Abstract:

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.

Key words: Monte Carlo search technique, multi-block upper bound method, bearing capacity, limit analysis