考虑坡顶倾角的土质裂隙边坡稳定性分析

自然界或人工填土边坡常因裂隙的出现而导致其稳定性降低。裂隙的发育不仅与岩土体的材料性质相关，还取决于边坡的几何形态。为了研究边坡的坡顶倾角对裂隙边坡稳定性的影响，基于极限分析上限定理，以坡顶存在一定倾角的裂隙边坡为研究对象，利用平面应变的对数螺旋旋转机构对其进行计算和分析。考虑静力作用和地震力作用的影响，构建了在这2种作用力下裂隙边坡的速度相容运动场及相应的能量平衡方程。采用裂隙的深度和位置均未知、裂隙的深度已知而位置未知、裂隙的位置已知而深度未知这3种计算模式，通过序列二次规划程序计算了不同坡体参数（坡角β、坡顶倾角α、内摩擦角φ）、不同地震力（k_h=0.1，0.2，0.3）作用下裂隙边坡的稳定性系数。结果表明：与坡顶水平相比，坡顶倾角越大，边坡的稳定性系数减小百分比越大；考虑坡顶倾角与否，稳定性系数相差高达15%，并且地震力越大，坡顶倾角对稳定性系数减小百分比的影响越明显；随着坡顶倾角增大，临界裂隙的深度会逐渐增大，其位置也会逐渐远离坡肩；裂隙在坡顶一定范围内时边坡的稳定性系数才会降低，而坡顶倾角和地震力的影响会使得这一坡顶范围增大；在静力作用下，随着边坡坡角增大，稳定性系数减小百分比呈先增大后减小的趋势。最后，通过OPTUMG2对计算结果进行验证可知，该研究对裂隙边坡坡顶倾角的考虑具有合理性。

Stability Analysis of the Soil Slope with Cracks Considering the Upper Slope Inclination

Cracks often adversely influence the slope stability. Crack development is not only related to the soil properties but also depends on the slope geometry. To study the influence of the inclination angle of an upper slope on the stability of slopes with cracks, this study considered an upper non-horizontal slope with cracks as a research object using the kinematic approach of limit analysis and logarithmic spiral rotating mechanism of plane strain. The effects of static and seismic forces were considered, and the velocity compatible motion field and corresponding energy balance equation were developed. Three different types of calculation models were employed, namely, unspecified depth and location of cracks, cracks with known depth but unknown location, and cracks with known location but unknown depth. The stability factor of the soil slope with cracks under different slope parameters (slope angle β, inclination angle of the upper slope α, and internal-friction angle φ) and different seismic forces (k_h=0.1, 0.2, and 0.3) was calculated using nonlinear sequential quadratic programming. The results demonstrate that the greater the inclination angle of the upper slope, the greater the percentage reduction in the slope-stability factor. The overvaluation of the stability factor is as high as 15%, if the upper slope inclination angle.is not considered. The larger the seismic force, the more significant the influence of the inclination angle of the upper slope on the percentage reduction in the stability factor. With the increase in the inclination angle of the upper slope, the depth of the critical crack gradually increases, and its position gradually moves far from the crest. Only when the crack is within a certain range does the stability factor decrease, and this range increases owing to the effect of the inclination angle of the upper slope and the seismic force. Under static forces, as the slope angle increases, the reduction percentage in the stability factor first increases and then decreases. In comparison with the results of OPTUMG2, the stability analysis of soil slopes with cracks considering the upper slope inclination angle in this work is reasonable.