考虑参数空间变异性的边坡稳定可靠性有限元极限分析

当土性参数空间变异性较大时,极限平衡法得到的滑移面不尽合理。阐述了基于广义变分原理的有限元极限分析方法,采用混合有限元方法,构筑了线性应力三角形单元与线性速度三角形单元,结合强度折减法与线性规划算法,建立了边坡稳定安全系数上下限分析方法,分析了土的抗剪强度参数空间变异性对边坡稳定性的影响,并与3种典型极限平衡法进行了对比。结果表明,FELA方法可有效搜索边坡临界滑移面,并给出安全系数的严格上下限。对于简单均质边坡,有限元极限分析与极限平衡法结果接近,极限平衡法结果大多位于极限分析的上下限内;对于空间变异性较大的边坡,有限元极限分析法可以有效搜索可能的多种临界滑移面,而极限平衡法则存在显著偏差,且往往高估滑坡风险。强度参数的空间变异性还导致边坡安全系数分布形式变化显著,仅采用安全系数无法反应这一变化。根据安全系数的分布形式,给出了土性参数设计值建议。

Finite element limit analysis of slope stability considering spatial variability of soil strengths

The slip surface obtained by the limit equilibrium method is not reasonable when the spatial variability of soil parameters is large. The finite element limit analysis method, FELA in simple, based on the generalized variational principle is introduced. By using the mixed finite element technology, the linear stress triangular elements and linear velocity triangular elements are proposed. By use of the strength reduction method and the optimization algorithm, the strict upper bound and lower bound of the safety factor of slopes are calculated. The influences of spatial variability of soil shear strength parameters on slope stability are analyzed, and the results are compared with those of the limit equilibrium methods. The results show that compared to the limit equilibrium method, the proposed FELA can search the critical slip surfaces effectively under spatial variability of soil strengths and provide the strict upper and lower bounds of safety factors of slopes. But the limit equilibrium method will search for unreasonable slip surfaces, and often overestimate the risk of landslides. The spatial variability of soil strengths results in the significant change in the distribution of safety factors. But the single safety factor can not reflect the change. According to the distribution of safety factors, the design value of soil parameters is suggested.