孔隙内填充单一固体的固-固孔隙介质中的声波传播

Wave propagation characteristics in porous medium containing a solid in pores

连通孔隙空间被有别于骨架固体的另一种固相介质充填而形成的双组分连通固体孔隙介质,简称固-固孔隙介质.推导出了固-固孔隙介质的声波动力学方程和本构关系,利用平面波分析的方法研究了各种波的频散和衰减特性.在此基础上,提出了基于一阶速度-应力方程的时间分裂的高阶交错网格有限差分算法,对其中的声场演化特点进行了模拟计算,分析了各种波的产生机制和能量分布,并详细讨论了两种固体间的摩擦系数和声源频率对各种波传播特性的影响.数值模拟表明:固-固孔隙介质中存在两种纵波(P1和P2)和两种横波(S1和S2),其中P1和S1波能量主要在骨架固体中传播;P2和S2波是骨架固体和孔隙固体之间相对运动产生的慢波,能量主要在孔隙固体中传播.固体骨架和孔隙固体之间的摩擦主要影响慢波(P2和S2)的衰减,且低频时衰减大于高频.

Aiming at the propagation characteristics of acoustic waves in a porous medium containing a solid in pores,the equations of motion and constitutive relation are deducted in the case of two-solid porous media.The frequency dispersion and attenuation characteristics of wave modes are analyzed by a plane wave analysis.In addition,based on the first-order velocity-stress equations,the time-splitting high-order staggered-grid finitedifference algorithm is proposed and constructed for understanding wave propagation mechanisms in such a medium,where the time-splitting method is used to solve the stiffness problem in the first-order velocity-stress equations.The generation mechanisms and energy distributions of different kinds of waves are investigated in detail.In particular,the influences of the friction coefficient between solid grains and pore solid as well as frequency on wave propagation are analyzed.It can be known from the results of plane wave analysis that there are two compression waves(P1 and P2)and two shear waves(S1 and S2)in a porous medium containing a solid in pores.The attenuations of P2 wave and S2 wave are much larger than those of P1 wave and Sl wave.This is due to the friction between the solid grains and the pore solid.The results show that our proposed numerical simulation algorithm can effectively solve the problem of stiffness in the velocity-stress equations,with high accuracy.The excitation mechanisms of the four wave modes are clearly revealed by the simulation results.The P1 wave and S1 wave propagate primarily in the solid grain frame,while P2 wave and S2 wave are concentrated mainly in the pore solid,which are caused by the relative motion between the solid grains and the pore solid.Besides,it should be pointed out that the wave diffusions of the P2 wave and S2 wave are influenced by the friction coefficient between solid grains and pore solid.The existence of friction coefficient between two solids makes P2 wave and S2 wave attenuate to a certain extent at high frequency,but the attenuation is much smaller than that at low frequency.This is the reason why it is difficult to observe the slow waves in practice.However,because the slow waves also carry some energy,it may not be ignored in the studying of the energy attenuation of acoustic waves in porous media.