Calculation methods of the collapse influence range of a simple rock slope in the Guangzhou area
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摘要: 广州市地形地貌复杂多样，经济发达，人类工程活动密集，由此产生的大量人工开挖边坡危岩体对当地生产生活带来了巨大隐患。为准确评估边坡危岩体影响范围，提升边坡危岩体灾害防治能力，降低崩塌威胁，亟需完善边坡危岩体的影响范围计算模型。本研究在广州市危岩体调查的基础上归纳出常见边坡危岩体的类型和坡形特征，并据此分类建立危岩体影响范围物理几何模型，综合考虑坡面摩擦力、块体碰撞、弹跳、碎裂、接触面覆盖物性质和回弹系数、地形条件、地震等崩塌运动过程的主要影响因素，通过合理概化运动过程要素建立起直线型、曲线型边坡在不同坡度条件下的崩塌影响范围计算模型，并根据地震峰值加速度对崩塌体动能的影响求得地震工况下崩塌影响范围的扩大系数。该模型在前人研究基础上进一步归纳总结坡形分类，完整给出常见地形条件和工况下边坡危岩体最大影响范围的计算模型，在获取坡高、坡度和地表特征后即可计算得出危岩体影响范围。与实际验证比对，模型结果在保证一定安全距离的基础上相对误差较小，可做到快速准确的对常见人工边坡边坡危岩体最大影响范围进行评价，为边坡危岩体防治提供可靠依据。Abstract: The terrain and landforms of Guangzhou are complex and diverse, with developed economy and intensive human engineering activities. As a result, a large number of manually excavated slopes and dangerous rock masses have brought huge hidden dangers to local production and life. In order to accurately evaluate the impact range of slope dangerous rock mass, improve the prevention and control ability of slope dangerous rock mass disasters, and reduce the threat of collapse, it is urgent to improve the calculation models of the impact range of slope dangerous rock mass. Based on the investigation of dangerous rock mass in Guangzhou, this study summarizes the types and shape characteristics of common dangerous rock mass on slopes, and establishes a physical geometric modelling of the influence range of dangerous rock mass according to the classification, comprehensively considering the main influencing factors of the collapse movement process, such as slope friction, block collision, bounce, fragmentation, contact surface cover property and rebound coefficient, terrain conditions, earthquakes. A linear calculation model for the collapse impact range of curved slopes under different slope conditions is established, and the expansion coefficient of the collapse impact range under seismic conditions is obtained based on the influence of seismic peak acceleration on the kinetic energy of the collapse body. This model further summarizes the classification of slope shape based on previous researches, and provides a complete calculation model for the maximum impact range of dangerous rock mass on slopes under common terrain conditions and working conditions. After obtaining the slope height, slope, and surface characteristics, the impact range of dangerous rock mass can be calculated. Compared with the actual verification, the model results have relatively small errors while ensuring a certain safety distance, which can quickly and accurately evaluate the maximum impact range of common artificial slope dangerous rock masses, and provide a reliable basis for the prevention and control of slope dangerous rock masses.
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Key words:
- rock collapse /
- movement distance /
- scope of influence /
- coefficient of restitution
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图 1 广州市南沙区大井天山石场边坡
Figure 1. Slope of the Dajing Tianshan Stone Farm in Nansha District of Guangzhou
图 2 广州市南沙区芦湾上街63号后侧边坡
Figure 2. Side slope behind No.63 Luwan Street in Nansha District of Guangzhou
图 3 广州市南沙区大岗镇砂岩质陡坡
Figure 3. Sandstone steep slope near Dagang Town in Nansha District of Guangzhou
图 4 直线型边坡崩塌块体运动过程概化图
Figure 4. Schematic diagram of motion process of a collapse block in the linear slope
图 5 地面向边坡方向倾斜运动过程概化图
Figure 5. Schematic diagram of the inclined movement process of the threatened area towards the slope
图 6 地面向远离边坡方向倾斜运动过程概化图
Figure 6. Schematic diagram of the tilted movement process of the threatened area away from the slope
图 8 曲线型边坡地面向边坡方向倾斜运动过程概化图
Figure 8. Generalized diagram of the sloping motion process of curved slope facing the slope direction
图 9 曲线型边坡地面向远离边坡方向倾斜运动过程概化图
Figure 9. Generalized diagram of the sloping motion process of the curved slope away from the slope
图 11 南沙区进港大道北侧边坡剖面图
Figure 11. The north side slope section of the Jingang Avenue in Nansha District
表 1 常见坡面岩块滚动摩擦系数[22]
Table 1. Rolling friction coefficients of common slope blocks
坡面特征 滚动摩擦系数 光滑岩面、混凝土表面 0.30～0.60 软岩面、强风化硬岩面 0.40～0.60 块石堆积坡面 0.55～0.70 密实碎石堆积坡面、硬土坡面、（植被灌木从）发育 0.55～0.85 密实碎石堆积坡面、硬土坡面、植被不发育或少量杂草 0.50～0.75 松散碎石坡面、软土坡面、植被（灌木丛为主）发育 0.50～0.85 软土坡面、植被不发育或少量杂草 0.50～0.85 
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表 2 崩塌防治工程勘察规范推荐岩块回弹系数
Table 2. Block springback coefficient recommended by the investigation code of collapse prevention engineering
碰撞系数 地面岩性 硬岩 软岩 硬土 普通土 松土 法向回弹系数$ {R}_{n} $ 0.4 0.35 0.30 0.26 0.22 切向回弹系数$ {R}_{t} $ 0.86 0.84 0.81 0.75 0.65
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表 3 铁道部运输局推荐岩块回弹系数
Table 3. Rock springback coefficient recommended by the Transportation Bureau of the Ministry of Railways
坡面特征 法向恢复系数$ {\mathit{R}}_{\mathit{n}} $ 光滑而坚硬的表面和铺砌面，如人行道或光滑的基岩面 0.37～0.42 多数为基岩和砾岩区的斜面 0.33～0.37 硬土边坡 0.30～0.33 软土边坡 0.28～0.30 坡面特征 切向恢复系数$ {\mathit{R}}_{\mathit{t}} $ 光滑而坚硬的表面和铺砌面，如人行道或光滑的基岩面 0.87～0.92 多数为基岩和无植被覆盖的斜坡 0.83～0.87 多数为有少量植被的斜坡 0.82～0.85 植被覆盖的斜坡和有稀少植被覆盖的土质边坡 0.80～0.83 灌木林覆盖的土质边坡 0.78～0.82
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表 4 不同计算方法所得影响范围对照表
Table 4. Comparison of the influence range obtained with different calculation methods
边坡名称 南沙区大角一路北侧边坡 南沙进港大道北侧边坡 坡高h（m） 20 7 边坡坡度θ1（°） 85 80 边坡摩擦系数f 0.5 0.5 威胁区摩擦系数f' 0.7 0.4 法向恢复系数Rn 0.25 0.4 切向恢复系数Rt 0.75 0.87 模型计算运动距离（m） 1.54 2.32 模型计算影响范围（m） 5.52 3.7 RocFall模型影响范围（m） 4.65 8.9 实际崩塌体堆积范围（m） 3.65 2.6
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