两种不同势函数下半空间饱和多孔介质中Rayleigh波求解比较

Comparative Study on Different Solutions to Rayleigh Waves in Half-space Saturated Porous Media under Two Different Potential Functions

摘要:

分别对"考虑两种压缩波和幅值比例系数"和"考虑一种压缩波(P₁或P₂波)但不考虑幅值比例系数"两种不同势函数下的半空间饱和多孔介质中Rayleigh波求解进行详细推导,理论分析表明"考虑两种压缩波和幅值比例系数"下Rayleigh波求解推导更为严密,与饱和多孔介质中存在两种压缩波的事实相一致。在研究半空间饱和多孔介质中Rayleigh波时应采用"考虑两种压缩波和幅值比例系数"的势函数。

Abstract:

Theoretical solutions of the Rayleigh wave in half-space saturated porous media were derived under two different potential functions corresponding to a case with two kinds of compressional waves and amplitude ratio coefficient and a case with a compressional wave (P₁ or P₂ wave) without considering the amplitude ratio coefficient,respectively.The theoretical analysis shows that the derivation of the solution of the Rayleigh waves for the case with two kinds of compressional waves and amplitude ratio coefficient is more rigorous,which is consistent with the fact that there exist two kinds of compressional waves in saturated porous media.Through numerical calculation,we compared the propagation velocities and attenuations of the Rayleigh wave in three different cases,namely,the case with two kinds of compressional waves and amplitude ratio coefficient,the case with P₁ wave without the amplitude ratio coefficient,and the case with P₂ wave without the amplitude ratio coefficient.The numerical calculation shows that there exists distinctive differences among the results obtained in the three cases above.We recommend that the potential functions that consider the two kinds of compressional waves and the amplitude ratio coefficient be applied when studying Rayleigh waves in half-space saturated porous media.