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Merge pull request #162 from USACE-RMC/docs/fix/bep-progression-sellmeijer-equation
[Content] Updated equation 22 in 06-sellmeijer.mdx
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‎docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/00-document-info.mdx‎

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---
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title: Document Info
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reportDate: November 2023
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reportType: Computer Program Document
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reportTitle: RMC Backward Erosion Piping (Progression) Toolbox
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reportSubTitle: RMC Internal Erosion Suite
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reportAuthors: ["Tim O'Leary, Risk Management Center"]
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reportAbstract: The spreadsheet tools contained in this toolbox deterministically and probabilistically assess the likelihood of backward erosion piping progression (hydraulic condition) using the adjusted Schmertmann (2000) method and the adjusted calculation rule of Sellmeijer et al. (2011) in addition to creep ratio methods of Bligh (1910) and Lane (1935).
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reportSubjectTerms: ["Internal erosion", "backward erosion piping", "Schmertmann", "Sellmeijer", "Bligh", "Lane", "creep ratio"]
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responsiblePersonName: Tim O'Leary
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responsiblePersonNumber: 502-315-6599
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citationGuide: "T. M. O'Leary, <i>RMC Backward Erosion Piping (Progression) Toolbox Technical Manual</i>, Lakewood, CO: U.S. Army Corps of Engineers, Risk Management Center, 2025. Accessed on <i>{enter current date here}</i>."
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---
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import NavContainer from "@site/src/components/NavContainer";
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import DocumentMetadata from "@site/src/components/DocumentMetadata";
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import Link from "@docusaurus/Link";
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import addBaseUrl from "@docusaurus/useBaseUrl";
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<NavContainer
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link="/toolboxes/internal-erosion-suite"
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linkTitle="Internal Erosion Suite"
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document="toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression"
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></NavContainer>
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# Document Information
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<DocumentMetadata metadata={frontMatter} />

‎docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/00-version-history.mdx‎

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import Link from '@docusaurus/Link';
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import NavContainer from '@site/src/components/NavContainer';
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import TableVersionHistory from '@site/src/components/TableVersionHistory';
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<NavContainer
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link="/toolboxes/internal-erosion-suite"
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linkTitle="Internal Erosion Suite"
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document="toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression"
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></NavContainer>
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# Version History
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<TableVersionHistory
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versions={['1.1', '1.0']}
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dates={['October 2026', 'March 2026']}
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descriptions={[
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'Updated the Scale Factor equation in the Sellmeijer chapter to correct the exponents for the intrinsic permeability of the piping layer multiplied by the horizontal seepage path length.',
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'Initial release as an online document. Source is RMC CPD-2023-06.',
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]}
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modifiedBy={['Adam Gohs', '-']}
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reviewedBy={["Tim O'Leary", 'Damon Amlung']}
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approvedBy={['-', 'Nate Snorteland']}
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/>

‎docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/01-preface.mdx‎

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---
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title: Preface
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---
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import NavContainer from "@site/src/components/NavContainer";
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import VersionSelector from "@site/src/components/VersionSelector";
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import Link from "@docusaurus/Link";
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import addBaseUrl from "@docusaurus/useBaseUrl";
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<NavContainer
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link="/toolboxes/internal-erosion-suite"
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linkTitle="Internal Erosion Suite"
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document="toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression"
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></NavContainer>
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# Preface
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The Risk Management Center (RMC) of the U.S. Army Corps of Engineers (USACE) has developed a suite of Microsoft Excel spreadsheets to support
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risk assessments for dam and levee safety. Each analysis suite is composed of multiple toolboxes (Microsoft Excel workbooks), and each toolbox
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contains multiple spreadsheet tools or calculation worksheets (Microsoft Excel worksheets). The RMC Backward Erosion Piping (Progression) Toolbox
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is part of the RMC Internal Erosion Suite.
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The information from these spreadsheet tools, along with other pertinent information, informs judgment when developing a list of more and less
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likely factors and estimating probabilities. USACE best practice for estimating probabilities is to use the best available and multiple methods,
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but all final probabilities are estimated using team elicitation based on the totality and strength of the evidence.
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The RMC continuously works to improve the performance of RMC software; report possible bugs directly to the RMC at the address listed below.
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Ideally, report suspected errors in written form with a description of the problem and the steps that lead to its occurrence. Suggestions for
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improvement are also welcomed.
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U.S. Army Corps of Engineers
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Institute for Water Resources
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Risk Management Center
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[rmc.software@usace.army.mil](mailto:rmc.software@usace.army.mil)

