Abstract: The non-sand-cover (NS) vacuum preloading (VP) has been widely used in China. Based on the equal-strain assumption, a new set of analytical solutions to consolidation drainage under VP and NS-VP, called JJJ-solution, are developed from original equations by Terzaghi and Barron for vertical and radial drainage, by introducing the original definite conditions, that is, highly under-consolidated initial state of soil and severe vacuum loss along PVD drain boundary. The JJJ-solution is consistent with all the existing equal-strain solutions and verified through experiments. It is capable of accurately predicting the unusual dissipation and distribution of the excess pore-water pressure in consolidation under NS-VP on soft-muddy foundation. In addition, the JJJ-solution is suitable for simulating soil consolidation in general vacuum, surcharge and vacuum-surcharge preloading.