Driven piles normally generate excess pore pressures in the surrounding soil. Dissipation of the pore pressures following driving is predicted currently by available elastic theory. However, viscosity is pronounced for many soft clays, therefore, its effect should be suitably accounted for. The gradual increase in pile capacity is dominated by the dissipation of excess pore pressure as has been widely explored both experimentally and theoretically. To predict the load-settlement response, the variation of pile-soil stiffness with the dissipation of pore pressure must also be quantified. This paper presents closed form solutions for the radial consolidation of the soil around a driven pile, assuming that the soil skeleton deforms visco-elastically. The solutions are theoretically valid for any initial distribution of excess pore pressure. However, the current study is focussed on the logarithmic variation of the initial pore pressure with radius, due to the expansion of a cylindrical cavity in an ideal elastic, perfectly plastic soil. The overall pile response measured from three cases has been used to backfigure the time-dependent variation of the two key facets: shear modulus and strength. The back analysis shows that variation of the two key facets can be well predicted with the presented radial consolidation theory.