diff --git a/docs/web-applications/system-response/continuation-screening/v1.0/00-document-info.mdx b/docs/web-applications/system-response/continuation-screening/v1.0/00-document-info.mdx new file mode 100644 index 000000000..3aadd3f08 --- /dev/null +++ b/docs/web-applications/system-response/continuation-screening/v1.0/00-document-info.mdx @@ -0,0 +1,40 @@ +--- +title: Document Info +reportDate: October 2026 +reportType: Technical Reference +reportTitle: Continuation (Filter Evaluation) Screening Technical Reference Manual +reportSubTitle: System Response Library +reportAuthors: ['Adam Gohs, P.E.'] +reportAbstract: + Technical reference documenting the continuation (filter evaluation) screening method in the System Response library. The method computes the + probability of continuing erosion at the continuation node of an internal-erosion event tree, given that erosion has initiated in a base soil + upstream of a filter or transition zone. It selects, for each base soil, the most informative of three methods the available information + supports — a year-of-construction prior, a Monte Carlo comparison of the filter with the no-erosion particle retention criterion using soil + classification ranges, or a full-gradation Foster and Fell evaluation — and reports the largest probability across the base soils. The method + is mechanism-neutral and provides a screening-level assessment for internal-erosion failure modes. +reportSubjectTerms: + [ + 'Internal Erosion', + 'Continuation', + 'Filter Evaluation', + 'Particle Retention', + 'Foster and Fell', + 'No-Erosion Criterion', + 'Screening', + 'Event Tree', + 'Monte Carlo', + ] +citationGuide: + 'U.S. Army Corps of Engineers, Risk Management Center, Continuation (Filter Evaluation) 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/continuation-screening/v1.0/00-version-history.mdx b/docs/web-applications/system-response/continuation-screening/v1.0/00-version-history.mdx new file mode 100644 index 000000000..36c30ea9a --- /dev/null +++ b/docs/web-applications/system-response/continuation-screening/v1.0/00-version-history.mdx @@ -0,0 +1,19 @@ +--- +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/continuation-screening/v1.0/01-preface.mdx b/docs/web-applications/system-response/continuation-screening/v1.0/01-preface.mdx new file mode 100644 index 000000000..af33fdc7b --- /dev/null +++ b/docs/web-applications/system-response/continuation-screening/v1.0/01-preface.mdx @@ -0,0 +1,51 @@ +--- +title: Preface +--- + +import NavContainer from '@site/src/components/NavContainer'; + + + +# Preface + +This document provides a technical reference for the continuation (filter evaluation) screening model in the System Response library. The model +computes the probability of continuing erosion — the probability that a filter or transition zone downstream of an eroding base soil fails to +stop the erosion — for the continuation node of an internal-erosion event tree. It is a screening-level model: it accepts whatever filter +information is available, from a construction date alone to full gradation envelopes, and selects the most informative method that information +supports. It is mechanism-neutral, so any internal-erosion screening model whose event tree includes a continuation node can use it. + +The intended audience includes dam and levee safety engineers evaluating whether the model is appropriate for their assessment, and peer reviewers +checking the technical basis of screening-level results. Readers are assumed to have a general background in internal-erosion risk analysis and +filter design — event trees, particle-size distributions, and filter retention criteria — but no familiarity with the software implementation is +required. + +The document covers the model's complete execution pathway: how a method is selected for each base soil from the information supplied, how each +of the three methods computes a probability of continuing erosion, how the results for several base soils are combined into one node probability, +the assumptions made along the way with their engineering bases, the inputs the user provides and the options available, and the results the +model produces. The underlying filter evaluation procedures are documented in the +[Filter Evaluation (Continuation) Toolbox](/docs/toolbox-technical-manuals/internal-erosion-suite/filter-evaluation-continuation/v1.0/preface) +technical manual; this document links the chapter of that manual each step follows and documents only what the screening model adds, fixes, or +simplifies. + +## 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 the full filter evaluation procedure, and how several base soils are treated. +- **[Input Parameters](./03-input-parameters.mdx)** — Every user input: the base soils and their classifications, gradations, dispersivity, and + regrading characteristics; the filter category and gradation; the optional filter segregation adjustment; the confidence interval; and the + year of construction, with units, valid ranges, defaults, and the choices available for each selection. +- **[Method Selection and Governing Base Soil](./04-method-selection-and-governing-base-soil.mdx)** — The rule that selects one of the three + methods (or the no-information default) for each base soil, and how the governing probability of continuing erosion is chosen across base + soils. +- **[Year-of-Construction Method](./05-year-of-construction-method.mdx)** — The probability of continuing erosion assigned from the period in + which the embankment was built. +- **[Soil Classification Method](./06-soil-classification-method.mdx)** — The Monte Carlo comparison of the filter with the no-erosion particle + retention criterion, using particle-size ranges for the base soil classification and the filter category, or values taken from a single + supplied gradation. +- **[Gradation Method](./07-gradation-method.mdx)** — The full filter evaluation from the base and filter gradation envelopes: the derived + regrading characteristics, the particle retention check, the Foster and Fell erosion-boundary evaluation, and the screening-level combination + of its probabilities. +- **[Assumptions and Limitations](./08-assumptions-and-limitations.mdx)** — Each modeling assumption with its engineering basis, its effect on + results, and the conditions under which it may not hold. +- **[Output and Interpretation](./09-output-and-interpretation.mdx)** — The results the model produces, how to read them, how to tell which + method and which base soil govern, and the role of screening results relative to a detailed filter evaluation. diff --git a/docs/web-applications/system-response/continuation-screening/v1.0/02-model-overview.mdx b/docs/web-applications/system-response/continuation-screening/v1.0/02-model-overview.mdx new file mode 100644 index 000000000..9fb65b08e --- /dev/null +++ b/docs/web-applications/system-response/continuation-screening/v1.0/02-model-overview.mdx @@ -0,0 +1,151 @@ +--- +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 continuation screening model computes the probability of continuing erosion $P_{cont}$ for the continuation node of an internal-erosion event +tree. The node asks whether, once erosion has initiated in a base soil, a filter or transition zone downstream of the eroding soil is too coarse +to stop it. $P_{cont}$ is the conditional probability that erosion continues through the filter, given that it has initiated. + +Continuation is the phase of internal erosion in which the relationship between the particle-size distributions of the base soil and the +adjacent filter controls whether erosion will continue. A filter that is fine enough seals against the base soil after little or no erosion; a +filter that is too coarse lets the eroded particles pass, and erosion continues unrestricted (see the +[Background](/docs/toolbox-technical-manuals/internal-erosion-suite/filter-evaluation-continuation/v1.0/background) chapter of the Filter +Evaluation (Continuation) Toolbox manual). + +## Intended Use + +The model is a screening-level assessment of continuation. It serves the continuation node of any internal-erosion screening model, such as the +concentrated leak erosion screening models in the System Response library, and it is independent of the erosion mechanism and of the pool level: +the same filter and base soils give the same $P_{cont}$ at every headwater. The calling screening model decides whether its continuation node +applies — for example, whether a filter lies downstream of the flaw at all — and uses this model only where it does. + +The model is designed around two goals: + +- **Accepting the information that is available** — At the screening stage, filter information ranges from a construction date to full gradation + envelopes for the base soil and the filter. The model accepts any of these and uses the most informative method the information supports, so + better data refines the estimate without changing the inputs a user must otherwise provide. +- **Preventing false negatives** — Two rules resolve missing information in the direction of continuing erosion: when no method can be selected and no + year of construction is supplied, continuation is certain ($P_{cont} = 1.0$), and with several base soils the worst one governs. Not every default does. An undetermined broad + grading is taken as not broadly graded, so a gravelly base soil may not be regraded; a band with more gravel than sand but no more than 50 + percent gravel is held to the sand limit in the broad-grading assessment and may not be regraded; a single gradation used by the soil + classification method is not regraded; the category 3 floor raises the allowable filter $D_{15}$; the gradation method does not count some + erosion; the adjusted filter gradation does not set the probability; and in the gradation method, a filter whose fine band does not extend down + to 15 percent passing gives $P_{cont,j} = 0$ however coarse it is. Each of these can lower $P_{cont}$ (see Assumptions 11, 12, 14, 15, 16, and 20 + and the gradation coverage limitation in [Assumptions and Limitations](./08-assumptions-and-limitations.mdx)). + +The model is not intended to replace a detailed filter evaluation. The full Filter Evaluation (Continuation) Toolbox procedure gives the analyst +control over every step that the screening model fixes or derives automatically (see +[Comparison with Detailed Models](#comparison-with-detailed-models)). + +## How the Model Works + +The model executes three stages: + +1. **Method selection for each base soil** — Each base soil that the filter must protect is paired with the filter, and each pair is assigned the + most informative method its inputs support: the gradation method when both the base soil and the filter have gradation envelopes, the soil + classification method when the base soil's particle sizes and the filter's particle size can each be resolved from a classification, a + category, or a single gradation, and the year-of-construction method otherwise. With none of these inputs, the pair takes $P_{cont} = 1.0$ + (see [Method Selection and Governing Base Soil](./04-method-selection-and-governing-base-soil.mdx)). + +2. **Probability of continuing erosion for each pair** — The selected method computes $P_{cont}$ for the pair: + - The **year-of-construction method** assigns a probability from the period in which the embankment was built + (see [Year-of-Construction Method](./05-year-of-construction-method.mdx)). + - The **soil classification method** compares the filter's $D_{15}$ with the maximum $D_{15}$ allowed by the no-erosion particle retention + criterion over Monte Carlo realizations of the particle sizes, and reports the fraction of realizations in which the filter is too coarse + (see [Soil Classification Method](./06-soil-classification-method.mdx)). + - The **gradation method** runs the full filter evaluation on the gradation envelopes — base-soil regrading, the particle retention check, and + the Foster and Fell erosion-boundary evaluation — and combines the probabilities of excessive and continuing erosion + (see [Gradation Method](./07-gradation-method.mdx)). + +3. **Governing base soil** — The node probability is the largest $P_{cont}$ among the pairs, because the filter must stop erosion of every base + soil it protects (see [Method Selection and Governing Base Soil](./04-method-selection-and-governing-base-soil.mdx)). + +## Engineering Basis + +The model combines the following engineering methods: + +- **The no-erosion particle retention criterion** for filters, which relates the maximum allowable filter $D_{15}$ to the base soil's $D_{85}$ + and fines content by base soil category, with stricter limits for dispersive soils . The soil classification method evaluates it over ranges of particle sizes, and the gradation method + evaluates it on the gradation envelopes. +- **Mathematical regrading of the base soil** to remove the gravel and gap-graded coarse fractions that provide no retention capability for the + finer fraction , with broadly graded soils identified by the coefficients of uniformity and curvature . +- **The Foster and Fell erosion boundaries** for filters coarser than the no-erosion criterion, which divide the range of filter $D_{15}$ into + no-erosion, some-erosion, excessive-erosion, and continuing-erosion zones from continuing erosion filter tests , with representative base soil gradations selected and weighted from the gradation envelope . +- **A year-of-construction prior** for embankments with no filter or base soil information beyond the construction period (the basis of the + assigned values is requested at marker IN-04 in [Year-of-Construction Method](./05-year-of-construction-method.mdx)). + +## Comparison with Detailed Models + +The detailed counterpart of the screening model is the soil-to-soil filter evaluation in the Filter Evaluation (Continuation) Toolbox. The +screening gradation method runs the same sequence of evaluations: