Zhang et al 2023a - Revision history

Rimni at 07:22, 9 June 2023

2023-06-09T07:22:09Z

Rimni at 07:21, 9 June 2023

2023-06-09T07:21:32Z

Rimni at 07:19, 9 June 2023

2023-06-09T07:19:47Z

Rimni at 13:05, 7 June 2023

2023-06-07T13:05:03Z

Rimni at 13:04, 7 June 2023

2023-06-07T13:04:16Z

Rimni at 14:32, 6 June 2023

2023-06-06T14:32:35Z

Rimni: /* 6. Reconsolidation settlement of goundation after earthquake */

2023-06-06T13:34:06Z

‎6. Reconsolidation settlement of goundation after earthquake

Rimni at 13:32, 6 June 2023

2023-06-06T13:32:46Z

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Rimni at 12:08, 6 June 2023

2023-06-06T12:08:28Z

Rimni at 12:00, 6 June 2023

2023-06-06T12:00:21Z

@@ Line 173: / Line 173: @@
 |}
-where  <math display="inline">\alpha =\left(1-\lambda +\lambda \chi \right)/\left(1- \lambda \right)</math> .
+where  <math display="inline">\alpha =\left(1-\lambda +\lambda \chi \right)/\left(1- \lambda \right)</math>.
 ===2.3 Solving conditions===

@@ Line 110: / Line 110: @@
 |}
-where  <math>\lambda =\pi r_0^2/\left(\pi r_\mbox{e}^2\right)</math>, and  <math>\chi =E_{p}/E_{s}</math> .
+where  <math>\lambda =\pi r_0^2/\left(\pi r_\mbox{e}^2\right)</math>, and  <math>\chi =E_{p}/E_{s}</math>.
 The rate of change of total stress  <math>\partial \sigma /\partial t</math> is regarded as the rate of excess pore pressure induced by earthquake [14], that is

@@ Line 584: / Line 584: @@
 [13] Chen X., Xiang N., Li C. Influence of higher-order modes of slender tall pier bridge columns on the seismic performance of pile foundations. Soil Dynamics and Earthquake Engineering, 142, 106543, 2021.
-[14] Xu Z. Calculation of pore pressure of sand foundation in resistance to seismic liquefaction by gravel drainage pile (in Chinese). Earthquake Engineering and Engineering Vibration, 12(4):88-92, 1992.
+[14] Xu Z. Calculation of pore pressure of liquefiable sand deposits using gravel drains (in Chinese). Earthquake Engineering and Engineering Vibration, 12(4):88-92, 1992.
 [15] Seed H.B., Booker J.R. Stabilization of potentially liquefiable sand deposits using gravel drains. Journal of the Geotechnical Engineering Division, 103(7):757-768, 1977.

@@ Line 184: / Line 184: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <math>{{\overline{u}}_{s}\Bigg\} }_{t=0}=0</math>
+| <math>{{\overline{u}}_{s}\Bigg| }_{t=0}=0</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (7)
@@ Line 197: / Line 197: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <math>{{\overline{u}}_{s}\vert }_{z=0}={\frac{\partial {\overline{u}}_{s}}{\partial z}\Bigg\} }_{z=H}=</math><math>0</math>
+| <math>{{\overline{u}}_{s}\Bigg| }_{z=0}={\frac{\partial {\overline{u}}_{s}}{\partial z}\Bigg| }_{z=H}=</math><math>0</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (8)

@@ Line 184: / Line 184: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <math>{{\overline{u}}_{s}\vert }_{t=0}=0</math>
+| <math>{{\overline{u}}_{s}\Bigg\} }_{t=0}=0</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (7)
@@ Line 197: / Line 197: @@
 {| style="text-align: center; margin:auto;"
 |-
-| <math>{{\overline{u}}_{s}\vert }_{z=0}={\frac{\partial {\overline{u}}_{s}}{\partial z}\vert }_{z=H}=</math><math>0</math>
+| <math>{{\overline{u}}_{s}\vert }_{z=0}={\frac{\partial {\overline{u}}_{s}}{\partial z}\Bigg\} }_{z=H}=</math><math>0</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (8)
 |}
 ===2.4 Normalization===

