基于Schwarz 交替法的岩溶区双孔土洞地基稳定性分析

为分析岩溶区双孔圆形土洞的地基稳定性,利用柯西积分法求出存在单一土洞时的复应力函数,基于Schwarz交替法进行二次迭代导出双极坐标系下土层中任意一点的应力大小;通过应力坐标转换求得土体的最大、最小应力,利用Mohr-Coulomb强度准则判定土洞洞边最危险点的稳定状态;将本文方法计算结果与精确解析解以及ABAQUS数值模拟结果进行对比,并结合工程算例验证了Schwarz交替法具有较高的精度;引入稳定系数,从土体的侧压力系数、土洞半径比以及土洞相对位置3个方面对双孔土洞的稳定性进行参数分析,结果表明:土洞稳定系数与土体侧压力系数呈线性正相关,随土洞半径比的增大而非线性减小,随土洞相对位置的增大先保持不变而后线性增大。

Stability analysis of double soil cave foundation in karst area based on Schwarz alternating method

To analyze the foundation stability of the circular soil cave with double holes, the complex stress function is obtained for a single hole by the Cauchy integral method. The stress of any point in the soil layer under bipolar coordinates is derived based on the Schwarz alternating method by two iterations. The maximum and minimum stresses of the soil are obtained by stress coordinate transformation and the Mohr-Coulomb strength criterion is used to determine the stability state of the most dangerous point of the soil cave. The calculated results in this paper are compared with the exact analytical solutions and the ABAQUS numerical simulation results. Application to an engineering example proves that the Schwarz alternating method has higher precision. The stability coefficient is introduced to analyze the stability of the double-hole soil cave from three aspects, the lateral pressure coefficient, the ratio of the soil cave radius and the relative position of the soil cave. The results reveal that the stability coefficient of soil cave has a linear positive relationship with the lateral pressure coefficient. It decreases nonlinearly with the increasing value of the ratio of the soil cave radius and remains unchanged first and then increases linearly with the increase of the relative position of the soil cave.