the filter and base soil gradations +([Filter Gradation](/docs/toolbox-technical-manuals/internal-erosion-suite/filter-evaluation-continuation/v1.0/filter-gradation) and +[Base Gradation](/docs/toolbox-technical-manuals/internal-erosion-suite/filter-evaluation-continuation/v1.0/base-gradation)), the +[Design for Particle Retention](/docs/toolbox-technical-manuals/internal-erosion-suite/filter-evaluation-continuation/v1.0/design-for-particle-retention) +check, and the [Foster and Fell](/docs/toolbox-technical-manuals/internal-erosion-suite/filter-evaluation-continuation/v1.0/foster-and-fell) +evaluation. The year-of-construction and soil classification methods have no counterpart in the toolbox; they extend the evaluation to cases +where gradations are not available. summarizes the differences. + + + +## Base Soils and the Filter + +The model evaluates one filter against one or more base soils. A base soil is any non-filter material upstream of the filter whose particles the +filter must retain — for example, the core and an upstream shell that an eroding pipe can pass through on its way to the filter. Each base soil +carries its own classification, gradation, dispersivity, and regrading characteristics; the filter's category, gradation, and segregation +characteristics, the confidence interval, and the year of construction are shared by every pair. Because each pair selects its own method, the +pairs of one evaluation may use different methods, and the governing pair identifies both the base soil and the method that set the node +probability (see [Output and Interpretation](./09-output-and-interpretation.mdx)). + + diff --git a/docs/web-applications/system-response/continuation-screening/v1.0/03-input-parameters.mdx b/docs/web-applications/system-response/continuation-screening/v1.0/03-input-parameters.mdx new file mode 100644 index 000000000..37effbf4b --- /dev/null +++ b/docs/web-applications/system-response/continuation-screening/v1.0/03-input-parameters.mdx @@ -0,0 +1,269 @@ +--- +title: Input Parameters +--- + +import Citation from '@site/src/components/Citation'; +import CitationFootnote from '@site/src/components/CitationFootnote'; +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'; + + + +# Input Parameters + +This chapter documents every user input to the continuation screening model. Inputs are organized into five groups: the base soils, the filter, +the optional filter segregation adjustment, the confidence interval for the representative base soil gradations, and the year of construction. +Each group gives the short facts for its quantities in a table, followed by a description of each input and, for selections, a list of the +available choices and what each implies. + +Almost every input is optional. Which inputs are supplied decides which method evaluates each base soil, as described in +[Method Selection and Governing Base Soil](./04-method-selection-and-governing-base-soil.mdx). +lists the inputs each method uses. + + + +## Gradation Envelopes + +A gradation envelope describes the range of particle-size distributions measured for one material. It consists of two bands: + +- **Coarse band** — the coarsest gradation of the material (the coarse limit of the envelope). +- **Fine band** — the finest gradation of the material (the fine limit of the envelope). + +Each band is a table of sieve designations, the corresponding particle sizes in millimeters listed in descending order (sizes finer than the No. +200 sieve may come from a hydrometer analysis), and the percent passing by weight at each size, from 0 to 100 percent. The model performs a +particle-size analysis of each band as described in the +[Filter Gradation](/docs/toolbox-technical-manuals/internal-erosion-suite/filter-evaluation-continuation/v1.0/filter-gradation#filter-gradation) +chapter of the Filter Evaluation (Continuation) Toolbox manual, interpolating particle sizes on a logarithmic scale against percent passing on a +linear scale. A characteristic size such as $D_{15}$ (the particle size at 15 percent passing) is undetermined for a band whose smallest +measured percent passing is greater than that percentage; such a band then cannot supply that size to the soil classification method (see +[Input Resolution](./06-soil-classification-method.mdx#input-resolution) in the Soil Classification Method chapter). + +When only one gradation is available for a material, the same gradation is entered as both bands. Because the gradation method averages the two +bands of the base soil gradation point by point, both bands should be reported at the same sieve sizes (see Assumption 19 in +[Assumptions and Limitations](./08-assumptions-and-limitations.mdx#gradation-method)). + +## Base Soils + +At least one base soil is required. Each base soil is a non-filter material upstream of the filter whose particles the filter must retain +(). Supply one entry for each such material — for example, the core and an upstream +shell — in any order. The order does not affect $P_{cont}$, but when pairs tie for the largest probability, the governing base soil and method +reported are those of the first entered (see +[Governing Base Soil](./04-method-selection-and-governing-base-soil.mdx#governing-base-soil)). A base soil entry with neither a classification nor a gradation is valid and is +evaluated by the year-of-construction method or the no-information default. + +gap', '—'], + ['—', 'mm, %', '—', '—', 'mm', '—'], + [ + 'One of 15 USCS classes', + 'See Gradation Envelopes', + 'Yes or No', + 'Yes or No', + '> 0', + 'Yes, No, or derived', + ], + ['Not supplied', 'Not supplied', 'No', 'No', 'Required when gap graded', 'Derived from the gradation'], + ]} +/> + +- **Soil classification** — The Unified Soil Classification System (USCS) group of the base soil : GP, GW, + GP-GM, GM, GC, SP, SW, SP-SM, SM, SC, ML, CL-ML, CL, MH, or CH. The soil classification method uses the classification to set ranges for the + base soil's $D_{85}$ and fines content, and only nine classes carry those ranges: SM, GM, SC, GC, ML, CL-ML, CL, MH, and CH. When a filter + category other than Unknown is supplied, the model rejects an input set in which any base soil carries one of the other six classes (GP, GW, + GP-GM, SP, SW, or SP-SM) — even when gradations are also supplied that would select the gradation method for it. A clean or slightly silty + sand or gravel base soil is therefore evaluated from its gradation, with its classification left out, or without a filter category (see + [Classification Ranges](./06-soil-classification-method.mdx#classification-ranges) in the Soil Classification Method chapter and Assumption 9 in + [Assumptions and Limitations](./08-assumptions-and-limitations.mdx)). +- **Gradation envelope** — The coarse and fine bands of the base soil gradation (see [Gradation Envelopes](#gradation-envelopes)). With the + filter gradation envelope, it selects the gradation method. Without a filter gradation, it can supply the base soil's $D_{85}$ and fines content + to the soil classification method. +- **Dispersive base soil** (Yes or No) — Whether the base soil is dispersive. A dispersive base soil uses the stricter no-erosion particle + retention criterion in both the soil classification and gradation methods, and the stricter no-erosion boundary in the Foster and Fell + evaluation . +- **Gap graded** (Yes or No, for each band) — Whether the band of the base soil gradation is gap graded. Identifying a gap-graded soil requires + visual examination of the gradation curve and judgment, so the model does not derive it. A gap-graded band is regraded on its missing particle + size (see [Base soil regrading](./07-gradation-method.mdx#base-soil-regrading) in the Gradation Method chapter). +- **Missing particle size** $d_{gap}$ (for each band) — The particle size, in millimeters, at the upper end of the gap, where the gradation curve + has its point of inflection. Required for each band marked gap graded. +- **Broadly graded** (Yes, No, or derived, for each band) — Whether the band of the base soil gradation is broadly graded. When it is not + supplied, the model derives it from the coefficients of uniformity and curvature of the band; a supplied Yes or No replaces the derived value. + Supply it when the gradation does not extend to the 10 percent passing size, because the coefficients, and therefore the derived value, are then + undetermined (see + [Step 2: Base Soil Regrading Characteristics](./07-gradation-method.mdx#step-2-base-soil-regrading-characteristics) in the Gradation Method + chapter). + +The gap-graded, missing-size, and broadly graded inputs affect only the gradation method. Dispersivity affects both the soil classification and +gradation methods. + +## Filter + +The filter is the zone downstream of the base soils that is expected to retain them — a designed filter, a transition zone, or another adjacent +material (). One filter is shared by every base soil. + + + +- **Filter category** — A qualitative description of the filter material, used by the soil classification method to set the range of the + filter's $D_{15}$ when no filter gradation is available: + - Sand — a sand filter. + - Sand with gravel — a sand filter containing gravel. + - Gravel with sand — a gravel filter containing sand. + - Gravel — a gravel filter. + - Unknown — the filter material is not known. An Unknown filter category supplies no filter $D_{15}$, so a pair with no filter gradation falls + to the year-of-construction method or, when no year of construction is supplied, the no-information default ($P_{cont} = 1.0$). + + The $D_{15}$ range for each category is given in + [Classification Ranges](./06-soil-classification-method.mdx#classification-ranges) in the Soil Classification Method chapter. + +:::warning[INPUT NEEDED IN-01 — Definition] +The four filter categories (Sand, Sand with gravel, Gravel with sand, Gravel) are defined in the model only by their names and their filter +$D_{15}$ ranges. Provide the definition of each category — in particular the gravel or sand content that separates Sand from Sand with gravel, +Sand with gravel from Gravel with sand, and Gravel with sand from Gravel — so a user can assign a filter to a category consistently. + +Also state why the filter is described by these categories rather than by USCS classes. + +Proposed (unconfirmed): the categories follow the USCS naming convention for the secondary component, in which a sand "with gravel" contains 15 +percent or more gravel, and a gravel is a soil with more gravel than sand. They may be used in place of USCS classes because a clean sand or +gravel class can fall in either of two categories, depending on its gravel or sand content, which only a gradation can resolve. +::: + +- **Filter gradation envelope** — The coarse and fine bands of the filter gradation (see [Gradation Envelopes](#gradation-envelopes)). With a base + soil gradation envelope, it selects the gradation method for that base soil. Otherwise, it supplies the filter's $D_{15}$ to the soil + classification method in place of the filter category. + +## Filter Segregation Adjustment + +A filter may be coarser in place than its design gradation, because of segregation during placement or washout of its finer fraction by internal +instability. The filter segregation adjustment describes, for each band of the filter gradation, an adjusted gradation after segregation or +washout (), following the +[Filter Gradation After Segregation or Washout](/docs/toolbox-technical-manuals/internal-erosion-suite/filter-evaluation-continuation/v1.0/filter-gradation#filter-gradation-after-segregation-or-washout) +section of the Filter Evaluation (Continuation) Toolbox manual. The adjustment is optional and applies only to the gradation method; each band is +adjusted only when its parameters are supplied. + + + +:::warning[INPUT NEEDED IN-02 — Engineering Basis] +The reshaping exponent $k$ of the gap-graded segregation adjustment defaults to 0.5 and is limited to the range 0.4 to 0.7. Provide a literature +citation (full bibliographic details for the bibliography) or the engineering-judgment attribution for the default and for the range. +::: + +- **Gradation shape** — The shape of the filter band's gradation curve, which selects how the band is reshaped: + - Broadly graded — above the finer-fraction breakpoint, the percent passing is lowered uniformly by $FF \cdot W/100$; below it, the percent + passing is scaled in proportion by $(100 - W)/100$. + - Gap graded — the band is blended linearly above the breakpoint and reshaped below it by a power curve with exponent $k$. +- **Finer fraction** $FF$ — The percent passing at the breakpoint between the coarse and finer fractions of the band (the gap or inflection + point). +- **Washout** $W$ — The percentage of the finer fraction lost to segregation or washout. The adjusted percent passing at the breakpoint is + $FF \cdot (100 - W)/100$. +- **Reshaping exponent** $k$ — The exponent of the power-curve reshape below the breakpoint, used only for a gap-graded band. The 0.4 to 0.7 + range is checked for every adjusted band, including a broadly graded band that does not use $k$. + +The effect of the adjusted gradation on the result is limited: it decides whether the Foster and Fell evaluation runs, but the probabilities are +computed from the original filter gradation (see [Gradation Method](./07-gradation-method.mdx#use-of-the-adjusted-filter-gradation)). + +:::warning[INPUT NEEDED IN-03 — Bibliography] +The reshape relationships of the segregation adjustment (for a broadly graded band, a uniform lowering of the percent passing by +$FF \cdot W/100$ above the breakpoint and a proportional scaling by $(100 - W)/100$ below it; the linear blend above the breakpoint and the +power curve $(D/D_{FF})^k$ below it for a gap-graded band, where $D_{FF}$ is the particle size at the finer fraction) are not documented in the +Filter Evaluation (Continuation) Toolbox manual, which describes the adjustment