CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available" lang="en" dir="ltr"> <head> <meta charset="UTF-8"> <title>Slope stability analysis - Wikipedia</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available";var cookie=document.cookie.match(/(?:^|; )enwikimwclientpreferences=([^;]+)/);if(cookie){cookie[1].split('%2C').forEach(function(pref){className=className.replace(new RegExp('(^| )'+pref.replace(/-clientpref-\w+$|[^\w-]+/g,'')+'-clientpref-\\w+( |$)'),'$1'+pref+'$2');});}document.documentElement.className=className;}());RLCONF={"wgBreakFrames":false,"wgSeparatorTransformTable":["",""],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"dmy", "wgMonthNames":["","January","February","March","April","May","June","July","August","September","October","November","December"],"wgRequestId":"1a4fd9ff-7d36-442e-ac4f-a6c8acced143","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Slope_stability_analysis","wgTitle":"Slope stability analysis","wgCurRevisionId":1251997464,"wgRevisionId":1251997464,"wgArticleId":23897117,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["All articles with dead external links","Articles with dead external links from July 2022","Articles with short description","Short description is different from Wikidata","Wikipedia articles that are too technical from December 2012","All articles that are too technical","Wikipedia spam cleanup from March 2023","Wikipedia further reading cleanup","Commons category link is on Wikidata","Landslide analysis, prevention and mitigation"],"wgPageViewLanguage":"en", "wgPageContentLanguage":"en","wgPageContentModel":"wikitext","wgRelevantPageName":"Slope_stability_analysis","wgRelevantArticleId":23897117,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":false,"wgFlaggedRevsParams":{"tags":{"status":{"levels":1}}},"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"en","pageLanguageDir":"ltr","pageVariantFallbacks":"en"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":false,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":40000,"wgRelatedArticlesCompat":[],"wgCentralAuthMobileDomain":false,"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q961278", "wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false,"wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false};RLSTATE={"ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready","user.options":"loading","ext.cite.styles":"ready","ext.math.styles":"ready","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","jquery.tablesorter.styles":"ready","jquery.makeCollapsible.styles":"ready","ext.wikimediamessages.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","wikibase.client.init":"ready","ext.wikimediaBadges":"ready"};RLPAGEMODULES=["ext.cite.ux-enhancements","mediawiki.page.media","ext.scribunto.logs","site", "mediawiki.page.ready","jquery.tablesorter","jquery.makeCollapsible","mediawiki.toc","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.gadget.ReferenceTooltips","ext.gadget.switcher","ext.urlShortener.toolbar","ext.centralauth.centralautologin","mmv.bootstrap","ext.popups","ext.visualEditor.desktopArticleTarget.init","ext.visualEditor.targetLoader","ext.echo.centralauth","ext.eventLogging","ext.wikimediaEvents","ext.navigationTiming","ext.uls.interface","ext.cx.eventlogging.campaigns","ext.cx.uls.quick.actions","wikibase.client.vector-2022","ext.checkUser.clientHints","ext.quicksurveys.init","ext.growthExperiments.SuggestedEditSession","wikibase.sidebar.tracking"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=en&modules=ext.cite.styles%7Cext.math.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.styles%7Cjquery.makeCollapsible.styles%7Cjquery.tablesorter.styles%7Cskins.vector.icons%2Cstyles%7Cskins.vector.search.codex.styles%7Cwikibase.client.init&only=styles&skin=vector-2022"> <script async="" src="/w/load.php?lang=en&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=en&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.4"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/9/98/Pett_bish.gif"> <meta property="og:image:width" content="1200"> <meta property="og:image:height" content="810"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/9/98/Pett_bish.gif"> <meta property="og:image:width" content="800"> <meta property="og:image:height" content="540"> <meta property="og:image:width" content="640"> <meta property="og:image:height" content="432"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Slope stability analysis - Wikipedia"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//en.m.wikipedia.org/wiki/Slope_stability_analysis"> <link rel="alternate" type="application/x-wiki" title="Edit this page" href="/w/index.php?title=Slope_stability_analysis&action=edit"> <link rel="apple-touch-icon" href="/static/apple-touch/wikipedia.png"> <link rel="icon" href="/static/favicon/wikipedia.ico"> <link rel="search" type="application/opensearchdescription+xml" href="/w/rest.php/v1/search" title="Wikipedia (en)"> <link rel="EditURI" type="application/rsd+xml" href="//en.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://en.wikipedia.org/wiki/Slope_stability_analysis"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en"> <link rel="alternate" type="application/atom+xml" title="Wikipedia Atom feed" href="/w/index.php?title=Special:RecentChanges&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="//login.wikimedia.org"> </head> <body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-Slope_stability_analysis rootpage-Slope_stability_analysis skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Jump to content</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="Main menu" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">Main menu</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">Main menu</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">hide</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navigation </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Main_Page" title="Visit the main page [z]" accesskey="z"><span>Main page</span></a></li><li id="n-contents" class="mw-list-item"><a href="/wiki/Wikipedia:Contents" title="Guides to browsing Wikipedia"><span>Contents</span></a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Portal:Current_events" title="Articles related to current events"><span>Current events</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Special:Random" title="Visit a randomly selected article [x]" accesskey="x"><span>Random article</span></a></li><li id="n-aboutsite" class="mw-list-item"><a href="/wiki/Wikipedia:About" title="Learn about Wikipedia and how it works"><span>About Wikipedia</span></a></li><li id="n-contactpage" class="mw-list-item"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us" title="How to contact Wikipedia"><span>Contact us</span></a></li> </ul> </div> </div> <div id="p-interaction" class="vector-menu mw-portlet mw-portlet-interaction" > <div class="vector-menu-heading"> Contribute </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-help" class="mw-list-item"><a href="/wiki/Help:Contents" title="Guidance on how to use and edit Wikipedia"><span>Help</span></a></li><li id="n-introduction" class="mw-list-item"><a href="/wiki/Help:Introduction" title="Learn how to edit Wikipedia"><span>Learn to edit</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedia:Community_portal" title="The hub for editors"><span>Community portal</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Special:RecentChanges" title="A list of recent changes to Wikipedia [r]" accesskey="r"><span>Recent changes</span></a></li><li id="n-upload" class="mw-list-item"><a href="/wiki/Wikipedia:File_upload_wizard" title="Add images or other media for use on Wikipedia"><span>Upload file</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Main_Page" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="The Free Encyclopedia" src="/static/images/mobile/copyright/wikipedia-tagline-en.svg" width="117" height="13" style="width: 7.3125em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Special:Search" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Search Wikipedia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Search</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Search Wikipedia" aria-label="Search Wikipedia" autocapitalize="sentences" title="Search Wikipedia [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Special:Search"> </div> <button class="cdx-button cdx-search-input__end-button">Search</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Personal tools"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Appearance" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Appearance</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="https://donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_en.wikipedia.org&uselang=en" class=""><span>Donate</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:CreateAccount&returnto=Slope+stability+analysis" title="You are encouraged to create an account and log in; however, it is not mandatory" class=""><span>Create account</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:UserLogin&returnto=Slope+stability+analysis" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o" class=""><span>Log in</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Log in and more options" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Personal tools" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Personal tools</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="User menu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_en.wikipedia.org&uselang=en"><span>Donate</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:CreateAccount&returnto=Slope+stability+analysis" title="You are encouraged to create an account and log in; however, it is not mandatory"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Create account</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:UserLogin&returnto=Slope+stability+analysis" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Log in</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Pages for logged out editors <a href="/wiki/Help:Introduction" aria-label="Learn more about editing"><span>learn more</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Special:MyContributions" title="A list of edits made from this IP address [y]" accesskey="y"><span>Contributions</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:MyTalk" title="Discussion about edits from this IP address [n]" accesskey="n"><span>Talk</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Contents" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Contents</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Top)</div> </a> </li> <li id="toc-Limit_equilibrium_analysis" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Limit_equilibrium_analysis"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Limit equilibrium analysis</span> </div> </a> <button aria-controls="toc-Limit_equilibrium_analysis-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Limit equilibrium analysis subsection</span> </button> <ul id="toc-Limit_equilibrium_analysis-sublist" class="vector-toc-list"> <li id="toc-Analytical_techniques:_Method_of_slices" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Analytical_techniques:_Method_of_slices"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Analytical techniques: Method of slices</span> </div> </a> <ul id="toc-Analytical_techniques:_Method_of_slices-sublist" class="vector-toc-list"> <li id="toc-Swedish_Slip_Circle_Method_of_Analysis" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Swedish_Slip_Circle_Method_of_Analysis"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1.1</span> <span>Swedish Slip Circle Method of Analysis</span> </div> </a> <ul id="toc-Swedish_Slip_Circle_Method_of_Analysis-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ordinary_Method_of_Slices" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Ordinary_Method_of_Slices"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1.2</span> <span>Ordinary Method of Slices</span> </div> </a> <ul id="toc-Ordinary_Method_of_Slices-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Modified_Bishop’s_Method_of_Analysis" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Modified_Bishop’s_Method_of_Analysis"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1.3</span> <span>Modified Bishop’s Method of Analysis</span> </div> </a> <ul id="toc-Modified_Bishop’s_Method_of_Analysis-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lorimer's_method" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Lorimer's_method"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1.4</span> <span>Lorimer's method</span> </div> </a> <ul id="toc-Lorimer's_method-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Spencer’s_Method" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Spencer’s_Method"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1.5</span> <span>Spencer’s Method</span> </div> </a> <ul id="toc-Spencer’s_Method-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sarma_method" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Sarma_method"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1.6</span> <span>Sarma method</span> </div> </a> <ul id="toc-Sarma_method-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Comparisons" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Comparisons"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Comparisons</span> </div> </a> <ul id="toc-Comparisons-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Rock_slope_stability_analysis" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Rock_slope_stability_analysis"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Rock slope stability analysis</span> </div> </a> <ul id="toc-Rock_slope_stability_analysis-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Limit_analysis" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Limit_analysis"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Limit analysis</span> </div> </a> <ul id="toc-Limit_analysis-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Stereographic_and_kinematic_analysis" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Stereographic_and_kinematic_analysis"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Stereographic and kinematic analysis</span> </div> </a> <ul id="toc-Stereographic_and_kinematic_analysis-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Rockfall_simulators" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Rockfall_simulators"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Rockfall simulators</span> </div> </a> <ul id="toc-Rockfall_simulators-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Numerical_methods_of_analysis" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Numerical_methods_of_analysis"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Numerical methods of analysis</span> </div> </a> <button aria-controls="toc-Numerical_methods_of_analysis-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Numerical methods of analysis subsection</span> </button> <ul id="toc-Numerical_methods_of_analysis-sublist" class="vector-toc-list"> <li id="toc-Continuum_modelling" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Continuum_modelling"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Continuum modelling</span> </div> </a> <ul id="toc-Continuum_modelling-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Discontinuum_modelling" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Discontinuum_modelling"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Discontinuum modelling</span> </div> </a> <ul id="toc-Discontinuum_modelling-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Hybrid/coupled_modelling" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Hybrid/coupled_modelling"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>Hybrid/coupled modelling</span> </div> </a> <ul id="toc-Hybrid/coupled_modelling-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Slope stability analysis</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 11 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-11" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">11 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A7%D8%B3%D8%AA%D9%82%D8%B1%D8%A7%D8%B1_%D8%A7%D9%84%D9%85%D9%86%D8%AD%D8%AF%D8%B1" title="استقرار المنحدر – Arabic" lang="ar" hreflang="ar" data-title="استقرار المنحدر" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Estabilitat_de_talussos" title="Estabilitat de talussos – Catalan" lang="ca" hreflang="ca" data-title="Estabilitat de talussos" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Gleitkreisverfahren" title="Gleitkreisverfahren – German" lang="de" hreflang="de" data-title="Gleitkreisverfahren" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Estabilidad_de_taludes" title="Estabilidad de taludes – Spanish" lang="es" hreflang="es" data-title="Estabilidad de taludes" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AA%D8%AD%D9%84%DB%8C%D9%84_%D9%BE%D8%A7%DB%8C%D8%AF%D8%A7%D8%B1%DB%8C_%D8%B4%DB%8C%D8%A8" title="تحلیل پایداری شیب – Persian" lang="fa" hreflang="fa" data-title="تحلیل پایداری شیب" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E6%96%9C%E9%9D%A2%E5%AE%89%E5%AE%9A%E8%A7%A3%E6%9E%90" title="斜面安定解析 – Japanese" lang="ja" hreflang="ja" data-title="斜面安定解析" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Skr%C3%A5ningsstabilitet" title="Skråningsstabilitet – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Skråningsstabilitet" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Stateczno%C5%9B%C4%87_zboczy" title="Stateczność zboczy – Polish" lang="pl" hreflang="pl" data-title="Stateczność zboczy" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/An%C3%A1lise_de_estabilidade_de_declive" title="Análise de estabilidade de declive – Portuguese" lang="pt" hreflang="pt" data-title="Análise de estabilidade de declive" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%90%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7_%D1%83%D1%81%D1%82%D0%BE%D0%B9%D1%87%D0%B8%D0%B2%D0%BE%D1%81%D1%82%D0%B8_%D0%BE%D1%82%D0%BA%D0%BE%D1%81%D0%BE%D0%B2" title="Анализ устойчивости откосов – Russian" lang="ru" hreflang="ru" data-title="Анализ устойчивости откосов" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Kastabilan_l%C3%A9r%C3%A9ng" title="Kastabilan léréng – Sundanese" lang="su" hreflang="su" data-title="Kastabilan léréng" data-language-autonym="Sunda" data-language-local-name="Sundanese" class="interlanguage-link-target"><span>Sunda</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q961278#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Slope_stability_analysis" title="View the content page [c]" accesskey="c"><span>Article</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Talk:Slope_stability_analysis" rel="discussion" title="Discuss improvements to the content page [t]" accesskey="t"><span>Talk</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Change language variant" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">English</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Views"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Slope_stability_analysis"><span>Read</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Slope_stability_analysis&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Slope_stability_analysis&action=history" title="Past revisions of this page [h]" accesskey="h"><span>View history</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Tools" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Tools</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Tools</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">hide</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="More options" > <div class="vector-menu-heading"> Actions </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Slope_stability_analysis"><span>Read</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Slope_stability_analysis&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Slope_stability_analysis&action=history"><span>View history</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> General </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Special:WhatLinksHere/Slope_stability_analysis" title="List of all English Wikipedia pages containing links to this page [j]" accesskey="j"><span>What links here</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Special:RecentChangesLinked/Slope_stability_analysis" rel="nofollow" title="Recent changes in pages linked from this page [k]" accesskey="k"><span>Related changes</span></a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/Wikipedia:File_Upload_Wizard" title="Upload files [u]" accesskey="u"><span>Upload file</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Special:SpecialPages" title="A list of all special pages [q]" accesskey="q"><span>Special pages</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Slope_stability_analysis&oldid=1251997464" title="Permanent link to this revision of this page"><span>Permanent link</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Slope_stability_analysis&action=info" title="More information about this page"><span>Page information</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Special:CiteThisPage&page=Slope_stability_analysis&id=1251997464&wpFormIdentifier=titleform" title="Information on how to cite this page"><span>Cite this page</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Special:UrlShortener&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FSlope_stability_analysis"><span>Get shortened URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Special:QrCode&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FSlope_stability_analysis"><span>Download QR code</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Print/export </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Special:DownloadAsPdf&page=Slope_stability_analysis&action=show-download-screen" title="Download this page as a PDF file"><span>Download as PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Slope_stability_analysis&printable=yes" title="Printable version of this page [p]" accesskey="p"><span>Printable version</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> In other projects </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Slope_stability_analysis" hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q961278" title="Structured data on this page hosted by Wikidata [g]" accesskey="g"><span>Wikidata item</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Method for analyzing stability of slopes of soil or rock</div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Technical plainlinks metadata ambox ambox-style ambox-technical" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/40px-Edit-clear.