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	<id>https://damtoolbox.org/index.php?action=history&amp;feed=atom&amp;title=Linear_vs._Non-linear</id>
	<title>Linear vs. Non-linear - Revision history</title>
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	<updated>2026-04-29T09:29:45Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
	<generator>MediaWiki 1.40.0</generator>
	<entry>
		<id>https://damtoolbox.org/index.php?title=Linear_vs._Non-linear&amp;diff=7164&amp;oldid=prev</id>
		<title>Mpollei@gfnet.com at 20:51, 11 July 2023</title>
		<link rel="alternate" type="text/html" href="https://damtoolbox.org/index.php?title=Linear_vs._Non-linear&amp;diff=7164&amp;oldid=prev"/>
		<updated>2023-07-11T20:51:00Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 20:51, 11 July 2023&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l12&quot;&gt;Line 12:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 12:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Best Practices Resources==  &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Best Practices Resources==  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{Document Icon}} [[Stability Analysis of Concrete Structures (EM 1110-2-2100) | Stability Analysis of Concrete Structures (EM 1110-2-2100), USACE]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{Document Icon}} [[Stability Analysis of Concrete Structures (EM 1110-2-2100) | Stability Analysis of Concrete Structures (EM 1110-2-2100), USACE]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{Document Icon}} [[Gravity Dam Design (EM 1110-2-2200) | Gravity Dam Design (EM 1110-2-2200), USACE&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;, 1995&lt;/del&gt;]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{Document Icon}} [[Gravity Dam Design (EM 1110-2-2200) | Gravity Dam Design (EM 1110-2-2200), USACE]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{Document Icon}} [[Arch Dam Design (EM 1110-2-2201) | Arch Dam Design (EM 1110-2-2201), USACE&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;, 1994&lt;/del&gt;]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{Document Icon}} [[Arch Dam Design (EM 1110-2-2201) | Arch Dam Design (EM 1110-2-2201), USACE]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{Document Icon}} [[Design of Small Dams | Design of Small Dams, USBR&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;, 1987&lt;/del&gt;]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{Document Icon}} [[Design of Small Dams | Design of Small Dams, USBR]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{Document Icon}} [[Sliding Stability for Concrete Structures (ETL 1110-2-256) | Sliding Stability for Concrete Structures (ETL 1110-2-256), USACE&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;, 1981&lt;/del&gt;]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{Document Icon}} [[Sliding Stability for Concrete Structures (ETL 1110-2-256) | Sliding Stability for Concrete Structures (ETL 1110-2-256), USACE]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Trainings==  &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Trainings==  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Mpollei@gfnet.com</name></author>
	</entry>
	<entry>
		<id>https://damtoolbox.org/index.php?title=Linear_vs._Non-linear&amp;diff=5761&amp;oldid=prev</id>
		<title>Grichards at 23:42, 14 December 2022</title>
		<link rel="alternate" type="text/html" href="https://damtoolbox.org/index.php?title=Linear_vs._Non-linear&amp;diff=5761&amp;oldid=prev"/>
		<updated>2022-12-14T23:42:07Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 23:42, 14 December 2022&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l8&quot;&gt;Line 8:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 8:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|}&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;!-- Introductory paragraph or topic page summary --&amp;gt;  &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;!-- Introductory paragraph or topic page summary --&amp;gt;  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&quot;Both new and existing structures are constantly being examined to determine if they meet [[stability]] criteria. The traditional procedure is to evaluate [[Sliding Stability|sliding stability]] of these structures using the limit equilibrium method of analysis and to evaluate [[Rotational Stability|rotational stability]] using rigid body assumptions and bearing pressure distributions that vary linearly across the base. Soil and uplift loads on the structure are often based on simplifying assumptions. In the limit equilibrium method, only the stress at failure is considered, usually as represented by the