有限元强度折减法在土坡与岩坡中的应用

通过有限元强度折减，使边坡达到破坏状态时，滑动面上的位移将产生突变，产生很大的且无限制的塑性流动，有限元程序无法从有限元方程组中找到一个既能满足静力平衡又能满足应力．应变关系和强度准则的解，此时不管是从力的收敛标准，还是从位移的收敛标准来判断有限元计算都不收敛，因此采用力和位移的收敛标准作为边坡破坏的判据是合理的。对有限元强度折减法的计算精度和影响因素进行了详细分析，包括屈服准则、流动法则、有限元模型本身以及计算参数对安全系数计算精度的影响，并给出了提高计算精度的具体措施。研究表明：采用徐干成、郑颖人(1990年)提出的摩尔一库仑等面积圆屈服准则求得的稳定安全系数与传统Spencer法的误差在5％左右，证实了其实用于工程的可行性。在平面应变条件下则可采用摩尔匹配DP准则。该文还将此法应用于岩质边坡的稳定分析，得到了岩质边坡的滑动面和安全系数，开创了求节理岩质边坡滑动面与稳定安全系数的先例。

Application of Strength Reduction FEM in Soil and Rock Slope

With the c-tanj reduction,the FEM model of slope reaches instability,and the value of the nodal displacement just after slope failure has a big jump compared with that before failure. This actually means that no stress distribution can be achieved to satisfy both the yield criterion and global equilibrium. Slope failure and numerical non-convergence take place at the same time. So non-convergence in finite element program can be taken as a suitable evaluation criterion of slope failure. The influence on safety factor precision of different yield criterions,flow rule,FEM itself is thoroughly analyzed. At the same time some measures to improve the precision are put forward. A cone characterizes the Mohr-Coulomb surface in three-dimensional stress space with the vertices in deviatoric cross section. It brings difficulty to numerical analysis. For convenience this surface can be replaced by a smooth surface yield criterion,Mohr-Coulomb equivalent area circle DP yield criterion,which was proposed by professor Xu Gancheng and Zheng Yingren in 1990. The results show that the average error of safety factors obtained by FEM with Mohr-Coulomb equivalent area circle DP yield criterion and by Spencer method is about 5%. The average error of safety factor obtained by FEM with the plane strain Mohr-Coulomb matching DP yield criterion and by Spencer method is about 2%. The strength reduction FEM can also be used in the jointed rock slope. Through a series of case studies,the applicability of the proposed method is clearly exhibited.