diff --git a/docs/web-applications/system-response/cle-wall-cliff-settlement-screening/v1.0/00-document-info.mdx b/docs/web-applications/system-response/cle-wall-cliff-settlement-screening/v1.0/00-document-info.mdx new file mode 100644 index 000000000..ed88d4223 --- /dev/null +++ b/docs/web-applications/system-response/cle-wall-cliff-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 Wall/Cliff Settlement Screening Technical Reference Manual +reportSubTitle: System Response Library +reportAuthors: ['Adam Gohs, P.E.'] +reportAbstract: Technical reference documenting the concentrated leak erosion (CLE) wall or cliff 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 near the crest by differential settlement of the embankment against a steep wall or cliff. The probability of a continuous crack is estimated by risk-factor and likelihood-factor scoring of three site factors (the ratio of the bench width to the wall or cliff height, the post-construction settlement ratio, and the abutment slope below the wall or cliff), and the crack depth is estimated from tabulated relationships for the effective wall height and the normalized crack depth. The crack depth sets the headwater level above which initiation is taken as certain. The remaining nodes of the eight-node event tree follow the methods shared by the concentrated leak erosion screening models, which are documented in a companion manual. +reportSubjectTerms: ['CLE', 'Concentrated Leak Erosion', 'Screening', 'Event Tree', 'System Response Probability', 'System Response Curve', 'Differential Settlement', 'Wall', 'Cliff', 'Transverse Cracking', 'Risk Factor', 'Likelihood Factor', 'Crack Depth'] +citationGuide: 'U.S. Army Corps of Engineers, Risk Management Center, Concentrated Leak Erosion Wall/Cliff 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-wall-cliff-settlement-screening/v1.0/00-version-history.mdx b/docs/web-applications/system-response/cle-wall-cliff-settlement-screening/v1.0/00-version-history.mdx new file mode 100644 index 000000000..eeb0b9aba --- /dev/null +++ b/docs/web-applications/system-response/cle-wall-cliff-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-wall-cliff-settlement-screening/v1.0/01-preface.mdx b/docs/web-applications/system-response/cle-wall-cliff-settlement-screening/v1.0/01-preface.mdx new file mode 100644 index 000000000..a0714fadd --- /dev/null +++ b/docs/web-applications/system-response/cle-wall-cliff-settlement-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 concentrated leak erosion (CLE) wall or cliff 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 near the crest, opened by differential settlement of the embankment fill against a steep wall or cliff at an +abutment. 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 in the library. The eight share one event tree and most of its nodes. Those shared methods 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/preface), +and the continuation node is evaluated by the shared 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/preface). +This manual documents what is specific to the wall or cliff settlement mechanism: its flaw assessment, which estimates both the probability of a +continuous crack and the depth of that crack, its inputs, and how it populates the shared event tree. Each shared method is referenced at the +chapter and section that documents it. + +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, 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 this model — the dam geometry, the wall or cliff geometry, and the + settlement information — with units, valid ranges, and defaults, and a guide to the shared inputs documented in the common methods manual. +- **[Flaw Assessment](./04-flaw-assessment.mdx)** — The calculation of the probability of a continuous transverse crack by risk-factor and + likelihood-factor scoring, and of the crack width, effective wall height, crack depth, and bottom-of-crack elevation. +- **[Event Tree](./05-event-tree.mdx)** — How the model populates each of the eight event-tree nodes at each headwater 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 the flaw assessment shapes the system + response curve, how to check a result, and the role of screening results relative to detailed analysis. diff --git a/docs/web-applications/system-response/cle-wall-cliff-settlement-screening/v1.0/02-model-overview.mdx b/docs/web-applications/system-response/cle-wall-cliff-settlement-screening/v1.0/02-model-overview.mdx new file mode 100644 index 000000000..13c4e4256 --- /dev/null +++ b/docs/web-applications/system-response/cle-wall-cliff-settlement-screening/v1.0/02-model-overview.mdx @@ -0,0 +1,153 @@ +--- +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 wall or cliff settlement screening model computes a system response curve for concentrated leak erosion through a transverse crack caused by +differential settlement of the embankment adjacent to a steep wall or cliff. The 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. The curve of SRP values across the range of +headwater levels characterizes the embankment's vulnerability to the mechanism. + +Where embankment fill is placed against a steep wall or cliff at an abutment, the fill settles after construction while the wall or cliff does +not. The resulting differential settlement can open a transverse crack in the embankment near the crest, alongside the wall or cliff. The +mechanism is a crest-crack mechanism: the crack is open at the crest and extends down to a bottom-of-crack elevation, and concentrated leak +erosion can begin once the pool rises above the bottom of the crack. The model takes three site characteristics as the controls on the crack: +the width of any bench at the base of the wall or cliff relative to its height, the post-construction settlement relative to the dam height, and +the slope of the abutment below the wall or cliff. + +## Intended Use + +The model is a screening-level assessment of concentrated leak erosion through a settlement crack adjacent to a wall or cliff. 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 model is designed to avoid underestimating risk at the screening level, so that embankments with a + potential cracking concern at a wall or cliff are flagged for further analysis. +- **Reducing input burden** — The flaw assessment uses four geometric measurements and either a measured settlement or the year of construction. + When the settlement is not known, a default settlement ratio based on the era of construction is used. + +The model is not intended for detailed or semi-quantitative risk assessments. A detailed analysis estimates the crack and its likelihood from the +totality of the site evidence (see [Comparison with Detailed Models](#comparison-with-detailed-models)). + +## How the Model Works + +The model executes the three stages common to the CLE screening models (see the +[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) section of +the common methods manual): + +1. **Flaw assessment** — The model forms two dimensionless ratios, the bench-width ratio (bench width to wall or cliff height) and the normalized + settlement (post-construction settlement as a percentage of the dam height), and scores them, together with the abutment slope below the wall + or cliff, as three likelihood factors. The weighted sum of the scores is converted to the probability of a continuous transverse crack. The + same three quantities then set, through tabulated relationships, the crack width, the effective height of the wall, and the crack depth, and + the crack depth fixes the bottom-of-crack elevation below the crest. The flaw probability and the bottom-of-crack elevation are the same at + every pool level (see [Flaw Assessment](./04-flaw-assessment.mdx)). + +2. **Pathway resolution** — The user resolves the failure pathway along the crack: whether a drain or filter intersects it and where the + filter's top lies, which materials must hold a roof over the enlarging pipe below and above the filter's top, and which upstream + seepage-limiting elements are present and how high any wall reaches (see [Input Parameters](./03-input-parameters.mdx#shared-inputs)). + +3. **Event-tree assembly** — At each headwater level, the model composes the eight node probabilities of the CLE event tree and multiplies them to + produce the SRP. Initiation is certain once the pool rises above the bottom of the crack and zero at or below it. Continuation, roof support, + and flow limitation each depend on where the pool stands relative to the top of the filter and the top of any wall (see + [Event Tree](./05-event-tree.mdx)). + +Every node is deterministic except continuation, which the shared continuation method evaluates by Monte Carlo simulation when a filter +intercepts the pathway and the method's soil classification route applies. + +## Physics Basis + +The model combines the following engineering methods: + +- **Risk-factor and likelihood-factor scoring** of the bench-width ratio, the normalized settlement, and the abutment slope for the probability of + a continuous transverse crack, with the weighted sum mapped to a probability by a log-linear curve (see + [Flaw Assessment](./04-flaw-assessment.mdx) and the + [Risk-Factor and Likelihood-Factor Scoring](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/flaw-conventions#risk-factor-and-likelihood-factor-scoring) + section of the common methods manual) +- **Tabulated crack width and crack depth relationships** in terms of the same three quantities, in which the crack depth is a fraction of an + effective wall height (see [Flaw Assessment](./04-flaw-assessment.mdx#crack-depth)) +- **A headwater gate** at the bottom of the open crack for initiation, shared by the crest-crack CLE models (see 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) +- **Roof-support, crack-filling, and flow-limitation