砂土地基上圆形浅基础三维破坏包络面的理论研究

对砂土地基上圆形浅基础在竖向荷载V、水平荷载H及力矩M复合加载条件下的承载力进行了系统的三维有限元分析。在分析中，砂土假定为纯摩擦材料，遵循基于Mohr-Coulomb破坏准则的理想弹塑性本构关系。首先，对圆形浅基础的竖向承载力进行了有限元计算, 并与滑移线解法进行了对比，两种方法所得结果比较吻合。进而探讨了砂土内摩擦角对于基础在V-H、V-M荷载平面与V-H-M三维荷载空间内的破坏包络轨迹的影响。计算结果表明，与不排水情况下软黏土地基上基础破坏包络面相比，砂土地基上圆形浅基础的破坏包络面形状有较大差异, 但V-H和V-M平面内的破坏包络面形状仍具有较好的归一化特性。基于有限元计算结果，建立了圆形浅基础在V-H-M三维荷载空间内的破坏包络面方程, 该方程可用来合理评价复合加载条件下砂土地基上圆形浅基础的整体稳定性。

Theoretical analysis on three dimensional failure envelope of circular footings on sand

The bearing capacity of circular shallow footings subjected to combined loading composed of vertical component V, horizontal component H and moment M on sand is explored through three dimensional finite element numerical analyses. The sand is assumed to be purely frictional and obey elasto-perfectly plastic relationship following the Mohr-Coulomb failure criterion. The capacity of circular footing under centrally vertical load is computed, and the calculated results agree well with those derived from slip-line field theory. Then the influence of soil friction angle on the failure locus in the V-H and V-M load plane and V-H-M load space is investigated. The results show that the shape of failure envelopes of shallow foundations on sand is different from that on undrained clay, whilst normalization of the failure envelope on the V-H and V-M load plane by the pure vertical bearing capacity allow it to be generalized for varying conditions. Based on finite element analyses, the equation of failure envelope in the V-H-M three dimensional load space is proposed, which can be used to evaluate the general stability of circular footings on sand under combined loading condition.