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/60px-Edit-clear.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/80px-Edit-clear.svg.png 2x" data-file-width="48" data-file-height="48" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article <b>may be too technical for most readers to understand</b>.<span class="hide-when-compact"> Please <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Slope_stability_analysis&action=edit">help improve it</a> to <a href="/wiki/Wikipedia:Make_technical_articles_understandable" title="Wikipedia:Make technical articles understandable">make it understandable to non-experts</a>, without removing the technical details.</span> <span class="date-container"><i>(<span class="date">December 2012</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Pett_bish.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/Pett_bish.gif/250px-Pett_bish.gif" decoding="async" width="250" height="169" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/Pett_bish.gif/375px-Pett_bish.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/9/98/Pett_bish.gif 2x" data-file-width="400" data-file-height="270" /></a><figcaption>Method of slices</figcaption></figure> <p><b>Slope stability analysis</b> is a static or dynamic, analytical or empirical method to evaluate the <i><a href="/wiki/Stability_of_slopes" class="mw-redirect" title="Stability of slopes">stability of slopes</a></i> of soil- and rock-fill dams, embankments, excavated slopes, and natural slopes in soil and rock. It is performed to assess the safe design of a human-made or natural <a href="/wiki/Slope" title="Slope">slopes</a> (e.g. <a href="/wiki/Embankment_(transportation)" class="mw-redirect" title="Embankment (transportation)">embankments</a>, <a href="/wiki/Road_cut" class="mw-redirect" title="Road cut">road cuts</a>, <a href="/wiki/Open-pit_mining" title="Open-pit mining">open-pit mining</a>, excavations, <a href="/wiki/Landfill" title="Landfill">landfills</a> etc.) and the equilibrium conditions.<sup id="cite_ref-Eberhardt2003p4_1-0" class="reference"><a href="#cite_note-Eberhardt2003p4-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Abramson2002p2_2-0" class="reference"><a href="#cite_note-Abramson2002p2-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Slope_stability" title="Slope stability">Slope stability</a> is the resistance of inclined surface to <a href="/wiki/Failure" title="Failure">failure</a> by <a href="/wiki/Landslide" title="Landslide">sliding</a> or collapsing.<sup id="cite_ref-Kliche1999p2_3-0" class="reference"><a href="#cite_note-Kliche1999p2-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> The main objectives of slope stability analysis are finding endangered areas, investigation of potential failure mechanisms, determination of the slope sensitivity to different triggering mechanisms, designing of optimal slopes with regard to <a href="/wiki/Safety" title="Safety">safety</a>, <a href="/wiki/Reliability_engineering" title="Reliability engineering">reliability</a> and <a href="/wiki/Economics" title="Economics">economics</a>, and designing possible remedial measures, e.g. barriers and <a href="/wiki/Stabilization_(architecture)" title="Stabilization (architecture)">stabilization</a>.<sup id="cite_ref-Eberhardt2003p4_1-1" class="reference"><a href="#cite_note-Eberhardt2003p4-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Abramson2002p2_2-1" class="reference"><a href="#cite_note-Abramson2002p2-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>Successful <a href="/wiki/Design" title="Design">design</a> of the slope requires <a href="/wiki/Geological" class="mw-redirect" title="Geological">geological</a> information and site characteristics, e.g. properties of <a href="/wiki/Soil" title="Soil">soil</a>/<a href="/wiki/Rock_(geology)" title="Rock (geology)">rock</a> mass, slope <a href="/wiki/Geometry" title="Geometry">geometry</a>, <a href="/wiki/Groundwater" title="Groundwater">groundwater</a> conditions, alternation of materials by <a href="/wiki/Faulting" class="mw-redirect" title="Faulting">faulting</a>, <a href="/wiki/Joint_(geology)" title="Joint (geology)">joint</a> or <a href="/wiki/Fracture_(geology)" title="Fracture (geology)">discontinuity</a> systems, movements and <a href="/wiki/Tension_(physics)" title="Tension (physics)">tension</a> in joints, earthquake activity etc.<sup id="cite_ref-USArmyCorps2003pp1-2_4-0" class="reference"><a href="#cite_note-USArmyCorps2003pp1-2-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Abramson2002p1_5-0" class="reference"><a href="#cite_note-Abramson2002p1-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> The presence of water has a detrimental effect on slope stability. Water pressure acting in the pore spaces, fractures or other discontinuities in the materials that make up the pit slope will reduce the strength of those materials.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Choice of correct analysis technique depends on both site conditions and the potential mode of failure, with careful consideration being given to the varying <a href="/wiki/Strength_of_materials" title="Strength of materials">strengths</a>, weaknesses and limitations inherent in each <a href="/wiki/Methodology" title="Methodology">methodology</a>.<sup id="cite_ref-Stead2001p615_7-0" class="reference"><a href="#cite_note-Stead2001p615-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>Before the <a href="/wiki/Computer_age" class="mw-redirect" title="Computer age">computer age</a> stability analysis was performed graphically or by using a hand-held calculator. Today <a href="/wiki/Engineer" title="Engineer">engineers</a> have a lot of possibilities to use analysis <a href="/wiki/Software" title="Software">software</a>, ranges from simple <i>limit equilibrium</i> techniques through to computational limit analysis approaches (e.g. <a href="/wiki/Finite_element_limit_analysis" title="Finite element limit analysis">Finite element limit analysis</a>, <a href="/wiki/Discontinuity_layout_optimization" title="Discontinuity layout optimization">Discontinuity layout optimization</a>) to complex and sophisticated <i><a href="/wiki/Numerical_analysis" title="Numerical analysis">numerical solutions</a></i> (<a href="/wiki/Finite_element_method" title="Finite element method">finite-</a>/<a href="/wiki/Discrete_element_method" title="Discrete element method">distinct</a>-element codes).<sup id="cite_ref-Eberhardt2003p4_1-2" class="reference"><a href="#cite_note-Eberhardt2003p4-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> The engineer must fully understand limitations of each technique. For example, limit equilibrium is most commonly used and simple solution method, but it can become inadequate if the slope fails by complex mechanisms (e.g. internal <a href="/wiki/Deformation_(mechanics)" class="mw-redirect" title="Deformation (mechanics)">deformation</a> and <a href="/wiki/Brittle_fracture#Brittle" class="mw-redirect" title="Brittle fracture">brittle fracture</a>, progressive <a href="/wiki/Creep_(deformation)" title="Creep (deformation)">creep</a>, <a href="/wiki/Soil_liquefaction" title="Soil liquefaction">liquefaction</a> of weaker soil layers, etc.). In these cases more sophisticated <a href="/wiki/Numerical_analysis" title="Numerical analysis">numerical modelling</a> techniques should be utilised. Also, even for very simple slopes, the results obtained with typical limit equilibrium methods currently in use (Bishop, Spencer, etc.) may differ considerably. In addition, the use of the <a href="/wiki/Risk_assessment" title="Risk assessment">risk assessment</a> concept is increasing today. Risk assessment is concerned with both the consequence of slope failure and the <a href="/wiki/Probability" title="Probability">probability</a> of failure (both require an understanding of the failure mechanism).<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Limit_equilibrium_analysis">Limit equilibrium analysis</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Slope_stability_analysis&action=edit&section=1" title="Edit section: Limit equilibrium analysis"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Slope_2d_plain.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Slope_2d_plain.svg/250px-Slope_2d_plain.svg.png" decoding="async" width="250" height="164" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Slope_2d_plain.svg/375px-Slope_2d_plain.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Slope_2d_plain.svg/500px-Slope_2d_plain.svg.png 2x" data-file-width="663" data-file-height="434" /></a><figcaption>A typical cross-section of a slope used in two-dimensional analyses.</figcaption></figure> <p>Conventional methods of slope stability analysis can be divided into three groups: <a href="/wiki/Kinematics" title="Kinematics">kinematic</a> analysis, limit equilibrium analysis, and <a href="/wiki/Rock_(geology)" title="Rock (geology)">rock</a> <a href="/wiki/Falling_(physics)" class="mw-redirect" title="Falling (physics)">fall</a> simulators.<sup id="cite_ref-Eberhardt2003p6_10-0" class="reference"><a href="#cite_note-Eberhardt2003p6-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> Most slope stability analysis <a href="/wiki/Computer_program" title="Computer program">computer programs</a> are based on the limit equilibrium concept for a <a href="/wiki/Two-dimensional" class="mw-redirect" title="Two-dimensional">two-</a> or <a href="/wiki/Three-dimensional_space" title="Three-dimensional space">three-dimensional</a> model.<sup id="cite_ref-Abramson2002p329_11-0" class="reference"><a href="#cite_note-Abramson2002p329-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Abramson2002p363_12-0" class="reference"><a href="#cite_note-Abramson2002p363-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> Two-dimensional sections are analyzed assuming <a href="/wiki/Strain_(mechanics)" title="Strain (mechanics)">plane strain</a> conditions. Stability analyses of two-dimensional slope geometries using simple analytical approaches can provide important insights into the initial design and risk assessment of slopes. </p><p>Limit equilibrium methods investigate the equilibrium of a soil mass tending to slide down under the influence of <a href="/wiki/Gravity" title="Gravity">gravity</a>. Translational or rotational movement is considered on an assumed or known potential slip surface below the soil or <a href="/wiki/Rock_(geology)" title="Rock (geology)">rock</a> mass.<sup id="cite_ref-USArmyCorps2003p2_13-0" class="reference"><a href="#cite_note-USArmyCorps2003p2-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> In rock slope engineering, methods may be highly significant to simple block failure along distinct discontinuities.<sup id="cite_ref-Eberhardt2003p6_10-1" class="reference"><a href="#cite_note-Eberhardt2003p6-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> All these methods are based on the comparison of <a href="/wiki/Force" title="Force">forces</a>, <a href="/wiki/Torque" title="Torque">moments</a>, or <a href="/wiki/Stress_(mechanics)" title="Stress (mechanics)">stresses</a> resisting movement of the mass with those that can cause <a href="/wiki/Instability" title="Instability">unstable</a> motion (disturbing forces). The output of the analysis is a <a href="/wiki/Factor_of_safety" title="Factor of safety">factor of safety</a>, defined as the <a href="/wiki/Ratio" title="Ratio">ratio</a> of the shear strength (or, alternatively, an equivalent measure of shear resistance or capacity) to the shear stress (or other equivalent measure) required for equilibrium. If the value of factor of safety is less than 1.0, the slope is unstable. </p><p>All limit equilibrium methods assume that the <a href="/wiki/Shear_strength" title="Shear strength">shear strengths</a> of the materials along the potential failure surface are governed by linear (<i><a href="/wiki/Mohr-Coulomb_theory" class="mw-redirect" title="Mohr-Coulomb theory">Mohr-Coulomb</a></i>) or non-linear relationships between shear strength and the normal stress on the failure surface.<sup id="cite_ref-USArmyCorps2003p2_13-1" class="reference"><a href="#cite_note-USArmyCorps2003p2-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> The most commonly used variation is <a href="/wiki/Shear_strength_(soil)#Drained_shear_strength" title="Shear strength (soil)">Terzaghi's theory</a> of shear strength which states that </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau =\sigma '\tan \phi '+c'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>τ</mi> <mo>=</mo> <msup> <mi>σ</mi> <mo>′</mo> </msup> <mi>tan</mi> <mo>⁡</mo> <msup> <mi>ϕ</mi> <mo>′</mo> </msup> <mo>+</mo> <msup> <mi>c</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau =\sigma '\tan \phi '+c'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/03d2f8e8f5e38bd679cfb4e9fbea4373543956fd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:17.052ex; height:2.843ex;" alt="{\displaystyle \tau =\sigma '\tan \phi '+c'}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>τ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38a7dcde9730ef0853809fefc18d88771f95206c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.202ex; height:1.676ex;" alt="{\displaystyle \tau }"></span> is the shear strength of the interface, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma '=\sigma -u}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>σ</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>σ</mi> <mo>−</mo> <mi>u</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma '=\sigma -u}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43045856644607ef1e01c27f5d0a30f4d926a7a7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:10.613ex; height:2.676ex;" alt="{\displaystyle \sigma '=\sigma -u}"></span> is the effective stress (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59f59b7c3e6fdb1d0365a494b81fb9a696138c36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle \sigma }"></span> is the total stress normal to the interface and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3e6bb763d22c20916ed4f0bb6bd49d7470cffd8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle u}"></span> is the pore water pressure on the interface), <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi '}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>ϕ</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi '}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac5304c739c4deec1d259e3235a419e6177fe77a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.07ex; height:2.843ex;" alt="{\displaystyle \phi '}"></span> is the effective friction angle, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>c</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f295e32663780aa8800e3106dba9d6e04e57cdc6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.692ex; height:2.509ex;" alt="{\displaystyle c'}"></span> is the effective cohesion. </p><p>The <a href="/wiki/Slope_stability#Method_of_slices" title="Slope stability">methods of slices</a> is the most popular limit equilibrium technique. In this approach, the soil mass is discretized into vertical slices.<sup id="cite_ref-Abramson2002p363_12-1" class="reference"><a href="#cite_note-Abramson2002p363-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Zhu2003pp377-395_14-0" class="reference"><a href="#cite_note-Zhu2003pp377-395-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> Several versions of the method are in use. These variations can produce different results (factor of safety) because of different <a href="https://en.wiktionary.org/wiki/assumption" class="extiw" title="wikt:assumption">assumptions</a> and inter-slice boundary conditions.<sup id="cite_ref-USArmyCorps2003p2_13-2" class="reference"><a href="#cite_note-USArmyCorps2003p2-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Abramson2002pp363-367_15-0" class="reference"><a href="#cite_note-Abramson2002pp363-367-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p><p>The location of the interface is typically unknown but can be found using numerical optimization methods.<sup id="cite_ref-USArmyCorps2003p5_16-0" class="reference"><a href="#cite_note-USArmyCorps2003p5-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> For example, <b>functional slope design</b> considers the <i>critical</i> slip surface to be the location where that has the lowest value of factor of safety from a range of possible surfaces. A wide variety of slope stability software use the limit equilibrium concept with automatic critical slip surface determination. </p><p>Typical slope stability software can analyze the stability of generally layered soil slopes, embankments, earth cuts, and anchored sheeting <a href="/wiki/Architectural_structure" class="mw-redirect" title="Architectural structure">structures</a>. Earthquake effects, external <a href="/wiki/Structural_load" title="Structural load">loading</a>, groundwater conditions, <a href="/wiki/Stabilization_(architecture)" title="Stabilization (architecture)">stabilization</a> forces (i.e., anchors, geo-reinforcements etc.) can also be included. </p> <div class="mw-heading mw-heading3"><h3 id="Analytical_techniques:_Method_of_slices">Analytical techniques: Method of slices</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Slope_stability_analysis&action=edit&section=2" title="Edit section: Analytical techniques: Method of slices"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Pett_bish.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/Pett_bish.gif/250px-Pett_bish.gif" decoding="async" width="250" height="169" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/Pett_bish.gif/375px-Pett_bish.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/9/98/Pett_bish.gif 2x" data-file-width="400" data-file-height="270" /></a><figcaption>Schematic of the method of slices showing rotation center.