diff --git a/docs/web-applications/system-response/cle-cross-valley-settlement-screening/v1.0/00-document-info.mdx b/docs/web-applications/system-response/cle-cross-valley-settlement-screening/v1.0/00-document-info.mdx new file mode 100644 index 000000000..4940ac9d7 --- /dev/null +++ b/docs/web-applications/system-response/cle-cross-valley-settlement-screening/v1.0/00-document-info.mdx @@ -0,0 +1,25 @@ +--- +title: Document Info +reportDate: October 2026 +reportType: Technical Reference +reportTitle: Concentrated Leak Erosion Cross-Valley Settlement Screening Technical Reference Manual +reportSubTitle: System Response Library +reportAuthors: ['Adam Gohs, P.E.'] +reportAbstract: Technical reference documenting the concentrated leak erosion (CLE) cross-valley settlement screening model in the System Response library. The model computes a system response probability (SRP) at each headwater level for concentrated leak erosion through a transverse crack opened at the crest by differential settlement of the embankment across the valley. The flaw assessment converts the normalized crest settlement and the abutment slope, with an optional abutment step, into a localized tensile strain, and from that strain into the probability of a continuous transverse crack, the crack width, and the crack depth. The bottom of the crack gates initiation, and the remaining nodes of the eight-node CLE event tree follow the methods shared by the CLE screening models. The flaw assessment is deterministic, and the model applies simplifications appropriate for screening-level risk analysis. +reportSubjectTerms: ['CLE', 'Concentrated Leak Erosion', 'Screening', 'Cross-Valley Differential Settlement', 'Transverse Cracking', 'Localized Tensile Strain', 'Crack Depth', 'Event Tree', 'System Response Probability', 'System Response Curve'] +citationGuide: 'U.S. Army Corps of Engineers, Risk Management Center, Concentrated Leak Erosion Cross-Valley Settlement 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/cle-cross-valley-settlement-screening/v1.0/00-version-history.mdx b/docs/web-applications/system-response/cle-cross-valley-settlement-screening/v1.0/00-version-history.mdx new file mode 100644 index 000000000..6415796a9 --- /dev/null +++ b/docs/web-applications/system-response/cle-cross-valley-settlement-screening/v1.0/00-version-history.mdx @@ -0,0 +1,23 @@ +--- +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/cle-cross-valley-settlement-screening/v1.0/01-preface.mdx b/docs/web-applications/system-response/cle-cross-valley-settlement-screening/v1.0/01-preface.mdx new file mode 100644 index 000000000..46e6647fd --- /dev/null +++ b/docs/web-applications/system-response/cle-cross-valley-settlement-screening/v1.0/01-preface.mdx @@ -0,0 +1,45 @@ +--- +title: Preface +--- + +import NavContainer from '@site/src/components/NavContainer'; + + + +# Preface + +This document provides a technical reference for the concentrated leak erosion (CLE) cross-valley settlement screening model in the System +Response library. The model computes a system response probability (SRP) as a function of headwater elevation for concentrated leak erosion +through a transverse crack that differential settlement of the embankment across the valley opens at the crest. 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 model is one of eight CLE screening models that share one event tree and most of their methods. Those shared methods — the event-tree +structure, the headwater gate that governs initiation in a crest crack, the failure-pathway conventions behind the continuation and progression +nodes, and the form of the results — are documented once in the +[Concentrated Leak Erosion Common Methods Screening Technical Reference Manual](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/model-overview). +The continuation node is evaluated by the shared continuation method documented in the +[Continuation (Filter Evaluation) Screening Technical Reference Manual](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/continuation-screening/v1.0/model-overview). +This manual documents what is specific to cross-valley settlement — its flaw assessment, its inputs, how its flaw sets the elevations the +downstream nodes use, and its assumptions — and refers to the specific chapters of those two manuals for the rest. + +The intended audience includes dam 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, +concentrated leak erosion mechanics, embankment cracking, and probability concepts — but no familiarity with the software implementation is +required. + +## 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 engineering basis, a comparison with detailed methods, and its relationship to the shared CLE methods. +- **[Input Parameters](./03-input-parameters.mdx)** — The inputs specific to cross-valley settlement — the length unit, the dam height, the + abutment slope and step, the settlement or year of construction, and the observation of continuous transverse cracking — and a guide to the + shared inputs documented in the common methods manual. +- **[Flaw Assessment](./04-flaw-assessment.mdx)** — The calculation of the normalized settlement, the localized tensile strain with and without + an abutment step, the flaw probability, the crack width, the crack depth, and the bottom-of-crack elevation, with a worked example. +- **[Event Tree](./05-event-tree.mdx)** — How the eight nodes of the CLE event tree are populated for this mechanism at each pool level, and how + the SRP is computed. +- **[Assumptions and Limitations](./06-assumptions-and-limitations.mdx)** — Each assumption specific to this model with its engineering basis, its + effect on results, and the conditions under which it may not hold. +- **[Output and Interpretation](./07-output-and-interpretation.mdx)** — The results the model produces, how to read the system response curve and + the flaw-assessment results, and the role of screening results relative to detailed analysis. diff --git a/docs/web-applications/system-response/cle-cross-valley-settlement-screening/v1.0/02-model-overview.mdx b/docs/web-applications/system-response/cle-cross-valley-settlement-screening/v1.0/02-model-overview.mdx new file mode 100644 index 000000000..e58fda26d --- /dev/null +++ b/docs/web-applications/system-response/cle-cross-valley-settlement-screening/v1.0/02-model-overview.mdx @@ -0,0 +1,140 @@ +--- +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 cross-valley settlement screening model computes a system response curve for concentrated leak erosion through a transverse crack caused by +differential settlement of the embankment across the valley. The system response probability (SRP) at each headwater level is the conditional +probability of breach of the embankment by concentrated leak erosion through such a crack, given that pool level. + +An embankment settles more where the fill beneath the crest is thicker, so the crest settles most over the deepest part of the valley and least +near the abutments. Where the abutment is steep, or where it carries an abrupt step, the settlement changes rapidly along the +crest and stretches the fill near the top of the embankment. If that stretching exceeds what the fill can sustain, a transverse crack opens at the +crest and extends some depth into the embankment. Once the pool rises above the bottom of the crack, water can flow through it, and the crack +becomes the flaw from which concentrated leak erosion can develop. + +## Intended Use + +The model is a screening-level assessment of concentrated leak erosion through a cross-valley settlement crack. Like the other CLE screening +models, it makes simplifying and generally conservative assumptions with two goals (see the +[Intended Use](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/model-overview#intended-use) section of the common +methods manual): + +- **Preventing false negatives** — The flaw probability is read from the more conservative of two available relationships, the one for a pool + above the period of record, and initiation is taken as certain once the pool rises above the bottom of the crack. +- **Reducing input burden** — The flaw assessment needs only the dam height, the abutment slope, an optional abutment step, and either the + measured settlement or the year of construction, from which a default settlement is assigned. + +The model is not intended for detailed or semi-quantitative risk assessments of transverse cracking. Its flaw assessment uses tabulated +relationships over a limited range of settlement and abutment slope (see [Flaw Assessment](./04-flaw-assessment.mdx)), and its initiation +treatment does not analyze the hydraulics of the crack. + +## How the Model Works + +The model executes the three stages common to the CLE screening models (see +[How the Model Works](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/model-overview#how-the-model-works) in the common +methods manual), with a flaw assessment specific to cross-valley settlement: + +1. **Flaw assessment** — The maximum post-construction crest settlement, or a default from the year of construction, is normalized by the dam + height. The normalized settlement and the abutment slope give the localized tensile strain at the crest, interpolated from tables for an abutment + without a step or, when a step is described, from tables for three relative step heights. The strain then gives the probability of a continuous + transverse crack, the crack width, and, through a relationship between crack width and crack depth, the depth of the crack below the crest and + so the bottom-of-crack elevation. An observation of continuous transverse cracking sets the flaw probability to 1.0 (see + [Flaw Assessment](./04-flaw-assessment.mdx)). +2. **Pathway description** — The model applies the user's description of the failure pathway along the crack, taken at the bottom-of-crack + elevation: the top of the first filter the pathway meets, the materials of the full and the below-filter pathways, and the