only conceptually. Provide the source of these relationships (full +bibliographic details for the bibliography), or confirm that they are the toolbox's own formulation and supply the attribution to state. +::: + +## Confidence Interval + +The confidence interval $CI$ sets how the representative base soil gradations of the Foster and Fell evaluation are selected from the base soil +gradation envelope and how their results are weighted (). It applies only to the +gradation method. + + + +- **Confidence interval** $CI$ — The percentage of the base soil gradations considered representative. The coarse and fine representative + gradations each exclude $(100 - CI)/2$ percent of the envelope at its coarse and fine limits. The default of 90 percent follows the + recommendation of Fell et al. (2008) to select representative gradations indicative of the finer 5 percent, the average, and the coarser 5 + percent of the base soil gradations . At 100 percent, the representative coarse and fine gradations + are the bands themselves and receive zero weight in the erosion probabilities + (). Only the coarse and fine representative gradations lose their weight: the + two bands still define the average gradation, and the fine band of the regraded base soil still sets the particle retention check. The toolbox manual uses 100 percent when the representative base soil gradation is entered directly (see the + [Base Soil Characterization](/docs/toolbox-technical-manuals/internal-erosion-suite/filter-evaluation-continuation/v1.0/foster-and-fell#base-soil-characterization) + section of the Foster and Fell chapter); in this model, that gradation is entered as both bands. + +## Year of Construction + +The year of construction is shared by every base soil (). + + + +- **Year of construction** $Y$ — The year the embankment was constructed. It is used by the year-of-construction method for every base soil whose + information supports neither the gradation method nor the soil classification method (see + [Year-of-Construction Method](./05-year-of-construction-method.mdx)). When it is not supplied, those base soils take the no-information default, + $P_{cont} = 1.0$. + + diff --git a/docs/web-applications/system-response/continuation-screening/v1.0/04-method-selection-and-governing-base-soil.mdx b/docs/web-applications/system-response/continuation-screening/v1.0/04-method-selection-and-governing-base-soil.mdx new file mode 100644 index 000000000..fd85b94f8 --- /dev/null +++ b/docs/web-applications/system-response/continuation-screening/v1.0/04-method-selection-and-governing-base-soil.mdx @@ -0,0 +1,106 @@ +--- +title: Method Selection and Governing Base Soil +--- + +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'; + + + +# Method Selection and Governing Base Soil + +The model evaluates each base soil against the filter as a separate pair, selects a method for each pair from the inputs that pair has, and then +combines the pair results into the single probability of continuing erosion $P_{cont}$ for the continuation node. This chapter documents both +rules. The methods themselves are documented in the three chapters that follow. + +## Method Selection for Each Pair + +Each pair is assigned the first method in the following order whose inputs are present. The order runs from the most to the least informative +method, so a pair always uses the best information available to it, and inputs for a lower-priority method are ignored when a higher-priority +method applies. + +1. **Gradation method** — selected when the base soil has a gradation envelope *and* the filter has a gradation envelope (see + [Gradation Method](./07-gradation-method.mdx)). +2. **Soil classification method** — selected when all three of its particle sizes can be resolved for the pair: + - the filter's $D_{15}$, from the coarse band of the filter gradation envelope when one is supplied and its $D_{15}$ is determined, otherwise + from the $D_{15}$ range of the filter category (any category other than Unknown); and + - the base soil's $D_{85}$ and fines content $FC$, together, from the fine band of the base soil gradation envelope when one is supplied and + both values are determined, otherwise from the ranges of the base soil classification. + + If either the filter $D_{15}$ or the base soil pair cannot be resolved from either source, the method is not selected (see + [Soil Classification Method](./06-soil-classification-method.mdx)). +3. **Year-of-construction method** — selected when the year of construction is supplied (see + [Year-of-Construction Method](./05-year-of-construction-method.mdx)). +4. **No-information default** — when neither the gradation method nor the soil classification method can be selected and no year of + construction is supplied, the pair takes $P_{cont} = 1.0$: without information that resolves both the filter and the base soil, the model + cannot credit the filter with stopping erosion. This covers a pair with no information, and also a pair with a full base soil gradation but + no filter information. + +Because the gradation method needs both envelopes, a gradation supplied for only one of the two materials does not select it. That single +gradation can still supply its values to the soil classification method, provided the other material has a classification (for the base soil) +or a category (for the filter). A lone gradation with no classification or category for the other material supplies nothing, and the pair falls +to the year-of-construction method or the default. summarizes the outcomes. + + + +In the table, the second row assumes the base soil gradation determines both $D_{85}$ and $FC$ in its fine band; if it does not, the base soil's +classification ranges are used instead, and without a supported classification the pair falls to the year-of-construction method or, when no +year of construction is supplied, the no-information default ($P_{cont} = 1.0$). Likewise, the third row assumes the filter gradation determines +$D_{15}$ in its coarse band; if it does not, the filter category's range is used instead, and without a category other than Unknown the pair +falls to the year-of-construction method or, when no year is supplied, the no-information default. "Year of +construction, or the default" means the year-of-construction method when the year is supplied, and $P_{cont} = 1.0$ otherwise. + +## Governing Base Soil + +The node probability is the largest pair probability: + + + +where: + +> $P_{cont}$ = probability of continuing erosion for the continuation node +> $P_{cont,j}$ = probability of continuing erosion for the pair formed by base soil $j$ and the filter +> $m$ = number of base soils + +The filter must stop erosion of every base soil it protects, so the base soil it is least able to retain governs. When two or more pairs share +the largest probability, the first of them in the order entered is reported as governing; the node probability is the same whichever is chosen. +The governing pair also identifies the method that produced the node probability (see +[Output and Interpretation](./09-output-and-interpretation.mdx)). + +When no year of construction is supplied, a base soil entry with no classification and no gradation takes the default $P_{cont,j} = 1.0$ and +therefore makes continuation certain for the whole evaluation. A base soil with a classification or a gradation also takes $P_{cont,j} = 1.0$ +when the filter side is unresolved (no filter gradation and no filter category other than Unknown) and no year of construction is supplied. +When a year is supplied, such pairs take the year-of-construction probability instead. diff --git a/docs/web-applications/system-response/continuation-screening/v1.0/05-year-of-construction-method.mdx b/docs/web-applications/system-response/continuation-screening/v1.0/05-year-of-construction-method.mdx new file mode 100644 index 000000000..cb0af85e1 --- /dev/null +++ b/docs/web-applications/system-response/continuation-screening/v1.0/05-year-of-construction-method.mdx @@ -0,0 +1,50 @@ +--- +title: Year-of-Construction Method +--- + +import NavContainer from '@site/src/components/NavContainer'; +import TableReference from '@site/src/components/TableReference'; +import TableVertical from '@site/src/components/TableVertical'; + + + +# Year-of-Construction Method + +The year-of-construction method assigns the probability of continuing erosion from the period in which the embankment was built. It is the least +informative of the three methods and is used for a pair only when neither the gradation method nor the soil classification method can be +selected (see [Method Selection and Governing Base Soil](./04-method-selection-and-governing-base-soil.mdx)). It uses no property of the base +soil or the filter, so every pair evaluated by this method receives the same probability. + +## Calculation + +The method looks up $P_{cont,j}$ from the year of construction $Y$ in . No Monte +Carlo simulation is involved, and the result is a single value. + + 1970 and Y ≤ 1985', 'Y > 1985'], + ['0.9 [INPUT NEEDED]', '0.5 [INPUT NEEDED]', '0.25 [INPUT NEEDED]', '0.1 [INPUT NEEDED]'], + ]} +/> + +:::warning[INPUT NEEDED IN-04 — Engineering Basis] +The four construction periods (before 1950, 1950 to 1970, 1971 to 1985, after 1985) and the probability of continuing erosion assigned to each +(0.9, 0.5, 0.25, and 0.1) require an engineering basis. Provide a literature citation (full bibliographic details for the bibliography) or the +engineering-judgment attribution to state, including the reasoning for each period boundary and for the assigned probabilities. + +Proposed (unconfirmed): the periods follow the development of filter design practice for embankment dams — filters designed before the modern +no-erosion criteria were established from laboratory filter tests in the mid-1980s are progressively more likely to be too coarse to retain the +base soil the earlier they were designed. +::: + +The probability decreases with later construction, so a later year never increases $P_{cont,j}$. Because the method uses only the construction +period, it does not distinguish a fine base soil from a coarse one, a dispersive base soil from a non-dispersive one, or a designed filter from an +adjacent zone that was never intended as one; any of these differences can move the true probability far from the period value. Where +gradations or classifications are available, the soil classification and gradation methods take precedence automatically, provided the filter +side is also resolved, through a filter gradation or a filter category other than Unknown. A base soil gradation or classification with neither +still falls to this method. diff --git a/docs/web-applications/system-response/continuation-screening/v1.0/06-soil-classification-method.mdx b/docs/web-applications/system-response/continuation-screening/v1.0/06-soil-classification-method.mdx new file mode 100644 index 000000000..e28eb8452 --- /dev/null +++ b/docs/web-applications/system-response/continuation-screening/v1.0/06-soil-classification-method.mdx @@ -0,0 +1,206 @@ +--- +title: Soil Classification Method +--- + +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'; + + + +# Soil Classification Method + +**Step served:** the probability of continuing erosion $P_{cont,j}$ for a pair whose base soil and filter lack a complete pair of gradation +envelopes, but whose base soil particle sizes and filter particle size can each be resolved from a classification, a category, or a single +gradation (see [Method Selection and Governing Base Soil](./04-method-selection-and-governing-base-soil.mdx)). + +**Question answered:** Is the filter fine enough to satisfy the no-erosion particle retention criterion for the base soil? The criterion compares +the filter's $D_{15}$ with a maximum allowable $D_{15}$ set by the base soil's $D_{85}$ and fines content . Where the particle sizes are known only as ranges for a soil classification or filter category, the method +answers the question over Monte Carlo realizations of those sizes and reports the fraction of realizations in which the filter is too coarse. The +criterion itself is documented in the +[Particle Retention Criterion](/docs/toolbox-technical-manuals/internal-erosion-suite/filter-evaluation-continuation/v1.0/design-for-particle-retention#particle-retention-criterion) +section of the Filter Evaluation (Continuation) Toolbox manual; this chapter documents how the screening model supplies its inputs and uses its +result. + +## Input Resolution + +The method needs three quantities for each realization: the filter's $D_{15F}$, and the base soil's $D_{85B}$ and fines content $FC$ (percent +finer than the No. 200 sieve, 0.075 mm). Each comes either from a supplied gradation, as a single fixed value, or from a range, as a sampled +value: + +- **Filter $D_{15F}$** — the $D_{15}$ of the coarse band of the filter gradation envelope when a filter gradation is supplied and that size is + determined. This is the coarsest filter $D_{15}$, the value the particle retention check in the toolbox compares with the criterion. Otherwise, + $D_{15F}$ is sampled from the range of the filter category (). +- **Base soil $D_{85B}$ and $FC$** — the $D_{85}$ and fines content of the fine band of the base soil gradation envelope when a base soil + gradation is supplied and both values are determined. These describe the finest base soil, the gradation the toolbox's particle retention check + uses. Otherwise, both are sampled from the ranges of the base soil classification + (). + +$D_{85B}$ and $FC$ always come from the same source. They describe the same fine fraction of one soil, so the model never pairs a measured +$D_{85B}$ with a sampled $FC$ or the reverse: when the base soil gradation determines only one of them, both are taken from the classification +ranges. A gradation supplied for only one material is used without the regrading of the gradation method (see +[Assumption 11](./08-assumptions-and-limitations.mdx#soil-classification-method) in