基于Hoek-Brown破坏准则的岩溶区圆形基础下伏孔洞冲切破坏上限分析

Upper bound punching failure analysis of circular foundation overlying a cave in Karst area based on the Hoek-Brown failure criterion

基于Hoek−Brown(H−B)破坏准则及相关联流动法则,构建圆形刚性基础下伏孔洞的轴对称冲切破坏机制;根据极限分析上限定理,计算冲切破坏机制的内能耗散功率和外力功率;利用变分原理,推导出冲切破坏曲面在x−z平面上投影函数的一阶导数,利用差分原理迭代出满足边界条件的破坏曲线,进一步得到在自由冲切和非自由冲切条件下的圆形基础极限承载力;并分析了岩体单一参数变化时,圆形刚性基础极限承载力的变化趋势和破坏模式。研究结果表明:材料参数B对圆形基础的极限承载力的影响较为显著。随着材料参数B的增大,圆形基础极限承载力不断减小,且趋势趋于平缓。

Considering the rigid circular foundation overlying a cave,the punching failure mechanism of overlying surrounding rocks was constructed based on the Hoek−Brown failure criterion and an associated flow rule.In the framework of the upper bound theorem of limit analysis,the work rate of internal energy dissipation and the power of external forces of the punching failure mechanism were calculated,and the first derivative of the failure surface function projected in the x−z plane was deduced through the variation method.The failure surface satisfied boundary conditions was obtained by the difference theorem.Further,the ultimate bearing capacity(UBC)of circular foundations under free punching and non-free punching conditions was calculated.And the UBC and failure mechanism trends of the rigid circular foundation were analyzed with a single parameter changing.The results show that the material parameter B has a great effect on the UBC,which decreases constantly with the increases of B,and the trend becomes gentler.