基于在机开挖离心模型试验的改进MSD法评估

曹明洋; 马险峰

doi:10.11779/CJGE20220745

基于在机开挖离心模型试验的改进MSD法评估 English Version

曹明洋^{1, 2,},
马险峰^{1, 2, ,}

1.
同济大学地下建筑与工程系, 上海 200092
2.
同济大学岩土及地下工程教育部重点实验室, 上海 200092

基金项目:

国家自然科学基金项目 41272290

详细信息

作者简介:
曹明洋(1992—)，男，博士研究生，主要从事岩土工程数值计算及离心模型试验方面的研究工作。E-mail: mingyangcao@tongji.edu.cn

通讯作者:
马险峰, E-mail: xf.ma@tongji.edu.cn

中图分类号: TU43
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出版历程
- 收稿日期: 2022-06-10
- 网络出版日期: 2024-01-08
- 刊出日期: 2023-12-31

Evaluation of improved MSD method based on centrifugal model tests on in-flight excavation of foundation pits

CAO Mingyang^{1, 2,},
MA Xianfeng^{1, 2, ,}

1.
Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China
2.
Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai 200092, China

摘要

摘要: 研发了一套应用于高离心力场条件下在机基坑开挖装置和支撑施加系统，开展了多支撑支护的黏土基坑开挖的离心模型试验。将开挖引起的墙后地表沉降与挡墙变形的试验数据与已发表的相关研究成果进行对比分析，证明了该套在机开挖装置和支撑系统可有效模拟实际基坑工程的土体开挖及支撑。在离心试验数据的基础上，对基坑体系的变形机制进行了修正，提出了全量变形机制计算的改进动员强度法（mobilizable strength design，MSD）。应用改进MSD法计算多支撑开挖的挡墙变形曲线，并将计算结果与现场监测数据对比。结果表明：改进MSD法预测结果与实测数据较吻合，论证了改进MSD法的有效性。
- 基坑开挖 /
- 离心模型试验 /
- 在机开挖装置 /
- 改进MSD法
Abstract: A set of novel device for the centrifugal model tests on the whole process of excavation is developed to investigate the influences of excavation on wall displacement and ground settlement. The test data of excavation-induced ground settlement behind the retaining wall and wall deformation are compared with the published research results, and it is determined that the device can effectively simulate the excavation process under high centrifugal force field test conditions. Based on the centrifugal test data, the deformation mechanism of the foundation pit system is modified and the improved mobilizable strength design (MSD) is proposed. The improved MSD method is used to calculate the deformation curves of retaining walls for multi-pillar excavation, and the calculated results are compared with the field monitoring data. It is shown that the predicted results by the improved MSD method are consistent with the measured data, and the applicability of the improved MSD is demonstrated.
- excavation of foundation pit /
- centrifugal model test /
- in-flight excavator /
- improved MSD method

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图 1 开挖装置图

Figure 1. Photos of in-flight excavator

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图 2 内支撑系统图

Figure 2. Layout of internal strut system

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图 3 试验装置示意图

Figure 3. Schematic diagram of experimental set-up

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图 4 数字图像变形测量(DPDM) 装置

Figure 4. Configuration of digital picture deformation measurement (DPDM) cameras

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图 5 侧表面标记的模型土

Figure 5. Marked surface soil at lateral sides

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图 6 内支撑及应变片位置图

Figure 6. Positions of internal struts and strain gauges

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图 7 土体不排水抗剪强度与深度的关系

Figure 7. Relationship between shear strength of undrained soil and depth

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图 8 离心模型试验开挖过程

Figure 8. Excavation process of centrifugal model tests

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图 9 地表沉降曲线图

Figure 9. Development of ground surface settlement profiles at different excavation depths

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图 10 基坑开挖过程中的土体变形（单位：mm）

Figure 10. Deepseated soil deformation mechanism observed at different excavation stages

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图 11 挡墙变形曲线图

Figure 11. Observed wall displacements at different excavation depths

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图 12 挡墙水平位移变形与开挖深度关系

Figure 12. Relationship between normalized lateral displacement of wall and excavation depth