probabilities** from tables by soil classification, embankment type, and upstream + element (see 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) +- **Filter evaluation** for the probability that erosion continues past a filter intersecting the crack, applied through the shared continuation + method (see the + [Model Overview](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/continuation-screening/v1.0/model-overview) chapter of the Continuation (Filter + Evaluation) Screening Technical Reference Manual) + +## Comparison with Detailed Models + +The detailed counterpart of the screening model is a full concentrated leak erosion risk analysis in which the risk team estimates the +likelihood, location, and dimensions of a settlement crack adjacent to the wall or cliff from the totality of the site evidence, informed by the +methods of Fell et al. (2024) . +summarizes the differences. + + + +## Relationship to the Shared CLE Methods + +The model is one of the four crest-crack models of the CLE family, with cross-valley differential settlement, 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 follows every convention of that group: the headwater gate at the bottom of the crack, the per-pool-level gates at +the top of the filter and the top of a wall, and the tabulated progression nodes. What sets it apart is its flaw assessment, which scores the bench-width +ratio, the normalized settlement, and the abutment slope, and derives the crack depth from an effective wall height. It is also one of two models +in the family with no observation override: an observation of cracking does not set its flaw probability (see +[Flaw Assessment](./04-flaw-assessment.mdx#no-observation-override)). + +The model calls no toolbox method. The continuation node is the only delegated calculation, handed to the shared continuation method whenever a +filter intersects the failure pathway (see [Event Tree](./05-event-tree.mdx#node-3-continuation)). + + diff --git a/docs/web-applications/system-response/cle-wall-cliff-settlement-screening/v1.0/03-input-parameters.mdx b/docs/web-applications/system-response/cle-wall-cliff-settlement-screening/v1.0/03-input-parameters.mdx new file mode 100644 index 000000000..85a66d677 --- /dev/null +++ b/docs/web-applications/system-response/cle-wall-cliff-settlement-screening/v1.0/03-input-parameters.mdx @@ -0,0 +1,140 @@ +--- +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 wall or cliff settlement model: the dam geometry, the geometry of the wall or cliff, and the +settlement information. These inputs drive the flaw assessment of [Flaw Assessment](./04-flaw-assessment.mdx). The model's remaining inputs — +hydraulic loading, the embankment type, the failure-pathway inputs, the upstream seepage-limiting elements, and the intervention and breach +probabilities — are shared with the other crest-crack CLE models and 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; [Shared Inputs](#shared-inputs) below lists them and notes how this model uses each. + +All elevations are on one common datum, and every length is in the same unit as the elevations. Every relationship in the flaw assessment is +written in dimensionless ratios — the bench width to the wall or cliff height, and the settlement to the dam height — and the crack depth is a +fraction of the wall or cliff height, so the model gives the same result in any consistent length unit and needs no unit conversion. The one +quantity with a fixed unit is the crack width, reported in millimeters whatever the length unit +(see [Flaw Assessment](./04-flaw-assessment.mdx#crack-width)). + +## Dam and Wall or Cliff Geometry + +c', 'H', 'Hw', 'Wb', 'β1'], + ['elevation', 'length', 'length', 'length', 'degrees'], + ['Any elevation', '> 0', '> 0', '≥ 0', 'Greater than 0 and less than 90'], + ['Required', 'Required', 'Required', 'Required', 'Required'], + ]} +/> + +- **Crest elevation** $z_c$ — the top of the embankment. The crack depth is measured down from it to give the bottom-of-crack elevation (see + [Flaw Assessment](./04-flaw-assessment.mdx#bottom-of-the-crack)). +- **Dam height** $H$ — the height of the embankment. It enters the model only as the denominator of the normalized settlement, and only when a measured + settlement is supplied; under the era default it has no effect. +- **Wall or cliff height** $H_w$ — the height of the steep wall or cliff against which the embankment fill is placed. It is the denominator of + the bench-width ratio and the height of which the effective wall height, and so the crack depth, is a fraction. +- **Bench width** $W_b$ — the width of the bench at the base of the wall or cliff. A bench width of zero states that there is no bench: the fill + rests directly against the full height of the wall or cliff. +- **Abutment slope below the wall or cliff** $\beta_1$ — the inclination, in degrees from horizontal, of the abutment below the wall or cliff. It + is scored as one of the three flaw factors, and it also enters the crack width and effective wall height relationships. Where an embankment has + walls or cliffs on both abutments, the slope supplied is the one below the wall or cliff being evaluated. + +The model checks each geometric input against its own range and does not compare the geometric inputs with one another. In particular, it does not require the wall or +cliff height to be less than the dam height, or the bottom of the crack to lie above the base of the embankment. + +:::warning[INPUT NEEDED IN-01 — Definition] +The geometric definitions of the wall or cliff height $H_w$, the bench width $W_b$, and the abutment slope below the wall or cliff $\beta_1$ +require confirmation, ideally with a reference to the defining sketch. State (1) whether $H_w$ is the full height of the wall or cliff or only the +part in contact with the embankment fill, and whether it may exceed the dam height $H$; (2) where the bench width $W_b$ is measured — horizontally +from the base of the wall or cliff to the edge of the bench — and whether it is measured along or across the dam axis; and (3) which surface +$\beta_1$ describes — the abutment foundation surface between the bench and the valley floor — and how it is measured where that surface is not +planar; and (4) whether the top of the wall or cliff is assumed to be at or near crest level, since the crack depth is measured down from the +crest elevation and the model takes no top-of-wall or top-of-cliff elevation. +::: + +:::warning[INPUT NEEDED IN-02 — Definition] +The physical meaning of the dam height $H$ and the maximum post-construction settlement $s$ requires confirmation. State (1) whether $H$ is the +maximum height of the dam or the height of the embankment at the wall or cliff section; and (2) whether $s$ is the settlement of the crest, at the +wall or cliff section or the maximum along the crest, and over what period it is taken (for example, from the end of construction to the time of +the assessment, or the expected long-term settlement). +::: + +:::warning[INPUT NEEDED IN-03 — Applicability] +State how an embankment with more than one wall or cliff — for example, one on each abutment, or several steps along one abutment — is to be +screened. The model evaluates one wall or cliff geometry per run. + +Proposed (unconfirmed): each wall or cliff is evaluated in its own run with its own geometry and abutment slope, and the run giving the largest +SRP governs the mechanism. Confirm or replace. +::: + +## Settlement Information + +The normalized settlement is formed from a measured post-construction settlement when one is supplied, or from a default ratio selected by the +year of construction when it is not (). At least one of the two inputs +must be supplied. + + + +- **Maximum post-construction settlement** $s$ — the settlement of the embankment after the end of construction, in the same length unit as the + dam height. When it is supplied, the normalized settlement is computed from it and the year of construction is not used by the flaw assessment. +- **Year of construction** $Y$ — the year the dam was completed. It is used only when no settlement is supplied, to select the default normalized + settlement for the era of construction: 0.5 percent 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)). + +The continuation method takes its own year of construction among the continuation inputs, for the filter evaluation (see +[Shared Inputs](#shared-inputs)). The two inputs are separate: the year supplied here does not reach the continuation method. + +## Shared Inputs + +The following inputs are documented in full in the common methods manual. The notes give how this model uses each. + +- **Hydraulic loading** — the headwater series and the optional tailwater series (see + [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)). The + tailwater is reported with the results but does not enter any node of this model. +- **Embankment type** — homogeneous earthfill, zoned earthfill, or central-core earth and rockfill, which sets the crack-filling node (see + [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; its flaw assessment uses only the inputs of this chapter. +- **Failure-pathway inputs** — the top-of-filter elevation, the full-pathway roof materials, the below-filter roof materials, and the + continuation inputs, in the crest-crack form (see + [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 they are listed after that + elevation is known (see [Flaw Assessment](./04-flaw-assessment.mdx#bottom-of-the-crack)). The continuation inputs themselves are documented in + the + [Input Parameters](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/continuation-screening/v1.0/input-parameters) chapter of the Continuation (Filter + Evaluation) Screening Technical Reference Manual. +- **Upstream seepage-limiting elements** — the elements present and, when one is a wall, the top-of-wall