</figcaption></figure> <p>Many slope stability analysis tools use various versions of the methods of slices such as <i><a href="/wiki/Bishop%27s_Method" class="mw-redirect" title="Bishop's Method">Bishop simplified</a></i>, <i>Ordinary method of slices</i> (<i>Swedish circle method/Petterson/Fellenius</i>), <i>Spencer</i>, <i><a href="/wiki/Sarma_method" title="Sarma method">Sarma</a></i> etc. <i><a href="/wiki/Sarma_method" title="Sarma method">Sarma</a></i> and <i>Spencer</i> are called rigorous methods because they satisfy all three conditions of equilibrium: force equilibrium in horizontal and vertical direction and moment equilibrium condition. Rigorous methods can provide more <a href="/wiki/Accurate" class="mw-redirect" title="Accurate">accurate</a> results than non-rigorous methods. <i>Bishop simplified</i> or <i>Fellenius</i> are non-rigorous methods satisfying only some of the equilibrium conditions and making some simplifying assumptions.<sup id="cite_ref-Zhu2003pp377-395_14-1" class="reference"><a href="#cite_note-Zhu2003pp377-395-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Abramson2002pp363-367_15-1" class="reference"><a href="#cite_note-Abramson2002pp363-367-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> Some of these approaches are discussed below. </p> <div class="mw-heading mw-heading4"><h4 id="Swedish_Slip_Circle_Method_of_Analysis">Swedish Slip Circle Method of Analysis</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Slope_stability_analysis&action=edit&section=3" title="Edit section: Swedish Slip Circle Method of Analysis"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Swedish Slip Circle method assumes that the friction angle of the soil or rock is equal to zero, i.e., <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau =c'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>τ</mi> <mo>=</mo> <msup> <mi>c</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau =c'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e8be2541dfaaa5839b0226a69d20235093082d2e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.992ex; height:2.509ex;" alt="{\displaystyle \tau =c'}"></span>. In other words, when friction angle is considered to be zero, the effective stress term goes to zero, thus equating the shear strength to the cohesion parameter of the given soil. The Swedish slip circle method assumes a circular failure interface, and analyzes stress and strength parameters using circular geometry and statics. The moment caused by the internal driving forces of a slope is compared to the moment caused by forces resisting slope failure. If resisting forces are greater than driving forces, the slope is assumed stable. </p> <div class="mw-heading mw-heading4"><h4 id="Ordinary_Method_of_Slices">Ordinary Method of Slices</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Slope_stability_analysis&action=edit&section=4" title="Edit section: Ordinary Method of Slices"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Slope_2d_mos_plain.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/06/Slope_2d_mos_plain.svg/250px-Slope_2d_mos_plain.svg.png" decoding="async" width="250" height="164" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/06/Slope_2d_mos_plain.svg/375px-Slope_2d_mos_plain.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/06/Slope_2d_mos_plain.svg/500px-Slope_2d_mos_plain.svg.png 2x" data-file-width="663" data-file-height="434" /></a><figcaption>Division of the slope mass in the method of slices.</figcaption></figure> <p>In the method of slices, also called OMS or the Fellenius method, the sliding mass above the failure surface is divided into a number of slices. The forces acting on each slice are obtained by considering the mechanical (force and moment) equilibrium for the slices. Each slice is considered on its own and interactions between slices are neglected because the resultant forces are parallel to the base of each slice. However, Newton's third law is not satisfied by this method because, in general, the resultants on the left and right of a slice do not have the same magnitude and are not collinear.<sup id="cite_ref-FredlundKrahn_17-0" class="reference"><a href="#cite_note-FredlundKrahn-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p><p>This allows for a simple static equilibrium calculation, considering only soil weight, along with shear and normal stresses along the failure plane. Both the friction angle and cohesion can be considered for each slice. In the general case of the method of slices, the forces acting on a slice are shown in the figure below. The normal (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{r},E_{l}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{r},E_{l}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cfaec9e0c722a3a04d0b126060abd2693d0382ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.161ex; height:2.509ex;" alt="{\displaystyle E_{r},E_{l}}"></span>) and shear (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{r},S_{l}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{r},S_{l}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/df8556d08a435ce30856bdced0fc8d018db8b1f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.58ex; height:2.509ex;" alt="{\displaystyle S_{r},S_{l}}"></span>) forces between adjacent slices constrain each slice and make the problem <a href="/wiki/Statically_indeterminate" title="Statically indeterminate">statically indeterminate</a> when they are included in the computation. </p> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Slope_2d_equil_mos_plain.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Slope_2d_equil_mos_plain.svg/250px-Slope_2d_equil_mos_plain.svg.png" decoding="async" width="250" height="194" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Slope_2d_equil_mos_plain.svg/375px-Slope_2d_equil_mos_plain.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Slope_2d_equil_mos_plain.svg/500px-Slope_2d_equil_mos_plain.svg.png 2x" data-file-width="467" data-file-height="362" /></a><figcaption>Force equilibrium for a slice in the method of slices. The block is assumed to have thickness <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span>. The slices on the left and right exert normal forces <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{l},E_{r}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{l},E_{r}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0e363761b8c62b8513590f944a5b7c6635e3231a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.161ex; height:2.509ex;" alt="{\displaystyle E_{l},E_{r}}"></span> and shear forces <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{l},s_{r}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{l},s_{r}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4edd52979f9c57712b327a12c8bea3ada1fe6264" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.246ex; height:2.509ex;" alt="{\displaystyle S_{l},s_{r}}"></span>, the weight of the slice causes the force <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle W}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>W</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/54a9c4c547f4d6111f81946cad242b18298d70b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.435ex; height:2.176ex;" alt="{\displaystyle W}"></span>. These forces are balanced by the pore pressure and reactions of the base <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N,T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo>,</mo> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N,T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e4e96a2057a24903dbb91c39e84cf2442af3e4f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.734ex; height:2.509ex;" alt="{\displaystyle N,T}"></span>.</figcaption></figure> <p>For the ordinary method of slices, the resultant vertical and horizontal forces are </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}\sum F_{v}=0&=W-N\cos \alpha -T\sin \alpha \\\sum F_{h}=0&=kW+N\sin \alpha -T\cos \alpha \end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mo>∑</mo> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>W</mi> <mo>−</mo> <mi>N</mi> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> <mo>−</mo> <mi>T</mi> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> </mtd> </mtr> <mtr> <mtd> <mo>∑</mo> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>k</mi> <mi>W</mi> <mo>+</mo> <mi>N</mi> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> <mo>−</mo> <mi>T</mi> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\sum F_{v}=0&=W-N\cos \alpha -T\sin \alpha \\\sum F_{h}=0&=kW+N\sin \alpha -T\cos \alpha \end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b63e999a3673cc2489129ae2c2f1292f30cd3062" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:38.044ex; height:7.843ex;" alt="{\displaystyle {\begin{aligned}\sum F_{v}=0&=W-N\cos \alpha -T\sin \alpha \\\sum F_{h}=0&=kW+N\sin \alpha -T\cos \alpha \end{aligned}}}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}"></span> represents a linear factor that determines the increase in horizontal force with the depth of the slice. Solving for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}"></span> gives </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N=W\cos \alpha -kW\sin \alpha \,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo>=</mo> <mi>W</mi> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> <mo>−</mo> <mi>k</mi> <mi>W</mi> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N=W\cos \alpha -kW\sin \alpha \,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6731abd125fb52a9c90523803a63dba71e9226a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:25.608ex; height:2.343ex;" alt="{\displaystyle N=W\cos \alpha -kW\sin \alpha \,.}"></span></dd></dl> <p>Next, the method assumes that each slice can rotate about a center of rotation and that moment balance about this point is also needed for equilibrium. A balance of moments for all the slices taken together gives </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum M=0=\sum _{j}(W_{j}x_{j}-T_{j}R_{j}-N_{j}f_{j}-kW_{j}e_{j})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∑</mo> <mi>M</mi> <mo>=</mo> <mn>0</mn> <mo>=</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </munder> <mo stretchy="false">(</mo> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>−</mo> <mi>k</mi> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msub> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum M=0=\sum _{j}(W_{j}x_{j}-T_{j}R_{j}-N_{j}f_{j}-kW_{j}e_{j})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01fba7d2fb7e5bdc4c996cc6cf07e43c891e3efb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:48.646ex; height:5.843ex;" alt="{\displaystyle \sum M=0=\sum _{j}(W_{j}x_{j}-T_{j}R_{j}-N_{j}f_{j}-kW_{j}e_{j})}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle j}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f461e54f5c093e92a55547b9764291390f0b5d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.027ex; width:0.985ex; height:2.509ex;" alt="{\displaystyle j}"></span> is the slice index, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{j},R_{j},f_{j},e_{j}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{j},R_{j},f_{j},e_{j}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/12feb0fe1bab90048f4193a21a78dc70d445db4f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:12.057ex; height:2.843ex;" alt="{\displaystyle x_{j},R_{j},f_{j},e_{j}}"></span> are the moment arms, and loads on the surface have been ignored. The moment equation can be used to solve for the shear forces at the interface after substituting the expression for the normal force: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{j}T_{j}R_{j}=\sum _{j}[W_{j}x_{j}-(W_{j}\cos \alpha _{j}-kW_{j}\sin \alpha _{j})f_{j}-kW_{j}e_{j}]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </munder> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>=</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </munder> <mo stretchy="false">[</mo> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>−</mo> <mo stretchy="false">(</mo> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>−</mo> <mi>k</mi> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mi>sin</mi> <mo>⁡</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo stretchy="false">)</mo> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>−</mo> <mi>k</mi> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msub> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{j}T_{j}R_{j}=\sum _{j}[W_{j}x_{j}-(W_{j}\cos \alpha _{j}-kW_{j}\sin \alpha _{j})f_{j}-kW_{j}e_{j}]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/729fcdf037460203c87a8db2cf1dc944b1cf98d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:60.188ex; height:5.843ex;" alt="{\displaystyle \sum _{j}T_{j}R_{j}=\sum _{j}[W_{j}x_{j}-(W_{j}\cos \alpha _{j}-kW_{j}\sin \alpha _{j})f_{j}-kW_{j}e_{j}]}"></span></dd></dl> <p>Using Terzaghi's strength theory and converting the stresses into moments, we have </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{j}\tau l_{j}R_{j}=l_{j}R_{j}\sigma _{j}'\tan \phi '+l_{j}R_{j}c'=R_{j}(N_{j}-u_{j}l_{j})\tan \phi '+l_{j}R_{j}c'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </munder> <mi>τ</mi> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msubsup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> <mo>′</mo> </msubsup> <mi>tan</mi> <mo>⁡</mo> <msup> <mi>ϕ</mi> <mo>′</mo> </msup> <mo>+</mo> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msup> <mi>c</mi> <mo>′</mo> </msup> <mo>=</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mi>tan</mi> <mo>⁡</mo> <msup> <mi>ϕ</mi> <mo>′</mo> </msup> <mo>+</mo> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msup> <mi>c</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{j}\tau l_{j}R_{j}=l_{j}R_{j}\sigma _{j}'\tan \phi '+l_{j}R_{j}c'=R_{j}(N_{j}-u_{j}l_{j})\tan \phi '+l_{j}R_{j}c'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3f756284d0fce9b39207c03e4406fb6547558a20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:65.899ex; height:5.843ex;" alt="{\displaystyle \sum _{j}\tau l_{j}R_{j}=l_{j}R_{j}\sigma _{j}'\tan \phi '+l_{j}R_{j}c'=R_{j}(N_{j}-u_{j}l_{j})\tan \phi '+l_{j}R_{j}c'}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u_{j}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u_{j}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86f8d397f4684f948df846413e6d62b009718724" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.239ex; height:2.343ex;" alt="{\displaystyle u_{j}}"></span> is the pore pressure. The factor of safety is the ratio of the maximum moment from Terzaghi's theory to the estimated moment, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{Factor of safety}}={\frac {\sum _{j}\tau l_{j}R_{j}}{\sum _{j}T_{j}R_{j}}}\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Factor of safety</mtext> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </munder> <mi>τ</mi> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mrow> <mrow> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </munder> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{Factor of safety}}={\frac {\sum _{j}\tau l_{j}R_{j}}{\sum _{j}T_{j}R_{j}}}\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8d872f3b686c85a6a06b149adfed833cd478c140" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:29.88ex; height:7.176ex;" alt="{\displaystyle {\text{Factor of safety}}={\frac {\sum _{j}\tau l_{j}R_{j}}{\sum _{j}T_{j}R_{j}}}\,.}"></span></dd></dl> <div class="mw-heading mw-heading4"><h4 id="Modified_Bishop’s_Method_of_Analysis"><span id="Modified_Bishop.E2.80.99s_Method_of_Analysis"></span>Modified Bishop’s Method of Analysis</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Slope_stability_analysis&action=edit&section=5" title="Edit section: Modified Bishop’s Method of Analysis"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Modified Bishop's method<sup id="cite_ref-Bishop_18-0" class="reference"><a href="#cite_note-Bishop-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> is slightly different from the ordinary method of slices in that normal interaction forces between adjacent slices are assumed to be collinear and the resultant interslice shear force is zero. The approach was proposed by <a href="/wiki/Alan_W._Bishop" title="Alan W. Bishop">Alan W. Bishop</a> of <a href="/wiki/Imperial_College_Civil_%26_Environmental_Engineering" class="mw-redirect" title="Imperial College Civil & Environmental Engineering">Imperial College</a>. The constraint introduced by the normal forces between slices makes the problem statically indeterminate. As a result, iterative methods have to be used to solve for the factor of safety. The method has been shown to produce factor of safety values within a few percent of the "correct" values. </p><p>The factor of safety for moment equilibrium in Bishop's method can be expressed as </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F={\cfrac {\sum _{j}{\cfrac {\left[c'l_{j}+(W_{j}-u_{j}l_{j})\tan \phi '\right]}{\psi _{j}}}}{\sum _{j}W_{j}\sin \alpha _{j}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mrow> <msup> <mi>c</mi> <mo>′</mo> </msup> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>+</mo> <mo stretchy="false">(</mo> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mi>tan</mi> <mo>⁡</mo> <msup> <mi>ϕ</mi> <mo>′</mo> </msup> </mrow> <mo>]</mo> </mrow> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow /> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </munder> <msub> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mi>sin</mi> <mo>⁡</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F={\cfrac {\sum _{j}{\cfrac {\left[c'l_{j}+(W_{j}-u_{j}l_{j})\tan \phi '\right]}{\psi _{j}}}}{\sum _{j}W_{j}\sin \alpha _{j}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2c8537f95e33c99ce7b7975c8a374f463b212fe0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:35.49ex; height:11.009ex;" alt="{\displaystyle F={\cfrac {\sum _{j}{\cfrac {\left[c'l_{j}+(W_{j}-u_{j}l_{j})\tan \phi '\right]}{\psi _{j}}}}{\sum _{j}W_{j}\sin \alpha _{j}}}}"></span></dd></dl> <p>where </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \psi _{j}=\cos \alpha _{j}+{\frac {\sin \alpha _{j}\tan \phi '}{F}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mi>tan</mi> <mo>⁡</mo> <msup> <mi>ϕ</mi> <mo>′</mo> </msup> </mrow> <mi>F</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi _{j}=\cos \alpha _{j}+{\frac {\sin \alpha _{j}\tan \phi '}{F}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bb562b382a60ddddf337087ee782a3cd6ad6e81d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:26.937ex; height:5.676ex;" alt="{\displaystyle \psi _{j}=\cos \alpha _{j}+{\frac {\sin \alpha _{j}\tan \phi '}{F}}}"></span></dd></dl> <p>where, as before, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle j}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f461e54f5c093e92a55547b9764291390f0b5d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.027ex; width:0.985ex; height:2.509ex;" alt="{\displaystyle j}"></span> is the slice index, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>c</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f295e32663780aa8800e3106dba9d6e04e57cdc6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.692ex; height:2.509ex;" alt="{\displaystyle c'}"></span> is the effective cohesion, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi '}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>ϕ</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi '}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac5304c739c4deec1d259e3235a419e6177fe77a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.07ex; height:2.843ex;" alt="{\displaystyle \phi '}"></span> is the effective internal angle of internal friction, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle l}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>l</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/829091f745070b9eb97a80244129025440a1cfac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.693ex; height:2.176ex;" alt="{\displaystyle l}"></span> is the width of each slice, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle W}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>W</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/54a9c4c547f4d6111f81946cad242b18298d70b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.435ex; height:2.176ex;" alt="{\displaystyle W}"></span> is the weight of each slice, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3e6bb763d22c20916ed4f0bb6bd49d7470cffd8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle u}"></span> is the water pressure at the base of each slice. An iterative method has to be used to solve for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/545fd099af8541605f7ee55f08225526be88ce57" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.741ex; height:2.176ex;" alt="{\displaystyle F}"></span> because the factor of safety appears both on the left and right hand sides of the equation. </p> <div class="mw-heading mw-heading4"><h4 id="Lorimer's_method"><span id="Lorimer.27s_method"></span>Lorimer's method</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Slope_stability_analysis&action=edit&section=6" title="Edit section: Lorimer's method"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Lorimer's Method is a technique for evaluating slope stability in cohesive soils. It differs from Bishop's Method in that it uses a <a href="/wiki/Clothoid" class="mw-redirect" title="Clothoid">clothoid</a> slip surface in place of a circle. This mode of failure was determined experimentally to account for effects of particle cementation. The method was developed in the 1930s by Gerhardt Lorimer (Dec 20, 1894-Oct 19, 1961), a student of geotechnical pioneer <a href="/wiki/Karl_von_Terzaghi" title="Karl von Terzaghi">Karl von Terzaghi</a>. </p> <div class="mw-heading mw-heading4"><h4 id="Spencer’s_Method"><span id="Spencer.E2.80.99s_Method"></span>Spencer’s Method</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Slope_stability_analysis&action=edit&section=7" title="Edit section: Spencer’s Method"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Spencer's Method of analysis<sup id="cite_ref-Spencer_19-0" class="reference"><a href="#cite_note-Spencer-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> requires a computer program capable of cyclic algorithms, but makes slope stability analysis easier. Spencer's algorithm satisfies all equilibria (horizontal, vertical and driving moment) on each slice. The method allows for unconstrained slip plains and can therefore determine the factor of safety along any slip surface. The rigid equilibrium and unconstrained slip surface result in more precise safety factors than, for example, Bishop's Method or the Ordinary Method of Slices.