the progression and - blanket-theory analyses, and the mean Schmertmann factor-of-safety series behind the progression digest; a blanket-theory digest also - carries the engine's own consistency checks. -- **Run metadata** — the wall-clock computation time and the UTC completion timestamp, and any non-fatal validation warnings raised while - resolving the inputs (for example, an ignored daylight ground-surface elevation). - -The audit record is requested with the analysis and is included by default; a caller may omit it, which changes no numerical output. - -### Monte Carlo Controls - -The delegated analyses sample their distributions by Monte Carlo simulation under three controls that the request may override and that -the audit record echoes. The screening defaults are 10,000 realizations, a fixed random seed of 6414, and 50 points in the expanded -headwater analysis grid; the synchronous service rejects more than 20,000 realizations. Because the seed is fixed by default, repeated -analyses of the same inputs reproduce the same results, and the blowout and heave analyses draw identical realizations (see -[Delegated Models](./07-delegated-models.mdx)); supplying no seed draws a fresh seed for each delegated analysis and removes both -properties. The flaw assessment runs its own simulation of 5,000 realizations with the same default seed, independent of the screening -realization count. - -### Provenance - -Every response, including a failed one, carries three provenance values: the model key (`bep-screening`), which identifies the screening -model among the models the service exposes; the engineering model version, which changes whenever a formula, default, lookup value, -sampling order, or seed treatment changes, so a stored result can be tied to the model revision that computed it; and the service build, -a deployment identifier for troubleshooting only, never to be compared when deciding whether a stored result is current. The audit record -repeats the model key and version together with the Monte Carlo controls in effect. +Every pool-dependent result is a series over the evaluated pool levels: every supplied headwater value and additional pool levels distributed +between them (see [Input Parameters](./03-input-parameters.mdx)). The daylight-pathway series +are produced only when a confining layer may be present (its presence is Yes or Unknown) *and* the daylighting exit is distinct from the toe +exit. When the berm toe is itself the daylighting exit — a berm over a confirmed layer that reaches or clears its downstream extent, or overlies +a confirmed layer of unknown extent — there are no daylight series and the toe series carry the governing curve (see [Event Tree](./06-event-tree.mdx)). -## Interpreting the System Response Curve +**Hydraulic series:** -The governing SRP series is the system response curve — the conditional probability of breach by backward erosion piping as a function of pool -level. The curve is non-decreasing with pool level: the flaw, roof-support, intervention, and breach nodes are constant; the blowout and heave -probabilities rise with net head; and the progression node is explicitly constrained to be non-decreasing. Pools at or below the governing exit -reference elevation carry effectively zero SRP because no net driving head exists there; the reported value is floored at 10−16 -rather than exactly zero, so the curve can be plotted on a logarithmic axis. +- **Pool levels** — the headwater elevations at which the event tree is evaluated. +- **Tailwater** — the tailwater at each pool level, interpolated between the supplied pairs, and blank wherever no tailwater exists. +- **Toe control level** — the downstream control level used by the toe progression pathway: the higher of the tailwater and the toe reference + elevation. +- **Daylight control level** — the downstream control level used by the blowout, heave, and daylight-progression analyses: the higher of the + tailwater and the daylight reference elevation. -### Which Pathway Governs +**Toe pathway series:** -The toe and daylight pathways trade off against each other: +- **Unfiltered-exit probability** — Node 2: the defect–blowout composition with its overrides applied; 1.0 at every pool when no confining layer + is present. +- **Blowout probability** — the blowout probability alone, before it is combined with the defect probability, so the two contributions to + Node 2 can be compared; produced only when a confining layer may be present. +- **Initiation probability** — Node 3: the heave probability with the berm and trigger-elevation overrides applied; 1.0 at every pool when no + confining layer is present. +- **Progression probability** — Node 5: the mean probability of advancement over the toe path, non-decreasing with pool level. +- **SRP** — the product of the seven nodes on the toe pathway. -- The **toe pathway** carries unfiltered-exit and initiation probabilities below one (the confining layer resists both), but its progression - analysis benefits from a shorter seepage path — and, when the layer is confirmed, from the concentrated (hole-type) exit that halves the - Schmertmann critical gradient. -- The **daylight pathway** carries certain unfiltered exit and initiation (nothing confines the exit there), but its progression analysis runs - over the longer path to the layer's termination with a plane-type exit. +**Daylight pathway series:** -When the confining layer is thick and well characterized, its resistance suppresses the toe pathway and the daylight pathway tends to govern. -When the layer is thin — or its thickness band is wide because it is unknown — the defect pathway drives the toe unfiltered-exit probability -up and the toe pathway tends to govern. When both pathways are evaluated, both are reported, so the trade-off is visible directly in the -results. When the berm toe is itself the daylighting exit, only the toe pathway is reported — it *is* the daylighting exit, carrying certain -unfiltered-exit and initiation probabilities over the berm-extended progression path. +- **Unfiltered-exit probability** — Node 2: 1.0 at every pool level. +- **Initiation probability** — Node 3: 1.0 at every pool level. +- **Progression probability** — Node 5: the mean probability of advancement over the longer daylight path, non-decreasing with pool level. +- **SRP** — the product of the seven nodes on the daylight pathway. -### Sensitivity to Key Inputs +**Governing series:** -The inputs with the greatest influence on the screening SRP are: +- **Governing SRP** — the system response curve: the larger of the toe and daylight SRP at each pool level, equal to the toe SRP when no + daylight pathway is evaluated. + +## Interpreting the System Response Curve + +The governing SRP series is the system response curve — the conditional probability of breach by backward erosion piping as a function of pool +level. While the net head does not decrease as the pool rises, the curve is non-decreasing with pool level: the flaw, roof-support, +intervention, and breach nodes are constant; the blowout and heave probabilities rise with net head; and the progression node is explicitly +constrained to be non-decreasing. Where the tailwater rises faster than the headwater, the net head can fall and the blowout and heave +probabilities with it. Pools at or below the governing exit reference elevation carry zero SRP because no net driving head exists there. + +### Which Pathway Governs -- **Flaw evidence selections** — the flaw probability scales the entire curve. Moving the geologic environment, strength of evidence, or - observed-seepage selections shifts every pool level proportionally. -- **Confining layer thickness category** — thickness controls both the defect probability (steeply, at small thickness) and the vertical exit - gradients in the blowout and heave analyses. -- **Downstream layer extent** — sets the daylight path length and the head remaining at the exit; the unknown-extent default spans a wide - range and widens the result accordingly. -- **Relative density category** — denser sand raises the Schmertmann critical gradient and suppresses progression. -- **Embankment materials** — the minimum roof-support probability governs; a single clean sand or gravel in the list reduces the SRP sharply - when no confining layer is confirmed. -- **Reference elevations** — the toe and daylight ground surfaces position the zero-head threshold and thereby the low-pool end of the curve. +The governing curve is the larger of the two pathway SRPs at each pool level, and the two pathways differ in opposite directions: + +- The **toe pathway** carries unfiltered-exit and initiation probabilities that can be below one, because the confining layer resists both. Its + progression analysis runs over a path no longer than the daylight path — shorter with no berm, or with a berm inside a confirmed layer's + known extent — which raises the average applied gradient, and, when the layer is confirmed and the exit stays beneath it, uses the hole-type + exit that halves the Schmertmann critical gradient. +- The **daylight pathway** carries certain unfiltered exit and initiation, because nothing confines the exit there. Its progression analysis + runs over the path to the layer's termination with a plane-type exit. + +The daylight pathway governs at a pool level when the reduction the confining layer gives the toe pathway through Nodes 2 and 3 outweighs any +progression advantage the toe pathway gains from its shorter path and exit type; otherwise the toe pathway governs. Under a layer of unknown +presence with a berm, the two paths are equal and both exits are plane-type, so where the two exit datums coincide the daylight pathway governs +(see [Event Tree](./06-event-tree.mdx)). (The path-length and depth +corrections of the Schmertmann method also change with path length, so the progression comparison itself depends on the site.) Which side of that balance a site falls on depends on the +layer thickness band, the unit weights, the downstream extent, and the foundation sand properties, and it can change with pool level. When both +pathways are evaluated, both are produced, so the balance can be read directly from the results. When the berm toe is itself the daylighting +exit, only the toe pathway is evaluated: it *is* the daylighting exit, with certain unfiltered-exit and initiation probabilities over the +berm-extended progression path. + +### How Key Inputs Affect the SRP + +The effect of each input depends on the site configuration. The following describes the mechanism by which each key input changes the SRP and +the conditions under which it controls the result: + +- **Flaw evidence selections** — the flaw probability multiplies the SRP at every pool level, so the effect of the geologic environment, the + strength of evidence, and the observed-seepage selections on the flaw likelihood scales the whole curve by the same factor, whatever