A finite element nonlocal strain-softening algorithm based on the critical state theory for geomaterials：a case study with csuh model

Geomaterials can exhibit dilatancy and softening behavior in engineering practice. When simulating the strain-softening characteristics as well as the accompanied shear bands with the standard finite element(FE) method，the predicted results suffer from strong mesh dependency，which greatly affects the accuracy of the results and may even result in convergence difficulties. In this paper，a novel FE algorithm of nonlocal strain regularisation is proposed based on the critical state theory for soils. Compared to the conventional constitutive integration scheme used in a FE analysis，the proposed algorithm in this study is capable of effectively solving the mesh dependency and convergence problem when modelling the strain-softening behaviour of geomaterials. Meanwhile，the presented algorithm can adequately incorporate the nonlocal strains into the integration process ensuring its application to all critical state type models such as the modified Cam-clay model. The implementation procedures of the proposed method in a finite element program were explained in detail by taking the unified hardening model for clay and sand(CSUH) as an example. The effectiveness of the method was subsequently verified through a series of numerical analyses of biaxial compression tests. The numerical results become almost unchanged with the mesh discretization once the adopted mesh is sufficiently fine，while the associated iterative process exhibits robust performance. © 2023 Academia Sinica. All rights reserved.