基于位移变化率和强度折减有限元的边坡失稳判定方法

Slope instability evaluation method using finite element method of strength reduction and displacement rate

采用强度折减有限元法计算边坡稳定时,以变形为基础的失稳判据具有显著的物理意义和工程意义。该文采用变步长的折减方法,基于位移变化率-强度折减系数曲线的转折突变作为失稳判据,并研究特征点的敏感性及选取范围。计算结果表明,当折减系数为1.42时,坡顶水平位移变化率、竖向位移变化率和总位移变化率均发生急剧性的转折。与位移相比,位移变化率-强度折减系数的曲线存在明显的转折突变,可更准确、明显地判断边坡稳定的安全度。至坡顶一定距离范围内的特征点,如位于非塑性区域且非滑动土体时,其位移变化率-强度折减系数的曲线发生转折突变,但曲线在转折点附近存在振荡现象。通过位移变化率计算得到的54个安全系数,平均值为1.420,变异系数为0.005 3,不同特征点根据水平位移变化率、竖向位移变化率和总位移变化率得到的安全系数基本一致。当特征点至坡顶的距离≤1倍坡高时,特征点的位移>12 mm,且位移变化率均较大,此时特征点对位移变化率较敏感;当特征点至坡顶的距离>1倍坡高时,特征点位移在5~18 mm之间,但位移变化率大幅度降低,此时特征点对位移变化率的敏感性大幅度降低。考虑边界约束的影响及特征点的敏感性,建议特征点的选取范围为:与坡顶距离为1倍坡高的范围。

Finite element method of strength reduction is an important and effective measure to evaluate the stability safety of geotechnical engineering. Also, finite element method of strength reduction is widely used in slope stability computation, and failure criterion using deformation has obvious significance in aspects of physical and engineering meaning. However, there is no consensus among researchers regarding location selection of critical points, step-size of strength reduction, determination from horizontal displacement, vertical displacement and total displacement. Also, there is no consensus with regard to how to judge the limit state of slope when there is no obvious knee point on the curve of displacement versus strength reduction factor.The strength reduction of variable step-size is proposed in the paper. The curves of displacement, displacement rate versus strength reduction factor, are calculated automatically with the main program of Fortran and subroutine program of ANSYS software. The knee point on curve of displacement rate versus strength reduction factor is chosen as the failure criterion, and the sensitivity and location range of critical points are also studied. When strength reduction factor is 1.42, there is definite and specific knee point on curve of horizontal displacement rate, vertical displacement rate and total displacement rate of slope top versus strength reduction factor, which shows displacement rate is more accurate and sensitive than displacement in terms of slope failure criterion. When the critical point is in the vicinity of slope top and it is not located in plastic zone or sliding soil mass, there is also abrupt turning on the curve of displacement rate versus strength reduction factor with oscillation phenomenon although the critical points are relatively far from the slope point; and the corresponding safety factor is also about 1.42. Eighteen critical points are selected from different locations of slope, and by means of curves of horizontal displacement rate, vertical displacement rate and total displacement rate versus strength reduction factor, 54 safety factors are obtained. Consequently, the mean value of 54 safety factors is 1.420 and the variation coefficient is 0.005 3, which show that different critical points have nearly same safety factors and there is little difference between safety factors judged by horizontal displacement rate, vertical displacement rate or total displacement rate. When the distance from critical point to slope top is smaller than 20 m, about the height of slope, the total displacement of critical point is larger than 12 mm and the total displacement rate is large, which indicate that the critical points have high sensitivity. When the distance from critical point to slope top is larger than slope height, the total displacement of critical point ranges from 5 to 18 mm but the total displacement rate decreases drastically, which show that the critical points are also not sensitive either. Considering the influence of boundary range and the critical points＇ sensitivity, it is suggested that the distance from the critical points to slope top should be less than the slope height. The step-size of strength reduction should be decreased gradually and small step-size should be used when the slope deformation is close to instable sliding.