Rheological model for sludge dewatering with vacuum-assisted horizontal drains

Prefabricated horizontal drains (PHDs) are increasingly popular for vacuum dewatering of sludge with high water content. However, traditional consolidation models based on the principle of effective stress and Darcy’s law fail to capture solid–fluid interactions in the early dewatering stages given the absence of a soil skeleton. To address this limitation, this study proposes a two-dimensional compression rheological model that simulates the coupled filtration–consolidation behavior of sludge dewatering, incorporating drag forces on solid/fluid, critical particle contact condition, and solid/fluid movement obstructions. The governing equation, derived from force balance, continuity, and kinetics equations, is solved using the alternative direction implicit difference method and verified through two one-dimensional cases, a laboratory model test, and a large-scale field trial. With unique constitutive relationships—compressive yield stress and hindered setting factor—the proposed rheological model presents more rational solid–solid and solid–fluid interactions compared to conventional consolidation models, particularly during filtration. Parametric analyses suggest that reducing horizontal or vertical spacing of the PHDs accelerates dewatering without affecting final soil deformation, while constitutive parameters influence both the dewatering rate and final vertical strain of the soil in distinct manners.