From 8bf70cbe067e8790ba6778a7b6d26735397af45f Mon Sep 17 00:00:00 2001 From: Adam Gohs Date: Mon, 26 Oct 2026 13:18:26 -0400 Subject: [PATCH 1/2] Updated equation 22 in 06-sellmeijer.mdx --- .../v1.0/06-sellmeijer.mdx | 117 +++++++----------- 1 file changed, 44 insertions(+), 73 deletions(-) diff --git a/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.0/06-sellmeijer.mdx b/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.0/06-sellmeijer.mdx index 67a480518..97ba49ab3 100644 --- a/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.0/06-sellmeijer.mdx +++ b/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.0/06-sellmeijer.mdx @@ -2,18 +2,18 @@ title: Sellmeijer --- -import Figure from "@site/src/components/Figure"; -import FigReference from "@site/src/components/FigureReference"; -import TableVertical from "@site/src/components/TableVertical"; -import TableReference from "@site/src/components/TableReference"; -import Equation from "@site/src/components/Equation"; -import EquationNoRef from "@site/src/components/EquationNoRef"; -import EquationReference from "@site/src/components/EquationReference"; -import Citation from "@site/src/components/Citation"; -import CitationFootnote from "@site/src/components/CitationFootnote"; -import NavContainer from "@site/src/components/NavContainer"; -import Link from "@docusaurus/Link"; -import addBaseUrl from "@docusaurus/useBaseUrl"; +import Link from '@docusaurus/Link'; +import addBaseUrl from '@docusaurus/useBaseUrl'; +import Citation from '@site/src/components/Citation'; +import CitationFootnote from '@site/src/components/CitationFootnote'; +import Equation from '@site/src/components/Equation'; +import EquationNoRef from '@site/src/components/EquationNoRef'; +import EquationReference from '@site/src/components/EquationReference'; +import Figure from '@site/src/components/Figure'; +import FigReference from '@site/src/components/FigureReference'; +import NavContainer from '@site/src/components/NavContainer'; +import TableReference from '@site/src/components/TableReference'; +import TableVertical from '@site/src/components/TableVertical'; . - Particle size with 70 percent finer by weight,{" "} + Particle size with 70 percent finer by weight,{' '} d70 - {" "} + {' '} (millimeters) , <> @@ -61,13 +59,13 @@ piping model testing parameters shown in . Relative density, RD (percent) , ], // Column 1 - ["0.150", "1.3", "35", "50"], // Row 2 - ["0.430", "2.6", "70", "100"], // Row 3 + ['0.150', '1.3', '35', '50'], // Row 2 + ['0.430', '2.6', '70', '100'], // Row 3 ]} alt="Sellmeijer parameter limits." caption="Sellmeijer parameter limits." colWidths={[55, 20, 20]} - colAlign={["center", "center", "center"]} + colAlign={['center', 'center', 'center']} widthMode="intrinsic" /> @@ -153,15 +151,12 @@ of the fine sand (piping) layer, seepage water temperature (_T_), and seepage pa The intrinsic permeability of the fine sand (piping) layer is calculated using . - + where: > _kh_ = permeability of the fine sand (piping) layer in the horizontal direction (m/s) -> _μ_ = dynamic viscosity of water (N·s/m2) +> _μ_ = dynamic viscosity of water (N·s/m2) Use the drop-down list to indicate the presence of a multi-layer foundation (fine sand layer over coarse sand layer). Cells that do not apply have a gray background. Van Beek et al. (2012) conducted piping experiments on multi-layer sand @@ -181,10 +176,7 @@ using . caption="Step 3 of Sellmeijer worksheet: Multi-layer foundation input." > - + where: @@ -192,7 +184,7 @@ where: > _Df_ = thickness of the fine (piping) layer > _kh,c_ = permeability of the coarse underlayer in the horizontal direction (centimeter/second) > _Dc_ = thickness of coarse underlayer (feet) -> _D_ = total aquifer thickness (feet) +> _D_ = total aquifer thickness (feet) When the contrast of permeability is large and the aquifer thickness is relatively large compared to the seepage path length, assuming predominant horizontal flow is no longer valid. Hence, the extension of Sellmeijer’s calculation rule for multi-layer foundations can be applied to elongated aquifers @@ -202,10 +194,7 @@ and . - + For deterministic analysis of single-layer aquifer, input only the most likely value for the fine sand (piping) layer. The mean value used for subsequent calculations is the most likely (or mode) value. illustrates the deterministic @@ -244,8 +233,7 @@ input for single-layer aquifer without using @RISK. For probabilistic analysis of multi-layer aquifer without using @RISK, input the most likely values for the fine sand (piping) layer and underlying coarse sand layer. The mean values used for subsequent calculations are the average of the minimum, most likely, and maximum values. - illustrates -the probabilistic input for multi-layer aquifer without using @RISK. + illustrates the probabilistic input for multi-layer aquifer without using @RISK.
. -, for the critical horizontal gradient -for BEP progression (_ich_), is composed of three terms: a resistance -factor that accounts for the strength of the layer subject to BEP; a scale -factor that relates pore size and seepage size; and a geometrical shape factor. +, for the critical horizontal gradient for BEP progression (_ich_), is composed of three +terms: a resistance factor that accounts for the strength of the layer subject to BEP; a scale factor that relates pore size and seepage size; and a +geometrical shape factor. - + where: > _FR_ = resistance factor (strength of the layer subject to BEP) > _FS_ = scale factor (relating pore size and seepage size) -> _FG_ = geometrical shape factor +> _FG_ = geometrical shape factor The resistance factor is a function of White's constant (_η_), bedding angle (_θ_), relative density (_RD_), roundness of the particles (_KAS_), and coefficient of uniformity (_U_) and is calculated using . @@ -316,7 +300,7 @@ where: > _γ'p_ = submerged unit weight of soil particles (N/m3) > _γw_ = unit weight of water (N/m3) > _θ_ = bedding angle (degrees) -> _η_ = White's constant +> _η_ = White's constant Since it is easier to estimate the specific gravity of soil particles than the submerged unit weight of soil particles, the substitution in is made to the equation for _FR_. @@ -335,15 +319,12 @@ terms from the equation for _FR_ as illustrated in 70_), the horizontal seepage path length (_L_), and the intrinsic permeability of the piping layer (_κ_) and is calculated using . - + where: > _d70_ = particle size (m) for which 70 percent is finer (by weight) -> _κ_ = intrinsic permeability (m2) of the piping layer +> _κ_ = intrinsic permeability (m2) of the piping layer The intrinsic permeability of the piping layer in Equation 20 is either _κf_ for a single-layer aquifer or _kh,avg_ for a multi-layer aquifer. @@ -354,15 +335,12 @@ the value for the fine sand (piping) layer. For multi-layer aquifers, it is the The geometrical factor is a function of the ratio of the depth of the piping layer to the horizontal seepage path length {" "} and is calculated using . - + where: > _D_ = thickness of the piping layer (m) where _D_ = _Df_ for a single-layer aquifer -> _L_ = seepage path length (m) through the piping layer (measured horizontally) +> _L_ = seepage path length (m) through the piping layer (measured horizontally)
. Step 5 calculates the average hydraulic gradient in the foundation by dividing the net hydraulic head by the seepage path length using . - + where: > _∆H_ = net hydraulic head (feet) > _HW_ = headwater level (feet) > _TW_ = tailwater level (feet) -> _L_ = seepage path length (feet) +> _L_ = seepage path length (feet) The FS against BEP progression is calculated using . @@ -424,7 +399,7 @@ The FS against BEP progression is calculated using _ich_ = critical horizontal gradient for BEP progression -> _iavf_ = average horizontal gradient in the foundation at the pipe head +> _iavf_ = average horizontal gradient in the foundation at the pipe head For deterministic analysis, the _FS_ is calculated using the most likely values of the random variables and is summarized in a table. Cells that do not apply have a gray background. @@ -470,12 +445,10 @@ on the secondary axis. Horizontal reference lines display for the mean field cri caption="Step 6 of Sellmeijer worksheet: Deterministic graphical output." >
- illustrates the plot -options for this chart. The maximum value for the primary y-axis (FS against BEP -progression), maximum value for the secondary y-axis (average horizontal gradient -at the pipe head), and minimum and maximum values for the x-axis (headwater level) -are user-specified. Users can input up to five vertical reference elevations, and -user-specified labels display at the top of the chart. + illustrates the plot options for this chart. The maximum value for the primary y-axis (FS against BEP +progression), maximum value for the secondary y-axis (average horizontal gradient at the pipe head), and minimum and maximum values for the x-axis +(headwater level) are user-specified. Users can input up to five vertical reference elevations, and user-specified labels display at the top of the +chart.
- illustrates the plot -options for this chart. The vertical reference elevations and minimum and maximum -values for the x-axis (headwater level) are the same as the input for the previous -chart. Only the maximum value for the y-axis (probability of BEP progression) is -user-specified. + illustrates the plot options for this chart. The vertical reference elevations and minimum and maximum values for +the x-axis (headwater level) are the same as the input for the previous chart. Only the maximum value for the y-axis (probability of BEP progression) +is user-specified.
