The self-weight consolidation of deposits consisting of fine-grained materials takes a long time. Using a suitable improvement method such as vacuum preloading can accelerate the consolidation. The first innovation is to experimentally assess the vacuum preloading effectiveness for expediting the settlement process of slurry tailings from the Sungun copper mine located in Iran. A new laboratory set-up is configured for radial and vertical consolidations of slurry samples. Effects of initial water content, suction level, and drainage zone size (i.e., sample relative size and vertical drain dimensions) on the tailings consolidation are evaluated through 272 tests. Previous studies indicate that analytical and numerical approaches are limited to particular assumptions and yield correct predictions only if various parameters during consolidation can be accurately determined. Therefore, as the second novelty, new empirical correlations are derived based on a modified multiple linear regression to simply predict vertical strain versus time curves under self-weight and vacuum consolidations with high accuracy. The data required for the statistical analysis are collected from the experimental results of Sungun tailings and a set of previous studies with a wide range of input values. The formulas proposed in this research are verified through several past in-situ and experimental studies with errors of less than 9%.