the other + inputs. A sand-boil or concentrated-seepage observation also enables the seepage-through-layer and trigger-elevation inputs, which can set + Nodes 2 and 3 to certainty and so change the curve beyond that factor (see [Event Tree](./06-event-tree.mdx)). +- **Confining-layer thickness category** — thickness enters the defect probability (pool-independent, and rising steeply as the layer thins) + and the vertical exit gradient in the blowout and heave analyses (a thinner layer gives a larger gradient for the same head). It affects the + toe pathway only, and only where a confining layer may be present. Where no layer is present, or where a berm daylights the exit over a + confirmed layer, Nodes 2 and 3 are certain and thickness has no effect. Under a layer of unknown presence with a berm, Node 2 is certain but + Node 3 stays at the heave probability (unless the berm reaches or clears a supplied extent), so thickness still affects it. +- **Downstream confining-layer extent** — with no berm, a longer downstream path $L_3$ leaves a larger share of the net head at the toe + (raising the toe blowout and heave probabilities) and lengthens the daylight progression path (lowering the daylight progression + probability). With a berm ending inside a confirmed layer's known extent, the blowout and heave are evaluated at the offset exit point, + where the head is the net head times the berm length divided by the total path length, so a longer extent lowers them. When no berm is + present and the extent or the layer's presence is unknown, the 1 to 5 embankment-height default spreads these effects across a wide range. + With a berm, the extent also decides which exit treatment applies (see [Event Tree](./06-event-tree.mdx)). +- **Relative density category** — denser sand raises the Schmertmann critical gradient through the density correction and lowers the + progression probability on both pathways. It has little effect at pool levels where the progression probability is already close to 0 or 1. +- **Coefficient of uniformity, effective grain size, and fines content** — these set the base critical gradient, the grain-size correction, + and the fines-content correction of the Schmertmann analysis, and they act on Node 5 of both pathways in the same way as relative density. +- **Embankment materials** — when the confining layer is not confirmed, the minimum roof-support probability multiplies the SRP at every pool + level, so a single listed material with a low roof-support probability lowers the whole curve by that factor. With a confirmed layer, the + materials have no effect. +- **Reference elevations** — the toe and daylight ground surfaces set the pool level below which there is no net head, and so position the + low-pool end of the curve. + +### Checking the Result + +The documented method implies several relationships that every result must satisfy. A result that breaks one of the identities below +indicates a computation error in the model, not a property of the site: + +- **Product of nodes** — at each pool level, each pathway SRP equals the product of its seven node probabilities, all of which are reported. +- **Governing value** — the governing SRP equals the larger of the toe and daylight SRP at each pool level, or the toe SRP when no daylight + pathway is evaluated. +- **Upper bound** — no SRP exceeds the product of the pool-independent nodes: the flaw, roof-support, unsuccessful-intervention, and breach + probabilities. +- **Unfiltered-exit floor** — on the toe pathway, the unfiltered-exit probability is never less than either the defect probability or the + blowout probability. +- **Certain nodes** — on the daylight pathway, the unfiltered-exit and initiation probabilities are 1.0 at every pool level; on the toe pathway + they are 1.0 at every pool level when the confining-layer presence is No. +- **Zero-head threshold** — each pathway's SRP is zero at pool levels where its progression analysis has no net head: at or below the higher + of the tailwater and the toe reference elevation for the toe pathway, and of the tailwater and the daylight reference elevation for the + daylight pathway. +- **Monotonic progression** — the progression probabilities never decrease with pool level. +- **Trigger elevation** — where a trigger elevation is supplied, the toe initiation probability is 1.0 at every pool level at or above it. + +Two further checks follow from the method and help judge whether a result is reasonable for the site: + +- **Flaw ceiling** — the governing SRP never exceeds the flaw probability, so a curve that approaches the flaw probability at high pools means + every other node is close to certain there; the analyst can confirm that this matches the site's confining layer, materials, and berm. +- **Low-pool unfiltered exit** — for a confirmed layer with no berm, the blowout probability falls toward zero as the net head falls, so at low + pools the toe unfiltered-exit probability should approach the defect probability; a much larger value at low pools points to a forcing + condition (for example, observed seepage through the layer) that the analyst can confirm. ### Screening Versus Detailed Analysis A high screening SRP does not by itself indicate a high risk of failure — it indicates that the structure warrants analysis with the full -toolbox models -([BEP Initiation](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-initiation/v1.0/preface), -[BEP Progression](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.0/preface)), where: +toolbox models, where: -- the blanket-theory case matching the actual stratigraphy can be selected from all eight configurations; +- the blanket-theory case matching the actual stratigraphy can be selected from all eight configurations (see the + [General Overview](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-initiation/v1.0/general-overview) of the BEP Initiation manual); - site-specific blanket geometry replaces the screening defaults and unknown-value ranges; -- the anisotropy, underlayer, and pipe-inclination corrections can be applied to the Schmertmann analysis; -- the Sellmeijer method is available as an alternative progression formulation; and +- the anisotropy and underlayer corrections (see + [Field Horizontal Critical Gradient](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.0/schmertmann#field-horizontal-critical-gradient)) and the pipe-inclination correction (see + [Pipe Path Inclination](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.0/schmertmann#pipe-path-inclination)) can be applied to the Schmertmann analysis; +- the Sellmeijer method is available as an alternative progression formulation (see + [Sellmeijer](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.0/sellmeijer)); and - the flaw judgment can be refined by targeted subsurface investigation rather than screening-level evidence categories. A low screening SRP provides reasonable confidence that backward erosion piping is not a critical concern at the screening level, subject to diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/_input-needed.md b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/_input-needed.md index c908d850f..906aa6f0c 100644 --- a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/_input-needed.md +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/_input-needed.md @@ -1,8 +1,8 @@ -# Input Needed — BEP Screening Model (v1.0) +# Input Needed — Backward Erosion Piping Screening Technical Reference Manual (v1.0) Answer inline and return this file (or paste its contents into the conversation). Leave an Answer blank to keep that marker in place. Do not renumber — the IDs tie each entry to its -admonition in the document. (IN-17 was retired in the August 2026 update: the mean-of- +admonition in the document. IN-18 to IN-21 were added in the October 2026 revision. (IN-17 was retired in the August 2026 update: the mean-of- distribution treatment it questioned no longer exists — supplied seepage-path lengths are now single values by design.) @@ -164,8 +164,8 @@ for scaling the range to embankment height. **Regarding:** The physical interpretation of the exit-offset distance used when a berm overlies a confirmed confining layer whose supplied downstream extent exceeds the berm length — the berm-within-known-extent case in which the through-layer defect/blowout -composition is retained. The model design notes record the intended evaluation location as -the berm toe, but the model computes the offset as (supplied confining-layer extent − berm +composition is retained. The intended evaluation location is the berm toe, but the model +computes the offset as (supplied confining-layer extent − berm length), measured from the embankment toe. Under the linear head profile, the head fraction remaining at the computed offset equals (berm length ÷ confining-layer extent) — whereas an exit evaluated at the berm toe (one berm length from the embankment toe) would retain the @@ -230,15 +230,70 @@ pathways in the unfiltered-exit union formula. --- -## IN-16 — Engineering Basis — `07-delegated-models.mdx` +## IN-16 — Engineering Basis — `07-delegated-methods.mdx` -**Regarding:** The fines-content correction applied by the Schmertmann analysis engine — a -step from 1.0 to 1.4, with the higher factor applying at exactly 5% fines and above. The -screening model passes no override; the dedicated Schmertmann documentation does not describe -the term. +**Regarding:** The fines-content correction applied in the Schmertmann analysis — a step from +1.0 to 1.4, with the higher factor applying at exactly 5% fines and above. The same step +applies in the toolbox Schmertmann analysis; the Schmertmann chapter of the BEP Progression +manual does not describe the term. **Needed:** Source or engineering-judgment attribution for the step form, the 5% threshold, -and the 1.4 value, and an addition to the dedicated Schmertmann documentation. +and the 1.4 value, and an addition to the Schmertmann chapter of the BEP Progression manual. + +**Answer:** + +--- + +## IN-18 — Bibliography — `04-flaw-assessment.mdx` + +**Regarding:** The Bayesian formulation of the flaw assessment: each evidence source expressed +as a likelihood ratio, the prior updated in log-odds form, and the subsurface likelihood ratio +weighted by the data-quality factor as an exponent. The same formulation is named in the +Physics Basis section of `02-model-overview.mdx`. + +**Needed:** Full bibliographic details for the source of the formulation (for the +bibliography), or the engineering-judgment attribution for the quality-factor weighting if it +is specific to this model. + +**Answer:** + +--- + +## IN-19 — Engineering Basis — `08-assumptions-and-limitations.mdx` + +**Regarding:** Assumption 11 (horizontal pipe path): the statements that the neglected +inclination effect is small at shallow angles and becomes significant beyond about 10° from +horizontal. + +**Needed:** Literature