Date: Mon, 26 Oct 2026 14:42:50 -0400 Subject: [PATCH 2/2] Add v1.1 of BEP Progression Toolbox Technical Manual with corrected equation 22 Restore v1.0 Sellmeijer chapter to the published version, scaffold v1.1 with figures and bibliography, update version history and changelog. --- .../v1.0/06-sellmeijer.mdx | 117 ++-- .../v1.1/00-document-info.mdx | 28 + .../v1.1/00-version-history.mdx | 23 + .../v1.1/01-preface.mdx | 34 ++ .../v1.1/02-terms-and-conditions-for-use.mdx | 46 ++ .../v1.1/03-general-overview.mdx | 143 +++++ .../v1.1/04-background.mdx | 60 ++ .../v1.1/05-schmertmann.mdx | 521 ++++++++++++++++++ .../v1.1/06-sellmeijer.mdx | 483 ++++++++++++++++ .../v1.1/07-creep-ratios.mdx | 179 ++++++ .../v1.1/08-summary.mdx | 85 +++ .../v1.1/09-references.mdx | 18 + .../v1.1/10-appendix-acronyms.mdx | 33 ++ src/pages/changelog.js | 6 +- .../v1.1/bib.json | 129 +++++ .../v1.1/figure1.png | Bin 0 -> 36344 bytes .../v1.1/figure10.png | Bin 0 -> 69948 bytes .../v1.1/figure11.png | Bin 0 -> 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b/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.0/06-sellmeijer.mdx @@ -2,18 +2,18 @@ title: Sellmeijer --- -import Link from '@docusaurus/Link'; -import addBaseUrl from '@docusaurus/useBaseUrl'; -import Citation from '@site/src/components/Citation'; -import CitationFootnote from '@site/src/components/CitationFootnote'; -import Equation from '@site/src/components/Equation'; -import EquationNoRef from '@site/src/components/EquationNoRef'; -import EquationReference from '@site/src/components/EquationReference'; -import Figure from '@site/src/components/Figure'; -import FigReference from '@site/src/components/FigureReference'; -import NavContainer from '@site/src/components/NavContainer'; -import TableReference from '@site/src/components/TableReference'; -import TableVertical from '@site/src/components/TableVertical'; +import Figure from "@site/src/components/Figure"; +import FigReference from "@site/src/components/FigureReference"; +import TableVertical from "@site/src/components/TableVertical"; +import TableReference from "@site/src/components/TableReference"; +import Equation from "@site/src/components/Equation"; +import EquationNoRef from "@site/src/components/EquationNoRef"; +import EquationReference from "@site/src/components/EquationReference"; +import Citation from "@site/src/components/Citation"; +import CitationFootnote from "@site/src/components/CitationFootnote"; +import NavContainer from "@site/src/components/NavContainer"; +import Link from "@docusaurus/Link"; +import addBaseUrl from "@docusaurus/useBaseUrl"; . - Particle size with 70 percent finer by weight,{' '} + Particle size with 70 percent finer by weight,{" "} d70 - {' '} + {" "} (millimeters) , <> @@ -59,13 +61,13 @@ piping model testing parameters shown in . Relative density, RD (percent) , ], // Column 1 - ['0.150', '1.3', '35', '50'], // Row 2 - ['0.430', '2.6', '70', '100'], // Row 3 + ["0.150", "1.3", "35", "50"], // Row 2 + ["0.430", "2.6", "70", "100"], // Row 3 ]} alt="Sellmeijer parameter limits." caption="Sellmeijer parameter limits." colWidths={[55, 20, 20]} - colAlign={['center', 'center', 'center']} + colAlign={["center", "center", "center"]} widthMode="intrinsic" /> @@ -151,12 +153,15 @@ of the fine sand (piping) layer, seepage water temperature (_T_), and seepage pa The intrinsic permeability of the fine sand (piping) layer is calculated using . - + where: > _kh_ = permeability of the fine sand (piping) layer in the horizontal direction (m/s) -> _μ_ = dynamic viscosity of water (N·s/m2) +> _μ_ = dynamic viscosity of water (N·s/m2) Use the drop-down list to indicate the presence of a multi-layer foundation (fine sand layer over coarse sand layer). Cells that do not apply have a gray background. Van Beek et al. (2012) conducted piping experiments on multi-layer sand @@ -176,7 +181,10 @@ using . caption="Step 3 of Sellmeijer worksheet: Multi-layer foundation input." >
- + where: @@ -184,7 +192,7 @@ where: > _Df_ = thickness of the fine (piping) layer > _kh,c_ = permeability of the coarse underlayer in the horizontal direction (centimeter/second) > _Dc_ = thickness of coarse underlayer (feet) -> _D_ = total aquifer thickness (feet) +> _D_ = total aquifer thickness (feet) When the contrast of permeability is large and the aquifer thickness is relatively large compared to the seepage path length, assuming predominant horizontal flow is no longer valid. Hence, the extension of Sellmeijer’s calculation rule for multi-layer foundations can be applied to elongated aquifers @@ -194,7 +202,10 @@ and . - + For deterministic analysis of single-layer aquifer, input only the most likely value for the fine sand (piping) layer. The mean value used for subsequent calculations is the most likely (or mode) value. illustrates the deterministic @@ -233,7 +244,8 @@ input for single-layer aquifer without using @RISK. For probabilistic analysis of multi-layer aquifer without using @RISK, input the most likely values for the fine sand (piping) layer and underlying coarse sand layer. The mean values used for subsequent calculations are the average of the minimum, most likely, and maximum values. - illustrates the probabilistic input for multi-layer aquifer without using @RISK. + illustrates +the probabilistic input for multi-layer aquifer without using @RISK.
. -, for the critical horizontal gradient for BEP progression (_ich_), is composed of three -terms: a resistance factor that accounts for the strength of the layer subject to BEP; a scale factor that relates pore size and seepage size; and a -geometrical shape factor. +, for the critical horizontal gradient +for BEP progression (_ich_), is composed of three terms: a resistance +factor that accounts for the strength of the layer subject to BEP; a scale +factor that relates pore size and seepage size; and a geometrical shape factor. - + where: > _FR_ = resistance factor (strength of the layer subject to BEP) > _FS_ = scale factor (relating pore size and seepage size) -> _FG_ = geometrical shape factor +> _FG_ = geometrical shape factor The resistance factor is a function of White's constant (_η_), bedding angle (_θ_), relative density (_RD_), roundness of the particles (_KAS_), and coefficient of uniformity (_U_) and is calculated using . @@ -300,7 +316,7 @@ where: > _γ'p_ = submerged unit weight of soil particles (N/m3) > _γw_ = unit weight of water (N/m3) > _θ_ = bedding angle (degrees) -> _η_ = White's constant +> _η_ = White's constant Since it is easier to estimate the specific gravity of soil particles than the submerged unit weight of soil particles, the substitution in is made to the equation for _FR_. @@ -319,12 +335,15 @@ terms from the equation for _FR_ as illustrated in 70_), the horizontal seepage path length (_L_), and the intrinsic permeability of the piping layer (_κ_) and is calculated using . - + where: > _d70_ = particle size (m) for which 70 percent is finer (by weight) -> _κ_ = intrinsic permeability (m2) of the piping layer +> _κ_ = intrinsic permeability (m2) of the piping layer The intrinsic permeability of the piping layer in Equation 20 is either _κf_ for a single-layer aquifer or _kh,avg_ for a multi-layer aquifer. @@ -335,12 +354,15 @@ the value for the fine sand (piping) layer. For multi-layer aquifers, it is the The geometrical factor is a function of the ratio of the depth of the piping layer to the horizontal seepage path length {" "} and is calculated using . - + where: > _D_ = thickness of the piping layer (m) where _D_ = _Df_ for a single-layer aquifer -> _L_ = seepage path length (m) through the piping layer (measured horizontally) +> _L_ = seepage path length (m) through the piping layer (measured horizontally)
. Step 5 calculates the average hydraulic gradient in the foundation by dividing the net hydraulic head by the seepage path length using . - + where: > _∆H_ = net hydraulic head (feet) > _HW_ = headwater level (feet) > _TW_ = tailwater level (feet) -> _L_ = seepage path length (feet) +> _L_ = seepage path length (feet) The FS against BEP progression is calculated using . @@ -399,7 +424,7 @@ The FS against BEP progression is calculated using _ich_ = critical horizontal gradient for BEP progression -> _iavf_ = average horizontal gradient in the foundation at the pipe head +> _iavf_ = average horizontal gradient in the foundation at the pipe head For deterministic analysis, the _FS_ is calculated using the most likely values of the random variables and is summarized in a table. Cells that do not apply have a gray background. @@ -445,10 +470,12 @@ on the secondary axis. Horizontal reference lines display for the mean field cri caption="Step 6 of Sellmeijer worksheet: Deterministic graphical output." >
- illustrates the plot options for this chart. The maximum value for the primary y-axis (FS against BEP -progression), maximum value for the secondary y-axis (average horizontal gradient at the pipe head), and minimum and maximum values for the x-axis -(headwater level) are user-specified. Users can input up to five vertical reference elevations, and user-specified labels display at the top of the -chart. + illustrates the plot +options for this chart. The maximum value for the primary y-axis (FS against BEP +progression), maximum value for the secondary y-axis (average horizontal gradient +at the pipe head), and minimum and maximum values for the x-axis (headwater level) +are user-specified. Users can input up to five vertical reference elevations, and +user-specified labels display at the top of the chart.
- illustrates the plot options for this chart. The vertical reference elevations and minimum and maximum values for -the x-axis (headwater level) are the same as the input for the previous chart. Only the maximum value for the y-axis (probability of BEP progression) -is user-specified. + illustrates the plot +options for this chart. The vertical reference elevations and minimum and maximum +values for the x-axis (headwater level) are the same as the input for the previous +chart. Only the maximum value for the y-axis (probability of BEP progression) is +user-specified.
