非均质土坡稳定性分析评价的刚体单元上限法

UPPER BOUND APPROACH OF RIGID ELEMENTS FOR INHOMOGENEOUS SOIL SLOPE STABILITY ANALYSIS

非均质土坡的稳定性分析评价是土力学的经典课题之一。以极限分析方法为理论基础,建立分段对数螺旋线滑面的旋转破坏机制。在滑体被视为刚性体条件下,通过ANSYS有限元软件的前处理功能,对层状土质边坡潜在滑体进行三角形单元离散和网格化。按照极限分析法上限原理,分别计算每个三角形单元滑体在重力及地震作用力条件下所作的外力功率,以及分段对数螺旋线滑面上阻力产生的内能耗散。采用强度折减法和极限分析上限定理的虚功率方程,推导得到非均质土坡稳定性评价的刚体单元上限法安全系数计算公式。以土质边坡为例,分别使用瑞典条分法、Bishop法、Janbu法和刚体单元上限法进行稳定性分析计算比较。结果表明,刚体单元上限法可以得到层状介质土坡安全系数的上限解,而Bishop法计算得到的安全系数则接近下限解。综合分析认为,当安全系数的上限和下限界定后,合理的选用安全系数对边坡工程非常重要。与其他方法比较,刚体单元上限法对层状介质组成的非均质土坡有一定的适用性。

Stability analysis of inhomogeneous soil slope is one of classical problems for soil mechanics. The authors establish a rotational failure mechanism with combination of different logarithmic spiral arcs based on the theory of limit analysis method. When slip mass is looked upon as rigid-body, the layered soil slope can be discretized and meshed by triangle elements which are the pre-processor of the ANSYS software. According to upper bound theory of limit analysis method, not only every triangle element＇s external work-rate done by self-weight and seismic force but also the internal energy dissipation produced in different logarithmic spiral arcs can be totally calculated. By means of strength reduction method and virtual work-rate equation for upper bound theorem, the calculation formula of upper bound solution with rigid elements for inhomogeneous soil slope stability analysis can be deduced. As an example of two layered soil slope, the factor of safety is computed by different methods such as Sweden slice method, Bishop method, Janbu method and upper bound approach of rigid elements. The results show that the new method can obtain the upper-bound solution for layered soil slope, but the value of factor of safety calculated by the method of Bishop is close to the lower-bound solution. It is very important to choose proper solution of factor of safety when the upper limit and lower limits are certainly made. At last, the new method has good applicability for layered soil slope stability analysis.