Assumptions and Limitations). + +:::warning[INPUT NEEDED IN-05 — Engineering Basis] +When the soil classification method uses a value from a single supplied gradation, it uses the gradation as entered, without the mathematical +regrading on the No. 4 sieve or on a missing particle size that the gradation method applies. Where the gradation method would regrade the +band — a gap-graded band, or a band containing gravel unless it has less than 15 percent fines and is not broadly graded — the unregraded +$D_{85B}$ is larger than the regraded value and the maximum allowable $D_{15F}$ is correspondingly larger. Provide the engineering basis or the +engineering-judgment attribution for using the unregraded gradation, or confirm that regrading should be applied in this case. +::: + +## Classification Ranges + + gives the base soil ranges, and + the filter ranges. + + + +:::warning[INPUT NEEDED IN-06 — Engineering Basis] +The base soil ranges in require an engineering basis: each $D_{85}$ range (SM and +GM 0.4 to 1.0 mm; SC and GC 0.3 to 0.8 mm; ML and CL-ML 0.005 to 0.05 mm; CL and MH 0.005 to 0.02 mm; CH 0.005 to 0.01 mm) and each fines content +range (5 to 50 percent for the silty and clayey sands and gravels; 50 to 100 percent for the silts and clays). Provide a literature citation (full +bibliographic details for the bibliography) or the engineering-judgment attribution, and state why the clean and slightly silty sands and gravels +(GP, GW, GP-GM, SP, SW, SP-SM) carry no ranges. + +Proposed (unconfirmed): the fines content ranges follow the USCS boundaries between coarse-grained soils with fines (more than 5 and at most 50 +percent fines) and fine-grained soils (50 percent fines or more) . +::: + + + +:::warning[INPUT NEEDED IN-07 — Engineering Basis] +The filter $D_{15}$ ranges in (Sand 0.1 to 1.0 mm, Sand with gravel 0.5 to 3.0 mm, +Gravel with sand 3.0 to 10.0 mm, Gravel 10.0 to 50.0 mm) require an engineering basis. Provide a literature citation (full bibliographic details +for the bibliography) or the engineering-judgment attribution, including the reasoning for the overlap between the Sand and Sand with gravel +ranges. +::: + +## Monte Carlo Evaluation + +In each Monte Carlo realization, every quantity resolved from a range is drawn from a uniform distribution between the range's bounds, +independently of the others, and every quantity resolved from a gradation keeps its fixed value. + +:::warning[INPUT NEEDED IN-08 — Engineering Basis] +Each range-resolved quantity is sampled from a uniform distribution, and $D_{85B}$, $FC$, and $D_{15F}$ are sampled independently of one another +— including $D_{85B}$ and $FC$ of the same base soil, which describe the same fine fraction. Provide the engineering basis or the +engineering-judgment attribution for the uniform distribution and for sampling $D_{85B}$ and $FC$ independently. + +Proposed (unconfirmed): with only a classification or category known, a uniform distribution takes no position on where within the range the +soil lies. +::: + +### Base soil category + +The realization's base soil category $BSC$ follows from its fines content : + + + +A classification whose fines content range spans a category boundary — the silty and clayey sands and gravels span categories 2, 3, and 4, and +the silts and clays span categories 1 and 2 — produces realizations in more than one category. + +### Maximum allowable filter D15 + +The maximum allowable filter $D_{15}$ for the no-erosion condition, $D_{15F}^{max}$, depends on the category and on whether the base soil is +dispersive . For a non-dispersive base soil: + + + +For a dispersive base soil: + + + +where: + +> $D_{15F}^{max}$ = maximum allowable filter $D_{15}$ for the no-erosion condition (mm) +> $D_{85B}$ = base soil $D_{85}$ (mm) +> $FC$ = base soil fines content (%) + +In category 3, the criterion interpolates linearly in fines content between the category 2 limit at 40 percent fines and the category 4 limit +$4\,D_{85B}$ at 15 percent fines. When $4\,D_{85B}$ is smaller than the category 2 limit (0.7 mm, or 0.5 mm for a dispersive soil), the model uses +the category 2 limit for category 3 instead of interpolating, so that a category 3 soil, which has fewer fines than a category 2 soil, is never +given a more restrictive limit than a category 2 soil. The floor raises the allowable $D_{15F}$ above the interpolated value, so it is the less +conservative of the two choices: it can lower $P_{cont,j}$. + +:::warning[INPUT NEEDED IN-09 — Engineering Basis] +The category 3 floor — using the category 2 limit (0.7 mm, or 0.5 mm for a dispersive base soil) whenever $4\,D_{85B}$ is smaller than it — +requires a basis. Provide the literature citation or engineering-judgment attribution. Note also that the no-erosion boundary of the Foster and +Fell evaluation in the gradation method interpolates category 3 without this floor (see +[Erosion boundaries](./07-gradation-method.mdx#erosion-boundaries) in the Gradation Method chapter); confirm +whether the two should agree. + +Proposed (unconfirmed): the floor corresponds to the instruction in published filter criteria to use the category 2 limit when $4\,D_{85B}$ is less +than it. +::: + +### Probability of continuing erosion + +The filter fails the criterion in a realization when $D_{15F} > D_{15F}^{max}$. The probability of continuing erosion is the fraction of +realizations in which it fails: + + + +where $N_{fail}$ is the number of realizations in which the filter fails the no-erosion criterion and $N$ is the number of realizations. The +method makes no distinction between a filter that just fails the no-erosion criterion and one that is coarse enough for continuing erosion: every +failing realization counts as continuing erosion. + +:::warning[INPUT NEEDED IN-10 — Engineering Basis] +The method counts every realization that fails the no-erosion criterion ( and +) as continuing erosion, although a filter coarser than the no-erosion limit may +still seal after some or excessive erosion (see the +[Foster and Fell](/docs/toolbox-technical-manuals/internal-erosion-suite/filter-evaluation-continuation/v1.0/foster-and-fell) chapter). Provide the +engineering basis or the engineering-judgment attribution for this treatment. + +Proposed (unconfirmed): without gradation envelopes, the some-erosion and excessive-erosion boundaries cannot be evaluated, so the screening +method resolves the uncertainty conservatively by treating any filter coarser than the no-erosion limit as allowing continuing erosion. +::: + +## Behavior of the Result + +- When the filter $D_{15F}$ is fixed by a gradation and the base soil is sampled, $P_{cont,j}$ is the fraction of the base soil's classification + range for which that filter is too coarse. When the base soil is fixed by a gradation and the filter is sampled, it is the fraction of the + filter category's $D_{15}$ range that is too coarse for that base soil. +- With the classification ranges of the silts and clays (categories 1 and 2), $D_{15F}^{max}$ lies between 0.2 mm and 0.7 mm (0.5 mm for a + dispersive soil). A filter whose $D_{15F}$ lies entirely above the upper limit — any Gravel with sand or Gravel filter — then fails in every + realization, giving $P_{cont,j} = 1.0$, and a filter whose $D_{15F}$ lies entirely below 0.2 mm passes in every realization, giving zero. +- A dispersive base soil never raises $D_{15F}^{max}$ — it lowers or leaves unchanged the category 1, 2, and 3 limits and leaves category 4 + unchanged — so it does not reduce the likelihood that the filter fails the criterion. In category 1, both criteria give 0.2 mm when $D_{85B}$ + is about 0.022 mm or less, which covers the whole CL, MH, and CH ranges, so dispersivity has no effect there. +- The result is a single value for the pair; it does not depend on the pool level. + + diff --git a/docs/web-applications/system-response/continuation-screening/v1.0/07-gradation-method.mdx b/docs/web-applications/system-response/continuation-screening/v1.0/07-gradation-method.mdx new file mode 100644 index 000000000..b2aa06cc9 --- /dev/null +++ b/docs/web-applications/system-response/continuation-screening/v1.0/07-gradation-method.mdx @@ -0,0 +1,313 @@ +--- +title: Gradation Method +--- + +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'; + + + +# Gradation Method + +**Step served:** the probability of continuing erosion $P_{cont,j}$ for a pair in which both the base soil and the filter have gradation +envelopes (see [Method Selection and Governing Base Soil](./04-method-selection-and-governing-base-soil.mdx)). + +**Question answered:** How much erosion of the base soil must occur before the filter seals, and how likely is it that the filter never seals? +A filter that satisfies the no-erosion particle retention criterion stops erosion with little or none; a coarser filter may still seal after some +or excessive erosion, or may allow erosion to continue. The Foster and Fell method divides the range of filter $D_{15}$ into those outcomes from +continuing erosion filter tests , and is applied to filters that do not satisfy the no-erosion +criterion. + +The method runs the soil-to-soil filter evaluation of the Filter Evaluation (Continuation) Toolbox. The theory of each step lives in that manual. +Each section below links the chapter the step follows and documents only what the screening model supplies, what it uses from the result, and +every screening-level adjustment relative to the manual. + +## Step 1: Particle-Size Analysis + +The model analyzes each band of the base soil and filter gradation envelopes as described in the +[Filter Gradation](/docs/toolbox-technical-manuals/internal-erosion-suite/filter-evaluation-continuation/v1.0/filter-gradation#filter-gradation) +chapter. For each band it determines the gravel content (75 mm to 4.75 mm), the fines content $FC$ (finer than 0.075 mm), the characteristic +sizes $D_{10}$, $D_{15}$, $D_{30}$, $D_{60}$, $D_{85}$, $D_{90}$, and $D_{95}$, and the coefficients of uniformity and curvature: + + + +$C_u$ and $C_c$ are undetermined for a band that does not extend to 10 percent passing. + +## Step 2: Base Soil Regrading Characteristics + +The need to regrade the base soil is assessed for each band from four characteristics, following the +[Needs Assessment for Regrading](/docs/toolbox-technical-manuals/internal-erosion-suite/filter-evaluation-continuation/v1.0/base-gradation#needs-assessment-for-regrading) +section of the Base Gradation chapter. In the toolbox the analyst answers each characteristic; the screening model derives three of them from the +particle-size analysis of the base soil: + +- **Particles larger than the No. 4 sieve** — present when the band's gravel content is greater than zero; absent when it is zero or + undetermined. +- **Fines content less than 15 percent** — when the band's $FC$ is less than 15 percent or undetermined. +- **Broadly graded** — derived from the band's coefficients by the ASTM D2487 limits , treating the band as a + gravel when its gravel content exceeds 50 percent and as a sand otherwise: + + + +The gravel-or-sand test is the model's own simplification. ASTM D2487 treats a coarse-grained soil as a gravel when more than half of its coarse +fraction is gravel, that is, when its gravel content exceeds its sand content ; the model instead compares the +gravel content with 50 percent of the whole band. A band with more gravel than sand but no more than 50 percent gravel is therefore treated as a +sand and needs $C_u \ge 6$, rather than 4, to be broadly graded. + +:::warning[INPUT NEEDED IN-17 — Engineering Basis] +The broad-grading assessment treats a band as a gravel when its gravel content exceeds 50 percent of the band, rather than when its gravel +content exceeds its sand content as in ASTM D2487. A gravelly band with a substantial sand or fines content is then held to the sand limit +$C_u \ge 6$; with less than 15 percent fines it is more often taken as not broadly graded and not regraded, which gives a larger $D_{85B}$ and a +less restrictive no-erosion limit. Provide the engineering basis or the engineering-judgment attribution for the 50 percent rule, or confirm +that the ASTM D2487 comparison of gravel with sand is intended. +::: + +When a band's fines content is undetermined, because its gradation does not extend down to 0.075 mm (and does not end at zero percent +passing), the model treats the band as having less than 15 percent fines. When a band's gravel content is undetermined, because its gradation +does not cover the 75 mm and 4.75 mm sizes, the model treats the band as having no particles larger than the No. 4 sieve. When the fine band's +fines content is undetermined, the particle retention check also places the base soil in category 4 (see +[Particle retention check](#particle-retention-check)). These defaults can skip regrading, and they can change the no-erosion limit in either +direction: an unregraded band keeps a larger $D_{85B}$, while category 4 can give a larger or smaller limit than the category of the soil's actual +fines content. + +:::warning[INPUT NEEDED IN-18 — Engineering Basis] +When a base soil band's fines content is undetermined, the model treats it as less than 15 percent; when its gravel content is undetermined, the +model treats the band as having no particles larger than the No. 4 sieve; and when the fine band's fines content is undetermined, the particle +retention check uses base soil category 4. These defaults can skip regrading and can raise or lower the no-erosion limit. Provide the engineering +basis or the engineering-judgment attribution for these defaults, or state how an undetermined fines or gravel content should be handled (for +example, rejecting the input). +::: + +The fourth characteristic, **gap graded**, requires visual examination of the gradation curve and judgment, so the user supplies it with the +missing particle size $d_{gap}$ (see [Input Parameters](./03-input-parameters.mdx#base-soils)). A