RMC Backward Erosion Piping (Progression) Toolbox Technical Manual, Lakewood, CO: U.S. Army Corps of Engineers, Risk Management Center, 2025. Accessed on {enter current date here}." +--- + +import NavContainer from "@site/src/components/NavContainer"; +import DocumentMetadata from "@site/src/components/DocumentMetadata"; +import Link from "@docusaurus/Link"; +import addBaseUrl from "@docusaurus/useBaseUrl"; + + + +# Document Information + + diff --git a/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/00-version-history.mdx b/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/00-version-history.mdx new file mode 100644 index 000000000..cf0b7943c --- /dev/null +++ b/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/00-version-history.mdx @@ -0,0 +1,23 @@ +import Link from '@docusaurus/Link'; +import NavContainer from '@site/src/components/NavContainer'; +import TableVersionHistory from '@site/src/components/TableVersionHistory'; + + + +# Version History + + diff --git a/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/01-preface.mdx b/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/01-preface.mdx new file mode 100644 index 000000000..d9c34ae88 --- /dev/null +++ b/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/01-preface.mdx @@ -0,0 +1,34 @@ +--- +title: Preface +--- + +import NavContainer from "@site/src/components/NavContainer"; +import VersionSelector from "@site/src/components/VersionSelector"; +import Link from "@docusaurus/Link"; +import addBaseUrl from "@docusaurus/useBaseUrl"; + + + +# Preface + +The Risk Management Center (RMC) of the U.S. Army Corps of Engineers (USACE) has developed a suite of Microsoft Excel spreadsheets to support +risk assessments for dam and levee safety. Each analysis suite is composed of multiple toolboxes (Microsoft Excel workbooks), and each toolbox +contains multiple spreadsheet tools or calculation worksheets (Microsoft Excel worksheets). The RMC Backward Erosion Piping (Progression) Toolbox +is part of the RMC Internal Erosion Suite. + +The information from these spreadsheet tools, along with other pertinent information, informs judgment when developing a list of more and less +likely factors and estimating probabilities. USACE best practice for estimating probabilities is to use the best available and multiple methods, +but all final probabilities are estimated using team elicitation based on the totality and strength of the evidence. + +The RMC continuously works to improve the performance of RMC software; report possible bugs directly to the RMC at the address listed below. +Ideally, report suspected errors in written form with a description of the problem and the steps that lead to its occurrence. Suggestions for +improvement are also welcomed. + +U.S. Army Corps of Engineers +Institute for Water Resources +Risk Management Center +[rmc.software@usace.army.mil](mailto:rmc.software@usace.army.mil) diff --git a/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/02-terms-and-conditions-for-use.mdx b/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/02-terms-and-conditions-for-use.mdx new file mode 100644 index 000000000..d0a7330c2 --- /dev/null +++ b/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/02-terms-and-conditions-for-use.mdx @@ -0,0 +1,46 @@ +--- +title: Terms and Conditions +--- + +import NavContainer from "@site/src/components/NavContainer"; +import VersionSelector from "@site/src/components/VersionSelector"; +import Link from "@docusaurus/Link"; +import addBaseUrl from "@docusaurus/useBaseUrl"; + + + +# Terms and Conditions for Use + +By using Institute for Water Resources (IWR) software, users voluntarily accept the following terms and conditions. Users that do not agree to these terms and conditions should uninstall the IWR software and return any program materials to IWR and its technical centers. If users downloaded the software and do not have disk media, delete all copies and cease using the software. + +## Terms and Conditions for Use of Institute for Water Resources Software + +The United States Government, U.S. Army Corps of Engineers, Institute for Water Resources (“IWR”), and IWR’s technical centers including the Risk Management Center (“RMC”) and Hydrologic Engineering Center (“HEC”) grant to the user the rights to install “IWR Software” (either from a disk copy obtained from IWR and IWR’s technical centers, a distributor or another user or by downloading it from a network) and to use, copy and/or distribute copies of the IWR Software to other users, subject to the following Terms and Conditions of Use: + +- All copies of the IWR Software received or reproduced by or for user pursuant to the authority of this Terms and Conditions of Use will be and remain the property of IWR. + +- User may reproduce and distribute the IWR Software provided that the recipient agrees to the Terms and Conditions for Use noted herein. + +- IWR and IWR’s technical centers are solely responsible for the content of the IWR Software. The IWR Software may not be modified, abridged, decompiled, disassembled, unobfuscated or reverse engineered. The user is solely responsible for the content, interactions, and effects of any and all amendments, if present, whether they be extension modules, language resource bundles, scripts, or any other amendment. + +- The name of the IWR Software must not be used to endorse or promote products derived from the IWR Software. Products derived from the IWR Software may not be called the IWR Software nor may any part of the IWR Software name appear within the name of derived products. + +- No part of this Terms and Conditions for Use may be modified, deleted or obliterated from the IWR Software. + +- No part of the IWR Software may be exported or re-exported in contravention of U.S. export laws or regulations. + +## Waiver of Warranty + +THE UNITED STATES GOVERNMENT AND ITS AGENCIES, OFFICIALS, REPRESENTATIVES, AND EMPLOYEES, INCLUDING ITS CONTRACTORS AND SUPPLIERS PROVIDE THE IWR SOFTWARE “AS IS,” WITHOUT ANY WARRANTY OR CONDITION, EXPRESS, IMPLIED OR STATUTORY, AND SPECIFICALLY DISCLAIM ANY IMPLIED WARRANTIES OF TITLE, MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. Depending on state law, the foregoing disclaimer may not apply to you, and you may also have other legal rights that vary from state to state. + +## Limitation of Liability + +IN NO EVENT SHALL THE UNITED STATES GOVERNMENT AND ITS AGENCIES, OFFICIALS, REPRESENTATIVES, AND EMPLOYEES, INCLUDING ITS CONTRACTORS AND SUPPLIERS, BE LIABLE FOR LOST PROFITS OR ANY SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF OR IN CONNECTION WITH USE OF THE IWR SOFTWARE REGARDLESS OF CAUSE, INCLUDING NEGLIGENCE. THE UNITED STATES GOVERNMENT’S LIABILITY, AND THE LIABILITY OF ITS AGENCIES, OFFICIALS, REPRESENTATIVES, AND EMPLOYEES, INCLUDING ITS CONTRACTORS AND SUPPLIERS, TO YOU OR ANY THIRD PARTIES IN ANY CIRCUMSTANCE IS LIMITED TO THE REPLACEMENT OF CERTIFIED COPIES OF THE IWR SOFTWARE WITH IDENTIFIED ERRORS CORRECTED. Depending on state law, the above limitation or exclusion may not apply to you. + +## Indemnity + +As a voluntary user of the IWR Software you agree to indemnify and hold the United States Government, and its agencies, officials, representatives, and employees, including its contractors and suppliers, harmless from any claim or demand, including reasonable attorneys’ fees, made by any third party due to or arising out of your use of the IWR Software or breach of this Agreement or your violation of any law or the rights of a third party. diff --git a/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/03-general-overview.mdx b/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/03-general-overview.mdx new file mode 100644 index 000000000..2ed03df47 --- /dev/null +++ b/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/03-general-overview.mdx @@ -0,0 +1,143 @@ +--- +title: General Overview +--- + +import Link from '@docusaurus/Link'; +import addBaseUrl from '@docusaurus/useBaseUrl'; +import Citation from '@site/src/components/Citation'; +import CitationFootnote from '@site/src/components/CitationFootnote'; +import Figure from '@site/src/components/Figure'; +import FigReference from '@site/src/components/FigureReference'; +import NavContainer from '@site/src/components/NavContainer'; + + + +# General Overview + +## Getting Started + +Copy or download the toolbox file to the computer. To open the toolbox file, either: + +- Find the file on the computer and double-click it. This opens the file in Microsoft Excel. +- Open Microsoft Excel and use the application to open the file: Once Microsoft Excel is open, go to the File menu at the top of the window and select Open. + +The toolbox is an Excel binary workbook (.xlsb) that uses macros. You may need to enable the macros, either before opening the file or by clicking +“Enable Content” in the yellow Security Warning message bar with a shield icon that appears after the file is opened. The actual message in the +message bar will vary depending on the computer’s settings and installed add-ins. displays examples of different wordings that may appear in the message bar. + +
+ +## Organization + +Although the toolbox does not provide a calculation cover sheet, adding one is strongly recommended. A calculation cover sheet captures project +information, a description and purpose of the calculation, the assumptions for critical input parameters, a summary of the major conclusion and +results, and a revision history. + +Each toolbox has a similar appearance and organizational structure: + +- The first worksheet, About, summarizes the purpose of the toolbox and gives contact information for the RMC software development team. +- The second worksheet, Terms and Conditions, contains the terms and conditions for use of the toolbox (IWR software). +- The third worksheet, Version History, contains the revision history. Semantic versioning is used in the format of MAJOR.MINOR.PATCH: + - MAJOR - significant worksheet changes not compatible with previous versions. + - MINOR - additional features or enhancements that do not fundamentally change the calculations. + - PATCH - backward-compatible bug fixes. +- The fourth worksheet, References, lists the references cited for each calculation worksheet. + +The workbook and worksheets are not protected to prevent unwanted changes. However, because the toolbox has user-defined functions (UDFs) and +subroutines in Visual Basic, you cannot directly copy worksheets to another workbook without potentially losing functionality. A note in a bold +red font at the upper right margin indicates if the selected worksheet includes such features. + +At the top of each calculation worksheet, input information for the preparer and checker for quality control (QC) documentation and the calculation +title in case multiple copies of the worksheet are created for different analysis scenarios (). +The footer of each calculation worksheet contains the version number, which can be cross-referenced with the revision history on the third worksheet. + +