upstream + seepage-limiting elements and the top of any wall (see [Input Parameters](./03-input-parameters.mdx#shared-inputs)). +3. **Event-tree assembly** — At each headwater level, the model evaluates the eight nodes of the CLE event tree and multiplies them. Initiation + steps from zero to 1.0 where the pool rises above the bottom of the crack; continuation, roof support, and flow limitation change where the pool + crosses the top of a filter or of a wall (see [Event Tree](./05-event-tree.mdx)). + +Every step is deterministic. The only part of the calculation that can involve sampling is the continuation probability, when the shared +continuation method evaluates the filter by its route through the soil classifications of the base and filter soils (see +[Method Selection and Governing Base Soil](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/continuation-screening/v1.0/method-selection-and-governing-base-soil) +in the continuation manual). + +## Physics Basis + +The model combines the following engineering relationships: + +- **Localized tensile strain from settlement and abutment geometry** — tabulated relationships between the normalized crest settlement, the + abutment slope, the relative height of an abutment step, and the localized tensile strain at the crest (see + [Flaw Assessment](./04-flaw-assessment.mdx#localized-tensile-strain)) +- **Flaw probability and crack width from the localized tensile strain** — tabulated relationships between the strain, the probability of a + continuous transverse crack, and the crack width (see [Flaw Assessment](./04-flaw-assessment.mdx#flaw-probability)) +- **Crack depth from crack width** — an empirical relationship attributed to Pierson (2023) (see + [Flaw Assessment](./04-flaw-assessment.mdx#crack-depth-and-bottom-of-crack-elevation)) +- **Initiation in an open crest crack** — the headwater gate shared by the crest-crack models, documented in the + [Crest-Crack Models: Headwater Gate](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/initiation#crest-crack-models-headwater-gate) + section of the common methods manual +- **Continuation, roof support, crack filling, and flow limitation** — the failure-pathway conventions and the tabulated progression + probabilities of Fell et al. (2024) , documented in the + [Failure Pathway and Progression](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/failure-pathway-and-progression) + chapter of the common methods manual, with filter evaluation by the shared continuation method + +## Comparison with Detailed Models + +In a detailed risk analysis, the likelihood, width, and depth of a transverse crack are estimated by the risk team from the totality of the +evidence, and initiation in the crack is assessed with a shear stress analysis of the crack geometry, for example with the +[Vertical Rectangular Crack](/docs/toolbox-technical-manuals/internal-erosion-suite/concentrated-leak-erosion-initiation/v1.0/vertical-rectangular-crack) +or [Vertical Triangular Crack](/docs/toolbox-technical-manuals/internal-erosion-suite/concentrated-leak-erosion-initiation/v1.0/vertical-triangular-crack) +geometry of the Concentrated Leak Erosion Initiation toolbox. summarizes the differences. + + + +## Relationship to the Common CLE Methods + +The model is one of the four crest-crack models of the CLE family, with settlement adjacent to a wall or cliff, desiccation cracking, and frost +cracking (see [The Two Model Groups](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/model-overview#the-two-model-groups) +in the common methods manual). It differs from the other three in its flaw assessment: it is the one CLE model that does not use risk-factor and +likelihood-factor scoring, estimating the flaw probability instead from the settlement-based relationships documented in +[Flaw Assessment](./04-flaw-assessment.mdx). It is also the one crest-crack model that derives the crack depth from a crack width rather than +from tabulated depths. + +Everything downstream of the flaw assessment follows the common methods: the eight-node event tree, the headwater grid, the initiation gate, the +pathway gates on the top of the filter and the top of a wall, and the progression tables. This manual does not repeat them; [Event Tree](./05-event-tree.mdx) +states how each node is populated for this model and links the section of the common methods manual that documents it. + + diff --git a/docs/web-applications/system-response/cle-cross-valley-settlement-screening/v1.0/03-input-parameters.mdx b/docs/web-applications/system-response/cle-cross-valley-settlement-screening/v1.0/03-input-parameters.mdx new file mode 100644 index 000000000..cbdc7c020 --- /dev/null +++ b/docs/web-applications/system-response/cle-cross-valley-settlement-screening/v1.0/03-input-parameters.mdx @@ -0,0 +1,159 @@ +--- +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 the inputs specific to the cross-valley settlement model: the length unit, the dam height, the abutment geometry, the +settlement or the year of construction, and the observation that overrides the flaw probability. The model also takes the inputs shared by the +CLE crest-crack models — hydraulic loading, the crest elevation and embankment type, the failure-pathway inputs, the upstream seepage-limiting +elements, and the intervention and breach probabilities — which are documented in the +[Common Input Parameters](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/input-parameters) chapter of the common +methods manual and summarized under [Shared Inputs](#shared-inputs) below. The model takes none of the initiation material inputs of the +compaction models (see +[The Two Model Groups](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/model-overview#the-two-model-groups)). + +The dam geometry, abutment geometry, and settlement groups give the short facts for their quantities in a table, followed by a description of each +input; the length unit and the observation of cracking are single selections described in prose, with the choices and what each implies. + +## Length Unit + +The user declares the length unit of the analysis, feet or meters (default feet). Every length and elevation the model takes — headwater and +tailwater, the crest, filter, and wall elevations, the dam height, the step height, and the settlement — is entered in that unit, on the common +datum described in [Units and Datum](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/input-parameters#units-and-datum). +The declared unit affects one step of the calculation: the crack-depth relationship, which is evaluated in metric units and converted to feet +when the analysis is in feet (see [Flaw Assessment](./04-flaw-assessment.mdx#crack-depth-and-bottom-of-crack-elevation)). The normalized +settlement, the tensile strain, the flaw probability, and the crack width are unaffected by the unit, so an analysis in meters gives the same +system response curve as the equivalent analysis in feet. + +## Dam Geometry + +H', 'zc'], + ['ft or m', 'ft or m'], + ['> 0', 'Any'], + ['Required', 'Required'], + ]} +/> + +- **Dam height** $H$ — the height of the embankment, used to normalize the crest settlement (see + [Flaw Assessment](./04-flaw-assessment.mdx#normalized-settlement)) and, when an abutment step is described, the step height. +- **Crest elevation** $z_c$ — the top of the embankment, from which the crack depth is measured down to the bottom of the crack. It is the shared + input described in + [Embankment Description](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/input-parameters#embankment-description). + +:::warning[INPUT NEEDED IN-01 — Definition] +The dam height $H$ and the maximum post-construction settlement $s$ (see [Settlement](#settlement)) are used only as the ratio $s/H$, and +neither is defined beyond its name. State how each is to be measured: for $H$, whether it is the maximum height of the embankment at the deepest +section of the valley, measured from the crest to the lowest foundation contact or to the original ground surface; and for $s$, whether it is the +largest crest settlement measured along the crest since the end of construction, and whether it includes settlement of the foundation. + +Proposed (unconfirmed): $H$ is the maximum embankment height at the deepest section, and $s$ is the largest crest settlement observed since the +end of construction, both from survey records. Confirm or replace. +::: + +## Abutment Geometry + +θ', 'h1'], + ['degrees', 'ft or m'], + ['> 0; tabulated from 15 to 60', '≥ 0'], + ['Required', 'No step'], + ]} +/> + +- **Abutment slope** $\theta$ — the inclination of the abutment, in degrees, which with the normalized settlement sets the localized tensile + strain at the crest. One slope is entered; the model analyzes one abutment. The strain tables cover slopes from 15 to 60 degrees; a slope outside + that range takes the strain at the nearer end (see + [Range of the Relationships](./04-flaw-assessment.mdx#range-of-the-relationships)). +- **Abutment step height** $h_1$ — the height of an abrupt step in the abutment profile. When no step is described, the abutment has no step and + the no-step strain tables are used. When a step is described — including one of zero height — the step tables are used, interpolated on the relative step height + $h_1/H$ (see [Flaw Assessment](./04-flaw-assessment.mdx#abutment-with-a-step)). + +:::warning[INPUT NEEDED IN-02 — Definition] +The abutment slope $\theta$ is not defined beyond its name and unit. State how it is measured — for example, the angle of the abutment surface +from the horizontal in the cross-valley profile beneath the crest, taken over what height — and which abutment the user should analyze when the +two differ (for example, the steeper, or each in turn as separate analyses). Also state the engineering basis for describing the +crack with one abutment per analysis (Assumption 3 in [Assumptions and Limitations](./06-assumptions-and-limitations.mdx#settlement-and-abutment-geometry)). + +Proposed (unconfirmed): the angle from the horizontal of the abutment surface in the longitudinal profile along the dam axis, with the steeper +abutment analyzed, or each abutment analyzed separately. Confirm or replace. +::: + +:::warning[INPUT NEEDED IN-03 — Definition] +The abutment step height $h_1$ is not defined beyond its name. State how the step and its height are to be identified in the abutment profile, +including the reference from which $h_1$ is measured (for example, the height of the step above the valley floor, or the height of the near-vertical +face of the step), so that $h_1/H$ is consistent with the tabulated relative step heights of 0.6, 0.8, and 0.9. +::: + +## Settlement + +The settlement may be entered directly, or estimated from the year of construction when no settlement record is available +(). One of the two must be supplied. + +s', 'Y'], + ['ft or m', 'year'], + ['≥ 0', 'Any year'], + ['From the year of construction', 'Required when no settlement is supplied'], + ]} +/> + +- **Maximum post-construction settlement** $s$ — the settlement of the crest after construction, in the same length unit as the dam height. When + it is supplied, it sets the normalized settlement directly and the year of construction is not used. +- **Year of construction** $Y$ — the year the dam was completed. It is used only when no settlement is supplied, to assign a default normalized + settlement: 0.5 percent of the dam height for a dam completed before 1950, and 0.25 percent for a dam completed in 1950 or later (see + [Flaw Assessment](./04-flaw-assessment.mdx#normalized-settlement)). + +## Observed Continuous Transverse Cracking + +The user states whether continuous transverse cracking has been observed at the crest, with a cause attributable to settlement or unknown (default: +not observed). When it has, the flaw probability is set to 1.0; the strain, crack width, crack depth, and bottom-of-crack elevation are still +computed from the settlement and abutment inputs, so the observation changes Node 1 only (see +[Flaw Assessment](./04-flaw-assessment.mdx#observation-override) and +[Observation Overrides](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/flaw-conventions#observation-overrides) in the +common methods manual). + +## Shared Inputs + +The remaining inputs are those of the CLE crest-crack models, documented in the common methods manual: + +- **Hydraulic loading** — the headwater series and the optional tailwater series + ([Hydraulic Loading](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/input-parameters#hydraulic-loading)). Tailwater + is reported with the results but does not enter the calculation. +- **Embankment type** — homogeneous earthfill, zoned earthfill, or central-core earth and rockfill, which sets the crack-filling probability + ([Embankment Description](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/input-parameters#embankment-description)). + The model takes no slope-segment description of the embankment section. +- **Failure-pathway inputs** — the top-of-filter elevation, the continuation inputs, and the full-pathway and below-filter roof materials of the + crest-crack models + ([Failure-Pathway Inputs](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/input-parameters#failure-pathway-inputs)). + The below-filter materials are taken at the bottom-of-crack elevation that the flaw assessment computes, so the user resolves them after the + crack depth is known. +- **Upstream seepage-limiting elements** — the elements present and the top of any wall + ([Upstream Seepage-Limiting Elements](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/input-parameters#upstream-seepage-limiting-elements)). +- **Intervention and breach** — the probabilities of unsuccessful intervention and of breach, each defaulting to 1.0 + ([Intervention and Breach](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/input-parameters#intervention-and-breach)). diff --git a/docs/web-applications/system-response/cle-cross-valley-settlement-screening/v1.0/04-flaw-assessment.mdx b/docs/web-applications/system-response/cle-cross-valley-settlement-screening/v1.0/04-flaw-assessment.mdx new file mode 100644 index 000000000..59d1bf5d3 --- /dev/null +++ b/docs/web-applications/system-response/cle-cross-valley-settlement-screening/v1.0/04-flaw-assessment.mdx @@ -0,0 +1,420 @@ +--- +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 + +Node 1 of the event tree is the probability $P_{flaw}$ that a continuous transverse crack exists through the embankment. The flaw assessment also +supplies the one flaw quantity the downstream nodes use, the bottom-of-crack elevation $z_{bc}$ +(see [Crest-Crack Models: Bottom of the Crack](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/flaw-conventions#crest-crack-models-bottom-of-the-crack) +in the common methods manual). Unlike the other CLE screening models, the assessment does not score qualitative site factors. It is a chain of +relationships driven by the settlement and the abutment geometry: + +1. The crest settlement is normalized by the dam height. +2. The normalized settlement and the abutment slope, with any abutment step, give the localized tensile strain at the crest. +3. The strain gives the flaw probability and the crack width. +4. The crack width gives the crack depth, and the crack depth gives the bottom-of-crack elevation. + +Every step is deterministic, and every quantity is the same at every pool level. + +:::warning[INPUT NEEDED IN-04 — Engineering Basis] +The flaw assessment treats the settlement (or the year-of-construction default), the dam height, the abutment slope, and the step height as single +values, so the flaw probability, crack width, and crack depth carry no uncertainty and the bottom of the crack is one elevation. State the +engineering basis for this deterministic treatment, or provide the engineering-judgment attribution to state here. + +Proposed (unconfirmed): the inputs are geometric and survey quantities entered as best estimates at the screening stage, and the analyst brackets +their uncertainty by repeating the analysis. Confirm or replace. +::: + +## Normalized Settlement + +When the maximum post-construction settlement $s$ is supplied, the normalized settlement, in percent of the dam height, is + + + +where $H$ is the dam height, in the same length unit as $s$. When no settlement is supplied, the normalized settlement is assigned from the year +of construction $Y$: + + + +A dam completed in 1950 takes the smaller default. A supplied settlement always takes precedence over the year of construction. + +:::warning[INPUT NEEDED IN-05 — Engineering Basis] +The default normalized settlement assigned from the year of construction +(: 0.5 percent of the dam height for a dam completed before 1950, +0.25 percent for a dam completed in 1950 or later) requires an engineering basis. Provide the literature source for the two values and for the +1950 boundary, or the engineering-judgment attribution to state here. + +Proposed (unconfirmed): dams built before about 1950 were generally compacted less thoroughly than later dams and settled more after +construction, so the older dams take the larger default. Confirm or replace. +::: + +## Localized Tensile Strain + +The localized tensile strain $e_L$, in percent, is the measure of crest stretching from which the flaw probability and the crack width are read. +It is interpolated from tables of strain against the normalized settlement $\bar{s}$ and the abutment slope $\theta$. Which tables apply depends on +whether the abutment has a step. + +:::warning[INPUT NEEDED IN-06 — Definition] +State the physical meaning of the localized tensile strain $e_L$: where along the crest and at what depth it applies (for example, the +horizontal tensile strain along the dam axis in the crest region over the abutment), and over what gauge length it is "localized." The tables +below are stated in percent, and the flaw probability and crack width relationships are stated in the same strain. +::: + +### Abutment without a step + +When no step height is entered, the strain is interpolated bilinearly from and +, which tabulate it at eight normalized settlements and seven abutment slopes. +With $\bar{s}_i \le \bar{s} \le \bar{s}_{i+1}$ and $\theta_j \le \theta \le \theta_{j+1}$ on the tabulated axes, + + + +where $e_{i,j}$ is the tabulated strain at normalized settlement $\bar{s}_i$ and slope $\theta_j$. The tables are split at an abutment slope of +35 degrees only to keep them readable; they form one relationship. Like the step tables that follow, they list the normalized settlement by row +and the abutment slope by column. The values of these no-step tables are rounded to three decimal places; the step tables that follow are exact +as shown, to two decimal places. + + + + + +The strain rises with both the normalized settlement and the abutment slope throughout the tables: a steeper abutment, or a larger settlement, +stretches the crest more. + +:::warning[INPUT NEEDED IN-07 — Engineering Basis] +The strain tables for an abutment without a step ( and +) require a literature source, and the bilinear interpolation between their +tabulated values () requires a basis. Provide the source (author, year, title, +publisher or report number, and the figure or table digitized), or the engineering-judgment attribution, and state whether the source presents +the relationship as curves that are to be interpolated linearly in both settlement and slope. +::: + +### Abutment with a step + +When a step height $h_1$ is entered, the strain depends also on the relative step height $r = h_1/H$. Three tables give the strain at relative +step heights of 0.6, 0.8, and 0.9 ( to +), each at six normalized settlements and four abutment slopes. The calculation has +two stages: + +1. Each of the three tables is interpolated bilinearly at $(\bar{s}, \theta)$ as in + , giving the strains $e_{0.6}$, $e_{0.8}$, and $e_{0.9}$. +2. The strain at the dam's relative step height is interpolated