Stochastic boundary element method for fracture reliability analysis

摘要

The analysis of random stress-strain fields and the rock structure reliability are important in the rock engineering design. Since the joint systems of rock mass are always with uncertainties, it is very difficult to solve the random stress-strain field of a rock structure in a jointed rock mass. Stochastic finite element methods have been applied to solve the problems of random stress-strain fields. However, boundary element methods provide alternatives with the advantages including efficiency and simplicity. In this study, a stochastic boundary element was developed for the analysis of fracture reliability. Displacement discontinuity method, an indirect boundary element method, was adopted due to its suitability of crack simulation. The integral equations and solutions are established by the partial derivation of the original integral equations and solutions. And the fundamental solutions were derived and implemented to a computer program. For calibration, an example problem was analyzed by the developed model, and the results were compared with those from Monte Carlo analysis. The results show that developed model can accurately analyze fracture reliability problems. And the developed model is much more efficient than the Monte Carlo analysis approach. The developed stochastic boundary element method can be applied to the reliability analysis of rock structures.