+ +User-specified input includes values and selections from drop-down lists. User input cells are light yellow, and these cells are unprotected. +When cells use drop-down lists, a note in blue font in the right margin of the row alerts the user to use the drop-down list. Conditional formatting +applies a gray background to cells that are not based on a user selection. When a user-specified value or calculated value is outside of acceptable +ranges, the cell is orange to indicate caution to the user. + +All units for user-specified input values are clearly labeled. Most user-specified input values use English units. However, values may be in metric +where metric units are more common in practice (e.g., particle size in millimeters or permeability in centimeters per second). The toolbox may convert +English units to metric units to perform some calculations or if required for a specific formula based on the reference material for the equation. + +If the calculation worksheet is a function of headwater level, up to seven headwater and tailwater levels may be specified at the top of the worksheet. +Tailwater may be required to calculate the net hydraulic head and hydraulic gradient. Specify the elevation datum by selecting one of three options +from the drop-down list: ft-NAVD88, ft-NGVD29, and Other. The two datum selections include English units of length (feet). If Other is selected, provide +a user-specified datum along with feet (e.g., ft-MSL [Mean Sea Level]). , , and illustrate +the three possible scenarios. + +
+ +
+ +
+ +Most calculation worksheets break down complex analysis into computational steps following a logical sequence (). Some simpler +worksheets do not have steps. Generally, different methodologies are unique worksheets. Some worksheets may include multiple methodologies, which +are labeled as options (). + +
+ +
+ +Some calculation worksheets can perform either a deterministic or probabilistic analysis. Although not required to perform a probabilistic +analysis, Palisade @RISK software (standalone version or as part of the Palisade DecisionTools Suite) can customize the probabilistic analysis. +A note appears in a bold red font at the upper right-hand margin of a calculation worksheet indicating if this feature is included with the toolbox. + +User notes generally appear in the right margin of each calculation worksheet. Some notes are in blue or red font for heightened awareness. These +notes include references to source materials for equations, figures, tables, pages, etc. If the RMC modified the source material, the reference +citation says “adapted from” instead of “from.” + +Tabular and/or graphical summaries are generally the primary output of the toolbox. The UDFs in the PlotScale module change the minimum and maximum +values of the x-axis and y-axis for charts. If the calculation worksheet is a function of headwater level, you can define up to five headwater levels +of interest and plot them as vertical reference lines. By selecting the chart and then selecting the Filter icon to display the filter pane, you can +choose which data series to display. This is useful when computing the results from multiple methodologies, but not all are applicable or desired to display. diff --git a/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/04-background.mdx b/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/04-background.mdx new file mode 100644 index 000000000..6c24d521d --- /dev/null +++ b/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/04-background.mdx @@ -0,0 +1,60 @@ +--- +title: Background +--- + +import Figure from "@site/src/components/Figure"; +import FigReference from "@site/src/components/FigureReference"; +import Citation from "@site/src/components/Citation"; +import CitationFootnote from "@site/src/components/CitationFootnote"; +import NavContainer from "@site/src/components/NavContainer"; +import Link from "@docusaurus/Link"; +import addBaseUrl from "@docusaurus/useBaseUrl"; + + + +# Background + +Backward erosion piping (BEP) is the detachment of soil particles that occurs at a free, unfiltered surface in which the process gradually +works its way toward the upstream or floodside of the embankment or its foundation until a continuous pipe is formed. +Erosion initiates at the downstream side of a dam or the landside of a levee through unfiltered seepage exits that may exist due to penetrations +or weaknesses in the overlying blanket, such as ditches, animal burrows (such as rodent or crawfish holes), root holes, former sand boils, cracks, +or other thin or weak spots. Once erosion initiates, the pipe may progress horizontally through the foundation in the direction toward the +impounded water if hydraulic gradients in the foundation are sufficiently high. The hydraulic gradients and flow must remain high near the upstream +or floodside tip of the progressing pipe for particles to continue eroding. + +To assess the likelihood of BEP progression (hydraulic condition), the global or average horizontal gradient in the foundation at the pipe +head, _iavf = ΔH/L_, as illustrated in , can be compared to the +critical horizontal gradient for BEP progression. + +There are several methods for assessing the critical horizontal gradient. Creep ratios are an empirical method based on observations of seepage +performance for a range of soil types and are among the oldest methods. The inverse of the creep ratio is the average horizontal gradient if +there are no vertical structures. More recently, methods based on horizontal gradient have gained more attention for evaluating the potential for BEP of cohesionless soils, +specifically based on laboratory research involving laboratory flume tests to study the hydraulic gradient across a structure required to achieve +complete pipe formation. + +
+ +This toolbox deterministically and probabilistically assesses the likelihood of BEP progression using the adjusted Schmertmann (2000) method +and the adjusted calculation rule of Sellmeijer et al. (2011) , in +addition to the creep ratio methods of Bligh (1910) and Lane (1935) . + +Applying these methods correctly requires an understanding of the context from which each method was developed. Robbins and van Beek (2015) +provide a more detailed review of the background, advantages, and disadvantages of each method and the various laboratory test conditions (such +as density, exit configuration, soil characteristics, and scale effects) that significantly impact the findings. For example, the adjusted +Schmertmann method and adjusted calculation rule of Sellmeijer et al. can be used only for situations that have a purely two-dimensional (2D) +seepage regime (applicable only to situations that have uniform boundary conditions parallel to the embankment centerline, such as an exposed +ditch or no confining layer). Some methods may not apply to the materials under consideration. For example, the adjusted calculation rule of +Sellmeijer et al. applies only within the range of soils tested. For soils beyond the suggested ranges and differing exit configurations, the +methods are not necessarily applicable, and the actual critical horizontal gradients may be quite different from what is estimated. + + diff --git a/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/05-schmertmann.mdx b/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/05-schmertmann.mdx new file mode 100644 index 000000000..c5efe9de1 --- /dev/null +++ b/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/05-schmertmann.mdx @@ -0,0 +1,521 @@ +--- +title: Schmertmann +--- + +import Link from '@docusaurus/Link'; +import addBaseUrl from '@docusaurus/useBaseUrl'; +import Citation from '@site/src/components/Citation'; +import CitationFootnote from '@site/src/components/CitationFootnote'; +import Equation from '@site/src/components/Equation'; +import EquationNoRef from '@site/src/components/EquationNoRef'; +import EquationReference from '@site/src/components/EquationReference'; +import Figure from '@site/src/components/Figure'; +import FigReference from '@site/src/components/FigureReference'; +import NavContainer from '@site/src/components/NavContainer'; +import TableReference from '@site/src/components/TableReference'; +import TableVertical from '@site/src/components/TableVertical'; + + + +# Schmertmann + +Schmertmann (2000) developed an approach for estimating the factor of safety +(_FS_) regarding piping using the concept of ambient, pre-pipe, hydraulic gradients along the potential piping path based on laboratory flume tests. The FS for +pipe progression is given in : + + + +where: + +> _ipmt_ = maximum pre-pipe hydraulic gradient along the pipe path in the reference laboratory test (that is, laboratory horizontal critical gradient) +> _if_ = maximum pre-pipe hydraulic gradient along the pipe path in the field +> _CD_ = depth/length factor +> _CL_ = total pipe length factor +> _CS_ = grain-size factor +> _CK_ = anisotropic permeability factor +> _Cγ_ = density factor +> _CZ_ = underlayer factor +> _Cα_ = adjustment for pipe inclination +> _CR_ = embankment axis curvature factor + +Schmertmann applied these correction factors to more than 100 laboratory flume tests to adjust the laboratory results to the reference values shown +in . + + + Seepage path length, L + , + <> + Piping Layer Depth, D + , + <> + Particle size with 10% passing by weight,{' '} + + d10 + + , + <> + Anisotropy,{' '} + + + + , + <> + Relative density,{' '} + + Dr + + , + <> + Pipe path inclination, α + , + ], // Column 1 + ['5 feet', '1 foot', '0.20 millimeters', '1.5', '60 percent', '0 degrees'], // Row 2 + ]} + alt="Schmertmann reference test values" + caption="Schmertmann reference test values" + colWidths={[30, 20]} + colAlign={['center', 'center']} + widthMode="intrinsic" +/> + +From the corrected values, Schmertmann proposed a no-test default relationship as the default value of _ipmt_ to use in assessments if +laboratory flume tests were not conducted, shown in +and . + + + +where + +> _Cu_ = coefficient of uniformity + +
+ + and + can be used along with the correction factors to assess the FS for BEP progression in the field. While this +figure is quite useful, it is difficult to estimate the uncertainty in the critical point gradient because study averages were presented. For example, +one of the single data points is the average from 14 individual laboratory tests. + +To assess the likelihood of BEP progression, Robbins and Sharp (2016) compiled +all the data in Schmertmann (2000) and developed a probabilistic chart for +determining ipmt, again relative to the reference values, as shown in . +Robbins and O’Leary (2020) expanded this chart to include 0 percent and 100 +percent probability trend lines based on linear extrapolation of the slopes and intercepts of the quantile regression lines. + +