Mohr-Coulomb limit-state criterion. The simplified loads and the Mohr-Coulomb limit-state criterion are then used to obtain a single overall factor of safety against a [[Sliding Stability|sliding stability]] failure. This traditional approach is appropriate for many structures where it is difficult to predict just how a particular failure &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[&lt;/del&gt;mechanism&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;]] &lt;/del&gt;may develop. However, for existing structures where more is known about service state conditions and uplift pressures, it is possible to more precisely predict what stress changes must occur to develop a failure condition. The margin of safety can be more accurately determined when the path to failure, from initial stress conditions to limit state conditions, is known. This path to failure can be investigated using linear elastic and nonlinear finite-element numerical solutions and facture mechanics concepts. Because the deformation of the structure and its foundation is considered in finite element analyses, and because the path to failure can be more realistically characterized through facture mechanics, a more accurate assessment of safety can often be made using advanced analytical methods.&quot;&amp;lt;ref name=&quot;EM 1110-2-2100&quot;&amp;gt;[[Stability Analysis of Concrete Structures (EM 1110-2-2100) | Stability of Concrete Structures (EM 1110-2-2100), USACE, 2005]]&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&quot;Both new and existing structures are constantly being examined to determine if they meet [[stability]] criteria. The traditional procedure is to evaluate [[Sliding Stability|sliding stability]] of these structures using the limit equilibrium method of analysis and to evaluate [[Rotational Stability|rotational stability]] using rigid body assumptions and bearing pressure distributions that vary linearly across the base. Soil and uplift loads on the structure are often based on simplifying assumptions. In the limit equilibrium method, only the stress at failure is considered, usually as represented by the Mohr-Coulomb limit-state criterion. The simplified loads and the Mohr-Coulomb limit-state criterion are then used to obtain a single overall factor of safety against a [[Sliding Stability|sliding stability]] failure. This traditional approach is appropriate for many structures where it is difficult to predict just how a particular failure mechanism may develop. However, for existing structures where more is known about service state conditions and uplift pressures, it is possible to more precisely predict what stress changes must occur to develop a failure condition. The margin of safety can be more accurately determined when the path to failure, from initial stress conditions to limit state conditions, is known. This path to failure can be investigated using linear elastic and nonlinear finite-element numerical solutions and facture mechanics concepts. Because the deformation of the structure and its foundation is considered in finite element analyses, and because the path to failure can be more realistically characterized through facture mechanics, a more accurate assessment of safety can often be made using advanced analytical methods.&quot;&amp;lt;ref name=&quot;EM 1110-2-2100&quot;&amp;gt;[[Stability Analysis of Concrete Structures (EM 1110-2-2100) | Stability of Concrete Structures (EM 1110-2-2100), USACE, 2005]]&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Best Practices Resources==  &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Best Practices Resources==  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Grichards</name></author>
	</entry>
	<entry>
		<id>https://damtoolbox.org/index.php?title=Linear_vs._Non-linear&amp;diff=5702&amp;oldid=prev</id>
		<title>Grichards at 18:11, 14 December 2022</title>
		<link rel="alternate" type="text/html" href="https://damtoolbox.org/index.php?title=Linear_vs._Non-linear&amp;diff=5702&amp;oldid=prev"/>
		<updated>2022-12-14T18:11:30Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 18:11, 14 December 2022&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot;&gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;!-- Delete any sections that are not necessary to your topic. Add pictures/sections as needed --&amp;gt;  &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;!-- Delete any sections that are not necessary to your topic. Add pictures/sections as needed --&amp;gt;  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;__NOTOC__  &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;__NOTOC__  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
