Based on radial consolidation theory and equal stain assumption, third-order quasilinear partial differential equations for ultra-static pore water pressure of drainage are deduced under cylindrical coordinate system. The equations consider the effects of vacuum pump failure, air leakage, and the spatial and temporal nonlinearity on drainage well resistance. The variation of vacuum degree under film with time is used as a boundary condition, the analytic solutions for consolidation of vacuum preloading foundation under self-weight are derived with the consideration of influence of air leakage and the permeability coefficient of drainage water decreases with depth linear attenuation and time exponential decay. By comparisons, the solutions given by previous studies are found as a special case of the general solution in this article. Through examples, the results show that the well resistance coefficient A2 on the degree of consolidation is sensitive than A1, and the air leakage has a direct impact on the consolidation degree of the foundation in the process of vacuum preloading. The consolidation is slower under serious air leaking conditions. Therefore, the vacuum preloading time should be extended to ensure the vacuum pre-pressure results.