水平受荷桩的弹性有限元虚拟加载上限分析

基于将塑性上限分析等效为弹性迭代计算的总量虚拟加载上限分析理论，在商业化有限元软件ABAQUS中实现了弹性有限元虚拟加载上限方法（弹性有限元T-EMSD）。应用弹性有限元T-EMSD法分析了不排水黏土中的二维水平受荷桩，其获得的荷载-位移曲线与弹塑性有限元分析结果一致，其极限承载力与塑性解相近。在极限位移加载量下弹性有限元T-EMSD法对应的上限机构从弹性始速度场开始随迭代逐渐演化，迭代收敛后的速度场和解析塑性破坏机构相似。与其他基于可变强度概念（MSD）的方法相比，弹性有限元T-EMSD法对水平受荷桩桩身的分析具有更高的精度。弹性有限元T-EMSD法最大的优势在于可在计算中自然地获得塑性机构，因而可被用于研究一些塑性机构难以构造的复杂问题，并对弹塑性数值方法进行验证。

Analysis of laterally loaded pile by elastic finite element based EMSD method

Based on the fictitious loading upper bound limit analysis approach i.e. total-displacement-loading approach based on extend mobilizable strength design method (T-EMSD), by which the traditional upper bound limit analysis is equivalently converted into iteration of elastic solution, the elastic finite element based T-EMSD method is realized in commercial FEM software ABAQUS. The numerical T-EMSD method is applied to analyzing the shaft of laterally loaded pile in undrained clay. The load-displacement curves obtained by the proposed method are generally consistent with those obtained by elasto-plastic FEM, and the corresponding ultimate bearing capacities are close to plastic solutions. Under large displacements, the mechanisms underlining the elastic finite element based T-EMSD analysis transform from elastic into plastic mechanisms through iteration process, which finally become similar to the plastic collapse mechanisms. Compared with other mobilizable strength design (MSD) methods, the proposed approach are more accurate in the analysis of laterally loaded pile. Moreover, since corresponding mechanisms can be simultaneously obtained in the process of the numerical T-EMSD analysis, it can be utilized in studying complicated problems whose plastic deformation mechanisms are not acquired yet, and in verifying the results of other numerical methods.