ONE-DIMENSIONAL CONSOLIDATION OF FRACTIONAL DERIVATIVE VISCOELASTIC SATURATED SOIL LAYER WITH SYMMETRIC SEMI-PERMEABLE BOUNDARIES UNDER ARBITRARY LOADING

Based on one-dimensional consolidation theory of Terzaghi, this paper studies the one-dimensional consolidation problem of saturated soil layer with fractional viscoelastic model under symmetric semi-permeable boundaries subjected to arbitrary loading. By using the Laplace transform upon the one-dimensional consolidation equation of saturated soils and the fractional Kelvin-Voigt viscoelastic constitutive equation, the analytical solutions of effective stress and settlement in the Laplace transform domain are obtained. Crump's method is adopted to perform the inverse Laplace transform in order to obtain semi-analytical solutions in the time domain. It is shown that the present solution is reliable and in a good agreement with the existing solutions from literatures by reducing the proposed solution. Last, several numerical examples are provided to investigate the consolidation behavior of saturated soils with the fractional viscoelastic model under symmetric semi-permeable boundaries subjected to arbitrary loading. The results illustrate that, in the case of arbitrary loading, the consolidation rate is affected by the semi-permeable boundary parameters, fractional order, viscosity coefficient and load parameters. The final settlement of saturated soil layer is affected by the modulus of compressibility. In addition, the consolidation behavior of soil layer is consistent with the characteristics of loadings.