基于极限分析的边坡实时动态Newmark滑块位移法

 Newmark滑块位移法常被用于计算边坡的震后位移，但其计算过程所使用的均为边坡失稳瞬间状态的参数，并未考虑到滑坡体在地震时程中不断变形下滑所引起的参数变化。基于极限分析原理，考虑滑坡体下滑转角对各做功功率以及边坡几何参数的影响，推导了边坡实时屈服加速度系数、实时角加速度以及震后水平位移的计算表达式；使用Matlab编程并以地震波记录时间间隔为单位对滑坡体的动态参数进行实时更新，实现了实时动态的Newmark滑块位移法计算过程；将该方法应用于典型边坡算例中，并与传统的Newmark滑块位移法进行了对比。结果表明：边坡实时屈服加速度系数会随着滑坡体转角的增大而增大，考虑实时动态效应的边坡震后位移比不考虑的结果要小，且两者之间的差异会随着边坡整体稳定性的提高而逐渐减小。该方法弥补了传统Newmark滑块位移法应用中忽略实时动态效应的不足，其成果可为相关边坡的抗震设计与震后变形计算提供新的参考。

A real-time dynamic Newmark sliding block method for slopes based on limit analysis

The Newmark sliding block method was generally employed to calculate the seismic displacement of slopes. The calculation procedure considers only the parameters of the initial sliding moment，while the variation of the parameters due to the sliding rotation is not taken into account. Based on the theory of limit analysis，the influences of the sliding rotation angle on all the work rate and geometrical parameters are taken into account. The expressions of the real-time yielding acceleration factor，angular acceleration，seismic horizontal displacements are derived. Besides，a program was developed using Matlab software to update real-timely the dynamic parameters of the sliding soil mass in each sampling time-interval of the seismic wave and to realize the real-time dynamic Newmark sliding block method. This method was applied in a typical slope case and compared with the traditional Newmark sliding block method. The comparison indicated that the real-time yielding acceleration factor increased with the rotation angle increasing. The displacement considering the real-time dynamic effect was smaller than that from the traditional Newmark method，and the difference between them decreased as the global stability of slope increased.