@@ Line 559: / Line 559: @@
-[1] Xu Chengshun, Dou Pengfei, Du Xiuli, et al. Seismic performance of pile group-structure system in liquefiable and non-liquefiable soil from large-scale shake table tests. Soil Dynamics and Earthquake Engineering, 2020, 138, 106299.
+[1] Xu C., Dou P., Du X., et al. Seismic performance of pile group-structure system in liquefiable and non-liquefiable soil from large-scale shake table tests. Soil Dynamics and Earthquake Engineering, 138, 106299, 2020.
-[2] Finn WDL, Fujita N. Piles in liquefiable soils: seismic analysis and design issues. Soil Dynamics and Earthquake Engineering, 2002, 22(9-12), 731-742.
+[2] Finn W.D.L, Fujita N. Piles in liquefiable soils: seismic analysis and design issues. Soil Dynamics and Earthquake Engineering, 22(9-12):731-742, 2002.
-[3] Cubrinovski Misko, Bray Jonathan D, De La Torre Christopher, et al. Liquefaction effects and associated damages observed at the Wellington CentrePort from the 2016 Kaikoura earthquake. Bulletin of the New Zealand Society for Earthquake Engineering, 2017, 50(2), 152-173.
+[3] Cubrinovski M., Bray J.D., De La Torre C., et al. Liquefaction effects and associated damages observed at the Wellington CentrePort from the 2016 Kaikoura earthquake. Bulletin of the New Zealand Society for Earthquake Engineering, 50(2):152-173, 2017.
-[4] Pal Suravi, Deb Kousik. Postearthquake reconsolidation settlement of stone column-treated liquefiable sand. International Journal of Geomechanics, 2020, 20(10), 04020183.
+[4] Pal S., Deb K. Postearthquake reconsolidation settlement of stone column-treated liquefiable sand. International Journal of Geomechanics, 20(10), 04020183, 2020.
-[5] Su Lei, Tang Liang, Ling Xian-zhang, et al. Responses of reinforced concrete pile group in two-layered liquefied soils: shake-table investigations. Journal of Zhejiang University-SCIENCE A, 2015, 2(16), 93-104.
+[5] Su L., Tang L., Ling X.-Z., et al. Responses of reinforced concrete pile group in two-layered liquefied soils: shake-table investigations. Journal of Zhejiang University-SCIENCE A, 2(16):93-104, 2015.
-[6] Knappett JA, Madabhushi SP. Liquefaction-induced settlement of pile groups in liquefiable and laterally spreading soils. Journal of Geotechnical and Geoenvironmental Engineering, 2008, 134(11), 1609-1618.
+[6] Knappett J.A., Madabhushi S.P. Liquefaction-induced settlement of pile groups in liquefiable and laterally spreading soils. Journal of Geotechnical and Geoenvironmental Engineering, 134(11):1609-1618, 2008.
-[7] Bao Xiaohua, Ye Guanlin, Ye Bin, et al. (2014). Seismic Performance of Multi-story Building with Pile Foundation in Liquefiable Ground Including Post-earthquake Consolidation Settlement.  Advances in Soil Dynamics and Foundation Engineering, 353-362.
+[7] Bao X., Ye G., Ye B., et al. Seismic performance of multi-story building with pile foundation in liquefiable ground including post-earthquake consolidation settlement.  Advances in Soil Dynamics and Foundation Engineering, pp. 353-362, Shanghai, China, May 26-28 2014.