‎docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/02-terms-and-conditions-for-use.mdx‎

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---
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title: Terms and Conditions
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---
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import NavContainer from "@site/src/components/NavContainer";
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import VersionSelector from "@site/src/components/VersionSelector";
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import Link from "@docusaurus/Link";
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import addBaseUrl from "@docusaurus/useBaseUrl";
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<NavContainer
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link="/toolboxes/internal-erosion-suite"
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linkTitle="Internal Erosion Suite"
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document="toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression"
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></NavContainer>
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# Terms and Conditions for Use
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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.
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## Terms and Conditions for Use of Institute for Water Resources Software
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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:
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- 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.
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- User may reproduce and distribute the IWR Software provided that the recipient agrees to the Terms and Conditions for Use noted herein.
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- 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.
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- 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.
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- No part of this Terms and Conditions for Use may be modified, deleted or obliterated from the IWR Software.
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- No part of the IWR Software may be exported or re-exported in contravention of U.S. export laws or regulations.
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## Waiver of Warranty
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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.
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## Limitation of Liability
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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.
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## Indemnity
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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.

‎docs/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/03-general-overview.mdx‎

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---
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title: General Overview
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---
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import Link from '@docusaurus/Link';
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import addBaseUrl from '@docusaurus/useBaseUrl';
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import Citation from '@site/src/components/Citation';
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import CitationFootnote from '@site/src/components/CitationFootnote';
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import Figure from '@site/src/components/Figure';
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import FigReference from '@site/src/components/FigureReference';
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import NavContainer from '@site/src/components/NavContainer';
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<NavContainer
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link="/toolboxes/internal-erosion-suite"
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linkTitle="Internal Erosion Suite"
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document="toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression"
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></NavContainer>
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# General Overview
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## Getting Started
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Copy or download the toolbox file to the computer. To open the toolbox file, either:
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- Find the file on the computer and double-click it. This opens the file in Microsoft Excel.
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- 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.
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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
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“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
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message bar will vary depending on the computer’s settings and installed add-ins. <FigReference figKey="figure-1"/> displays examples of different wordings that may appear in the message bar.
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<Figure
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docId="03-general-overview.mdx"
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figKey="figure-1"
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src="/figures/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/figure1.png"
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alt="Security warning message bars with the 'Enable Content' option to enable macros"
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caption="Security warning message bars with the 'Enable Content' option to enable macros."
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background="transparent"
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></Figure>
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## Organization
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Although the toolbox does not provide a calculation cover sheet, adding one is strongly recommended. A calculation cover sheet captures project
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information, a description and purpose of the calculation, the assumptions for critical input parameters, a summary of the major conclusion and
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results, and a revision history.
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Each toolbox has a similar appearance and organizational structure:
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- The first worksheet, About, summarizes the purpose of the toolbox and gives contact information for the RMC software development team.
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- The second worksheet, Terms and Conditions, contains the terms and conditions for use of the toolbox (IWR software).
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- The third worksheet, Version History, contains the revision history. Semantic versioning is used in the format of MAJOR.MINOR.PATCH:
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- MAJOR - significant worksheet changes not compatible with previous versions.
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- MINOR - additional features or enhancements that do not fundamentally change the calculations.
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- PATCH - backward-compatible bug fixes.
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- The fourth worksheet, References, lists the references cited for each calculation worksheet.
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The workbook and worksheets are not protected to prevent unwanted changes. However, because the toolbox has user-defined functions (UDFs) and
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subroutines in Visual Basic, you cannot directly copy worksheets to another workbook without potentially losing functionality. A note in a bold