linearly through those three values and a fourth point fixed at zero strain for a + relative step height of 0.4: + + + +A relative step height of 0.4 or less takes zero strain, and one of 0.9 or more takes $e_{0.9}$. + + + + + + + +The tables for relative step heights of 0.6 and 0.8 differ only at zero normalized settlement. The step tables are not uniformly higher than the +no-step tables at the same settlement and slope — at zero settlement and a 60-degree slope, for example, the no-step strain is 1.6 percent and the +step strain at a relative step height of 0.6 is 0.75 percent — and the zero-strain point at a relative step height of 0.4 lowers the strain of a +small step further. Entering a step therefore does not necessarily raise the strain above the no-step value, and an entered step height of zero +gives zero strain. + +:::warning[INPUT NEEDED IN-08 — Engineering Basis] +The strain tables for an abutment with a step ( to +) require a literature source, and the linear interpolation over the relative step +height () requires a basis. Provide the source (author, year, title, publisher or +report number, and the figure or table digitized) or the engineering-judgment attribution, and confirm that the tables for relative step heights +of 0.6 and 0.8 are intended to differ only at zero settlement. +::: + +:::warning[INPUT NEEDED IN-09 — Engineering Basis] +The zero-strain point at a relative step height of 0.4 () requires an +engineering basis, and its consequence requires a decision. With it, a step with $h_1/H \le 0.4$ — including an entered step height of zero — +gives zero strain, the smallest flaw probability, and a negligible crack, while the same abutment entered with no step can give a substantial +strain; a step between 0.4 and 0.6 is interpolated toward zero. State the basis for the point, and state how a user should enter an abutment with +a small step (for example, describe no step when $h_1/H \le 0.4$, or take the larger of the step and no-step strains). + +Proposed (unconfirmed): small steps contribute no strain in addition to the baseline abutment geometry, so the point was intended to represent +"no added strain" rather than "no strain." Confirm or replace. +::: + +## Flaw Probability + +The strain, converted from percent to a decimal strain $\varepsilon_L = e_L / 100$, gives the probability of a continuous transverse crack from +the relationship of . That probability, $P_{raw}$, is +the flaw probability from the strain before any observation override (see [Observation Override](#observation-override)). Between two +tabulated points $(\varepsilon_k, P_k)$ the logarithm of the probability is interpolated linearly in the strain: + + + +A strain below the first tabulated point takes $5 \times 10^{-5}$, and one at or above the last takes 1.0. + +-5', + '2 × 10-4', + '1 × 10-3', + '3 × 10-3', + '2 × 10-2', + '1 × 10-1', + '1.0', + ], + ]} +/> + +The source relationship gives one set of probabilities for a pool at or below the period of record (the highest pool of record) and another for +a pool above it. The model adopts the set for a pool above the period of record as the conservative choice and applies it at every pool level +(see marker IN-11 below). + +The last point, at a strain of 0.0443, extends the relationship to a probability of 1.0 beyond its last value of 0.1 at a strain of 0.03. The +strain tables reach at most 3.29 percent without a step and 3.5 percent with one, so the flaw probability from the relationship is at most about +0.16 without a step and about 0.22 with one; a probability of 1.0 arises only from the observation override. + +:::warning[INPUT NEEDED IN-10 — Engineering Basis] +The flaw probability relationship of requires a literature source, including +(1) the tabulated probabilities from a strain of 0.0005 to 0.03, (2) the added point at a strain of 0.0443 with a probability of 1.0, which +extends the relationship beyond its last value of 0.1, (3) the interpolation of the logarithm of probability linearly in strain +(), and (4) the floor of $5 \times 10^{-5}$ held for every smaller strain, +including zero strain. Provide the source (author, year, title, publisher or report number, and the figure or table) or the engineering-judgment +attribution for each. +::: + +:::warning[INPUT NEEDED IN-11 — Engineering Basis] +The source relationship carries two sets of probabilities, one for a pool at or below the period of record and one for a pool above it, and the +model always uses the set for a pool above the period of record, at every pool level. State the engineering basis for always using it — and +whether the at-or-below set should be offered when the pool range of interest has already been experienced — or provide the engineering-judgment +attribution. + +Proposed (unconfirmed): a conservative screening choice, since a crack that existed would likely have revealed itself at pools already +experienced, so the above-record set represents the untested condition. Confirm or replace. +::: + +### Observation override + +When continuous transverse cracking has been observed at the crest, with a cause attributable to settlement or unknown, the flaw probability is set +to 1.0: + + + +The override changes the flaw probability only. The crack width, crack depth, and bottom-of-crack elevation are still computed from the strain, so +the pool level at which the observed crack begins to contribute is set by the settlement and abutment inputs, not by the observed crack. This +follows the common convention for observation overrides (see +[Observation Overrides](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/flaw-conventions#observation-overrides) in the +common methods manual). + +## Crack Width + +The decimal strain also gives the crack width $W$, in millimeters, interpolated linearly from +: + + + +A strain at or below 0.0005 gives a negligible width, and a strain at or above 0.025 gives 75 mm. The crack width is in millimeters whatever the +length unit of the analysis. + + + +:::warning[INPUT NEEDED IN-12 — Engineering Basis] +The crack-width relationship of requires a literature source, including its +linear interpolation (), the negligible width at a strain of 0.0005 and below, +and the width held at 75 mm for every strain above 0.025. Note that the width relationship ends at a strain of 0.025 while the flaw probability +relationship continues to 0.0443. Provide the source (author, year, title, publisher or report number, and the figure or table) or the +engineering-judgment attribution. +::: + +## Crack Depth and Bottom-of-Crack Elevation + +The crack depth $d_c$ follows from the crack width by an empirical relationship attributed to Pierson (2023), fitted with the width in millimeters +and the depth in meters: + + + +where $W$ is the crack width in millimeters and $d_{c,m}$ the crack depth in meters. Over the range of widths the model produces, 0 to 75 mm, the +depth increases with the width, from negligible to about 11.3 m (37.0 ft) at 75 mm. The bottom of the crack is then + + + +as in the common convention for the crest-crack models (see +[Crest-Crack Models: Bottom of the Crack](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/flaw-conventions#crest-crack-models-bottom-of-the-crack)). +A negligible crack width gives a bottom of the crack at the crest, so the pool must rise above the crest before initiation can occur. + +:::warning[INPUT NEEDED IN-13 — Bibliography] +The crack-depth relationship () is attributed to Pierson (2023), whose +bibliographic details are not recorded. Provide the full reference — authors, year, title, journal or publisher, and report number — so that it +can be added to the bibliography and cited here, and confirm that the published form gives the depth in feet as +$d_c = (W/1000)(250 - 1.33\,W)/0.3048$ with the width in millimeters. +::: + +:::warning[INPUT NEEDED IN-14 — Applicability] +The crack depth is not limited by the height of the embankment. Up to about 37 ft (11.3 m) of crack depth is possible, so for a low dam the +bottom-of-crack elevation can fall below the foundation contact, and initiation then begins at the lowest pool evaluated. State whether the crack +depth should be limited to the dam height (or to another bound) or whether the model is not intended for dams lower than the largest crack depth, +and whether the relationship applies to the full range of widths the model produces. +::: + +## Range of the Relationships + +Each relationship is tabulated over a limited range, and an input beyond the range takes the value at the nearer end: + +- **Abutment slope** — tabulated from 15 to 60 degrees. A flatter slope takes the strain at 15 degrees; a steeper one takes the strain at 60 + degrees. +- **Normalized settlement** — tabulated from 0 to 2.5 percent without a step and from 0 to 2 percent with one. A larger settlement takes the strain + at the end of the table. +- **Relative step height** — interpolated from 0.4 to 0.9; see [Abutment with a Step](#abutment-with-a-step). +- **Strain** — the flaw probability is held at $5 \times 10^{-5}$ below a strain of 0.0005 and at 1.0 above 0.0443; the crack width is held + negligible below 0.0005 and at 75 mm above 0.025. + +:::warning[INPUT NEEDED IN-15 — Applicability] +State the range of abutment slopes, normalized settlements, and relative step heights over which the model is applicable. Beyond the tabulated +range the model holds the end value rather than extrapolating, so a slope steeper than 60 degrees or a normalized settlement above 2.5 percent +(2 percent with a step) is assessed as if it were at the end of the table, which may understate the strain. State whether such inputs are outside +the intended use of the model, or whether holding the end value is an accepted screening treatment. +::: + +## Worked Example + + follows the flaw assessment for a dam 60 ft high with its crest at elevation +265 ft, an abutment slope of 35 degrees with no step, and a maximum post-construction settlement of 7 in (0.583 ft), with no observation of +continuous transverse cracking. The analysis is in feet. + + + +In step 2, the slope of 35 degrees is a tabulated value, so the strain is interpolated in settlement only, between 1.0 percent at a normalized +settlement of 0.5 percent and 1.4 percent at 1 percent. In step 3, the strain of 0.01378 lies 0.378 of the way from 0.01 to 0.02, so the +logarithm of the flaw probability lies 0.378 of the way from $\log_{10}(0.003)$ to $\log_{10}(0.02)$. The crack is open from the crest down to +elevation 240.0 ft, and the event tree for the same dam is continued in +[Event Tree](./05-event-tree.mdx#worked-example). diff --git a/docs/web-applications/system-response/cle-cross-valley-settlement-screening/v1.0/05-event-tree.mdx b/docs/web-applications/system-response/cle-cross-valley-settlement-screening/v1.0/05-event-tree.mdx new file mode 100644 index 000000000..c1c0c2595 --- /dev/null +++ b/docs/web-applications/system-response/cle-cross-valley-settlement-screening/v1.0/05-event-tree.mdx @@ -0,0 +1,184 @@ +--- +title: Event Tree +--- + +import Equation from '@site/src/components/Equation'; +import NavContainer from '@site/src/components/NavContainer'; +import TableReference from '@site/src/components/TableReference'; +import TableVertical from '@site/src/components/TableVertical'; + + + +# Event Tree + +The model evaluates the eight-node event tree shared by the CLE screening models at each pool level and multiplies the node probabilities to give +the SRP. The tree, its node questions, and the reasons for its structure are documented in the +[Event Tree](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/event-tree) chapter of the common methods manual. This +chapter states how each node is populated for cross-valley settlement. Every node follows the common treatment of the crest-crack models; the +model adds no node and changes no node rule. + +## Node Summary + + + +### Node 1: Flaw + +$P_{flaw}$ is the result of the flaw assessment, $P_{raw}$ from the localized tensile strain or 1.0 when continuous transverse cracking has +been observed (see [Flaw Assessment](./04-flaw-assessment.mdx#flaw-probability)). It is the same at every pool level. + +### Node 2: Initiation + +Initiation is the headwater gate of the crest-crack models at the bottom-of-crack elevation $z_{bc}$ from the flaw assessment: zero while the pool +is at or below $z_{bc}$, and 1.0 once it rises above it (see +[Crest-Crack Models: Headwater Gate](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/initiation#crest-crack-models-headwater-gate) +in the common methods manual). Tailwater takes no part. Because $z_{bc}$ is the crest elevation less the crack depth, the settlement and abutment +inputs set the pool level at which the SRP rises from negligible. Between strains of 0.0005 and 0.025 (0.05 and 2.5 percent), a larger strain gives a +wider and deeper crack and so a lower pool level at which the SRP rises; at or below 0.0005 the crack width is negligible and the bottom of the +crack stays at the crest; above 0.025 the crack width holds at 75 mm, and the crack depth and that pool level +no longer change (see [Crack Width](./04-flaw-assessment.mdx#crack-width)). + +### Node 3: Continuation + +Where a filter intersects the pathway along the crack, the probability of continuing erosion $P_{ce}$ is evaluated by the shared continuation +method from the filter and base-soil description (see +[Method Selection and Governing Base Soil](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/continuation-screening/v1.0/method-selection-and-governing-base-soil) +in the continuation manual). It applies at pool levels at or below the top-of-filter elevation $z_{tf}$, and at every pool level when the filter +caps the pathway; above the filter's top, and at every pool level when no filter intersects the pathway, continuation is 1.0 (see +[Node 3: Continuation](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/failure-pathway-and-progression#node-3-continuation) +in the common methods manual). + +### Node 4: Progression — Roof Support + +Roof support is the minimum roof-support probability over the below-filter materials at pool levels at or below $z_{tf}$, and over the +full-pathway materials above it or with no filter (see +[Node 4: Progression — Roof Support](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/failure-pathway-and-progression#node-4-progression--roof-support)). +The below-filter materials are those on the pathway from the upstream face to the filter at the bottom-of-crack elevation computed in +[Flaw Assessment](./04-flaw-assessment.mdx#crack-depth-and-bottom-of-crack-elevation). + +### Node 5: Progression — No Crack Filling + +The probability of no crack filling is set by the embankment type and is the same at every pool level (see +[Node 5: Progression — No Crack Filling](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/failure-pathway-and-progression#node-5-progression--no-crack-filling)). + +### Node 6: Progression — No Flow Limitation + +The probability of no flow limitation is the minimum over the upstream elements present. When a top-of-wall elevation $z_{tw}$ is given, the +walls apply only at pool levels at or below it, and only the upstream facing element applies above it (see +[Walls That Stop Below the Crest](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/failure-pathway-and-progression#walls-that-stop-below-the-crest)). + +### Nodes 7 and 8: Unsuccessful Intervention and Breach + +The user-specified probabilities $P_{int}$ and $P_{br}$, each one value at every pool level, defaulting to 1.0 (see +[Nodes 7 and 8](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/event-tree#nodes-7-and-8-unsuccessful-intervention-and-breach)). + +## SRP Computation + +The SRP at each headwater (pool) elevation $h$ — not to be confused with the abutment step height $h_1$ — is the product of the eight node probabilities, as in the common methods manual's +[SRP Computation](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/event-tree#srp-computation): + + + +where: + +- $P_{flaw}$ is the flaw probability of Node 1; +- $P_{init}(h)$ is the initiation probability of Node 2; +- $P_{cont}(h)$ is the continuation probability of Node 3: the probability of continuing erosion $P_{ce}$ from the shared continuation method at + pool levels at or below $z_{tf}$ (at every pool level when the filter caps the pathway), and 1.0 above $z_{tf}$ or when no filter intersects the + pathway; +- $P_{roof}(h)$ is the roof-support probability of Node 4; +- $P_{nf}$ is the probability of no crack filling of Node 5; +- $P_{nl}(h)$ is the probability of no flow limitation of Node 6; +- $P_{int}$ and $P_{br}$ are the probabilities of unsuccessful intervention and of breach of Nodes 7 and 8. + +$P_{init}$, $P_{cont}$, $P_{roof}$, and $P_{nl}$ are evaluated at $h$, and the other nodes are the same at every pool level. Where the product is +zero — for example at and below the bottom of the crack, or wherever a user-specified intervention or breach probability or the continuation +probability is zero — the SRP is reported as a negligibly small value. The tree is evaluated on the headwater +grid of the common methods +([Headwater Grid](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/event-tree#headwater-grid)): every supplied headwater +value and additional levels between them. The bottom of the crack is not inserted into the grid, so the rise of the curve is located to within +one grid interval; supplying headwater values at $z_{bc}$ and just above it places the rise exactly. + +## Elevations Where the Curve Changes + +Three elevations decide where the curve can change: the bottom of the crack $z_{bc}$, the top of the filter $z_{tf}$, and the top of a wall +$z_{tw}$. Because initiation is zero at and below $z_{bc}$, a filter or wall top matters only where it lies above the bottom of the crack: + +- **A filter top at or below $z_{bc}$** — unless the filter caps the pathway, every pool level at which initiation is non-zero is above the + filter's top, so continuation is 1.0 and the full-pathway roof materials govern there. The filter then has no effect on the SRP. +- **A filter top above $z_{bc}$** — between $z_{bc}$ and $z_{tf}$ the below-filter pathway governs, with continuation $P_{ce}$; above $z_{tf}$ the + full pathway governs. The curve can jump up or down at $z_{tf}$, depending on $P_{ce}$ and the two roof-support minimums (see + [Node 3: Continuation](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/failure-pathway-and-progression#node-3-continuation)). +- **A wall top at or below $z_{bc}$** — the walls never apply at a pool level where initiation is non-zero, so only the upstream facing element, + if present, limits flow. +- **A wall top above $z_{bc}$** — between $z_{bc}$ and $z_{tw}$ the walls apply with the other elements present; above $z_{tw}$ the wall credit + drops out and only the upstream facing element, if present, limits flow. The curve rises at $z_{tw}$ unless the facing element alone gives the + same minimum. + +Because the crack depth comes from the flaw assessment, a change in the settlement or abutment inputs can move $z_{bc}$ across a filter or wall top +and so change which of these cases applies. + +## Worked Example + +The dam of the flaw-assessment [worked example](./04-flaw-assessment.mdx#worked-example) has a flaw probability of 0.00614 and a bottom of the +crack at elevation 240.0 ft. Take it as a homogeneous earthfill embankment of silty sand (SM) with no filter on the pathway, no upstream +seepage-limiting element, and the default intervention and breach probabilities +(). + + + +The system response curve is negligible up to elevation 240.0 ft and constant at 0.00522 above it. Adding a modern cutoff wall that reaches the +crest would multiply the SRP above the bottom of the crack by its probability of no flow limitation, 0.001, giving $5.2 \times 10^{-6}$; an +observation of continuous transverse cracking would raise the flaw probability to 1.0 and the SRP above the bottom