-[8] Rollins KM, Strand SR. Downdrag forces due to liquefaction surrounding a pile. Proc. 8th National Conference on Earthquake Engineering, Earthquake Engineering Research Institute, 2006.
+[8] Rollins K.M., Strand S.R. Downdrag forces due to liquefaction surrounding a pile. Proc. 8th National Conference on Earthquake Engineering, Earthquake Engineering Research Institute, Paper No. 1646, San Francisco, CA, April 18-22 2006.
-[9] Chen Xu, Guan Zhongguo, Spencer Jr Billie F, et al. A simplified procedure for estimating nonlinear seismic demand of tall piers. Engineering Structures, 2018, 174, 778-791.
+[9] Chen X., Guan Z., Spencer Jr B.F., et al. A simplified procedure for estimating nonlinear seismic demand of tall piers. Engineering Structures, 174:778-791, 2018.
-[10] Hussein A Fouad, El Naggar M Hesham. Seismic axial behaviour of pile groups in non-liquefiable and liquefiable soils. Soil Dynamics and Earthquake Engineering, 2021, 149, 106853.
+[10] Hussein A.F., El Naggar M.H. Seismic axial behaviour of pile groups in non-liquefiable and liquefiable soils. Soil Dynamics and Earthquake Engineering, 149, 106853, 2021.
-[11] Chiou Jiunn-Shyang, Huang Tzu-Jui, Chen Ching-Lin, et al. Shaking table testing of two single piles of different stiffnesses subjected to liquefaction-induced lateral spreading. Engineering Geology, 2021, 281, 105956.
+[11] Chiou J.-S., Huang T.-J., Chen C.-L., et al. Shaking table testing of two single piles of different stiffnesses subjected to liquefaction-induced lateral spreading. Engineering Geology, 281, 105956, 2021.
-[12] Xu Ling-Yu, Song Cheng-Xiang, Chen Wei-Yun, et al. Liquefaction-induced settlement of the pile group under vertical and horizontal ground motions. Soil Dynamics and Earthquake Engineering, 2021, 144, 106709.
+[12] Xu L.-Y., Song C.-X., Chen W.-Y., et al. Liquefaction-induced settlement of the pile group under vertical and horizontal ground motions. Soil Dynamics and Earthquake Engineering, 144, 106709, 2021.
-[13] Chen Xu, Xiang Nailiang, Li Chunxiang. Influence of higher-order modes of slender tall pier bridge columns on the seismic performance of pile foundations. Soil Dynamics and Earthquake Engineering, 2021, 142, 106543.
+[13] Chen X., Xiang N., Li C. Influence of higher-order modes of slender tall pier bridge columns on the seismic performance of pile foundations. Soil Dynamics and Earthquake Engineering, 142, 106543, 2021.
-[14] Xu Zhiying. Calculation of pore pressure of sand foundation in resistance to seismic liquefaction by gravel drainage pile. Earthquake Engineering and Engineering Vibration, 1992, 12(4), 88-92 (in Chinese).
+[14] Xu Z. Calculation of pore pressure of sand foundation in resistance to seismic liquefaction by gravel drainage pile (in Chinese). Earthquake Engineering and Engineering Vibration, 12(4):88-92, 1992.
-[15] Seed H Bolton, Booker John R. Stabilization of potentially liquefiable sand deposits using gravel drains. Journal of the Geotechnical Engineering Division, 1977, 103(7), 757-768.
+[15] Seed H.B., Booker J.R. Stabilization of potentially liquefiable sand deposits using gravel drains. Journal of the Geotechnical Engineering Division, 103(7):757-768, 1977.

