Validity of fully drained, fully undrained and u-p formulations for modeling a poroelastic half-space under a moving harmonic point load

摘要

Biot's theory has been widely employed to study responses of saturated soil under dynamic loads. To simplify the analysis, three simplified formulations based on Biot's theory have been proposed, including the u-p formulation, fully undrained formulation and fully drained formulation. The u-p formulation is established by neglecting the relative pore fluid acceleration. The fully undrained formulation founds on the assumption of no relative pore fluid displacement. The fully drained formulation supposes an infinite soil permeability. Nevertheless, the successful applications of these simplified formulations are hindered because of their indefinite application scopes. To overcome this, this paper carries out a comparative study of the simplified formulations for modeling a saturated poroelastic half-space subjected to a moving harmonic point load. The three simplified formulations are investigated by comparing with Biot's u-w formulation. A triple Fourier transform is first used to transform the four formulations into the frequency-wavenumber domain. Then an analytical inverse transform with respect to the frequency is performed to obtain the vertical soil displacement and pore pressure in the time-wavenumber domain. A parameter R_Ω defined in the wavenumber domain, which integrates effects of the soil permeability, load oscillating frequency and moving load velocity, is proposed to determine the validity ranges of the three simplified formulations. Some critical values of R_Ω are suggested and applied to a model in a previously published paper by Siddharthan et al.