A Theoretical Model about the Runout Distance of Bedding Rock Landslide under Excavation Uploading
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摘要: 顺层岩质滑坡在边坡工程中普遍存在，其运动距离不仅是表征滑坡形态的重要参数，也是风险评价的重要指标。基于顺层岩质滑坡演化过程的分析，推导了其运动距离的理论计算公式，并将公式应用于新嘉南滑坡进行验算。结果表明：开挖卸荷下顺层岩质滑坡的运动距离由三部分组成即块体在空中做自由落体产生的水平距离、与地面碰撞的移动距离以及最后在地面的滑动距离，此外，选取的新嘉南滑坡3个剖面运动距离理论计算值和实际值的相对误差分别为9.99%、2.53%以及0.58%，误差结果较小，表明公式适用性良好。研究成果对该类型滑坡预测与防治有一定的参考价值.Abstract: Bedding rock landslide exists widely in slope engineering. Its movement distance is an important parameter to characterize the landslide form and a significant index for risk evaluation. Based on the analysis of the evolution process, the runout distance of the bedding rock landslide is obtained by the theoretical derivation, and the achievements are applied to the Xinjianan landslide. The results showed three parts consisting of movement distance. The horizontal distance of the block in the air is the first, and the mobile distance of the collision with the ground is the next while the sliding distance on the ground is the last. Besides, the relative error between theoretical calculation and the actual measurements selected for the three profiles of the landslide are 9.99%, 2.53%, and 0.58% respectively. The error is small and shows the good application of the model. The research has a reference value for predicting and preventing this type of landslide.
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图 1 开挖卸荷下顺层岩质滑坡演化过程
Fig. 1. Evolution process of bedding rock landslide under excavation unloading
图 2 边坡失稳前后力学计算模型
a. 失稳前；b. 运动中；c. 最终平衡时
Fig. 2. Mechanical calculation model of slope instability
表 1 不同坡面的恢复系数
Table 1. Recovery coefficient of different slopes
序号 坡表概况 法向恢复系数 切向恢复系数 1 光滑坚硬表面或铺砌面 0.37~0.42 0.87~0.92 2 基岩和砾岩 0.33~0.37 0.83~0.87 3 硬土（少量植被） 0.30~0.33 0.82~0.85 4 软土（稀少植被覆盖） 0.28~0.30 0.80~0.83 5 软土（灌木林覆盖） 0.28~0.30 0.78~0.82 
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表 2 新嘉南滑坡各剖面计算参数
Table 2. Calculation parameters of each section of Xinjianan landslide
剖面编号 γ滑(kN/m3) b0 (m) h0 (m) L0 (m) W0 (kN/m) d (m) H (m) S0(m) 1-1’ 21.5 1.5 5.5 196.0 48 800.94 11.2 28.0 48.5 2-2’ 21.5 1.2 5.5 216.0 48 800.94 13.4 42.6 39.6 3-3’ 21.5 2.2 3.5 30.0 48 800.94 16.5 21.7 11.6
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表 3 滑坡理论计算值与实际值对比
Table 3. Comparison between theoretical calculated and actual of landslide
剖面编号 V边max X0 X1+…X7 X8 X总 实际运动（m） 绝对误差 相对误差 1-1’ 17.36 22.56 37.01 3.05 62.62 69.5 6.88 9.99% 2-2’ 15.23 28.19 40.03 2.35 70.57 72.4 1.83 2.53% 3-3’ 9.59 10.15 14.77 0.93 25.85 25.7 0.15 0.58%
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