user-supplied broadly graded answer replaces the +derived value. + +When $C_u$ and $C_c$ are undetermined and no broadly graded answer is supplied, the band is treated as not broadly graded. The toolbox manual +instead directs the analyst to extrapolate the gradation curve and calculate the coefficients externally. + +:::warning[INPUT NEEDED IN-11 — Engineering Basis] +When the broad-grading assessment of a band is undetermined (its $C_u$ and $C_c$ cannot be calculated) and the user supplies no answer, the +model treats the band as not broadly graded. For a band containing gravel with less than 15 percent fines, this skips regrading on the No. 4 +sieve, leaving a larger $D_{85B}$ and a less restrictive no-erosion limit. Provide the engineering basis or the engineering-judgment attribution +for this default, or confirm that the opposite (broadly graded, and therefore regraded) default is intended. +::: + +## Step 3: Filter Evaluation + +### Filter segregation adjustment + +When segregation parameters are supplied for a filter band (see +[Input Parameters](./03-input-parameters.mdx#filter-segregation-adjustment)), the model forms an adjusted filter gradation in which that band is +reshaped after segregation or washout of its finer fraction, following the +[Filter Gradation After Segregation or Washout](/docs/toolbox-technical-manuals/internal-erosion-suite/filter-evaluation-continuation/v1.0/filter-gradation#filter-gradation-after-segregation-or-washout) +section. A band without parameters keeps its original curve in the adjusted gradation. The adjusted gradation enters only the particle retention +check below; see [Use of the adjusted filter gradation](#use-of-the-adjusted-filter-gradation). + +### Base soil regrading + +Each band of the base soil gradation is regraded according to its characteristics, following the +[Base Soil Gradation After Regrading](/docs/toolbox-technical-manuals/internal-erosion-suite/filter-evaluation-continuation/v1.0/base-gradation#base-soil-gradation-after-regrading) +section : + +1. A gap-graded band is regraded on its missing particle size $d_{gap}$. +2. Otherwise, a band with no particles larger than the No. 4 sieve is not regraded. +3. Otherwise, the band is regraded to 100 percent passing the No. 4 sieve (4.75 mm), unless its fines content is less than 15 percent and it is not + broadly graded, in which case it is not regraded. + +Regrading divides the percent passing at each size at or below the regrading size by the percent passing at the regrading size (interpolated on +the band), multiplied by 100 percent, and sets the percent passing at larger sizes to 100 percent. + +### Particle retention check + +The coarsest filter $D_{15}$ (the $D_{15}$ of the coarse band) is compared with the maximum allowable $D_{15F}^{max}$ of the no-erosion criterion +( and , including +the category 3 floor), evaluated from the $D_{85}$ and fines content of the fine band of the regraded base soil — the finest base soil, placed in +category 4 when its fines content is undetermined — following the +[Particle Retention Criterion](/docs/toolbox-technical-manuals/internal-erosion-suite/filter-evaluation-continuation/v1.0/design-for-particle-retention#particle-retention-criterion) +section . When an adjusted filter gradation exists, its coarsest $D_{15}$ is checked against the same limit. + +If the original filter gradation, and the adjusted gradation when there is one, both satisfy the criterion, the filter is taken to stop erosion +with no or practically no erosion of the base soil. The Foster and Fell evaluation is not performed, and the pair takes + + + +Otherwise, the Foster and Fell evaluation follows. + +### Representative base soil gradations + +The Foster and Fell evaluation uses three representative gradations of the regraded base soil — coarse, average, and fine — selected from the +envelope with the confidence interval $CI$, following the +[Base Soil Characterization](/docs/toolbox-technical-manuals/internal-erosion-suite/filter-evaluation-continuation/v1.0/foster-and-fell#base-soil-characterization) +section of the Foster and Fell chapter . The toolbox manual denotes the percentage of the gradations +considered representative by $N$; this document calls it the confidence interval $CI$ and keeps $N$ for the number of Monte Carlo realizations +of the soil classification method. With the tail percentage + + + +the representative coarse gradation moves the coarse band of the regraded envelope toward the fine band by $t$ percent of the distance between +them at each particle size of the coarse band, and the representative fine gradation moves the fine band toward the coarse band by the same +fraction at each particle size of the fine band: + + + +where: + +> $F_c$, $F_f$ = percent passing of the coarse and fine bands of the regraded base soil envelope at the particle size +> $F_{rc}$, $F_{rf}$ = percent passing of the representative coarse and fine gradations +> $t$ = percentage of the envelope excluded at each limit + +With the default $CI$ of 90 percent, $t = 5$ percent. + +The representative average gradation is formed by averaging the representative coarse and fine gradations point by point: the percent passing +at each listed size of the coarse gradation is averaged with the percent passing at the same position in the list of the fine gradation, and +each average is assigned the particle size of the coarse band. This assumes that both bands of the base soil gradation are reported at the same +sieve sizes (Assumption 19 in [Assumptions and Limitations](./08-assumptions-and-limitations.mdx#gradation-method)). The fines content $FC$ and +the fine-to-medium sand content $fm$ of the average gradation are the means of those of the representative coarse and fine gradations. + +### Erosion boundaries + +For each representative gradation, the model evaluates the filter $D_{15}$ boundaries between the erosion conditions, following the +[No-Erosion Boundary](/docs/toolbox-technical-manuals/internal-erosion-suite/filter-evaluation-continuation/v1.0/foster-and-fell#no-erosion-boundary), +[Continuing Erosion Boundary](/docs/toolbox-technical-manuals/internal-erosion-suite/filter-evaluation-continuation/v1.0/foster-and-fell#continuing-erosion-boundary), +and +[Excessive Erosion Boundary](/docs/toolbox-technical-manuals/internal-erosion-suite/filter-evaluation-continuation/v1.0/foster-and-fell#excessive-erosion-boundary) +sections : + +- **No-erosion boundary** $(D_{15F})_{NE}$ — the no-erosion criterion of + or , evaluated + from the representative gradation's $D_{85B}$ and $FC$. Unlike the particle retention check, the category 3 boundary is interpolated without + the floor at the category 2 limit. +- **Continuing erosion boundary**: + + + +- **Excessive erosion boundary**, by the base soil grouping of the representative gradation: + + + +where: + +> $D_{85B}$, $D_{90B}$, $D_{95B}$ = characteristic sizes of the representative base soil gradation (mm) +> $FC$ = fines content of the representative gradation (%) +> $fm$ = fine-to-medium sand content of the representative gradation, the percentage between 1.18 mm and 0.075 mm (%) + +The excessive erosion boundary is the same for a dispersive and a non-dispersive base soil; dispersivity enters the evaluation only through the +no-erosion boundary. + +:::warning[INPUT NEEDED IN-12 — Decision] +The Excessive Erosion Boundary section of the Filter Evaluation (Continuation) Toolbox manual states that the excessive erosion boundary depends on +whether the base soil is non-dispersive or dispersive, but the model's excessive erosion boundary +() does not depend on dispersivity. Confirm which is intended, and whether this +document or the toolbox manual should be corrected. +::: + +### Erosion probabilities + +For each representative gradation, the range of filter $D_{15}$ from the finest filter $D_{15}$ (the fine band of the original filter gradation) +to the coarsest (the coarse band) is divided among the four erosion conditions, following the +[Likelihood of Erosion](/docs/toolbox-technical-manuals/internal-erosion-suite/filter-evaluation-continuation/v1.0/foster-and-fell#likelihood-of-erosion) +section. The proportion of the range coarser than $(D_{15F})_{CE}$ is the continuing erosion proportion; the proportion between +$(D_{15F})_{EE}$ and $(D_{15F})_{CE}$ is the excessive erosion proportion; the proportion between $(D_{15F})_{NE}$ and $(D_{15F})_{EE}$ is the +some-erosion proportion; and the remainder is the no-erosion proportion. Proportions are measured on a logarithmic scale of particle size. + +The division needs both filter $D_{15}$ values. When a filter band's smallest measured percent passing is greater than 15 percent, so that the +gradation does not extend down to that size, its $D_{15}$ is undetermined (see +[Gradation Envelopes](./03-input-parameters.mdx#gradation-envelopes)). An undetermined coarse-band $D_{15}$ makes the particle retention check +fail, so the Foster and Fell evaluation runs. In the division, an undetermined $D_{15}$ is taken as zero, and the proportions then follow: + +- When the fine band's $D_{15}$ is undetermined, every proportion except no erosion is zero, so $P_{cont,j} = 0$ however coarse the filter is. +- When only the coarse band's $D_{15}$ is undetermined, the continuing erosion proportion of each representative gradation is 1 if the fine + band's $D_{15}$ is at or above that gradation's $(D_{15F})_{CE}$, and every proportion except no erosion is zero otherwise. + +The first case can report no continuing erosion for a filter that is far too coarse. + +:::warning[INPUT NEEDED IN-16 — Decision] +When the $D_{15}$ of a filter band is undetermined because the band's smallest measured percent passing is greater than 15 percent, the Foster and Fell division takes it as +zero. With the fine band's $D_{15}$ undetermined, every erosion proportion except no erosion is zero and $P_{cont,j} = 0$, even for a coarse +filter whose coarse band fails the particle retention check; with only the coarse band's $D_{15}$ undetermined, the result depends only on +whether the fine band's $D_{15}$ reaches the continuing erosion boundary of each representative gradation. Confirm whether this treatment is intended and supply the wording of +its basis, or state how an undetermined filter $D_{15}$ should be handled (for example, rejecting the input or taking $P_{cont,j} = 1.0$). +::: + +The probabilities of the four conditions weight the proportions of the three representative gradations, giving the average gradation the +weight $CI/100$ and the coarse and fine gradations $(100 - CI)/200$ each: + + + +where $P_{NE}$, $P_{SE}$, $P_{EE}$, and $P_{CE}$ are the probabilities of no, some, excessive, and continuing erosion, and $X_{coarse}$, +$X_{average}$, and $X_{fine}$ are the proportions of condition $X$ for the representative coarse, average, and fine gradations. + +## Step 4: Screening Probability of Continuing Erosion + +The screening model folds the probability of excessive erosion into the probability of continuing erosion: + + + +Excessive erosion is erosion extensive enough to damage the embankment before the filter seals (see the +[Foster and Fell](/docs/toolbox-technical-manuals/internal-erosion-suite/filter-evaluation-continuation/v1.0/foster-and-fell) chapter), so the +screening model treats it as continuing erosion. Some erosion, after which the filter quickly seals, is not counted. + +:::warning[INPUT NEEDED IN-13 — Engineering Basis] +The screening probability of continuing erosion is the sum of the Foster and Fell probabilities of continuing and excessive erosion +(). Provide a literature citation (full bibliographic details for the +bibliography) or the engineering-judgment attribution for treating excessive erosion as continuing erosion at the screening level. +::: + +## Use of the Adjusted Filter Gradation + +The adjusted filter gradation from the segregation adjustment affects only whether the Foster and Fell evaluation runs. When the original +filter gradation satisfies the particle retention check but the adjusted gradation does not, the Foster and Fell evaluation is performed — but +its probabilities, and therefore $P_{cont,j}$, are computed from the original filter gradation. The toolbox procedure instead evaluates the +adjusted gradation in parallel with the original one, as a separate event-tree branch for a segregated or internally unstable filter. + +:::warning[INPUT NEEDED IN-14 — Decision] +The screening probability of continuing erosion always comes from the Foster and Fell evaluation of the original filter gradation; the adjusted +(segregated or washed-out) filter gradation only decides whether that evaluation runs. Confirm that this is the intended screening treatment, and +supply the wording of its basis, or state how the adjusted gradation should enter the probability (for example, the larger of the two results). +::: + +## Permeability + +The toolbox's soil-to-soil evaluation also checks the permeability (drainage) criterion of the filter, documented in the +[Permeability](/docs/toolbox-technical-manuals/internal-erosion-suite/filter-evaluation-continuation/v1.0/permeability) chapter. The screening +model does not use the permeability result: $P_{cont,j}$ depends on particle retention alone. + +:::warning[INPUT NEEDED IN-15 — Engineering Basis] +The probability of continuing erosion does not consider the permeability criterion of the filter. Provide the engineering basis or the +engineering-judgment attribution for excluding drainage from the continuation node. + +Proposed (unconfirmed): the continuation node addresses whether the filter retains the eroding base soil; whether the filter drains freely +bears on other aspects of performance and is outside this node. +::: + +## Screening-Level Adjustments + +Relative to the soil-to-soil filter evaluation of the Filter Evaluation (Continuation) Toolbox, the screening gradation method fixes the +following: + +- **Regrading characteristics are derived** — the No. 4, fines content, and broad-grading characteristics come from the particle-size analysis, + with a user override for broad grading; only gap grading is supplied by the user (Step 2). +- **The confidence interval defaults to 90 percent** for the representative base soil gradations. +- **One probability is reported** — the sum of the continuing and excessive erosion probabilities (Step 4). +- **The adjusted filter gradation decides only whether the Foster and Fell evaluation runs** (see + [Use of the Adjusted Filter Gradation](#use-of-the-adjusted-filter-gradation)). +- **Permeability is not used** (see [Permeability](#permeability)). +- **Constricted exits are not evaluated** — the toolbox's separate + [Constricted Exit](/docs/toolbox-technical-manuals/internal-erosion-suite/filter-evaluation-continuation/v1.0/constricted-exit) evaluation, for + base soil eroding into a pipe, conduit, or crack, is not part of the screening model. + + diff --git a/docs/web-applications/system-response/continuation-screening/v1.0/08-assumptions-and-limitations.mdx b/docs/web-applications/system-response/continuation-screening/v1.0/08-assumptions-and-limitations.mdx new file mode 100644 index 000000000..d135a6afd --- /dev/null +++ b/docs/web-applications/system-response/continuation-screening/v1.0/08-assumptions-and-limitations.mdx @@ -0,0 +1,208 @@ +--- +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 continuation screening model applies deliberate simplifications relative to a full filter evaluation. They let the model accept whatever +filter information is available. Several resolve missing information in the direction of continuing erosion, but not all: Assumptions 11, 12, +15, 16, and 20 can each lower the probability, the gradation method does not count some erosion (Assumption 14), and a filter gradation whose +fine band does not extend down to 15 percent passing gives zero in the gradation method (see Gradation coverage under +[Limitations](#limitations)). 