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&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;!-- Add Category to drive breadcrumb menus --&gt;  &lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category: Global Stability of a Dam]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Category: Global Stability of a Dam]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{| align=&amp;quot;right&amp;quot; style=&amp;quot;width:10%;&amp;quot; cellpadding=&amp;quot;7&amp;quot;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{| align=&amp;quot;right&amp;quot; style=&amp;quot;width:10%;&amp;quot; cellpadding=&amp;quot;7&amp;quot;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| [[Image:GravityDamUplift1.png|350px|x350px|link=https://damfailures.org/lessons-learned/concrete-gravity-dams-should-be-evaluated-to-accommodate-full-uplift/]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;| [[Image:GravityDamUplift1.png|350px|x350px|link=https://damfailures.org/lessons-learned/concrete-gravity-dams-should-be-evaluated-to-accommodate-full-uplift/]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|-&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|-&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|style=&quot;text-align:center; font-size:90%;&quot;| Learn more &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[&lt;/del&gt;about&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;]] &lt;/del&gt;the need to consider uplift pressure when designing a gravity structure at [https://damfailures.org/lessons-learned/concrete-gravity-dams-should-be-evaluated-to-accommodate-full-uplift/ DamFailures.org]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|style=&quot;text-align:center; font-size:90%;&quot;| Learn more about the need to consider uplift pressure when designing a gravity structure at [https://damfailures.org/lessons-learned/concrete-gravity-dams-should-be-evaluated-to-accommodate-full-uplift/ DamFailures.org]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|}&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;!-- Introductory paragraph or topic page summary --&amp;gt;  &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;!-- Introductory paragraph or topic page summary --&amp;gt;  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&quot;Both new and existing structures are constantly being examined to determine if they meet [[stability]] criteria. The traditional procedure is to evaluate [[Sliding Stability|sliding stability]] of these structures using the limit equilibrium method of analysis and to evaluate [[Rotational Stability|rotational stability]] using rigid body assumptions and bearing pressure distributions that vary linearly across the base. Soil and uplift loads on the structure are often based on simplifying assumptions. In the limit equilibrium method, only the stress at failure is considered, usually as represented by the Mohr-Coulomb limit-state criterion. The simplified loads and the Mohr-Coulomb limit-state criterion are then used to obtain a single overall factor of safety against a [[Sliding Stability|sliding stability]] failure. This traditional approach is appropriate for many structures where it is difficult to predict just how a particular failure [[mechanism]] may develop. However, for existing structures where more is known about service state conditions and uplift pressures, it is possible to more precisely predict what stress changes must occur to develop a failure condition. The margin of safety can be more accurately determined when the path to failure, from initial stress conditions to limit state conditions, is known. This path to failure can be investigated using linear elastic and nonlinear finite-element numerical solutions and facture mechanics concepts. Because the deformation of the structure and its foundation is considered in finite element analyses, and because the path to failure can be more realistically characterized through facture mechanics, a more accurate assessment of safety can often be made using advanced analytical methods.