基于弹塑性区间有限元的边坡稳定性分析

Slope Stability Analysis Based on Elastic- plastic Interval Finite Element

区间分析法是工程中对不确定问题进行分析的方法之一。现有区间分析法大多采用区间参数摄动法求解,其存在明显的局限性,特别对于弹塑性问题需采用增量法计算时,很难得到有效的解答。在边坡稳定性计算中采用区间变量来描述工程中的不确定性,将区间数学与弹塑性有限元相结合,建立了弹塑性区间有限元,推导了基于弹塑性区间有限元方法的边坡稳定性区间安全系数计算公式,这一方法能有效的避免区间参数摄动法的局限性。通过工程实例,验证了该方法的可行性和有效性。在此基础上探讨了岩土体参数对区间安全系数的影响。结果表明,内摩擦角对边坡安全系数的影响明显,重度、黏聚力影响较大,弹性模量和泊松比影响小。

Interval analysis is one of the methods to analyze the uncertain problem in engineering. The interval parameter perturbation method is used to solve the existing interval analysis method, which has obvious limitations. It is difficult to get effective solutions for the elastic plastic problem using incremental method. Interval variables are used to describe the uncertainty in the slope. In this research the interval mathematics and elastic-plastic finite element method is adopted to- gether to establish the elastic-plastic interval finite element method. The calculation formula of Interval safety factor of slope stability is derived based on the elastic-plastic interval finite element method. This method can effectively avoid the limitation of interval parameter perturbation method. The feasibility and effectiveness of the proposed method were then verified by engineering examples. The influence of the parameters of the rock and soil on the safety factor was discussed. The results show that the inner friction angle has sensitive impact on the safety factor of the slope. The effect of elastic modulus and Poisson＇ s ratio on the safety factor is smaller than that of cohesion and unit weight.