基于黏聚区域模型的边坡渐进破坏过程强化有限元分析

Enhanced finite element analysis of progressive failure of slopes based on cohesive zone model

剪切带非连续变形描述及剪切带扩展过程模拟是边坡渐进破坏过程分析的关键,基于黏聚区域模型及强化有限单元法提出一种剪切带渐进扩展过程模拟的有限元分析方法。首先,将剪切带两侧相对变形分解成分别由常规应变和附加应变确定的相对位移,提出具有弱非连续变形特征的剪切带变形等效强非连续变形描述方法,并采用黏聚区域模型表征剪切带应力和附加相对位移间的软化本构关系。其次,基于强化有限单元法描述强非连续变形,并构造相应的无厚度剪切带单元。在此基础上,提出剪切带渐进扩展模拟的有限元算法。算例表明,此方法不仅能够很好地模拟剪切带的应变软化特性,而且有效地克服了常规剪切带模拟具有的网格敏感性问题。

The description of discontinuous deformation and the simulation of shear band propagation are the key to the progressive failure analysis of slopes. A novel numerical method is presented based on the cohesive zone model and the enhanced finite element method. Firstly, the deformation of the shear band is resolved into the relative displacements determined by regular strain and additional strain respectively, a description which equally replaces the weak discontinuous deformation with strong form is adopted, and the shear band stress-additional relative displacement softening constitutive relation is represented by means of the cohesive law. Secondly, the relative displacement is described by the enhanced finite element method, and corresponding shear band element without thickness is constructed. Finally, a finite element algorithm for modeling the propagation of shear bands is proposed. Through numerical examples, it is demonstrated that the proposed method is not only able to consider the softening character of shear band, but also overcomes the mesh sensitivity in modeling the standard shear band.