开挖问题摩擦效应的有限元计算方法

A FINITE ELEMENT METHOD TO EXCAVATION PROBLEM CONSIDERING FRICTIONAL EFFECT OF MATERIAL

采用有限单元法计算砂性土中的开挖卸载,根据既有的散粒体材料开挖应力释放和弹塑性卸载理论研究成果,将卸载过程中材料荷载–位移曲线的非线性等效成为开挖荷载的逐步释放,该过程中卸荷模量与加载模量一致。在此基础上,推导用卸荷刚度表示的计算域内开挖荷载计算式;同时,根据现有试验结果,将八面体剪应力引入以表征单次加卸载情况下颗粒间的摩擦作用力,并利用虚功原理建立颗粒间摩擦作用与卸载应力释放特性的关系,将应力释放效应对开挖荷载的影响等效成为修正开挖卸载阶段材料的弹塑性本构关系矩阵,从而实现考虑卸载摩擦效应的开挖问题计算方法。从节点平衡方程的推导来看,开挖荷载对整个计算区域均有影响,和应力释放效应存在对应关系。设计砂的室内单向加卸载模型试验,并采用该有限元方法对室内模型试验进行模拟,结果表明,单次加卸载过程中,计算曲线可以较好地反映对应试验条件下土体的应力释放特性,计算结果与现有的理论研究成果相符,该方法对开挖问题的描述具有一定的可行性。

A finite element method(FEM) was proposed to solve the excavation problem in sandy soil. Based on the stress release and elasto-plastic unloading theory of bulk solids,the non-linear characteristics of loaddisplacement curve were made to be equivalent to the release process of the excavation load with the loading and unloading modulus to be the same. The octahedral shear stress was introduced to calculate the internal friction force and the excavation load considering the internal friction resistance of material was deduced. The relationship between the internal friction resistance of material and the residual stress during excavation was established according to the virtual work principle. The FEM of stress release considering the excavation load was carried out by adjusting the unloading stiffness of material during excavation on the basis of stress release properties. The derivation of equilibrium equations on nodes indicated that the excavation load had influence on the whole computational domain and also had corresponding relation with the effect of stress release. The static loading-unloading model test on sandy soil was undertaken and simulated with the proposed FEM as well. The residual stresses calculated by the FEM were basically identical with the results from the test.