基于方位离散线性化的上限原理有限元法

上限原理有限元法不仅可以得到边坡的安全系数,还可以给出临界滑动面,且具有比极限平衡法更严谨的理论基础,因此,拥有更广阔的应用前景。针对传统的上限有限元法不能考虑强度各向异性的问题,提出了一种新的摩尔-库仑屈服面线性化方法。该方法在对方位角离散化的基础上,建立了线性化的方位离散塑性流动约束方程,丰富了基于线性规划的上限法理论。两个算例结果表明:该方法可以稳定地从极限解的上方收敛;且对边坡进行稳定性分析,若忽略了边坡的强度各向异性,则会高估边坡的稳定性,得到较大的安全系数。

An upper-bound limit finite element method based on linearized spatial discretization

With a theoretical basis more rigorous than the limit equilibrium method, the upper-bound limit finite element method can be used to determine not only the safety factor of slope but also the critical slip surface so that it will have a broad prospect of application. To remove the limitation that the traditional upper-bound limit finite element method cannot address the effect of heterogeneity, a new Mohr-Coulomb yield surface linearization method is proposed herein, based on the linearized spatial discretization. Within this context, the linearized constraint equations for plastic flow are developed, which enriches the upper-bound limit method based on linear programming and lays a solid foundation for the application of linear programming technics to the upper-bound limit analysis. Two examples are analyzed, showing that the proposed method stably yields a convergent solution from above the upper-bound solution. In analyzing the stability of a slope, if the strength anisotropy is ignored, the factor of safety is overestimated, resulting in a larger factor of safety of the slope.