Analytical solutions for the consolidation of sludge by vacuum preloading

The vacuum preloading is an effective method for the in-situ consolidation of sludge in landfills. Considering its time effects, the analytical solutions for the consolidation by the vacuum preloading combined with the prefabricated vertical drain are obtained based on the equivalent elliptical cylinder model. Then, the parameter reflecting the time effects is obtained by fitting the measured data. The comparative analysis is carried out to validate the rationality and the practicability of the proposed solutions by comparing the settlement curve calculated from the proposed solutions to the measured one. The analysis results show that the elliptic cylinder equivalent model is the optimum choice to consider the shape effects of the PVD, and the calculated results based on the perimeter equivalent models are closer to those based on the elliptic cylinder equivalent model. The larger parameter α means the vacuum pressure is applied on the soil more quickly, which will lead to a quicker consolidation process.