Dynamic Response And Wave Propagation Of Saturated Soil In Half Space Based On Nonlocal Theory

The study of elastic wave propagation characteristics and dynamic response of saturated soil has always been a major topic in the domain of soil dynamics and geotechnical engineering.Most of the existing theories for studying two-phase saturated porous media are based on Biot’s saturated soil theory and porous media theory,but they do not take into account the influence of nonlocal effects such as pore size.In order to consider the nonlocal effect,this paper replaces the elastic constitutive relationship of classical continuum mechanics with a nonlocal elastic constitutive relationship.Based on the incompressible porous media model,a nonlocal porous media theory is established,and the control equation of saturated soil in incompressible porous media expressed by displacement is obtained.On this basis,the dynamic response and wave propagation properties of saturated soil in half space are studied as follows:(1)A differential equation for vibration of one-dimensional saturated soil is established,which is expressed by displacement and considers nonlocal effects.By considering the boundary conditions and initial conditions of the problem,and solving the characteristic equations and eigenvectors,analytical solutions for the solid phase displacement,liquid phase displacement,and pore water pressure of one-dimensional saturated soil layers in the frequency domain are obtained.The numerical results show that there is resonance phenomenon in one-dimensional saturated soil layer under simple harmonic load.When considering the nonlocal effect of saturated soil,the resonance amplitude will weaken and the system damping will increase;The liquid-solid coupling coefficient mainly affects the peak values of solid phase displacement,liquid phase displacement,and pore water pressure versus frequency curves.(2)Using the wave function expansion method,analytical solutions for the velocity,attenuation,reflection coefficient,and displacement and stress of the free boundary interface of the reflected compression wave under oblique incidence of the compression wave are obtained under corresponding boundary conditions.The effects of non local parameters on the propagation properties of the compression wave and the response of the saturated soil site when the frequency and incident angle change are numerically analyzed.The results show that the nonlocal effect has little influence on the propagation properties of compressed waves at low frequencies;At high frequencies,the larger the nonlocal parameters at the same frequency,the stronger the wave dissipation;When the incident angle is 0 ° and 90 °,the amplitude of horizontal displacement is zero,while the vertical displacement is the largest at vertical incidence and the smallest at grazing incidence.(3)The propagation properties of Rayleigh surface waves generated by a force source at a negative infinite distance are studied.The dispersion equation of Rayleigh waves and the analytical solutions of displacement and stress in saturated half-space are obtained under the influence of nonlocal parameters.The effects of nonlocal parameters and permeability coefficient on the phase velocity and attenuation rate of Rayleigh wave,as well as the dynamic response of saturated half-space when the free surface is permeable,are investigated under the two boundary conditions of permeable and impermeable.The results show that the higher the frequency,the smaller the wavelength,the more obvious the nonlocal effect,and the greater the influence of the pore size of the saturated two-phase medium on the wave propagation properties;The stronger the permeability,the smaller the corresponding frequency when the wave velocity and attenuation reach the limit value;The weaker the permeability,the faster the attenuation of displacement and stress amplitude in the saturated half space.