<sup id="cite_ref-Spencer_19-1" class="reference"><a href="#cite_note-Spencer-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Sarma_method">Sarma method</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Slope_stability_analysis&action=edit&section=8" title="Edit section: Sarma method"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Sarma_method" title="Sarma method">Sarma method</a></div> <p>The <a href="/wiki/Sarma_method" title="Sarma method">Sarma method</a>,<sup id="cite_ref-Sarma_20-0" class="reference"><a href="#cite_note-Sarma-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> proposed by <a href="/wiki/Sarada_K._Sarma" title="Sarada K. Sarma">Sarada K. Sarma</a> of <a href="/wiki/Imperial_College_Civil_%26_Environmental_Engineering" class="mw-redirect" title="Imperial College Civil & Environmental Engineering">Imperial College</a> is a <a href="#Limit_equilibrium_analysis">Limit equilibrium</a> technique used to assess the stability of slopes under seismic conditions. It may also be used for static conditions if the value of the horizontal load is taken as zero. The method can analyse a wide range of slope failures as it may accommodate a multi-wedge failure mechanism and therefore it is not restricted to planar or circular failure surfaces. It may provide information about the factor of safety or about the critical acceleration required to cause collapse. </p> <div class="mw-heading mw-heading3"><h3 id="Comparisons">Comparisons</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Slope_stability_analysis&action=edit&section=9" title="Edit section: Comparisons"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The assumptions made by a number of limit equilibrium methods are listed in the table below.<sup id="cite_ref-FredLund_21-0" class="reference"><a href="#cite_note-FredLund-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p> <table class="wikitable"> <tbody><tr> <th>Method</th> <th>Assumption </th></tr> <tr> <td>Ordinary method of slices</td> <td>Interslice forces are neglected </td></tr> <tr> <td>Bishop's simplified/modified<sup id="cite_ref-Bishop_18-1" class="reference"><a href="#cite_note-Bishop-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup></td> <td>Resultant interslice forces are horizontal. There are no interslice shear forces. </td></tr> <tr> <td>Janbu's simplified<sup id="cite_ref-Janbu_22-0" class="reference"><a href="#cite_note-Janbu-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup></td> <td>Resultant interslice forces are horizontal. An empirical correction factor is used to account for interslice shear forces. </td></tr> <tr> <td>Janbu's generalized<sup id="cite_ref-Janbu_22-1" class="reference"><a href="#cite_note-Janbu-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup></td> <td>An assumed <a href="/wiki/Line_of_thrust" title="Line of thrust">line of thrust</a> is used to define the location of the interslice normal force. </td></tr> <tr> <td>Spencer<sup id="cite_ref-Spencer_19-2" class="reference"><a href="#cite_note-Spencer-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup></td> <td>The resultant interslice forces have constant slope throughout the sliding mass. The <a href="/wiki/Line_of_thrust" title="Line of thrust">line of thrust</a> is a degree of freedom. </td></tr> <tr> <td>Chugh<sup id="cite_ref-Chugh_23-0" class="reference"><a href="#cite_note-Chugh-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup></td> <td>Same as Spencer's method but with a constant acceleration force on each slice. </td></tr> <tr> <td>Morgenstern-Price<sup id="cite_ref-Morgenstern_24-0" class="reference"><a href="#cite_note-Morgenstern-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup></td> <td>The direction of the resultant interslice forces is defined using an arbitrary function. The fractions of the function value needed for force and moment balance is computed. </td></tr> <tr> <td>Fredlund-Krahn (GLE)<sup id="cite_ref-FredlundKrahn_17-1" class="reference"><a href="#cite_note-FredlundKrahn-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup></td> <td>Similar to Morgenstern-Price. </td></tr> <tr> <td>Corps of Engineers<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup></td> <td>The resultant interslice force is either parallel to the ground surface or equal to the average slope from the beginning to the end of the slip surface.. </td></tr> <tr> <td>Lowe and Karafiath<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup></td> <td>The direction of the resultant interslice force is equal to the average of the ground surface and the slope of the base of each slice. </td></tr> <tr> <td>Sarma<sup id="cite_ref-Sarma_20-1" class="reference"><a href="#cite_note-Sarma-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup></td> <td>The shear strength criterion is applied to the shears on the sides and bottom of each slice. The inclinations of the slice interfaces are varied until a critical criterion is met. </td></tr></tbody></table> <p>The table below shows the statical equilibrium conditions satisfied by some of the popular limit equilibrium methods.<sup id="cite_ref-FredLund_21-1" class="reference"><a href="#cite_note-FredLund-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p> <table class="wikitable sortable"> <tbody><tr> <th>Method</th> <th>Force balance (vertical)</th> <th>Force balance (horizontal)</th> <th>Moment balance </th></tr> <tr> <td>Ordinary MS</td> <td>Yes</td> <td>No</td> <td>Yes </td></tr> <tr> <td>Bishop's simplified</td> <td>Yes</td> <td>No</td> <td>Yes </td></tr> <tr> <td>Janbu's simplified</td> <td>Yes</td> <td>Yes</td> <td>No </td></tr> <tr> <td>Janbu's generalized</td> <td>Yes</td> <td>Yes</td> <td>Used to compute interslice shear forces </td></tr> <tr> <td>Spencer</td> <td>Yes</td> <td>Yes</td> <td>Yes </td></tr> <tr> <td>Chugh</td> <td>Yes</td> <td>Yes</td> <td>Yes </td></tr> <tr> <td>Morgenstern-Price</td> <td>Yes</td> <td>Yes</td> <td>Yes </td></tr> <tr> <td>Fredlund-Krahn</td> <td>Yes</td> <td>Yes</td> <td>Yes </td></tr> <tr> <td>Corps of Engineers</td> <td>Yes</td> <td>Yes</td> <td>No </td></tr> <tr> <td>Lowe and Karafiath</td> <td>Yes</td> <td>Yes</td> <td>No </td></tr> <tr> <td>Sarma</td> <td>Yes</td> <td>Yes</td> <td>Yes </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Rock_slope_stability_analysis">Rock slope stability analysis</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Slope_stability_analysis&action=edit&section=10" title="Edit section: Rock slope stability analysis"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Rock slope stability analysis based on limit equilibrium techniques may consider following modes of failures: </p> <ul><li><b>Planar failure</b> -> case of rock mass sliding on a single surface (special case of general <i>wedge</i> type of failure); two-dimensional analysis may be used according to the concept of a block resisting on an inclined plane at limit equilibrium<sup id="cite_ref-Kliche1999pp125-137_27-0" class="reference"><a href="#cite_note-Kliche1999pp125-137-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Kovari1978pp103-124_28-0" class="reference"><a href="#cite_note-Kovari1978pp103-124-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup></li> <li><b>Polygonal failure</b> -> sliding of a nature rock usually takes place on <i>polygonally-shaped</i> surfaces; calculation is based on a certain assumptions (e.g. sliding on a polygonal surface which is composed from <i>N</i> parts is kinematically possible only in case of development at least <i>(N - 1)</i> internal shear surfaces; rock mass is divided into blocks by internal shear surfaces; blocks are considered to be rigid; no tensile strength is permitted etc.)<sup id="cite_ref-Kovari1978pp103-124_28-1" class="reference"><a href="#cite_note-Kovari1978pp103-124-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup></li> <li><b>Wedge failure</b> -> <a href="/wiki/Three-dimensional_space" title="Three-dimensional space">three-dimensional</a> analysis enables modelling of the wedge sliding on two planes in a direction along the line of intersection<sup id="cite_ref-Kovari1978pp103-124_28-2" class="reference"><a href="#cite_note-Kovari1978pp103-124-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Kliche1999pp153-169_29-0" class="reference"><a href="#cite_note-Kliche1999pp153-169-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup></li> <li><b>Toppling failure</b> -> long thin rock columns formed by the steeply dipping discontinuities may rotate about a pivot point located at the lowest corner of the block; the sum of the moments causing toppling of a block (i.e. horizontal weight component of the block and the sum of the driving forces from adjacent blocks behind the block under consideration) is compared to the sum of the moments resisting toppling (i.e. vertical weight component of the block and the sum of the resisting forces from adjacent blocks in front of the block under consideration); toppling occur if driving moments exceed resisting moments<sup id="cite_ref-Kliche1999p15_30-0" class="reference"><a href="#cite_note-Kliche1999p15-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Kliche1999pp139-152_31-0" class="reference"><a href="#cite_note-Kliche1999pp139-152-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading2"><h2 id="Limit_analysis">Limit analysis</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Slope_stability_analysis&action=edit&section=11" title="Edit section: Limit analysis"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Slope_stability" title="Slope stability">Slope stability</a></div> <p>A more rigorous approach to slope stability analysis is <a href="/wiki/Limit_analysis" title="Limit analysis">limit analysis</a>. Unlike limit equilibrium analysis which makes ad hoc though often reasonable assumptions, limit analysis is based on rigorous plasticity theory. This enables, among other things, the computation of upper and lower bounds on the true factor of safety. </p><p>Programs based on limit analysis include: </p> <ul><li><a rel="nofollow" class="external text" href="https://www.optumce.com">OptumG2</a> (2014-) General purpose software for geotechnical applications (also includes elastoplasticity, seepage, consolidation, staged construction, tunneling, and other relevant geotechnical analysis types).</li> <li>LimitState:GEO (2008-) General purpose geotechnical software application based on <a href="/wiki/Discontinuity_layout_optimization" title="Discontinuity layout optimization">Discontinuity layout optimization</a> for plane strain problems including slope stability.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Stereographic_and_kinematic_analysis">Stereographic and kinematic analysis</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Slope_stability_analysis&action=edit&section=12" title="Edit section: Stereographic and kinematic analysis"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Stereonet#Geology" class="mw-redirect" title="Stereonet">Stereonet § Geology</a></div> <p>Kinematic analysis examines which modes of failure can possibly occur in the rock mass. Analysis requires the detailed evaluation of rock mass structure and the geometry of existing discontinuities contributing to block <a href="/wiki/Instability" title="Instability">instability</a>.<sup id="cite_ref-Eberhardt2003p7_32-0" class="reference"><a href="#cite_note-Eberhardt2003p7-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Kliche1999p111_33-0" class="reference"><a href="#cite_note-Kliche1999p111-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Stereographic_projection" title="Stereographic projection">Stereographic</a> representation (<a href="/wiki/Stereonet" class="mw-redirect" title="Stereonet">stereonets</a>) of the planes and lines is used.<sup id="cite_ref-Kliche1999pp111-123_34-0" class="reference"><a href="#cite_note-Kliche1999pp111-123-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> Stereonets are useful for analyzing discontinuous rock blocks.<sup id="cite_ref-Kliche1999pp43-65_35-0" class="reference"><a href="#cite_note-Kliche1999pp43-65-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> Program <b>DIPS</b> allows for visualization structural data using stereonets, determination of the kinematic feasibility of rock mass and statistical analysis of the discontinuity properties.<sup id="cite_ref-Eberhardt2003p7_32-1" class="reference"><a href="#cite_note-Eberhardt2003p7-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Rockfall_simulators">Rockfall simulators</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Slope_stability_analysis&action=edit&section=13" title="Edit section: Rockfall simulators"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Rock slope stability analysis may design protective measures near or around structures endangered by the falling blocks. <a href="/wiki/Rockfall" title="Rockfall">Rockfall</a> simulators determine travel paths and trajectories of unstable blocks separated from a rock slope face.<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Analytical_solution" class="mw-redirect" title="Analytical solution">Analytical solution</a> method described by Hungr & Evans<sup id="cite_ref-Hungr1988pp685-690_37-0" class="reference"><a href="#cite_note-Hungr1988pp685-690-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> assumes rock block as a point with mass and <a href="/wiki/Velocity" title="Velocity">velocity</a> moving on a ballistic trajectory with regard to potential contact with slope surface. Calculation requires two restitution coefficients that depend on fragment shape, slope surface roughness, momentum and deformational properties and on the chance of certain conditions in a given impact.<sup id="cite_ref-Eberhardt2003pp15-17_38-0" class="reference"><a href="#cite_note-Eberhardt2003pp15-17-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Numerical_methods_of_analysis">Numerical methods of analysis</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Slope_stability_analysis&action=edit&section=14" title="Edit section: Numerical methods of analysis"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Numerical modelling techniques provide an approximate solution to problems which otherwise cannot be solved by conventional methods, e.g. complex geometry, material <a href="/wiki/Anisotropy" title="Anisotropy">anisotropy</a>, non-linear behavior, in situ stresses. <a href="/wiki/Numerical_analysis" title="Numerical analysis">Numerical analysis</a> allows for material <a href="/wiki/Deformation_(mechanics)" class="mw-redirect" title="Deformation (mechanics)">deformation</a> and failure, modelling of <a href="/wiki/Pore_pressure" class="mw-redirect" title="Pore pressure">pore pressures</a>, <a href="/wiki/Creep_(deformation)" title="Creep (deformation)">creep deformation</a>, dynamic loading, assessing effects of parameter variations etc. However, numerical modelling is restricted by some limitations. For example, input parameters are not usually measured and availability of these data is generally poor. User also should be aware of boundary effects, meshing errors, hardware memory and time restrictions. <a href="/wiki/Numerical_method" title="Numerical method">Numerical methods</a> used for slope stability analysis can be divided into three main groups: <a href="/wiki/Continuum_mechanics" title="Continuum mechanics">continuum</a>, discontinuum and hybrid modelling.<sup id="cite_ref-Eberhardt2003pp17-38_39-0" class="reference"><a href="#cite_note-Eberhardt2003pp17-38-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Continuum_modelling">Continuum modelling</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Slope_stability_analysis&action=edit&section=15" title="Edit section: Continuum modelling"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Finite_element_method" title="Finite element method">Finite element method</a> and <a href="/wiki/Finite_difference_method" title="Finite difference method">Finite difference method</a></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Mesh_fem.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Mesh_fem.jpg/250px-Mesh_fem.jpg" decoding="async" width="250" height="134" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Mesh_fem.jpg/375px-Mesh_fem.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Mesh_fem.jpg/500px-Mesh_fem.jpg 2x" data-file-width="800" data-file-height="428" /></a><figcaption>Figure 3: Finite element mesh</figcaption></figure> <p>Modelling of the <a href="/wiki/Continuum_mechanics" title="Continuum mechanics">continuum</a> is suitable for the analysis of soil slopes, massive intact rock or heavily jointed rock masses. This approach includes the <i><a href="/wiki/Finite_difference_method" title="Finite difference method">finite-difference</a></i> and <i>finite element</i> methods that <a href="/wiki/Discretization" title="Discretization">discretize</a> the whole mass to finite number of elements with the help of generated mesh (Fig. 3). In <i><a href="/wiki/Finite_difference_method" title="Finite difference method">finite-difference</a></i> method (FDM) <a href="/wiki/Differential_equation" title="Differential equation">differential</a> equilibrium equations (i.e. strain-displacement and <a href="/wiki/Stress-strain_relations" class="mw-redirect" title="Stress-strain relations">stress-strain relations</a>) are solved. <i>finite element</i> method (FEM) uses the approximations to the connectivity of elements, continuity of <a href="/wiki/Displacement_field_(mechanics)" title="Displacement field (mechanics)">displacements</a> and stresses between elements.<sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> Most of numerical codes allows modelling of discrete <a href="/wiki/Fracture" title="Fracture">fractures</a>, e.g. <a href="/wiki/Bedding_plane" class="mw-redirect" title="Bedding plane">bedding planes</a>, <a href="/wiki/Fault_(geology)" title="Fault (geology)">faults</a>. Several constitutive models are usually available, e.g. <a href="/wiki/Elasticity_(physics)" title="Elasticity (physics)">elasticity</a>, elasto-plasticity, strain-softening, <a href="/wiki/Viscoplasticity#Elastic_perfectly_viscoplastic_solid" title="Viscoplasticity">elasto-viscoplasticity</a> etc.