基于内外功率比的非直线坡面型边坡的稳定系数研究

在边坡稳定性上极限分析中, 由于考虑了材料的理想弹塑性本构关系与相关流动法则, 相比极限平衡法更符合岩土材料的特征。在以往的二维边坡极限分析上限法中, 要求坡面形态为规则的直线, 而无论是天然边坡还是人工边坡, 边坡的坡面形态往往并非规则的直线。此外, 以往的边坡极限上限分析中得到的稳定数N_s=c/γH主要针对土坡的临界高度计算, 且未考虑孔压等外力对边坡施加的外功率。不同于传统极限平衡法采用静力学的平衡条件, 本研究针对非直线型坡面边坡稳定性问题, 假定滑动面为对数螺旋线, 基于极限分析上限定理和虚功原理, 提出了一种边坡发生旋转破坏时旋转中心的确定方法, 推导出了非直线型坡面边坡的重力虚功功率和能量平衡方程的解析解, 并提出了基于内、外功率之比的稳定系数K用以评价边坡的稳定性。通过算例比较了不同形态天然边坡的稳定性和人工削坡对边坡稳定性的影响, 并分析了边坡的坡度(β)、土体的内摩擦角(φ)、黏聚力(c)以及孔压系数(r_u)对稳定系数K的影响规律。对于坡度较大的边坡, 通过削坡改变坡面形态提高了边坡的稳定系数K。稳定系数K随黏聚力的增加而非线性增大, 随孔压系数的增加而降低。当黏聚力相对于孔压系数对边坡稳定性影响更大时, 稳定系数K随内摩擦角的增加而增大; 反之, 稳定系数K则随内摩擦角的增加而减小。以上结果符合对边坡稳定性分析的普遍认知, 验证了模型的合理性。另外, 通过将该方法与传统的Bishop法的计算结果进行对比, 发现安全系数F_s=1与稳定系数K=0的临界状态物理意义相同, 稳定系数K随黏聚力非线性增加, 更符合边坡的渐进破坏过程。 

Stability coefficient analysis of soil slopes with non-linear topography based on the ratio of internal to external power

The limit analysis of slope stability has a relatively higher calculation efficiency and accuracy because it ignores the constitutive relation of materials. Compared to the limit equilibrium method, its assumptions are strict and realistic. In the classical upper bound limit analysis, the slope surfaces are required to be a regular straight line. However, the surfaces of natural or cutting slopes are normally nonlinear. In addition, the stability number N_s=c/γH is used to calculate the critical height of slopes without considering the external power caused by pore pressure. Different from the static equilibrium conditions adopted by the traditional limit equilibrium method, this paper aimed to evaluate the stability of slopes with nonlinear surfaces based on kinetic analysis. First, a method for determining the rotation center of landslides with nonlinear surfaces based on upper bound limit analysis and the principle of virtual work was proposed. Second, it was assumed that the sliding surface was a logarithmic helix, and the virtual work under gravity and energy equilibrium equation of slopes were established. Third, the stability coefficient K defined by the ratio of internal power to external power was proposed to evaluate the stability of the slope, and the results were compared with the Bishop method to verify its effectiveness. The influences of slope degree (β), internal friction angle (φ), cohesion (c) and pore pressure coefficient (r_u) on the stability coefficient K of different natural and cutting slopes were analyzed. The results confirmed that the stability of steep slopes would be improved by cutting. The stability coefficient K increased with increasing cohesion and decreased with increasing pore water pressure coefficient. When the impact of cohesion on the stability coefficient K was more significant than that on the pore water pressure coefficient, K increased with increasing internal friction angle (φ). In contrast, the stability coefficient K decreases with increasing internal friction angle (φ). The above results followed the general understanding of slope stability analysis, and the rationality of the model was verified. By comparing the calculation results with the Bishop method, it was found that the intension of the critical state represented by safety factor F_S=1 was the same as the stability coefficient K=0 defined in this paper. The stability coefficient K increased nonlinearly with increasing cohesion, which was in line with the progressive failure mode of the soil slopes.