Dynamic responses of unsaturated half‐space soil to a moving harmonic rectangular load

Abstract

Summary The problem of the dynamic responses of a semi‐infinite unsaturated poroelastic medium subjected to a moving rectangular load is investigated analytical/numerically. The dynamic governing equations are obtained with consideration of the compressibility of solid grain and pore fluid, inertial coupling, and viscous drag as well as capillary pressure in the unsaturated soil, and they can be easily degraded to the complete Biot's theory. Using the Fourier transform, the general solution for the equations is derived in the transformed domain, and then a corresponding boundary value problem is formulated. By introducing fast Fourier transform algorithm, the unsaturated soil vertical displacements, effective stresses, and pore pressures induced by moving load are computed, and some of the calculated results are compared with those for the degenerated solution of saturated soils and confirmed. The influences of the saturation, the load speed, and excitation frequency on the response of the unsaturated half‐space soil are investigated. The numerical results reveal that the effects of these parameters on the dynamic response of the unsaturated soil are significant.

Study on vibration isolation performance of wave impeding block in unsaturated soil foundation under an underground dynamic load

“…Substituting equations (27)(28)(29)(30) into the boundary conditions (31-34), the following matrix equations can be obtained as follows:…”

“…where the elements in matrix ½T and vectors fxg and ff g are detailed in Appendix B. By solving the equation ( 35), the wave amplitudes of various types of waves in fxg are obtained, and the stress and displacement responses at any point in the unsaturated soil and in the WIB can be obtained by combining equations (27)(28)(29)(30).…”

Study on vibration isolation performance of composite multilayer wave impeding block based on wave impedance ratio under an underground dynamic load

“…For unsaturated soil, due to the change of saturation lead to a change in the shear modulus in the soil (Lu et al, 2018;Xu and Wei, 2011), then the modified dynamic shear modulus is used in this paper:…”

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“…First of all, it should be noted that the variation in saturation causes a series of changes in the physical parameters of the soil. Therefore, taking the angle of internal friction ϕ′ = 21 ° , the dynamic shear modulus is corrected by the following equation 36,37 where α vg is the parameter of van Genuchten model. 38 S e is the effective degree of saturation given by literature.…”