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. + +## Method Selection and Combination + +1. **Each base soil is evaluated by the most informative method its inputs support.** Inputs for a lower-priority method are ignored when a + higher-priority method applies (see [Method Selection and Governing Base Soil](./04-method-selection-and-governing-base-soil.mdx)). + - *Engineering basis:* Screening design decision (engineering judgment): measured gradations describe the base soil and filter more + completely than classification ranges, which in turn describe them more completely than a construction period. + - *Effect on results:* Supplying better data changes the method and can move the result in either direction. A year of construction + supplied alongside a gradation or classification has no effect on that pair only when the gradation method applies (both materials have + gradation envelopes), or when both sides of the pair resolve for the soil classification method: the filter side through a filter + gradation that determines $D_{15}$ or a filter category other than Unknown, and the base side through a supported classification or a base + soil gradation whose fine band determines both $D_{85}$ and fines content. Otherwise the pair falls to the year-of-construction method, and + the year decides the result — for example, a base soil classification or gradation with no filter gradation and no filter category (or an + Unknown category). + - *When it may not hold:* Gradations that are not representative of the materials in place (for example, a few tests from a borrow area + rather than the constructed zone), where a less detailed method could be the better indicator. +2. **The base soil the filter is least able to retain governs.** The node probability is the largest pair probability. + - *Engineering basis:* Screening design decision (engineering judgment): the filter must stop erosion of every base soil it protects, so + the worst pair controls. + - *Effect on results:* Adding a base soil can only raise or leave unchanged the node probability. An entry with no information takes + $P_{cont} = 1.0$ and governs. + - *When it may not hold:* A base soil listed that cannot in fact reach the filter along the erosion path under consideration, which then + controls the result without physical justification. +3. **When no method can be selected for a pair and no year of construction is supplied, continuation is certain.** No method can be selected + when neither the gradation method nor the soil classification method has its inputs: the pair lacks either envelope, and the filter + $D_{15}$ or the base soil $D_{85}$ and fines content cannot be resolved. This covers a pair with no information, and also a pair with a full + base soil gradation but no filter information. + - *Engineering basis:* Screening design decision (engineering judgment): without evidence that the filter can retain the base soil, the + filter cannot be credited with stopping erosion. + - *Effect on results:* $P_{cont} = 1.0$ for such pairs, the most conservative value. + - *When it may not hold:* Filters known from construction records or inspection to be well designed, for which supplying a gradation, + classification, or construction year gives a more realistic result. +4. **Continuation does not depend on the pool level or on the erosion mechanism.** The same inputs give the same probability at every + headwater, for any internal-erosion failure mode. + - *Engineering basis:* Particle retention is governed by the relationship between the particle-size distributions of the base soil and the + filter , and the Foster and Fell erosion boundaries were derived from continuing erosion filter tests under + high water pressures . + - *Effect on results:* The calling screening model applies one continuation probability across its range of pool levels. + - *When it may not hold:* Flow conditions at the filter face well beyond those of the filter tests on which the criteria rest, such as much + higher hydraulic gradients or flow velocities, where the head could affect whether and how quickly the filter seals. + +## Year-of-Construction Method + +5. **The construction period alone sets the probability of continuing erosion when nothing else is known.** The probability is 0.9 before 1950, + 0.5 from 1950 to 1970, 0.25 from 1971 to 1985, and 0.1 after 1985. + - *Engineering basis:* Basis requested — see marker IN-04 in [Year-of-Construction Method](./05-year-of-construction-method.mdx). + - *Effect on results:* Every pair evaluated by this method receives the same probability, whatever its base soil. + - *When it may not hold:* Embankments whose filters were designed ahead of, or behind, the practice of their period, and zones that were + never designed as filters. + +## Soil Classification Method + +6. **The ranges for each soil classification represent the base soil's $D_{85}$ and fines content.** + - *Engineering basis:* Basis requested — see marker IN-06 in [Soil Classification Method](./06-soil-classification-method.mdx). + - *Effect on results:* The ranges set the spread of maximum allowable filter $D_{15}$ and therefore the fraction of realizations that fail. + - *When it may not hold:* Base soils whose measured particle sizes fall outside the ranges for their classification; a base soil gradation + then gives a better result. +7. **The ranges for each filter category represent the filter's $D_{15}$.** + - *Engineering basis:* Basis requested — see markers IN-07 in [Soil Classification Method](./06-soil-classification-method.mdx) and IN-01 + (category definitions) in [Input Parameters](./03-input-parameters.mdx). + - *Effect on results:* A category range that lies wholly above the base soil's maximum allowable $D_{15F}$ gives $P_{cont,j} = 1.0$, and one + that lies wholly below it gives zero, whatever the actual filter $D_{15}$ is within that range. The Gravel range (10 to 50 mm) lies above + every limit the base soil classification ranges can produce, so a Gravel filter gives 1.0 against any base soil evaluated from its + classification ranges. + - *When it may not hold:* Filters near a category boundary or outside their category's range; a filter gradation then gives a better + result. +8. **Range-resolved quantities are uniform and independent.** $D_{85B}$, $FC$, and $D_{15F}$ are each drawn from a uniform distribution, with no + correlation between them. + - *Engineering basis:* Basis requested — see marker IN-08 in [Soil Classification Method](./06-soil-classification-method.mdx). + - *Effect on results:* Realizations can pair a coarse $D_{85B}$ with a high fines content, combinations that may be rare in real soils of + that classification. + - *When it may not hold:* Soils in which the $D_{85}$ and fines content are strongly related, as they are within one gradation curve. +9. **Only silty and clayey sands and gravels, silts, and clays carry classification ranges.** The clean and slightly silty sands and gravels + (GP, GW, GP-GM, SP, SW, SP-SM) have no ranges, and an input set that pairs one of these classes with a filter category other than Unknown is + rejected. + - *Engineering basis:* Basis requested — see marker IN-06 in [Soil Classification Method](./06-soil-classification-method.mdx). + - *Effect on results:* Such base soils need a gradation for any method other than the year-of-construction method or the default. With a + filter category other than Unknown, the input set is rejected even when a gradation is supplied, unless the classification is left out + (see [Base Soils](./03-input-parameters.mdx#base-soils) in Input Parameters). + - *When it may not hold:* Embankments with clean sand or gravel zones upstream of the filter and no gradations available. +10. **Failing the no-erosion criterion counts as continuing erosion.** The method does not distinguish some or excessive erosion from + continuing erosion. + - *Engineering basis:* Basis requested — see marker IN-10 in [Soil Classification Method](./06-soil-classification-method.mdx). + - *Effect on results:* For the same materials, the probability can exceed the gradation method's, which credits filters that seal after + some erosion. + - *When it may not hold:* Filters only moderately coarser than the no-erosion limit, which the Foster and Fell evaluation would place in the + some-erosion or excessive-erosion zone. +11. **A single supplied base soil gradation is used without regrading.** The base soil $D_{85}$ and fines content are taken from the gradation + as entered. + - *Engineering basis:* Basis requested — see marker IN-05 in [Soil Classification Method](./06-soil-classification-method.mdx). + - *Effect on results:* Where the full evaluation would regrade the band — a gap-graded band, or a band containing gravel unless it has less + than 15 percent fines and is not broadly graded — the unregraded $D_{85}$ is larger than the regraded value, which raises the allowable + filter $D_{15}$ and can lower the probability. + - *When it may not hold:* Gravelly or gap-graded base soils, for which regrading would apply in a full evaluation. +12. **The category 3 limit is not allowed to fall below the category 2 limit.** When $4\,D_{85B}$ is smaller than 0.7 mm (0.5 mm for a dispersive + soil), the category 3 criterion uses the category 2 limit. + - *Engineering basis:* Basis requested — see marker IN-09 in [Soil Classification Method](./06-soil-classification-method.mdx). + - *Effect on results:* Fine base soils in category 3 receive the same limit as category 2 soils rather than a more restrictive one. The floor + raises the allowable filter $D_{15}$, so it can lower the probability. The Foster and Fell no-erosion boundary in the gradation method does + not apply the floor, so the particle retention check and the Foster and Fell evaluation can use different no-erosion limits for the same + soil. + - *When it may not hold:* Category 3 soils whose fine fraction is fine enough that the interpolated limit lies well below the category 2 + value, for which the floored limit may be coarser than needed to retain them. + +## Gradation Method + +13. **A filter that satisfies the no-erosion criterion with every filter gradation considered stops erosion.** The Foster and Fell evaluation is + not performed, and the probability of continuing erosion is zero. + - *Engineering basis:* Filters meeting the no-erosion particle retention criterion seal with no or practically no erosion of the base soil ; see the + [Design for Particle Retention](/docs/toolbox-technical-manuals/internal-erosion-suite/filter-evaluation-continuation/v1.0/design-for-particle-retention) + chapter. + - *Effect on results:* The result is zero while the coarsest filter $D_{15}$ is within the limit for the finest regraded base soil, unless + an adjusted filter gradation fails the check. The Foster and Fell evaluation then runs on the original gradation with no-erosion + boundaries that do not apply the category 3 floor, so in edge cases the result can be positive. Beyond the limit, the Foster and Fell + evaluation sets the result, which is positive only when part of the filter range lies in the excessive or continuing erosion zone. + - *When it may not hold:* Filters whose gradation in place is coarser than the gradations supplied, through segregation or internal + instability not captured by the segregation adjustment. +14. **Excessive erosion counts as continuing erosion.** The screening probability is the sum of the Foster and Fell probabilities of continuing + and excessive erosion. + - *Engineering basis:* Basis requested — see marker IN-13 in [Gradation Method](./07-gradation-method.mdx). + - *Effect on results:* The probability is at least the Foster and Fell probability of continuing erosion, and larger whenever part of the + filter range lies in the excessive erosion zone. + - *When it may not hold:* Embankments that can tolerate the erosion and leakage that occur before an excessive-erosion filter seals. +15. **An undetermined broad-grading assessment is taken as not broadly graded.