阻滑桩加固土坡稳定性分析的上限解法

Stability analysis of slopes with stabilizing piles based on upper-bound method of limit analysis

从极限分析机动学方法出发, 利用土的抗剪强度折减系数概念, 建立了土坡的极限平衡状态方程, 由此确定土坡的临界稳定安全系数及其相应的潜在破坏模式。对于典型问题, 通过与现有极限平衡解和有限元数值解的对比分析, 验证了这种上限解法的合理性。进而对于在给定的荷载条件下不能满足抗滑稳定性要求的土坡, 考虑采用阻滑桩加固方式, 根据桩侧有效土压力的合理分布模式确定桩体与滑动面相交的截面上等效抗滑力和抗滑力矩, 利用极限分析上限定理建立了阻滑桩加固土坡的极限平衡状态方程, 将桩侧土压力作为目标函数, 运用数学规划方法确定了极限平衡状态时的临界桩侧土压力,以此为土坡加固中阻滑桩设计提供依据。通过数值计算与分析探讨了阻滑桩加固位置的优化布置等问题。

Based on the kinematic method of limit analysis and the shear strength reduction technique, the equation for expressing the critical limit-equilibrium state is formulated and is employed to define the safety factor and its corresponding critical failure mechanism for a given slope. Through numerical analyses for typical examples, the solutions computed by the proposed approach are compared with the results given by limitequilibrium methods and finite element methods to verify the reasonability of the method. For the slopes of which the safety factor cannot fulfill the requirement of overall stability for the given loading condition, the stabilizing pile is considered for reinforcement of the slopes. As the key issue in this circumstance, the equivalent force and moment against sliding induced at the cross-section which intersects the potential slip surface are determined on the basis of the rational distribution mode of net lateral effective earth pressure acting on the stabilizing pile. Then the upper bound theorem of limit analysis is employed again for establishing the limit-equilibrium equation of the slopes reinforced by stabilizing pile in which the mobilized strength parameters are given by the actual strength parameters with a reduction by the desirable overall safety factor. The net lateral effective earth pressure acting on the pile can be chosen as the objective function, mathematical programming method and the optimization technique are utilized to define the critical state. The critical net overall lateral earth pressure acting on the pile will be used in the structural design of pile. Numerical computations are made to examine the optimum location of pile placement.