+ +To calculate a probability of BEP progression using the lines shown on the probability chart, the value of _ipmt_ must be calculated +for a given field scenario as shown in . + + + +The probabilistic chart from Robbins and Sharp (2016) shows that the uncertainty +with the laboratory critical gradient increases with increasing _Cu_, where there is less data. In addition, at higher _Cu_ values, +soils tend to become internally unstable. Therefore, the probabilistic chart is limited to a _Cu_ between 1.1 and about 4. + +## Method of Analysis + +In step 1, use the drop-down list to select the method of analysis (probabilistic or deterministic). There are two options for probabilistic analysis. The +first performs 1,000 iterations (judged adequate for most applications) without using Palisade's @RISK software. This provides flexibility if an @RISK +software license is not available. The second uses @RISK to customize the probabilistic analysis. Use the drop-down list to select Yes if @RISK is to +be used and No if @RISK is not used. The three possible scenarios are illustrated in +through . + +
+ +
+ +
+ +## Piping Layer Characterization + +Step 2 characterizes the piping layer. The input includes the depth (thickness) of the piping layer (_D_), coefficient of uniformity (_Cu_), grain size +in the field with 10 percent finer by weight (_d10f_), anisotropy in the field of the piping layer (_Rkf_), relative density in the field (_Drf_), and +angle of the pipe path (_α_). The adjusted Schmertmann method uses the probabilistic chart of Robbins and Sharp (2016) , +expanded by Robbins and O’Leary (2020) , for both the deterministic and probabilistic +methods and is limited to _Cu_ between 1.1 and 4. _Cu_ values outside of this range have an orange background. The depth (thickness of the piping layer) +is in the direction perpendicular to the angle of the pipe path discussed later in this section. + +The selections in Step 1 affect the input for Step 2, and cells that do not apply have a gray background. These cells are not used in subsequent +calculations even if data is present. + +For deterministic analysis, input only the most likely values. The mean value used for subsequent calculations is the most likely (or mode) +value. illustrates the deterministic input. + +
+ +For probabilistic analysis without using @RISK, input the minimum and maximum values in addition to the most likely value, and triangular distributions +represent the random variables. The mean values used in subsequent calculations are the average of the minimum, most likely, and maximum +values. illustrates probabilistic input without using @RISK. + +
+ +For probabilistic analysis using @RISK, input the minimum, most likely, and maximum values, and use an @RISK formula for a triangular distribution in +the third column as a default. Alternatively, input a valid @RISK distribution in lieu of this default formula, and the user-specified input displays +in the fourth column. The mean values used for subsequent calculations are the means for the @RISK distributions entered in the third +column. illustrates the probabilistic input without using @RISK. + +
+ +If using @RISK to perform probabilistic analysis, delete unnecessary calculation worksheets because the simulation is performed for all worksheets in +the workbook, which is time consuming. If cycling through iterations using @RISK, the displayed results are no longer mean values of the random +variables; they are the selected iteration’s values. + +The remaining input for step 2 addresses pipe path geometry as illustrated in and +includes the angle of the pipe path (_α_) with respect to horizontal and the direct (not meandered) length between ends of a completed pipe path (_L_). +A figure is included in this step as a guide. + +In most cases, the pipe path is horizontal, and _α_ = 0 degrees. The angle is positive for pipe paths that progress upwards and negative for pipe paths +that progress downwards. Based on Schmertmann (2000) , the range for _α_ is +between -90 degrees and 40 degrees. Cells where the input parameter is outside these limits have an orange background. + +Based on the user-specified anisotropy, the ratio of the depth of the piping layer to the length of the pipe path in the field +is calculated, and the transformed length of the piping path in the field (_Lf_) is calculated using . + + + +where: + +> _Rkf_ = anisotropy in the field of the piping layer (_kh/kv_) + +
+ +## Laboratory Horizontal Critical gradient + +Step 3 estimates the laboratory horizontal critical gradient. Use the drop-down list to indicate if a laboratory flume test was performed. Cells that +do not apply have a gray background. For a laboratory flume test, input the measured laboratory horizontal critical gradient as illustrated +in . In practice, laboratory flume tests are rarely conducted to measure the critical +horizontal gradient, and the linear relationship proposed by Schmertmann (2000) is +the primary means for estimating critical gradient values as a function of coefficient of uniformity (_Cu_). In this toolbox, the 50 percent quantile +line from Robbins and Sharp (2016) is used in lieu of Schmertmann’s no-test default +line using as illustrated in . + + + +Robbins and Sharp found that the best fit, median line of all test results indicates Schmertmann's no-test default line is conservative for _Cu_ < 3 +and unconservative for _Cu_ > 3. + +
+ +
+ +## Field Horizontal Critical Gradient + +Step 4 calculates the field horizontal critical gradient by applying the various correction factors to the estimated or measured laboratory horizontal critical +gradient as illustrated in . The correction factors for foundation depth, seepage path +length, grain size, anisotropy, and soil density are estimated using , +{" "}, , +{" "}, and . +Since a straight axis is assumed for the embankment, there is no correction factor for curvature in the embankment axis, and _CR_ = 1. + + + + + + + + + + + +where: + +{/* prettier-ignore */} +> = ratio of depth of piping layer to length of pipe path in the field +> _Lf_ = transformed length (feet) of the pipe path in the field +> = anisotropy in the field (_Rkf_) +> _Drf_ = relative density in the field + +
+ +A higher permeability layer beneath the piping layer increases the flow toward the pipe and decreases the critical gradient. Use the drop-down list to indicate +the presence of a higher permeability underlayer (for example, fine sand layer over coarse sand layer). If there is no higher permeability underlayer, _CZ_ = 1 +as illustrated in . Cells that do not apply have a gray background. If a higher permeability +underlayer exists, input the permeability of the piping layer (_kp_), permeability of the underlayer (_ku_), and equivalent radius of the +developing pipe cross section (_r_) to estimate the underlayer correction factor (_CZ_). + +Schmertmann (2000) provided _CZ_ as a function +of for , +{" "}, and +based on very limited data derived from flow nets of the University of Florida flume. CZ is obtained from two-way linear interpolation using these three curves +as illustrated in . Fell et al. (2008) +suggests using _CZ_ = 1 since r is very small and is typically very +large in practice; _CZ_ is approximately 1 when is greater than about 80. +For very thin erodible layers (less than a couple of feet), Fell et al. (2008) suggested using r = 2.5 +to 10 mm, where the horizontal critical gradient decreases as r increases. If thin alternating layers of erodible and non-erodible soil are modeled as a homogenous layer +with high anisotropy, use _CZ_ = 1. + +
+ +
+ +The field horizontal critical gradient is calculated using the above correction factors and +as illustrated in . + + + +
+ +## Pipe Path Inclination + +Step 5 determines the adjustment for pipe path inclination. In most cases, the pipe path is horizontal (_α_ = 0 degrees), and _Cα_= 1. Cells that do not apply +have a gray background. If the pipe path inclination is not zero, Schmertmann (2000) provided +the field critical gradient adjusted for pipe path inclination (_ipα_) as a function of _α_ for field horizontal critical gradients (_ipo_) of 0.05, +0.10, 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, 0.45, and 0.50 or greater, as illustrated in . _ipα_ is +obtained from two-way linear interpolation using these ten curves. The back-calculated adjustment for pipe path inclination uses . + + + +
+ +## Field Critical Gradient for BEP progression + +Step 6 adjusts the field horizontal critical gradient for pipe path inclination using the adjustment for pipe path inclination (_Cα_) from step 4 +using . + + + +If the pipe path is horizontal, _ipα_ = _ich_ because _Cα_ = 1. + +Schmertmann’s adjusted model applies to 2D seepage with plane or ditch exits parallel to the embankment centerline. Van Beek et al. (2015) found +that three-dimensional (3D) configurations with flow toward a single point (such as a hole in a confining layer) resulted in significantly smaller critical gradients than +predicted by the Dutch piping model. In both the small and medium-scale experiments, the model overestimated the critical gradient by a factor of approximately two. Although +not developed and calibrated for this method, a similar reduction for a 3D exit condition is appropriate. If the field horizontal critical gradient is further adjusted for +3D flow, input a user-specified gradient reduction factor (GRF). Cells that do not apply have a gray background. +and illustrate the two scenarios. + +
+ +
+ +## Likelihood of Backward Erosion Piping Progression + +Robbins and Sharp (2016) presented the results of a best-fit quantile regression analysis +from the individual laboratory flume tests, which were expanded by Robbins and O'Leary (2020) +to include 0 percent and 100 percent probability trend lines based on linear extrapolation of the slopes and intercepts of the quantile regression lines. Step 7 +uses this modified chart to develop a cumulative density function to estimate the probability of BEP progression as illustrated +in . + +
+ +The average horizontal gradient in the foundation at the pipe head is calculated by dividing the net hydraulic head by the seepage path length +using . + + + +where: + +> _ΔH_ = net hydraulic head (feet) +> _HW_ = headwater level (feet) +> _TW_ = tailwater level (feet) +> _L_ = direct (not meandered) seepage path length (feet) + +The FS against BEP progression is calculated using . + + + +where: + +> _ipα_ = critical gradient for BEP progression (adjusted for pipe path inclination) +> _iavf_ = average horizontal gradient in the foundation at the pipe head + +For deterministic analysis, the FS is calculated using the most likely values of the random variables and summarized in a table. Cells that do not apply have +a gray background. For probabilistic analysis, the FS is calculated as described for the deterministic analysis but for the mean values of the random variables, +and multiple iterations are performed by sampling the distributions in step 2. The probability of BEP progression is equal to the percentage of iterations that +resulted in a FS less than 1 [P(FS < 1)]. For probabilistic analysis performed without using @RISK, 1,000 iterations are used. For probabilistic analysis using +@RISK, the number of iterations is user-specified, and “@RISK” displays in parentheses after the number of iterations for this scenario. If cycling through +iterations using @RISK, the displayed results are no longer mean values; they are the selected iteration’s values. For deterministic and probabilistic analyses, +cells with FS less than 1 have an orange background. illustrates the deterministic +tabular output, and illustrates the probabilistic tabular output without using @RISK. + +
