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摘要: 为了有效防治高速公路边坡坡面滚石破坏, 建立了滚石运动自由飞落分析模型, 计算了滚石落地后的水平运动距离, 由能量守恒定律推导了滚石在防护栏处的撞击能, 并由撞击能确定合理的防护方式。计算结果表明: 滚石撞击坡面后的水平运动距离(2.156 m) 小于撞击点到公路路缘的水平距离(2.820 m), 滚石飞落至地面的撞击能为132 kJ, 设计采用型号为AXI-015 (防护能级为150 kJ) 的被动防护网, 可对高速公路坡面滚石灾害进行有效防护。Abstract: In order to control rolling stone damage on expressway slope, a free rolling model of stone was built. The horizontal moving distance of stone was calculated while reaching the ground. Based on the energy conservation law, the impact energy of rolling stone to guardrail was deduced, and the reasonable way of protection was defined according to the energy. Computation result shows that the horizontal distance (2.156 m) is less than the distance between impact point and road curb (2.820 m), the impact energy is 132 kJ, so passive protecting mesh named AXI-015 (its protecting level is 150 kJ) can provide effective protection, and the model is feasible.
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表 1 恢复系数
Table 1. Restitution coefficients
坡面特征 Kn Kτ 光滑而坚硬的表面和铺砌面 0.37~0.42 0.87~0.92 多数为基岩和砾岩区的斜面 0.33~0.37 0.83~0.87 硬土边坡 0.30~0.33 0.80~0.83 软土边坡 0.28~0.30 0.78~0.82 
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表 2 边坡及滚石参数
Table 2. Parameters of slope and rolling stone
滚石槽 滚石 上口宽度/cm 深度/cm 沿x轴初速度/ (m·s-1) 沿y轴初速度/ (m·s-1) 120 52 2 0
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表 3 边坡参数
Table 3. Parameters of slope
边坡开挖台阶 坡高/m 坡度 设计防护方案 第1级 15 1∶0.3 SNS被动防护网 第2级 10 1∶0.5
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表 4 滚石在点C的运动速度与坐标
Table 4. Velocities and coordinates of rolling stone at point C
V′Cx/ (m·s-1) V′Cy/ (m·s-1) x轴坐标/m y轴坐标/m 1.96 12.26 2.72 9.07
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表 5 滚石飞落参数
Table 5. Moving parameters of rolling stone
β H/m Δh/m t1/s L/m Δl/m 1∶0.3 15 5.41 1.1 2.156 2.820
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表 6 滚石撞击能
Table 6. Impact energy of rolling stone
体积/m3 质量/kg 平均落差/m 坡面角度/ (°) 冲击能量/kJ 0.4 960 15 70 132
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