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考虑土颗粒、孔隙流体的压缩性及各相物质间的黏性、惯性耦合作用,采用理论上更加严谨的饱和度本构关系式,建立了非饱和土的动力控制方程。该组方程与饱和土的经典Biot波动方程完全兼容,因此,具有更广泛的适用性。通过引入一组状态向量,在圆柱坐标系下将非饱和土满足的波动方程转化为状态方程组,利用Hankel变换,求解状态方程组,得到了传递矩阵。结合边界条件及层间接触连续条件,求解了层状非饱和地基的稳态动力响应问题。数值算例表明:土层对地表动位移的影响主要集中在临界深度范围内;软硬土层的相对次序对地表动位移幅值有显著影响;饱和度增大会引起土的物理参数发生相应的改变,尤其是动剪切模量通常降幅较大,而动剪切模量是决定位移幅值的关键因素,最终的结果是导致地表动位移幅值明显增大。
Considering the compressibility of soil particles, the compressibility of pore fluid and the viscous and inertial coupling between the phases, a more rigorous saturation constitutive equation is theoretically established to establish the dynamic governing equations for unsaturated soils. This set of equations is fully compatible with the classical Biot wave equation for saturated soils and therefore has broader applicability. By introducing a set of state vectors, the wave equations of unsatisfied saturated soil are transformed into state equations under the cylindrical coordinate system. The state matrix is solved by using Hankel transform, and the transfer matrix is obtained. Combined with the boundary conditions and the continuous contact conditions, the steady-state dynamic response of layered unsaturated soil is solved. The numerical example shows that the influence of soil layer on the ground moving displacement mainly lies in the critical depth range; the relative order of soft and hard soil layer has a significant effect on the amplitude of dynamic ground surface displacement; and the increase of saturation will cause the corresponding physical parameters of soil The change, especially the dynamic shear modulus, usually decreases a lot. The dynamic shear modulus is the key factor that determines the displacement amplitude. The final result is that the dynamic displacement amplitude of the surface increases obviously.