@@ Line 476: / Line 476: @@
 {| class="wikitable" style="margin: 0em auto 0.1em auto;border-collapse: collapse;width:auto;"
 |-style="background:white;"
-|style="text-align: center;padding:10px;"| [[Image:Review_979873928567-image58.png|300px]]
+|style="text-align: center;padding:10px;"| [[Image:Review_979873928567-image58.png|350px]]
 |-
 | style="background:#efefef;text-align:left;padding:10px;font-size: 85%;"| '''Figure 10'''. Effect of ''n'' on reconsolidation settlement of foundation after earthquake
@@ Line 487: / Line 487: @@
 {| class="wikitable" style="margin: 0em auto 0.1em auto;border-collapse: collapse;width:auto;"
 |-style="background:white;"
-|style="text-align: center;padding:10px;"| [[Image:Review_979873928567-image59.png|300px]]
+|style="text-align: center;padding:10px;"| [[Image:Review_979873928567-image59.png|350px]]
 |-
 | style="background:#efefef;text-align:left;padding:10px;font-size: 85%;"| '''Figure 11'''. Effect of <math display="inline">\eta</math> on reconsolidation settlement of foundation after earthquake
@@ Line 498: / Line 498: @@
 {| class="wikitable" style="margin: 0em auto 0.1em auto;border-collapse: collapse;width:auto;"
 |-style="background:white;"
-|style="text-align: center;padding:10px;"| [[Image:Review_979873928567-image60.png|300px]]
+|style="text-align: center;padding:10px;"| [[Image:Review_979873928567-image60.png|350px]]
 |-
 | style="background:#efefef;text-align:left;padding:10px;font-size: 85%;"| '''Figure 12'''. Effect of <math display="inline"> \chi </math> on reconsolidation settlement of foundation after earthquake
@@ Line 509: / Line 509: @@
 {| class="wikitable" style="margin: 0em auto 0.1em auto;border-collapse: collapse;width:auto;"
 |-style="background:white;"
-|style="text-align: center;padding:10px;"| [[Image:Review_979873928567-image61.png|300px]]
+|style="text-align: center;padding:10px;"| [[Image:Review_979873928567-image61.png|350px]]
 |-
 | style="background:#efefef;text-align:left;padding:10px;font-size: 85%;"| '''Figure 13'''. Effect of <math display="inline">k_v</math> on reconsolidation settlement of foundation after earthquake
@@ Line 520: / Line 520: @@
 {| class="wikitable" style="margin: 0em auto 0.1em auto;border-collapse: collapse;width:auto;"
 |-style="background:white;"
-|style="text-align: center;padding:10px;"| [[Image:Review_979873928567-image62.png|300px]]
+|style="text-align: center;padding:10px;"| [[Image:Review_979873928567-image62.png|350px]]
 |-
 | style="background:#efefef;text-align:left;padding:10px;font-size: 85%;"| '''Figure 14'''. Effect of  <math display="inline">N_{eq}</math>/<math>N_1</math> on reconsolidation settlement of foundation after earthquake
@@ Line 531: / Line 531: @@
 {| class="wikitable" style="margin: 0em auto 0.1em auto;border-collapse: collapse;width:auto;"
 |-style="background:white;"
-|style="text-align: center;padding:10px;"| [[Image:Review_979873928567-image63.png|300px]]
+|style="text-align: center;padding:10px;"| [[Image:Review_979873928567-image63.png|350px]]
 |-
 | style="background:#efefef;text-align:left;padding:10px;font-size: 85%;"| '''Figure 15'''. Effect of <math display="inline">t_d</math> on reconsolidation settlement of foundation after earthquake
 |}
 ==7. Conclusions==