+ +
+ +## Summary Plots + +Step 8 generates the summary plots. The first plot is the mean FS against BEP progression (red solid line) and average horizontal gradient at the pipe head (green +solid line) as functions of headwater level. If cycling through iterations using @RISK, the displayed results are no longer mean values; they are the selected +iteration. FS against BEP progression is plotted on the primary axis, and average horizontal gradient at the pipe head is plotted on the secondary axis. +Horizontal reference lines display for the mean field critical gradient for BEP progression (green dashed line) and FS of 1 (red shaded line). + + illustrates the deterministic graphical output. + +
+ + illustrates the plot options this chart. The maximum value for the primary y-axis (FS +against BEP progression), maximum value for the secondary y-axis (average horizontal gradient at the pipe head), and minimum and maximum values for +the x-axis (headwater level) are user-specified. Users can input up to five vertical reference elevations, and user-specified labels display at the +top of the chart. + +
+ +Because the adjusted Schmertmann method uses the probabilistic chart of Robbins and Sharp (2016) , +expanded by Robbins and O’Leary (2020) , a probability of BEP progression is calculated +for both the deterministic and probabilistic methods as illustrated in +and , respectively. The mean probability of BEP progression is plotted as a +function headwater level. For probabilistic analysis, the 90 percent uncertainty bounds (5th and 95th percentiles) are also plotted as a function headwater +level using dashed lines, as shown in . + +
+ +
+ + illustrates the plot options for the charts in + and +. The vertical reference elevations and minimum and maximum values for the x-axis +(headwater level) are the same as +. Only the maximum value for the y-axis (probability of BEP progression) is +user-specified. + +
+ + diff --git a/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/06-sellmeijer.mdx b/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/06-sellmeijer.mdx new file mode 100644 index 000000000..9155d98cf --- /dev/null +++ b/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/06-sellmeijer.mdx @@ -0,0 +1,483 @@ +--- +title: Sellmeijer +--- + +import Link from '@docusaurus/Link'; +import addBaseUrl from '@docusaurus/useBaseUrl'; +import Citation from '@site/src/components/Citation'; +import CitationFootnote from '@site/src/components/CitationFootnote'; +import Equation from '@site/src/components/Equation'; +import EquationNoRef from '@site/src/components/EquationNoRef'; +import EquationReference from '@site/src/components/EquationReference'; +import Figure from '@site/src/components/Figure'; +import FigReference from '@site/src/components/FigureReference'; +import NavContainer from '@site/src/components/NavContainer'; +import TableReference from '@site/src/components/TableReference'; +import TableVertical from '@site/src/components/TableVertical'; + + + +# Sellmeijer + +Between 1988 and 1993, Hans Sellmeijer and his coworkers developed a mathematical model for BEP progression. Curve-fitting numerical solutions in the +process yielded a simplified calculation rule used in the Netherlands. The Sellmeijer model provided a relationship between pipe length and hydraulic +head at which sand grains are in equilibrium. For any head less than the critical head (_Hc_), the development of the piping channels stops. +If the head is increased, erosion begins again. The critical head occurs when the length of the channel (_l_) is about 0.3 to 0.5 of flow path length +(_L_). For net hydraulic head (_H_) less than _Hc_, progression of the pipe reaches a stable condition. For _H_ greater than _Hc_, the piping +channel extends upstream and breaks through to the impounded water. + +Sellmeijer’s model was implemented in a 2D numerical groundwater model to account for different configurations and used to derive a calculation rule for +a standard levee located on top of a homogeneous confined aquifer. The original and adjusted calculation rules are described in Sellmeijer et +al. (2011) . The adjusted calculation rule extended and updated the piping model +based on results of a wide range of tests (several small-scale, seven medium-scale, and four large-scale field Ijkdijk experiments). Thus, the Sellmeijer +model is known to result in good predictions for large-scale experiments with 2D configurations. The method is applicable only within the limits of the +piping model testing parameters shown in . + + + Particle size with 70 percent finer by weight,{' '} + + d70 + {' '} + (millimeters) + , + <> + Coefficient of uniformity, U + , + <> + Roundness of particles, KAS (percent) + , + <> + Relative density, RD (percent) + , + ], // Column 1 + ['0.150', '1.3', '35', '50'], // Row 2 + ['0.430', '2.6', '70', '100'], // Row 3 + ]} + alt="Sellmeijer parameter limits." + caption="Sellmeijer parameter limits." + colWidths={[55, 20, 20]} + colAlign={['center', 'center', 'center']} + widthMode="intrinsic" +/> + +## Method of Analysis + +The method of analysis is the same as the Schmertmann worksheet. + +## Soil Particle Characterization + +Step 2 characterizes the soil particles in the piping layer. The input includes the specific gravity of sand particles (_Gs_), bedding angle of +sand (_θ_), and White’s constant (_η_) as illustrated in . The bedding angle and White’s +constant are set to 37 degrees and 0.25, respectively, due to model calibration and are not changed in Dutch practice. + +
+ +The selections in step 1 affect the remaining input for step 2. Cells that do not apply have a gray background. These cells are not used in subsequent +calculations even if data is present. The input includes the particle size with 70 percent finer by weight (_d70_), coefficient of uniformity (_U_), +roundness of particles (_KAS_), and relative density (_RD_). The method is applicable only within the limits of the piping model testing parameters. Cells +where the input parameter is outside the model parameter limits have an orange background, and a caution displays for those parameters. Mean values are used +to normalize project-specific values. + +The roundness of particles can be analyzed using optical images. Software such as ImageJ approximates an ellipse for each individual particle and calculates +the roundness of each ellipse. For example, a perfect circle has a resulting roundness of 100 percent. Each image contains a variable number of particles, +and multiple images of each soil sample should be analyzed. In practice, optical images of soil samples are rarely conducted to obtain _KAS_. Van Beek et +al. (2009) provides guidance for visual estimation of _KAS_ as illustrated +in . + +
+ +For deterministic analysis, input only the most likely values. The mean values used for subsequent calculations are the most likely (or mode) +values. illustrates the deterministic input. + +
+ +For probabilistic analysis without using @RISK, input the minimum and maximum values in addition to the most likely value, and triangular distributions represent +the random variables. The mean values used in subsequent calculations are the average of the minimum, most likely, and maximum +values. illustrates the probabilistic input without using @RISK. + +
+ +For probabilistic analysis using @RISK, input the minimum, most likely, and maximum values, and use an @RISK formula for a triangular distribution in the +third column as a default. Alternatively, input a valid @RISK distribution in lieu of this default formula, and the user-specified input displays in the +fourth column. The mean values used for subsequent calculations are the means for the @RISK distributions entered in the third +column. illustrates the probabilistic input using @RISK. + +
+ +If using @RISK to perform probabilistic analysis, delete unnecessary calculation worksheets because the simulation is performed for all worksheets in the workbook, +which this is time consuming. If cycling through iterations using @RISK, the displayed results are no longer mean values of the random variables; they are the +selected iteration. + +## Piping Layer Characterization + +The selections in step 1 affect the input for step 3, and cells that do not apply have a gray background. These cells are not used in subsequent calculations +even if data is present. Step 3 characterizes the piping layer. The input includes the horizontal permeability (_kh,f_) and thickness (_Df_) +of the fine sand (piping) layer, seepage water temperature (_T_), and seepage path length (_L_). A lookup table is used to obtain the dynamic viscosity of water +(_μ_) as a function of seepage water temperature. + +The intrinsic permeability of the fine sand (piping) layer is calculated using . + + + +where: + +> _kh_ = permeability of the fine sand (piping) layer in the horizontal direction (m/s) +> _μ_ = dynamic viscosity of water (N·s/m2) + +Use the drop-down list to indicate the presence of a multi-layer foundation (fine sand layer over coarse sand layer). Cells that do not apply have a gray +background. Van Beek et al. (2012) conducted piping experiments on multi-layer sand +samples to validate Sellmeijer’s model, and the calculation rule was extended for multi-layer aquifers. A coarse layer beneath the piping layer increases the +flow toward the pipe and decreases the critical head (and critical gradient). If a multi-layer foundation exists, the input also includes the horizontal +permeability (_kh,c_) and thickness (_Dc_) of the underlying coarse sand layer. + +For a multi-layer aquifer, when flow toward the pipe is predominantly horizontal (for elongated aquifers), the increase of flow toward the pipe is reflected by +the average horizontal permeability of a multilayer aquifer. A layer-weighted average of horizontal permeability (_kh,avg_) is used in lieu of the +horizontal permeability of the fine sand (piping) layer, shown in , +using . + +
