中文摘要：

基于极限分析上限法和Newmark刚塑性滑块模型，推导考虑水平与竖向地震效应下，对数螺旋线型滑面边坡屈服加速度和边坡永久位移的计算公式；采用序列二次规划法编制非线性规划迭代程序对边坡地震永久位移计算模型进行优化求解，由此探讨竖向地震对边坡永久位移的影响规律。算例分析证明了本文方法的正确性。在此基础上，绘制边坡屈服加速度、位移系数以及4个典型地震加速度时程的2次积分图表，以便于边坡地震永久位移的查表计算。并给出具体算例，说明采用本文表格进行查表计算的流程。

英文摘要：

The formulas of yield acceleration and permanent displacement of slopes against logarithmic spiral fail- ure surface are deduced considering horizontal and vertical seismic effect based on upper bound limit analysis and Newmark rigid -plastic sliding block model. The nonlinear programming iteration procedure is compiled to cal- culate the optimal solution of slope seismic permanent displacement by adopting sequential quadratic program- ming, thus the influence rule of vertical earthquake on the slope permanent displacement is studied. Example a- nalysis proves the correctness of this method. On this basis, graphs of yield acceleration, displacement coefficient and the two integral tables of four typical earthquake acceleration time history are drawn, which make it easy to get the seismic permanent displacement. And calculation process of adopting this article tables is illustrated by a specific example.