of the crack to 0.85. diff --git a/docs/web-applications/system-response/cle-cross-valley-settlement-screening/v1.0/06-assumptions-and-limitations.mdx b/docs/web-applications/system-response/cle-cross-valley-settlement-screening/v1.0/06-assumptions-and-limitations.mdx new file mode 100644 index 000000000..3ddb2d5ae --- /dev/null +++ b/docs/web-applications/system-response/cle-cross-valley-settlement-screening/v1.0/06-assumptions-and-limitations.mdx @@ -0,0 +1,110 @@ +--- +title: Assumptions and Limitations +--- + +import NavContainer from '@site/src/components/NavContainer'; + + + +# Assumptions and Limitations + +The cross-valley settlement model applies deliberate simplifications relative to a detailed assessment of transverse cracking and concentrated +leak erosion. They reduce input requirements, and most are designed to avoid false negatives at the screening level; Assumptions 2, 4, 5, and 10 +note where they may not. This chapter lists the assumptions +of the model's flaw assessment. The assumptions it shares with the other CLE screening models — the product form of the event tree, the +headwater grid, the pool-independent flaw probability, the certain initiation of an open crest crack, the pathway gate at the top of the filter, +and the progression tables — are listed in the +[Assumptions and Limitations](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/assumptions-and-limitations) chapter of +the common methods manual, where they are numbered 1 to 4, 7, 9, 15, and 17 to 19. 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. + +## Settlement and Abutment Geometry + +1. **The settlement, the dam height, the abutment slope, and any abutment step are single values.** The flaw assessment carries no uncertainty in + them, and the flaw probability, crack width, and crack depth are each one value. + - *Engineering basis:* Basis requested — see marker IN-04 in [Flaw Assessment](./04-flaw-assessment.mdx). + - *Effect on results:* The SRP reflects the entered geometry exactly; uncertainty in a measured settlement or slope does not spread the result, + and the bottom of the crack is one elevation rather than a range. + - *When it may not hold:* Where the settlement record or the abutment profile is uncertain and the result is sensitive to it; the analysis may + then be repeated at candidate values. +2. **Without a settlement record, the normalized settlement is 0.5 percent of the dam height for a dam completed before 1950 and 0.25 percent for + one completed in 1950 or later.** + - *Engineering basis:* Basis requested — see marker IN-05 in [Flaw Assessment](./04-flaw-assessment.mdx#normalized-settlement). + - *Effect on results:* The default fixes the strain, flaw probability, and crack depth for a given abutment; the two eras differ by a factor of + two in normalized settlement. + - *When it may not hold:* Where the embankment was built by methods atypical of its era, or where it sits on a compressible + foundation and the default may understate the settlement (non-conservative). +3. **One abutment is analyzed.** One abutment slope, and at most one step, describe the abutment geometry. + - *Engineering basis:* Basis requested — see marker IN-02 in [Input Parameters](./03-input-parameters.mdx#abutment-geometry), + which also asks the basis for analyzing one abutment. + - *Effect on results:* The result describes a crack at the abutment entered; a crack at the other abutment is not assessed in the same + analysis. + - *When it may not hold:* Where both abutments are steep or stepped; each may then be analyzed in turn. + +## Localized Tensile Strain + +4. **The localized tensile strain at the crest is a tabulated function of the normalized settlement and the abutment slope, and, with a step, of + the relative step height.** The tables are interpolated linearly, and an input beyond them takes the value at the nearer end. + - *Engineering basis:* Basis requested — see markers IN-07 and IN-08 in + [Flaw Assessment](./04-flaw-assessment.mdx#localized-tensile-strain), and IN-15 in + [Flaw Assessment](./04-flaw-assessment.mdx#range-of-the-relationships) for the range. + - *Effect on results:* The strain rises with settlement and slope within the tables, and is held constant beyond them, so a slope steeper than + 60 degrees or a normalized settlement above the tabulated range does not raise the strain further and may understate it + (non-conservative). + - *When it may not hold:* For abutment profiles that are not well described by one slope and one step, for valleys whose shape concentrates + settlement differently, and for inputs beyond the tabulated range. +5. **A step with a relative height of 0.4 or less contributes zero strain.** The strain is interpolated toward zero between relative step + heights of 0.6 and 0.4. + - *Engineering basis:* Basis requested — see marker IN-09 in [Flaw Assessment](./04-flaw-assessment.mdx#abutment-with-a-step). + - *Effect on results:* Entering a step with a relative height of 0.4 or less, including a step height of zero, gives a strain, flaw + probability, and crack depth no higher — and generally lower — than describing no step for the same abutment slope and settlement + (non-conservative relative to the no-step result). + - *When it may not hold:* Where a small step sits on a steep abutment whose slope alone would produce significant strain. + +## Flaw Probability and Crack Geometry + +6. **The flaw probability is read from the relationship for a pool above the period of record, at every pool level.** + - *Engineering basis:* Basis requested — see marker IN-11 in [Flaw Assessment](./04-flaw-assessment.mdx#flaw-probability). + - *Effect on results:* For pools within the period of record, the flaw probability is no lower than the at-or-below-record set would give, + so the SRP there may be overstated (conservative). + - *When it may not hold:* Where the pool range of interest has been experienced without cracking or leakage; a detailed assessment may then + credit that performance. +7. **The flaw probability is interpolated in the logarithm of probability between tabulated strains, with a floor of 5 × 10-5.** + - *Engineering basis:* Basis requested — see marker IN-10 in [Flaw Assessment](./04-flaw-assessment.mdx#flaw-probability). + - *Effect on results:* Even a strain of zero — from zero settlement on an abutment slope of 15 degrees or + flatter, or from a step with $h_1/H$ of 0.4 or less — gives a flaw probability of 5 × 10-5; within the tabulated strains the + flaw probability does not exceed about 0.16 without a step and about 0.22 with one. + - *When it may not hold:* For strains near the ends of the relationship, where the floor and the added end point control the value. +8. **The crack width is a tabulated function of the strain, and the crack depth follows from the width by an empirical relationship.** + - *Engineering basis:* Pierson (2023) for the width-depth relationship, whose bibliographic details are requested at marker IN-13; the basis of + the width relationship is requested at marker IN-12 (both in + [Flaw Assessment](./04-flaw-assessment.mdx#crack-depth-and-bottom-of-crack-elevation)). + - *Effect on results:* The crack depth, and so the pool level at which the SRP rises, follows the strain: a crack can reach about 37 ft + (11.3 m) below the crest at the largest width, 75 mm. + - *When it may not hold:* Where cracks have been observed and their depth is known, or where the fill's tensile behavior differs from that + underlying the relationships. +9. **The crack depth is not limited by the height of the embankment.** + - *Engineering basis:* Basis requested — see marker IN-14 in + [Flaw Assessment](./04-flaw-assessment.mdx#crack-depth-and-bottom-of-crack-elevation). + - *Effect on results:* For a dam lower than the computed crack depth, the bottom of the crack falls below the base of the embankment and + initiation is certain at every pool level evaluated above it (conservative). + - *When it may not hold:* For low dams, where a crack cannot physically extend below the foundation contact. +10. **An observation of continuous transverse cracking sets the flaw probability to 1.0 but not the crack geometry.** The crack width, depth, and + bottom-of-crack elevation are still computed from the settlement and abutment inputs. + - *Engineering basis:* The common CLE observation convention, under which the override sets Node 1 only (Assumption 7 of the common methods + manual; see [Observation Overrides](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/flaw-conventions#observation-overrides)). + - *Effect on results:* The SRP above the bottom of the crack rises to the product of the downstream nodes, while the elevation at which it + rises stays at the computed bottom of the crack. + - *When it may not hold:* Where the observed cracking extends deeper than the computed crack; the computed bottom of the crack may then place + the rise of the curve too high. + +## Limitations + +- **One crack, one mechanism.** The model assesses one transverse crack formed by cross-valley differential settlement at one abutment. Cracking + from settlement adjacent to a wall or cliff, from desiccation, or from frost is assessed by the corresponding CLE screening models. +- **No crack hydraulics.** Initiation is a gate on the bottom of the crack (see + [Crest-Crack Models: Headwater Gate](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/initiation#crest-crack-models-headwater-gate)); + the crack width is used only to estimate the crack depth, not to compute the flow or shear stress in the crack. +- **Tabulated range.