位移不连续模型在黏弹性节理刚度计算的应用

考虑节理质量对应力波传播的影响，运用波的位移位函数推导了谐波在厚黏弹性节理的透、反射系数计算公式，采用波形相关系数描述子波穿过黏弹性节理的波形变化，讨论具有一定厚度的黏弹性节理简化位移不连续模型的适用条件。设厚黏弹性节理模型和位移不连续模型的透射波波形相关系数为0.9时对应的节理厚度为临界厚度，岩体与节理的阻抗比对临界厚度的影响很小；临界厚度随子波中心频率增大呈负指数减小，入射角越大，临界厚度随中心频率减小得越慢。试验数据分析表明：当节理厚度为0.03 m时，采用位移不连续模型和厚黏弹性模型计算得到的节理力学参数非常接近，随节理厚度和子波中心频率增加，运用位移不连续模型的计算结果偏差越大，试验结果与理论分析是一致的。

Application of displacement discontinuity model for calculating the viscoelastic stiffness of joints

Considering the effect of joint mass on the propagation of stress waves, this study derived formulas for the transmission and reflection coefficients of harmonic waves through the thick viscoelastic joints based on the displacement function of waves. The correlation coefficient of waves was used to describe the waveform changes of the wavelet through viscoelastic joints. Then, we discussed the applicable conditions of a simplified displacement discontinuity model with thick viscoelastic joints. When the correlation coefficient of transmission wave was 0.9, which was calculated by the thick viscoelastic joint model and the displacement discontinuity model, the corresponding thickness of the joint was defined as critical thickness. It was found that there was little impact of the impedance ratio between the rock mass and joint on the critical thickness. The relationship between the critical thickness and the centre frequency followed a negative exponential law. Meanwhile, the larger incident angle was, the lesser impact of centre frequency on critical thickness was. The field tests showed that when the thickness of the joint was 0.03 m, mechanical parameters were extremely close to the results calculated by the thick viscoelastic joint model and the displacement discontinuity model. With the increase of the joint thickness and the centre frequency of the wavelet, the deviation of calculated results using the displacement discontinuity model was larger, which was consistent with the results of theoretical analysis.