** + - *Engineering basis:* Basis requested — see marker IN-11 in [Gradation Method](./07-gradation-method.mdx). + - *Effect on results:* A gravelly band with less than 15 percent fines is then not regraded, giving a larger $D_{85B}$ and a less + restrictive no-erosion limit. + - *When it may not hold:* Base soil gradations that do not extend to 10 percent passing; supplying the broad-grading answer removes the + default. +16. **The adjusted filter gradation decides only whether the Foster and Fell evaluation runs.** The probabilities are computed from the original + filter gradation. + - *Engineering basis:* Basis requested — see marker IN-14 in [Gradation Method](./07-gradation-method.mdx). + - *Effect on results:* The adjustment matters only when the original gradation passes the particle retention check and the adjusted one + fails it. The original gradation's Foster and Fell result is then zero only when its filter range lies at or below the excessive erosion + boundary of every representative gradation. Passing the particle retention check does not ensure this: for very fine clays ($D_{95B}$ + below about 0.022 mm), $9\,D_{95B}$ falls below the 0.2 mm no-erosion limit, so a filter that passes the check can still lie in the + continuing erosion zone and give a positive result. + - *When it may not hold:* Filters for which segregation or washout is likely, where the adjusted gradation's own Foster and Fell result + would be larger. +17. **The permeability criterion does not enter the probability.** + - *Engineering basis:* Basis requested — see marker IN-15 in [Gradation Method](./07-gradation-method.mdx). + - *Effect on results:* A filter that retains the base soil but drains poorly is credited fully at the continuation node. + - *When it may not hold:* Filters whose limited permeability allows pressures to build up and the filter or the base soil to be bypassed. +18. **The excessive erosion boundary does not depend on dispersivity.** + - *Engineering basis:* Decision requested — see marker IN-12 in [Gradation Method](./07-gradation-method.mdx). + - *Effect on results:* For a dispersive base soil, the excessive erosion zone is the same as for a non-dispersive soil of the same gradation. + - *When it may not hold:* Dispersive base soils, if the excessive erosion boundary should be stricter for them. +19. **Both bands of the base soil gradation are reported at the same sieve sizes.** The representative average gradation is formed by averaging + the representative coarse and fine gradations point by point. + - *Engineering basis:* The average gradation is obtained for each input sieve size across the envelope (see + [Base Soil Characterization](/docs/toolbox-technical-manuals/internal-erosion-suite/filter-evaluation-continuation/v1.0/foster-and-fell#base-soil-characterization) + in the Foster and Fell chapter of the toolbox manual). + - *Effect on results:* With matching sieve sizes, the average gradation lies midway between the representative coarse and fine gradations at + every size, and its characteristic sizes set the average gradation's erosion boundaries, which carry the weight $CI/100$. + - *When it may not hold:* Bands reported at different sieve sizes or in a different number of sizes, for which the averaged points do not + correspond to a common particle size and the average gradation, and therefore the result, is distorted. +20. **A band is treated as a gravel in the broad-grading assessment when its gravel content exceeds 50 percent.** Otherwise it is treated as a + sand. + - *Engineering basis:* Basis requested — see marker IN-17 in [Gradation Method](./07-gradation-method.mdx#step-2-base-soil-regrading-characteristics). + - *Effect on results:* A band with more gravel than sand but no more than 50 percent gravel must reach $C_u \ge 6$, not 4, to be broadly + graded. With less than 15 percent fines, it is then more often taken as not broadly graded and not regraded, which leaves a larger + $D_{85B}$ and a less restrictive no-erosion limit. + - *When it may not hold:* Gravelly base soils with a substantial sand or fines content, which the classification standard would call a + gravel. + +## Limitations + +- **One filter boundary per evaluation.** The model evaluates one filter against its base soils. For a multi-stage filter, each zone boundary is + a separate evaluation, from the finest to the coarsest filter material, with the finer filter acting as the base soil for the next (see the + [Background](/docs/toolbox-technical-manuals/internal-erosion-suite/filter-evaluation-continuation/v1.0/background) chapter of the toolbox + manual). +- **Gradation coverage.** A characteristic size outside the range of a supplied gradation is undetermined. A filter gradation whose smallest + measured percent passing is greater than 15 percent, or a base soil gradation whose smallest measured percent passing is greater than 85 + percent, does not extend down to that size and cannot supply it; the representative gradations + and erosion boundaries of the Foster and Fell evaluation also depend on the bands covering a common range of particle sizes. In the gradation + method, a filter band that does not extend down to 15 percent passing gives an unconservative result: when the fine band's $D_{15}$ is undetermined, + $P_{cont,j} = 0$ however coarse the filter (see + [Erosion probabilities](./07-gradation-method.mdx#erosion-probabilities) in the Gradation Method chapter and marker IN-16). +- **Soil filters only.** Erosion into a concentrated exit such as an open joint, defect, or crack in a pipe or conduit is not evaluated. The + toolbox evaluates it separately as a + [Constricted Exit](/docs/toolbox-technical-manuals/internal-erosion-suite/filter-evaluation-continuation/v1.0/constricted-exit) rather than as + a soil filter. +- **Very high fine-to-medium sand content.** For a representative base soil gradation with more than 35 percent fines and a very high + fine-to-medium sand content, the excessive erosion boundary can exceed the continuing erosion boundary. The some-erosion and continuing erosion + zones then overlap and the proportions no longer divide the filter range consistently. The literature does not address this combination. +- **Screening level.** The result is a screening-level estimate. A detailed filter evaluation with the Filter Evaluation (Continuation) Toolbox + gives the analyst control over the representative gradations, the regrading assessment, the segregation branch, and the permeability check. + + diff --git a/docs/web-applications/system-response/continuation-screening/v1.0/09-output-and-interpretation.mdx b/docs/web-applications/system-response/continuation-screening/v1.0/09-output-and-interpretation.mdx new file mode 100644 index 000000000..abe87da0f --- /dev/null +++ b/docs/web-applications/system-response/continuation-screening/v1.0/09-output-and-interpretation.mdx @@ -0,0 +1,82 @@ +--- +title: Output and Interpretation +--- + +import NavContainer from '@site/src/components/NavContainer'; + + + +# Output and Interpretation + +The model produces one probability of continuing erosion for the continuation node, the method and base soil that produced it, and the result of +each base soil pair. None of the results depends on the pool level. + +## Node Result + +- **Probability of continuing erosion** $P_{cont}$ — the continuation-node probability: the largest of the pair probabilities + (see [Method Selection and Governing Base Soil](./04-method-selection-and-governing-base-soil.mdx)). +- **Governing method** — the method that produced $P_{cont}$ for the governing pair: the gradation method, the soil classification method, the + year-of-construction method, or the no-information default. +- **Governing base soil** — the base soil whose pair produced $P_{cont}$. When pairs tie, the first of them in the order entered. + +The governing pair's details, listed under Pair Results, also describe the node result. + +## Pair Results + +For each base soil, in the order entered: + +- **Probability of continuing erosion** $P_{cont,j}$ and the **method** that produced it. +- **Foster and Fell probabilities** (gradation method only) — $P_{NE}$, $P_{SE}$, $P_{EE}$, and $P_{CE}$, the probabilities of no, some, + excessive, and continuing erosion before they are combined into $P_{cont,j} = P_{CE} + P_{EE}$. When the filter satisfied the particle + retention check, they are 1, 0, 0, and 0 (see [Gradation Method](./07-gradation-method.mdx)). + +How the regrading characteristics and the particle sizes used by each method are resolved from the inputs is described in +[Gradation Method](./07-gradation-method.mdx#step-2-base-soil-regrading-characteristics) and +[Soil Classification Method](./06-soil-classification-method.mdx#input-resolution). + +## Reading the Result + +**Which method governs.** The governing method shows how much information stands behind $P_{cont}$. A result from the gradation method rests on +measured gradations of both materials; a result from the soil classification method rests on classification ranges for at least one of them; a +result from the year-of-construction method rests on the construction period alone; and the default, $P_{cont} = 1.0$, rests on no information. +When the governing pair used a less informative method than the other pairs, the least-characterized base soil may be controlling the node: +supplying its gradation or classification is the most direct way to refine the result. + +**Which base soil governs.** Because the worst pair governs, adding base soils never lowers $P_{cont}$. A base soil entered with no +classification, no gradation, and no year of construction makes $P_{cont} = 1.0$. + +**Gradation method results.** $P_{cont,j} = 0$ results either when the filter satisfied the no-erosion criterion for the finest regraded base +soil with every filter gradation considered, or when the whole filter range falls in the no-erosion and some-erosion zones of every +representative gradation. It also results when the fine band of the filter gradation does not extend down to 15 percent passing, so that its +$D_{15}$ is undetermined, and when only the coarse band's $D_{15}$ is undetermined and the fine band's $D_{15}$ is below the continuing erosion +boundary of every representative gradation (see +[Erosion probabilities](./07-gradation-method.mdx#erosion-probabilities) in the Gradation Method chapter). A positive result is the share of the filter $D_{15}$ range, weighted over the representative base soil +gradations, that lies in the excessive or continuing erosion zones; comparing $P_{EE}$ and $P_{CE}$ shows whether the filter is expected to seal +after damaging erosion or not at all. Because $P_{SE}$ is not counted, a filter range lying entirely between the no-erosion and excessive erosion +boundaries of every representative gradation gives zero even though the filter fails the no-erosion criterion. + +**Soil classification method results.** The result is the fraction of Monte Carlo realizations in which the filter is coarser than the +no-erosion limit. It is sensitive to the classification and category ranges: a filter category whose $D_{15}$ range lies entirely above the +limits of a fine-grained base soil gives a result of 1.0 (see [Soil Classification Method](./06-soil-classification-method.mdx)). Because every +failing realization counts as continuing erosion, the result does not credit a filter that seals after some erosion. + +**Reasonableness checks.** + +- A gradation-method result of zero alongside a supplied filter segregation adjustment does not show that the adjusted filter gradation + satisfied the criterion. When the original gradation passes and the adjusted one fails, the Foster and Fell evaluation runs on the original + gradation, which returns zero whenever the original filter range lies at or below the excessive erosion boundary of every representative + gradation. For very fine clays ($D_{95B}$ below about 0.022 mm), $9\,D_{95B}$ falls below the 0.2 mm no-erosion limit, so an original filter + that passes the check can still lie in the continuing erosion zone and return a positive result (see Assumption 16 in + [Assumptions and Limitations](./08-assumptions-and-limitations.mdx#gradation-method)). +- A large difference between pairs using different methods can reflect the methods rather than the soils; supplying gradations for the + less-characterized base soils puts the pairs on a common footing. + +## Screening Versus Detailed Analysis + +The model gives a screening-level estimate. Its no-information default and its governing-pair rule resolve incomplete information in the +direction of continuing erosion, but several of its defaults can lower the result (see [Intended Use](./02-model-overview.mdx#intended-use)). It fixes or derives steps that a +detailed evaluation leaves to the analyst, reports a single probability rather than the separate erosion conditions, and does not evaluate the +segregation branch, the permeability criterion, or constricted exits on their own terms (see +[Gradation Method](./07-gradation-method.mdx#screening-level-adjustments)). Where the continuation node is important to the risk estimate, a +detailed evaluation with the Filter Evaluation (Continuation) Toolbox — beginning with representative gradations selected by the analyst from all +available gradation tests — provides the basis for a higher-level analysis. diff --git a/docs/web-applications/system-response/continuation-screening/v1.0/_input-needed.md b/docs/web-applications/system-response/continuation-screening/v1.0/_input-needed.md new file mode 100644 index 000000000..514d23561 --- /dev/null +++ b/docs/web-applications/system-response/continuation-screening/v1.0/_input-needed.md @@ -0,0 +1,278 @@ +# Input Needed — Continuation (Filter Evaluation) 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 four filter categories (Sand, Sand with gravel, Gravel with