source with full bibliographic details, or the engineering-judgment +attribution; confirm or replace the 10° threshold. + +**Answer:** + +--- + +## IN-20 — Engineering Basis — `08-assumptions-and-limitations.mdx` + +**Regarding:** Assumption 17. Where a daylight ground-surface elevation is supplied (and the +daylighting exit is not the berm toe), the toe blowout and heave analyses measure the net head +to the daylight reference elevation rather than the toe ground, so the elevation difference +between the daylight ground and the toe does not enter the uplift at the toe. + +**Needed:** Engineering basis or judgment attribution for this datum choice, or confirmation +of whether the toe ground should be the datum for the toe blowout and heave analyses. + +**Answer:** + +--- + +## IN-21 — Engineering Basis — `08-assumptions-and-limitations.mdx` + +**Regarding:** Assumption 18. Under a confining layer of unknown presence, the toe exit is +treated as plane-type (exit-geometry factor 1.0), which is less conservative than the +hole-type factor (0.5) applied to a confirmed layer whose exit stays beneath it. + +**Needed:** Engineering basis or judgment attribution for this choice, or confirmation of +whether a possibly present layer should take the hole-type factor. **Answer:** From 29ddea85379d5909ec7be23a56077a0ff22e0800 Mon Sep 17 00:00:00 2001 From: Adam Gohs Date: Thu, 15 Oct 2026 16:27:42 -0400 Subject: [PATCH 3/5] Space citations like ordinary words in the sentence Each citation now has one space before it and one space between consecutive citations, matching the rest of the site. --- .../v1.0/02-model-overview.mdx | 8 ++++---- .../v1.0/05-hydraulic-loading-and-seepage-paths.mdx | 2 +- .../v1.0/06-event-tree.mdx | 2 +- .../v1.0/07-delegated-methods.mdx | 6 +++--- .../v1.0/08-assumptions-and-limitations.mdx | 4 ++-- 5 files changed, 11 insertions(+), 11 deletions(-) diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/02-model-overview.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/02-model-overview.mdx index 058d10e04..7e2fac235 100644 --- a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/02-model-overview.mdx +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/02-model-overview.mdx @@ -68,12 +68,12 @@ The model combines the following engineering methods: - **Bayesian updating in log-odds form** for the probability of a continuous foundation flaw, combining a geology-based prior with likelihood ratios for the site evidence (see [Flaw Assessment](./04-flaw-assessment.mdx); the source of the formulation is requested at marker IN-18) - **Blanket theory** for the excess head beneath the downstream confining layer and the vertical exit gradient through it, from which the - blowout and heave probabilities follow + blowout and heave probabilities follow - **A Weibull defect-survival relationship** for the probability that a pre-existing defect fully penetrates the confining layer (see [Event Tree](./06-event-tree.mdx)) -- **Roof-support probabilities by soil classification** for the mechanical condition of pipe progression -- **The Schmertmann critical-gradient method** for the hydraulic condition of pipe progression, with - an exit-geometry factor that distinguishes concentrated from distributed exits +- **Roof-support probabilities by soil classification** for the mechanical condition of pipe progression +- **The Schmertmann critical-gradient method** for the hydraulic condition of pipe progression , with + an exit-geometry factor that distinguishes concentrated from distributed exits ## Comparison with Detailed Models diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/05-hydraulic-loading-and-seepage-paths.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/05-hydraulic-loading-and-seepage-paths.mdx index 07f02c7a7..c61440b2f 100644 --- a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/05-hydraulic-loading-and-seepage-paths.mdx +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/05-hydraulic-loading-and-seepage-paths.mdx @@ -68,7 +68,7 @@ control level (and so slightly understates the net head); the effect is bounded ## Seepage Path Components -Blanket theory idealizes the seepage path in three segments: the upstream entry length $L_1$ through or +Blanket theory idealizes the seepage path in three segments : the upstream entry length $L_1$ through or beneath the upstream top stratum, the path $L_2$ beneath the embankment, and the downstream path $L_3$ from the embankment toe to the seepage exit. The screening model resolves each from the site inputs. diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/06-event-tree.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/06-event-tree.mdx index 42e6bdb3a..dcff6b23c 100644 --- a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/06-event-tree.mdx +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/06-event-tree.mdx @@ -200,7 +200,7 @@ pool level. A pipe can only progress if the material above it sustains a stable roof. When the confining layer's presence is confirmed (answered Yes), the layer itself provides the roof and the probability is 1.0. Otherwise, the probability is evaluated from the embankment materials: each USCS class maps to a roof-support probability per , following Fell et -al. (2024), and the minimum across the listed materials governs — every material along the pipe path must +al. (2024) , and the minimum across the listed materials governs — every material along the pipe path must hold a roof, so the least capable material controls. The probability is constant across pool levels. . +unit weight, which is what blanket theory computes . ### Blanket-theory configuration @@ -117,7 +117,7 @@ Relative to the blanket-theory chapters of the BEP Initiation manual, the screen **Question answered:** Once erosion has initiated at the exit and a roof is available, is the average hydraulic gradient along the seepage path large enough to keep advancing the pipe upstream through the foundation sand until it reaches the reservoir? The Schmertmann -method answers it by comparing the average applied gradient with a field critical gradient derived from +method answers it by comparing the average applied gradient with a field critical gradient derived from laboratory piping tests and corrected for site conditions. The complete method is documented in the [Schmertmann](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.0/schmertmann) chapter of the BEP Progression manual; the subsections below link the part of that chapter each step follows. @@ -195,7 +195,7 @@ The overall field correction is: The exit-geometry factor $C_{3d}$ distinguishes concentrated (hole-type) exits from distributed (plane-type) exits. Van Beek et -al. (2015) found that three-dimensional flow converging toward a single exit point produces critical +al. (2015) found that three-dimensional flow converging toward a single exit point produces critical gradients roughly half those predicted for the two-dimensional configuration. Their comparison was made against the Dutch (Sellmeijer) piping model, and the BEP Progression manual notes that the reduction was not developed and calibrated for the Schmertmann method; the screening model applies it to the Schmertmann critical gradient by engineering judgment, as the manual does, so a hole-type exit takes $C_{3d} = 0.5$ and a diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/08-assumptions-and-limitations.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/08-assumptions-and-limitations.mdx index adfd450fa..7c06fa032 100644 --- a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/08-assumptions-and-limitations.mdx +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/08-assumptions-and-limitations.mdx @@ -27,7 +27,7 @@ primary location in this document. toolbox models apply directly to such sites. 2. **The downstream confining layer carries a linear head profile.** The excess head decays from its value at the toe to zero at the layer's downstream termination. - - *Engineering basis:* Blanket theory. The landside layer is analyzed as an impervious top stratum + - *Engineering basis:* Blanket theory . The landside layer is analyzed as an impervious top stratum whatever permeability is selected; the permeability selection affects only the upstream credit. - *Effect on results:* Exit heads are reduced by the path-length ratio, which is less conservative than an infinite-blanket idealization. - *When it may not hold:* Blankets with strong lateral heterogeneity, or relief wells and toe drains that alter the head profile. A @@ -96,7 +96,7 @@ primary location in this document. ## Progression 10. **A confirmed confining layer provides a certain pipe roof; otherwise the least capable embankment material governs roof support.** - - *Engineering basis:* Roof-support values follow Fell et al. (2024). Layer-as-roof: engineering + - *Engineering basis:* Roof-support values follow Fell et al. (2024) . Layer-as-roof: engineering judgment adopted in the model design — a fine-grained layer able to confine the foundation also sustains the pipe roof. - *Effect on results:* With a confirmed layer, no roof-support reduction applies. Otherwise the governing roof-support probability multiplies the SRP at every pool level, so a single listed clean sand or gravel (roof-support probability 0.01) lowers the whole curve by two orders From 391c80ad6f9dd64d0899312a005fc99e37c94589 Mon Sep 17 00:00:00 2001 From: Adam Gohs Date: Thu, 15 Oct 2026 16:36:31 -0400 Subject: [PATCH 4/5] Remove the References headings above the citation footnotes The site's citation footnote list carries no heading on any other page. --- .../v1.0/02-model-overview.mdx | 2 -- .../v1.0/05-hydraulic-loading-and-seepage-paths.mdx | 2 -- .../backward-erosion-piping-screening/v1.0/06-event-tree.mdx | 2 -- .../v1.0/07-delegated-methods.mdx | 2 -- .../v1.0/08-assumptions-and-limitations.mdx | 2 -- 5 files changed, 10 deletions(-) diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/02-model-overview.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/02-model-overview.mdx index 7e2fac235..81a62cbeb 100644 --- a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/02-model-overview.mdx +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/02-model-overview.mdx @@ -156,6 +156,4 @@ them: it builds their geometry and material inputs from the screening selections the analyst (). [Delegated Methods](./07-delegated-methods.mdx) documents each fixed choice and its basis. -## References - diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/05-hydraulic-loading-and-seepage-paths.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/05-hydraulic-loading-and-seepage-paths.mdx index c61440b2f..d050620ad 100644 --- a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/05-hydraulic-loading-and-seepage-paths.mdx +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/05-hydraulic-loading-and-seepage-paths.mdx @@ -210,6 +210,4 @@ when no berm is present and the downstream extent or the layer's presence is unk enters as a single value. A longer path reduces the average applied gradient. When the presence is Unknown and a berm is present, $L_3 = L_b$, so the two progression paths are equal. -## References - diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/06-event-tree.