<sup id="cite_ref-Eberhardt2003pp17-38_39-1" class="reference"><a href="#cite_note-Eberhardt2003pp17-38-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Discontinuum_modelling">Discontinuum modelling</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Slope_stability_analysis&action=edit&section=16" title="Edit section: Discontinuum modelling"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Discrete_element_method" title="Discrete element method">Discrete element method</a> and <a href="/wiki/Discontinuous_Deformation_Analysis" class="mw-redirect" title="Discontinuous Deformation Analysis">Discontinuous Deformation Analysis</a></div> <p>Discontinuum approach is useful for rock slopes controlled by discontinuity behaviour. Rock mass is considered as an aggregation of distinct, interacting blocks subjected to external loads and assumed to undergo motion with time. This methodology is collectively called the <i><a href="/wiki/Discrete_element_method" title="Discrete element method">discrete-element</a></i> method (DEM). Discontinuum modelling allows for sliding between the blocks or particles. The DEM is based on solution of dynamic equation of equilibrium for each block repeatedly until the boundary conditions and laws of contact and <a href="/wiki/Newton%27s_laws_of_motion" title="Newton's laws of motion">motion</a> are satisfied. Discontinuum modelling belongs to the most commonly applied numerical approach to rock slope analysis and following variations of the DEM exist:<sup id="cite_ref-Eberhardt2003pp17-38_39-2" class="reference"><a href="#cite_note-Eberhardt2003pp17-38-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> </p> <ul><li>distinct-element method</li> <li><a href="/wiki/Discontinuous_Deformation_Analysis" class="mw-redirect" title="Discontinuous Deformation Analysis">Discontinuous Deformation Analysis</a> (DDA)</li> <li>particle flow codes</li></ul> <p>The <i><a href="/wiki/Discrete_element_method" title="Discrete element method">distinct-element</a></i> approach describes mechanical behaviour of both, the discontinuities and the solid material. This methodology is based on a force-displacement law (specifying the interaction between the deformable rock blocks) and a <a href="/wiki/Newton%27s_laws_of_motion" title="Newton's laws of motion">law of motion</a> (determining displacements caused in the blocks by out-of-balance forces). <a href="/wiki/Joint_(geology)" title="Joint (geology)">Joints</a> are treated as [boundary conditions. Deformable blocks are discretized into internal constant-strain elements.<sup id="cite_ref-Eberhardt2003pp17-38_39-3" class="reference"><a href="#cite_note-Eberhardt2003pp17-38-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> </p><p>Discontinuum program <b>UDEC</b><sup id="cite_ref-UDEC2009_41-0" class="reference"><a href="#cite_note-UDEC2009-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> (Universal distinct element code) is suitable for high jointed rock slopes subjected to static or dynamic loading. Two-dimensional analysis of translational failure mechanism allows for simulating large displacements, modelling deformation or material yielding.<sup id="cite_ref-UDEC2009_41-1" class="reference"><a href="#cite_note-UDEC2009-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> Three-dimensional discontinuum code <b>3DEC</b><sup id="cite_ref-3DEC2009_42-0" class="reference"><a href="#cite_note-3DEC2009-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> contains modelling of multiple intersecting discontinuities and therefore it is suitable for analysis of wedge instabilities or influence of rock support (e.g. rockbolts, cables).<sup id="cite_ref-Eberhardt2003pp17-38_39-4" class="reference"><a href="#cite_note-Eberhardt2003pp17-38-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> </p><p>In <i><a href="/wiki/Discontinuous_Deformation_Analysis" class="mw-redirect" title="Discontinuous Deformation Analysis">Discontinuous Deformation Analysis</a></i> (DDA) displacements are unknowns and equilibrium equations are then solved analogous to <i>finite element</i> method. Each unit of <i>finite element</i> type mesh represents an isolated block bounded by discontinuities. Advantage of this methodology is possibility to model large deformations, rigid body movements, coupling or failure states between rock blocks.<sup id="cite_ref-Eberhardt2003pp17-38_39-5" class="reference"><a href="#cite_note-Eberhardt2003pp17-38-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> </p><p>Discontinuous rock mass can be modelled with the help of <i><a href="/wiki/Discrete_element_method" title="Discrete element method">distinct-element</a></i> methodology in the form of <i>particle flow</i> code, e.g. program <b>PFC2D/3D</b>.<sup id="cite_ref-PFC2D2009_43-0" class="reference"><a href="#cite_note-PFC2D2009-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-PFC3D2009_44-0" class="reference"><a href="#cite_note-PFC3D2009-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> Spherical particles interact through frictional sliding contacts. Simulation of joint bounded blocks may be realized through specified bond strengths. Law of motion is repeatedly applied to each particle and force-displacement law to each contact. <i>Particle flow</i> methodology enables modelling of granular flow, fracture of intact rock, transitional block movements, dynamic response to blasting or seismicity, deformation between particles caused by shear or tensile forces. These codes also allow to model subsequent failure processes of rock slope, e.g. simulation of rock<sup id="cite_ref-Eberhardt2003pp17-38_39-6" class="reference"><a href="#cite_note-Eberhardt2003pp17-38-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Hybrid/coupled_modelling"><span id="Hybrid.2Fcoupled_modelling"></span>Hybrid/coupled modelling</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Slope_stability_analysis&action=edit&section=17" title="Edit section: Hybrid/coupled modelling"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Hybrid codes involve the coupling of various methodologies to maximize their key advantages, e.g. <i>limit equilibrium</i> analysis combined with <i>finite element</i> groundwater flow and stress analysis; coupled <i>particle flow</i> and <i><a href="/wiki/Finite_difference_method" title="Finite difference method">finite-difference</a></i> analyses; hydro-mechanically coupled finite element and material point methods for simulating the entire process of rainfall-induced landslides.<sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> Hybrid techniques allows investigation of piping slope failures and the influence of high groundwater pressures on the failure of weak rock slope. Coupled <i>finite-distinct-element</i> codes provide for the modelling of both intact rock behavior and the development and behavior of fractures. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Slope_stability_analysis&action=edit&section=18" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 30em;"> <ul><li><a href="/wiki/Discontinuous_Deformation_Analysis" class="mw-redirect" title="Discontinuous Deformation Analysis">Discontinuous Deformation Analysis</a></li> <li><a href="/wiki/Discontinuity_layout_optimization" title="Discontinuity layout optimization">Discontinuity layout optimization</a></li> <li><a href="/wiki/Discrete_element_method" title="Discrete element method">Discrete element method</a></li> <li><a href="/wiki/Finite_difference_method" title="Finite difference method">Finite difference method</a></li> <li><a href="/wiki/Finite_element_limit_analysis" title="Finite element limit analysis">Finite element limit analysis</a></li> <li><a href="/wiki/Finite_element_method" title="Finite element method">Finite element method</a></li> <li><a href="/wiki/Mohr-Coulomb_theory" class="mw-redirect" title="Mohr-Coulomb theory">Mohr-Coulomb theory</a></li> <li><a href="/wiki/PLAXIS" class="mw-redirect" title="PLAXIS">PLAXIS</a></li> <li><a href="/wiki/SMR_classification" class="mw-redirect" title="SMR classification">SMR classification</a></li> <li><a href="/wiki/Stereonet#Geology" class="mw-redirect" title="Stereonet">Stereonet</a></li></ul></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Slope_stability_analysis&action=edit&section=19" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-Eberhardt2003p4-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-Eberhardt2003p4_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Eberhardt2003p4_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Eberhardt2003p4_1-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFEberhardt2003">Eberhardt 2003</a>, p. 4</span> </li> <li id="cite_note-Abramson2002p2-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-Abramson2002p2_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Abramson2002p2_2-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFAbramson2002">Abramson 2002</a>, p. 2</span> </li> <li id="cite_note-Kliche1999p2-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-Kliche1999p2_3-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFKliche1999">Kliche 1999</a>, p. 2</span> </li> <li id="cite_note-USArmyCorps2003pp1-2-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-USArmyCorps2003pp1-2_4-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFUSArmyCorps2003">USArmyCorps 2003</a>, pp. 1–2</span> </li> <li id="cite_note-Abramson2002p1-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-Abramson2002p1_5-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFAbramson2002">Abramson 2002</a>, p. 1</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFBeale,_GeoffRead,_John2014" class="citation book cs1">Beale, Geoff; Read, John, eds. (2014). <i>Guidelines for Evaluating Water in Pit Slope Stability</i>. CSIRO Publishing. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780643108356" title="Special:BookSources/9780643108356"><bdi>9780643108356</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Guidelines+for+Evaluating+Water+in+Pit+Slope+Stability&rft.pub=CSIRO+Publishing&rft.date=2014&rft.isbn=9780643108356&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></span> </li> <li id="cite_note-Stead2001p615-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-Stead2001p615_7-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFStead2001">Stead 2001</a>, p. 615</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCardenas2019" class="citation journal cs1">Cardenas, IC (2019). "On the use of Bayesian networks as a meta-modelling approach to analyse uncertainties in slope stability analysis". <i>Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards</i>. <b>13</b> (1): 53–65. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2019GAMRE..13...53C">2019GAMRE..13...53C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F17499518.2018.1498524">10.1080/17499518.2018.1498524</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:216590427">216590427</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Georisk%3A+Assessment+and+Management+of+Risk+for+Engineered+Systems+and+Geohazards&rft.atitle=On+the+use+of+Bayesian+networks+as+a+meta-modelling+approach+to+analyse+uncertainties+in+slope+stability+analysis&rft.volume=13&rft.issue=1&rft.pages=53-65&rft.date=2019&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A216590427%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1080%2F17499518.2018.1498524&rft_id=info%3Abibcode%2F2019GAMRE..13...53C&rft.aulast=Cardenas&rft.aufirst=IC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLiuWang2023" class="citation journal cs1">Liu, Xin; Wang, Yu (2023). <a rel="nofollow" class="external text" href="https://linkinghub.elsevier.com/retrieve/pii/S0013795222004549">"Analytical solutions for annual probability of slope failure induced by rainfall at a specific slope using bivariate distribution of rainfall intensity and duration"</a>. <i>Engineering Geology</i>. <b>313</b>: 106969. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2023EngGe.31306969L">2023EngGe.31306969L</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.enggeo.2022.106969">10.1016/j.enggeo.2022.106969</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:254807263">254807263</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Engineering+Geology&rft.atitle=Analytical+solutions+for+annual+probability+of+slope+failure+induced+by+rainfall+at+a+specific+slope+using+bivariate+distribution+of+rainfall+intensity+and+duration&rft.volume=313&rft.pages=106969&rft.date=2023&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A254807263%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1016%2Fj.enggeo.2022.106969&rft_id=info%3Abibcode%2F2023EngGe.31306969L&rft.aulast=Liu&rft.aufirst=Xin&rft.au=Wang%2C+Yu&rft_id=https%3A%2F%2Flinkinghub.elsevier.com%2Fretrieve%2Fpii%2FS0013795222004549&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></span> </li> <li id="cite_note-Eberhardt2003p6-10"><span class="mw-cite-backlink">^ <a href="#cite_ref-Eberhardt2003p6_10-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Eberhardt2003p6_10-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFEberhardt2003">Eberhardt 2003</a>, p. 6</span> </li> <li id="cite_note-Abramson2002p329-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-Abramson2002p329_11-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFAbramson2002">Abramson 2002</a>, p. 329</span> </li> <li id="cite_note-Abramson2002p363-12"><span class="mw-cite-backlink">^ <a href="#cite_ref-Abramson2002p363_12-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Abramson2002p363_12-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFAbramson2002">Abramson 2002</a>, p. 363</span> </li> <li id="cite_note-USArmyCorps2003p2-13"><span class="mw-cite-backlink">^ <a href="#cite_ref-USArmyCorps2003p2_13-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-USArmyCorps2003p2_13-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-USArmyCorps2003p2_13-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFUSArmyCorps2003">USArmyCorps 2003</a>, p. 2</span> </li> <li id="cite_note-Zhu2003pp377-395-14"><span class="mw-cite-backlink">^ <a href="#cite_ref-Zhu2003pp377-395_14-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Zhu2003pp377-395_14-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFZhu2003">Zhu 2003</a>, pp. 377–395</span> </li> <li id="cite_note-Abramson2002pp363-367-15"><span class="mw-cite-backlink">^ <a href="#cite_ref-Abramson2002pp363-367_15-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Abramson2002pp363-367_15-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFAbramson2002">Abramson 2002</a>, pp. 363–367</span> </li> <li id="cite_note-USArmyCorps2003p5-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-USArmyCorps2003p5_16-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFUSArmyCorps2003">USArmyCorps 2003</a>, p. 5</span> </li> <li id="cite_note-FredlundKrahn-17"><span class="mw-cite-backlink">^ <a href="#cite_ref-FredlundKrahn_17-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FredlundKrahn_17-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFredlundKrahn1977" class="citation cs2">Fredlund, DG; Krahn, J (1977), "Comparison of slope stability methods of analysis", <i>Canadian Geotechnical Journal</i>, <b>14</b> (3): 429–439, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1139%2Ft77-045">10.1139/t77-045</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Canadian+Geotechnical+Journal&rft.atitle=Comparison+of+slope+stability+methods+of+analysis&rft.volume=14&rft.issue=3&rft.pages=429-439&rft.date=1977&rft_id=info%3Adoi%2F10.1139%2Ft77-045&rft.aulast=Fredlund&rft.aufirst=DG&rft.au=Krahn%2C+J&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></span> </li> <li id="cite_note-Bishop-18"><span class="mw-cite-backlink">^ <a href="#cite_ref-Bishop_18-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Bishop_18-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBishop1955" class="citation journal cs1">Bishop, A. W. (1955). "The use of the Slip Circle in the Stability Analysis of Slopes". <i>Géotechnique</i>. <b>5</b> (1): 7–17. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1955Getq....5....7B">1955Getq....5....7B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1680%2Fgeot.1955.5.1.7">10.1680/geot.1955.5.1.7</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=G%C3%A9otechnique&rft.atitle=The+use+of+the+Slip+Circle+in+the+Stability+Analysis+of+Slopes&rft.volume=5&rft.issue=1&rft.pages=7-17&rft.date=1955&rft_id=info%3Adoi%2F10.1680%2Fgeot.1955.5.1.7&rft_id=info%3Abibcode%2F1955Getq....5....7B&rft.aulast=Bishop&rft.aufirst=A.+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></span> </li> <li id="cite_note-Spencer-19"><span class="mw-cite-backlink">^ <a href="#cite_ref-Spencer_19-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Spencer_19-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Spencer_19-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSpencer1967" class="citation journal cs1">Spencer, E. (1967). "A Method of analysis of the Stability of Embankments Assuming Parallel Inter-Slice Forces". <i>Géotechnique</i>. <b>17</b> (1): 11–26. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1967Getq...17...11S">1967Getq...17...11S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1680%2Fgeot.1967.17.1.11">10.1680/geot.1967.17.1.11</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=G%C3%A9otechnique&rft.atitle=A+Method+of+analysis+of+the+Stability+of+Embankments+Assuming+Parallel+Inter-Slice+Forces&rft.volume=17&rft.issue=1&rft.pages=11-26&rft.date=1967&rft_id=info%3Adoi%2F10.1680%2Fgeot.1967.17.1.11&rft_id=info%3Abibcode%2F1967Getq...17...11S&rft.aulast=Spencer&rft.aufirst=E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></span> </li> <li id="cite_note-Sarma-20"><span class="mw-cite-backlink">^ <a href="#cite_ref-Sarma_20-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Sarma_20-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSarma1975" class="citation journal cs1">Sarma, S. K. (1975). "Seismic stability of earth dams and embankments". <i>Géotechnique</i>. <b>25</b> (4): 743–761. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1975Getq...25..743S">1975Getq...25..743S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1680%2Fgeot.1975.25.4.743">10.1680/geot.1975.25.4.743</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=G%C3%A9otechnique&rft.atitle=Seismic+stability+of+earth+dams+and+embankments&rft.volume=25&rft.issue=4&rft.pages=743-761&rft.date=1975&rft_id=info%3Adoi%2F10.1680%2Fgeot.1975.25.4.743&rft_id=info%3Abibcode%2F1975Getq...25..743S&rft.aulast=Sarma&rft.aufirst=S.+K.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></span> </li> <li id="cite_note-FredLund-21"><span class="mw-cite-backlink">^ <a href="#cite_ref-FredLund_21-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FredLund_21-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFredlund1984" class="citation cs2">Fredlund, D.G. (1984), <a rel="nofollow" class="external text" href="http://www.academia.edu/download/34280588/Analytical_methods_for_slope_stability_analysis.pdf">"Analytical methods for slope stability analysis"</a> <span class="cs1-format">(PDF)</span>, <i>Proceedings of the Fourth International Symposium on Landslides, State-of-the-Art</i>: 229–250</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+Fourth+International+Symposium+on+Landslides%2C+State-of-the-Art&rft.atitle=Analytical+methods+for+slope+stability+analysis&rft.pages=229-250&rft.date=1984&rft.aulast=Fredlund&rft.aufirst=D.G.&rft_id=http%3A%2F%2Fwww.academia.edu%2Fdownload%2F34280588%2FAnalytical_methods_for_slope_stability_analysis.