sand, Gravel), +which the model defines only by name and by their filter D15 ranges. + +**Needed:** The definition of each category — in particular the gravel or sand content that +separates Sand from Sand with gravel, Sand with gravel from Gravel with sand, and Gravel with +sand from Gravel. Also the reason the filter is described by these categories rather than by +USCS classes. + +**Proposed (unconfirmed):** The categories follow the USCS naming convention for the secondary +component, in which a sand "with gravel" contains 15 percent or more gravel, and a gravel has +more gravel than sand. They may be used in place of USCS classes because a clean sand or gravel +class can fall in either of two categories, depending on its gravel or sand content, which only +a gradation can resolve. + +**Answer:** + +--- + +## IN-02 — Engineering Basis — `03-input-parameters.mdx` + +**Regarding:** The reshaping exponent k of the gap-graded filter segregation adjustment: default +0.5, valid range 0.4 to 0.7. + +**Needed:** Literature citation (full bibliographic details for the bibliography) or the +engineering-judgment attribution for the default and for the range. + +**Answer:** + +--- + +## IN-03 — Bibliography — `03-input-parameters.mdx` + +**Regarding:** The reshape relationships of the filter segregation adjustment: for a broadly +graded band, a uniform lowering of the percent passing by FF × W / 100 above the finer-fraction +breakpoint and a proportional scaling by (100 − W) / 100 below it; a linear blend above the +breakpoint and a power curve (D / D_FF)^k below it for a gap-graded band; adjusted percent +passing at the breakpoint FF × (100 − W) / 100. The Filter Evaluation (Continuation) Toolbox +manual describes the adjustment only conceptually. + +**Needed:** The source of these relationships (full bibliographic details), or confirmation that +they are the toolbox's own formulation with the attribution to state. + +**Answer:** + +--- + +## IN-04 — Engineering Basis — `05-year-of-construction-method.mdx` + +**Regarding:** The construction periods (before 1950, 1950 to 1970, 1971 to 1985, after 1985) +and the probability of continuing erosion assigned to each (0.9, 0.5, 0.25, 0.1). + +**Needed:** Literature citation or engineering-judgment attribution, including the reasoning for +each period boundary and each probability. + +**Proposed (unconfirmed):** The periods follow the development of filter design practice; +filters designed before the modern no-erosion criteria of the mid-1980s are progressively more +likely to be too coarse the earlier they were designed. + +**Answer:** + +--- + +## IN-05 — Engineering Basis — `06-soil-classification-method.mdx` + +**Regarding:** When the soil classification method takes the base soil D85 and fines content +from a single supplied base soil gradation, it uses the gradation as entered, without +the regrading on the No. 4 sieve or on a missing particle size that the gradation method +applies. + +**Needed:** Engineering basis or engineering-judgment attribution for using the unregraded +gradation, or confirmation that regrading should be applied. + +**Answer:** + +--- + +## IN-06 — Engineering Basis — `06-soil-classification-method.mdx` + +**Regarding:** The base soil ranges by USCS classification — D85: SM and GM 0.4–1.0 mm; SC and +GC 0.3–0.8 mm; ML and CL-ML 0.005–0.05 mm; CL and MH 0.005–0.02 mm; CH 0.005–0.01 mm. Fines +content: 5–50 percent for SM, GM, SC, GC; 50–100 percent for ML, CL-ML, CL, MH, CH. Also the +exclusion of GP, GW, GP-GM, SP, SW, and SP-SM (no ranges; rejected with a filter category). + +**Needed:** Literature citation or engineering-judgment attribution for each range, and the +reason the clean and slightly silty sands and gravels carry no ranges. + +**Proposed (unconfirmed):** The fines content ranges follow the USCS boundaries between +coarse-grained soils with fines (more than 5 and at most 50 percent fines) and fine-grained +soils (50 percent fines or more). + +**Answer:** + +--- + +## IN-07 — Engineering Basis — `06-soil-classification-method.mdx` + +**Regarding:** The filter D15 ranges by category — Sand 0.1–1.0 mm, Sand with gravel 0.5–3.0 mm, +Gravel with sand 3.0–10.0 mm, Gravel 10.0–50.0 mm. + +**Needed:** Literature citation or engineering-judgment attribution, including the reasoning for +the overlap between the Sand and Sand with gravel ranges. + +**Answer:** + +--- + +## IN-08 — Engineering Basis — `06-soil-classification-method.mdx` + +**Regarding:** Range-resolved quantities are sampled from uniform distributions, and the base +soil D85, the base soil fines content, and the filter D15 are sampled independently of one +another (including D85 and fines content of the same soil). + +**Needed:** Engineering basis or engineering-judgment attribution for the uniform distribution +and for independent sampling of D85 and fines content. + +**Proposed (unconfirmed):** With only a classification or category known, a uniform +distribution takes no position on where within the range the soil lies. + +**Answer:** + +--- + +## IN-09 — Engineering Basis — `06-soil-classification-method.mdx` + +**Regarding:** The category 3 floor of the no-erosion criterion: when 4 × D85B is smaller than +the category 2 limit (0.7 mm, or 0.5 mm dispersive), the category 2 limit is used. The particle +retention check applies the floor; the Foster and Fell no-erosion boundary does not. + +**Needed:** Literature citation or engineering-judgment attribution for the floor, and +confirmation of whether the Foster and Fell no-erosion boundary should apply it too. + +**Proposed (unconfirmed):** The floor corresponds to the instruction in published filter +criteria to use the category 2 limit when 4 × D85B is less than it. + +**Answer:** + +--- + +## IN-10 — Engineering Basis — `06-soil-classification-method.mdx` + +**Regarding:** The soil classification method counts every realization that fails the +no-erosion criterion as continuing erosion, although a filter coarser than the no-erosion limit +may still seal after some or excessive erosion. + +**Needed:** Engineering basis or engineering-judgment attribution for this treatment. + +**Proposed (unconfirmed):** Without gradation envelopes the some-erosion and excessive-erosion +boundaries cannot be evaluated, so the screening method resolves the uncertainty conservatively. + +**Answer:** + +--- + +## IN-11 — Engineering Basis — `07-gradation-method.mdx` + +**Regarding:** When a base soil band's broad-grading assessment is undetermined (Cu and Cc +cannot be calculated) and no answer is supplied, the band is treated as not broadly graded. For +a gravelly band with less than 15 percent fines, this skips regrading on the No. 4 sieve. + +**Needed:** Engineering basis or engineering-judgment attribution for this default, or +confirmation that the opposite default (broadly graded, therefore regraded) is intended. + +**Answer:** + +--- + +## IN-12 — Decision — `07-gradation-method.mdx` + +**Regarding:** The toolbox manual's Excessive Erosion Boundary section says the boundary +depends on whether the base soil is dispersive, but the model's excessive erosion boundary does +not depend on dispersivity. + +**Needed:** Confirmation of which is intended, and whether this document or the toolbox manual +should be corrected. + +**Answer:** + +--- + +## IN-13 — Engineering Basis — `07-gradation-method.mdx` + +**Regarding:** The screening probability of continuing erosion is the sum of the Foster and +Fell probabilities of continuing and excessive erosion. + +**Needed:** Literature citation or engineering-judgment attribution for treating excessive +erosion as continuing erosion at the screening level. + +**Answer:** + +--- + +## IN-14 — Decision — `07-gradation-method.mdx` + +**Regarding:** The probability always comes from the Foster and Fell evaluation of the original +filter gradation; the adjusted (segregated or washed-out) filter gradation only decides whether +that evaluation runs. + +**Needed:** Confirmation that this is the intended screening treatment and the wording of its +basis, or a statement of how the adjusted gradation should enter the probability (for example, +the larger of the two results). + +**Answer:** + +--- + +## IN-15 — Engineering Basis — `07-gradation-method.mdx` + +**Regarding:** The probability of continuing erosion does not consider the permeability +(drainage) criterion of the filter, although the toolbox evaluation checks it. + +**Needed:** Engineering basis or engineering-judgment attribution for excluding drainage from +the continuation node. + +**Proposed (unconfirmed):** The continuation node addresses whether the filter retains the +eroding base soil; drainage bears on other aspects of performance. + +**Answer:** + +--- + +## IN-16 — Decision — `07-gradation-method.mdx` + +**Regarding:** When a filter band does not reach 15 percent passing, its D15 is undetermined and +the Foster and Fell division takes it as zero. With the fine band's D15 undetermined, every +erosion proportion except no erosion is zero and the probability of continuing erosion is 0, +even for a coarse filter whose coarse band fails the particle retention check. With only the +coarse band's D15 undetermined, the result depends only on whether the fine band's D15 reaches +the continuing erosion boundary of each representative gradation. + +**Needed:** Confirmation that this treatment is intended and the wording of its basis, or a +statement of how an undetermined filter D15 should be handled (for example, rejecting the input +or taking the probability as 1.0). + +**Answer:** + +--- + +## IN-17 — Engineering Basis — `07-gradation-method.mdx` + +**Regarding:** The broad-grading assessment treats a band as a gravel when its gravel content +exceeds 50 percent of the band, rather than when its gravel content exceeds its sand content as +in ASTM D2487. A band with more gravel than sand but no more than 50 percent gravel is held to +the sand limit Cu ≥ 6; with less than 15 percent fines it is more often taken as not broadly +graded and not regraded, giving a larger D85B and a less restrictive no-erosion limit. + +**Needed:** Engineering basis or engineering-judgment attribution for the 50 percent rule, or +confirmation that the ASTM D2487 comparison of gravel with sand is intended. + +**Answer:** + +--- + +## IN-18 — Engineering Basis — `07-gradation-method.mdx` + +**Regarding:** When a base soil band's fines content is undetermined (its gradation does not +extend down to 0.075 mm), the band is treated as having less than 15 percent fines; when its +gravel content is undetermined, it is treated as having no particles larger than the No. 4 +sieve; and when the fine band's fines content is undetermined, the particle retention check uses +base soil category 4. These defaults can skip regrading and can raise or lower the no-erosion +limit. + +**Needed:** Engineering basis or engineering-judgment attribution for these defaults, or a +statement of how an undetermined fines or gravel content should be handled (for example, +rejecting the input). + +**Answer:** + +--- diff --git a/src/docConfig.js b/src/docConfig.js index 3aa150ad4..059208b56 100644 --- a/src/docConfig.js +++ b/src/docConfig.js @@ -341,7 +341,8 @@ const docs = [ software: 'system-response', doc_location: 'web-applications/system-response/continuation-screening', doc_name: 'Continuation (Filter Evaluation) Screening Technical Reference Manual', - active: false, + sidebar_label: 'Continuation (Filter Evaluation) Screening', + active: true, draft: true, }, { diff --git a/static/bibliographies/web-applications/system-response/continuation-screening/v1.0/bib.json b/static/bibliographies/web-applications/system-response/continuation-screening/v1.0/bib.json new file mode 100644 index 000000000..3dfe781e5 --- /dev/null +++ b/static/bibliographies/web-applications/system-response/continuation-screening/v1.0/bib.json @@ -0,0 +1,59 @@ +[ + { + "citationKey": "FEMA2011", + "author": "Federal Emergency Management Agency", + "year": 2011, + "title": "Filters for embankment dams: Best practices for design and construction", + "url": "https://www.fema.gov/sites/default/files/2020-08/filters_embankment_dams_update.pdf" + }, + { + "citationKey": "FosterFell2001", + "author": ["M. A. Foster", "R. Fell"], + "year": 2001, + "title": "Assessing embankment dam filters that do not satisfy design criteria", + "journal": "J. Geotech. Geoenviron. Eng.", + "volume": 127, + "edition": 5, + "pages": "398-407", + "doi": "10.1061/(ASCE)1090-0241(2001)127:5(398)" + }, + { + "citationKey": "Toolbox2008", + "author": ["R. Fell", "M. A. Foster", "J. Cyganiewicz", "G. L. Sills", "N. D. Vroman", "R. R. Davidson"], + "year": 2008, + "title": "Risk analysis for dam safety: A unified method for estimating probabilities of failure of embankment dams by internal erosion and piping guidance document", + "report": "UNICIV Rep. No. R-446 (Version: Delta)", + "institution": "Univ. of New South Wales, Sydney, Australia", + "url": "http://vm.civeng.unsw.edu.au/uniciv/R-446.pdf" + }, + { + "citationKey": "ASTM2487", + "author": "ASTM International", + "year": 2017, + "title": "ASTM D2487-17, Standard practice for classification of soils for engineering purposes (Unified Soil Classification System)", + "publisher": "American Society for Testing and Materials International", + "doi": "10.1520/D2487-17" + }, + { + "citationKey": "Sherard1989", + "author": ["J. L. Sherard", "L. P. Dunnigan"], + "year": 1989, + "title": "Critical filters for impervious soils", + "journal": "J. Geotech. Eng.", + "volume": 115, + "edition": 7, + "pages": "927-947", + "doi": "10.1061/(ASCE)0733-9410(1989)115:7(927)" + }, + { + "citationKey": "Sherard1984", + "author": ["J. L. Sherard", "L. P. Dunnigan", "J. R. Talbot"], + "year": 1984, + "title": "Basic properties of sand and gravel filters", + "journal": "J. Geotech. Eng.", + "volume": 110, + "edition": 6, + "pages": "684-700", + "doi": "10.1061/(ASCE)0733-9410(1984)110:6(684)" + } +]