Prefabricated vertical drains with coupled surcharge-vacuum preloading is the most effective ground improvement approach to accelerate the consolidation of soft clay soil. This study used the equal strain concept, only radial flow in the soil system, constant permeability in the smear zone, and the Taylor series approach for solving analytical problems. Additionally, the study takes into account the realistic time-dependent application of surcharge. Drain discharge capacity decreases with time due to lateral confining pressure, twisting, folding, deformation, and clogging in the filter material of the drain; hence, this phenomenon is considered in this study. Analytical solutions are developed for average excess pore water pressure and average degree of consolidation. Comparisons of the proposed study are made with an available solution from the literature. The consolidation process is delayed when time-dependent discharge capacity is considered in contrast to constant discharge capacity. For short periods of consolidation, well resistance in the drains has less effect on the consolidation process observed.