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/06-event-tree.mdx index dcff6b23c..e2205d946 100644 --- a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/06-event-tree.mdx +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/06-event-tree.mdx @@ -293,6 +293,4 @@ When both pathways are evaluated, the governing SRP at each pool level is the la When only the toe pathway exists — no confining layer, or a berm-toe daylighting exit — it governs directly. -## References - diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/07-delegated-methods.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/07-delegated-methods.mdx index 1f5f0b0b6..a782cd8c7 100644 --- a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/07-delegated-methods.mdx +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/07-delegated-methods.mdx @@ -239,6 +239,4 @@ A pool producing no positive net head yields no probability of advancement. The Node 5 probability at each pool level is the mean probability of advancement across the Monte Carlo realizations, then constrained to be non-decreasing with pool level as described in [Event Tree](./06-event-tree.mdx). -## References - diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/08-assumptions-and-limitations.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/08-assumptions-and-limitations.mdx index 7c06fa032..19de3712d 100644 --- a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/08-assumptions-and-limitations.mdx +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/08-assumptions-and-limitations.mdx @@ -199,6 +199,4 @@ Three aspects of the screening formulation deserve particular attention when rea zero SRP. The reference elevations — and the daylight ground surface in particular — directly position the low-pool end of the system response curve. -## References - From 583b00313812ba384024458c4a5f6904ade1692d Mon Sep 17 00:00:00 2001 From: Adam Gohs Date: Fri, 23 Oct 2026 13:23:00 -0400 Subject: [PATCH 5/5] Update the BEP screening manual for model version 1.1 - Add the Head Beneath the Confining Layer section: the daylight ground sets the exit level, the net head is measured against the water on the layer at the toe or berm toe, and a pool below the exit level loads the layer at pool level. - Evaluate blowout and heave at the berm toe (x = berm length) for a berm within the layer's known extent; retire IN-12. - Route to Blanket Theory Case 2 only when an upstream path length is credited, so a Very Thin layer uses Case 4. - Treat a berm over a layer of unknown presence as a single berm-toe exit. - Apply daylight initiation only while the pool drives seepage out of the daylighting exit. - Rewrite assumption 17 for the revised datum treatment and retire IN-20. - Add the version-history entry for the results-changing model update. --- .../v1.0/00-version-history.mdx | 11 +- .../v1.0/02-model-overview.mdx | 15 +-- .../v1.0/03-input-parameters.mdx | 19 ++-- ...05-hydraulic-loading-and-seepage-paths.mdx | 104 ++++++++++++------ .../v1.0/06-event-tree.mdx | 66 +++++------ .../v1.0/07-delegated-methods.mdx | 24 ++-- .../v1.0/08-assumptions-and-limitations.mdx | 60 +++++----- .../v1.0/09-output-and-interpretation.mdx | 46 ++++---- .../v1.0/_input-needed.md | 41 +------ 9 files changed, 202 insertions(+), 184 deletions(-) diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/00-version-history.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/00-version-history.mdx index 89f6b753a..2cf70b5bf 100644 --- a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/00-version-history.mdx +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/00-version-history.mdx @@ -14,8 +14,8 @@ import TableVersionHistory from '@site/src/components/TableVersionHistory'; # Version History diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/02-model-overview.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/02-model-overview.mdx index 81a62cbeb..11459322b 100644 --- a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/02-model-overview.mdx +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/02-model-overview.mdx @@ -52,7 +52,8 @@ The screening model executes three stages: 2. **Hydraulic and seepage-geometry resolution** — The model resolves the downstream reference elevations that control net driving head, the upstream seepage path length $L_1$, the embankment base width $L_2$, and the downstream seepage path length $L_3$ from the site inputs, and - selects the blanket-theory configuration — Case 2 when an upstream seepage barrier is present, Case 4 otherwise + selects the blanket-theory configuration — Case 2 when an upstream seepage barrier is credited with an upstream path length, Case 4 + otherwise (see [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx)). 3. **Event-tree assembly** — At each headwater level, the model composes seven node probabilities and multiplies them to produce the SRP. Blanket @@ -138,12 +139,12 @@ The model evaluates up to two seepage exit pathways: - **Daylight pathway** — Seepage exits at the downstream termination of the confining layer, where the underlying sand daylights at the ground surface. This pathway is evaluated whenever a confining layer may be present (its presence is confirmed or unknown) *and* the daylighting - exit is distinct from the toe exit. At the daylight exit there is no confining layer to penetrate, so the unfiltered-exit and initiation - probabilities are both certain. With no berm, or with a berm inside a confirmed layer's known extent, the daylight pathway is also - distinguished by its longer seepage path to the exit. When a berm over a confirmed layer reaches or clears the layer's downstream extent — or - overlies a confirmed layer whose extent is unknown — the berm toe is itself the daylighting exit: the toe pathway then represents that exit - directly, and no separate daylight pathway is evaluated. A layer of unknown presence always retains both pathways; with a berm, both then - share the berm-extended path length and differ in the toe initiation node and the exit datum (see [Event Tree](./06-event-tree.mdx)). + exit is distinct from the toe exit. At the daylight exit there is no confining layer to penetrate, so the unfiltered exit is certain, and + initiation is certain whenever the pool stands above the exit level and drives seepage out of the sand. With no berm, or with a berm inside a + confirmed layer's known extent, the daylight pathway is also distinguished by its longer seepage path to the exit. When a berm reaches or + clears a confirmed layer's downstream extent, overlies a confirmed layer whose extent is unknown, or overlies a layer of unknown presence, + the berm toe is itself the daylighting exit: the toe pathway then represents that exit directly, and no separate daylight pathway is + evaluated (see [Event Tree](./06-event-tree.mdx)). The governing SRP at each headwater level is the larger of the two pathway SRPs, so the more critical exit condition controls the screening result. When only the toe pathway is evaluated, it governs directly. diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/03-input-parameters.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/03-input-parameters.mdx index 422e611e5..5f8b8f6af 100644 --- a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/03-input-parameters.mdx +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/03-input-parameters.mdx @@ -92,8 +92,11 @@ accommodate compound slopes and intermediate benches. lowest segment elevation defines the downstream toe, which must lie below the crest. - **Daylight ground-surface elevation** $E_{day}$ — Ground-surface elevation at the downstream termination of the confining layer, where the foundation sand daylights. It may lie above or below the embankment toe. When it is left blank, the daylight exit is assumed to share the toe - reference elevation (the berm toe when a berm with a specified toe elevation is present, otherwise the downstream embankment toe). When the - daylighting exit is the berm toe itself, a supplied value is not used, because the berm-toe reference elevation is then the exit datum (see [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx)). + reference elevation (the berm toe when a berm with a specified toe elevation is present, otherwise the downstream embankment toe). It sets the + exit level that controls the driving head for the blowout, heave, and daylight progression analyses; the blowout and heave net head is still + measured against the water standing on the layer at the toe or berm toe. When the daylighting exit is the berm toe itself, a supplied value + is not used, because the berm-toe reference elevation is then the exit datum (see + [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx)). Three geometric quantities are derived from the cross-section rather than entered directly: @@ -133,7 +136,7 @@ Theory Case 2, which represents impervious strata on both sides of the embankmen A downstream seepage or stability berm moves the seepage exit beyond the berm. The model credits no berm weight in the blowout and heave factors of safety, which depend on the confining-layer thickness alone (). Its effect on the event tree depends on where the berm ends relative to the confining -layer: a berm ending within a confirmed layer's known extent retains the through-layer exit mechanisms at an exit point beyond the berm, while a +layer: a berm ending within a confirmed layer's known extent retains the through-layer exit mechanisms, evaluated at the berm toe, while a berm that reaches or clears the layer's extent — or overlies a confirmed layer of unknown extent, or a layer of unknown presence — is assumed to produce a daylighting exit at the berm toe, where the unfiltered exit is certain. Every berm lengthens the toe progression path. The full rules are documented in [Event Tree](./06-event-tree.mdx) and [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx). @@ -242,8 +245,8 @@ are: Whether the confirmed impervious layer continues upstream beneath the reservoir. An engineered upstream blanket takes precedence as the upstream barrier, so the question is not asked when one is present. The choices are: -- Yes — the layer is treated as the upstream seepage barrier and its upstream length is entered; a Very Thin layer still selects Blanket - Theory Case 2 but is credited with zero upstream length +- Yes — the layer is treated as the upstream seepage barrier and its upstream length is entered; a Very Thin layer is credited with zero + upstream length and so uses Blanket Theory Case 4 - No — no upstream head loss is credited - Unknown — no upstream