elevation (see + [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 (see + [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)). + +The model takes none of the initiation material inputs of the compaction models — no initiation soil classification, critical shear stress, initial +pipe diameter, or seepage path length — because its initiation node is the headwater gate, and it takes no observation of cracking (see +[Flaw Assessment](./04-flaw-assessment.mdx#no-observation-override)). diff --git a/docs/web-applications/system-response/cle-wall-cliff-settlement-screening/v1.0/04-flaw-assessment.mdx b/docs/web-applications/system-response/cle-wall-cliff-settlement-screening/v1.0/04-flaw-assessment.mdx new file mode 100644 index 000000000..74a654caf --- /dev/null +++ b/docs/web-applications/system-response/cle-wall-cliff-settlement-screening/v1.0/04-flaw-assessment.mdx @@ -0,0 +1,463 @@ +--- +title: Flaw Assessment +--- + +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'; + + + +# Flaw Assessment + +The flaw assessment answers two questions about the transverse crack that differential settlement against the wall or cliff can open near the +crest. How likely is a continuous crack through the embankment (Node 1 of the event tree)? And how deep is it, which sets the pool level above +which the crack can carry a concentrated leak (Node 2)? Both answers come from the same three quantities — the bench-width ratio, the normalized +settlement, and the abutment slope below the wall or cliff — and both are the same at every pool level. The calculation proceeds in the order of +this chapter: + +1. Form the bench-width ratio and the normalized settlement. +2. Score the three factors as likelihood factors and form their weighted sum. +3. Convert the weighted sum to the flaw probability. +4. Compute the crack width. +5. Compute the effective wall height and the crack depth, and from the crack depth the bottom-of-crack elevation. + +Steps 2 and 3 apply the risk-factor and likelihood-factor scoring scheme shared by seven of the CLE screening models, documented in the +[Risk-Factor and Likelihood-Factor Scoring](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/flaw-conventions#risk-factor-and-likelihood-factor-scoring) +section of the common methods manual; this chapter documents the factors, bands, and curve of this model. The flaw probability is used directly as +Node 1: the model applies no flaw-continuity stage and no observation override. + +## Normalized Ratios + +### Bench-width ratio + +The bench-width ratio compares the width of the bench at the base of the wall or cliff with the height of the wall or cliff: + + + +where $W_b$ is the bench width and $H_w$ is the wall or cliff height. A ratio of zero describes fill placed directly against the wall or cliff +with no bench; a large ratio describes a wide bench that sets the fill well back from the wall or cliff. + +### Normalized settlement + +The normalized settlement $r_s$ is the post-construction settlement expressed as a percentage of the dam height. When the maximum +post-construction settlement $s$ is supplied, + + + +with $s$ and $H$ in the same length unit. When no settlement is supplied, the normalized settlement takes a default value set by the year of +construction $Y$: + + + +A dam completed in 1950 itself takes the 0.25 percent default. A supplied settlement always takes precedence over the default, whatever the year. + +:::warning[INPUT NEEDED IN-04 — Engineering Basis] +The default normalized settlement used when no settlement is supplied +(: 0.5 percent of the dam height for dams completed before 1950, +0.25 percent for dams completed in 1950 or later, with the year 1950 itself classed with the later dams) requires an engineering basis. Provide the +literature source for the two values and the 1950 boundary (with full bibliographic details if it is not Fell et al. (2024), and the table or +section if it is), or the engineering-judgment attribution to state here. + +Proposed (unconfirmed): the two values represent typical post-construction crest settlements of embankments built before and after the general +adoption of controlled compaction of earthfill, with older, less well compacted embankments settling more. Confirm or replace. +::: + +## Likelihood Factors + +Each of the three flaw factors is scored as a likelihood factor from 1, the condition least likely to produce a continuous crack, to 4, the most +likely, by placing its input in one of four bands (). Each factor carries +a risk factor that weights its score (), following Fell et al. +(2024) : + +- **Cross-valley profile** — scored on the bench-width ratio $r_b$. A narrow bench, or none, scores high; a wide bench scores low. +- **Settlement** — scored on the normalized settlement $r_s$. Larger settlement relative to the dam height scores higher. +- **Abutment slope** — scored on the abutment slope below the wall or cliff $\beta_1$. A steeper slope scores higher. + +b' }, { value: 'Settlement, rs (%)' }, { value: 'Abutment Slope, β1 (°)' }]]} + columns={[ + ['1', '2', '3', '4'], + ['> 2.5', '> 1 to 2.5', '0.25 to 1', 'Less than 0.25'], + ['≤ 0.25', '> 0.25 to 0.75', '> 0.75 to 2', '> 2'], + ['≤ 25', '> 25 to 45', '> 45 to 60', '> 60'], + ]} +/> + +The settlement and abutment slope bands each include their upper limit. The cross-valley profile bands differ: the band for a likelihood factor +of 2 includes its upper limit of 2.5, the band for 3 includes both of its limits, 0.25 and 1, and the band for 4 excludes its upper limit of 0.25. +A bench-width ratio of exactly 2.5 therefore scores 2, and ratios of exactly 1 and exactly 0.25 both score 3. In the source, the cross-valley +bands for 2 and 3 both include a ratio of 1. The model assigns that ratio to the band for 3, the more conservative of the two (a screening design +decision made by engineering judgment), which is why the band for 2 appears in the table as starting above 1. Both era defaults of +the normalized settlement fall in the two lowest settlement bands: the 0.25 percent default of a dam completed in 1950 or later scores 1, and the +0.5 percent default of an earlier dam scores 2. + +b', 'rs', 'β1'], + ['3', '2', '1'], + ['Yes', 'No', 'Yes'], + ]} +/> + +:::warning[INPUT NEEDED IN-05 — Engineering Basis] +The likelihood-factor bands of and the risk factors of + (3 for the cross-valley profile, 2 for settlement, 1 for the abutment +slope) are attributed to Fell et al. (2024). Cite the table or section of Fell et al. (2024) that gives them, and confirm the factor names and +the band limits as printed, including that the source's cross-valley profile bands for likelihood factors of 2 and 3 both include a bench-width +ratio of 1. +::: + +### Weighted sum + +The three scores combine into the weighted sum defined in the +[Weighted Sum](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/flaw-conventions#weighted-sum) section of the common +methods manual: + + + +where $LF_{xv}$, $LF_{s}$, and $LF_{\beta}$ are the likelihood factors of the cross-valley profile, settlement, and abutment slope. Every +likelihood factor of this model is a whole number, so the weighted sum is a whole number between 6 and 24. + +### Incompatible-condition factors + +The cross-valley profile and the abutment slope are incompatible-condition factors (see the +[Flaw Probability from the Weighted Sum](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/flaw-conventions#flaw-probability-from-the-weighted-sum) +section of the common methods manual). When either scores 1 — a bench wider than 2.5 times the wall or cliff height, or an abutment slope of +25° or flatter — the flaw probability is zero whatever the other two factors score. The settlement factor is not an incompatible-condition factor: +a settlement score of 1 lowers the weighted sum but does not by itself rule out a crack. + +Once neither geometric factor scores 1, each scores at least 2, so every weighted sum that reaches the flaw-probability curve lies between 10 and +24, and every whole number in that range can occur. + +:::warning[INPUT NEEDED IN-06 — Engineering Basis] +The rule that a cross-valley profile score of 1 (bench-width ratio greater than 2.5) or an abutment slope score of 1 (slope of 25° or flatter) +forces the flaw probability to zero, while a settlement score of 1 does not, requires an engineering basis. Provide the literature source (the table +or section of Fell et al. (2024), if it is the source) or the engineering-judgment attribution. + +Proposed (unconfirmed): a bench that wide sets the fill far enough from the wall or cliff, and an abutment that flat gives a gradual enough +transition, that the geometry cannot concentrate differential settlement into a continuous transverse crack, whereas some settlement is always +present. Confirm or replace. +::: + +## Flaw Probability + +The weighted sum is converted to the flaw probability $P_{flaw}$ by the curve of +, interpolated with the logarithm of the probability linear in the +weighted sum, as documented in the +[Flaw Probability from the Weighted Sum](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/flaw-conventions#flaw-probability-from-the-weighted-sum) +section of the common methods manual. +The point at a weighted sum of 9 carries a negligible probability. Because no reachable weighted sum is less than 10 and none exceeds 24, the +curve is never held at either end value. + +-3', '5 × 10-3', '2 × 10-2', '2 × 10-1'], + ]} +/> + +Because the weighted sum is a whole number, the flaw probability takes one of fifteen values +(), or zero when an incompatible-condition factor scores 1. The lowest +reachable sum, 10, requires a cross-valley profile score of 2, a settlement score of 1, and an abutment slope score of 2. It lies between the +negligible point at 9 and the point at 11, so its flaw probability is negligible, many orders of magnitude below $1 \times 10^{-3}$, and the SRP +is effectively negligible. + +-3', + '2.2 × 10-3', + '5.0 × 10-3', + '6.3 × 10-3', + '7.9 × 10-3', + '1.0 × 10-2', + '1.3 × 10-2', + ], + ['18', '19', '20', '21', '22', '23', '24', '—'], + [ + '1.6 × 10-2', + '2.0 × 10-2', + '3.2 × 10-2', + '5.0 × 10-2', + '8.0 × 10-2', + '1.3 × 10-1', + '2.0 × 10-1', + '—', + ], + ]} +/> + +One step in the cross-valley profile score moves the weighted sum most: by 3, compared with 2 for the settlement and 1 for the abutment slope. A +score changes only where its input crosses a band limit, and the abutment slope, like the cross-valley profile, forces the flaw probability to +zero on its own when it scores 1. Across the reachable range the flaw probability spans from negligible to 0.2. + +:::warning[INPUT NEEDED IN-07 — Engineering Basis] +The flaw-probability curve of (weighted sums 9, 11, 13, 19, 24 → +negligible, 1 × 10-3, 5 × 10-3, 2 × 10-2, 2 × 10-1) is attributed to Fell et al. (2024). Cite the +table or figure of Fell et al. (2024) that gives it, and state whether the source gives a probability at a weighted sum of 9 (or a lower limit +below which the probability is zero) that the negligible point represents. The general interpolation form is documented, with its basis, in the +[Flaw Probability from the Weighted Sum](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/flaw-conventions#flaw-probability-from-the-weighted-sum) +section of the common methods manual. +::: + +## No Observation Override + +The model has no observation override: an observed transverse crack at the crest does not set the flaw probability to 1.0, and no observation is +taken as an input. The flaw probability is always the scored value. The common methods manual lists the overrides of the other models in its +[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) +section. + +:::warning[INPUT NEEDED IN-08 — Engineering Basis] +The absence of an observation override in this model — where the cross-valley settlement, desiccation, and frost-cracking models each accept an +observation of continuous transverse cracking that sets the flaw probability to 1.0 — requires an engineering basis or a documentation decision to +state here. State why an observed crack adjacent to the wall or cliff is not used to override the scored probability, and what a user who has +observed such a crack should do. +::: + +## Crack Width + +The crack width $w$ is computed in two steps, in millimeters whatever the length unit of the other inputs. First, the crack width for +an abutment slope of 45°, $w_{45}$, is interpolated bilinearly in the normalized settlement and the bench-width ratio from + and , which together form one +table split by bench-width ratio. Second, it is scaled to the abutment slope of the site by an adjustment factor $n_\beta$, interpolated linearly in $\beta_1$ from +: + + + +s (%)' }, + { value: 'rb = 0' }, + { value: 'rb = 0.25' }, + { value: 'rb = 0.5' }, + ]]} + columns={[ + ['0', '0.1', '0.25', '0.5', '1', '2'], + ['1', '5', '12', '25', '50', '100'], + ['1', '4', '10', '20', '40', '80'], + ['1', '2.5', '6', '12', '25', '50'], + ]} +/> + +s (%)' }, + { value: 'rb = 1' }, + { value: 'rb = 2' }, + { value: 'rb = 2.5' }, + ]]} + columns={[ + ['0', '0.1', '0.25', '0.5', '1', '2'], + ['1', '1', '2.5', '5', '10', '20'], + ['1', '1', '1', '1', '2.5', '5'], + ['0', '0', '0', '0', '0', '0'], + ]} +/> + +1 (°)' }, { value: 'Adjustment Factor, nβ' }]]} + columns={[ + ['15', '30', '45', '60'], + ['0.25', '0.75', '1.0', '1.0'], + ]} +/> + +The crack width is a supporting result. It does not enter the crack depth or any node of the event tree: in this model, initiation depends only on +whether the pool stands above the bottom of the crack (see [Event Tree](./05-event-tree.mdx#node-2-initiation)). + +At a bench-width ratio of exactly 2.5 the crack width is zero at every settlement and slope, and between ratios of 2 and 2.5 it falls toward zero. +The other results do not follow it to zero. A ratio of 2.5 still scores a cross-valley profile likelihood factor of 2, so the flaw probability +is not zero unless the abutment slope scores 1, and the effective wall height ratio is held at its value for a ratio of 2, so the crack depth is +not zero either. Initiation is then certain above the bottom of a crack that the width relationship gives as zero width. + +:::warning[INPUT NEEDED IN-09 — Engineering Basis] +The crack width relationships of , , and + are attributed to Fell et al. (2024). Cite the table or figure of +Fell et al. (2024) that gives each, and confirm three details: (1) the position at which the width is defined (for example, the width at the +crest surface); (2) the zero width at a bench-width ratio of 2.5 and the 1 mm width at zero settlement; and (3) that the abutment-slope axis of the +adjustment factor is 15°, 30°, 45°, 60°, where the effective wall height relationship of + and uses 15°, 25°, 45°, 60°. +::: + +## Crack Depth + +The crack depth is a fraction of an effective wall height $H_e$, which is itself a fraction of the wall or cliff height. The effective wall +height ratio $r_e = H_e/H_w$ is interpolated bilinearly in the abutment slope and the bench-width ratio from + and , which together form one +table split by bench-width ratio, and the effective wall height is + + + +1 (°)' }, + { value: 'rb = 0' }, + { value: 'rb = 0.25' }, + { value: 'rb = 0.5' }, + ]]} + columns={[ + ['15', '25', '45', '60'], + ['1', '1', '1', '1'], + ['0.93', '0.88', '0.75', '0.57'], + ['0.87', '0.77', '0.50', '0.14'], + ]} +/> + +1 (°)' }, + { value: 'rb = 1' }, + { value: 'rb = 2' }, + ]]} + columns={[ + ['15', '25', '45', '60'], + ['0.73', '0.54', '0.05', '0.05'], + ['0.46', '0.08', '0.05', '0.05'], + ]} +/> + +With no bench, the effective wall height is the full wall or cliff height at every abutment slope. At each abutment slope the ratio falls, or +stays the same, as the bench widens, and at each bench-width ratio it falls, or stays the same, as the abutment steepens. On the flatter slopes +of 15° and 25° it keeps falling up to a bench-width ratio of 2; on the steeper slopes of 45° and 60° it reaches 0.05 at a ratio of 1 and stays +there. + +The normalized crack depth $r_d = 100\, d_c/H_e$, in percent of the effective wall height, is interpolated linearly in the normalized settlement +from , and the crack depth is + + + +s (%)' }, { value: 'Normalized Crack Depth, rd = dc/He (%)' }]]} + columns={[ + ['0', '0.1', '0.25', '0.5', '1', '2'], + ['15', '50', '65', '90', '100', '100'], + ]} +/> + +The crack reaches the full effective wall height at a normalized settlement of 1 percent or more. At zero settlement the crack depth is still 15 +percent of the effective wall height: the relationship assigns a crack depth even where the settlement factor scores 1. The two era defaults give +65 percent (0.25 percent settlement) and 90 percent (0.5 percent settlement) of the effective wall height. + +Combining and +, the crack depth is the wall or cliff height multiplied by two +dimensionless ratios, which is why the result does not depend on the length unit. The crack depth can be no greater than the wall or cliff height. + +:::warning[INPUT NEEDED IN-10 — Engineering Basis] +The effective wall height relationship of and +, and the normalized crack depth +relationship of , are attributed to Fell et al. (2024). Cite the table or +figure of Fell et al. (2024) that gives each, confirm the definition of the effective wall height $H_e$, and confirm that a crack depth of 15 +percent of the effective wall height is intended at zero settlement. +::: + +## Bottom of the Crack + +The bottom-of-crack elevation is the crest elevation less the crack depth, as for every crest-crack model. The crack depth is measured down from +the crest whatever the elevation of the top of the wall or cliff; the model takes no top-of-wall or top-of-cliff elevation (see marker IN-01 in +[Input Parameters](./03-input-parameters.mdx#dam-and-wall-or-cliff-geometry)). The convention is documented in the +[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) +section of the common methods manual: + + + +It is the initiation gate of the event tree, and the elevation at which the below-filter roof materials are taken (see +[Event Tree](./05-event-tree.mdx)). It is computed whenever the inputs are valid, including when an incompatible-condition factor forces the flaw +probability to zero; the SRP is then negligible at every pool level regardless of the crack depth. + +## Range of the Tabulated Relationships + +The crack width, effective wall height, and crack depth relationships are tabulated over normalized settlements from 0 to 2 percent, bench-width +ratios from 0 to 2.5 (0 to 2 for the effective wall height), and abutment slopes from 15° to 60°. Beyond the tabulated range of an input, each +relationship takes its value at the nearest tabulated edge of that input; it is not extrapolated. In particular: + +- A normalized settlement above 2 percent gives the crack width and depth of 2 percent: the crack depth is the full effective wall height. +- An abutment slope steeper than 60° gives the values of 60°, and a slope flatter than 15° gives the values of 15° (such a slope also forces the + flaw probability to zero through the abutment slope factor). +- A bench-width ratio above 2 gives the effective wall height ratio of 2; above 2.5 the cross-valley profile factor also forces the flaw + probability to zero. + +The likelihood-factor bands of have no such limit: their outer bands +are open-ended. + +:::warning[INPUT NEEDED IN-11 — Applicability] +State whether the model is intended for inputs beyond the tabulated range of the crack width and depth relationships — in particular normalized +settlements above 2 percent and abutment slopes steeper than 60° — where the relationships are held at their edge values, and whether a caution +on such results belongs