&quot;&amp;lt;ref name=&quot;EM 1110-2-2100&quot;&amp;gt;[[Stability of Concrete Structures (EM 1110-2-2100) | Stability of Concrete Structures (EM 1110-2-2100), USACE, 2005]]&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&quot;Both new and existing structures are constantly being examined to determine if they meet [[stability]] criteria. The traditional procedure is to evaluate [[Sliding Stability|sliding stability]] of these structures using the limit equilibrium method of analysis and to evaluate [[Rotational Stability|rotational stability]] using rigid body assumptions and bearing pressure distributions that vary linearly across the base. Soil and uplift loads on the structure are often based on simplifying assumptions. In the limit equilibrium method, only the stress at failure is considered, usually as represented by the Mohr-Coulomb limit-state criterion. The simplified loads and the Mohr-Coulomb limit-state criterion are then used to obtain a single overall factor of safety against a [[Sliding Stability|sliding stability]] failure. This traditional approach is appropriate for many structures where it is difficult to predict just how a particular failure [[mechanism]] may develop. However, for existing structures where more is known about service state conditions and uplift pressures, it is possible to more precisely predict what stress changes must occur to develop a failure condition. The margin of safety can be more accurately determined when the path to failure, from initial stress conditions to limit state conditions, is known. This path to failure can be investigated using linear elastic and nonlinear finite-element numerical solutions and facture mechanics concepts. Because the deformation of the structure and its foundation is considered in finite element analyses, and because the path to failure can be more realistically characterized through facture mechanics, a more accurate assessment of safety can often be made using advanced analytical methods.&quot;&amp;lt;ref name=&quot;EM 1110-2-2100&quot;&amp;gt;[[Stability &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Analysis &lt;/ins&gt;of Concrete Structures (EM 1110-2-2100) | Stability of Concrete Structures (EM 1110-2-2100), USACE, 2005]]&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[&lt;/del&gt;Best Practices Resources&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;]]&lt;/del&gt;==  &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Best Practices Resources==  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{Document Icon}} [[Stability of Concrete Structures (EM 1110-2-2100) | Stability of Concrete Structures (EM 1110-2-2100), USACE&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;, 2005]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{Document Icon}} [[Stability &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Analysis &lt;/ins&gt;of Concrete Structures (EM 1110-2-2100) | Stability &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Analysis &lt;/ins&gt;of Concrete Structures (EM 1110-2-2100), USACE]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{Document Icon}} [[Evaluation and Comparison of Stability Analysis and Uplift Criteria for Concrete Gravity Dams by Three Federal Agencies (ERDC/ITL TR-00-1) | Evaluation and Comparison of Stability Analysis and Uplift Criteria for Concrete Gravity Dams by Three Federal Agencies (ERDC/ITL TR-00-1), USACE, 2000&lt;/del&gt;]]&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{Document Icon}} [[Gravity Dam Design (EM 1110-2-2200) | Gravity Dam Design (EM 1110-2-2200), USACE, 1995]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{Document Icon}} [[Gravity Dam Design (EM 1110-2-2200) | Gravity Dam Design (EM 1110-2-2200), USACE, 1995]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{Document Icon}} [[Arch Dam Design (EM 1110-2-2201) | Arch Dam Design (EM 1110-2-2201), USACE, 1994]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{Document Icon}} [[Arch Dam Design (EM 1110-2-2201) | Arch Dam Design (EM 1110-2-2201), USACE, 1994]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{Document Icon}} [[Design of Small Dams | Design of Small Dams, USBR, 1987]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{Document Icon}} [[Design of Small Dams | Design of Small Dams, USBR, 1987]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{Document Icon}} [[Sliding Stability for Concrete Structures (ETL &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;11102&lt;/del&gt;-256) | Sliding Stability for Concrete Structures (ETL &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;11102&lt;/del&gt;-256), USACE, 1981]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{Document Icon}} [[Sliding Stability for Concrete Structures (ETL &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;1110-2&lt;/ins&gt;-256) | Sliding Stability for Concrete Structures (ETL &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;1110-2&lt;/ins&gt;-256), USACE, 1981]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[&lt;/del&gt;Trainings&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;]]&lt;/del&gt;==  &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Trainings==  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{Video Icon}} [[On-Demand Webinar: Stability Evaluations of Concrete Dams]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{Video Icon}} [[On-Demand Webinar: Stability Evaluations of Concrete Dams]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{Video Icon}} [[On-Demand Webinar: Analysis of Concrete Arch Dams]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{Video Icon}} [[On-Demand Webinar: Analysis of Concrete Arch Dams]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Grichards</name></author>