+ + + +where: + +> _kh,f_ = permeability of the fine (piping) layer in the horizontal direction (centimeter/second) +> _Df_ = thickness of the fine (piping) layer +> _kh,c_ = permeability of the coarse underlayer in the horizontal direction (centimeter/second) +> _Dc_ = thickness of coarse underlayer (feet) +> _D_ = total aquifer thickness (feet) + +When the contrast of permeability is large and the aquifer thickness is relatively large compared to the seepage path length, assuming predominant horizontal +flow is no longer valid. Hence, the extension of Sellmeijer’s calculation rule for multi-layer foundations can be applied to elongated aquifers +{" "} with low contrasts of permeability +{" "}. +and values outside of these ranges have an orange background. + +The average intrinsic permeability is calculated using . + + + +For deterministic analysis of single-layer aquifer, input only the most likely value for the fine sand (piping) layer. The mean value used for subsequent +calculations is the most likely (or mode) value. illustrates the deterministic +input for single-layer aquifer. + +
+ +For deterministic analysis of multi-layer aquifer, input the most likely values for the fine sand (piping) layer and underlying coarse sand layer. The mean +values used for subsequent calculations are the most likely (or mode) values. +illustrates the deterministic input for multi-layer aquifer. + +
+ +For probabilistic analysis of single-layer aquifer without using @RISK, input the minimum and maximum values in addition to the most likely value, and a +triangular distribution represents the random variable for the fine sand (piping) layer. The mean value used in subsequent calculations is the average of +the minimum, most likely, and maximum values. illustrates the probabilistic +input for single-layer aquifer without using @RISK. + +
+ +For probabilistic analysis of multi-layer aquifer without using @RISK, input the most likely values for the fine sand (piping) layer and underlying coarse +sand layer. The mean values used for subsequent calculations are the average of the minimum, most likely, and maximum values. + + illustrates the probabilistic input for multi-layer aquifer without using @RISK. + +
+ +For probabilistic analysis of single-layer aquifer using @RISK, input the minimum, most likely, and maximum values for the fine sand (piping) layer, and +use an @RISK formula for a triangular distribution in the third column as a default. Alternatively, input a valid @RISK distribution in lieu of this +default formula, and the user-specified input displays in the fourth column. The mean value used for subsequent calculations is the mean for the @RISK +distribution entered in the third column. illustrates the +probabilistic input for single-layer aquifer using @RISK. + +
+ +For probabilistic analysis of multi-layer aquifer using @RISK, input the minimum, most likely, and maximum values for the fine sand (piping) layer and +underlying coarse sand layer, and use an @RISK formula for a triangular distribution in the third column as a default. Alternatively, input a valid @RISK +distribution in lieu of this default formula, and the user-specified input displays in the fourth column. The mean values used for subsequent calculations +are the mean for the @RISK distribution entered in the third column. +the probabilistic input for multi-layer aquifer using @RISK. + +
+ +## Field Critical Horizontal Gradient for BEP Progression + +Step 4 calculates the field critical horizontal gradient for BEP progression as illustrated in . + +, for the critical horizontal gradient for BEP progression (_ich_), is composed of three +terms: a resistance factor that accounts for the strength of the layer subject to BEP; a scale factor that relates pore size and seepage size; and a +geometrical shape factor. + + + +where: + +> _FR_ = resistance factor (strength of the layer subject to BEP) +> _FS_ = scale factor (relating pore size and seepage size) +> _FG_ = geometrical shape factor + +The resistance factor is a function of White's constant (_η_), bedding angle (_θ_), relative density (_RD_), roundness of the particles (_KAS_), and +coefficient of uniformity (_U_) and is calculated using . + + + +where: + +> _KAS_ = roundness of the particles (percent) +> _RD_ = relative density (percent) +> _U_ = coefficient of uniformity +> _γ'p_ = submerged unit weight of soil particles (N/m3) +> _γw_ = unit weight of water (N/m3) +> _θ_ = bedding angle (degrees) +> _η_ = White's constant + +Since it is easier to estimate the specific gravity of soil particles than the submerged unit weight of soil particles, the substitution in +is made to the equation for _FR_. + + + +The bedding angle and White’s constant have been set to 37 degrees and 0.25, respectively, due to model calibration and are not changed in Dutch practice. +Since the values were fixed in the multi-variate regression, any influence they had is accounted for in related variables. It is, therefore, not +appropriate to vary these parameters. + +Van Beek et al. (2010) indicate that _KAS_ and _U_ appear less important than other +sand characteristics, and the results of multivariate regression analysis show that they have a weak influence on critical gradient. Therefore, _U_ and +_KAS_ terms in equation for _FR_ are sometimes ignored in practice. The toolbox provides an option to neglect the expressions containing these +terms from the equation for _FR_ as illustrated in . + +The scale factor is a function of the particle size for which 70 percent is finer (by weight) (_d70_), the horizontal seepage path length (_L_), +and the intrinsic permeability of the piping layer (_κ_) and is calculated using . + + + +where: + +> _d70_ = particle size (m) for which 70 percent is finer (by weight) +> _κ_ = intrinsic permeability (m2) of the piping layer + +The intrinsic permeability of the piping layer in Equation 20 is either _κf_ for a single-layer aquifer or _kh,avg_ for a multi-layer +aquifer. + +The value of the horizontal permeability used to calculate the intrinsic permeability depends on the selection in step 3. For single-layer aquifers, it is +the value for the fine sand (piping) layer. For multi-layer aquifers, it is the layer-weighted average. + +The geometrical factor is a function of the ratio of the depth of the piping layer to the horizontal seepage path length +{" "} and is calculated using . + + + +where: + +> _D_ = thickness of the piping layer (m) where _D_ = _Df_ for a single-layer aquifer +> _L_ = seepage path length (m) through the piping layer (measured horizontally) + +
+ +
+ +Sellmeijer’s model applies to 2D seepage with plane or ditch exits parallel to the embankment centerline for fine to medium sands within the limits of +the model test parameters. Van Beek et al. (2015) found that 3D configurations +with flow toward a single point (such as a hole in a confining layer) resulted in significantly smaller critical gradients than predicted by the adjusted +calculation model. In both the small and medium-scale experiments, the model overestimated the critical gradient by a factor of approximately two. If +the field horizontal critical gradient is further adjusted for 3D flow, input a user-specified GRF. Cells that do not apply have a gray background. The +two scenarios are illustrated in +and . + +
+ +
+ +## Likelihood of Backward Erosion Piping Progression + +Step 5 calculates the average hydraulic gradient in the foundation by dividing the net hydraulic head by the seepage path length +using . + + + +where: + +> _∆H_ = net hydraulic head (feet) +> _HW_ = headwater level (feet) +> _TW_ = tailwater level (feet) +> _L_ = seepage path length (feet) + +The FS against BEP progression is calculated using . + + + +where: + +> _ich_ = critical horizontal gradient for BEP progression +> _iavf_ = average horizontal gradient in the foundation at the pipe head + +For deterministic analysis, the _FS_ is calculated using the most likely values of the random variables and is summarized in a table. Cells that do +not apply have a gray background. + +For probabilistic analysis, the _FS_ is calculated as described for the deterministic analysis but for the mean values of the random variables, and +multiple iterations are performed by sampling the distributions in step 2. The probability of BEP progression is equal to the percentage of iterations +that resulted in an _FS_ less than 1 \[P(FS < 1)\]. + +For probabilistic analysis performed without using @RISK, 1,000 iterations are used. For probabilistic analysis using @RISK, the number of iterations +is user-specified, and “@RISK” displays in parentheses after the number of iterations for this scenario. If cycling through iterations using @RISK, +the displayed results are no longer mean values; they are the selected iteration’s values. + +For deterministic and probabilistic analyses, cells with _FS_ less than 1 have an orange background. +illustrates the deterministic tabular output, and illustrates the +probabilistic tabular output without using @RISK. + +
+ +
+ +## Summary Plots + +Step 6 generates the summary plots. The first plot is the mean FS against BEP progression (red solid line) and average horizontal gradient at the pipe +head (green solid line) as functions of headwater level. If cycling through iterations using @RISK, the displayed results are no longer mean values; +they are the selected iteration. FS against BEP progression is plotted on the primary axis, and average horizontal gradient at the pipe head is plotted +on the secondary axis. Horizontal reference lines display for the mean field critical gradient for BEP progression (green dashed line) and FS of 1 +(red shaded line). illustrates the deterministic graphical output. + +
+ + illustrates the plot options for this chart. The maximum value for the primary y-axis (FS against BEP +progression), maximum value for the secondary y-axis (average horizontal gradient at the pipe head), and minimum and maximum values for the x-axis +(headwater level) are user-specified. Users can input up to five vertical reference elevations, and user-specified labels display at the top of the +chart. + +
+ +For probabilistic analysis, the mean probability of BEP progression is plotted as a function headwater level. If cycling through iterations using @RISK, +this plot has a gray background because the probability of initiation cannot be calculated from a single iteration. Similarly, this plot has a gray +background for deterministic analysis. illustrates the graphical output +for probabilistic analysis. + +
+ + illustrates the plot options for this chart. The vertical reference elevations and minimum and maximum values for +the x-axis (headwater level) are the same as the input for the previous chart. Only the maximum value for the y-axis (probability of BEP progression) +is user-specified. + +
