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

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.