Stormwater Uptake in Sponge-Like Porous Bodies Surrounded by a Pond: A Fluid Mechanics Analysis

Abstract

In this work, a previously published model for the water up take of stormwater in sponge-like porous bodies by the group is further developed. This is done by investigating the highest-performing model and considering the water uptake from the surroundings of a pond and rain-infiltrated soil. This implies that water uptake from impermeable to partially permeable surfaces is examined. Hence, the following cases are considered: (1) impervious bottom surface and no precipitation, (2) impervious bottom surface with precipitation, (3) permeable soil with no precipitation, and (4) permeable soil with precipitation. A mathematical model covering all these cases is presented, where the governing equations are the mass conservation and Darcy’s law together with an assumption of a sharp wetting front being a first-order approximation of the complete Richard’s equation. Results for the water uptake height, pond depth, and wetting front are computed numerically and plotted against time. Analytical solutions are also presented in certain cases, and critical values are obtained. The parametric study includes variations in the ratio of the model- to the surrounding ground surface area, initial pond depth, precipitation, and soil characteristics. To exemplify, the time it takes to absorb the water from the pond after a precipitation period is presented. The results are related to the Swedish rainfall data of 1 h duration with a return period of 10 years. When evaluating efficiency, the focus is on the absorption time. Results vary considerably, demonstrating a general trend that with soil infiltration, the water absorption rate is higher. For most cases, the considered water amount is absorbed completely, although depending on the parameters and conditions. These results serve to optimize the model for each of the cases. The main focus of the research lies in the theoretical aspect.