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..e92eecf39 --- /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: October 2026 +reportType: 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 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'; +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..2cf70b5bf --- /dev/null +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/00-version-history.mdx @@ -0,0 +1,31 @@ +--- +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..b00a40b0c --- /dev/null +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/01-preface.mdx @@ -0,0 +1,47 @@ +--- +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 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 — +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 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, 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. +- **[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 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 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 new file mode 100644 index 000000000..11459322b --- /dev/null +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/02-model-overview.mdx @@ -0,0 +1,160 @@ +--- +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'; + + + +# Model Overview + +## Purpose + +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 +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 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 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 + 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 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 + +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 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 + 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)). + +## Physics Basis + +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 +- **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 + +## Comparison with Detailed Models + +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. + + + +## 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 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. + +## 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. + + 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..5f8b8f6af --- /dev/null +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/03-input-parameters.mdx @@ -0,0 +1,494 @@ +--- +title: Input Parameters +--- + +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 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, 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). 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 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 +(). 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'], + [ + '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). 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: + +- **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 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 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)). + +1'], + ['—', 'ft'], + ['—', '> 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 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, 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). + +b', 'Ebt'], + ['—', 'ft', 'ft'], + ['—', '> 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 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. 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 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 + +The two confining-layer extents are entered as single lengths (). + +1 (when credited)', 'Lcl'], + ['ft', 'ft'], + ['≥ 0', '> 0'], + ['None (required when the layer extends upstream)', 'Unknown'], + ]} +/> + +- **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 over a confirmed layer, a supplied extent also decides whether the berm end remains beneath the layer (retaining the + through-layer exit mechanisms, evaluated at the berm toe) 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, and any berm is taken to end the layer at the berm toe. + + + +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 +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 +(). + +trigger'], + ['—', 'ft'], + ['—', '> 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; 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', '—'], + ['> 0', '0 to 100', '≥ 1', '> 0', '—'], + [ + '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. + +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. +::: + +:::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 +(). Both carry screening defaults that may be overridden. + +sand', 'γbl'], + ['pcf', 'pcf'], + ['> 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. + +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 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 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 new file mode 100644 index 000000000..2210b1237 --- /dev/null +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/04-flaw-assessment.mdx @@ -0,0 +1,183 @@ +--- +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 +($q < 1$). + +:::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. +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 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 + + 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..ca6758fa8 --- /dev/null +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/05-hydraulic-loading-and-seepage-paths.mdx @@ -0,0 +1,245 @@ +--- +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, the location of the exit evaluation point, and the head that acts across the confining +layer there. 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 that reaches or clears a confirmed layer's downstream extent, overlies a confirmed layer of unknown + extent, or overlies a layer of unknown presence — 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 two elevations play different roles. Seepage beneath the confining layer leaves the foundation sand at the daylighting exit, so the +daylight reference elevation sets the exit level that controls the driving head for the blowout, heave, and daylight progression analyses. +The toe reference elevation sets the level of the water standing on the confining layer at the exit evaluation point, against which the +blowout and heave net head is measured (see [Head Beneath the Confining Layer](#head-beneath-the-confining-layer)), and it controls the toe +progression pathway. Both elevations therefore enter the blowout and heave analyses whenever they differ. + +## 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 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 +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 + +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** — $L_1 = 0$. 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: + +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 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 default for no berm with an +unknown extent or unknown layer presence 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 (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 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: + + + +- **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. 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 moves to the berm toe, +the first exposed ground beyond the berm: + + + +where: + +> $x$ = distance of the exit evaluation point downstream of the embankment toe +> $L_b$ = berm length + +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)). + +## 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 + +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 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. + + 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..1312e329b --- /dev/null +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/06-event-tree.mdx @@ -0,0 +1,298 @@ +--- +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 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 +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 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: + + + +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** — 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 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 +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 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. + +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 + +*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 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 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. +4. **The pool reaches the trigger elevation** — sand boils or concentrated seepage 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. + +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). + +### Daylight pathway + +At the daylight exit the sand is exposed at the surface with no confining layer to resist heave, so initiation is certain once seepage +leaves the sand there. Seepage leaves the sand only while the pool stands above the exit level; a pool at or below it fills the sand without +flowing out. The initiation probability on the daylight pathway is therefore + + + +where $t$ is the tailwater elevation at that pool level, where one exists. + +## Node 4: Progression — Mechanical Condition + +*Question:* Can the material over the developing pipe sustain a stable roof? + +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 + +*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 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 + +*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 + +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, $P_{ue}$ 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 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: + + + +When only the toe pathway exists — no confining layer, or a berm-toe daylighting exit — it governs directly. + + 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..b95df3079 --- /dev/null +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/07-delegated-methods.mdx @@ -0,0 +1,252 @@ +--- +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 credited with an + upstream path length. 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 driving head $H$ above the exit level $E$ (both defined in +[Hydraulic Loading and Seepage Paths](./05-hydraulic-loading-and-seepage-paths.mdx)): + + + + + +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 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) +> $\gamma_w$ = 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 +upward gradient (no positive net head across the layer) 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. +- **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)). +- **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). + + 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..dc2943711 --- /dev/null +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/08-assumptions-and-limitations.mdx @@ -0,0 +1,204 @@ +--- +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'; + + + +# 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. 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 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. + - *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, 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 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 + 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 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. + - *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-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 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 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 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 new file mode 100644 index 000000000..1cd05e745 --- /dev/null +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/09-output-and-interpretation.mdx @@ -0,0 +1,171 @@ +--- +title: Output and Interpretation +--- + +import NavContainer from '@site/src/components/NavContainer'; + + + +# Output and Interpretation + +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 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 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 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:** + +- **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. + +**Daylight pathway series:** + +- **Unfiltered-exit probability** — Node 2: 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. + +**Governing series:** + +- **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. 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 + +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, 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. (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, 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 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 + 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 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 + +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 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. +- **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, where: + +- 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 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 +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..9c8761a57 --- /dev/null +++ b/docs/web-applications/system-response/backward-erosion-piping-screening/v1.0/_input-needed.md @@ -0,0 +1,265 @@ +# 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-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. 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.) + +--- + +## 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-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-methods.mdx` + +**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 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-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:** + +--- diff --git a/src/docConfig.js b/src/docConfig.js index 94aa4cf81..a7d909aae 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/" + } +]