基于多元线性回归分析的土坡有限元失稳判据定量研究

QUANTITATIVE STUDY ON CRITERIA FOR FEM EVALUATION OF SLOPE STABILITY WITH MULTIVARIATE LINEAR REGRESSIVE ANALYSIS

塑性区连通程度是有限单元法判别土坡是否达到极限状态的重要依据,鉴于此判据目前尚未取得统一,本文着重对均质土坡失稳判据进行了定量研究。在主要考虑对土坡稳定性影响较大的三大参数(黏聚力c、内摩擦角φ、坡比λ)的前提下,通过经典条分法选取了多组处于极限平衡状态的土坡参数组合,对这些参数组合进行有限元程序计算,求得极限平衡状态下土坡剪切带等效塑性应变中值连通率,再采用多元线性统计回归方法,得出塑性区中值连通率与土坡参数的关系公式y=0.020702c+0.024417φ-0.67898λ+0.46799,从而为土坡有限元稳定性分析提供了定量失稳判据,并且使得有限单元法与经典条分法计算成果具有一定的可比性。算例分析表明,利用本文判据公式得到的安全系数与Bishop法计算成果相吻合,从而验证了失稳判据公式的正确性。

Connectivity rate of plastic zone is one of the most important criteria of the finite element method for evaluating stability of soil slope whether or not it reaches instability.The criterion,however,is not uniformly recognized at present.Therefore,a quantitative study emphatically on the criterion for evaluating stability of homogeneous soil slope is discussed in this paper.At first,Considering the three main parameters（cohesion force c、angle of internal friction φ、slope ratio λ）of the slope stability,parameters of the slope which is in limiting state of equilibrium are selected by traditional slice method.Secondly,the connectivity rate of equivalent plastic strain median in shear band of the slope is got by adopting the above parameters.At last,the criteria formula（y=0.020702c＋0.024417φ-0.67898λ＋0.46799） for evaluating stability of slope is put forward though the multiple linear regression.The example indicates that the safety factor calculated by the formula is in accord with the Bishop slice method.So it validates that the quantitative criterion for evaluating stability of slope is reasonable.