Progressive Failure Mode and Stability Reliability of Strain-Softening Slope
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摘要: 针对现有考虑应变软化效应的边坡渐进破坏分析模型中计算假定条件不符合实际情况的不足，以三峡库区赵树岭滑坡为研究对象，考虑地下水位波动和地震力的影响，提出用于分析多场耦合条件下应变软化边坡渐进破坏模式及稳定性可靠度的方法.结果表明，地下水位波动和地震力会不同程度地影响滑坡的渐进破坏模式和破坏概率.滑坡在145 m、175 m水位和库水位从175 m陡降为145 m三种工况下整体稳定，但分别有14.119%、20.266%和21.797%的概率发生局部渐进破坏；在烈度为Ⅶ的地震力作用下同时考虑3种蓄水工况，该滑坡分别有34.067%、38.061%和38.405%的概率发生整体渐进破坏；根据滑坡渐进破坏模式指出最佳加固位置应在沿江大道前沿.该分析方法具备可靠性，可为边坡的渐进破坏模式及稳定性评价研究提供参考.Abstract: Aiming at the shortcomings of the calculation assumptions proposed in the existing slope progressive failure analysis model considering the effect of strain-softening, the Zhaoshuling landslide in the Three Gorges Reservoir area is taken as the research object, and the influence of groundwater level fluctuations and seismic forces is considered to propose the progressive failure mode and stability reliability analysis method of strain-softening slope under multi-field coupling conditions.The results show that the groundwater level fluctuation and seismic force would affect the progressive failure mode and failure probability of the landslide to various degrees.The landslide was stable at 145 m, 175 m water level and the steeply reduced reservoir water level from 175 m to 145 m, but it had a local progressive failure probability with 14.119%, 20.266% and 21.797% respectively. And the landslide had a total progressive failure probability with 34.067%, 38.061% and 38.405% respectively under the action of seismic force with intensity VII, also three kinds of water storage conditions were considered. Moreover, according to the progressive failure mode of landslide, it is pointed out that the best reinforcement position should be at the front of Yanjiang Avenue. The analysis method is reliable and can provide a reference for the progressive failure mode and stability evaluation of slopes.
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图 1 边坡复合式渐进破坏失稳过程示意图
Fig. 1. Schematic diagram of progressive failure process for combined slope
图 6 不同工况条件下滑坡渐进破坏事件及事件概率
Fig. 6. Progressive failure event and probability of landslide under different working conditions
表 1 滑坡物理-力学参数统计值
Table 1. Statistics of landslide physical-mechanical parameters
物理参数 天然密度(kg∙m-3) 饱和密度(kg∙m-3) 2 500 2 600 力学参数 天然内聚力（MPa） 残余内聚力（MPa） 饱和内聚力（MPa） 饱和残余内聚力（MPa） 天然内摩擦系数 残余内摩擦系数 饱和内摩擦系数 饱和残余内摩擦系数 0.020 0.015 0.015 0.010 0.364 0.325 0.325 0.287 变异系数 $ {\delta }_{{\mathrm{c}}_{\mathrm{p}}} $ $ {\delta }_{{\mathrm{c}}_{\mathrm{r}}} $ $ {\delta }_{{\mathrm{c}}_{\mathrm{s}\mathrm{p}}} $ $ {\delta }_{{\mathrm{c}}_{\mathrm{s}\mathrm{r}}} $ $ {\delta }_{{\mathrm{f}}_{\mathrm{p}}} $ $ {\delta }_{{\mathrm{f}}_{\mathrm{r}}} $ $ {\delta }_{{\mathrm{f}}_{\mathrm{s}\mathrm{p}}} $ $ {\delta }_{{\mathrm{f}}_{\mathrm{s}\mathrm{r}}} $ 0.13 0.13 0.18 0.18 0.19 0.19 0.20 0.20 相关系数 $ {\rho }_{{\mathrm{c}}_{\mathrm{p}}, {\mathrm{f}}_{\mathrm{p}}}={\rho }_{{\mathrm{c}}_{\mathrm{r}}, {\mathrm{f}}_{\mathrm{r}}}={\rho }_{{\mathrm{c}}_{\mathrm{s}\mathrm{p}}, {\mathrm{f}}_{\mathrm{s}\mathrm{p}}}={\rho }_{{\mathrm{c}}_{\mathrm{s}\mathrm{t}}, {\mathrm{f}}_{\mathrm{s}\mathrm{r}}}=-0.3 $ 注：变异系数与相关系数是根据现有研究成果进行的合理取值，其实际值应通过统计分析获得. 
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表 2 滑坡计算工况及滑体条分情况
Table 2. Calculation conditions of landslide and slice details of sliding body
滑坡计算工况 滑体条分情况 145 m水库蓄水 145 m水库蓄水+地震作用 175 m水库蓄水 175 m水库蓄水+地震作用 175 m库水位陡降为145 m库水位 175 m库水位陡降为145 m库水位+地震作用 注：红色实线为地下水位线；库水位陡降时，不考虑坡体内孔隙水压力的消散，即假定坡体内的地下水位线与降落前相同，仅考虑库水位的变动(郑颖人等，2004).
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表 3 各工况条件下滑坡峰值稳定性系数及渐进破坏路径
Table 3. Stability coefficient for peak parameters and progressive failure path of landslide under various working conditions
计算工况 峰值强度参数下滑坡稳定性系数 渐进破坏路径 145 m水库蓄水 中前部 中后部 1.217 1.322 145 m水库蓄水+地震作用 中前部 中后部 / 0.840 175 m水库蓄水 中前部 中后部 1.112 1.322 175 m水库蓄水+地震作用 中前部 中后部 / 0.840 175 m库水位陡降为145 m库水位 中前部 中后部 1.044 1.322 175 m库水位陡降为145 m库水位+地震作用 中前部 中后部 / 0.840 注：稳定性系数不唯一且小于0.840.
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表 4 滑坡最大概率发生的渐进破坏事件及概率值
Table 4. Progressive failure events with maximum probability and their probability values of landslide
计算工况 渐进破坏事件 发生概率(%) 145 m水库蓄水 整体渐进破坏 2.067×10-13 局部渐进破坏：16#条块发生破坏且破坏停止传递 14.119 145 m水库蓄水+地震作用 整体渐进破坏 34.067 175 m水库蓄水 整体渐进破坏 2.796×10-11 局部渐进破坏：16#条块发生破坏且破坏停止传递 20.266 175 m水库蓄水+地震作用 整体渐进破坏 38.061 175 m库水位陡降为145 m库水位 整体渐进破坏 4.104×10-10 局部渐进破坏：20#条块发生破坏且破坏停止传递 21.797 175 m库水位陡降为145 m库水位+地震作用 整体渐进破坏 38.405 注：计算所得概率值并非真实概率值，但计算结果具备较强的参考性.
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