地基承载力上限分析中的Monte Carlo搜索技术

Greco提出的临界滑裂面搜寻的Monte Carlo搜索技术具有原理简单、适应性强、搜索性能好及容易编程实现等优点,目前该类方法已在边坡稳定的优化计算中有许多成功的应用。为能够在多块体上限法求解地基极限承载力的优化计算中应用Monte Carlo搜索技术,基于上限法相容速度场的要求及地基承载力问题的特点,对Monte Carlo搜索技术实现中的目标函数、几何约束条件、初始破坏面的产生以及收敛准则等重新进行了设置。由于Monte Carlo搜索技术随机性的特点,某一次的搜索优化往往存在陷入局部极值的危险,为解决这一不足,采取了随机设置多次初始破坏面分别进行搜索优化的办法,计算表明,优化效果很好。通过对实际问题的计算以及对比发现,Monte Carlo搜索技术在此处多块体上限法求解地基承载力问题中的优化应用是相当成功的。此外,由于此处的优化是以破坏面上的节点为对象的,因此,不但可以方便地考虑三角形块体的优化,而且也可以方便地考虑四边形块体的优化问题,其适用性更强。

Application of Monte Carlo search technique to bearing capacity calculations by upper bound method

Monte Carlo search technique proposed by Greco is of the random walking type, and has been successfully used in the optimization calculation of the slope stability analysis. The method presented by Greco(1996) can provide solutions of the same quality as the best nonlinear programming methods, but the structure of the method is very simple. The Monte Carlo search technique can be easily programmed and implemented. In this paper, the Monte Carlo search technique presented by Greco(1996) is modified and improved to be applied to the optimization of the bearing capacity calculation by multi-block upper bound method. For this purpose, the following conditions must be taken into consideration, which are the kinematical admissibility requirement imposed by the upper bound method and the boundary conditions of the bearing capacity problems. Based on the above restrictions, the re-establishments have been done for the objective function, the geometrical constraints, and the generation of the starting slip surface and the criterion of arrest. After calculations, it has been found that, the search results tend to catch the local extremum due to the random characteristic of the Monte Carlo search technique and the more rigorous requirements imposed by the upper bound theorem. To solve this problem, many initial failure surfaces are generated to search respectively and the minimum value is selected as the final result. To examine the application quality of the Monte Carlo search technique, lots of calculations are done and comparisons are made. From the comparison, it is shown that the modified Monte Carlo search technique is efficient in optimization of bearing capacity calculation by upper bound. It should also be pointed out that the Monte Carlo search technique used here adopts the points on failure surface as the variables to optimize. So, it is convenient to optimize the failure mechanism employed which includes both the triangle blocks and quadrangle blocks in the multi-block upper bound method.