head loss is credited @@ -271,11 +274,11 @@ The two confining-layer extents are entered as single lengths ( $E_{ref}$ = the applicable reference elevation ($E_{day,ref}$ for the blowout, heave, and daylight-progression analyses; $E_{toe,ref}$ for > the toe-progression analysis) -A pool at or below the exit reference elevation produces zero net head — no water stands against the seepage path above its exit — so the -pool-dependent event-tree nodes contribute no failure probability there. +A pool at or below the exit reference elevation produces zero net driving head: no seepage flows out of that exit, so the progression analysis +along that pathway is not loaded. Zero driving head does not by itself mean zero load on the confining layer. Where the daylight ground sits +above the toe, a pool between the two elevations fills the foundation sand to pool level and still acts upward on the layer at the toe; the +blowout and heave analyses account for this static case (see [Head Beneath the Confining Layer](#head-beneath-the-confining-layer)). The control level is evaluated at each supplied headwater–tailwater pair and varies linearly between successive supplied headwater values. Within any interval between successive supplied headwater values where the supplied tailwater crosses the reference elevation, this linear treatment slightly overstates the @@ -145,8 +147,8 @@ The blowout and heave analyses run under one of two blanket-theory configuration - **Blanket Theory Case 2** — impervious top strata on both the riverside and the landside (see [Blanket Theory Case 2](/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-initiation/v1.0/blanket-theory-case-2) in the BEP Initiation manual). - Selected when an engineered upstream blanket is present, **or** when the confining layer is confirmed, impervious, and has a supplied - upstream extension length. The total seepage path is: + Selected whenever the upstream path length is credited ($L_1 > 0$): an engineered upstream blanket is present, or the confining layer is + confirmed, impervious, not Very Thin, and has a supplied upstream extension length. The total seepage path is: @@ -157,45 +159,75 @@ The blowout and heave analyses run under one of two blanket-theory configuration -where $d$ is the sampled foundation sand thickness. Case 2 is selected regardless of the thickness category: a confirmed Very Thin -impervious layer with a supplied upstream extension still routes to Case 2, but carries $L_1 = 0$ per the crediting rules above — the -configuration reflects the presence of an upstream barrier while crediting it with no head loss. +where $d$ is the sampled foundation sand thickness. A confirmed Very Thin layer is credited with $L_1 = 0$ per the crediting rules above, so it +routes to Case 4 and retains the open-entrance length $0.43\,d$; crediting neither an upstream path nor an entrance length would understate the +head loss upstream of the embankment. ## Exit Evaluation Point The blowout and heave probabilities are evaluated at an exit point along the downstream blanket. By default the evaluation point is the downstream toe (zero offset), where the excess head is highest. One site condition shifts it: when a berm overlies a confirmed confining layer whose supplied downstream extent exceeds the berm length — the configuration in which the toe exit remains beneath the layer and the -through-layer defect and blowout mechanisms are retained (see [Event Tree](./06-event-tree.mdx)) — the evaluation point is offset downstream -by +through-layer defect and blowout mechanisms are retained (see [Event Tree](./06-event-tree.mdx)) — the evaluation point moves to the berm toe, +the first exposed ground beyond the berm: where: -> $x$ = offset of the exit evaluation point from the embankment toe -> $L_{cl}$ = supplied downstream confining-layer extent +> $x$ = distance of the exit evaluation point downstream of the embankment toe > $L_b$ = berm length -The excess head available at the offset point follows the linear blanket-theory head profile documented in -[Delegated Methods](./07-delegated-methods.mdx); the offset therefore reduces the head (and the blowout and heave probabilities) relative to the -toe. When the berm instead reaches or clears the layer's downstream extent, no offset arises — the exit daylights at the berm toe and the +The confining layer then extends $L_3 - x$ beyond the evaluation point, and the excess head available there follows the linear blanket-theory +head profile, reduced by the factor $(L_3 - x)/L_3$ relative to the toe (see [Head Beneath the Confining Layer](#head-beneath-the-confining-layer)). +When the berm instead reaches or clears the layer's downstream extent, no offset arises — the exit daylights at the berm toe and the confined-exit nodes are set to certainty rather than computed (see [Event Tree](./06-event-tree.mdx)). -:::warning[INPUT NEEDED IN-12 — Definition] -The physical interpretation of the exit-offset distance requires confirmation. The intended evaluation location is the berm toe — the first -exposed ground beyond the berm. The model computes the offset as the supplied confining-layer extent minus the berm length, measured from the -embankment toe. Under the linear head profile (head decaying from the toe value to zero at the blanket termination), the head fraction -remaining at the computed offset equals the berm length divided by the confining-layer extent — whereas an exit evaluated *at the berm toe* -(a distance of one berm length from the embankment toe) would retain the complementary fraction, the extent minus the berm length divided by -the extent. The two constructions coincide only when the berm covers exactly half the extent; for a berm covering more than half the layer -the computed offset retains more head (conservative), and for a shorter berm it retains less (non-conservative). Confirm which exit location -the offset is intended to represent — if the berm toe, the computation may warrant review. The model's computed behavior is documented as-is -above. -::: +## Head Beneath the Confining Layer + +Blowout and heave depend on the net head across the confining layer at the exit evaluation point: the head in the foundation sand beneath the +layer less the head of the water standing on the layer there. The two heads are referenced to different ground surfaces. The seepage beneath +the layer exits at the daylighting exit, so the exit level is + + + +where: + +> $E$ = exit level, the control level at the daylighting exit +> $T$ = level of the water standing on the confining layer at the exit evaluation point +> $E_{check}$ = ground surface at the exit evaluation point: $E_{toe,ref}$ (the berm-toe ground when a berm is present) + +The head in the sand beneath the layer at the evaluation point combines the exit level with the share of the driving head that remains after +the head loss along the path upstream of that point : + + + +and the net head across the layer is + + + +where $L_{total}$ is the total seepage path of the selected configuration ( or +), evaluated per Monte Carlo realization, and $x$ is the evaluation-point distance of +. A distance $x$ at or beyond $L_3$ leaves no head from flow at the evaluation point. + +The first term covers two loading states. When the pool stands above the exit level, seepage flows and $\min(h, E) = E$: the head beneath the +layer is the exit level plus the remaining share of the driving head. When the pool stands at or below the exit level, no seepage flows, the +second term vanishes, and the foundation sand fills to pool level, so $h_{under} = h$. A daylight ground above the toe therefore adds the +difference between the two ground surfaces to the uplift at the toe, and a daylight ground below the toe reduces it. Where the daylight ground +equals the toe ground, reduces to the excess head of the blanket-theory toe solution. + +The blowout analysis compares the upward gradient $h_{net}/z_{bl}$ with the critical gradient of the confining layer, and the heave analysis +with the critical gradient of the foundation sand (see [Delegated Methods](./07-delegated-methods.mdx)). A realization with no positive net head +does not fail. ## Progression Path Lengths diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/06-event-tree.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/06-event-tree.mdx index e2205d946..1312e329b 100644 --- a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/06-event-tree.mdx +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/06-event-tree.mdx @@ -101,9 +101,10 @@ extent — seepage can reach the surface unfiltered at the toe through either of - **Hydraulic blowout** — rupture of the layer when uplift at its base exceeds its buoyant weight. The blowout probability $P_{blowout}(h)$ at each pool level is computed by the blanket-theory analysis using the confining layer's saturated unit weight - (see [Delegated Methods](./07-delegated-methods.mdx)); it increases with net head. The probability is evaluated at the exit evaluation - point — the toe by default, offset beyond a berm that ends within the layer's known extent - (see [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx)). + (see [Delegated Methods](./07-delegated-methods.mdx)); it increases with the net head across the layer. The probability is evaluated at the + exit evaluation point — the toe by default, or the berm toe when a berm ends within the layer's known extent — with the net head measured + against the water standing on the layer there + (see [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx#head-beneath-the-confining-layer)). The two mechanisms are combined as the union of independent pathways: @@ -115,17 +116,16 @@ The two mechanisms are combined as the union of independent pathways: Three site conditions override the composition and force $P_{ue} = 1.0$ at every pool level: 1. **No confining layer** — with the layer's presence answered No, nothing filters the exit. -2. **The exit daylights at the berm toe** — for a confirmed layer, a berm that reaches or clears the supplied downstream extent, or overlies - a layer of unknown extent: the berm toe then sits at or beyond the layer's termination, so nothing filters the exit there. In these cases - the berm toe is itself the daylighting exit and no separate daylight pathway is evaluated (see Governing SRP below). For a layer of - unknown presence, any berm forces this override — a daylighting exit at the berm toe is assumed rather than established — and both - pathways are retained. +2. **The exit daylights at the berm toe** — a berm that reaches or clears a confirmed layer's supplied downstream extent, or overlies a + confirmed layer of unknown extent: the berm toe then sits at or beyond the layer's termination, so nothing filters the exit there. For a + layer of unknown presence, any berm forces this override — a daylighting exit at the berm toe is assumed rather than established. In all + these cases the berm toe is itself the daylighting exit and no separate daylight pathway is evaluated (see Governing SRP below). 