花岗岩球砾法向恢复系数试验研究

Experimental study on the normal restitution coefficient of granite spheres

法向恢复系数是岩崩块石运动分析的关键参数,其取值直接决定了块石的运动轨迹。为了严格测定花岗岩球砾碰撞的法向恢复系数,分析其影响因素,试验采用自行设计的碰撞试验装置和声频采样技术,精确测定花岗岩球砾碰撞的法向恢复系数,研究球砾大小、碰撞速度、含水状态和板的弹性特性4个因素对恢复系数的影响;并基于弹性接触理论推导出碰撞过程的最大接触应力P_(0,max)、碰撞起裂速度v_(ci)和碰撞损伤速度v_(cd),构造接触应力割线变化率k来描述碰撞过程的率相关,分析碰撞法向恢复系数的尺寸效应和速率效应,对碰撞过程耗能机制进行探讨。试验结果表明:花岗岩球砾法向恢复系数存在明显的尺寸效应,低速下更加显著;法向恢复系数的速率效应同样较明显,并且速率效应受球砾尺寸和板的弹性特性影响,呈现较强的相关性;球砾大小和速度相同时,等效弹性模量E*越大,法向恢复系数越小;含水状态对法向恢复系数影响不大。理论分析表明:P_(0,max)和k为控制法向恢复系数变化规律的内在因素;尺寸和速度均是通过改变P_(0,max)和k使法向恢复系数呈现复杂的尺寸效应和速率效应。

The normal restitution coefficient is a key parameter in the analysis ofrockfall and its value determines directly the trajectory of rockfall. A device designed to simulate the collision process and the audio sampling technique was adopted in this paper in order to strictly measure the normal restitution coefficient of granite spheres and to analyze the influencing factors. The size of granite spheres, the elastic properties of plate, the impact velocity and the moisture state are considered to analyze the main influencing factors of the normal restitution coefficient. The maximum contact stress P0, max, the crack initiation velocity vci and the crack damage velocity Vcd are deduced based on the elastic contact theory. Moreover, the secant change rate of the contact stress is proposed to describe the rate-dependent collision process. Finally the size effect, the rate effect and the energy dissipation mechanism of the normal restitution coefficient are discussed. The experimental results show that the normal restitution coefficient of the granite spheres has strong size effect, which is more obvious under low velocity. The rate effect is also obvious and it is affected by the size of granite spheres and the elastic properties of the plate. The normal restitution coefficient reduces with the increasing of the equivalent elastic modulus E＊. The moisture state has little effect on the restitution coefficient. The theoretical analysis shows that Po, max and tcare the main internal factors which influence the variation of the normal restitution coefficient. By changing P0, max and K, the size of granite spheres and velocity make the normal restitution coefficient to show the complex size effect and rate effect.