Numerical modeling of vacuum preloading incorporating time-dependent well resistance and depth-attenuated vacuum with a reference-grid-mapped well-boundary correction

Existing consolidation for soft soil ground improved by theories on vacuum preloading often fail to simultaneously account for the smear effect, time-dependent well resistance degradation due to clogging, and non-uniform vacuum pressure transmission along depth. To address these limitations, this paper develops a two-dimensional axisymmetric consolidation model based on a single-well unit cell. The governing equations incorporate coupled radial and vertical flow, utilizing piecewise radial consolidation coefficients to describe the smear zone and a linear decay of vacuum pressure along the drain depth. A time-dependent well resistance model, defined by the exponential decay of drain permeability, is introduced to characterize clogging. Furthermore, a reference grid mapping method is proposed to correct the mesh sensitivity of the Robin boundary condition in the explicit finite difference solution, thereby enhancing numerical robustness. Validated against field data from the Shanghai Disney Resort, the model demonstrates high accuracy in predicting settlement and pore water pressure dissipation. It outperforms traditional simplified analytical solutions in characterizing the deceleration of consolidation rates during the middle and late stages. Sensitivity analyses indicate that well resistance degradation significantly retards the consolidation process, while the smear effect primarily controls early-stage drainage near the well but has a limited impact on the overall average degree of consolidation. Additionally, neglecting vacuum attenuation along depth tends to overestimate deep effective stress and final settlement. These findings can provide a valuable reference for parameter back-analysis, effect evaluation, and design optimization in vacuum preloading projects.