** The strain, flaw probability, and crack width relationships are tabulated over limited ranges, and inputs beyond them take + the end values (see [Range of the Relationships](./04-flaw-assessment.mdx#range-of-the-relationships)). diff --git a/docs/web-applications/system-response/cle-cross-valley-settlement-screening/v1.0/07-output-and-interpretation.mdx b/docs/web-applications/system-response/cle-cross-valley-settlement-screening/v1.0/07-output-and-interpretation.mdx new file mode 100644 index 000000000..0676417fd --- /dev/null +++ b/docs/web-applications/system-response/cle-cross-valley-settlement-screening/v1.0/07-output-and-interpretation.mdx @@ -0,0 +1,89 @@ +--- +title: Output and Interpretation +--- + +import NavContainer from '@site/src/components/NavContainer'; + + + +# Output and Interpretation + +The model reports the SRP at each evaluated pool level together with the probability of each of the eight event-tree nodes, in the form shared by +the CLE crest-crack models, and the results of its flaw assessment. The node results and the system response curve are described in the +[Output and Interpretation](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/output-and-interpretation) chapter of the +common methods manual; this chapter describes the flaw-assessment results and what is specific to reading a cross-valley settlement result. + +## Node Results + +The model reports the results of the crest-crack models (see +[Pool-Independent Results](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/output-and-interpretation#pool-independent-results) +and +[Pool-Dependent Series](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/output-and-interpretation#pool-dependent-series)): + +- **Pool-independent values** — the flaw probability; the roof-support minimums of the full pathway and of the below-filter pathway, each where + that pathway exists; the probability of no crack filling; and the probability of no flow limitation with every listed element applying. +- **Series at each pool level** — the pool levels and tailwater, and the initiation, continuation, roof-support, flow-limitation, + unsuccessful-intervention, and breach probabilities, and the SRP. +- **Continuation results** — when a filter intersects the pathway, the probability of continuing erosion from the shared continuation method and + the filter-evaluation method that set it (see the + [Output and Interpretation](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/continuation-screening/v1.0/output-and-interpretation) chapter of the + continuation manual). + +## Flaw-Assessment Results + +The flaw assessment reports each quantity in its chain, so that every stage can be traced (see [Flaw Assessment](./04-flaw-assessment.mdx)): + +- **Normalized settlement** $\bar{s}$ — in percent of the dam height, from the supplied settlement or the year-of-construction default. +- **Localized tensile strain** $e_L$ — in percent. +- **Crack width** $W$ — in millimeters, whatever the length unit of the analysis. +- **Crack depth** $d_c$ — in the length unit of the analysis. +- **Bottom-of-crack elevation** $z_{bc}$ — in the length unit and datum of the analysis. +- **Observed cracking** — whether the probability of a continuous transverse crack was set to 1.0 by the observation of continuous transverse + cracking. +- **Flaw probability** $P_{flaw}$ — the value used in Node 1. + +When the override applies, the reported strain, width, depth, and bottom of the crack are still those computed from the settlement and abutment +inputs. + +## Reading the System Response Curve + +The curve has the shape of every crest-crack curve (see +[Interpreting the System Response Curve](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/output-and-interpretation#interpreting-the-system-response-curve)): +negligible at and below the bottom of the crack, then piecewise constant, with further jumps possible at the top of a filter and the top of a wall +that lie above the bottom of the crack. Two features are specific to this model: + +- **The flaw-assessment inputs set both the level and the start of the curve.** The settlement and abutment inputs set the strain, and the strain + sets both the flaw probability, which scales the curve, and the crack depth, which sets the pool level at which it rises. Within the tabulated + range, a larger settlement or a steeper abutment gives a larger strain, except with a step whose relative height $h_1/H$ is 0.4 or less, which + holds the strain at zero. A larger strain raises the curve, unless continuous transverse cracking has been observed and the flaw probability is + held at 1.0. It also lowers the pool level at which the curve rises, until the crack width reaches 75 mm at a strain of 2.5 percent; the strain + tables reach 3.29 percent (3.5 percent with a step), so above 2.5 percent a larger strain can still raise the curve but no longer moves its rise. + At or below a strain of 0.05 percent the flaw probability stays at its floor, the crack width is negligible, and the bottom of the crack is at + the crest, so the curve stays negligible at every pool at or below the crest, and a small increase in settlement or slope within that range + changes neither the level nor the rise of the curve. Somewhat larger strains give a shallow but non-zero crack. +- **The observation override raises the curve but does not move its rise.** With continuous transverse cracking observed, the curve above the + bottom of the crack equals the product of the downstream nodes, but it still rises at the computed bottom of the crack. + +## Checking the Result + +Every value of the model can be reproduced by hand, except the continuation probability when the continuation method samples it: + +- **Flaw chain** — the normalized settlement, strain, flaw probability, crack width, and crack depth can be recomputed from the reported inputs + and the tables and relationships of [Flaw Assessment](./04-flaw-assessment.mdx), as in its worked example. +- **Bottom of the crack** — the reported bottom-of-crack elevation equals the crest elevation less the reported crack depth, and the first pool + level with non-zero initiation is the first one above it. +- **Level of the curve** — above the bottom of the crack, the SRP at each pool level equals the product of the node values reported for that pool + level. +- **Plausibility of the crack** — a crack depth comparable to or greater than the dam height, or a bottom of the crack below the foundation, + should be examined, because the crack depth is not limited by the dam height (see marker IN-14 in + [Flaw Assessment](./04-flaw-assessment.mdx#crack-depth-and-bottom-of-crack-elevation)). A settlement or slope at or beyond the end of the + tables is assessed at the end value (see [Range of the Relationships](./04-flaw-assessment.mdx#range-of-the-relationships)). + +## Screening Results Relative to Detailed Analysis + +The model is a screening tool. Its result indicates whether cross-valley settlement cracking warrants detailed analysis; it is not a substitute +for a detailed assessment of transverse cracking. Where the result is significant to a decision, the flaw probability, the crack depth, and the +governing downstream nodes should be re-examined with the settlement record, the abutment profile, and any observed cracking, and the detailed +methods and the judgment of the risk team should replace the screening values (see +[Screening Results Relative to Detailed Analysis](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/output-and-interpretation#screening-results-relative-to-detailed-analysis) +in the common methods manual). diff --git a/docs/web-applications/system-response/cle-cross-valley-settlement-screening/v1.0/_input-needed.md b/docs/web-applications/system-response/cle-cross-valley-settlement-screening/v1.0/_input-needed.md new file mode 100644 index 000000000..f3a28690e --- /dev/null +++ b/docs/web-applications/system-response/cle-cross-valley-settlement-screening/v1.0/_input-needed.md @@ -0,0 +1,169 @@ +# Input Needed — Concentrated Leak Erosion Cross-Valley Settlement Screening (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-01 — Definition — `03-input-parameters.mdx` + +**Regarding:** Definition of the dam height H and the maximum post-construction settlement s. + +**Needed:** The dam height $H$ and the maximum post-construction settlement $s$ (see [Settlement](#settlement)) are used only as the ratio $s/H$, and neither is defined beyond its name. State how each is to be measured: for $H$, whether it is the maximum height of the embankment at the deepest section of the valley, measured from the crest to the lowest foundation contact or to the original ground surface; and for $s$, whether it is the largest crest settlement measured along the crest since the end of construction, and whether it includes settlement of the foundation. + +**Proposed (unconfirmed):** $H$ is the maximum embankment height at the deepest section, and $s$ is the largest crest settlement observed since the end of construction, both from survey records. Confirm or replace. + +**Answer:** + +--- + +## IN-02 — Definition — `03-input-parameters.mdx` + +**Regarding:** Definition and measurement of the abutment slope, which abutment to analyze, and the basis for analyzing one abutment. + +**Needed:** The abutment slope $\theta$ is not defined beyond its name and unit. State how it is measured — for example, the angle of the abutment surface from the horizontal in the cross-valley profile beneath the crest, taken over what height — and which abutment the user should analyze when the two differ (for example, the steeper, or each in turn as separate analyses). Also state the engineering basis for describing the crack with one abutment per analysis (Assumption 3 in `06-assumptions-and-limitations.mdx`). + +**Proposed (unconfirmed):** the angle from the horizontal of the abutment surface in the longitudinal profile along the dam axis, with the steeper abutment analyzed, or each abutment analyzed separately. Confirm or replace. + +**Answer:** + +--- + +## IN-03 — Definition — `03-input-parameters.mdx` + +**Regarding:** Definition and measurement of the abutment step height h1. + +**Needed:** The abutment step height $h_1$ is not defined beyond its name. State how the step and its height are to be identified in the abutment profile, including the reference from which $h_1$ is measured (for example, the