	</entry>
	<entry>
		<id>https://damtoolbox.org/index.php?title=Linear_vs._Non-linear&amp;diff=4632&amp;oldid=prev</id>
		<title>Rmanwaring at 23:56, 29 November 2022</title>
		<link rel="alternate" type="text/html" href="https://damtoolbox.org/index.php?title=Linear_vs._Non-linear&amp;diff=4632&amp;oldid=prev"/>
		<updated>2022-11-29T23:56:34Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 23:56, 29 November 2022&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l13&quot;&gt;Line 13:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 13:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;!-- Introductory paragraph or topic page summary --&amp;gt;  &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;!-- Introductory paragraph or topic page summary --&amp;gt;  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&quot;Both new and existing structures are constantly being examined to determine if they meet [[stability]] criteria. The traditional procedure is to evaluate [[Sliding Stability|sliding stability]] of these structures using the limit equilibrium method of analysis and to evaluate [[Rotational Stability|rotational stability]] using rigid body assumptions and bearing pressure distributions that vary linearly across the base. Soil and uplift loads on the structure are often based on simplifying assumptions. In the limit equilibrium method, only the stress at failure is considered, usually as represented by the Mohr-Coulomb limit-state criterion. The simplified loads and the Mohr-Coulomb limit-state criterion are then used to obtain a single overall factor of safety against a sliding stability failure. This traditional approach is appropriate for many structures where it is difficult to predict just how a particular failure [[mechanism]] may develop. However, for existing structures where more is known about service state conditions and uplift pressures, it is possible to more precisely predict what stress changes must occur to develop a failure condition. The margin of safety can be more accurately determined when the path to failure, from initial stress conditions to limit state conditions, is known. This path to failure can be investigated using linear elastic and nonlinear finite-element numerical solutions and facture mechanics concepts. Because the deformation of the structure and its foundation is considered in finite element analyses, and because the path to failure can be more realistically characterized through facture mechanics, a more accurate assessment of safety can often be made using advanced analytical methods.&quot;&amp;lt;ref name=&quot;EM 1110-2-2100&quot;&amp;gt;[[Stability of Concrete Structures (EM 1110-2-2100) | Stability of Concrete Structures (EM 1110-2-2100), USACE, 2005]]&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&quot;Both new and existing structures are constantly being examined to determine if they meet [[stability]] criteria. The traditional procedure is to evaluate [[Sliding Stability|sliding stability]] of these structures using the limit equilibrium method of analysis and to evaluate [[Rotational Stability|rotational stability]] using rigid body assumptions and bearing pressure distributions that vary linearly across the base. Soil and uplift loads on the structure are often based on simplifying assumptions. In the limit equilibrium method, only the stress at failure is considered, usually as represented by the Mohr-Coulomb limit-state criterion. The simplified loads and the Mohr-Coulomb limit-state criterion are then used to obtain a single overall factor of safety against a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Sliding Stability|&lt;/ins&gt;sliding stability&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;]] &lt;/ins&gt;failure. This traditional approach is appropriate for many structures where it is difficult to predict just how a particular failure [[mechanism]] may develop. However, for existing structures where more is known about service state conditions and uplift pressures, it is possible to more precisely predict what stress changes must occur to develop a failure condition. The margin of safety can be more accurately determined when the path to failure, from initial stress conditions to limit state conditions, is known. This path to failure can be investigated using linear elastic and nonlinear finite-element numerical solutions and facture mechanics concepts. Because the deformation of the structure and its foundation is considered in finite element analyses, and because the path to failure can be more realistically characterized through facture mechanics, a more accurate assessment of safety can often be made using advanced analytical methods.