求解三维边坡安全系数的最小势能法研究

Study on minimum potential energy method for solving safety coefficient of three-dimensional slope

为有效评价岩土体的稳定性,运用最小势能法进行三维边坡的稳定性分析。通过引入土弹簧模型、依据滑体整体静力平衡方程,计算滑体系统的弹性压缩势能以及剪切势能。基于物体在自重作用下沿斜面运动规律,确定微面下滑方向,将整个滑体的潜在运动方向视为微面滑动方向的矢量和。将边坡的安全系数定义为沿着滑动方向得到的抗滑力与下滑力的比值。为验证文中计算方法的合理性,计算了一个经典算例的安全系数。研究结果表明:文中计算方法得到的解答与其他算法的相对误差在10%范围内,表明文中计算方法可用于三维边坡的稳定性分析;随着土体抗剪强度指标的增大,边坡的安全系数呈现线性增大的趋势;当三维滑体的横向尺寸与纵向尺寸之比大于5时,可以将三维边坡的稳定性分析视为平面应变问题处理。

In order to evaluate the stability of rock and soil effectively, the minimum potential energy method was used to analyze the stability of three-dimensional slope. The elastic compression potential energy and shear potential energy of the sliding body system were calculated by introducing the soil spring model and the overall static balance equation of the sliding body. At the same time, the sliding direction of the micro-plane was determined according to the law of motion of the object along the inclined plane under the action of gravity. The potential moving direction of the whole sliding body was regarded as the vector sum of the sliding direction of the micro-plane. Finally, the safety factor of slope was defined as the ratio of anti-sliding force to sliding force along the sliding direction. In order to verify the rationality of the calculation method in this paper, the safety factor of a classical example was calculated. The results show that the relative error between the solution and the other methods is within 10%, which indicates that the calculation method in this paper can be used for the stability analysis of three-dimensional slope. With the increase of the shear strength index of soil, the safety factor of slope presents a linear increase trend When the ratio of the lateral dimension to the longitudinal dimension of the three-dimensional sliding mass is greater than 5, the stability analysis of the three-dimensional slope can be treated as a plane strain problem.