3. **Observed seepage through the layer** — sand boils or concentrated seepage have been observed emerging through the confining layer, demonstrating that an unfiltered exit already exists. The override applies to any toe exit that remains beneath the layer, with or without a berm. A berm ending within a confirmed layer's known extent triggers none of these overrides: the through-layer composition above is retained, with -the blowout probability evaluated at the offset exit point beyond the berm. +the blowout probability evaluated at the berm toe. :::warning[INPUT NEEDED IN-13 — Engineering Basis] The Weibull defect-survival parameters — characteristic penetration depth $t_c = 3.5$ ft and shape parameter $k = 1.25$ — require an @@ -137,7 +137,7 @@ rationale, or engineering-judgment attribution to state here. Two judgments in the berm treatment require an engineering basis to state here: 1. No berm is ever credited with filtering the exit: where the berm end remains beneath the layer, the exit resistance is carried entirely - by the layer's defect and blowout composition (evaluated at the offset exit point), and where the berm daylights the exit, the unfiltered + by the layer's defect and blowout composition (evaluated at the berm toe), and where the berm daylights the exit, the unfiltered exit is certain. 2. When the layer's presence is unknown and a berm is present, a daylighting exit at the berm toe is assumed (forcing the unfiltered exit to certainty) rather than evaluated. @@ -166,14 +166,14 @@ daylight pathway is 1.0 at every pool level. The pathway itself is evaluated onl Initiation at a confined exit requires the vertical gradient through the layer (or through a defect in it) to fluidize the underlying sand. The initiation probability $P_{init}(h)$ at each pool level is the blanket-theory heave probability, computed with the foundation sand's -saturated unit weight (see [Delegated Methods](./07-delegated-methods.mdx)). Four site conditions override the computed value and force -$P_{init} = 1.0$: +saturated unit weight and the same net head across the layer as the blowout analysis (see [Delegated Methods](./07-delegated-methods.mdx)). +Four site conditions override the computed value and force $P_{init} = 1.0$: 1. **No confining layer** — with no overburden to resist heave, initiation accompanies the unfiltered exit. -2. **A berm overlies a confirmed layer of unknown downstream extent** — a daylighting exit is assumed at the berm toe, beyond the - characterized layer. +2. **A berm overlies a layer of unknown presence, or a confirmed layer of unknown downstream extent** — a daylighting exit is assumed at the + berm toe, beyond the characterized layer. 3. **The berm reaches or clears a supplied downstream extent** — the berm is at least as long as the layer's extent, so the exit sits at or - beyond the layer's termination. The override applies whether the layer's presence is confirmed or unknown. + beyond the layer's termination. 4. **The pool reaches the trigger elevation** — sand boils or concentrated seepage have historically activated at or above this pool, demonstrating initiation: + +where $t$ is the tailwater elevation at that pool level, where one exists. ## Node 4: Progression — Mechanical Condition @@ -269,20 +275,16 @@ where: > $P_{int}$ = probability of unsuccessful intervention (Node 6) > $P_{br}$ = probability of breach (Node 7) -On the daylight pathway, $P_{ue}$ and $P_{init}$ are both 1.0 and $P_{prog}$ reflects the daylight path. +On the daylight pathway, $P_{ue}$ is 1.0, $P_{init}$ follows , and $P_{prog}$ +reflects the daylight path. ## Governing SRP -A daylight pathway is evaluated only where the daylighting exit is distinct from the toe exit. When a berm over a confirmed layer reaches or -clears the layer's downstream extent — or overlies a confirmed layer of unknown extent — the berm toe is itself the daylighting exit: the toe -pathway then carries a certain unfiltered exit and certain initiation over the berm-extended path, which are exactly the daylighting-exit -conditions, so a separate daylight pathway would repeat the same exit node for node and is not evaluated. This merging applies only to a -confirmed layer: under a layer of unknown presence the model always evaluates both pathways. With a berm over a layer of unknown presence, the -downstream path resolves to the berm length, so both pathways share the same progression path length and plane-type exit. They then differ only -in two respects: the toe initiation node, which stays at the heave probability unless the berm reaches or clears a supplied downstream extent -(Node 3), and the exit datum, because the toe progression references the toe reference elevation and the daylight progression the daylight -reference elevation. Where the two datums coincide, the daylight SRP is at least the toe SRP, because its unfiltered-exit and initiation nodes -are certain. +A daylight pathway is evaluated only where the daylighting exit is distinct from the toe exit. When a berm reaches or clears a confirmed +layer's downstream extent, overlies a confirmed layer of unknown extent, or overlies a layer of unknown presence, the berm toe is itself the +daylighting exit: the toe pathway then carries a certain unfiltered exit and certain initiation over the berm-extended path, which are exactly +the daylighting-exit conditions, so a separate daylight pathway would repeat the same exit node for node and is not evaluated. A separately +supplied daylight ground-surface elevation is not used in these cases. When both pathways are evaluated, the governing SRP at each pool level is the larger of the two pathway values: diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/07-delegated-methods.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/07-delegated-methods.mdx index a782cd8c7..b95df3079 100644 --- a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/07-delegated-methods.mdx +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/07-delegated-methods.mdx @@ -41,7 +41,8 @@ unit weight, which is what blanket theory computes @@ -75,14 +76,18 @@ Within each Monte Carlo realization, and at each pool level with net head $H$ (d equation="h_x = \begin{cases} h_o \cdot \dfrac{L_3 - x}{L_3} & x < L_3 \\[6pt] 0 & x \geq L_3 \end{cases}" /> +The head in the sand beneath the layer at the evaluation point is $\min(h, E) + h_x$, and the net head across the layer, $h_{net}$, is that head +less the water standing on the layer there (). The gradient and factor of safety follow: + - + where: -> $h_o$ = excess head above the exit datum at the embankment toe -> $h_x$ = excess head at the exit evaluation point, offset $x$ from the toe +> $h_o$ = excess head above the exit level at the embankment toe, from flow beneath the layer +> $h_x$ = excess head above the exit level at the exit evaluation point, a distance $x$ downstream of the toe +> $h_{net}$ = net head across the confining layer at the exit evaluation point > $L_3$, $L_{total}$ = downstream and total seepage path lengths ($L_3$ sampled per realization when no berm is present and the extent or the layer's presence is unknown) > $i_{cv}$ = critical vertical gradient > $\gamma_{sat}$ = saturated unit weight ($\gamma_{bl}$ for blowout, $\gamma_{sand}$ for heave) @@ -91,8 +96,8 @@ where: > $z_{bl}$ = sampled confining-layer thickness > $FS$ = factor of safety against the vertical gradient -The blowout or heave probability at each pool level is the fraction of Monte Carlo realizations in which $FS < 1$. Realizations with no exit -gradient (zero net head) contribute no failure. +The blowout or heave probability at each pool level is the fraction of Monte Carlo realizations in which $FS < 1$. Realizations with no +upward gradient (no positive net head across the layer) contribute no failure. ### Screening-level adjustments @@ -101,6 +106,11 @@ Relative to the blanket-theory chapters of the BEP Initiation manual, the screen - **Finite-blanket head loss always applies** — the excess head at the toe is always reduced by the path-length ratio (). The idealization of an infinite downstream blanket carrying the full net head at the toe is not used. +- **The exit and the evaluation point may sit at different ground elevations** — the blanket-theory chapters measure the exit head against a + single landside ground surface. The screening model measures the driving head to the exit level at the daylighting exit and the net head + against the water standing on the layer at the evaluation point, so a daylighting exit above the toe adds the difference to the uplift and + one below the toe reduces it. With a pool below the exit level, no seepage flows and the foundation sand stands at pool level beneath the + layer. Where the two ground surfaces coincide, the net head equals the blanket-theory excess head $h_x$. - **Downstream blanket length follows the resolved downstream path** — $L_3$ enters as the supplied downstream extent, or is drawn per realization from the wide default range when no berm is present and the extent or the layer's presence is unknown (see [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx)). diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/08-assumptions-and-limitations.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/08-assumptions-and-limitations.mdx index 19de3712d..dc2943711 100644 --- a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/08-assumptions-and-limitations.mdx +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/08-assumptions-and-limitations.mdx @@ -25,8 +25,8 @@ primary location in this document. approximated by the nearer of the two configurations. - *When it may not hold:* Sites with well-characterized semi-pervious strata or geometries that need Cases 1, 3, or 5 through 8; the toolbox models apply directly to such sites. -2. **The downstream confining layer carries a linear head profile.** The excess head decays from its value at the toe to zero at the layer's - downstream termination. +2. **The downstream confining layer carries a linear head profile.** The excess head above the exit level decays from its value at the toe + to zero at the layer's downstream termination. - *Engineering basis:* Blanket theory . The landside layer is analyzed as an impervious top stratum whatever permeability is selected; the permeability selection affects only the upstream credit. - *Effect on results:* Exit heads are reduced by the path-length ratio, which is less conservative than an infinite-blanket idealization. @@ -74,19 +74,18 @@ primary location in this document. - *When it may not hold:* Where the two mechanisms share a common cause (both concentrated at thin spots in the layer), the union may misstate the combined probability. 8. **A downstream seepage berm is classified by where it ends relative to the confining layer.