Three-dimensional stability of slopes with cut-fill interface based on upper-bound limit analysis
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摘要: 针对工程实践中挖填交界面与边坡坡面走向线斜交的高边坡空间三维稳定分析问题，基于极限分析上限定理，构建拓展的三维牛角状破坏机构，通过引入机构参数挖填界面倾角α突出边坡特性，建立与之对应的功能平衡方程，采用序列二次规划优化算法求解强度折减后的边坡安全系数上限解。在此基础上，计算了宁夏黄土丘陵地区妙岭750 kV变电站高边坡以及相关文献中极限状态下边坡稳定性系数γH/c工程案例，并将计算结果与有限元极限分析软件模拟值进行对比分析。结果表明：随着挖填界面倾角α的增大，边坡安全系数Fs上限解和模拟值均减小，两种方法的计算结果相对误差在5.9%以内，且拓展的破坏机构与数值模拟的剪切耗散变形模式基本一致；在极限状态下，拓展机构的上限解和数值模拟结果都十分接近于1.0，二者相对误差未超过8.3%。研究工作为此类高边坡空间稳定分析问题提供了一种简便实用的计算方法。Abstract: For the problem of spatial three-dimensional stability analysis of high slopes in engineering practice where the cut-fill interface intersects obliquely crossing with the slope strike line, an expanded three-dimensional horn-shaped failure mechanism is established based on the upper-bound limit theorem in this paper. Then, the corresponding functional equilibrium equation is formulated by highlighting the slope characteristics by introducing the mechanism parameter dip angle α of the excavation-fill interface. The sequential quadratic programming optimization algorithm is used to solve the safety factor of the upper-bound limit analysis of the strength-discounted slope. On this basis, the high slope project of Miaoling 750 kV substation in Ningxia loess hilly area and the case of the stability factor γH/c under the limit state in the relevant literature are selected as examples, and the computations are compared with the simulated values of finite element limit analysis software. The results show that the upper-bound solution and the simulated value of the safety factor Fs of the slope both decrease with the increase of the dip angle α of the dredge-fill interface. The relative error of the calculated results of the two methods is within 5.9%, and the expanded damage mechanism is basically consistent with the shear dissipation deformation mode of the numerical simulation. In the limit state, the upper-bound solution of the expanded mechanism and the numerical simulation results are very close to 1.0, and the relative error of the two methods does not exceed 8.3%. The research work provides a simple and practical method for the spatial stability analysis of high slopes.
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图 1 含挖填界面边坡三维旋转破坏机构
Figure 1. Three-dimensional rotation failure mechanism of slope with cut-fill interface
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图 3 宁夏妙岭750 kV变电站挖填高边坡场景
Figure 3. Excavation and filling of high slope of Miaoling 750 kV substation in Ningxia
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图 4 算例的Optum G3剪切耗散变形图（H=5 m）
Figure 4. Optum G3 shear dissipative deformations of example(H=5 m)
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图 5 算例的Optum G3剪切耗散变形图（H=10 m）
Figure 5. Optum G3 shear dissipative deformations of example(H=10 m)
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图 6 本文破坏机构滑移面与数值模拟结果对比（H=5 m，α=45°）
Figure 6. Comparison of slip surfaces between proposed destructive mechanisms and numerical simulation(H=5 m, α=45°)
表 1 挖填土层基本物理力学参数
Table 1 Basic physical and mechanical parameters of excavated and filled soil layers
土层 黏聚力
c/kPa内摩擦角
φ/(°)重度
γ/(kN·m-3)上层黄土状粉土 12.5 31.0 16.8 下层黄土状粉质黏土 30.0 31.5 18.9 
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表 2 两种计算方法结果对比（H=5 m）
Table 2 Comparison of results of two methods(H=5 m)
工况 α/(°) Fs 相对误差/% Optum G3 本文 1 30 2.390 2.321 2.9 2 45 2.265 2.208 2.5 3 60 2.237 2.140 4.3
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表 3 两种计算方法结果对比（H=10 m）
Table 3 Comparison of results of two methods(H=10 m)
工况 α/(°) Fs 相对误差/% Optum G3 本文 1 30 1.608 1.574 2.1 2 45 1.581 1.490 5.8 3 60 1.555 1.464 5.9
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