@@ Line 455: / Line 455: @@
 ==6. Reconsolidation settlement of goundation after earthquake==
-Due to the assumption of equal strain, the reconsolidation settlement of pipe-soil foundation can be calculated by the reconsolidation settlement of soil around the pile. The reconsolidation settlement of soil around the pile can be expressed as follows<sup>[4]</sup>:
+Due to the assumption of equal strain, the reconsolidation settlement of pipe-soil foundation can be calculated by the reconsolidation settlement of soil around the pile. The reconsolidation settlement of soil around the pile can be expressed as follows [4]:
 {| class="formulaSCP" style="width: 100%; text-align: center;"
@@ Line 463: / Line 463: @@
 |-
 | <math>\begin{array}{c}
-\displaystyle S\left(T_\mbox{v}\right)=\frac{1}{E_\mbox{s}}{\int }_{T_{\mbox{vd}}}^{T_\mbox{v}}{\int }_0^H\frac{\partial {\gamma }_\mbox{w}H{\overline{U}}_\mbox{s}}{\partial t}\mbox{d}z\mbox{d}t\\
+\displaystyle S\left(T_{v}\right)=\frac{1}{E_{s}}{\int }_{T_{{vd}}}^{T_{v}}{\int }_0^H\frac{\partial {\gamma }_{w}H{\overline{U}}_{s}}{\partial t}{d}z{d}t\\
-\displaystyle =\frac{{\gamma }_\mbox{w}H}{E_\mbox{s}}\sum_{m=1}^{\infty }\frac{2N_{\mbox{eq}}}{N_\mbox{l}T_{\mbox{vd}}}\frac{{\left(-1\right)}^{m-1}\left[\mbox{e}^{\alpha M_m^2\left(T_{\mbox{vd}}-T_\mbox{v}\right)}-\mbox{e}^{-\alpha M_m^2T_\mbox{v}}+\mbox{e}^{-\alpha M_m^2T_{\mbox{vd}}}-1\right]}{\left(1-\lambda \right)\alpha M_m^5}
+\displaystyle =\frac{{\gamma }_{w}H}{E_{s}}\sum_{m=1}^{\infty }\frac{2N_{{eq}}}{N_{l}T_{{vd}}}\frac{{\left(-1\right)}^{m-1}\left[{e}^{\alpha M_m^2\left(T_{{vd}}-T_{v}\right)}-{e}^{-\alpha M_m^2T_{v}}+{e}^{-\alpha M_m^2T_{{vd}}}-1\right]}{\left(1-\lambda \right)\alpha M_m^5}
 \end{array}</math>
 |}
@@ Line 471: / Line 471: @@
-Figure 10 shows the reconsolidation settlement of foundation after earthquake under different ''n'' values. It can be found that reconsolidation settlement is mainly divided into two stages: one is the rapid settlement stage, in which reconsolidation settlement develops rapidly; then there is the slow settlement stage in which reconsolidation settlement develops slowly. It can be seen from Figure 10 that the larger the ''n'' value is, the slower the settlement rate in the early stage and the faster the settlement rate in the later stage. In general, the total settlement of foundation increases with the increase of ''n'' value.
+[[#img-10|Figure 10]] shows the reconsolidation settlement of foundation after earthquake under different <math display="inline">n</math> values. It can be found that reconsolidation settlement is mainly divided into two stages: one is the rapid settlement stage, in which reconsolidation settlement develops rapidly; then there is the slow settlement stage in which reconsolidation settlement develops slowly. It can be seen from [[#img-10|Figure 10]] that the larger the <math display="inline">n</math> value is, the slower the settlement rate in the early stage and the faster the settlement rate in the later stage. In general, the total settlement of foundation increases with the increase of <math display="inline">n</math> value.
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+<div id='img-10'></div>
- [[Image:Review_979873928567-image58.png|300px]] </div>
+{| class="wikitable" style="margin: 0em auto 0.1em auto;border-collapse: collapse;width:auto;"
-Figure 11 shows the reconsolidation settlement of foundation after earthquake under different ''η'' values. It can be seen that the total settlement of the foundation increases significantly as the value of ''η'' increases.
+[[#img-11|Figure 11]] shows the reconsolidation settlement of foundation after earthquake under different <math display="inline">\eta</math>  values. It can be seen that the total settlement of the foundation increases significantly as the value of <math display="inline">\eta</math> increases.
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+<div id='img-11'></div>
- [[Image:Review_979873928567-image59.png|300px]] </div>
+{| class="wikitable" style="margin: 0em auto 0.1em auto;border-collapse: collapse;width:auto;"
-Figure 12 shows the reconsolidation settlement of foundation after earthquake under different ''χ'' values. It can be seen from Figure 12 that the larger the ''χ'' value is, the faster the settlement rate in the early stage and the slower the settlement rate in the later stage. In general, the total settlement of foundation decreases with the increase of ''χ'' value.
+[[#img-12|Figure 12]] shows the reconsolidation settlement of foundation after earthquake under different <math display="inline"> \chi </math> values. It can be seen from [[#img-12|Figure 12]] that the larger the <math display="inline"> \chi </math> value is, the faster the settlement rate in the early stage and the slower the settlement rate in the later stage. In general, the total settlement of foundation decreases with the increase of <math display="inline"> \chi </math> value.
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+<div id='img-12'></div>
- [[Image:Review_979873928567-image60.png|300px]] </div>
+{| class="wikitable" style="margin: 0em auto 0.1em auto;border-collapse: collapse;width:auto;"
-Figure 13 shows the reconsolidation settlement of foundation after earthquake under different ''k''<sub>v</sub> values. It can be seen that the total settlement of the foundation decreases significantly as the value of ''k''<sub>v</sub> increases.
+[[#img-13|Figure 13]] shows the reconsolidation settlement of foundation after earthquake under different ''k''<sub>v</sub> values. It can be seen that the total settlement of the foundation decreases significantly as the value of ''k''<sub>v</sub> increases.
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">