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span><sup class="noprint Inline-Template"><span style="white-space: nowrap;">[<i><a href="/wiki/Wikipedia:Link_rot" title="Wikipedia:Link rot"><span title=" Dead link tagged July 2022">dead link</span></a></i><span style="visibility:hidden; color:transparent; padding-left:2px">‍</span>]</span></sup></span> </li> <li id="cite_note-Janbu-22"><span class="mw-cite-backlink">^ <a href="#cite_ref-Janbu_22-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Janbu_22-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJanbu1973" class="citation cs2"><a href="/wiki/Nilmar_Janbu" title="Nilmar Janbu">Janbu, Nilmar</a> (1973), RC Hirschfeld; SJ Poulos (eds.), "Slope stability computations", <i>In Embankment-dam Engineering</i>, Jon Wiley and Sons Inc., NY: 40P</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=In+Embankment-dam+Engineering&rft.atitle=Slope+stability+computations&rft.pages=40P&rft.date=1973&rft.aulast=Janbu&rft.aufirst=Nilmar&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></span> </li> <li id="cite_note-Chugh-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-Chugh_23-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChugh1982" class="citation cs2">Chugh, Ashok K (1982), "Slope stability analysis for earthquakes", <i>International Journal for Numerical and Analytical Methods in Geomechanics</i>, <b>6</b> (3): 307–322, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1982IJNAM...6..307C">1982IJNAM...6..307C</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fnag.1610060304">10.1002/nag.1610060304</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=International+Journal+for+Numerical+and+Analytical+Methods+in+Geomechanics&rft.atitle=Slope+stability+analysis+for+earthquakes&rft.volume=6&rft.issue=3&rft.pages=307-322&rft.date=1982&rft_id=info%3Adoi%2F10.1002%2Fnag.1610060304&rft_id=info%3Abibcode%2F1982IJNAM...6..307C&rft.aulast=Chugh&rft.aufirst=Ashok+K&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></span> </li> <li id="cite_note-Morgenstern-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-Morgenstern_24-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMorgensternPrice1965" class="citation cs2">Morgenstern, N. R.; Price, V. Eo (1965), "The analysis of the stability of general slip surfaces", <i>Geotechnique</i>, <b>15</b> (1): 79–93, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1965Getq...15...79M">1965Getq...15...79M</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1680%2Fgeot.1965.15.1.79">10.1680/geot.1965.15.1.79</a>, <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:122270517">122270517</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Geotechnique&rft.atitle=The+analysis+of+the+stability+of+general+slip+surfaces&rft.volume=15&rft.issue=1&rft.pages=79-93&rft.date=1965&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A122270517%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1680%2Fgeot.1965.15.1.79&rft_id=info%3Abibcode%2F1965Getq...15...79M&rft.aulast=Morgenstern&rft.aufirst=N.+R.&rft.au=Price%2C+V.+Eo&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="COE" class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.publications.usace.army.mil/Portals/76/Publications/EngineerManuals/EM_1110-2-1902.pdf">"Slope Stability"</a> <span class="cs1-format">(PDF)</span>. US Army Corps of Engineers<span class="reference-accessdate">. Retrieved <span class="nowrap">15 April</span> 2015</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Slope+Stability&rft.pub=US+Army+Corps+of+Engineers&rft_id=http%3A%2F%2Fwww.publications.usace.army.mil%2FPortals%2F76%2FPublications%2FEngineerManuals%2FEM_1110-2-1902.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLoweKarafiath1960" class="citation cs2">Lowe, John; Karafiath, Leslie (1960), "Stability of earth dams upon drawdown", <i>In Proc. 1st. Pan American Conference on Soil Mechanics and Foundation Engineering, México</i>, <b>2</b>: 537–552</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=In+Proc.+1st.+Pan+American+Conference+on+Soil+Mechanics+and+Foundation+Engineering%2C+M%C3%A9xico&rft.atitle=Stability+of+earth+dams+upon+drawdown&rft.volume=2&rft.pages=537-552&rft.date=1960&rft.aulast=Lowe&rft.aufirst=John&rft.au=Karafiath%2C+Leslie&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></span> </li> <li id="cite_note-Kliche1999pp125-137-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-Kliche1999pp125-137_27-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFKliche1999">Kliche 1999</a>, pp. 125–137</span> </li> <li id="cite_note-Kovari1978pp103-124-28"><span class="mw-cite-backlink">^ <a href="#cite_ref-Kovari1978pp103-124_28-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Kovari1978pp103-124_28-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Kovari1978pp103-124_28-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFKovari1978">Kovari 1978</a>, pp. 103–124</span> </li> <li id="cite_note-Kliche1999pp153-169-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-Kliche1999pp153-169_29-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFKliche1999">Kliche 1999</a>, pp. 153–169</span> </li> <li id="cite_note-Kliche1999p15-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-Kliche1999p15_30-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFKliche1999">Kliche 1999</a>, p. 15</span> </li> <li id="cite_note-Kliche1999pp139-152-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-Kliche1999pp139-152_31-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFKliche1999">Kliche 1999</a>, pp. 139–152</span> </li> <li id="cite_note-Eberhardt2003p7-32"><span class="mw-cite-backlink">^ <a href="#cite_ref-Eberhardt2003p7_32-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Eberhardt2003p7_32-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFEberhardt2003">Eberhardt 2003</a>, p. 7</span> </li> <li id="cite_note-Kliche1999p111-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-Kliche1999p111_33-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFKliche1999">Kliche 1999</a>, p. 111</span> </li> <li id="cite_note-Kliche1999pp111-123-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-Kliche1999pp111-123_34-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFKliche1999">Kliche 1999</a>, pp. 111–123</span> </li> <li id="cite_note-Kliche1999pp43-65-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-Kliche1999pp43-65_35-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFKliche1999">Kliche 1999</a>, pp. 43–65</span> </li> <li id="cite_note-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-36">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBourrierHungr2013" class="citation cs2">Bourrier, Franck; Hungr, Oldrich (2013-03-06), Lambert, Stéphane; Nicot, François (eds.), <a rel="nofollow" class="external text" href="http://doi.wiley.com/10.1002/9781118601532.ch6">"Rockfall Dynamics: A Critical Review of Collision and Rebound Models"</a>, <i>Rockfall Engineering</i>, Hoboken, NJ, USA: John Wiley & Sons, Inc., pp. 175–209, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2F9781118601532.ch6">10.1002/9781118601532.ch6</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-118-60153-2" title="Special:BookSources/978-1-118-60153-2"><bdi>978-1-118-60153-2</bdi></a><span class="reference-accessdate">, retrieved <span class="nowrap">2021-01-18</span></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Rockfall+Engineering&rft.atitle=Rockfall+Dynamics%3A+A+Critical+Review+of+Collision+and+Rebound+Models&rft.pages=175-209&rft.date=2013-03-06&rft_id=info%3Adoi%2F10.1002%2F9781118601532.ch6&rft.isbn=978-1-118-60153-2&rft.aulast=Bourrier&rft.aufirst=Franck&rft.au=Hungr%2C+Oldrich&rft_id=http%3A%2F%2Fdoi.wiley.com%2F10.1002%2F9781118601532.ch6&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></span> </li> <li id="cite_note-Hungr1988pp685-690-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-Hungr1988pp685-690_37-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFHungr1988">Hungr 1988</a>, pp. 685–690</span> </li> <li id="cite_note-Eberhardt2003pp15-17-38"><span class="mw-cite-backlink"><b><a href="#cite_ref-Eberhardt2003pp15-17_38-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFEberhardt2003">Eberhardt 2003</a>, pp. 15–17</span> </li> <li id="cite_note-Eberhardt2003pp17-38-39"><span class="mw-cite-backlink">^ <a href="#cite_ref-Eberhardt2003pp17-38_39-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Eberhardt2003pp17-38_39-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Eberhardt2003pp17-38_39-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Eberhardt2003pp17-38_39-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-Eberhardt2003pp17-38_39-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-Eberhardt2003pp17-38_39-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-Eberhardt2003pp17-38_39-6"><sup><i><b>g</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFEberhardt2003">Eberhardt 2003</a>, pp. 17–38</span> </li> <li id="cite_note-40"><span class="mw-cite-backlink"><b><a href="#cite_ref-40">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaczmarekPopielski2019" class="citation journal cs1">Kaczmarek, Łukasz D.; Popielski, Paweł (1 January 2019). <a rel="nofollow" class="external text" href="https://doi.org/10.1515%2Fgeo-2019-0017">"Selected components of geological structures and numerical modelling of slope stability"</a>. <i>Open Geosciences</i>. <b>11</b> (1): 208–218. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2019OGeo...11...17K">2019OGeo...11...17K</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1515%2Fgeo-2019-0017">10.1515/geo-2019-0017</a></span>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:195789446">195789446</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Open+Geosciences&rft.atitle=Selected+components+of+geological+structures+and+numerical+modelling+of+slope+stability&rft.volume=11&rft.issue=1&rft.pages=208-218&rft.date=2019-01-01&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A195789446%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1515%2Fgeo-2019-0017&rft_id=info%3Abibcode%2F2019OGeo...11...17K&rft.aulast=Kaczmarek&rft.aufirst=%C5%81ukasz+D.&rft.au=Popielski%2C+Pawe%C5%82&rft_id=https%3A%2F%2Fdoi.org%2F10.1515%252Fgeo-2019-0017&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></span> </li> <li id="cite_note-UDEC2009-41"><span class="mw-cite-backlink">^ <a href="#cite_ref-UDEC2009_41-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-UDEC2009_41-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFUDEC2009" class="citation cs2"><a rel="nofollow" class="external text" href="http://www.itascacg.com/udec/index.php">"UDEC - Universal Distinct Element Code"</a>, <i>Itascacg.com</i>, Minneapolis, USA: Itasca<span class="reference-accessdate">, retrieved <span class="nowrap">27 July</span> 2009</span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Itascacg.com&rft.atitle=UDEC+-+Universal+Distinct+Element+Code&rft_id=http%3A%2F%2Fwww.itascacg.com%2Fudec%2Findex.php&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></span> </li> <li id="cite_note-3DEC2009-42"><span class="mw-cite-backlink"><b><a href="#cite_ref-3DEC2009_42-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREF3DEC2009" class="citation cs2"><a rel="nofollow" class="external text" href="http://www.itascacg.com/3dec/index.php">"3DEC - Three Dimensional Distinct Element Code"</a>, <i>Itascacg.com</i>, Minneapolis, USA: Itasca<span class="reference-accessdate">, retrieved <span class="nowrap">27 July</span> 2009</span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Itascacg.com&rft.atitle=3DEC+-+Three+Dimensional+Distinct+Element+Code&rft_id=http%3A%2F%2Fwww.itascacg.com%2F3dec%2Findex.php&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></span> </li> <li id="cite_note-PFC2D2009-43"><span class="mw-cite-backlink"><b><a href="#cite_ref-PFC2D2009_43-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPFC2D2009" class="citation cs2"><a rel="nofollow" class="external text" href="http://www.itascacg.com/pfc2d/">"PFC2D - Particle Flow Code in Two Dimensions"</a>, <i>Itascacg.com</i>, Minneapolis, USA: Itasca<span class="reference-accessdate">, retrieved <span class="nowrap">27 July</span> 2009</span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Itascacg.com&rft.atitle=PFC2D+-+Particle+Flow+Code+in+Two+Dimensions&rft_id=http%3A%2F%2Fwww.itascacg.com%2Fpfc2d%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></span> </li> <li id="cite_note-PFC3D2009-44"><span class="mw-cite-backlink"><b><a href="#cite_ref-PFC3D2009_44-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPFC3D2009" class="citation cs2"><a rel="nofollow" class="external text" href="http://www.itascacg.com/pfc3d/">"PFC3D - Particle Flow Code in Three Dimensions"</a>, <i>Itascacg.com</i>, Minneapolis, USA: Itasca<span class="reference-accessdate">, retrieved <span class="nowrap">27 July</span> 2009</span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Itascacg.com&rft.atitle=PFC3D+-+Particle+Flow+Code+in+Three+Dimensions&rft_id=http%3A%2F%2Fwww.itascacg.com%2Fpfc3d%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></span> </li> <li id="cite_note-45"><span class="mw-cite-backlink"><b><a href="#cite_ref-45">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLiuWang2021" class="citation journal cs1">Liu, Xin; Wang, Yu (2021). <a rel="nofollow" class="external text" href="https://linkinghub.elsevier.com/retrieve/pii/S0266352X20305528">"Probabilistic simulation of entire process of rainfall-induced landslides using random finite element and material point methods with hydro-mechanical coupling"</a>. <i>Computers and Geotechnics</i>. <b>132</b>: 103989. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2021CGeot.13203989L">2021CGeot.13203989L</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.compgeo.2020.103989">10.1016/j.compgeo.2020.103989</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:233528112">233528112</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Computers+and+Geotechnics&rft.atitle=Probabilistic+simulation+of+entire+process+of+rainfall-induced+landslides+using+random+finite+element+and+material+point+methods+with+hydro-mechanical+coupling&rft.volume=132&rft.pages=103989&rft.date=2021&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A233528112%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1016%2Fj.compgeo.2020.103989&rft_id=info%3Abibcode%2F2021CGeot.13203989L&rft.aulast=Liu&rft.aufirst=Xin&rft.au=Wang%2C+Yu&rft_id=https%3A%2F%2Flinkinghub.elsevier.com%2Fretrieve%2Fpii%2FS0266352X20305528&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Slope_stability_analysis&action=edit&section=20" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Further_reading_cleanup plainlinks metadata ambox ambox-style" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/40px-Edit-clear.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/60px-Edit-clear.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/80px-Edit-clear.svg.png 2x" data-file-width="48" data-file-height="48" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">This "<a href="/wiki/Wikipedia:Manual_of_Style/Layout#Further_reading" title="Wikipedia:Manual of Style/Layout">Further reading</a>" section <b>may need cleanup</b>.<span class="hide-when-compact"> Please read the <a href="/wiki/Wikipedia:Further_reading" title="Wikipedia:Further reading">editing guide</a> and help improve the section.</span> <span class="date-container"><i>(<span class="date">March 2023</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWietek2021" class="citation book cs1">Wietek, B. (2021). <i>Slopes and Excavations - Design and Calculation</i>. <a href="/wiki/Springer_Vieweg" class="mw-redirect" title="Springer Vieweg">Springer Vieweg</a>. p. 381. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-658-35852-5" title="Special:BookSources/978-3-658-35852-5"><bdi>978-3-658-35852-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Slopes+and+Excavations+-+Design+and+Calculation&rft.pages=381&rft.pub=Springer+Vieweg&rft.date=2021&rft.isbn=978-3-658-35852-5&rft.aulast=Wietek&rft.aufirst=B.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDevotoCastelli2007" class="citation conference cs1">Devoto, S.; Castelli, E. (September 2007). <i>Slope stability in an old limestone quarry interested by a tourist project</i>. 15th Meeting of the Association of European Geological Societies: Georesources Policy, Management, Environment. Tallinn.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=conference&rft.btitle=Slope+stability+in+an+old+limestone+quarry+interested+by+a+tourist+project&rft.place=Tallinn&rft.date=2007-09&rft.aulast=Devoto&rft.aufirst=S.&rft.au=Castelli%2C+E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDouw2009" class="citation book cs1">Douw, W. (2009). <i>Entwicklung einer Anordnung zur Nutzung von Massenschwerebewegungen beim Quarzitabbau im Rheinischen Schiefergebirge</i>. Hackenheim, Germany: ConchBooks. p. 358. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-939767-10-7" title="Special:BookSources/978-3-939767-10-7"><bdi>978-3-939767-10-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Entwicklung+einer+Anordnung+zur+Nutzung+von+Massenschwerebewegungen+beim+Quarzitabbau+im+Rheinischen+Schiefergebirge&rft.place=Hackenheim%2C+Germany&rft.pages=358&rft.pub=ConchBooks&rft.date=2009&rft.isbn=978-3-939767-10-7&rft.aulast=Douw&rft.aufirst=W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHack2002" class="citation conference cs1">Hack, H.R.G.K. (25–28 November 2002). "An evaluation of slope stability classification. Keynote Lecture.". In Dinis da Gama, C.; Ribeira e Sousa, L. (eds.). <i>Proc. <a href="/wiki/ISRM" class="mw-redirect" title="ISRM">ISRM</a> EUROCK’2002</i>. Funchal, Madeira, Portugal: Sociedade Portuguesa de Geotecnia, Lisboa, Portugal. pp. 3–32. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/972-98781-2-9" title="Special:BookSources/972-98781-2-9"><bdi>972-98781-2-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=conference&rft.atitle=An+evaluation+of+slope+stability+classification.+Keynote+Lecture.&rft.btitle=Proc.+ISRM+EUROCK%E2%80%992002&rft.place=Funchal%2C+Madeira%2C+Portugal&rft.pages=3-32&rft.pub=Sociedade+Portuguesa+de+Geotecnia%2C+Lisboa%2C+Portugal&rft.date=2002-11-25%2F2002-11-28&rft.isbn=972-98781-2-9&rft.aulast=Hack&rft.aufirst=H.R.G.K.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLiuChen2005" class="citation journal cs1">Liu, Y.-C.; Chen, C.-S. (2005). "A new approach for application of rock mass classification on rock slope stability assessment". <i>Engineering Geology</i>. <b>89</b> (1–2): 129–143. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.enggeo.2006.09.017">10.1016/j.enggeo.2006.09.017</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Engineering+Geology&rft.atitle=A+new+approach+for+application+of+rock+mass+classification+on+rock+slope+stability+assessment&rft.volume=89&rft.issue=1%E2%80%932&rft.pages=129-143&rft.date=2005&rft_id=info%3Adoi%2F10.1016%2Fj.enggeo.2006.09.017&rft.aulast=Liu&rft.aufirst=Y.-C.&rft.au=Chen%2C+C.-S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPantelidis2009" class="citation journal cs1">Pantelidis, L. (2009). "Rock slope stability assessment through rock mass classification systems". <i>International Journal of Rock Mechanics and Mining Sciences</i>. <b>46</b> (2, number 2): 315–325. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2009IJRMM..46..315P">2009IJRMM..46..315P</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.ijrmms.2008.06.003">10.1016/j.ijrmms.2008.06.003</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=International+Journal+of+Rock+Mechanics+and+Mining+Sciences&rft.atitle=Rock+slope+stability+assessment+through+rock+mass+classification+systems&rft.volume=46&rft.issue=2%2C+number+2&rft.pages=315-325&rft.date=2009&rft_id=info%3Adoi%2F10.1016%2Fj.ijrmms.2008.06.003&rft_id=info%3Abibcode%2F2009IJRMM..46..315P&rft.aulast=Pantelidis&rft.aufirst=L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRupkeHuismanKruse2007" class="citation journal cs1">Rupke, J.; Huisman, M.; Kruse, H.M.G. (2007). "Stability of man-made slopes". <i>Engineering Geology</i>. <b>91</b> (1): 16–24. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2007EngGe..91...16R">2007EngGe..91...16R</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.enggeo.2006.12.009">10.1016/j.enggeo.2006.12.009</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Engineering+Geology&rft.atitle=Stability+of+man-made+slopes&rft.volume=91&rft.issue=1&rft.pages=16-24&rft.date=2007&rft_id=info%3Adoi%2F10.1016%2Fj.enggeo.2006.12.009&rft_id=info%3Abibcode%2F2007EngGe..91...16R&rft.aulast=Rupke&rft.aufirst=J.&rft.au=Huisman%2C+M.&rft.au=Kruse%2C+H.M.G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSinghGoel2002" class="citation book cs1">Singh, B.; Goel, R.K. (2002). <i>Software for engineering control of landslide and tunnelling hazards</i>. Vol. 1. <a href="/wiki/Taylor_%26_Francis" title="Taylor & Francis">Taylor & Francis</a>. p. 358. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-90-5809-360-8" title="Special:BookSources/978-90-5809-360-8"><bdi>978-90-5809-360-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Software+for+engineering+control+of+landslide+and+tunnelling+hazards&rft.pages=358&rft.pub=Taylor+%26+Francis&rft.date=2002&rft.isbn=978-90-5809-360-8&rft.aulast=Singh&rft.aufirst=B.&rft.au=Goel%2C+R.K.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></li></ul> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin" style=""> <ul><li>Coduto, Donald P. (1998). <i>Geotechnical Engineering: Principles and Practices.</i> Prentice-Hall. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-13-576380-0" title="Special:BookSources/0-13-576380-0">0-13-576380-0</a></li> <li>Fredlund, D. G., H. Rahardjo, M. D. Fredlund (2014). <i>Unsaturated Soil Mechanics in Engineering Practice.