** A berm within a confirmed layer of known - greater extent retains the through-layer exit mechanisms at an offset exit point. A berm that reaches or clears the extent, or overlies a - layer of unknown extent or unknown presence, produces a daylighting exit at the berm toe with a certain unfiltered exit. No berm is credited - with filtering, and every berm lengthens the toe progression path. - - *Engineering basis:* Basis requested — see marker IN-12 in - [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx) and marker IN-14 in [Event Tree](./06-event-tree.mdx). - - *Effect on results:* A berm within a known layer extent keeps the defect and blowout composition, with the head reduced at the offset exit - point. Over a confirmed layer, a berm that daylights the exit makes the unfiltered-exit and initiation nodes certain, and the toe pathway - then carries the governing curve. Over a layer of unknown presence, a berm makes the unfiltered-exit node certain (and the initiation node - too when it reaches or clears a supplied extent), and both pathways are still evaluated (see [Event Tree](./06-event-tree.mdx)). + greater extent retains the through-layer exit mechanisms, evaluated at the berm toe. A berm that reaches or clears the extent, or overlies a + layer of unknown extent or unknown presence, produces a daylighting exit at the berm toe with a certain unfiltered exit and certain + initiation. No berm is credited with filtering, and every berm lengthens the toe progression path. + - *Engineering basis:* Basis requested — see marker IN-14 in [Event Tree](./06-event-tree.mdx). + - *Effect on results:* A berm within a known layer extent keeps the defect and blowout composition, with the head at the berm toe reduced + by the share of the layer the berm covers. A berm that daylights the exit makes the unfiltered-exit and initiation nodes certain, and the + toe pathway then carries the governing curve (see [Event Tree](./06-event-tree.mdx)). - *When it may not hold:* Engineered filter berms designed to filter the exit; sites where the berm length relative to the layer extent is itself uncertain, since that comparison switches the exit treatment. 9. **A confining layer of unknown presence is evaluated as possibly present.** The defect and blowout analyses run with the Unknown thickness - band, roof support comes from the embankment materials, and both exit pathways are evaluated. + band, roof support comes from the embankment materials, and both exit pathways are evaluated unless a berm makes the berm toe the single + exit. - *Engineering basis:* Screening design objective (engineering judgment): an unverified layer is neither ignored nor fully credited, avoiding false negatives from either extreme. - *Effect on results:* Results for unknown-presence sites reflect deliberately wide parameter bands rather than either the confirmed-present @@ -148,14 +147,21 @@ attribution, and confirm or replace the 10° threshold. ## Exit Datum and Exit Type -17. **The toe blowout and heave analyses use the daylight datum.** Where a daylight ground-surface elevation is supplied (and the daylighting - exit is not the berm toe), the net head for the blowout and heave analyses is measured to the daylight reference elevation, although the - probabilities are evaluated at the toe. - - *Engineering basis:* Basis requested — see marker IN-20 below. - - *Effect on results:* The difference between the daylight ground and the toe ground is not added to or removed from the uplift at the toe. - Where the daylight ground lies below the toe, the toe uplift is overstated (conservative); where it lies above, the toe uplift is - understated (non-conservative). - - *When it may not hold:* Sites where the daylight ground differs markedly from the toe ground. +17. **The blowout and heave net head combines the daylight exit level with the ground at the evaluation point.** The seepage beneath the + layer exits at the daylight reference elevation, which sets the driving head; the net head across the layer is measured against the water + standing on the layer at the toe or berm toe. A pool below the exit level drives no seepage and fills the sand to pool level (see + [Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx#head-beneath-the-confining-layer)). + - *Engineering basis:* Blanket theory for the head remaining beneath the layer, with hydrostatic + conditions where no seepage flows. Two-dimensional steady-state seepage models of representative sections, with 10 ft of foundation sand, + reproduced the resulting net head at the toe to within about 0.25 ft across configurations with the daylight ground above, at, and below + the toe. + - *Effect on results:* A daylight ground above the toe adds the difference between the two ground surfaces to the uplift at the toe, so + pools between the toe and the daylight ground load the layer even though they drive no seepage; a daylight ground below the toe reduces + the uplift. + - *When it may not hold:* Ground that rises or falls steeply between the toe and the daylighting exit. Blanket theory measures the downstream + path horizontally and holds the sand thickness constant, while a steep rise lengthens and thins the sand path beneath the layer and leaves + more head at the toe: for a 57 ft rise over a 50 ft downstream extent, a two-dimensional model gave about 3 ft more net head at the toe at + full pool. Thick foundation sand exposed beyond the layer termination adds an exit loss of similar size that the method does not include. 18. **The toe exit type follows the presence answer.** The toe exit is hole-type only for a confirmed layer whose exit stays beneath it; for a layer of unknown presence it is plane-type (see [Delegated Methods](./07-delegated-methods.mdx)). - *Engineering basis:* Basis requested — see marker IN-21 below. @@ -164,12 +170,6 @@ attribution, and confirm or replace the 10° threshold. - *When it may not hold:* Sites where a confining layer is in fact present, so that toe seepage would emerge through defects as concentrated exits. -:::warning[INPUT NEEDED IN-20 — Engineering Basis] -Assumption 17: where a daylight ground-surface elevation is supplied, the toe blowout and heave analyses measure the net head to the daylight -reference elevation rather than the toe ground, so the elevation difference between them does not enter the uplift at the toe. Provide the -engineering basis or judgment attribution for this datum choice, or confirm whether the toe ground should be the datum for those analyses. -::: - :::warning[INPUT NEEDED IN-21 — Engineering Basis] Assumption 18: under a layer of unknown presence, the toe exit is treated as plane-type ($C_{3d} = 1.0$), which is less conservative than the hole-type treatment ($C_{3d} = 0.5$) applied to a confirmed layer. Provide the engineering basis or judgment attribution for this choice, or @@ -195,8 +195,10 @@ Three aspects of the screening formulation deserve particular attention when rea never fall below it (assumption 6), thickness bands that include thin layers keep Node 2 high even at low pools. Where that floor exceeds the blowout probability, the pool dependence of the toe SRP comes from the initiation and progression nodes instead. -- **No driving head below the exit reference.** Pools at or below the governing exit reference elevation produce zero net head and therefore - zero SRP. The reference elevations — and the daylight ground surface in particular — directly position the low-pool end of the - system response curve. +- **No driving head below the exit reference.** Pools at or below the toe reference elevation carry zero SRP on the toe pathway, and pools + at or below the daylight exit level carry zero SRP on the daylight pathway. A daylight ground above the toe does not shield the toe below + it: pools between the two elevations load the confining layer statically, so the toe blowout and heave probabilities can be high there + even though no seepage leaves the daylighting exit. The reference elevations — and the daylight ground surface in particular — directly + position the low-pool end of the system response curve. diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/09-output-and-interpretation.mdx b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/09-output-and-interpretation.mdx index 0ebc8ff86..1cd05e745 100644 --- a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/09-output-and-interpretation.mdx +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/09-output-and-interpretation.mdx @@ -28,17 +28,18 @@ governing SRP series is the system response curve. Every pool-dependent result is a series over the evaluated pool levels: every supplied headwater value and additional pool levels distributed between them (see [Input Parameters](./03-input-parameters.mdx)). The daylight-pathway series are produced only when a confining layer may be present (its presence is Yes or Unknown) *and* the daylighting exit is distinct from the toe -exit. When the berm toe is itself the daylighting exit — a berm over a confirmed layer that reaches or clears its downstream extent, or overlies -a confirmed layer of unknown extent — there are no daylight series and the toe series carry the governing curve (see [Event Tree](./06-event-tree.mdx)). +exit. When the berm toe is itself the daylighting exit — a berm that reaches or clears a confirmed layer's downstream extent, overlies a +confirmed layer of unknown extent, or overlies a layer of unknown presence — there are no daylight series and the toe series carry the +governing curve (see [Event Tree](./06-event-tree.mdx)). **Hydraulic series:** - **Pool levels** — the headwater elevations at which the event tree is evaluated. - **Tailwater** — the tailwater at each pool level, interpolated between the supplied pairs, and blank wherever no tailwater exists. -- **Toe control level** — the downstream control level used by the toe progression pathway: the higher of the tailwater and the toe reference - elevation. -- **Daylight control level** — the downstream control level used by the blowout, heave, and daylight-progression analyses: the higher of the - tailwater and the daylight reference elevation. +- **Toe control level** — the higher of the tailwater and the toe reference elevation: the downstream control level of the toe progression + pathway, and the water standing on the confining layer in the blowout and heave analyses. +- **Daylight control level** — the higher of the tailwater and the daylight reference elevation: the exit level that sets the driving head of + the blowout, heave, and daylight-progression analyses. **Toe pathway series:** @@ -54,7 +55,7 @@ a confirmed layer of unknown extent — there are no daylight series and the toe **Daylight pathway series:** - **Unfiltered-exit probability** — Node 2: 1.0 at every pool level. -- **Initiation probability** — Node 3: 1.0 at every pool level. +- **Initiation probability** — Node 3: 1.0 at pool levels above the daylight control