An evolution analysis of the impact energy damage of collapsed rolling stones under strong earthquakes
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摘要:
强震触发崩塌滚石冲击耗能损伤是防护工程设计的重要指标。为探索冲击过程中滚石耗能损伤演化过程，采用热力学定律分析了冲击过程中能量的传递与耗散，通过定义冲击耗能损伤因子D、Dmax，建立了滚石冲击耗能损伤理论模型与适用模型。结合工程实例，反算极限冲击力对模型进行论证与分析，提出模型的推广应用。结果表明：滚石冲击耗能损伤过程满足热力学第一定律，能量主要贡献于防护工程弹塑性势能的积聚，Dmax受滚石质量、弹性模量、抛射初速度、最大冲击力、有效作用面积等的影响；最大冲击力持续增加，极限冲击耗能损伤因子增大，达到线性函数与抛物线函数图像交点C（1031 kN，0.9965）时曲线出现拐点。模型推广得到广义范围下的冲击耗能损伤演化函数曲线，冲击耗能损伤全过程在损伤响应、损伤线性、损伤渐进三个阶段的临界位置出现2次损伤拐点；随滚石质量增加，最大冲击力增大，极限冲击耗能损伤因子曲线先呈抛物线减小，再呈线性增加，最后呈抛物线逐渐增加直到无限趋近于1。从能量角度定量分析其损伤本质，对探究滚石运动过程能量耗散机制及防护工程的设计具有重要意义。
Abstract:The impact energy dissipation damage of rockfall triggered by strong earthquake is an important indicator of protection engineering design. In order to explore the evolution process of the rolling stone energy consumption damage during the impact process, the law of thermodynamics was used to analyze the energy transfer and dissipation during the impact. By defining the impact energy dissipation damage factor D and Dmax, the theoretical model and applicable model of the rock impact energy dissipation damage are established. Combining engineering examples and back-calculating the ultimate impact force to demonstrate and analyze the model, a generalization and application of the model is proposed. The damage process of the impact energy of the rolling stone satisfies the first law of thermodynamics. The energy mainly contributes to the accumulation of the elastoplastic potential energy of protective engineering. Dmax is affected by the rolling stone mass, elastic modulus, initial velocity of ejection, maximum impact force, and effective area, etc. The maximum impact force continues to increase, and the limit impact energy dissipation damage factor increases. When the curve reaches the intersection point C (1031 kN, 0.9965) of the linear function and the parabolic function image, the curve has an inflection point. The model is extended to obtain the evolution function curve of the impact energy dissipation
damage in a generalized range. In the whole process of the impact energy dissipation damage, there are two damage inflection points at the critical position of the three stages of damage response, damage linearity, and damage progression. As the mass of the rolling stone increases, the maximum impact force increases, and the limit impact energy dissipation damage factor curve first decreases parabolically, then increases linearly, and finally increases parabolically until it reaches infinitely close to 1. A quantitative analysis of the damage nature from the view of energy point is of great significance in the exploration of energy dissipation mechanism of the rolling rock movement process and the design of protection engineering.
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表 1 岩石变形破坏各部分能量平均比值
Table 1. The average energy ratio of each part of rock deformation and failure
岩性 弹性势能/J 塑性势能/ J 比值 大理岩（硬岩） 0.0842 0.0410 0.487 砂岩（软岩） 0.0410 0.0395 0.963 
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表 2 崩塌滚石参数统计表
Table 2. Statistics of parameters of collapsed rocks
编号 质量/kg 初始高度/m 有效作用面积/m2 G01 0.206×103 10 0.162 G02 0.418×103 10 0.206 G03 0.603×103 10 0.312 G04 0.820×103 10 0.396 G05 1.018×103 10 0.468
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