关于强度折减有限元方法中边坡失稳判据的讨论

Discussion on criteria for evaluating stability of slope in elastoplastic FEM based on shear stre ngth reduction technique

在边坡稳定性分析中采用强度折减弹塑性有限元方法时,所得到的总体安全系数在一定程度上依赖于所采用的失稳评判标准,通常以数值计算的收敛性作为边坡失稳判据。而有限元计算的数值收敛性受多种因素的影响,因而由此所得到的安全系数的合理性及其唯一性受到了质疑。为了考查目前各种失稳判据的合理性及其适用性,分别依据计算的收敛性、特征部位位移的突变性和塑性区的贯通性等3个失稳判据,针对某一典型边坡算例,采用强度折减弹塑性有限元方法进行稳定性分析,并与Spencer极限平衡法所得到的总体安全系数进行了对比。对比分析表明,以有限元数值计算的收敛性作为失稳判据在某些情况下所得到的安全系数可能误差较大,而采用特征部位位移的突变性或塑性区的贯通性作为失稳判据所得到的边坡安全系数与Spencer极限平衡法的计算结果比较接近,考虑到实用性与简便性,建议在边坡稳定性分析的强度折减有限元方法中联合采用特征部位位移的突变性和塑性区的贯通性作为边坡的失稳判据。

While the elastoplastic finite element method based on the shear strength reduction (SSR) technique is employed to analyze slope stability, the overall factor of safety computed numerically is, in a certain degree, dependent on the criteria used for evaluating critical instability condition of slope. As usual, the convergence of the numerical computation of elastoplastic FEM is commonly employed in conventional studies. In fact, the convergence of the nonlinear analysis of elastoplastic FEM is controlled by a number of factors. Therefore the rationality and uniqueness of the numerical solution of the safety factor are in doubt. In order to examine the reasonability and applicability of various criteria including the convergence of numerical computations, the abruptness of the displacement or deformation at a certain characteristic location and connectivity of plastic zone, an example slope is analyzed by using the elastoplastic FEM based on the SSR technique. The computed results are compared with the solution of the Spencer's procedure of limit equilibrium. It is shown that the safety factors computed by using the criteria respectively based on the abruptness of the displacement or deformation at a certain characteristic location and connectivity of plastic zone are almost identical to the solution of limit equilibrium method, while the elastoplastic FEM analysis based on the convergence of numerical computations may give an incredible estimation of the safety factor in some circumstances. Considering the feasibility and simplification in engineering practices, both criteria based on the abruptness of the displacement or deformation at a certain characteristic location and connectivity of plastic zone are suggested to be jointly used in the elastoplastic FEM analysis of slope stability.