level, and 0 at or below it. - **Progression probability** — Node 5: the mean probability of advancement over the longer daylight path, non-decreasing with pool level. - **SRP** — the product of the seven nodes on the daylight pathway. @@ -69,7 +70,8 @@ The governing SRP series is the system response curve — the conditional probab level. While the net head does not decrease as the pool rises, the curve is non-decreasing with pool level: the flaw, roof-support, intervention, and breach nodes are constant; the blowout and heave probabilities rise with net head; and the progression node is explicitly constrained to be non-decreasing. Where the tailwater rises faster than the headwater, the net head can fall and the blowout and heave -probabilities with it. Pools at or below the governing exit reference elevation carry zero SRP because no net driving head exists there. +probabilities with it. Each pathway carries zero SRP at pools at or below its own control level, because its progression analysis has no +driving head there. ### Which Pathway Governs @@ -79,13 +81,11 @@ The governing curve is the larger of the two pathway SRPs at each pool level, an progression analysis runs over a path no longer than the daylight path — shorter with no berm, or with a berm inside a confirmed layer's known extent — which raises the average applied gradient, and, when the layer is confirmed and the exit stays beneath it, uses the hole-type exit that halves the Schmertmann critical gradient. -- The **daylight pathway** carries certain unfiltered exit and initiation, because nothing confines the exit there. Its progression analysis - runs over the path to the layer's termination with a plane-type exit. +- The **daylight pathway** carries certain unfiltered exit, because nothing confines the exit there, and certain initiation whenever seepage + leaves the sand there. Its progression analysis runs over the path to the layer's termination with a plane-type exit. The daylight pathway governs at a pool level when the reduction the confining layer gives the toe pathway through Nodes 2 and 3 outweighs any -progression advantage the toe pathway gains from its shorter path and exit type; otherwise the toe pathway governs. Under a layer of unknown -presence with a berm, the two paths are equal and both exits are plane-type, so where the two exit datums coincide the daylight pathway governs -(see [Event Tree](./06-event-tree.mdx)). (The path-length and depth +progression advantage the toe pathway gains from its shorter path and exit type; otherwise the toe pathway governs. (The path-length and depth corrections of the Schmertmann method also change with path length, so the progression comparison itself depends on the site.) Which side of that balance a site falls on depends on the layer thickness band, the unit weights, the downstream extent, and the foundation sand properties, and it can change with pool level. When both pathways are evaluated, both are produced, so the balance can be read directly from the results. When the berm toe is itself the daylighting @@ -103,13 +103,13 @@ the conditions under which it controls the result: Nodes 2 and 3 to certainty and so change the curve beyond that factor (see [Event Tree](./06-event-tree.mdx)). - **Confining-layer thickness category** — thickness enters the defect probability (pool-independent, and rising steeply as the layer thins) and the vertical exit gradient in the blowout and heave analyses (a thinner layer gives a larger gradient for the same head). It affects the - toe pathway only, and only where a confining layer may be present. Where no layer is present, or where a berm daylights the exit over a - confirmed layer, Nodes 2 and 3 are certain and thickness has no effect. Under a layer of unknown presence with a berm, Node 2 is certain but - Node 3 stays at the heave probability (unless the berm reaches or clears a supplied extent), so thickness still affects it. + toe pathway only, and only where a confining layer may be present. Where no layer is present, or where a berm daylights the exit, Nodes 2 + and 3 are certain and thickness has no effect. - **Downstream confining-layer extent** — with no berm, a longer downstream path $L_3$ leaves a larger share of the net head at the toe (raising the toe blowout and heave probabilities) and lengthens the daylight progression path (lowering the daylight progression - probability). With a berm ending inside a confirmed layer's known extent, the blowout and heave are evaluated at the offset exit point, - where the head is the net head times the berm length divided by the total path length, so a longer extent lowers them. When no berm is + probability). With a berm ending inside a confirmed layer's known extent, the blowout and heave are evaluated at the berm toe, where the + head from flow is the driving head times the layer length remaining beyond the berm divided by the total path length, so a longer extent + raises them. When no berm is present and the extent or the layer's presence is unknown, the 1 to 5 embankment-height default spreads these effects across a wide range. With a berm, the extent also decides which exit treatment applies (see [Event Tree](./06-event-tree.mdx)). - **Relative density category** — denser sand raises the Schmertmann critical gradient through the density correction and lowers the @@ -119,8 +119,9 @@ the conditions under which it controls the result: - **Embankment materials** — when the confining layer is not confirmed, the minimum roof-support probability multiplies the SRP at every pool level, so a single listed material with a low roof-support probability lowers the whole curve by that factor. With a confirmed layer, the materials have no effect. -- **Reference elevations** — the toe and daylight ground surfaces set the pool level below which there is no net head, and so position the - low-pool end of the curve. +- **Reference elevations** — the toe and daylight ground surfaces set the pool levels below which each pathway has no driving head, and so + position the low-pool end of the curve. Their difference also enters the blowout and heave analyses directly: a daylight ground above the toe + adds that difference to the uplift at the toe, including at pools below the daylight ground, and a daylight ground below the toe reduces it. ### Checking the Result @@ -134,8 +135,9 @@ indicates a computation error in the model, not a property of the site: probabilities. - **Unfiltered-exit floor** — on the toe pathway, the unfiltered-exit probability is never less than either the defect probability or the blowout probability. -- **Certain nodes** — on the daylight pathway, the unfiltered-exit and initiation probabilities are 1.0 at every pool level; on the toe pathway - they are 1.0 at every pool level when the confining-layer presence is No. +- **Certain nodes** — on the daylight pathway, the unfiltered-exit probability is 1.0 at every pool level and the initiation probability is + 1.0 above the daylight control level and 0 at or below it; on the toe pathway both are 1.0 at every pool level when the confining-layer + presence is No. - **Zero-head threshold** — each pathway's SRP is zero at pool levels where its progression analysis has no net head: at or below the higher of the tailwater and the toe reference elevation for the toe pathway, and of the tailwater and the daylight reference elevation for the daylight pathway. diff --git a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/_input-needed.md b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/_input-needed.md index 906aa6f0c..9c8761a57 100644 --- a/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/_input-needed.md +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/_input-needed.md @@ -4,7 +4,9 @@ Answer inline and return this file (or paste its contents into the conversation) Answer blank to keep that marker in place. Do not renumber — the IDs tie each entry to its admonition in the document. IN-18 to IN-21 were added in the October 2026 revision. (IN-17 was retired in the August 2026 update: the mean-of- distribution treatment it questioned no longer exists — supplied seepage-path lengths are now -single values by design.) +single values by design. IN-12 was retired in the October 2026 model update: blowout and heave beneath a berm +are now evaluated at the berm toe, the location the marker asked to confirm. IN-20 was retired in the same update: the +blowout and heave net head now combines the daylight exit level with the ground at the evaluation point.) --- @@ -159,29 +161,6 @@ for scaling the range to embankment height. --- -## IN-12 — Definition — `05-hydraulic-loading-and-seepage-paths.mdx` - -**Regarding:** The physical interpretation of the exit-offset distance used when a berm -overlies a confirmed confining layer whose supplied downstream extent exceeds the berm -length — the berm-within-known-extent case in which the through-layer defect/blowout -composition is retained. The intended evaluation location is the berm toe, but the model -computes the offset as (supplied confining-layer extent − berm -length), measured from the embankment toe. Under the linear head profile, the head fraction -remaining at the computed offset equals (berm length ÷ confining-layer extent) — whereas an -exit evaluated at the berm toe (one berm length from the embankment toe) would retain the -complementary fraction, (extent − berm length) ÷ extent. The two coincide only when the berm -covers exactly half the extent; the computed construction is conservative for longer berms -and non-conservative for shorter ones relative to the berm-toe reading. - -**Needed:** Confirmation of which exit location the offset is intended to represent, and the -engineering basis for the chosen construction. (If the intent is the berm toe, the -computation may warrant review — the document currently describes the computed behavior -as-is.) - -**Answer:** - ---- - ## IN-13 — Engineering Basis — `06-event-tree.mdx` **Regarding:** The Weibull defect-survival parameters — characteristic defect penetration @@ -272,20 +251,6 @@ attribution; confirm or replace the 10° threshold. --- -## IN-20 — Engineering Basis — `08-assumptions-and-limitations.mdx` - -**Regarding:** Assumption 17. Where a daylight ground-surface elevation is supplied (and the -daylighting exit is not the berm toe), the toe blowout and heave analyses measure the net head -to the daylight reference elevation rather than the toe ground, so the elevation difference -between the daylight ground and the toe does not enter the uplift at the toe. - -**Needed:** Engineering basis or judgment attribution for this datum choice, or confirmation -of whether the toe ground should be the datum for the toe blowout and heave analyses. - -**Answer:** - ---- - ## IN-21 — Engineering Basis — `08-assumptions-and-limitations.mdx` **Regarding:** Assumption 18. Under a confining layer of unknown presence, the toe exit is