&quot;&amp;lt;ref name=&quot;EM 1110-2-2100&quot;&amp;gt;[[Stability of Concrete Structures (EM 1110-2-2100) | Stability of Concrete Structures (EM 1110-2-2100), USACE, 2005]]&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==[[Best Practices Resources]]==  &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==[[Best Practices Resources]]==  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l21&quot;&gt;Line 21:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 21:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{Document Icon}} [[Arch Dam Design (EM 1110-2-2201) | Arch Dam Design (EM 1110-2-2201), USACE, 1994]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{Document Icon}} [[Arch Dam Design (EM 1110-2-2201) | Arch Dam Design (EM 1110-2-2201), USACE, 1994]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{Document Icon}} [[Design of Small Dams | Design of Small Dams, USBR, 1987]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{Document Icon}} [[Design of Small Dams | Design of Small Dams, USBR, 1987]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{Document Icon}} [[Sliding Stability for Concrete Structures (ETL 11102-256) | Sliding Stability for Concrete Structures (ETL 11102-256), USACE, 1981]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==[[Trainings]]==  &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==[[Trainings]]==  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Rmanwaring</name></author>
	</entry>
	<entry>
		<id>https://damtoolbox.org/index.php?title=Linear_vs._Non-linear&amp;diff=4631&amp;oldid=prev</id>
		<title>Rmanwaring at 23:55, 29 November 2022</title>
		<link rel="alternate" type="text/html" href="https://damtoolbox.org/index.php?title=Linear_vs._Non-linear&amp;diff=4631&amp;oldid=prev"/>
		<updated>2022-11-29T23:55:15Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 23:55, 29 November 2022&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l13&quot;&gt;Line 13:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 13:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;!-- Introductory paragraph or topic page summary --&amp;gt;  &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;!-- Introductory paragraph or topic page summary --&amp;gt;  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&quot;Both new and existing structures are constantly being examined to determine if they meet [[stability]] criteria. The traditional procedure is to evaluate sliding stability of these structures using the limit equilibrium method of analysis and to evaluate rotational stability using rigid body assumptions and bearing pressure distributions that vary linearly across the base. Soil and uplift loads on the structure are often based on simplifying assumptions. In the limit equilibrium method, only the stress at failure is considered, usually as represented by the Mohr-Coulomb limit-state criterion. The simplified loads and the Mohr-Coulomb limit-state criterion are then used to obtain a single overall factor of safety against a sliding stability failure. This traditional approach is appropriate for many structures where it is difficult to predict just how a particular failure [[mechanism]] may develop. However, for existing structures where more is known about service state conditions and uplift pressures, it is possible to more precisely predict what stress changes must occur to develop a failure condition. The margin of safety can be more accurately determined when the path to failure, from initial stress conditions to limit state conditions, is known. This path to failure can be investigated using linear elastic and nonlinear finite-element numerical solutions and facture mechanics concepts. Because the deformation of the structure and its foundation is considered in finite element analyses, and because the path to failure can be more realistically characterized through facture mechanics, a more accurate assessment of safety can often be made using advanced analytical methods.