</i> Wiley-Interscience. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1118133590" title="Special:BookSources/978-1118133590">978-1118133590</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKliche1999" class="citation cs2">Kliche, Charles A. (1999), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=34AIOUkjGukC"><i>Rock Slope Stability</i></a>, Colorado, USA: Society for Mining, Metallurgy, and Exploration, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-87335-171-1" title="Special:BookSources/0-87335-171-1"><bdi>0-87335-171-1</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Rock+Slope+Stability&rft.place=Colorado%2C+USA&rft.pub=Society+for+Mining%2C+Metallurgy%2C+and+Exploration&rft.date=1999&rft.isbn=0-87335-171-1&rft.aulast=Kliche&rft.aufirst=Charles+A.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D34AIOUkjGukC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEberhardt2003" class="citation cs2">Eberhardt, Erik (2003), <a rel="nofollow" class="external text" href="http://www.eos.ubc.ca/personal/erik/e-papers/EE-SlopeStabilityAnalysis.pdf"><i>Rock Slope Stability Analysis - Utilization of Advanced Numerical Techniques</i></a> <span class="cs1-format">(PDF)</span>, Vancouver, Canada: Earth and Ocean Sciences, University of British Columbia</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Rock+Slope+Stability+Analysis+-+Utilization+of+Advanced+Numerical+Techniques&rft.place=Vancouver%2C+Canada&rft.pub=Earth+and+Ocean+Sciences%2C+University+of+British+Columbia&rft.date=2003&rft.aulast=Eberhardt&rft.aufirst=Erik&rft_id=http%3A%2F%2Fwww.eos.ubc.ca%2Fpersonal%2Ferik%2Fe-papers%2FEE-SlopeStabilityAnalysis.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFUSArmyCorps2003" class="citation cs2">US Army Corps of Engineers (2003), <a rel="nofollow" class="external text" href="http://140.194.76.129/publications/eng-manuals/em1110-2-1902/entire.pdf"><i>Engineering and Design - Slope Stability</i></a> <span class="cs1-format">(PDF)</span>, Washington DC, USA: US Army Corps of Engineers</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Engineering+and+Design+-+Slope+Stability&rft.place=Washington+DC%2C+USA&rft.pub=US+Army+Corps+of+Engineers&rft.date=2003&rft.au=US+Army+Corps+of+Engineers&rft_id=http%3A%2F%2F140.194.76.129%2Fpublications%2Feng-manuals%2Fem1110-2-1902%2Fentire.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStead2001" class="citation conference cs1">Stead, Doug; Eberhardt, E.; Coggan, J.; Benko, B. (2001). M. Kühne; H.H. Einstein; E. Krauter; H. Klapperich; R. Pöttler (eds.). <a rel="nofollow" class="external text" href="http://www.eos.ubc.ca/personal/erik/e-papers/01EE_UEF-Modelling.pdf"><i>Advanced numerical techniques in rock slope stability analysis - Applications and limitations</i></a> <span class="cs1-format">(PDF)</span>. UEF International Conference on Landslides - Causes, Impacts and Countermeasures. Davos, Switzerland: Verlag Glückauf GmbH. pp. 615–624.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=conference&rft.btitle=Advanced+numerical+techniques+in+rock+slope+stability+analysis+-+Applications+and+limitations&rft.place=Davos%2C+Switzerland&rft.pages=615-624&rft.pub=Verlag+Gl%C3%BCckauf+GmbH&rft.date=2001&rft.aulast=Stead&rft.aufirst=Doug&rft.au=Eberhardt%2C+E.&rft.au=Coggan%2C+J.&rft.au=Benko%2C+B.&rft_id=http%3A%2F%2Fwww.eos.ubc.ca%2Fpersonal%2Ferik%2Fe-papers%2F01EE_UEF-Modelling.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAbramson2002" class="citation cs2">Abramson, Lee W.; Lee, Thomas S.; Sharma, Sunil; Boyce, Glenn M. (2002), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=cOI02OqUCdMC"><i>Slope Stability and Stabilization Methods</i></a> (2nd ed.), New York, USA: John Wiley & Sons, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-471-38493-3" title="Special:BookSources/0-471-38493-3"><bdi>0-471-38493-3</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Slope+Stability+and+Stabilization+Methods&rft.place=New+York%2C+USA&rft.edition=2nd&rft.pub=John+Wiley+%26+Sons&rft.date=2002&rft.isbn=0-471-38493-3&rft.aulast=Abramson&rft.aufirst=Lee+W.&rft.au=Lee%2C+Thomas+S.&rft.au=Sharma%2C+Sunil&rft.au=Boyce%2C+Glenn+M.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DcOI02OqUCdMC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFZhu2003" class="citation cs2">Zhu, D.Y.; Lee, C.F.; Jiang, H.D. (2003), "Generalised framework of limit equilibrium methods for slope stability analysis", <i>Geotechnique</i>, <b>53</b> (4), Telford, London, Great Britain: 377–395, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2003Getq...53..377Z">2003Getq...53..377Z</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1680%2Fgeot.2003.53.4.377">10.1680/geot.2003.53.4.377</a>, <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://hdl.handle.net/10722%2F71758">10722/71758</a></span>, <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0016-8505">0016-8505</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Geotechnique&rft.atitle=Generalised+framework+of+limit+equilibrium+methods+for+slope+stability+analysis&rft.volume=53&rft.issue=4&rft.pages=377-395&rft.date=2003&rft_id=info%3Ahdl%2F10722%2F71758&rft.issn=0016-8505&rft_id=info%3Adoi%2F10.1680%2Fgeot.2003.53.4.377&rft_id=info%3Abibcode%2F2003Getq...53..377Z&rft.aulast=Zhu&rft.aufirst=D.Y.&rft.au=Lee%2C+C.F.&rft.au=Jiang%2C+H.D.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKovari1978" class="citation conference cs1">Kovári, Kalman; Fritz, P. (1978). <a rel="nofollow" class="external text" href="http://fritz.ch:8080/www/search/PublicationDisplay.asp?publication=12"><i>Slope Stability with Plane, Wedge and Polygonal Sliding Surfaces</i></a>. International Symposium on Rock Mechanics related to Dam Foundations. Rio de Janeiro, Brazil. pp. 103–124.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=conference&rft.btitle=Slope+Stability+with+Plane%2C+Wedge+and+Polygonal+Sliding+Surfaces&rft.place=Rio+de+Janeiro%2C+Brazil&rft.pages=103-124&rft.date=1978&rft.aulast=Kov%C3%A1ri&rft.aufirst=Kalman&rft.au=Fritz%2C+P.&rft_id=http%3A%2F%2Ffritz.ch%3A8080%2Fwww%2Fsearch%2FPublicationDisplay.asp%3Fpublication%3D12&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFYang2004" class="citation cs2">Yang, Xiao-Li; Li, L.; Yin, J.H. (2004), "Stability analysis of rock slopes with a modified Hoek-Brown failure criterion", <i>International Journal for Numerical and Analytical Methods in Geomechanics</i>, <b>28</b> (2), Chichester, Great Britain: John Wiley & Sons: 181–190, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2004IJNAM..28..181Y">2004IJNAM..28..181Y</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fnag.330">10.1002/nag.330</a>, <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0363-9061">0363-9061</a>, <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:120421002">120421002</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=International+Journal+for+Numerical+and+Analytical+Methods+in+Geomechanics&rft.atitle=Stability+analysis+of+rock+slopes+with+a+modified+Hoek-Brown+failure+criterion&rft.volume=28&rft.issue=2&rft.pages=181-190&rft.date=2004&rft_id=info%3Adoi%2F10.1002%2Fnag.330&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A120421002%23id-name%3DS2CID&rft.issn=0363-9061&rft_id=info%3Abibcode%2F2004IJNAM..28..181Y&rft.aulast=Yang&rft.aufirst=Xiao-Li&rft.au=Li%2C+L.&rft.au=Yin%2C+J.H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBarton1990" class="citation conference cs1">Barton, N.R.; Bandis, S.C. (1990). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=00fDaqhru2cC&pg=PA603">"Review of predictive capabilities of JRC-JCS model in engineering practice"</a>. In Barton, Nick (ed.). <i>Rock Joints</i>. International Symposium on Rock Joints. Rotterdam: Balkema. pp. 603–610. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-90-6191-109-8" title="Special:BookSources/978-90-6191-109-8"><bdi>978-90-6191-109-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=conference&rft.atitle=Review+of+predictive+capabilities+of+JRC-JCS+model+in+engineering+practice&rft.btitle=Rock+Joints&rft.place=Rotterdam&rft.pages=603-610&rft.pub=Balkema&rft.date=1990&rft.isbn=978-90-6191-109-8&rft.aulast=Barton&rft.aufirst=N.R.&rft.au=Bandis%2C+S.C.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D00fDaqhru2cC%26pg%3DPA603&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHungr1988" class="citation conference cs1">Hungr, O.; Evans, S.G. (1988). "Engineering evaluation of fragmental rockfall hazards". In Bonnard, C. (ed.). <i>Landslides</i>. International Symposium on Landslides, Lausanne. Rotterdam: Balkema. pp. 685–690.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=conference&rft.atitle=Engineering+evaluation+of+fragmental+rockfall+hazards&rft.btitle=Landslides&rft.place=Rotterdam&rft.pages=685-690&rft.pub=Balkema&rft.date=1988&rft.aulast=Hungr&rft.aufirst=O.&rft.au=Evans%2C+S.G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASlope+stability+analysis" class="Z3988"></span></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Slope_stability_analysis&action=edit&section=21" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Slope_stability_analysis" class="extiw" title="commons:Category:Slope stability analysis">Slope stability analysis</a></span>.</div></div> </div> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Geotechnical_engineering" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Geotechnical_engineering" title="Template:Geotechnical engineering"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Geotechnical_engineering" title="Template talk:Geotechnical engineering"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Geotechnical_engineering" title="Special:EditPage/Template:Geotechnical engineering"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Geotechnical_engineering" style="font-size:114%;margin:0 4em"><a href="/wiki/Geotechnical_engineering" title="Geotechnical engineering">Geotechnical engineering</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div><a href="/wiki/Offshore_geotechnical_engineering" title="Offshore geotechnical engineering">Offshore geotechnical engineering</a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Geotechnical_investigation" title="Geotechnical investigation">Investigation</a> <br />and<br />instrumentation</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:10.0em;font-weight: normal;">Field (<i>in situ</i>)</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"><div class="div-col" style="column-width: 33em;"> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Core_sample.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Core_sample.svg/20px-Core_sample.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Core_sample.svg/30px-Core_sample.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Core_sample.svg/40px-Core_sample.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/wiki/Core_drill" title="Core drill">Core drill</a></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Cone_penetration_test.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/Cone_penetration_test.svg/20px-Cone_penetration_test.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/Cone_penetration_test.svg/30px-Cone_penetration_test.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/28/Cone_penetration_test.svg/40px-Cone_penetration_test.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/wiki/Cone_penetration_test" title="Cone penetration test">Cone penetration test</a></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Geo-electrical_sounding.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/10/Geo-electrical_sounding.svg/20px-Geo-electrical_sounding.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/10/Geo-electrical_sounding.svg/30px-Geo-electrical_sounding.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/10/Geo-electrical_sounding.svg/40px-Geo-electrical_sounding.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/w/index.php?title=Geo-electrical_sounding&action=edit&redlink=1" class="new" title="Geo-electrical sounding (page does not exist)">Geo-electrical sounding</a></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:In_situ_permeameter_test.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/In_situ_permeameter_test.svg/20px-In_situ_permeameter_test.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/In_situ_permeameter_test.svg/30px-In_situ_permeameter_test.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7b/In_situ_permeameter_test.svg/40px-In_situ_permeameter_test.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/wiki/Permeability_(Earth_sciences)" class="mw-redirect" title="Permeability (Earth sciences)">Permeability test</a></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Load_test.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Load_test.svg/20px-Load_test.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Load_test.svg/30px-Load_test.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Load_test.svg/40px-Load_test.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/wiki/Load_test" class="mw-redirect" title="Load test">Load test</a> <ul><li><a href="/wiki/Static_load_testing" title="Static load testing">Static</a></li> <li><a href="/wiki/Dynamic_load_testing" title="Dynamic load testing">Dynamic</a></li> <li><a href="/wiki/Statnamic_load_test" title="Statnamic load test">Statnamic</a></li></ul></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Pore_pressure_measurement.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Pore_pressure_measurement.svg/20px-Pore_pressure_measurement.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Pore_pressure_measurement.svg/30px-Pore_pressure_measurement.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Pore_pressure_measurement.svg/40px-Pore_pressure_measurement.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> Pore pressure measurement <ul><li><a href="/wiki/Piezometer" class="mw-redirect" title="Piezometer">Piezometer</a></li> <li><a href="/wiki/Well#Classification" title="Well">Well</a></li></ul></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Ram_sounding.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Ram_sounding.svg/20px-Ram_sounding.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Ram_sounding.svg/30px-Ram_sounding.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Ram_sounding.svg/40px-Ram_sounding.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/w/index.php?title=Ram_sounding&action=edit&redlink=1" class="new" title="Ram sounding (page does not exist)">Ram sounding</a></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Rock_control_drilling.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Rock_control_drilling.svg/20px-Rock_control_drilling.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Rock_control_drilling.svg/30px-Rock_control_drilling.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Rock_control_drilling.svg/40px-Rock_control_drilling.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/w/index.php?title=Rock_control_drilling&action=edit&redlink=1" class="new" title="Rock control drilling (page does not exist)">Rock control drilling</a></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Rotary_pressure_sounding.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/81/Rotary_pressure_sounding.svg/20px-Rotary_pressure_sounding.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/81/Rotary_pressure_sounding.svg/30px-Rotary_pressure_sounding.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/81/Rotary_pressure_sounding.svg/40px-Rotary_pressure_sounding.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/wiki/Rotary-pressure_sounding" title="Rotary-pressure sounding">Rotary-pressure sounding</a></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Rotary_weight_sounding.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Rotary_weight_sounding.svg/20px-Rotary_weight_sounding.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Rotary_weight_sounding.svg/30px-Rotary_weight_sounding.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Rotary_weight_sounding.svg/40px-Rotary_weight_sounding.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/w/index.php?title=Rotary_weight_sounding&action=edit&redlink=1" class="new" title="Rotary weight sounding (page does not exist)">Rotary weight sounding</a></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Sample_series.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/05/Sample_series.svg/20px-Sample_series.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/05/Sample_series.svg/30px-Sample_series.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/05/Sample_series.svg/40px-Sample_series.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/wiki/Soil_test#Soil_testing" title="Soil test">Sample series</a></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Screw_plate_test.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Screw_plate_test.svg/20px-Screw_plate_test.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Screw_plate_test.svg/30px-Screw_plate_test.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/75/Screw_plate_test.svg/40px-Screw_plate_test.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/w/index.php?title=Screw_plate_test&action=edit&redlink=1" class="new" title="Screw plate test (page does not exist)">Screw plate test</a></li></ul> <ul><li><a href="/wiki/Deformation_monitoring" title="Deformation monitoring">Deformation monitoring</a> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Inclinometer.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Inclinometer.svg/20px-Inclinometer.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Inclinometer.svg/30px-Inclinometer.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Inclinometer.svg/40px-Inclinometer.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/wiki/Inclinometer" title="Inclinometer">Inclinometer</a></li> <li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Settlement_recordings.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/Settlement_recordings.svg/20px-Settlement_recordings.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/Settlement_recordings.svg/30px-Settlement_recordings.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/35/Settlement_recordings.svg/40px-Settlement_recordings.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/wiki/Soil_consolidation" title="Soil consolidation">Settlement recordings</a></li></ul></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Shear_vane_test.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Shear_vane_test.svg/20px-Shear_vane_test.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Shear_vane_test.svg/30px-Shear_vane_test.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Shear_vane_test.svg/40px-Shear_vane_test.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/wiki/Shear_vane_test" title="Shear vane test">Shear vane test</a></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Simple_sounding.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Simple_sounding.svg/20px-Simple_sounding.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Simple_sounding.svg/30px-Simple_sounding.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Simple_sounding.svg/40px-Simple_sounding.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/w/index.php?title=Simple_sounding&action=edit&redlink=1" class="new" title="Simple sounding (page does not exist)">Simple sounding</a></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Standard_penetration_test.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Standard_penetration_test.svg/20px-Standard_penetration_test.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Standard_penetration_test.svg/30px-Standard_penetration_test.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Standard_penetration_test.svg/40px-Standard_penetration_test.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/wiki/Standard_penetration_test" title="Standard penetration test">Standard penetration test</a></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Total_sounding.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/Total_sounding.svg/20px-Total_sounding.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/Total_sounding.svg/30px-Total_sounding.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/60/Total_sounding.svg/40px-Total_sounding.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/wiki/Total_sounding" title="Total sounding">Total sounding</a></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Trial_pit.