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摘要:
桩板拦石墙是一种拦截落石的新型被动防护结构，由悬臂桩、桩间板和缓冲垫层组成。这种结构具有地形适应性强、占地面积小、拦截高度大等优点，在落石高发区得到了应用。然而，由于悬臂桩的极限承载力缺乏详细的报道，因此无法为工程实践提供指导。文章首先根据落石冲击力传播特征，提出缓冲垫层的合理厚度；然后根据桩身的受力和变形特性，采用弹性固支悬臂梁模型和Winkler弹性地基梁模型推导了桩身内力、位移的理论计算方法，实现了落石冲击作用下悬臂桩设计参数的自动求解。结果表明：当落石直径为2 m、冲击高度为7.0 m，冲击速度为10 m/s，且砂土垫层厚度为落石直径的1.5倍时，双排三肢钢筋1.5 m×1.2 m悬臂桩可承受冲击力为2.51×106 N且冲击能量为565 kJ的落石冲击。对于冲击能量更高的情况，建议优先提高拦石桩的抗弯能力。研究可为西部山区岩崩防灾减灾提供科学依据。
Abstract:Pile-slab rockfall retaining wall is a novel passive protective structure designed to intercept falling rocks. It is made up of cantilever piles, pile-intermediate slabs, and cushion layers. This structure features strong terrain adaptability , small footprint, and high interception height, making it applicable in high-risk rockfall areas. However, due to the lack of detailed reports on the ultimate bearing capacity of cantilever piles, guidance for engineering practice is unavailable. This paper first proposes a reasonable thickness for the cushion layer based on the characteristics of the propagation of falling rock impact forces. Then, according to the stress and deformation characteristics of the pile body, theoretical calculation methods of the internal forces and displacements of the pile body are derived using the elastic support cantilever beam model and the Winkler elastic foundation beam model, enabling the automatic determination of design parameters for cantilever pile under falling rock impact. The results indicate that for a rockfall with a diameter of 2 m, impact height of 7.0 m, impact velocity of 10 m/s, and a cushion layer thickness of 1.5 times the rockfall diameter, a double-row triple-limb steel-reinforced 1.5 m × 1.2 m cantilever pile can withstand an impact force of 2.51 × 106 N and impact energy of 565 kJ. For cases with higher falling rock impact energy, it is recommended to prioritize enhancing the bending resistance of the retaining wall. This research provides a scientific basis for disaster prevention and reduction in rockfall-prone areas in the western mountainous regions of China.
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Key words:
- rockfall /
- cushion /
- rockfall retaining pile /
- internal force of pile /
- optimal design
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表 1 落石冲击力计算结果
Table 1. Calculation results of rockfall impact force
参数 落石
半径
/m落石
质量
/kg冲击
速度
/（m·s−1）垫层
厚度
/m垫层变形
模量
/kPa垫层
内摩擦角
/（°）落石
冲击力
/MN取值 1 11309.7 5 3 35 000 39.0 1.09 1 11309.7 10 3 35 000 39.0 2.51 1 11309.7 15 3 35 000 39.0 4.08 1 11309.7 20 3 35 000 39.0 5.76 
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表 2 悬臂桩结构和材料参数
Table 2. Cantilever pile structure and material parameters
参数 悬臂段
长度
/m嵌固段
长度
/m冲击力
作用点距离
/m截面
宽度/m截面
高度/m地基抗力的
比例系数
/（kN·m−4）取值 9.5 9.5 7.0 1.2 1.5 10000
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表 3 混凝土物理力学参数
Table 3. Concrete physical mechanical parameters
材料
类型弹性
模量
/MPa泊松比 抗压强度
标准值
/MPa轴心抗压
强度设计值
/MPa轴心抗拉
强度设计值
/MPaC50混凝土 34500 0.20 32.4 23.1 1.89
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表 4 钢筋材料参数
Table 4. Reinforcement material parameters
型号 弹性
模量
/MPa泊松比 抗拉强度
设计值
/MPa钢筋抗压
强度设计值
/MPa极限
拉应变HRB400（纵筋） 2.0 × 105 0.27 360 360 0.0305 HRB335（箍筋） 2.0 × 105 0.27 300 300 0.0305
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表 5 桩身内力计算结果（h2=9.5 m）
Table 5. Calculation results of pile body internal forces (h2=9.5 m)
参数 冲击能量/kJ 横向荷载/MN 桩身最大弯矩/（MN·m） 允许弯矩/（MN·m） 桩身最大剪力/MN 允许剪力/MN 桩顶扰度/m 允许扰度/m 取值 141 0.286 3.34 6.57 0.578 3.06 0.031 0.3558 565 0.656 6.54 6.57 1.125 3.06 0.063 0.3558 1272 1.07 10.09 6.57 1.75 3.06 0.097 0.3558 2261 1.51 13.91 6.57 2.41 3.06 0.136 0.3558
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表 6 桩身内力计算结果（h2=8.5 m）
Table 6. Calculation results of pile body internal forces (h2=8.5 m)
参数 冲击能量/kJ 横向荷载/MN 桩身最大弯矩/（MN·m） 允许弯矩/（MN·m） 桩身最大剪力/MN 允许剪力/MN 桩顶扰度/m 允许扰度/m 取值 141 0.286 3.37 6.57 0.581 3.06 0.032 0.3558 565 0.656 6.58 6.57 0.952 3.06 0.063 0.3558 1272 1.07 10.15 6.57 1.425 3.06 0.098 0.3558 2261 1.51 13.98 6.57 1.984 3.06 0.136 0.3558
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表 7 桩身内力计算结果（h2=7.5 m）
Table 7. Calculation results of pile body internal forces (h2=7.5 m)
参数 冲击能量/kJ 横向荷载/MN 桩身最大弯矩/（MN·m） 允许弯矩/（MN·m） 桩身最大剪力/MN 允许剪力/MN 桩顶扰度/m 允许扰度/m 取值 141 0.286 3.48 6.57 0.581 3.06 0.031 0.3558 565 0.656 6.71 6.57 0.952 3.06 0.061 0.355 1272 1.07 10.33 6.57 1.363 3.06 0.095 0.3558 2261 1.51 14.21 6.57 1.803 3.06 0.132 0.3558
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表 8 桩身内力计算结果（h2=6.5 m）
Table 8. Calculation results of pile body internal forces (h2=6.5 m)
参数 冲击能量/kJ 横向荷载/MN 桩身最大弯矩/（MN·m） 允许弯矩/（MN·m） 桩身最大剪力/MN 允许剪力/MN 桩顶扰度/m 允许扰度/m 取值 141 0.286 3.88 6.57 0.581 3.06 0.028 0.3558 565 0.656 7.12 6.57 0.952 3.06 0.057 0.3558 1272 1.07 10.84 6.57 1.363 3.06 0.089 0.3558 2261 1.51 14.84 6.57 1.803 3.06 0.122 0.3558
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