Propagation Characteristics of Rayleigh Waves in Saturated Porous Media Based on the Couple-Stress Elastic Gradient Theory
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摘要: 基于偶应力弹性梯度理论，研究了饱和孔隙介质中Rayleigh波的传播特性. 首先，基于偶应力理论建立了包含材料内禀长度的波动方程，并在频域内通过位移场的势函数分解，将两组耦合的波动方程解耦为4个标量的Helmholtz方程，分别控制P1波、P2波、SV波和SH波的传播. 进一步，针对Rayleigh波，通过求解Helmholtz方程的特征值问题，确定了势函数的具体形式. 然后，通过引入边界条件，求解了Rayleigh波的传播特性. 最后，通过数值算例，研究了材料内禀长度对Rayleigh波的传播特性的影响规律.Abstract: The propagation characteristics of Rayleigh waves in saturated pore media were investigated based on the couple-stress poroelastic gradient theory. Firstly, the fluctuation equations containing material intrinsic lengths were established based on the couple-stress theory, and the 2 sets of coupled fluctuation equations were decoupled into 4 scalar Helmholtz equations through the potential function decomposition of the displacement field to control the propagation of the P1, P2, SV and SH waves, respectively. Further, for Rayleigh waves, the specific form of the potential function was determined through solution of the eigenvalue problem of the Helmholtz equation. Then, the propagation characteristics of Rayleigh waves were solved under introduced boundary conditions. Finally, the influence rule of the material intrinsic length on the propagation characteristics of Rayleigh waves was investigated by numerical examples.
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Key words:
- porous material /
- Rayleigh wave /
- couple stress /
- elastic gradient theory /
- normalized displacement
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图 2 不同材料内禀长度下Rayleigh波的波数和衰减系数随频率变化的曲线
注 为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.
Figure 2. Comparison curves of Rayleigh wave numbers and characteristic attenuation at different material intrinsic lengths
图 3 Rayleigh波质量因子随频率变化的曲线
Figure 3. Quality factors as a function of the frequency for the Rayleigh wave
图 4 固体骨架的归一化水平和竖向位移沿归一化深度的变化曲线(f=1 000 Hz)
Figure 4. The normalized horizontal and vertical displacement curves of the solid skeleton along the normalized depth(f=1 000 Hz)
表 1 饱和孔隙介质的材料参数
Table 1. Fluid saturated porous media material parameters(Hard sediment)
property parameter value frame shear modulus μ/MPa 26.1 frame bulk modulus K/MPa 43.6 porosity ϕ0/% 0.470 solid density ρ0s/(kg/m3) 2 650 pore-fluid density ρ0f/(kg/m3) 1 000 solid bulk modulus Ks/GPa 36.0 pore-fluid bulk modulus Kf/GPa 2.25 fluid viscosity coefficient η/(Pa·s) 1.0×10-3 permeability coefficient $\mathscr{K}$/m2 1.0×10-10 
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