基于动态加速度显式数值流形法的边坡稳定性分析

Slope Stability Analysis Based on Dynamic Acceleration Explicit Integral Numerical Manifold Method

为增强数值流形法(Numerical Manifold Method,NMM)处理大规模非线性动力学问题的精度,借助显式积分算法在处理大规模非线性问题方面的优势,同时延续NMM可在同一计算架构下处理连续—不连续问题的特点,提出了动态加速度显式数值流形法。定义加速度在单个时间步长内呈线性变化,推导了动态加速度显式积分算法公式,并进行了动态加速度显式数值流形法稳定性测试,最后将该方法应用到某露天矿岩质边坡稳定性分析中。研究表明:当程序运算总时步数越多,块体数目越多时,动态加速度显式数值流形法相较于传统NMM的优势越明显,进一步印证了该方法在处理大规模非线性动力学问题的可行性。露天矿边坡失稳模式为中上部推移式滑坡,考虑到滑坡体厚度约为30 m以及滑坡体的实际状况,推荐采取对滑坡体及失稳面进行注浆加固的方式,增强其自承载能力来提高其稳定性,进而也可支撑滑坡体后方边坡。

In order to strengthen the accuracy of Numerical Manifold Method(NMM)for processing large-scale nonlinear dynamics problems,the Numerical Manifold Method with dynamic acceleration is proposed,which takes advantage of explicit integration algorithm for processing large-scale nonlinear problems and extends the characteristics of NMM for processing continuous and discontinuous problems under the same computational framework.The acceleration is defined to change linearly in a single time step,the explicit integration algorithm formula of dynamic acceleration is derived,and the stability test of dynamic acceleration explicit numerical manifold method is carried out.Finally,this method is applied to the stability analysis of an open-pit rock slope.The results show that when the total number of steps and the number of blocks are increased,the advantages of dynamic acceleration explicit numerical manifold method over traditional NMM become more obvious,which further proves the feasibility of this method in dealing with large-scale nonlinear dynamics problems.The slope instability mode of open-pit mine is the upper and middle slide.Considering the thickness of the slope is about 30 m and the actual situation of the slope,it is recommended to reinforce the slope and the instability surface by grouting,so as to enhance its self-bearing capacity to improve its stability and support the slope behind the slope.