+ + diff --git a/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/07-creep-ratios.mdx b/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/07-creep-ratios.mdx new file mode 100644 index 000000000..618010b73 --- /dev/null +++ b/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/07-creep-ratios.mdx @@ -0,0 +1,179 @@ +--- +title: Creep Ratios +--- + +import Figure from "@site/src/components/Figure"; +import FigReference from "@site/src/components/FigureReference"; +import TableVertical from "@site/src/components/TableVertical"; +import TableReference from "@site/src/components/TableReference"; +import Equation from "@site/src/components/Equation"; +import EquationReference from "@site/src/components/EquationReference"; +import Citation from "@site/src/components/Citation"; +import CitationFootnote from "@site/src/components/CitationFootnote"; +import NavContainer from "@site/src/components/NavContainer"; +import Link from "@docusaurus/Link"; +import addBaseUrl from "@docusaurus/useBaseUrl"; + + + +# Creep Ratios + +Creep ratio methods such as Bligh (1910) and +Lane (1935) are empirical methods still used by some practitioners to +assess the likelihood of BEP progression (hydraulic condition) based on observations of seepage performance for a range of soil types. +Both empirical methods involve estimating the line of creep (or seepage path length) beneath concrete structures (such as weirs), +including seepage barrier walls. For embankment dams and levees, the seepage path length includes the impervious embankment, as well +as any upstream/floodside and downstream/landside impervious blankets or berms, seepage barrier walls, impervious foundation trenches, +etc. as illustrated in . + +
+ +To assess the likelihood of BEP progression (hydraulic condition), the creep ratio for the headwater level under consideration is compared +to the minimum (or safe) creep ratio for the piping material. The creep ratio is calculated as the line of creep (seepage path length) +divided by the net hydraulic head. For Lane’s method, horizontal seepage path lengths are weighted three times less than the vertical seepage +path lengths to account for the greater resistance to pipe development when a vertical structure (such as a seepage barrier wall) is present +in the path of the pipe. Hence, it is often referred to as a weighted creep method. BEP progression is expected if the creep ratio is less +than the minimum creep ratio. + +Evaluating creep ratio is informative where the levee consists of fine-grained material and no landside blanket exists. The method is not +appropriate for a compromised confining layer overlying a confined aquifer. Duncan et al. (2011) +state that while informative, the creep ratio is considered a “quick-and-dirty check.” The state of practice is to use rational methods +based on blanket theory, flow nets, or finite-element method analysis, and the greatest remaining value of creep ratios lies in indicating +the relative erosion potential of various soil types. + +## Line of Creep + +Step 1 calculates the line of creep (seepage path length) as illustrated in . The +input includes the horizontal impervious dimensions as well as the depth of any vertical structures (such as seepage barrier walls). The +depth of vertical structures is doubled in the line-of-creep calculation because seepage must pass down, around, and up the embedded structure. +If a blanket, berm, or vertical structure does not exist, input zero for those values. + +The line of creep (_L_) for Bligh’s method is calculated using . The +weighted line of creep for Lane’s method (_LW_) is calculated using . + + + + + +Where: + +> _D_ = depth (feet) of embedded vertical structure +> _L1_ = length (feet) of upstream/floodside impervious blanket or berm +> _L2_ = length (feet) of downstream/landside impervious blanket or berm +> _W_ = width (feet) of base of concrete weir or impervious embankment + +
+ +## Minimum Creep Ratio + +Step 2 characterizes the foundation to obtain the minimum (or safe) creep ratio for both empirical methods from +Lane (1935) based on soil type as illustrated +in . Use the drop-down list to select the material that best represents +the material along the piping path. + +
+ +When seepage exits horizontally, piping can progress with an average horizontal gradient in the foundation as low as 0.05. This critical +horizontal gradient is approximately the same as the inverse of Bligh’s creep ratio for fine sand. The field horizontal critical gradient +for BEP progression (_ich_) is the inverse of the minimum (or safe) creep ratio if there are no vertical structures (_D_ = 0). The +field horizontal critical gradient is calculated using +and for Bligh’s method and Lane’s method, respectively. For _D_ greater +than zero, “N/A” displays for _ich_. + + + + + +Where: + +> _Cmin_ = minimum (or safe) creep ratio for Bligh’s method +> _CW,min_ = minimum (or safe) weighted creep ratio for Lane’s method + +## Creep Ratio + +Step 3 calculates the creep ratio by dividing the line of creep from step 1 by the net hydraulic head (_ΔH_) for the headwater level under +consideration. The creep ratio for Bligh’s method (_C_) is calculated using . +The weighted creep ratio for Lane’s method (_CW_) is calculated using . + + + + + +Where: + +> _ΔH_ = net hydraulic head (feet) +> _HW_ = headwater level (feet) +> _TW_ = tailwater level (feet) +> _L_ = line of creep for Bligh’s method (feet) +> _LW_ = line of creep for Lane’s method (feet) + +The calculated creep ratio is compared to the minimum creep ratio from step 2, and cells where the calculated creep ratio exceeds the +minimum value have an orange background. illustrates the +tabular summary. + +
+ +The calculated creep ratio is plotted as a function of headwater level for both methods. Horizontal reference lines display the minimum +(or safe) creep ratios for each method. illustrates the +graphical output. The legend can be moved within the plot area as necessary for clarity. + +
+ + illustrates the plot options +for this chart. The maximum value for the y-axis (creep ratio) and minimum and maximum +values for the x-axis (headwater level) are user-specified. Users can input up to +five vertical reference elevations, and user-specified labels displayed at the top +of the chart. + +
+ +By selecting the chart and then selecting the filter icon to display the filter pane, the data series for display can be selected as +illustrated in . For example, if only the results from the Bligh’s +method are judged applicable, the data series for “Lane’s Weighted Creep Ratio” and “Lane’s Safe Weighted Creep Ratio” can be deselected +so that they do not plot or display in the legend. + +
+ + diff --git a/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/08-summary.mdx b/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/08-summary.mdx new file mode 100644 index 000000000..47cfed1d7 --- /dev/null +++ b/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/08-summary.mdx @@ -0,0 +1,85 @@ +--- +title: Summary +--- + +import Figure from "@site/src/components/Figure"; +import FigReference from "@site/src/components/FigureReference"; +import TableVertical from "@site/src/components/TableVertical"; +import TableReference from "@site/src/components/TableReference"; +import Citation from "@site/src/components/Citation"; +import CitationFootnote from "@site/src/components/CitationFootnote"; +import NavContainer from "@site/src/components/NavContainer"; +import Link from "@docusaurus/Link"; +import addBaseUrl from "@docusaurus/useBaseUrl"; + + + +# Summary + +This worksheet provides summary plots of the various methods used to assess the likelihood of BEP progression. The first plot +is the average hydraulic gradient at the pipe head (black solid line) as a function of headwater level. If cycling through +iterations using @RISK, the displayed results are no longer mean values; they are the selected iteration. Horizontal reference +lines display for the mean field critical gradient for the adjusted Schmertmann method (blue dashed line), mean field horizontal +critical gradient for the adjusted calculation rule of Sellmeijer et al. (green dashed line), inverse of Bligh’s minimum creep +ratio (red dashed line), and inverse of Lane’s minimum weighted creep ratio (orange dashed line). If cycling through iterations +using @RISK, the displayed results are no longer mean values; they are the selected +iteration. illustrates the deterministic graphical output. + +
+ + illustrates the plot options for this chart. The +maximum value for the y-axis (average horizontal gradient at the pipe head) and minimum and maximum values for the x-axis (headwater +level) are user-specified. Users can input up to five vertical reference elevations, and user-specified labels display at the +top of the chart. + +
+ +Select the chart and filter icon to display the filter pane to select or deselect data series, as shown +in . For example, if only the results from the adjusted +Schmertmann method and inverse of Bligh’s creep ratio are judged applicable, deselecting the other data series removes them from +the plot and the legend. + +
+ +The second plot of the worksheet is the probability of BEP progression for the adjusted Schmertmann method (blue solid line) and +adjusted calculation rule of Sellmeijer et al. (green solid line) as functions of headwater level. Because the adjusted Schmertmann +method uses the probabilistic chart of Robbins and Sharp (2016) , +expanded by Robbins and O’Leary (2020) , a probability of BEP +progression displays for both deterministic and probabilistic analysis. However, the adjusted calculation rule of Sellmeijer et al. +displays for probabilistic analysis only. illustrates +the probabilistic graphical output. + +
+ + illustrates the plot options for this chart. The vertical +reference elevations and minimum and maximum values for the x-axis (headwater level) are the same as the input +for . Only the maximum value for the y-axis (probability +of BEP progression) is user-specified. + +
+ + diff --git a/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/09-references.mdx b/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/09-references.mdx new file mode 100644 index 000000000..2bfcdcd5f --- /dev/null +++ b/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/09-references.mdx @@ -0,0 +1,18 @@ +--- +title: References +--- + +import Bibliography from "@site/src/components/Bibliography"; +import NavContainer from "@site/src/components/NavContainer"; +import Link from "@docusaurus/Link"; +import addBaseUrl from "@docusaurus/useBaseUrl"; + + + +# References + + diff --git a/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/10-appendix-acronyms.mdx b/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/10-appendix-acronyms.mdx new file mode 100644 index 000000000..de56e461c --- /dev/null +++ b/docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/10-appendix-acronyms.mdx @@ -0,0 +1,33 @@ +--- +title: Appendix A - Acronyms +--- + +import TableAcronyms from "@site/src/components/TableAcronyms"; +import NavContainer from "@site/src/components/NavContainer"; +import Link from "@docusaurus/Link"; +import addBaseUrl from "@docusaurus/useBaseUrl"; + + + +# Appendix A - Acronyms + + diff --git a/src/pages/changelog.js b/src/pages/changelog.js index 12c72c45a..fa1b2e1a5 100644 --- a/src/pages/changelog.js +++ b/src/pages/changelog.js @@ -16,6 +16,7 @@ export default function Changelog() {
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