基于改进对流粒子域插值物质点法的隧道大变形分析  

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

作　　者：王曼灵 李树忱 周慧颖[1,2] 王修伟 彭科峰 袁超 WANG Manling;LI Shuchen;ZHOU Huiying;WANG Xiuwei;PENG Kefeng;YUAN Chao(School of Qilu Transportation,Shandong University,Jinan 250002,China;Institue of Geotechnical and Underground Engineering,Shandong University,Jinan 250061,China;School of Mechanics and Civil Engineering,China University of Mining and Technology,Xuzhou 221116,China;School of Civil Engineering,Shandong University,Jinan 250061,China)

机构地区：[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

出　　处：《岩土工程学报》2024年第8期1632-1643,共12页Chinese Journal of Geotechnical Engineering

基　　金：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,ZR2021QE127)。

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。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.

关 键 词：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 

分 类 号：TU434[建筑科学—岩土工程]