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基于混合物理论,引入Bishop有效应力公式,建立了非饱和土中的动力控制方程。经过理论推导,给出了体波的传播速度及衰减的解析表达式。同时发现,在非饱和土中存在3种压缩波(P1、P2和P3波)和1种剪切波(S波)。数值分析表明:4种体波均具有不同程度的弥散性,在一定的频率范围,波速随着频率的升高而增大,其中P2、P3波的波速受频率的影响强烈;饱和度对波的传播速度亦有显著的影响,且在不同的频率范围,其影响规律不同,在有实际工程意义的低频段,饱和度的增高将导致P1、P3波的波速增大和P2、S波的波速减小。4种体波中P2、P3波的衰减较大,且随着频率的升高衰减迅速增加,而P1、S波的衰减则很小,受频率的影响也相对较小。
Based on the mixture theory, Bishop effective stress formula is introduced to establish the dynamic governing equation in unsaturated soil. After theoretical deduction, the analytical expressions of the propagation velocity and attenuation of body wave are given. It is also found that there are three kinds of compressional waves (P1, P2 and P3 waves) and one kind of shear waves (S waves) in unsaturated soils. The numerical analysis shows that all four body waves have different degrees of dispersion. In a certain frequency range, the wave speed increases with the increase of the frequency. The wave speeds of P2 and P3 are strongly influenced by the frequency. The saturation of the wave , And its influence law is different in different frequency ranges. In low-frequency section with practical engineering significance, the increase of saturation will result in the increase of wave velocity of P1 and P3 wave and the wave velocity of P2 and S wave Decrease The attenuation of P2 and P3 waves in four kinds of body waves is larger, and the attenuation increases rapidly with the increase of frequency, while the attenuation of P1 and S waves is very small and the influence of frequency is relatively small.