Study on Stratum Deformation and Surface Settlement Patterns after Water and Sand Leakage from a Foundation Pit Based on DEM-CFD Numerical Simulations

In response to the frequent water and sand leakage disasters caused by water-rich sandy strata in foundation pit engineering, this study utilizes a discrete-element method (DEM)–computational fluid dynamics (CFD) coupling simulation method based on a leakage incident in a deep foundation pit of Hangzhou Metro. The study investigates the deformation behavior of the stratum caused by foundation pit leakage and sand loss and proposes an empirical formula for predicting surface settlement. The results show that, first, compared to the no-flow condition, the slip region of soil particles develops more rapidly under seepage conditions, and its final extent is larger. Second, following soil particle loss, deep-layer displacement isovalues form elliptical surfaces of varying sizes. The effect of different water and sand leakage conditions on the extent of soil deformation is relatively minor. The two short semiaxes of the loosening ellipsoid are b = 0.69–0.77H and c = 0.6–0.68H. Furthermore, both water and sand leakage conditions, as well as sand loss-only conditions, exhibit a settlement trough in the surface settlement curves. At the same time step, the maximum surface settlement value Smax under water and sand leakage conditions is approximately 2–4 times that under sand-only leakage conditions. In addition, the surface settlement curve is fitted based on the Peck formula, and a simplified two-dimensional theoretical model is proposed. This model is then extended into three-dimensional space, resulting in an empirical formula that can effectively predict surface settlement. The theoretical value of the soil loss volume calculated using the formula shows a relative error of 6.5% compared to the actual value. The findings provide crucial theoretical guidance for emergency responses to water and sand leakage in foundation pits and for subsequent soil backfilling and layer compensation grouting.