&quot;&amp;lt;ref name=&quot;EM 1110-2-2100&quot;&amp;gt;[[Stability of Concrete Structures (EM 1110-2-2100) | Stability of Concrete Structures (EM 1110-2-2100), USACE, 2005]]&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&quot;Both new and existing structures are constantly being examined to determine if they meet [[stability]] criteria. The traditional procedure is to evaluate &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Sliding Stability|&lt;/ins&gt;sliding stability&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;]] &lt;/ins&gt;of these structures using the limit equilibrium method of analysis and to evaluate &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Rotational Stability|&lt;/ins&gt;rotational stability&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;]] &lt;/ins&gt;using rigid body assumptions and bearing pressure distributions that vary linearly across the base. Soil and uplift loads on the structure are often based on simplifying assumptions. In the limit equilibrium method, only the stress at failure is considered, usually as represented by the Mohr-Coulomb limit-state criterion. The simplified loads and the Mohr-Coulomb limit-state criterion are then used to obtain a single overall factor of safety against a sliding stability failure. This traditional approach is appropriate for many structures where it is difficult to predict just how a particular failure [[mechanism]] may develop. However, for existing structures where more is known about service state conditions and uplift pressures, it is possible to more precisely predict what stress changes must occur to develop a failure condition. The margin of safety can be more accurately determined when the path to failure, from initial stress conditions to limit state conditions, is known. This path to failure can be investigated using linear elastic and nonlinear finite-element numerical solutions and facture mechanics concepts. Because the deformation of the structure and its foundation is considered in finite element analyses, and because the path to failure can be more realistically characterized through facture mechanics, a more accurate assessment of safety can often be made using advanced analytical methods.&quot;&amp;lt;ref name=&quot;EM 1110-2-2100&quot;&amp;gt;[[Stability of Concrete Structures (EM 1110-2-2100) | Stability of Concrete Structures (EM 1110-2-2100), USACE, 2005]]&amp;lt;/ref&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==[[Best Practices Resources]]==  &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==[[Best Practices Resources]]==  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{Document Icon}} [[Stability of Concrete Structures (EM 1110-2-2100) | Stability of Concrete Structures (EM 1110-2-2100), USACE, 2005]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{Document Icon}} [[Stability of Concrete Structures (EM 1110-2-2100) | Stability of Concrete Structures (EM 1110-2-2100), USACE, 2005]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{Document Icon}} [[Evaluation and Comparison of Stability Analysis and Uplift Criteria for Concrete Gravity Dams by Three Federal Agencies (ERDC/ITL TR-00-1) | Evaluation and Comparison of Stability Analysis and Uplift Criteria for Concrete Gravity Dams by Three Federal Agencies (ERDC/ITL TR-00-1), USACE, 2000]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{Document Icon}} [[Gravity Dam Design (EM 1110-2-2200) | Gravity Dam Design (EM 1110-2-2200), USACE, 1995]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{Document Icon}} [[Arch Dam Design (EM 1110-2-2201) | Arch Dam Design (EM 1110-2-2201), USACE, 1994]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{Document Icon}} [[Design of Small Dams | Design of Small Dams, USBR, 1987]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br/&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==[[Trainings]]==  &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==[[Trainings]]==  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Rmanwaring</name></author>
	</entry>
	<entry>
		<id>https://damtoolbox.org/index.php?title=Linear_vs._Non-linear&amp;diff=4630&amp;oldid=prev</id>
		<title>Rmanwaring: Created page with &quot;&lt;!-- Delete any sections that are not necessary to your topic. Add pictures/sections as needed --&gt;  __NOTOC__   &lt;!-- Add Category to drive breadcrumb menus --&gt;    Category: Global Stability of a Dam  {| align=&quot;right&quot; style=&quot;width:10%;&quot; cellpadding=&quot;7&quot; | link=https://damfailures.org/lessons-learned/concrete-gravity-dams-should-be-evaluated-to-accommodate-full-uplift/ |- |style=&quot;text-align:center; font-size:90%;&quot;| Learn more...&quot;</title>
		<link rel="alternate" type="text/html" href="https://damtoolbox.org/index.php?title=Linear_vs._Non-linear&amp;diff=4630&amp;oldid=prev"/>
		<updated>2022-11-29T23:51:25Z</updated>

