Feng et al 2024a - Revision history

Rimni at 13:01, 12 February 2024

2024-02-12T13:01:02Z

Rimni at 12:58, 12 February 2024

2024-02-12T12:58:37Z

Rimni at 12:51, 12 February 2024

2024-02-12T12:51:52Z

Rimni at 12:50, 12 February 2024

2024-02-12T12:50:45Z

Rimni: /* 3.1.2 Failure stage */

2024-02-12T12:48:29Z

‎3.1.2 Failure stage

Rimni: /* 3.1.1 Undamaged stage */

2024-02-08T15:34:14Z

‎3.1.1 Undamaged stage

Rimni: /* 3.1.1 Undamaged stage */

2024-02-08T15:33:29Z

‎3.1.1 Undamaged stage

Rimni at 15:13, 7 February 2024

2024-02-07T15:13:50Z

Show changes

Rimni at 14:18, 7 February 2024

2024-02-07T14:18:49Z

Rimni at 14:18, 7 February 2024

2024-02-07T14:18:29Z

@@ Line 517: / Line 517: @@
 |-
 | <math>\left\{ \begin{array}{c}
-{u_3\left(t^{{''}},z\right)\vert }_{z=0}=q\mbox{e}^{-bt_1}\mbox{e}^{-bt^{{''}}}\mbox{ }\\
+{u_3\left(t^{{''}},z\right)\Big| }_{z=0}=q\mbox{e}^{-bt_1}\mbox{e}^{-bt^{{''}}}\mbox{ }\\
-{\frac{\partial u_3\left(t^{{''}},z\right)}{\partial z}\vert }_{z=H}\mbox{ }\mbox{ }=0
+{\displaystyle\frac{\partial u_3\left(t^{{''}},z\right)}{\partial z}\Big| }_{z=H}\mbox{ }\mbox{ }=0
 \end{array}\right.</math>
 |}
@@ Line 532: / Line 532: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <math>{u_3(t^{{''}},z)\vert }_{t^{{''}}=0}={u_2^1\left(t^{{'}},z\right)\vert }_{t^{{'}}=t_1-t_0}\mbox{=}{\sigma }_3\left(z\right)</math>
+| <math>{u_3(t^{{''}},z)\Big| }_{t^{{''}}=0}={u_2^1\left(t^{{'}},z\right)\Big| }_{t^{{'}}=t_1-t_0}\mbox{=}{\sigma }_3\left(z\right)</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (29)
@@ Line 571: / Line 571: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <math>{v_3\left(t^{{''}},z\right)\vert }_{z=0}=0,\mbox{ }{\frac{\partial v_3\left(t^{{''}},z\right)}{\partial z}\vert }_{z=H}\mbox{ }\mbox{ }=</math><math>0</math>
+| <math>{v_3\left(t^{{''}},z\right)\Big| }_{z=0}=0,\mbox{ }{\frac{\partial v_3\left(t^{{''}},z\right)}{\partial z}\Big| }_{z=H}\mbox{ }\mbox{ }=</math><math>0</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (32)
@@ Line 581: / Line 581: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <math>{v_3(t^{{''}},z)\vert }_{t^{{''}}=0}={\sigma }^{{''}}\left(z\right)=</math><math>{\sigma }_3\left(z\right)-q\mbox{e}^{-bt_1}</math>
+| <math>{v_3(t^{{''}},z)\Big| }_{t^{{''}}=0}={\sigma }^{{''}}\left(z\right)={\sigma }_3\left(z\right)-q\mbox{e}^{-bt_1}</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (33)

@@ Line 236: / Line 236: @@
 | <span id='ZEqnNum370091'></span>  <math>\left\{ \begin{array}{c}
 {u_2^1\Big|}_{z=h_1}={u_2^2\Big|}_{z=h_1}\\
-{k_{\mbox{v1}}\frac{\partial u_2^1}{\partial z}\Big| }_{z=h_1}={k_{\mbox{v2}}\frac{\partial u_2^2}{\partial z}\Big| }_{z=h_1}
+{k_{\mbox{v1}}\displaystyle\frac{\partial u_2^1}{\partial z}\Big| }_{z=h_1}={k_{\mbox{v2}}\displaystyle\frac{\partial u_2^2}{\partial z}\Big| }_{z=h_1}
 \end{array}\right.</math>
 |}

@@ Line 398: / Line 398: @@
 | <span id='ZEqnNum405293'></span>  <math>{\int }_0^{H_t}m_{\mbox{v1}}g_{m1}\left(z\right)\cdot g_{n1}\left(z\right)\mbox{d}z+</math><math>{\int }_{H_t}^Hm_{\mbox{v2}}g_{m2}\left(z\right)g_{n2}\left(z\right)\mbox{d}z=</math><math>\left\{ \begin{array}{c}
 \mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\mbox{ }\left(m\not =n\right)\\
-\frac{1}{2}Hm_{\mbox{v1}}\left({\rho }_1+\eta {\rho }_2A_m{}^2\right)\mbox{ }\left(m=n\right)
+\displaystyle\frac{1}{2}Hm_{\mbox{v1}}\left({\rho }_1+\eta {\rho }_2A_m{}^2\right)\mbox{ }\left(m=n\right)
 \end{array}\right.</math>
 |}