here. +::: + +## Worked Example + +For an embankment of height $H = 100$ ft against a wall of height $H_w = 40$ ft with a bench width $W_b = 10$ ft, a measured post-construction +settlement $s = 0.5$ ft, and an abutment slope $\beta_1 = 50°$: + +1. **Normalized ratios** — $r_b = 10 / 40 = 0.25$ and $r_s = 100 \times 0.5 / 100 = 0.5$ percent. +2. **Likelihood factors** — the cross-valley profile scores 3 ($0.25 \le r_b \le 1$), the settlement scores 2 ($0.25 < r_s \le 0.75$), and the + abutment slope scores 3 ($45° < \beta_1 \le 60°$). Neither incompatible-condition factor scores 1. +3. **Flaw probability** — $\Sigma = 3 \times 3 + 2 \times 2 + 1 \times 3 = 16$, which gives $P_{flaw} = 1.0 \times 10^{-2}$. +4. **Crack width** — $w_{45} = 20$ mm at $r_s = 0.5$ percent and $r_b = 0.25$, and $n_\beta = 1.0$ at 50°, so $w = 20$ mm. +5. **Crack depth** — the effective wall height ratio $r_e$ at 50° and $r_b = 0.25$ is interpolated between 0.75 at 45° and 0.57 at 60° as 0.69, so + $H_e = 0.69 \times 40 = 27.6$ ft. The normalized crack depth $r_d$ at 0.5 percent settlement is 90 percent, so $d_c = 0.90 \times 27.6 = 24.8$ ft, and + the bottom of the crack lies 24.8 ft below the crest. + + diff --git a/docs/web-applications/system-response/cle-wall-cliff-settlement-screening/v1.0/05-event-tree.mdx b/docs/web-applications/system-response/cle-wall-cliff-settlement-screening/v1.0/05-event-tree.mdx new file mode 100644 index 000000000..eaa38d903 --- /dev/null +++ b/docs/web-applications/system-response/cle-wall-cliff-settlement-screening/v1.0/05-event-tree.mdx @@ -0,0 +1,178 @@ +--- +title: Event Tree +--- + +import Equation from '@site/src/components/Equation'; +import EquationReference from '@site/src/components/EquationReference'; +import NavContainer from '@site/src/components/NavContainer'; +import TableVertical from '@site/src/components/TableVertical'; + + + +# Event Tree + +The model computes the SRP at each headwater level from the eight-node event tree shared by the CLE screening models. The tree, its node +questions, its relationship to the trees of the Typical Event Tree Database, and the headwater grid on which it is evaluated 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 this model populates each node. Nodes 1 and 2 carry the results of this model's flaw assessment; Nodes 3 through 8 follow the +crest-crack conventions of the family without change. + +## Node Summary + + + +## Node 1: Flaw + +*Question:* Does a continuous transverse crack caused by differential settlement against the wall or cliff exist through the embankment? + +The node probability is the flaw probability $P_{flaw}$ of [Flaw Assessment](./04-flaw-assessment.mdx#flaw-probability), the same at every pool +level. No flaw-continuity stage multiplies it and no observation override replaces it. It is zero when the cross-valley profile or the abutment +slope scores a likelihood factor of 1 (see +[Incompatible-Condition Factors](./04-flaw-assessment.mdx#incompatible-condition-factors)). + +## Node 2: Initiation + +*Question:* Is the hydraulic shear stress on the walls of the crack large enough to initiate concentrated leak erosion? + +The model applies the headwater gate of the crest-crack models, documented with its basis 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. With the bottom-of-crack elevation $z_{bc}$ of +, + + + +at each pool level $h$. The crack width plays no part, and neither does tailwater. The crack depth is therefore the controlling quantity of +initiation: a deeper crack lowers the pool level at which the SRP steps up from negligible. In this model the crack depth is proportional to the +wall or cliff height only at a fixed bench-width ratio. With a fixed bench width, a taller wall or cliff also lowers the bench-width ratio and so +raises the effective wall height ratio, or leaves it unchanged; wherever that ratio rises, the crack deepens by more than in proportion to the +height. The crack depth rises, or stays constant, as the normalized settlement increases, and falls, or stays constant, as the bench widens or the +abutment steepens. It stays constant at and above a normalized settlement of 1 percent, at and above a bench-width ratio of 2, and at abutment +slopes of 45° to 60° once the bench-width ratio reaches 1; with no bench, the abutment slope has no effect on it (see +[Crack Depth](./04-flaw-assessment.mdx#crack-depth)). + +## Node 3: Continuation + +*Question:* Does an unfiltered seepage exit exist that allows erosion to continue? + +Continuation follows the crest-crack pathway convention documented in the +[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) +section of the common methods manual. Where a filter intersects the failure pathway, its top elevation $z_{tf}$ gates the node at each pool +level: at or below $z_{tf}$, or at every pool level for a filter that caps the pathway (one whose top reaches the crest, so that no +full-pathway materials are listed), the node takes the probability of continuing erosion $P_{ce}$ computed by the shared continuation method; above $z_{tf}$ it is 1.0. With no filter on the pathway, it is 1.0 at every pool level. + +$P_{ce}$ is computed once, from the filter and the base soils upstream of it, and applies wherever the filter governs. The continuation method +selects, for each base soil, the most informative method its inputs support, and the worst base soil governs (see the +[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) +chapter of the Continuation (Filter Evaluation) Screening Technical Reference Manual). + +## Node 4: Progression — Roof Support + +*Question:* Does a continuous stable roof form over the enlarging pipe, so that it stays open? + +The node is the minimum roof-support probability over the materials that apply at the pool level, as documented in the +[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) +section of the common methods manual. The below-filter materials, taken at the bottom-of-crack elevation, apply at pool levels at or below +$z_{tf}$ (and at every pool level for a filter that caps the pathway, one whose top reaches the crest so that no full-pathway materials are +listed); the full-pathway materials apply above $z_{tf}$, and at every pool level when +no filter is present. Roof support therefore switches at the top of the filter, in step with continuation. + +## Node 5: Progression — No Crack Filling + +*Question:* Does the enlarging pipe remain unfilled, rather than being filled and healed by material carried in from upstream? + +The probability of no crack filling depends only on the embankment type and is the same at every pool level (see the +[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) +section of the common methods manual). + +## Node 6: Progression — No Flow Limitation + +*Question:* Does the flow into the enlarging pipe remain unrestricted by upstream seepage-limiting elements? + +The node is the minimum probability of no flow limitation over the applicable upstream elements, or 1.0 when none applies, gated per pool level at +the top of a wall as documented in the +[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) +section of the common methods manual. At pool levels at or below the top-of-wall elevation $z_{tw}$ every listed element applies; above it the +walls drop out and only an upstream facing element still limits flow. With no top-of-wall elevation, every listed element applies at every pool +level. The upstream wall of Node 6 is a seepage-limiting element on the upstream side of the embankment, distinct from the abutment wall or cliff +whose settlement effect the flaw assessment describes. + +## Nodes 7 and 8: Unsuccessful Intervention and Breach + +*Questions:* Do detection and intervention fail (Node 7)? Does an uncontrolled release of impounded water occur (Node 8)? + +Both nodes are the user-specified probabilities $P_{int}$ and $P_{br}$, each one value at every pool level and each defaulting to 1.0 (see the +[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) +section of the common methods manual). + +## Where the Crack Meets the Pathway Gates + +Three elevations can produce a step in the system response curve: 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 affects the SRP only where it lies above the bottom of +the crack: + +- **Filter top above the bottom of the crack** — between $z_{bc}$ and $z_{tf}$ the SRP carries $P_{ce}$ and the below-filter roof support; above + $z_{tf}$ it carries certain continuation and the full-pathway roof support. The SRP steps at $z_{tf}$, up or down depending on how $P_{ce}$ + compares with the ratio of the full-pathway to the below-filter roof support (see the + [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) + section of the common methods manual). +- **Filter top at or below the bottom of the crack** — at every pool level where initiation is possible the pool is above $z_{tf}$, so continuation + is 1.0 and the full-pathway materials govern; $P_{ce}$ and the below-filter materials have no effect on the SRP. A filter that caps the + pathway — one whose top reaches the crest, so that no full-pathway materials are listed — is the exception: it governs at every pool level. +- **Wall top above the bottom of the crack** — the walls' flow-limitation credit applies from $z_{bc}$ up to $z_{tw}$ and is lost above it. +- **Wall top at or below the bottom of the crack** — only an upstream facing element, if present, limits flow wherever initiation is possible. + +Because the crack depth of this model can approach the full wall or cliff height, the bottom of the crack can lie well below the crest, and a +filter or wall that reaches only partway up the embankment can still lie above it. + +## SRP Computation + +The SRP at each pool level is the product of the eight node probabilities, as documented in the +[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) section of the