基于改进对流粒子域插值物质点法的隧道大变形分析

王曼灵; 李树忱; 周慧颖; 王修伟; 彭科峰; 袁超

doi:10.11779/CJGE20230676

基于改进对流粒子域插值物质点法的隧道大变形分析 English Version

王曼灵^{1, 2,},
李树忱^{1, 2, 3, ,},
周慧颖^{1, 2},
王修伟^{1, 2},
彭科峰^{1, 2},
袁超^{2, 4}

1.
山东大学齐鲁交通学院, 山东济南 250002
2.
山东大学岩土与地下工程研究院, 山东济南 250061
3.
中国矿业大学力学与土木工程学院, 江苏徐州 221116
4.
山东大学土建与水利学院, 山东济南 250061

基金项目:

国家重点研发计划项目 2021YFC2902103

国家自然科学基金项目 52108373

山东省自然科学基金项目 ZR2021ZD36

山东省自然科学基金项目 ZR2021QE127

详细信息

作者简介:
王曼灵(1994—)，女，博士研究生，主要从事隧道大变形和数值计算方法等方面的研究工作。E-mail: manling_wang@163.com

通讯作者:
李树忱, E-mail: shuchenli@sdu.edu.cn

中图分类号: TU434
计量
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出版历程
- 收稿日期: 2023-07-17
- 网络出版日期: 2023-12-19
- 刊出日期: 2024-07-31

Improved convective particle domain interpolation material point method for large deformation analysis of tunnels

WANG Manling^{1, 2,},
LI Shuchen^{1, 2, 3, ,},
ZHOU Huiying^{1, 2},
WANG Xiuwei^{1, 2},
PENG Kefeng^{1, 2},
YUAN Chao^{2, 4}

1.
School of Qilu Transportation, Shandong University, Jinan 250002, China
2.
Institue of Geotechnical and Underground Engineering, Shandong University, Jinan 250061, China
3.
School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China
4.
School of Civil Engineering, Shandong University, Jinan 250061, China

摘要

摘要: 物质点法（MPM）在模拟大变形问题时具有很好的效果，然而传统的MPM在粒子穿越网格边界时存在单元穿越误差，导致精度降低。为克服传统MPM的单元穿越误差，基于对流粒子域插值物质点法（CPDI）理论框架，采用自适应正交改进插值移动最小二乘法（AOIIMLS），提出了改进CPDI方法。AOIIMLS通过构造加权正交基函数，并且忽略了新对角矩阵中的零元素或极小元素的贡献，以避免求解逆矩阵，增强了鲁棒性。改进CPDI采用速度梯度计算粒子域的速度场，粒子速度和粒子域角点速度用于重构背景网格速度函数。通过一维柱在自重作用下的压缩、砂柱坍塌和隧道坍塌离心机试验验证了改进CPDI方法的准确性和适用性，结果表明改进CPDI降低了单元穿越误差，得到了更高的精度。最后，采用改进CPDI方法模拟了青岛地铁4号线静沙区间地面塌陷全过程，验证了改进CPDI方法在岩土工程大变形领域的适用性及优势。
- 物质点法 /
- 对流粒子域插值 /
- 自适应正交改进移动最小二乘法 /
- 隧道大变形
Abstract: The material point method (MPM) has good effects in simulating large deformation problems. However, the conventional MPM suffers from cell-crossing errors when particles cross grid boundaries, resulting in reduced accuracy. In order to overcome the cell-crossing errors of the conventional MPM, an improved convective particle domain interpolation material point method (CPDI) is proposed based on the conventional CPDI framework and the adaptive orthogonal improved interpolation moving least squares method (AOIIMLS). By constructing weighted orthogonal basis functions and disregarding the minimal or zero elements in the new diagonal matrix, the inverse matrix computation is avoided, and the robustness is enhanced. In the improved CPDI method, the particle domain velocity field is calculated using the velocity gradients, and the AOIIMLS shape functions are employed to reconstruct the background grid velocity function using the particle velocity and particle domain corner point velocity. The accuracy and applicability of the improved CPDI method are verified through simulations of various scenarios such as the compaction of a one-dimensional column under self-weight, the collapse of a sand column and the centrifuge tests on tunnel collapse. The results show that the improved CPDI method reduces the cell-crossing errors caused by the particles cross grid boundaries and achieves higher accuracy. Finally, the improved CPDI method is employed to simulate the whole process of ground collapse in the Jinggang Road Station–Shazikou Station tunnel section of Qingdao Metro Line 4, effectively confirming the applicability and advantages of the method in addressing large deformation problems in geotechnical engineering.

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图 1 MPM计算流程

Figure 1. Simulation cycle of MPM

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图 2 CPDI的初始和更新的粒子域

Figure 2. Initial and updated particle domains in CPDI method

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图 3 粒子域速度场

Figure 3. Particle domain velocity field

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图 4 柱的几何模型和边界条件

Figure 4. Geometry and boundary conditions of column

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图 5 柱的垂直应力数值解和解析解(h_{x, y}=1/64 m, np=4)

Figure 5. Numerical and analytical solutions for vertical stresses of column (h_{x, y}=1/64 m, np=4)

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图 6 不同粒子密度下垂直应力解析解和数值解的误差(h_{x, y}=1.0 m)

Figure 6. Errors of analytical and numerical solutions for vertical stresses of column at different particle densities (h_{x, y}=1.0 m)

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图 7 不同网格尺寸下垂直应力解析解和数值解的误差(np=4)

Figure 7. Errors of analytical and numerical solutions for vertical stresses of column at different grid cell sizes (np=4)

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图 8 砂柱坍塌试验示意图、模型的网格和初始粒子设置

Figure 8. Experimental schematics, grid and initial particle setup of sand column

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图 9 砂柱坍塌改进CPDI模拟结果与试验结果^[30-31]对比

Figure 9. Comparison between improved CPDI simulation and experimental results^[30-31] for sand column collapse

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图 10 砂柱坍塌自由面对比

Figure 10. Comparison of free surface of collapsing sand column

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图 11 隧道几何模型和边界条件

Figure 11. Geometry and boundary conditions of tunnel

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图 12 离心机试验和改进CPDI计算的隧道坍塌

Figure 12. Centrifuge test and improved CPDI calculation for tunnel collapse

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图 13 地面塌陷

Figure 13. Ground collapse

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图 14 静沙区间地质剖面图

Figure 14. Geological profile of Jinggang Road Station-Shazikou Station section

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图 15 隧道几何模型和边界条件

Figure 15. Geometry and boundary conditions of tunnel

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图 16 隧道坍塌过程中的地面沉降

Figure 16. Ground subsidence during tunnel collapse

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图 17 隧道坍塌过程中的剪应变

Figure 17. Shear strains during tunnel collapse

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图 18 隧道坍塌后地面沉降曲线

Figure 18. Curve of ground subsidence after tunnel collapse

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图 19 监测点竖向位移和水平位移时程曲线

Figure 19. Time-history curves of vertical and horizontal displacements at monitoring points

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表 1 地层物理力学参数

Table 1 Physical and mechanical parameters of strata

地层	弹性模量E/MPa	泊松比 $\nu$	黏聚力c/kPa	内摩擦角φ/(°)	重度γ/(kN·m^-3)
杂填土	8.0	0.20	0	15	17.5
中粗砂	6.07	0.33	13.9	12.5	18.5
粉质黏土	5.671	0.30	8.2	12	19.7
强风化凝灰岩	20	0.30	3.0	30	22.5
中风化凝灰岩	50	0.25	3000	45	26.0
微风化凝灰岩	5000	0.22	11500	55	26.7

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