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/71/Trial_pit.svg/20px-Trial_pit.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/71/Trial_pit.svg/30px-Trial_pit.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/71/Trial_pit.svg/40px-Trial_pit.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/wiki/Trial_pit" title="Trial pit">Trial pit</a></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Visible_rock.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/14/Visible_rock.svg/20px-Visible_rock.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/14/Visible_rock.svg/30px-Visible_rock.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/14/Visible_rock.svg/40px-Visible_rock.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/wiki/Bedrock" title="Bedrock">Visible bedrock</a></li></ul> <ul><li><a href="/wiki/Nuclear_densometer" class="mw-redirect" title="Nuclear densometer">Nuclear densometer test</a></li></ul> <ul><li><a href="/wiki/Exploration_geophysics" title="Exploration geophysics">Exploration geophysics</a></li></ul> <ul><li><a href="/wiki/Crosshole_sonic_logging" title="Crosshole sonic logging">Crosshole sonic logging</a></li></ul> <ul><li><a href="/wiki/Pile_integrity_test" title="Pile integrity test">Pile integrity test</a></li></ul> <ul><li><a href="/wiki/Wave_equation_analysis" title="Wave equation analysis">Wave equation analysis</a></li></ul></div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:10.0em;font-weight: normal;"><a href="/wiki/Soil_test" title="Soil test">Laboratory <br />testing</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <li><a href="/wiki/Soil_classification" title="Soil classification">Soil classification</a></li> <li><a href="/wiki/Atterberg_limits" title="Atterberg limits">Atterberg limits</a></li> <li><a href="/wiki/California_bearing_ratio" title="California bearing ratio">California bearing ratio</a></li> <li><a href="/wiki/Direct_shear_test" title="Direct shear test">Direct shear test</a></li> <li><a href="/wiki/Hydrometer" title="Hydrometer">Hydrometer</a></li> <li><a href="/wiki/Proctor_compaction_test" title="Proctor compaction test">Proctor compaction test</a></li> <li><a href="/wiki/R-value_(soils)" title="R-value (soils)">R-value</a></li> <li><a href="/wiki/Sieve_analysis" title="Sieve analysis">Sieve analysis</a></li> <li><a href="/wiki/Triaxial_shear_test" title="Triaxial shear test">Triaxial shear test</a></li> <li><a href="/wiki/Oedometer_test" title="Oedometer test">Oedometer test</a></li> <li><a href="/wiki/Hydraulic_conductivity#Experimental_approach" title="Hydraulic conductivity">Hydraulic conductivity tests</a></li> <li><a href="/wiki/Water_content#Measurement" title="Water content">Water content tests</a></li> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Soil" title="Soil">Soil</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:10.0em;font-weight: normal;">Types</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Clay" title="Clay">Clay</a></li> <li><a href="/wiki/Silt" title="Silt">Silt</a></li> <li><a href="/wiki/Sand" title="Sand">Sand</a></li> <li><a href="/wiki/Gravel" title="Gravel">Gravel</a></li> <li><a href="/wiki/Peat" title="Peat">Peat</a></li> <li><a href="/wiki/Loam" title="Loam">Loam</a></li> <li><a href="/wiki/Loess" title="Loess">Loess</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:10.0em;font-weight: normal;">Properties</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Hydraulic_conductivity" title="Hydraulic conductivity">Hydraulic conductivity</a></li> <li><a href="/wiki/Water_content" title="Water content">Water content</a></li> <li><a href="/wiki/Void_ratio" title="Void ratio">Void ratio</a></li> <li><a href="/wiki/Bulk_density" title="Bulk density">Bulk density</a></li> <li><a href="/wiki/Thixotropy" title="Thixotropy">Thixotropy</a></li> <li><a href="/wiki/Reynolds%27_dilatancy" class="mw-redirect" title="Reynolds' dilatancy">Reynolds' dilatancy</a></li> <li><a href="/wiki/Angle_of_repose" title="Angle of repose">Angle of repose</a></li> <li><a href="/wiki/Friction#Angle_of_friction" title="Friction">Friction angle</a></li> <li><a href="/wiki/Cohesion_(geology)" title="Cohesion (geology)">Cohesion</a></li> <li><a href="/wiki/Porosity" title="Porosity">Porosity</a></li> <li><a href="/wiki/Permeability_(earth_sciences)" class="mw-redirect" title="Permeability (earth sciences)">Permeability</a></li> <li><a href="/wiki/Specific_storage" title="Specific storage">Specific storage</a></li> <li><a href="/wiki/Shear_strength_(soil)" title="Shear strength (soil)">Shear strength</a></li> <li><a href="/wiki/Soil_liquefaction" title="Soil liquefaction">Sensitivity</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Structures <br />(<a href="/wiki/Soil-structure_interaction" title="Soil-structure interaction">Interaction</a>)</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:10.0em;font-weight: normal;">Natural features</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Topography" title="Topography">Topography</a></li> <li><a href="/wiki/Vegetation" title="Vegetation">Vegetation</a></li> <li><a href="/wiki/Terrain" title="Terrain">Terrain</a></li> <li><a href="/wiki/Topsoil" title="Topsoil">Topsoil</a></li> <li><a href="/wiki/Water_table" title="Water table">Water table</a></li> <li><a href="/wiki/Bedrock" title="Bedrock">Bedrock</a></li> <li><a href="/wiki/Subgrade" title="Subgrade">Subgrade</a></li> <li><a href="/wiki/Subsoil" title="Subsoil">Subsoil</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:10.0em;font-weight: normal;"><a href="/wiki/Earthworks_(engineering)" title="Earthworks (engineering)">Earthworks</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li>Shoring structures <ul><li><a href="/wiki/Retaining_wall" title="Retaining wall">Retaining walls</a></li> <li><a href="/wiki/Gabion" title="Gabion">Gabion</a></li> <li><a href="/wiki/Ground_freezing" title="Ground freezing">Ground freezing</a></li> <li><a href="/wiki/Mechanically_stabilized_earth" title="Mechanically stabilized earth">Mechanically stabilized earth</a></li> <li><a href="/wiki/Pressure_grouting" title="Pressure grouting">Pressure grouting</a></li> <li><a href="/wiki/Slurry_wall" title="Slurry wall">Slurry wall</a></li> <li><a href="/wiki/Soil_nailing" title="Soil nailing">Soil nailing</a></li> <li><a href="/wiki/Tieback_(geotechnical)" title="Tieback (geotechnical)">Tieback</a></li></ul></li> <li><a href="/wiki/Land_development" title="Land development">Land development</a></li> <li><a href="/wiki/Landfill" title="Landfill">Landfill</a></li> <li><a href="/wiki/Digging" title="Digging">Excavation</a></li> <li><a href="/wiki/Trench" title="Trench">Trench</a></li> <li><a href="/wiki/Embankment_(earthworks)" title="Embankment (earthworks)">Embankment</a></li> <li><a href="/wiki/Cut_(earthworks)" title="Cut (earthworks)">Cut</a></li> <li><a href="/wiki/Causeway" title="Causeway">Causeway</a></li> <li><a href="/wiki/Terrace_(earthworks)" title="Terrace (earthworks)">Terracing</a></li> <li><a href="/wiki/Tunnel#Cut-and-cover" title="Tunnel">Cut-and-cover</a></li> <li><a href="/wiki/Cut_and_fill" title="Cut and fill">Cut and fill</a></li> <li><a href="/wiki/Fill_dirt" title="Fill dirt">Fill dirt</a></li> <li><a href="/wiki/Grading_(engineering)" class="mw-redirect" title="Grading (engineering)">Grading</a></li> <li><a href="/wiki/Land_reclamation" title="Land reclamation">Land reclamation</a></li> <li><a href="/wiki/Track_bed" title="Track bed">Track bed</a></li> <li><a href="/wiki/Erosion_control" title="Erosion control">Erosion control</a></li> <li><a href="/wiki/Earth_structure" title="Earth structure">Earth structure</a></li> <li><a href="/wiki/Expanded_clay_aggregate" title="Expanded clay aggregate">Expanded clay aggregate</a></li> <li><a href="/wiki/Crushed_stone" title="Crushed stone">Crushed stone</a></li> <li><a href="/wiki/Geosynthetics" title="Geosynthetics">Geosynthetics</a> <ul><li><a href="/wiki/Geotextile" title="Geotextile">Geotextile</a></li> <li><a href="/wiki/Geomembrane" title="Geomembrane">Geomembrane</a></li> <li><a href="/wiki/Geosynthetic_clay_liner" title="Geosynthetic clay liner">Geosynthetic clay liner</a></li> <li><a href="/wiki/Cellular_confinement" title="Cellular confinement">Cellular confinement</a></li></ul></li> <li><a href="/wiki/Infiltration_(hydrology)" title="Infiltration (hydrology)">Infiltration</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:10.0em;font-weight: normal;"><a href="/wiki/Foundation_(engineering)" title="Foundation (engineering)">Foundations</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Shallow_foundation" title="Shallow foundation">Shallow</a></li> <li><a href="/wiki/Deep_foundation" title="Deep foundation">Deep</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Soil_mechanics" title="Soil mechanics">Mechanics</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:10.0em;font-weight: normal;">Forces</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Effective_stress" title="Effective stress">Effective stress</a></li> <li><a href="/wiki/Pore_water_pressure" title="Pore water pressure">Pore water pressure</a></li> <li><a href="/wiki/Lateral_earth_pressure" title="Lateral earth pressure">Lateral earth pressure</a></li> <li><a href="/wiki/Overburden_pressure" title="Overburden pressure">Overburden pressure</a></li> <li><a href="/wiki/Preconsolidation_pressure" title="Preconsolidation pressure">Preconsolidation pressure</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:10.0em;font-weight: normal;">Phenomena/<br />problems</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Permafrost" title="Permafrost">Permafrost</a></li> <li><a href="/wiki/Frost_heaving" title="Frost heaving">Frost heaving</a></li> <li><a href="/wiki/Consolidation_(soil)" class="mw-redirect" title="Consolidation (soil)">Consolidation</a></li> <li><a href="/wiki/Soil_compaction" title="Soil compaction">Compaction</a></li> <li><a href="/wiki/Earthquake" title="Earthquake">Earthquake</a> <ul><li><a href="/wiki/Response_spectrum" title="Response spectrum">Response spectrum</a></li> <li><a href="/wiki/Seismic_hazard" title="Seismic hazard">Seismic hazard</a></li> <li><a href="/wiki/S_wave" title="S wave">Shear wave</a></li></ul></li> <li><a href="/wiki/Landslide" title="Landslide">Landslide</a> analysis <ul><li><a class="mw-selflink selflink">Stability analysis</a></li> <li><a href="/wiki/Landslide_mitigation" title="Landslide mitigation">Mitigation</a></li> <li><a href="/wiki/Landslide_classification" title="Landslide classification">Classification</a></li> <li><a href="/wiki/Sliding_criterion_(geotechnical_engineering)" title="Sliding criterion (geotechnical engineering)">Sliding criterion</a></li> <li><a href="/wiki/Road#Slab_stabilization" title="Road">Slab stabilisation</a></li></ul></li> <li><a href="/wiki/Bearing_capacity" title="Bearing capacity">Bearing capacity</a> * <a href="/wiki/Stress_distribution_in_soil" title="Stress distribution in soil">Stress distribution in soil</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Software" title="Software">Numerical analysis <br />software</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/SEEP2D" title="SEEP2D">SEEP2D</a></li> <li><a href="/w/index.php?title=STABL&action=edit&redlink=1" class="new" title="STABL (page does not exist)">STABL</a></li> <li><a href="/wiki/SVFlux" title="SVFlux">SVFlux</a></li> <li><a href="/wiki/SVSlope" title="SVSlope">SVSlope</a></li> <li><a href="/wiki/UTEXAS" title="UTEXAS">UTEXAS</a></li> <li><a href="/wiki/Plaxis" title="Plaxis">Plaxis</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Geoprofessions" title="Geoprofessions">Related fields</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Geology" title="Geology">Geology</a></li> <li><a href="/wiki/Geochemistry" title="Geochemistry">Geochemistry</a></li> <li><a href="/wiki/Petrology" title="Petrology">Petrology</a></li> <li><a href="/wiki/Earthquake_engineering" title="Earthquake engineering">Earthquake engineering</a></li> <li><a href="/wiki/Geomorphology" title="Geomorphology">Geomorphology</a></li> <li><a href="/wiki/Soil_science" title="Soil science">Soil science</a></li> <li><a href="/wiki/Hydrology" title="Hydrology">Hydrology</a></li> <li><a href="/wiki/Hydrogeology" title="Hydrogeology">Hydrogeology</a></li> <li><a href="/wiki/Biogeography" title="Biogeography">Biogeography</a></li> <li><a href="/wiki/Earth_materials" title="Earth materials">Earth materials</a></li> <li><a href="/wiki/Archaeology" title="Archaeology">Archaeology</a></li> <li><a href="/wiki/Agricultural_science" title="Agricultural science">Agricultural science</a> <ul><li><a href="/wiki/Agrology" class="mw-redirect" title="Agrology">Agrology</a></li></ul></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox authority-control" aria-label="Navbox" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control databases</a>: National <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q961278#identifiers" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh2002005457">United States</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://olduli.nli.org.il/F/?func=find-b&local_base=NLX10&find_code=UID&request=987007542116905171">Israel</a></span></li></ul></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Slope_stability_analysis&oldid=1251997464">https://en.wikipedia.org/w/index.php?title=Slope_stability_analysis&oldid=1251997464</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Category</a>: <ul><li><a href="/wiki/Category:Landslide_analysis,_prevention_and_mitigation" title="Category:Landslide analysis, prevention and mitigation">Landslide analysis, prevention and mitigation</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:All_articles_with_dead_external_links" title="Category:All articles with dead external links">All articles with dead external links</a></li><li><a href="/wiki/Category:Articles_with_dead_external_links_from_July_2022" title="Category:Articles with dead external links from July 2022">Articles with dead external links from July 2022</a></li><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_is_different_from_Wikidata" title="Category:Short description is different from Wikidata">Short description is different from Wikidata</a></li><li><a href="/wiki/Category:Wikipedia_articles_that_are_too_technical_from_December_2012" title="Category:Wikipedia articles that are too technical from December 2012">Wikipedia articles that are too technical from December 2012</a></li><li><a href="/wiki/Category:All_articles_that_are_too_technical" title="Category:All articles that are too technical">All articles that are too technical</a></li><li><a href="/wiki/Category:Wikipedia_spam_cleanup_from_March_2023" title="Category:Wikipedia spam cleanup from March 2023">Wikipedia spam cleanup from March 2023</a></li><li><a href="/wiki/Category:Wikipedia_further_reading_cleanup" title="Category:Wikipedia further reading cleanup">Wikipedia further reading cleanup</a></li><li><a href="/wiki/Category:Commons_category_link_is_on_Wikidata" title="Category:Commons category link is on Wikidata">Commons category link is on Wikidata</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 19 October 2024, at 06:48<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. By using this site, you agree to the <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use" class="extiw" title="foundation:Special:MyLanguage/Policy:Terms of Use">Terms of Use</a> and <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy" class="extiw" title="foundation:Special:MyLanguage/Policy:Privacy policy">Privacy Policy</a>. Wikipedia® is a registered trademark of the <a rel="nofollow" class="external text" href="https://wikimediafoundation.org/">Wikimedia Foundation, Inc.</a>, a non-profit organization.</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Privacy policy</a></li> <li id="footer-places-about"><a href="/wiki/Wikipedia:About">About Wikipedia</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedia:General_disclaimer">Disclaimers</a></li> <li id="footer-places-contact"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us">Contact Wikipedia</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Code of Conduct</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Developers</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/en.wikipedia.org">Statistics</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Cookie statement</a></li> <li id="footer-places-mobileview"><a href="//en.m.wikipedia.org/w/index.php?title=Slope_stability_analysis&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Mobile view</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/static/images/footer/wikimedia-button.svg" width="84" height="29" alt="Wikimedia Foundation" loading="lazy"></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/w/resources/assets/poweredby_mediawiki.svg" alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> </div> </div> </div> <div class="vector-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-694cf4987f-ch2wz","wgBackendResponseTime":151,"wgPageParseReport":{"limitreport":{"cputime":"0.829","walltime":"1.031","ppvisitednodes":{"value":4246,"limit":1000000},"postexpandincludesize":{"value":144426,"limit":2097152},"templateargumentsize":{"value":7314,"limit":2097152},"expansiondepth":{"value":17,"limit":100},"expensivefunctioncount":{"value":11,"limit":500},"unstrip-depth":{"value":1,"limit":20},"unstrip-size":{"value":156935,"limit":5000000},"entityaccesscount":{"value":1,"limit":400},"timingprofile":["100.00% 769.409 1 -total"," 37.77% 290.627 1 Template:Reflist"," 17.68% 136.013 5 Template:Navbox"," 16.76% 128.978 1 Template:Geotechnical_engineering"," 11.74% 90.320 4 Template:Cite_book"," 11.37% 87.482 17 Template:Citation"," 8.12% 62.489 1 Template:Short_description"," 7.83% 60.211 10 Template:Cite_journal"," 7.48% 57.585 25 Template:Harvnb"," 5.55% 42.730 1 Template:Technical"]},"scribunto":{"limitreport-timeusage":{"value":"0.507","limit":"10.000"},"limitreport-memusage":{"value":7968128,"limit":52428800},"limitreport-logs":"anchor_id_list = table#1 {\n [\"CITEREF3DEC2009\"] = 1,\n [\"CITEREFAbramson2002\"] = 1,\n [\"CITEREFBarton1990\"] = 1,\n [\"CITEREFBeale,_GeoffRead,_John2014\"] = 1,\n [\"CITEREFBishop1955\"] = 1,\n [\"CITEREFBourrierHungr2013\"] = 1,\n [\"CITEREFCardenas2019\"] = 1,\n [\"CITEREFChugh1982\"] = 1,\n [\"CITEREFDevotoCastelli2007\"] = 1,\n [\"CITEREFDouw2009\"] = 1,\n [\"CITEREFEberhardt2003\"] = 1,\n [\"CITEREFFredlund1984\"] = 1,\n [\"CITEREFFredlundKrahn1977\"] = 1,\n [\"CITEREFHack2002\"] = 1,\n [\"CITEREFHungr1988\"] = 1,\n [\"CITEREFJanbu1973\"] = 1,\n [\"CITEREFKaczmarekPopielski2019\"] = 1,\n [\"CITEREFKliche1999\"] = 1,\n [\"CITEREFKovari1978\"] = 1,\n [\"CITEREFLiuChen2005\"] = 1,\n [\"CITEREFLiuWang2021\"] = 1,\n [\"CITEREFLiuWang2023\"] = 1,\n [\"CITEREFLoweKarafiath1960\"] = 1,\n [\"CITEREFMorgensternPrice1965\"] = 1,\n [\"CITEREFPFC2D2009\"] = 1,\n [\"CITEREFPFC3D2009\"] = 1,\n [\"CITEREFPantelidis2009\"] = 1,\n [\"CITEREFRupkeHuismanKruse2007\"] = 1,\n [\"CITEREFSarma1975\"] = 1,\n [\"CITEREFSinghGoel2002\"] = 1,\n [\"CITEREFSpencer1967\"] = 1,\n [\"CITEREFStead2001\"] = 1,\n [\"CITEREFUDEC2009\"] = 1,\n [\"CITEREFUSArmyCorps2003\"] = 1,\n [\"CITEREFWietek2021\"] = 1,\n [\"CITEREFYang2004\"] = 1,\n [\"CITEREFZhu2003\"] = 1,\n [\"COE\"] = 1,\n}\ntemplate_list = table#1 {\n [\"Authority control\"] = 1,\n [\"Cbignore\"] = 1,\n [\"Citation\"] = 17,\n [\"Cite book\"] = 4,\n [\"Cite conference\"] = 6,\n [\"Cite journal\"] = 10,\n [\"Cite web\"] = 1,\n [\"Cmn\"] = 1,\n [\"Commons category\"] = 1,\n [\"Dead link\"] = 1,\n [\"Further reading cleanup\"] = 1,\n [\"Geotechnical engineering\"] = 1,\n [\"Harvnb\"] = 25,\n [\"ISBN\"] = 2,\n [\"Main\"] = 1,\n [\"Refbegin\"] = 1,\n [\"Refend\"] = 1,\n [\"Reflist\"] = 1,\n [\"See also\"] = 4,\n [\"Short description\"] = 1,\n [\"Technical\"] = 1,\n}\narticle_whitelist = table#1 {\n}\n"},"cachereport":{"origin":"mw-web.codfw.main-6b7f745dd4-zvhvk","timestamp":"20241125133610","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Slope stability analysis","url":"https:\/\/en.wikipedia.org\/wiki\/Slope_stability_analysis","sameAs":"http:\/\/www.wikidata.org\/entity\/Q961278","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q961278","author":{"@type":"Organization","name":"Contributors to Wikimedia projects"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2009-08-07T08:31:31Z","dateModified":"2024-10-19T06:48:25Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/9\/98\/Pett_bish.gif","headline":"property of soil-covered slopes"}</script> </body> </html>