应力波时延与结构面刚度的关联性分析

STUDY OF RELEVANCY BETWEEN STRESS WAVE TIME DELAYS AND STIFFNESS OF STRUCTURAL SURFACE

首先基于波动理论和非连续位移模型,推导倾斜入射P波在线弹性结构面处的透、反射关系式,得到的入射P波透、反射系数与结构面刚度之间的关系式与前人的结果一致。根据应力波的时延理论,进一步推导应力波透射线弹性结构面的相时延和群时延关系式。运用离散元法的数值软件UDEC模拟中心频率为100 Hz的高斯余弦应力波穿越单一节理与多条平行节理岩体,在此基础上分析应力波时延特征,并将该数值结果与相应的解析解进行比较。研究结果表明:(1)应力波垂直入射单一结构面的岩体模型后,利用未经滤波的透射波波形和包络线得到的应力波相时延与解析解基本一致,而群时延有一定差别;对透射波进行带宽为97~103 Hz滤波得到的相时延与群时延完全一致。(2)对存在多条平行结构面的岩体模型,当结构面间距大于1/2高斯余弦波波长λ时,经滤波后的群时延与解析解基本一致;当结构面间距小于1/2λ时,数值模拟得到相时延、群时延均与解析解相差很大。(3)透射波波前一般不会受到结构面多次反射波的干扰,在3种不同间距的结构面模型中利用透射波波前得到的初至波时延近乎相同,与单一结构面时初至波时延和结构面数量的乘积也相差不大。当结构面为线弹性体时,本文研究结果有助于利用应力波时延特征来预测结构面刚度或结构面数量。

First of all,the transmission coefficient and the reflection coefficient of P wave crossing a elastic joint are deduced based on the theories both of elastic waves and displacement discontinuity. According to the stress wave time delay theory,the analytical solution of phase delay and group delay are given when the joint obeys the elastic Hooke′s theory. A universal distinct element code(UDEC) is used to simulate stress waves propagation in rocks with a single joint and five parallel joints,respectively. And the incidence stress wave is cosine Gauss pulse. All of the main research results can be summarized as follows. (1) When P wave transmitting the rock model with only a single joint,the phase delay is consistent with the analytical solution calculating from the unfiltered waves, while the group delay deviates from the analytical solution. After the 97-103 Hz band-pass filtered,the phase delay and group delay are both consistent with the analytical solution. (2) For the rock models with multiparallel joints,when the distance of these joints is larger than one half of the wave length of the cosine Gauss pulse,the group delay from filtered wave is more or less in line with the analytical solution. However,if the distance of these joints is smaller than one half of the wave length,the phase delay and group delay both deviate from the analytical solution. (3) As we all know,the wave-front is never disturbed by the multiple reflection. The wave-front delays of three multiparallel joints models are in line with each other under different joint stiffnesses,and the difference between these delays and the analytical results is limited. Under the assumption that the joint is a liner elastic model,the results of this research can be used to predict the joint stiffness or number of joints in rock masses.