基于罚函数偶应力理论的土体应变局部化研究

与 Cosserat 理论相比，偶应力理论在一定程度上可以降低数值框架的复杂度，已逐渐应用于岩土体应变局部化分析中。然而，一般的偶应力有限元法需要满足 C¹连续性，即单元内部和单元交界面上的应变都需要具有连续性。为了避免开发较为复杂的C¹型偶应力单元，在 Cosserat 连续体理论框架下，通过借助罚函数方法对 C¹连续性进行松弛来获得偶应力理论的逼近解，建立了基于罚函数的偶应力有限元方法 PCS-FEM。通过平面应变条件下的弹性圆孔应力集中问题对 PCS-FEM 方法的有效性进行了验证，并应用于土体应变局部化分析中。通过对Ottawa砂的平面应变试验进行数值模拟，发现 PCS-FEM 方法获得的应力?应变曲线及剪切带破坏形态与试验结果基本一致，且能够克服经典连续体理论病态的网格敏感性问题，保证应变局部化问题的适定性；通过对承受偏心荷载作用下的土坡应变局部化经典算例进行分析，发现 PCS-FEM 方法同样可以克服土坡应变软化阶段的网格敏感性问题，展现土体的渐进破坏过程。

Analysis of geotechnical strain localization based on penalty-based couple stress theory

Compared with the Cosserat theory, the complexity of the numerical framework can be reduced in the couple stress theory to some extent, and it has been gradually applied to the geotechnical strain localization analysis. However, the C¹ continuity should be satisfied in the straight-forward couple stress finite element method, that is, the continuity of the strain inside the elements and on the interface of the elements should be satisfied. To avoid developing more complicated C¹ couple stress elements, within the framework of Cosserat continuum theory, the approximate solution of the couple stress theory can be obtained by relaxing the C¹ continuity with the aid of the penalty function method, and the penalty-based couple stress finite element method (named PCS-FEM) is developed. The effectiveness of the PCS-FEM is verified by the stress concentration problem of an elastic circular hole under plane strain condition, and it is further applied to the strain localization analysis of soil mass. Based on the numerical simulation of the plane strain experiment of Ottawa sand, it is found that the stress-strain curve and the failure form of shear band obtained by the PCS-FEM method are basically consistent with the test results, and the ill-conditioned mesh sensitivity problem of the classical continuum theory can be avoided by the PCS-FEM so that the well-posedness of the strain localization problem can be ensured. Based on the strain localization analysis of the soil slope subject to the eccentric load, it is found that the mesh sensitivity problem in the strain-softening stage of the soil slope can also be avoided, and the progressive failure process of the slope can be captured by the PCS-FEM.