Effects of axial static stress on stress wave propagation in rock considering porosity compaction and damage evolution

Abstract

A wave equation of rock under axial static stress is established using the equivalent medium method by modifying the Kelvin-Voigt model. The analytical formulas of longitudinal velocity, space and time attenuation coefficients and response frequency are obtained by solving the equation using the harmonic method. A series of experiments on stress wave propagation through rock under different axial static stresses have been conducted. The proposed models of stress wave propagation are then verified by comparing experimental results with theoretical solutions. Based on the verified theoretical models, the influences of axial static stress on longitudinal velocity, space and time attenuation coefficients and response frequency are investigated by detailed parametric studies. The results show that the proposed theoretical models can be used to effectively investigate the effects of axial static stress on the stress wave propagation in rock. The axial static stress influences stress wave propagation characteristics of porous rock by varying the level of rock porosity and damage. Moreover, the initial porosity, initial elastic modulus of the rock voids and skeleton, viscous coefficient and vibration frequency have significant effects on the P-wave velocity, attenuation characteristics and response frequency of the stress wave in porous rock under axial static stress.

摘要

本文基于等效介质方法,通过改进Kelvin-Voigt 模型,建立了具有轴向静应力空隙岩石的波动 方程。利用谐波法求解波动方程,得到了用纵波波速、时空衰减系数和响应频率等表征的应力波传播 理论模型。选用红砂岩制备岩石试件,进行了室内具有轴向静应力岩石的应力波传播试验。通过对比 试验和理论模型结果,验证了应力波传播模型的正确性。基于应力波传播理论模型,通过参数研究方 法探讨了轴向静应力对岩石应力波波速、时空衰减系数和响应频率的影响。结果表明,本文提出的应 力波传播理论可以有效表征轴向静应力对岩石应力波传播的影响,轴向静应力通过改变岩石的有效孔 隙度和损伤度影响岩石的应力波传播特性。初始空隙度、岩石空隙和骨架的初始模量、黏性系数和振 动频率对岩石应力波波速、衰减系数以及响应频率等都有较大的影响。