		<summary type="html">&lt;p&gt;Created page with &amp;quot;&amp;lt;!-- Delete any sections that are not necessary to your topic. Add pictures/sections as needed --&amp;gt;  __NOTOC__   &amp;lt;!-- Add Category to drive breadcrumb menus --&amp;gt;    &lt;a href=&quot;/index.php?title=Category:Global_Stability_of_a_Dam&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;Category:Global Stability of a Dam (page does not exist)&quot;&gt;Category: Global Stability of a Dam&lt;/a&gt;  {| align=&amp;quot;right&amp;quot; style=&amp;quot;width:10%;&amp;quot; cellpadding=&amp;quot;7&amp;quot; | &lt;a href=&quot;/wiki/File:GravityDamUplift1.png&quot; title=&quot;File:GravityDamUplift1.png&quot;&gt;350px|x350px|link=https://damfailures.org/lessons-learned/concrete-gravity-dams-should-be-evaluated-to-accommodate-full-uplift/&lt;/a&gt; |- |style=&amp;quot;text-align:center; font-size:90%;&amp;quot;| Learn more...&amp;quot;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;&amp;lt;!-- Delete any sections that are not necessary to your topic. Add pictures/sections as needed --&amp;gt; &lt;br /&gt;
__NOTOC__ &lt;br /&gt;
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&amp;lt;!-- Add Category to drive breadcrumb menus --&amp;gt;  &lt;br /&gt;
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[[Category: Global Stability of a Dam]]&lt;br /&gt;
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{| align=&amp;quot;right&amp;quot; style=&amp;quot;width:10%;&amp;quot; cellpadding=&amp;quot;7&amp;quot;&lt;br /&gt;
| [[Image:GravityDamUplift1.png|350px|x350px|link=https://damfailures.org/lessons-learned/concrete-gravity-dams-should-be-evaluated-to-accommodate-full-uplift/]]&lt;br /&gt;
|-&lt;br /&gt;
|style=&amp;quot;text-align:center; font-size:90%;&amp;quot;| Learn more [[about]] the need to consider uplift pressure when designing a gravity structure at [https://damfailures.org/lessons-learned/concrete-gravity-dams-should-be-evaluated-to-accommodate-full-uplift/ DamFailures.org]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&amp;lt;!-- Introductory paragraph or topic page summary --&amp;gt; &lt;br /&gt;
&amp;quot;Both new and existing structures are constantly being examined to determine if they meet [[stability]] criteria. The traditional procedure is to evaluate sliding stability of these structures using the limit equilibrium method of analysis and to evaluate rotational stability using rigid body assumptions and bearing pressure distributions that vary linearly across the base. Soil and uplift loads on the structure are often based on simplifying assumptions. In the limit equilibrium method, only the stress at failure is considered, usually as represented by the Mohr-Coulomb limit-state criterion. The simplified loads and the Mohr-Coulomb limit-state criterion are then used to obtain a single overall factor of safety against a sliding stability failure. This traditional approach is appropriate for many structures where it is difficult to predict just how a particular failure [[mechanism]] may develop. However, for existing structures where more is known about service state conditions and uplift pressures, it is possible to more precisely predict what stress changes must occur to develop a failure condition. The margin of safety can be more accurately determined when the path to failure, from initial stress conditions to limit state conditions, is known. This path to failure can be investigated using linear elastic and nonlinear finite-element numerical solutions and facture mechanics concepts. Because the deformation of the structure and its foundation is considered in finite element analyses, and because the path to failure can be more realistically characterized through facture mechanics, a more accurate assessment of safety can often be made using advanced analytical methods.&amp;quot;&amp;lt;ref name=&amp;quot;EM 1110-2-2100&amp;quot;&amp;gt;[[Stability of Concrete Structures (EM 1110-2-2100) | Stability of Concrete Structures (EM 1110-2-2100), USACE, 2005]]&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==[[Best Practices Resources]]== &lt;br /&gt;
{{Document Icon}} [[Stability of Concrete Structures (EM 1110-2-2100) | Stability of Concrete Structures (EM 1110-2-2100), USACE, 2005]]&lt;br /&gt;
&lt;br /&gt;
==[[Trainings]]== &lt;br /&gt;
{{Video Icon}} [[On-Demand Webinar: Stability Evaluations of Concrete Dams]]&lt;br /&gt;
{{Video Icon}} [[On-Demand Webinar: Analysis of Concrete Arch Dams]]&lt;br /&gt;
&lt;br /&gt;
&amp;lt;!-- In the location of an in text citation, simply enclose the citation as follows: &amp;lt;ref&amp;gt; citation &amp;lt;/ref&amp;gt;. Citations will automatically populate. Learn more at https://www.mediawiki.org/wiki/Help:Cite.--&amp;gt; &lt;br /&gt;
{{Citations}} &lt;br /&gt;
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&amp;lt;!-- Revision history information --&amp;gt; &lt;br /&gt;
{{revhistinf}}&lt;/div&gt;</summary>
		<author><name>Rmanwaring</name></author>
	</entry>
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