common +methods manual: + + + +Where the product is zero — at and below the bottom of the crack, or at every pool level when the flaw probability is zero — the SRP is reported as +a negligibly small value rather than zero. Above the bottom of the crack, with initiation equal to 1.0, the SRP at each pool level is the product +of the flaw probability and the progression, intervention, and breach nodes that govern there, and is constant between the steps at $z_{tf}$ and +$z_{tw}$. diff --git a/docs/web-applications/system-response/cle-wall-cliff-settlement-screening/v1.0/06-assumptions-and-limitations.mdx b/docs/web-applications/system-response/cle-wall-cliff-settlement-screening/v1.0/06-assumptions-and-limitations.mdx new file mode 100644 index 000000000..227028cd9 --- /dev/null +++ b/docs/web-applications/system-response/cle-wall-cliff-settlement-screening/v1.0/06-assumptions-and-limitations.mdx @@ -0,0 +1,125 @@ +--- +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 wall or cliff settlement model applies deliberate simplifications relative to a detailed concentrated leak erosion risk analysis. They reduce +input requirements and are designed to avoid false negatives at the screening level. This chapter lists the assumptions specific to this model. +Each assumption 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. + +## Shared Assumptions + +The model also makes the assumptions common to the CLE screening models, documented with their bases 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. Those that apply to this model are the event-tree assumptions (the SRP as the product of the nodes, the single-valued +intervention and breach probabilities, and the headwater grid), the pool-independent flaw probability, the scoring of site factors into a flaw +probability, the certain initiation of an open crest crack above its bottom, and the crest-crack pathway, roof-support, crack-filling, and +flow-limitation conventions. The compaction-model assumptions of that chapter do not apply. + +## Flaw Probability + +1. **The likelihood of a continuous crack is scored from three factors: the bench-width ratio, the normalized settlement, and the abutment slope + below the wall or cliff, with risk factors 3, 2, and 1.** (See [Likelihood Factors](./04-flaw-assessment.mdx#likelihood-factors).) + - *Engineering basis:* The risk-factor and likelihood-factor method of Fell et al. (2024) ; the source of the + bands and weights is requested at marker IN-05 in [Flaw Assessment](./04-flaw-assessment.mdx#likelihood-factors). + - *Effect on results:* One step in the cross-valley profile score moves the weighted sum three times as far as one step in the abutment slope + score, so the bench-width ratio carries the largest risk-factor weight. A score changes only where its input crosses a band limit, and the + abutment slope, like the bench-width ratio, forces the flaw probability to zero on its own when it scores 1. + - *When it may not hold:* Where cracking against the wall or cliff is controlled by conditions the three factors do not describe, such as + irregularities in the face of the wall or cliff or compressible foundation soils beneath the fill. The risk team's estimate then replaces the + screening value. +2. **A bench-width ratio of exactly 1 is scored in the band for a likelihood factor of 3.** + - *Engineering basis:* Screening design decision (engineering judgment): in the source, the cross-valley profile bands for likelihood factors of 2 + and 3 both include a ratio of 1, and the model assigns that ratio to the more conservative of the two (see marker IN-05 in + [Flaw Assessment](./04-flaw-assessment.mdx#likelihood-factors)). + - *Effect on results:* At a ratio of exactly 1 the weighted sum is 3 higher than it would be in the band for 2, which raises the flaw + probability (conservative). + - *When it may not hold:* Not applicable as a site condition; it affects only a ratio at the boundary itself. +3. **A bench wider than 2.5 times the wall or cliff height, or an abutment slope of 25° or flatter, rules out a continuous crack.** Either sets the + flaw probability to zero, whatever the settlement (see + [Incompatible-Condition Factors](./04-flaw-assessment.mdx#incompatible-condition-factors)). + - *Engineering basis:* Basis requested — see marker IN-06 in + [Flaw Assessment](./04-flaw-assessment.mdx#incompatible-condition-factors). + - *Effect on results:* The SRP is negligible at every pool level for such a geometry. + - *When it may not hold:* Where a large settlement or poor compaction against the wall or cliff could crack the embankment despite a wide + bench or a flat abutment; other CLE mechanisms, such as poor compaction adjacent to a wall or cliff, should then be considered (see the CLE Wall/Cliff Compaction Screening Technical Reference Manual). +4. **When the settlement is not known, the normalized settlement defaults to 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 [Normalized Settlement](./04-flaw-assessment.mdx#normalized-settlement).) + - *Engineering basis:* Basis requested — see marker IN-04 in [Flaw Assessment](./04-flaw-assessment.mdx#normalized-settlement). + - *Effect on results:* The later-era default scores a settlement likelihood factor of 1 and gives a crack depth of 65 percent of the effective + wall height; the earlier-era default scores 2 and gives 90 percent. Moving the year of construction across 1950 therefore always changes the + crack depth. It also changes the flaw probability unless an incompatible-condition factor already forces it to zero. + - *When it may not hold:* For embankments with settlement known or suspected to be larger than the default — compressible foundations, poorly + compacted fill, or a history of crest repairs — where a measured settlement should be supplied. +5. **The weighted sum is converted to a flaw probability by a log-linear curve with a negligible point at a weighted sum of 9.** (See + [Flaw Probability](./04-flaw-assessment.mdx#flaw-probability).) + - *Engineering basis:* Fell et al. (2024) ; the source of the curve is requested at marker IN-07 in + [Flaw Assessment](./04-flaw-assessment.mdx#flaw-probability). + - *Effect on results:* The lowest reachable weighted sum, 10, gives a negligible flaw probability, many orders of magnitude below + $1 \times 10^{-3}$, and an effectively negligible SRP; the highest, 24, gives 0.2. + - *When it may not hold:* Where site investigation supports a flaw probability more directly than the factor scores do. +6. **An observation of cracking does not override the scored flaw probability.** (See + [No Observation Override](./04-flaw-assessment.mdx#no-observation-override).) + - *Engineering basis:* Basis requested — see marker IN-08 in + [Flaw Assessment](./04-flaw-assessment.mdx#no-observation-override). + - *Effect on results:* An embankment with an observed transverse crack adjacent to the wall or cliff receives the same flaw probability as one + without it, which may understate the SRP. + - *When it may not hold:* Wherever such a crack has been observed; a detailed assessment should then weigh the observation directly. + +## Crack Geometry + +7. **The crack depth is a tabulated fraction of an effective wall height, which is itself a tabulated fraction of the wall or cliff height.** (See + [Crack Depth](./04-flaw-assessment.mdx#crack-depth).) + - *Engineering basis:* Fell et al. (2024) ; the source of the relationships is requested at marker IN-10 in + [Flaw Assessment](./04-flaw-assessment.mdx#crack-depth). + - *Effect on results:* The crack depth never exceeds the wall or cliff height, reaches the full effective wall height at 1 percent normalized + settlement, and is 15 percent of the effective wall height at zero settlement. A deeper crack lowers the pool level at which the SRP steps up. + - *When it may not hold:* Where the crack depth is known from investigation, such as test pits or trenches at the crest; a detailed analysis + then uses the observed depth. +8. **The crack width, crack depth, and effective wall height relationships take their edge values beyond their tabulated ranges.** (See + [Range of the Tabulated Relationships](./04-flaw-assessment.mdx#range-of-the-tabulated-relationships).) + - *Engineering basis:* Basis requested — see marker IN-11 in + [Flaw Assessment](./04-flaw-assessment.mdx#range-of-the-tabulated-relationships). + - *Effect on results:* A normalized settlement above 2 percent gives the crack depth of 2 percent, the full effective wall height; an abutment + slope steeper than 60° gives the values of 60°. + - *When it may not hold:* For settlements or slopes well outside the tabulated range, where the edge values may not represent the crack. +9. **The crack width does not enter the event tree.** Initiation depends only on whether the pool stands above the bottom of the crack, even + where the crack width is zero. + - *Engineering basis:* The headwater gate of the crest-crack models, documented with its basis 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. + - *Effect on results:* A narrow crack and a wide crack of the same depth give the same SRP. The assumption is conservative for narrow cracks: + it overstates initiation where a narrow crack would not erode. At a bench-width ratio of exactly 2.5 the crack width is zero, yet the flaw + probability and the crack depth are not, so initiation is certain above the bottom of a zero-width crack (see + [Crack Width](./04-flaw-assessment.mdx#crack-width)). + - *When it may not hold:* For narrow cracks in erosion-resistant soils; a crack-geometry initiation analysis then applies. +10. **One wall or cliff geometry is evaluated per run, and the inputs are not checked against one another.