地震效应下二级边坡三维动态稳定性上限分析

为了给二级边坡的抗震设计提供参考，对其在地震力作用下的稳定性进行研究。基于三维破坏模型，采用拟静力法将地震力引入计算模型中，运用极限分析上限定理分析二级边坡破坏时的能量耗散，并根据虚功率原理推导稳定系数的解析解。利用穷举法优化计算，得到约束条件下稳定系数的最优上限解，并与已有研究成果进行对比。利用该方法，分析宽高比、内摩擦角、深度系数、上、下台阶倾角、地震力等因素对二级边坡稳定性的影响。针对不同的计算精度，给出二级边坡可简化为二维平面应变问题的最小宽高比。研究结果表明：该方法正确可靠；宽高比对稳定系数影响显著，随着宽高比的增大，二级边坡的三维效应逐渐弱化，最终转变为二维平面应变问题，内摩擦角、深度系数、上、下台阶倾角对稳定系数有较大影响；对边坡进行放坡时，应尽量减小上、下台阶的倾角，并增大上台阶边坡的高度，以提高二级边坡的稳定性；水平地震力与竖直地震力对二级边坡的稳定性有显著影响，如果计算中不考虑地震力，则稳定系数的相对误差分别高达40%和15%。

Three-dimensional Seismic Stability Limit Analysis of Two-stage Slope by Kinematical Approach

In order to provide a reference for the seismic design of the two-stage slope, the stability of two-stage slopes under the earthquake was investigated. Based on the three-dimensional failure model, the seismic force was introduced into the calculation models by the quasi-static method. On the basis of the upper bound theorem of limit analysis, the energy dissipation of the failure state of two-stage slopes was analyzed, whilst analytical solutions of the stability factor were deduced by the fictitious power principle. By virtue of the exhaust algorithm, the optimal upper bound solutions under constraint conditions were obtained. The validity of the proposed method was demonstrated by comparing the results with ones of existing researches. Parametric analysis was carried out to investigate the impact of diverse parameters on the stability of two-stage slopes, including depth-width ratio, the internal friction angle, the depth coefficient, slope angles and the seismic force. The results show the depth-width ratio affects the stability factor greatly. With the increase of the depth-width ratio, the three-dimensional effect of two-stage slopes gradually decreases, and the problem becomes a plain-strain problem in the end. The minimum depth-width ratio of the transformation from three-dimensional problem to a plain-strain problem is given at different computational accuracy. The internal friction angle, depth coefficient and slope angles have significant influences on the stability factor. In order to improve the stability of two-stage slopes, the slope angles should decrease and the height of upper-stage slope should increase. The horizontal and vertical seismic forces affect the stability of two-stage slopes evidently. Failing to take them into consideration will cause a difference as high as 40% and 15% respectively.