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Coastal Wiki - Changes related to "Coastal and marine sediments" [en]
2024-03-29T08:11:15Z
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https://www.coastalwiki.org/w/index.php?title=Wave-induced_soil_liquefaction&diff=80915&oldid=80612
Wave-induced soil liquefaction
2024-03-07T16:38:26Z
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 16:38, 7 March 2024</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1" >Line 1:</td>
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<tr><td class='diff-marker'>−</td><td style="color: #222; 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;"><div><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; 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;"><div><del style="font-weight: bold; text-decoration: none;">'''Article under review'''</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; 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;"><div><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; 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;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; 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;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; 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;"><div>{{ Definition| title = Soil liquefaction</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; 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;"><div>{{ Definition| title = Soil liquefaction</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l90" >Line 90:</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; 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;"><div>The volume compression implies a change in the volumetric strain (also called 'bulk strain') <math>d\epsilon=\Large\frac{1}{V}\normalsize (dV_1+dV_2)</math>,  </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; 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;"><div>The volume compression implies a change in the volumetric strain (also called 'bulk strain') <math>d\epsilon=\Large\frac{1}{V}\normalsize (dV_1+dV_2)</math>,  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; 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;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; 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;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; 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;"><div><math>\Large\frac{d \epsilon}{dt}\normalsize = \Large\frac{n}{\beta}\frac{\partial p}{\partial t}\normalsize + \Large\frac{k}{\rho g}\frac{\partial^2 p}{\partial^2 <del class="diffchange diffchange-inline">z</del>}\normalsize . \qquad (2)</math>   </div></td><td class='diff-marker'>+</td><td style="color: #222; 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;"><div><math>\Large\frac{d \epsilon}{dt}\normalsize = \Large\frac{n}{\beta}\frac{\partial p}{\partial t}\normalsize + \Large\frac{k}{\rho g}\frac{\partial^2 p}{\partial <ins class="diffchange diffchange-inline">z</ins>^2}\normalsize . \qquad (2)</math>   </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; 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;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; 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;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; 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;"><div>The soil is considered a poroelastic medium for which [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's law] applies. The volumetric strain <math>\epsilon</math> (degree of soil compression) is then linearly related to the effective stress (inter-grain stress) <math>\sigma'</math> by the formula  </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; 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;"><div>The soil is considered a poroelastic medium for which [https://en.wikipedia.org/wiki/Hooke%27s_law Hooke's law] applies. The volumetric strain <math>\epsilon</math> (degree of soil compression) is then linearly related to the effective stress (inter-grain stress) <math>\sigma'</math> by the formula  </div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l107" >Line 107:</td>
<td colspan="2" class="diff-lineno">Line 104:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; 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;"><div><math>p(x,z,t) = p_{seafloor} + \large\frac{m}{1+m}\normalsize p_0 \Bigg[- \cos \Big( 2 \pi (\large\frac{x}{L}-\frac{t}{T}\normalsize)\Big)  +  e^{-\Large\frac{z}{d}\normalsize} \cos \Big( 2 \pi \large (\frac{x}{L}-\frac{t}{T})+\frac{z}{d}\normalsize\Big) \Bigg] .\qquad (5)</math></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; 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;"><div><math>p(x,z,t) = p_{seafloor} + \large\frac{m}{1+m}\normalsize p_0 \Bigg[- \cos \Big( 2 \pi (\large\frac{x}{L}-\frac{t}{T}\normalsize)\Big)  +  e^{-\Large\frac{z}{d}\normalsize} \cos \Big( 2 \pi \large (\frac{x}{L}-\frac{t}{T})+\frac{z}{d}\normalsize\Big) \Bigg] .\qquad (5)</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; 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;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; 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;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; 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;"><div>This expression is only valid near the soil surface, as the amplitude <math>p_0</math> of the wave-induced pressure fluctuation is a gradually decreasing function of depth. The depth <math>d</math> is given by</div></td><td class='diff-marker'>+</td><td style="color: #222; 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;"><div>This expression is only valid near the soil surface <ins class="diffchange diffchange-inline">(<math>z << L</math>)</ins>, as the amplitude <math>p_0</math> of the wave-induced pressure fluctuation is a gradually decreasing function of depth. The depth <math>d</math> is given by</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; 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;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; 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;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; 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;"><div><math>d = \Big( \Large\frac{T \, c_v}{\pi}\normalsize \Big)^{1/2} = \Big( \Large\frac{T \, k \, \beta \, m}{\pi \, \rho \, n \, g \, (1+m)}\normalsize \Big)^{1/2}  . \qquad (6)</math>  </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; 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;"><div><math>d = \Big( \Large\frac{T \, c_v}{\pi}\normalsize \Big)^{1/2} = \Big( \Large\frac{T \, k \, \beta \, m}{\pi \, \rho \, n \, g \, (1+m)}\normalsize \Big)^{1/2}  . \qquad (6)</math>  </div></td></tr>
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