@@ Line 278: / Line 278: @@
 | style="text-align: center;" |<math>\left\{ \begin{array}{c}
 {v_1\left(t',z\right)\Big|}_{z=0}=0\\
-{\frac{\partial v_2\left(t',z\right)}{\partial z}\Big| }_{z=H}\mbox{ }\mbox{ }=0
+{\displaystyle\frac{\partial v_2\left(t',z\right)}{\partial z}\Big| }_{z=H}\mbox{ }\mbox{ }=0
 \end{array}\right.</math>
 |}
@@ Line 309: / Line 309: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <math>{k_{\mbox{v1}}\frac{\partial v_1}{\partial z}\vert }_{z=h_1}=</math><math>{k_{\mbox{v2}}\frac{\partial v_2}{\partial z}\vert }_{z=h_1}</math>
+| <math>{k_{\mbox{v1}}\frac{\partial v_1}{\partial z}\Big| }_{z=h_1}={k_{\mbox{v2}}\frac{\partial v_2}{\partial z}\Big| }_{z=h_1}</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (14)

@@ Line 219: / Line 219: @@
 |-
 | <math>\left\{ \begin{array}{c}
-{u_2^1\left(t',z\right)\vert }_{z=0}=q\mbox{e}^{-b\left(t'+t_0\right)}\\
+{u_2^1\left(t',z\right)\Big| }_{z=0}=q\mbox{e}^{-b\left(t'+t_0\right)}\\
-{\frac{\partial u_2^2\left(t',z\right)}{\partial z}\vert }_{z=H}\mbox{ }=0
+{\frac{\partial u_2^2\left(t',z\right)}{\partial z}\Big| }_{z=H}\mbox{ }=0
 \end{array}\right.</math>
 |}
@@ Line 235: / Line 235: @@
 |-
 | <span id='ZEqnNum370091'></span>  <math>\left\{ \begin{array}{c}
-{u_2^1\vert }_{z=h_1}={u_2^2\vert }_{z=h_1}\\
+{u_2^1\Big|}_{z=h_1}={u_2^2\Big|}_{z=h_1}\\
-{k_{\mbox{v1}}\frac{\partial u_2^1}{\partial z}\vert }_{z=h_1}={k_{\mbox{v2}}\frac{\partial u_2^2}{\partial z}\vert }_{z=h_1}
+{k_{\mbox{v1}}\frac{\partial u_2^1}{\partial z}\Big| }_{z=h_1}={k_{\mbox{v2}}\frac{\partial u_2^2}{\partial z}\Big| }_{z=h_1}
 \end{array}\right.</math>
 |}
@@ Line 277: / Line 277: @@
 |-
 | style="text-align: center;" |<math>\left\{ \begin{array}{c}
-{v_1\left(t',z\right)\vert }_{z=0}=0\\
+{v_1\left(t',z\right)\Big|}_{z=0}=0\\
-{\frac{\partial v_2\left(t',z\right)}{\partial z}\vert }_{z=H}\mbox{ }\mbox{ }=0
+{\frac{\partial v_2\left(t',z\right)}{\partial z}\Big| }_{z=H}\mbox{ }\mbox{ }=0
 \end{array}\right.</math>
 |}
@@ Line 289: / Line 289: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <span id='ZEqnNum310255'></span>  <math>{v_i(t',z)\vert }_{t'=0}={\sigma }_2\left(z\right)-</math><math>q\mbox{e}^{-b\left(t'+t_0\right)}\mbox{=}{\sigma }'\left(z\right)</math>
+| <span id='ZEqnNum310255'></span>  <math>{v_i(t',z)\Big| }_{t'=0}={\sigma }_2\left(z\right)-</math><math>q\mbox{e}^{-b\left(t'+t_0\right)}\mbox{=}{\sigma }'\left(z\right)</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (12)
@@ Line 299: / Line 299: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <math>{v_1\vert }_{z=h_1}={v_2\vert }_{z=h_1}</math>
+| <math>{v_1\Big| }_{z=h_1}={v_2\Big|}_{z=h_1}</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (13)

@@ Line 155: / Line 155: @@
 | <math>\left\{ \begin{array}{c}
 {u_1\Big| }_{z=0}=q\left(t\right)\mbox{e}^{-bt}\\
-{\frac{\partial u_1}{\partial t}\Big| }_{z=H}=0
+{\displaystyle\frac{\partial u_1}{\partial t}\Big| }_{z=H}=0
 \end{array}\right.</math>
 |}

@@ Line 842: / Line 842: @@
 The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
-===Acknowledgements===
+==Acknowledgements==
 This work was supported by the National Natural Science Foundation of China (52008124, 52268054 and 52208345), the China Postdoctoral Science Foundation (2020M683210), and the Natural Science Foundation of Guangxi Province (2021AC18008).

@@ Line 838: / Line 838: @@
 (4) For remolded soil, without considering the three failure stages, the degree of consolidation can be underestimated, leading to extremely conservative design in practice of ground improvement.
-===Declaration of interests===
+==Declaration of interests==
 The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.