基于Hertz理论的泥石流大块石冲击力修正计算

摘要

Impact model between boulder and pier was built based on the Hertz contact theory and structural mechanics. Three main influence factors of impact force, including the material properties, relative size, and structure displacement were quantized and the modified formula was presented to calculate impact force. It shows that, material correction coefficient ranges from 0. 20 to 0. 45, which is proportional to material yield strength Y while correlated reciprocally with the equivalent modulus of system, E. The correction coefficient of ball diameter ratio exhibits that, along with the increase of structure size, it increases stably after rapid growth. Structure displacement correction coefficient is affected by the constraint condition of pier top and impact location. The practical application of this modifier formula in Dengjigou engineering result is only 6.7% of the calculated value by Hertz elastic collision theory, and according to the outcome that, relation curve between impact force and impact velocity is relatively flat, which performs in accordance with practical estimation.%为合理确定泥石流块石对构筑物的冲击力，以Hertz接触理论和结构力学为基础，建立泥石流大块石对桥梁的冲击模型，量化冲击系统中对象的材料特性、相对尺寸大小及结构变位对冲击力的影响，导出泥石流大块石冲击力修正计算公式．结果表明：材料修正系数在0．20～0．45之间，其值与材料屈服强度Y成正比，与冲击系统的等效模量E呈反相关关系；球径比修正系数随构筑物尺寸的增大先迅速增大而后平稳增长；结构变位修正系数受墩顶约束及冲击位置双重影响．将提出的计算方法应用于登基沟泥石流大块石对桥墩的冲击力计算，结果仅为Hertz弹性碰撞理论的6．7％，冲击力－冲击速度关系曲线平缓，与工程实践估值结果基本一致．