基于Griffith强度准则的岩溶区桩基溶洞稳定性分析

为了给出桩端荷载作用于不同位置溶洞的稳定性评价方法，首先，依据岩溶区桩基承载特性，不考虑桩身侧摩阻力的影响，将上覆土层等效为相同重度的岩层，建立简化计算模型。其次，将桩端荷载等效为一集中力，基于Mindlin解求得桩端荷载作用下半无限空间内的地层应力。再次，利用复变函数的方法求得溶洞在重力作用下的地层应力，其主要思想是通过映射函数将溶洞所在平面映射到单位圆外域上，根据边界条件对地层应力进行求解。最后，将桩端荷载作用下产生的地层应力与溶洞在重力作用下产生的地层应力进行叠加，从而得到桩端荷载作用在含有溶洞地层中的应力表达式，并在此基础上求得最大、最小主应力，同时引入Griffith强度破坏准则，对溶洞稳定性进行评价。结果表明：通过计算可得溶洞边界上的应力最为集中，因此在实际工程应用中，可对溶洞边界上关键点进行验算来判断溶洞在桩基荷载作用下是否会发生破坏；理论计算结果与工程实际情况吻合良好，为岩溶区桩端荷载作用下溶洞稳定性评价提供了一种新的、更为接近工程实际情况的理论计算方法；值得注意的是，所提计算模型是基于平面应变假定，不能考虑桩和溶洞之间的空间效应，因此该方法也只能考虑单个溶洞的影响，这些问题在后续研究中值得深入探讨。

Stability Analysis of Cavity Under Rock-socketed Pile in Karst Areas Based on Griffith Criterion

The aim of this paper is to provide a stability assessment method of cavity under the pile-tip load at different locations. Firstly, according to the bearing characteristics of pile in karst areas, the effect of the side friction on the pile was ignored. A simplified calculative model was built taking the overlying soil layer as the same heavy rock stratum. Secondly, the pile-tip load was considered as a concentrated force, whilst the equation of formation stress in semi-finite space under the pile-tip load was introduced by Mindlin solution. Meanwhile, the formation stress in the semi-finite space under the pile-tip load was obtained, based on the complex variable function. It was plausible that the map function was deployed to map the plane of the cave to the outer domain of the unit circle, and the formation stress can be calculated on the basis of the boundary conditions. Finally, the formation stress of cavity under the pile-tip load was superimposed on the formation stress under the gravity, thus obtaining the equation of formation stress. On this basis, the major principal stress and minor principal stress were induced, and the cavity stability was evaluated based on Griffith failure criterion. The results show that, according to the calculation, the stresses mainly concentrate on the boundary of the cave. Therefore, in the practical engineering application, it is necessary to check key points of the cave boundary to estimate whether the cave will be damaged under the pile-tip load. The theoretical results agree well with practical engineering. The theoretical method has been proved to be valid to evaluate cavity stability under the pile-tip load in karst areas. However, it is noteworthy that the proposed calculation model is based on the plane strain assumption. The spatial effect between the pile and the cave may be ignored, and the method can only be used to estimate the influence of single cave. These problems need to be further investigated in the following researches.