Based on the layered visco-elastic soil model, according to the Terzaghi's
one dimensional consolidation theory, by the method of Laplace transform an
d matrix transfer technique, the problems about the consolidation of layere
d and saturated visco-elastic soils under arbitrary loading were solved. Th
rough deductions, the general solution, in the terms of layer thickness, th
e modulus and the coefficients of permeability and Laplacian transform's pa
rameters was obtained. The strain and deformation of the layered and satura
ted visco-elastic soils under arbitrary loading can be calculated by Laplac
e inversion. According to the results of several numerical examples, the co
nsolidation of visco-elastic soils logs behind that of elastic soils. The d
evelopment of effective stress and the displacement is vibrant process unde
r cyclic loading. Finally, an engineering case is studied and the results p
rove that the methods are very effective.