潘家铮极值原理的优化算法实现

REALIZATION OF PAN JIAZHENG′S EXTREMUM PRINCIPLE WITH OPTIMIZATION METHODS

边坡极限平衡分析法通常情况下是静不定的,需要引入一些简化假定来求得安全系数。条间力函数f(x)作为其中的主要假设条件,其对安全系数的影响在过去的研究中并没有得到足够的重视。对二维极限平衡法采用优化算法求得满足潘家铮极值原理的安全系数,对于某一确定的滑裂面,将条间力函数f(xi)视为控制变量,采用模拟退火方法不断调整f(xi)以求解安全系数极大值,实际上是一种下限法;而搜索临界滑裂面的过程,采用粒子群法或和声法搜索最危险滑动面。另外,还探讨求解安全系数时通常会碰到的收敛性问题,结果证明f(x)不能随意设定,否则会引起不符合实际的条间力。相比传统的极限平衡法,该极值优化法极大地提高了收敛性。

Slope stability analysis based on the limit equilibrium method is statically indeterminate, which requires various assumptions to evaluate the factor of safety. The interslice force functionf（x） is a major assumption that is important but is not adequately considered in the past. The authors propose that the factor of safety and the interslice force function can be determined in accordance with the Pan Jiazheng＇s extremum principle from an optimization analysis. For any prescribed failure surface, the interslice force function f（xi） is taken as the control variable： and the maximum factor of safety will be computed by tuning function f（xi） with the simulated annealing method, which is actually equivalent to a lower bound approach. For locating the critical failure surface, the particle swarm or the harmony method is used, which is an upper bound approach. In addition, the problem of convergence in evaluating the factor of safety is investigated; and it is demonstrated that interslice force function f（x） cannot be arbitrarily assigned if consistent and acceptable internal forces are required. The presented approach has a further advantage that convergence during the stability analysis is greatly reduced which is not possible with all the other existing ＂rigorous＂ methods, and an interslice force function is not required in the analysis .