Modelling Pore Size Distribution, Water Retention and Hydraulic Conductivity of Granular substrates using a Universal Multifractal-based approach for Nature-Based Solutions

The hydrological behavior of granular substrates is of critical interest in Nature-Based Solutions (NBS) like green roofs. To simulate this behavior in a physically realistic manner it is indispensable to model the substrate’s Hydraulic Conductivity (HC) as it determines infiltration rate at various degrees of saturation. Since HC is directly dependent on water content retained by the substrate, it is necessary to physically model this Water Retention (WR) behavior too. Capillary water is stored or retained in pore spaces and this water content that can be retained by a substrate under different suction pressures is therefore dependent upon its Pore Size Distribution (PSD). Since pores in any granular media are spaces where grains are absent, their size distribution too is intrinsically related to the substrate’s Grain Size Distribution (GSD) which provides the probability of finding grains smaller than some diameter d_gs. Although some earlier studies have attempted to model PSD, WR, and HC, they frequently use simplifying mono-fractal (fractal) approximations, whereas this study proposes a more generalized multifractal-based approach. Furthermore, while it is quite usual to incorporate pore tortuosity through some indirect parameter l in the HC model, a related ink-bottle effect which even though capable of affecting WR behavior is commonly ignored. Therefore this study suggests the use of a new parameter i in the WR model to physically represent this ink-bottle effect (a consequence of the substrate’s pore configuration or arrangement) which additionally takes into account the pore tortuosity without using l. The proposed models are validated using experimental measurements from 4 different commercially used green roof substrates.

Keywords: Multifractals, Non-linear geophysical systems, Cascade dynamics, Scaling, Hydrology, Green roof substrates.