** The model does not require the wall or + cliff height to be less than the dam height or the bottom of the crack to lie above the base of the embankment. + - *Engineering basis:* Basis requested — see markers IN-01 and IN-03 in [Input Parameters](./03-input-parameters.mdx#dam-and-wall-or-cliff-geometry). + - *Effect on results:* A wall or cliff height that exceeds the embankment height can place the bottom of the crack below the base of the + embankment, so that initiation is certain at every pool level above that elevation. + - *When it may not hold:* Where the embankment abuts several walls or cliffs, or a wall or cliff taller than the embankment; each geometry and + the height in contact with the fill should then be considered (see marker IN-01). + +## Limitations + +- **Scope of the mechanism** — The model addresses cracking by differential settlement against a steep wall or cliff at an abutment. Poor + compaction of the fill against the wall or cliff is a separate CLE mechanism with its own screening model (see the CLE Wall/Cliff Compaction Screening Technical Reference Manual). +- **Screening-level geometry** — The flaw is described by four measurements and a settlement. Irregular abutment profiles, several benches, or a + wall or cliff whose height varies along the embankment are represented only through the values the user chooses to supply. +- **Deterministic flaw assessment** — The flaw probability and crack depth carry no uncertainty in the inputs. Where an input is uncertain, the + effect can be bracketed by running the model with alternative values. + + diff --git a/docs/web-applications/system-response/cle-wall-cliff-settlement-screening/v1.0/07-output-and-interpretation.mdx b/docs/web-applications/system-response/cle-wall-cliff-settlement-screening/v1.0/07-output-and-interpretation.mdx new file mode 100644 index 000000000..6c28fff9a --- /dev/null +++ b/docs/web-applications/system-response/cle-wall-cliff-settlement-screening/v1.0/07-output-and-interpretation.mdx @@ -0,0 +1,131 @@ +--- +title: Output and Interpretation +--- + +import Citation from '@site/src/components/Citation'; +import CitationFootnote from '@site/src/components/CitationFootnote'; +import EquationNoRef from '@site/src/components/EquationNoRef'; +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, and the intermediate +results of its flaw assessment. The node results take the form common to the crest-crack CLE models, documented 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 summarizes them and documents the flaw-assessment results and how they shape the curve. + +## Node Results + +**Pool-independent results:** + +- **Flaw probability** — Node 1, the scored flaw probability of [Flaw Assessment](./04-flaw-assessment.mdx#flaw-probability). +- **Crack-filling probability** — Node 5, the probability of no crack filling for the embankment type. +- **Flow-limitation probability** — the minimum across all listed upstream elements, or 1.0 when none is listed. It is the Node 6 value at pool + levels at or below the top of a wall, and at every pool level when no top-of-wall elevation is given. +- **Roof-support probabilities** — the minimum across the full-pathway materials, not applicable for a filter that caps the pathway (one whose + top reaches the crest, so that no full-pathway materials are listed), and the minimum across the below-filter materials, not applicable when no + filter is present. + +**Pool-dependent series**, evaluated at every pool level of the headwater grid (see the +[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) +section of the common methods manual): + +- **Pool levels and tailwater** — the evaluated headwater elevations and the tailwater at each. Tailwater is reported for reference only; there is + none when no tailwater is given. +- **Initiation probability** — Node 2: zero at and below the bottom of the crack, 1.0 above it. +- **Continuation probability** — Node 3: the continuation method's result at or below the filter's top, and 1.0 above it or where no filter is + present. +- **Roof-support probability** — Node 4: the below-filter or full-pathway value that governs at each pool level. +- **Flow-limitation probability** — Node 6 after any wall has dropped out above its top. +- **Unsuccessful-intervention and breach probabilities** — Nodes 7 and 8, the user-specified values. +- **SRP** — the product of the eight nodes: the system response curve. + +When a filter intersects the failure pathway, the continuation method also reports which method it applied to each base soil and the result of +each (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 (Filter Evaluation) Screening Technical Reference Manual). + +## Flaw-Assessment Results + +The flaw assessment reports each intermediate quantity of [Flaw Assessment](./04-flaw-assessment.mdx), so that the calculation can be followed +step by step: + +- **Normalized ratios** — the bench-width ratio $r_b$ and the normalized settlement $r_s$ (in percent), whether measured or the era default. +- **Likelihood factors** — the scores of the cross-valley profile, the settlement, and the abutment slope. +- **Weighted sum** $\Sigma$ — the risk-factor-weighted sum of the three scores. +- **Crack width** $w$ — in millimeters, at the abutment slope of the site. It is a supporting result only and does not enter the event tree. +- **Effective wall height ratio and effective wall height** — $r_e = H_e/H_w$ and $H_e$. +- **Normalized crack depth and crack depth** — $r_d = 100\, d_c/H_e$ (in percent) and $d_c$. +- **Bottom-of-crack elevation** $z_{bc}$ — the initiation gate of the event tree. + +The flaw probability is reported with the node results. It equals the scored value, since the model has no observation override. + +## Interpreting the System Response Curve + +The curve has the piecewise-constant form of every crest-crack model (see the +[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) +section of the common methods manual). It is negligible at and below the bottom of the crack and steps up as soon as the pool rises above it. +Above the bottom of the crack, at each pool level, + + + +with continuation, roof support, and flow limitation taking the values that govern at that pool level. The flaw assessment controls two features +of the curve: + +- **The pool level of the first step** is the bottom of the crack, $z_{bc} = z_c - d_c$. It moves down as the wall or cliff height increases. + It moves down, or stays where it is, as the normalized settlement increases, and moves up, or stays where it is, as the bench widens. It no + longer changes once the normalized settlement reaches 1 percent, once the bench-width ratio reaches 2, or, at abutment slopes of 45° to 60°, + once the bench-width ratio reaches 1. With no bench and a normalized settlement of 1 percent or more, the crack extends + the full height of the wall or cliff below the crest. +- **The height of the curve** scales with the flaw probability, which ranges from negligible to 0.2 (see + [Flaw Probability](./04-flaw-assessment.mdx#flaw-probability)). A flaw probability of zero — a bench wider than 2.5 times the wall or cliff + height, or an abutment slope of 25° or flatter — leaves the curve negligible at every pool level, and the lowest reachable weighted sum, 10, leaves it effectively negligible. + +The bench-width ratio enters both features: a narrower bench raises, or leaves unchanged, the cross-valley profile score and so the flaw +probability, and it raises, or leaves unchanged, the effective wall height and so the crack depth. The normalized settlement likewise raises, or +leaves unchanged, both the settlement score and the crack depth. The abutment slope can act in both directions: a steeper slope raises its score +where it crosses a band limit, and where there is a bench it lowers the effective wall height, or leaves it unchanged, and so makes the crack +shallower or leaves it unchanged. The effective wall height does not change with slope between 45° and 60° at bench-width ratios of 1 or more, +nor beyond 60° or below 15°. + +Further steps occur where the pool crosses the top of a filter or the top of a wall above the bottom of the crack (see +[Where the Crack Meets the Pathway Gates](./05-event-tree.mdx#where-the-crack-meets-the-pathway-gates)). The node series show which node changes +at each step; the common methods manual's +[Reading the Node Breakdown](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/output-and-interpretation#reading-the-node-breakdown) +section describes the typical readings. + +## Checking the Result + +Every node except continuation is deterministic, so the curve can be reproduced from the reported values. The continuation probability itself may +be a Monte Carlo estimate when the continuation method uses its soil classification route. The following checks apply in addition to those of the +[Checking the Result](https://usace-rmc.github.io/RMC-Software-Documentation/docs/web-applications/system-response/cle-common-methods-screening/v1.0/output-and-interpretation#checking-the-result) +section of the common methods manual: + +- **Likelihood factors** — each score can be read against the bands of + [Likelihood Factors](./04-flaw-assessment.mdx#likelihood-factors) from the reported ratios and the abutment slope, and the weighted sum is + $3\,LF_{xv} + 2\,LF_{s} + LF_{\beta}$. +- **Crack depth** — the crack depth equals $(r_d/100) \times r_e \times H_w$ and is no greater than the wall or cliff height; the + bottom of the crack lies that distance below the crest. +- **Era default** — when no settlement was supplied, the normalized settlement is exactly 0.5 or 0.25 percent, according to the year of + construction. +- **Bottom of the crack against the embankment** — the crack depth is a multiple of the wall or cliff height and does not depend on any datum. + Because it is no greater than the wall or cliff height, a bottom of the crack more than the dam height below the crest indicates a wall or cliff + height greater than the dam height; a bottom of