height of the step above the valley floor, or the height of the near-vertical face of the step), so that $h_1/H$ is consistent with the tabulated relative step heights of 0.6, 0.8, and 0.9. + +**Answer:** + +--- + +## IN-04 — Engineering Basis — `04-flaw-assessment.mdx` + +**Regarding:** Deterministic treatment of the settlement, dam height, abutment slope, and step height. + +**Needed:** The flaw assessment treats the settlement (or the year-of-construction default), the dam height, the abutment slope, and the step height as single values, so the flaw probability, crack width, and crack depth carry no uncertainty and the bottom of the crack is one elevation. State the engineering basis for this deterministic treatment, or provide the engineering-judgment attribution to state here. + +**Proposed (unconfirmed):** the inputs are geometric and survey quantities entered as best estimates at the screening stage, and the analyst brackets their uncertainty by repeating the analysis. Confirm or replace. + +**Answer:** + +--- + +## IN-05 — Engineering Basis — `04-flaw-assessment.mdx` + +**Regarding:** Default normalized settlement from the year of construction (0.5% before 1950; 0.25% in 1950 or later). + +**Needed:** The default normalized settlement assigned from the year of construction (: 0.5 percent of the dam height for a dam completed before 1950, 0.25 percent for a dam completed in 1950 or later) requires an engineering basis. Provide the literature source for the two values and for the 1950 boundary, or the engineering-judgment attribution to state here. + +**Proposed (unconfirmed):** dams built before about 1950 were generally compacted less thoroughly than later dams and settled more after construction, so the older dams take the larger default. Confirm or replace. + +**Answer:** + +--- + +## IN-06 — Definition — `04-flaw-assessment.mdx` + +**Regarding:** Physical meaning of the localized tensile strain eL. + +**Needed:** State the physical meaning of the localized tensile strain $e_L$: where along the crest and at what depth it applies (for example, the horizontal tensile strain along the dam axis in the crest region over the abutment), and over what gauge length it is "localized." The tables below are stated in percent, and the flaw probability and crack width relationships are stated in the same strain. + +**Answer:** + +--- + +## IN-07 — Engineering Basis — `04-flaw-assessment.mdx` + +**Regarding:** Source of the no-step strain tables and their bilinear interpolation. + +**Needed:** The strain tables for an abutment without a step ( and ) require a literature source, and the bilinear interpolation between their tabulated values () requires a basis. Provide the source (author, year, title, publisher or report number, and the figure or table digitized), or the engineering-judgment attribution, and state whether the source presents the relationship as curves that are to be interpolated linearly in both settlement and slope. + +**Answer:** + +--- + +## IN-08 — Engineering Basis — `04-flaw-assessment.mdx` + +**Regarding:** Source of the with-step strain tables (h1/H = 0.6, 0.8, 0.9) and the interpolation over h1/H. + +**Needed:** The strain tables for an abutment with a step ( to ) require a literature source, and the linear interpolation over the relative step height () requires a basis. Provide the source (author, year, title, publisher or report number, and the figure or table digitized) or the engineering-judgment attribution, and confirm that the tables for relative step heights of 0.6 and 0.8 are intended to differ only at zero settlement. + +**Answer:** + +--- + +## IN-09 — Engineering Basis — `04-flaw-assessment.mdx` + +**Regarding:** Zero-strain point at h1/H = 0.4 and how a small step should be entered. + +**Needed:** The zero-strain point at a relative step height of 0.4 () requires an engineering basis, and its consequence requires a decision. With it, a step with $h_1/H \le 0.4$ — including an entered step height of zero — gives zero strain, the smallest flaw probability, and a negligible crack, while the same abutment entered with no step can give a substantial strain; a step between 0.4 and 0.6 is interpolated toward zero. State the basis for the point, and state how a user should enter an abutment with a small step (for example, describe no step when $h_1/H \le 0.4$, or take the larger of the step and no-step strains). + +**Proposed (unconfirmed):** small steps contribute no strain in addition to the baseline abutment geometry, so the point was intended to represent "no added strain" rather than "no strain." Confirm or replace. + +**Answer:** + +--- + +## IN-10 — Engineering Basis — `04-flaw-assessment.mdx` + +**Regarding:** Source of the strain-to-flaw-probability relationship, its added end point, log-linear interpolation, and floor. + +**Needed:** The flaw probability relationship of requires a literature source, including (1) the tabulated probabilities from a strain of 0.0005 to 0.03, (2) the added point at a strain of 0.0443 with a probability of 1.0, which extends the relationship beyond its last value of 0.1, (3) the interpolation of the logarithm of probability linearly in strain (), and (4) the floor of $5 \times 10^{-5}$ held for every smaller strain, including zero strain. Provide the source (author, year, title, publisher or report number, and the figure or table) or the engineering-judgment attribution for each. + +**Answer:** + +--- + +## IN-11 — Engineering Basis — `04-flaw-assessment.mdx` + +**Regarding:** Use of the above-period-of-record probabilities at every pool level. + +**Needed:** The source relationship carries two sets of probabilities, one for a pool at or below the period of record and one for a pool above it, and the model always uses the set for a pool above the period of record, at every pool level. State the engineering basis for always using it — and whether the at-or-below set should be offered when the pool range of interest has already been experienced — or provide the engineering-judgment attribution. + +**Proposed (unconfirmed):** a conservative screening choice, since a crack that existed would likely have revealed itself at pools already experienced, so the above-record set represents the untested condition. Confirm or replace. + +**Answer:** + +--- + +## IN-12 — Engineering Basis — `04-flaw-assessment.mdx` + +**Regarding:** Source of the strain-to-crack-width relationship. + +**Needed:** The crack-width relationship of requires a literature source, including its linear interpolation (), the negligible width at a strain of 0.0005 and below, and the width held at 75 mm for every strain above 0.025. Note that the width relationship ends at a strain of 0.025 while the flaw probability relationship continues to 0.0443. Provide the source (author, year, title, publisher or report number, and the figure or table) or the engineering-judgment attribution. + +**Answer:** + +--- + +## IN-13 — Bibliography — `04-flaw-assessment.mdx` + +**Regarding:** Bibliographic details of Pierson (2023), the crack width-depth relationship. + +**Needed:** The crack-depth relationship () is attributed to Pierson (2023), whose bibliographic details are not recorded. Provide the full reference — authors, year, title, journal or publisher, and report number — so that it can be added to the bibliography and cited here, and confirm that the published form gives the depth in feet as $d_c = (W/1000)(250 - 1.33\,W)/0.3048$ with the width in millimeters. + +**Answer:** + +--- + +## IN-14 — Applicability — `04-flaw-assessment.mdx` + +**Regarding:** Crack depth not limited by the dam height. + +**Needed:** The crack depth is not limited by the height of the embankment. Up to about 37 ft (11.3 m) of crack depth is possible, so for a low dam the bottom-of-crack elevation can fall below the foundation contact, and initiation then begins at the lowest pool evaluated. State whether the crack depth should be limited to the dam height (or to another bound) or whether the model is not intended for dams lower than the largest crack depth, and whether the relationship applies to the full range of widths the model produces. + +**Answer:** + +--- + +## IN-15 — Applicability — `04-flaw-assessment.mdx` + +**Regarding:** Applicable range of abutment slope, normalized settlement, and relative step height. + +**Needed:** State the range of abutment slopes, normalized settlements, and relative step heights over which the model is applicable. Beyond the tabulated range the model holds the end value rather than extrapolating, so a slope steeper than 60 degrees or a normalized settlement above 2.5 percent (2 percent with a step) is assessed as if it were at the end of the table, which may understate the strain. State whether such inputs are outside the intended use of the model, or whether holding the end value is an accepted screening treatment. + +**Answer:** + +--- diff --git a/src/docConfig.js b/src/docConfig.js index 3aa150ad4..98b7a3e41 100644 --- a/src/docConfig.js +++ b/src/docConfig.js @@ -356,8 +356,9 @@ const docs = [ category: 'web-applications', software: 'system-response', doc_location: 'web-applications/system-response/cle-cross-valley-settlement-screening', - doc_name: 'CLE Cross-Valley Settlement Screening Technical Reference Manual', - active: false, + doc_name: 'Concentrated Leak Erosion Cross-Valley Settlement Screening Technical Reference Manual', + sidebar_label: 'Concentrated Leak Erosion Cross-Valley Settlement Screening', + active: true, draft: true, }, { diff --git a/static/bibliographies/web-applications/system-response/cle-cross-valley-settlement-screening/v1.0/bib.json b/static/bibliographies/web-applications/system-response/cle-cross-valley-settlement-screening/v1.0/bib.json new file mode 100644 index 000000000..e5c80cf3b --- /dev/null +++ b/static/bibliographies/web-applications/system-response/cle-cross-valley-settlement-screening/v1.0/bib.json @@ -0,0 +1,17 @@ +[ + { + "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" + } +]