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图 13 改进MSD法内支撑开挖变形机制示意图

Figure 13. Deformation mechanism of braced excavations by modified MSD method

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图 14 改进MSD法计算步骤

Figure 14. Computational step of improved MSD method

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图 15 施工参数

Figure 15. Construction parameters

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图 16 土的应变强度曲线

Figure 16. Strength curves of soil

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图 17 现场测量和计算结果对比

Figure 17. Comparison between field measurements and calculated results

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表 1 模型尺寸下离心模型试验的基坑开挖参数

Table 1 Excavation parameters for centrifugal model tests under model sizes

开挖深度/m		开挖宽度/m		挡墙高度/m		挡墙厚度/m
原型	模型	原型	模型	原型	模型	原型	模型
12.8	0.15	18.7	0.22	22.1	0.26	0.9	0.0077

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表 2 原型/模型挡墙参数

Table 2 Parameters of prototype/model retaining walls

参数	挡墙弹性模量/GPa	挡墙泊松比	挡墙厚度/mm
原型	30	0.17	900
模型	72	0.33	7.7

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表 3 改进MSD法计算的水平和竖向位移

Table 3 Vertical and horizontal displacements by improved MSD method

坐标	竖向位移增量 ${w_y}$	水平位移增量 ${w_x}$
ABC，B为坐标原点	$\begin{array}{l} {w_y} = {w_{{\text{max}}}} \cdot \left[ { - {{\left( {\frac{r}{{kl}}} \right)}^2} + \frac{{2r}}{{kl}}} \right] \cdot \frac{x}{r}{\text{ }}\;\;\;0 \leqslant r \leqslant kl \hfill \\ {w_y} = {w_{{\text{max}}}} \cdot \left[ {\frac{1}{{{l^2} - 2k{l^2} + {k^2}{l^2}}}( - {r^2} + 2klr + {l^2} - 2k{l^2})} \right] \cdot \frac{x}{r}{\text{ }}kl \leqslant r \leqslant l \hfill \\ \end{array}$	$\begin{array}{l} {w_x} = {w_{{\text{max}}}} \cdot \left[ { - {{\left( {\frac{r}{{kl}}} \right)}^2} + \frac{{2r}}{{kl}}} \right] \cdot \frac{y}{r}{\text{ }}\;\;\;0 \leqslant r \leqslant kl \hfill \\ {w_x} = {w_{{\text{max}}}} \cdot \left[ {\frac{1}{{{l^2} - 2k{l^2} + {k^2}{l^2}}}( - {r^2} + 2klr + {l^2} - 2k{l^2})} \right] \cdot \frac{y}{r}{\text{ }}kl \leqslant r \leqslant l \hfill \\ \end{array}$
CDE，D为坐标原点	$\begin{array}{l} {w_y} = - {w_{{\text{max}}}} \cdot \left[ { - {{\left( {\frac{{r{\text{ + }}kl}}{{kl}}} \right)}^2} + \frac{{2(r + kl)}}{{kl}}} \right] \cdot \frac{x}{r}{\text{ }}\;\;\;0 \leqslant r \leqslant k(l - H) \hfill \\ {w_y} = - {w_{{\text{max}}}} \cdot \left[ {\frac{1}{{{l^2} - 2k{l^2} + {k^2}{l^2}}}( - {{(r + kl)}^2} + 2kl(r + kl) + {l^2} - 2k{l^2})} \right] \cdot \frac{x}{r} \hfill \\ {\text{ }}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;k(l - H) \leqslant r \leqslant l - H \hfill \\ \end{array}$	$\begin{array}{l} {w_x} = {w_{{\text{max}}}} \cdot \left[ { - {{\left( {\frac{{r{\text{ + }}kl}}{{kl}}} \right)}^2} + \frac{{2(r + kl)}}{{kl}}} \right] \cdot \frac{y}{r}{\text{ }}\;\;\;0 \leqslant r \leqslant {\kern 1pt} k(l - H) \hfill \\ {w_x} = {w_{{\text{max}}}} \cdot \left[ {\frac{1}{{{l^2} - 2k{l^2} + {k^2}{l^2}}}( - {{(r + kl)}^2} + 2kl(r + kl) + {l^2} - 2k{l^2})} \right] \cdot \frac{y}{r}{\text{ }} \hfill \\ {\text{ }}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;k(l - H) \leqslant r \leqslant l - H \hfill \\ \end{array}$
DEF，F为坐标原点	$\begin{array}{l} {w_y} = - \frac{{\sqrt {\text{2}} }}{{\text{2}}}{w_{{\text{max}}}} \cdot \left[ { - {{\left( {\frac{{{{\sqrt 2 } \mathord{\left/ {\vphantom {{\sqrt 2 } 2}} \right. } 2}(x - y) + kl}}{{kl}}} \right)}^2} + \frac{{\sqrt 2 (x - y) + 2kl}}{{kl}}} \right]{\text{ }} \hfill \\ {\text{ }}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;0 \leqslant {{\sqrt 2 } \mathord{\left/ {\vphantom {{\sqrt 2 } 2}} \right. } 2}(x - y) \leqslant k(l - H) \hfill \\ w_y=-\frac{\sqrt{2}}{2} w_{max } \cdot\left[\frac { 1 } { l ^ { 2 } - 2 k l ^ { 2 } + k ^ { 2 } l ^ { 2 } } \left(-(\sqrt{2} / 2(x-y)+k l)^2+\right.\right. \\ \;\;\left.\left.2 k l(\sqrt{2} / 2(x-y)+k l)+l^2-2 k l^2\right)\right] k(l-H) \leqslant \sqrt{2} / 2(x-y) \leqslant l-H\\ \end{array}$	$\begin{array}{l} {w_x} = \frac{{\sqrt {\text{2}} }}{{\text{2}}}{w_{\max}} \cdot \left[ { - {{\left( {\frac{{{{\sqrt 2 } \mathord{\left/ {\vphantom {{\sqrt 2 } 2}} \right. } 2}(x - y) + kl}}{{kl}}} \right)}^2} + \frac{{\sqrt 2 (x - y) + 2kl}}{{kl}}} \right]{\text{ }} \hfill \\ {\text{ }}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;0 \leqslant {{\sqrt 2 } \mathord{\left/ {\vphantom {{\sqrt 2 } 2}} \right. } 2}(x - y) \leqslant k(l - H) \hfill \\ {w_x} = \frac{{\sqrt {\text{2}} }}{{\text{2}}}{w_{{\text{max}}}} \cdot \left[ {\frac{1}{{{l^2} - 2k{l^2} + {k^2}{l^2}}}( - {{({{\sqrt 2 } \mathord{\left/ {\vphantom {{\sqrt 2 } 2}} \right. } 2}(x - y) + kl)}^2} + } \right.{\text{ }} \hfill \\ {\text{ }}\;\;\;\;\;\;\;\;\left. {\begin{array}{*{20}{c}} {} \\ {} \end{array}{\text{ }}2kl({{\sqrt 2 } \mathord{\left/ {\vphantom {{\sqrt 2 } 2}} \right. } 2}(x - y) + kl) + {l^2} - 2k{l^2})} \right]{\text{ }}k(l - H) \leqslant {{\sqrt 2 } \mathord{\left/ {\vphantom {{\sqrt 2 } 2}} \right. } 2}(x - y) \leqslant l - H \hfill \\ \end{array}$
注：H为开挖深度（m）；r为到圆弧中心的径向距离（m）， $r=\sqrt{x^2+y^2}$ （m）。

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表 4 基坑开挖参数

Table 4 Excavation parameters for foundation pit

挡墙厚/mm	挡墙刚度/(kN·m^-2)	挡墙长/m	最大开挖深度/m	开挖宽度/m
600	540000	27	17.3	20.8

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