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red font at the upper right margin indicates if the selected worksheet includes such features.
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At the top of each calculation worksheet, input information for the preparer and checker for quality control (QC) documentation and the calculation
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title in case multiple copies of the worksheet are created for different analysis scenarios (<FigReference figKey="figure-2"/>).
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The footer of each calculation worksheet contains the version number, which can be cross-referenced with the revision history on the third worksheet.
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<Figure
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docId="03-general-overview.mdx"
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figKey="figure-2"
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src="/figures/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/figure2.png"
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alt="Calculation worksheet heading"
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caption="Calculation worksheet heading."
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></Figure>
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User-specified input includes values and selections from drop-down lists. User input cells are light yellow, and these cells are unprotected.
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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
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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
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ranges, the cell is orange to indicate caution to the user.
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All units for user-specified input values are clearly labeled. Most user-specified input values use English units. However, values may be in metric
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where metric units are more common in practice (e.g., particle size in millimeters or permeability in centimeters per second). The toolbox may convert
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English units to metric units to perform some calculations or if required for a specific formula based on the reference material for the equation.
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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.
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Tailwater may be required to calculate the net hydraulic head and hydraulic gradient. Specify the elevation datum by selecting one of three options
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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
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a user-specified datum along with feet (e.g., ft-MSL [Mean Sea Level]). <FigReference figKey="figure-3"/>, <FigReference figKey="figure-4"/>, and <FigReference figKey="figure-5"/> illustrate
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the three possible scenarios.
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<Figure
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docId="03-general-overview.mdx"
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figKey="figure-3"
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src="/figures/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/figure3.png"
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alt="Headwater and tailwater input: NAVD88"
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caption="Headwater and tailwater input: NAVD88."
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></Figure>
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<Figure
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docId="03-general-overview.mdx"
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figKey="figure-4"
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src="/figures/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/figure4.png"
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alt="Headwater and tailwater input: NGVD29"
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caption="Headwater and tailwater input: NGVD29."
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></Figure>
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<Figure
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docId="03-general-overview.mdx"
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figKey="figure-5"
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src="/figures/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/figure5.png"
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alt="Headwater and tailwater input: User-specified datum"
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caption="Headwater and tailwater input: User-specified datum."
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></Figure>
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Most calculation worksheets break down complex analysis into computational steps following a logical sequence (<FigReference figKey="figure-6"/>). Some simpler
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worksheets do not have steps. Generally, different methodologies are unique worksheets. Some worksheets may include multiple methodologies, which
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are labeled as options (<FigReference figKey="figure-7"/>).
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<Figure
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docId="03-general-overview.mdx"
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figKey="figure-6"
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src="/figures/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/figure6.png"
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alt="Example of step banner"
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caption="Example of step banner."
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></Figure>
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<Figure
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docId="03-general-overview.mdx"
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figKey="figure-7"
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src="/figures/toolbox-technical-manuals/internal-erosion-suite/backward-erosion-piping-progression/v1.1/figure7.png"
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alt="Example of option banner"
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caption="Example of option banner."
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></Figure>
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Some calculation worksheets can perform either a deterministic or probabilistic analysis. Although not required to perform a probabilistic
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analysis, Palisade @RISK software (standalone version or as part of the Palisade DecisionTools Suite) can customize the probabilistic analysis.
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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.
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User notes generally appear in the right margin of each calculation worksheet. Some notes are in blue or red font for heightened awareness. These
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notes include references to source materials for equations, figures, tables, pages, etc. If the RMC modified the source material, the reference
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citation says “adapted from” instead of “from.”
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Tabular and/or graphical summaries are generally the primary output of the toolbox. The UDFs in the PlotScale module change the minimum and maximum
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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
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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
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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.

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