基于岩土材料临界状态理论的有限元非局部软化算法——以CSUH模型为例  

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

作　　者：姚仰平[1] 武孝天 崔文杰 YAO Yangping;WU Xiaotian;CUI Wenjie(School of Transportation Science and Engineering,Beihang University,Beijing 100083,China)

机构地区：[1]北京航空航天大学交通科学与工程学院,北京100083

出　　处：《岩石力学与工程学报》2023年第7期1759-1766,共8页Chinese Journal of Rock Mechanics and Engineering

基　　金：国家自然科学基金重点项目(52238007);国家重点研发计划资助(2018YFE0207100);国家自然科学基金资助项目(51979001)。

摘　　要：实际工程中岩土材料往往表现出剪胀和软化特性。采用传统有限元方法模拟这种材料软化特性及其产生的剪切带时,预测结果往往表现出较强的网格依赖性,从而极大地影响了土体软化阶段计算结果的准确性且计算过程中极易出现不收敛的问题。提出一种基于岩土材料临界状态理论的有限元非局部软化新算法,该方法与有限元传统本构积分算法相比,有效地避免了模拟材料软化特性时的网格依赖性和收敛性问题。同时,该方法能够合理地将非局部应变与本构模型的有限元本构积分过程相结合,对于以修正剑桥模型为代表的经典临界状态弹塑性本构模型具有普适性。以适用于黏土和砂土的统一硬化(CSUH)模型为例,详细介绍该方法在有限元中的实现步骤,并以典型的双轴压缩问题为例进行验证。结果表明,当网格划分超过一定数量后,有限元计算结果差异性显著减小,计算过程具有良好的收敛性和稳定性。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.

关 键 词：土力学 非局部软化算法 CSUH模型 有限元法 网格依赖性 双轴压缩 

分 类 号：TU43[建筑科学—岩土工程]