An enhanced polar-based GPGPU-parallelized contact detection algorithm for 3D FDEM and its application to cracking analysis of shield tunnel segmental linings

Abstract

This study introduces the three-dimensional combined finite-discrete element method (3D FDEM) to perform cracking analysis of segmental linings under extreme conditions. Considering the complex contact interactions of segments, this study first proposes a polar-based GPGPU-parallelized contact detection algorithm to handle memory issues confronted by existing FDEM algorithms. Initially, a spatial decomposition approach based on the polar coordinate system is implemented during the broad search phase. Each tetrahedral element is positioned within suitable search cells according to the axis-aligned bounding box. Subsequently, element pairs within each search cell are iteratively traversed, and potential contact pairs are identified using the judge cell criteria. After the broad search, a narrow search phase is executed to determine all real contacts. Following the above implementation, a load-structure model encompassing soil spring and external pressure calculations is then proposed. Based on the shape functions and coordinate transformation, the formulations of soil springs and external loads are derived and parallelized in the 3D FDEM framework. Three numerical tests are presented to validate the effectiveness of the proposed approach. Simulation results confirm the suitability of the proposed method for cracking analysis of segmental linings. Compared to the existing methods, it reduces GPU memory usage by 56 ∼ 76 % without extending time, which enhances the computational scale of 3D FDEM simulations. Furthermore, the proposed method is applied to two engineering scenarios, i.e., straight and curved segmental linings, both considering the absence and presence of contact defects between segments. The results show that contact defects can significantly reduce the resistance of the structural system comprising bolts and concrete segments for straight and curved scenarios.