Delay of flood formation by sponge-like porous bodies on unsaturated soil: a Richards' equation model

Sponge-like porous bodies (SPBs) offer a potential distributed storage approach for stormwater management in urban areas where space for conventional drainage solutions is limited. This paper builds upon our earlier up-flow SPB models, which are governed by mass conservation and Darcy's law. In contrast to earlier studies, infiltration into unsaturated soil with a water table at the bottom is described by the Richards equation. The soil is modeled with the Brooks–Corey relations, which is the reference model, and the problem is solved numerically. In addition, Gardner's conductivity model linearizes the Richards equation. This gives an analytical solution without the SPB and a semi-analytical solution with the SPB, and it allows the averaging over the soil surface that reduces the problem to one-dimensional. The analysis distinguishes two phases: absorption by the soil alone, and joint absorption by the soil and the SPB until ponding. The performance of the SPB is evaluated by comparing the flood formation times with and without the SPB, expressed as the efficiency, i.e., the relative delay of the flood formation. The results show that the SPB delays flood formation, and that the delay increases with the surface ratio and with the magnitude of the capillary head of the SPB.