the crack below a known foundation elevation can also indicate a dam height inconsistent with + the crest elevation (see [Input Parameters](./03-input-parameters.mdx#dam-and-wall-or-cliff-geometry)). + +## Screening Results Relative to Detailed Analysis + +The model is a screening tool. Its results indicate whether settlement cracking adjacent to a wall or cliff warrants detailed analysis; they are +not a substitute for a detailed assessment. The flaw probability and crack depth come from tabulated relationships in four measurements and a +settlement, the era default stands in for an unknown settlement, and an open crack is taken to initiate erosion as soon as the pool reaches it. +Where a screening result is significant to a decision, the crack likelihood and depth should be re-examined with site-specific information — +settlement records, crest inspections, and investigation at the wall or cliff — and the methods of Fell et al. (2024) +and the judgment of the risk team should replace the screening values. + + diff --git a/docs/web-applications/system-response/cle-wall-cliff-settlement-screening/v1.0/_input-needed.md b/docs/web-applications/system-response/cle-wall-cliff-settlement-screening/v1.0/_input-needed.md new file mode 100644 index 000000000..e93eca4d8 --- /dev/null +++ b/docs/web-applications/system-response/cle-wall-cliff-settlement-screening/v1.0/_input-needed.md @@ -0,0 +1,178 @@ +# Input Needed — Concentrated Leak Erosion Wall/Cliff Settlement 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-01 — Definition — `03-input-parameters.mdx` + +**Regarding:** The geometric definitions of the wall or cliff height Hw, the bench width Wb, +and the abutment slope below the wall or cliff β1. + +**Needed:** (1) Whether Hw is the full height of the wall or cliff or only the part in contact +with the embankment fill, and whether it may exceed the dam height H; (2) where Wb is measured +(horizontally from the base of the wall or cliff to the edge of the bench?) and whether along or +across the dam axis; (3) which surface β1 describes (the abutment foundation surface between the +bench and the valley floor?) and how it is measured where that surface is not planar; (4) +whether the top of the wall or cliff is assumed to be at or near crest level, since the crack +depth is measured down from the crest elevation and the model takes no top-of-wall or +top-of-cliff elevation. A reference to the defining sketch is ideal. + +**Answer:** + +--- + +## IN-02 — Definition — `03-input-parameters.mdx` + +**Regarding:** The dam height H and the maximum post-construction settlement s that form the +normalized settlement s/H. + +**Needed:** (1) Whether H is the maximum dam height or the embankment height at the wall or +cliff section; (2) whether s is the crest settlement at the wall or cliff section or the maximum +along the crest, and over what period it is taken (end of construction to the assessment, or +expected long-term settlement). + +**Answer:** + +--- + +## IN-03 — Applicability — `03-input-parameters.mdx` + +**Regarding:** Screening an embankment with more than one wall or cliff (one on each abutment, +or several steps along one abutment). The model evaluates one wall or cliff geometry per run. + +**Needed:** How such an embankment is to be screened. + +**Proposed (unconfirmed):** Each wall or cliff is evaluated in its own run with its own +geometry and abutment slope, and the run giving the largest SRP governs the mechanism. + +**Answer:** + +--- + +## IN-04 — Engineering Basis — `04-flaw-assessment.mdx` + +**Regarding:** The default normalized settlement used when no settlement is supplied: 0.5 +percent of the dam height for dams completed before 1950, 0.25 percent for dams completed in +1950 or later (the year 1950 itself classed with the later dams). + +**Needed:** Literature source for the two values and the 1950 boundary (full bibliographic +details if not Fell et al. (2024); the table or section if it is), or the engineering-judgment +attribution. + +**Proposed (unconfirmed):** The two values represent typical post-construction crest +settlements of embankments built before and after the general adoption of controlled compaction +of earthfill, with older, less well compacted embankments settling more. + +**Answer:** + +--- + +## IN-05 — Engineering Basis — `04-flaw-assessment.mdx` + +**Regarding:** The likelihood-factor bands (cross-valley profile on Wb/Hw: > 2.5 / > 1 to 2.5 / +0.25 to 1 / < 0.25; settlement on s/H: ≤ 0.25 / > 0.25 to 0.75 / > 0.75 to 2 / > 2 percent; +abutment slope: ≤ 25 / > 25 to 45 / > 45 to 60 / > 60 degrees, scoring 1 to 4) and the risk +factors (3, 2, 1), attributed to Fell et al. (2024). + +**Needed:** The table or section of Fell et al. (2024) that gives them, and confirmation of the +factor names and band limits as printed, including that the source's cross-valley profile +bands for likelihood factors of 2 and 3 both include Wb/Hw = 1 (the model scores 1 as 3). + +**Answer:** + +--- + +## IN-06 — Engineering Basis — `04-flaw-assessment.mdx` + +**Regarding:** The rule that a cross-valley profile score of 1 (Wb/Hw > 2.5) or an abutment +slope score of 1 (β1 ≤ 25°) forces the flaw probability to zero, while a settlement score of 1 +does not. + +**Needed:** Literature source (table or section of Fell et al. (2024), if it is the source) or +the engineering-judgment attribution. + +**Proposed (unconfirmed):** A bench that wide sets the fill far enough from the wall or cliff, +and an abutment that flat gives a gradual enough transition, that the geometry cannot +concentrate differential settlement into a continuous transverse crack, whereas some settlement +is always present. + +**Answer:** + +--- + +## IN-07 — Engineering Basis — `04-flaw-assessment.mdx` + +**Regarding:** The flaw-probability curve: weighted sums 9, 11, 13, 19, 24 → negligible, +1 × 10⁻³, 5 × 10⁻³, 2 × 10⁻², 2 × 10⁻¹, interpolated log-linearly. The lowest reachable +weighted sum is 10. + +**Needed:** The table or figure of Fell et al. (2024) that gives the curve, and whether the +source gives a probability at a weighted sum of 9 (or a lower limit below which the probability +is zero) that the negligible point represents. (The general interpolation form is documented in the +Flaw Probability from the Weighted Sum section of the common methods manual.) + +**Answer:** + +--- + +## IN-08 — Engineering Basis — `04-flaw-assessment.mdx` + +**Regarding:** The absence of an observation override in this model, where the cross-valley +settlement, desiccation, and frost-cracking models each accept an observation of continuous +transverse cracking that sets the flaw probability to 1.0. + +**Needed:** The engineering basis or documentation decision: why an observed crack adjacent to +the wall or cliff is not used to override the scored probability, and what a user who has +observed such a crack should do. + +**Answer:** + +--- + +## IN-09 — Engineering Basis — `04-flaw-assessment.mdx` + +**Regarding:** The crack width relationships: the 6 × 6 table of crack width w45 at an abutment +slope of 45° (mm), printed in two parts split by bench-width ratio, by normalized settlement (0, 0.1, 0.25, 0.5, 1, 2 percent) and bench-width +ratio (0, 0.25, 0.5, 1, 2, 2.5), and the adjustment factor by abutment slope (15°, 30°, 45°, +60° → 0.25, 0.75, 1.0, 1.0), attributed to Fell et al. (2024). + +**Needed:** The table or figure of Fell et al. (2024) that gives each, and confirmation of +(1) where the width is defined (for example, at the crest surface); (2) the zero width at a +bench-width ratio of 2.5 and the 1 mm width at zero settlement; and (3) that the adjustment +factor's slope axis is 15°, 30°, 45°, 60°, where the effective wall height table uses 15°, +25°, 45°, 60°. + +**Answer:** + +--- + +## IN-10 — Engineering Basis — `04-flaw-assessment.mdx` + +**Regarding:** The effective wall height ratio He/Hw (4 × 5 table by abutment slope 15°, 25°, +45°, 60° and bench-width ratio 0, 0.25, 0.5, 1, 2) and the normalized crack depth rd = dc/He (0, 0.1, +0.25, 0.5, 1, 2 percent settlement → 15, 50, 65, 90, 100, 100 percent), attributed to Fell et +al. (2024). + +**Needed:** The table or figure of Fell et al. (2024) that gives each, the definition of the +effective wall height He, and confirmation that a crack depth of 15 percent of He is intended +at zero settlement. + +**Answer:** + +--- + +## IN-11 — Applicability — `04-flaw-assessment.mdx` + +**Regarding:** Inputs beyond the tabulated range of the crack width and depth relationships +(normalized settlement above 2 percent, abutment slopes steeper than 60° or flatter than 15°, +bench-width ratios above 2), where each relationship is held at its edge value. + +**Needed:** Whether the model is intended for such inputs, and whether a caution on such +results belongs in the document. + +**Answer:** + +--- diff --git a/src/docConfig.js b/src/docConfig.js index 3aa150ad4..24c993592 100644 --- a/src/docConfig.js +++ b/src/docConfig.js @@ -364,8 +364,9 @@ const docs = [ category: 'web-applications', software: 'system-response', doc_location: 'web-applications/system-response/cle-wall-cliff-settlement-screening', - doc_name: 'CLE Wall/Cliff Settlement Screening Technical Reference Manual', - active: false, + doc_name: 'Concentrated Leak Erosion Wall/Cliff Settlement Screening Technical Reference Manual', + sidebar_label: 'Concentrated Leak Erosion Wall/Cliff Settlement Screening', + active: true, draft: true, }, { diff --git a/static/bibliographies/web-applications/system-response/cle-wall-cliff-settlement-screening/v1.0/bib.json b/static/bibliographies/web-applications/system-response/cle-wall-cliff-settlement-screening/v1.0/bib.json new file mode 100644 index 000000000..e5c80cf3b --- /dev/null +++ b/static/bibliographies/web-applications/system-response/cle-wall-cliff-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" + } +]