Analysis of Lamb Problem in Non-Locally Non-Uniform Semi-Infinite Saturated Foundation

Currently, Lamb problems of many engineering foundations investigated are still assuming that foundation soils are two-phase homogeneous saturated porous medium. However, actual engineering foundation soils are not ideal homogeneous elastic bodies, and the impact of soil pores variation along depth on Lamb problems cannot be ignored. A non-uniform gradient factor has been proposed by means of taking foundation depth non-linear effects on soil porosity, density, shear modulus, Lame constant, and permeability coefficient into account, which has been coupled with Eringen's non-local theory and Biot's theory to introduce the potential function for solving wave equations by means of the Helm-holtz principle, and the corresponding mass conservation equation, momentum balance equation and effective stress principle are utilized in this solving process, meanwhile, verification of the correctness of the derived formula has been done through equation degradation. The proposed analysis method firstly is able to provide analytical solutions for soil skeleton displacement, relative fluid displacement, pore water pressure, and stress components considering and not considering fluid non local effects, respectively. Secondly, the influence of vertical non-uniformity of soil on Lamb problem of non-local semi-infinite saturated half space under surface excitation has been revealed. Taking the analytical solution without considering the non-local effects of the fluid as an example, the analysis results show that: The non-uniform gradient parameter not only affects the magnitude of the soil peak, but also affects the period of the amplitude peak, while non local parameters only affect the magnitude of the amplitude and have no effect on the period of the amplitude peak. The achievements have practical significance for earthquake engineering, engineering seismic resistance, and engineering vibration.