基于上限定理的三维边坡稳定性分析探讨

利用上限定理,对纯黏性长大边坡的三维稳定性进行了研究。以边坡外某点为圆心,构建了球形破坏机构。利用三重积分,计算了该破坏机构下边坡的外力功率与内部能量耗散。基于功能相等定理,得到了边的三维稳定系数表达式。结合强度折减法,进一步研究了边坡的三维安全系数。通过与已有结果的对比,证明了该方法的正确性。分析了安全系数的变化规律,结果表明随着边坡宽度的增大,三维安全系数逐渐减小。为分析普通黏土边坡的三维稳定性奠定了基础。

Discussion for Three-dimension Upper Bound Stability Analysis Based on Theorem

Based on upper bound theorem, the three-dimension （3D） stability for purely cohesion slope was analyzed. Using some certain point above the slope surface as the circle center, the spherical failure mechanism was constructed. Appling the triple integral, the external work rate and internal energy dissipation was calculated. Based on the equality of work rate and energy, the expression for 3D stability can be obtained. Combining the strength reducing method, the 3D safety factor was studied further. By the comparison with the previous achievement, the correctness has been proved. The results show that the 3D safety factor reduced with the slope width. The presented study is the fundament for the cohesion-friction soil slope.