Physics-Informed Machine Learning of Soil-Water Characteristics Curve for Unsaturated Flow

A sound understanding of unsaturated soil properties is critical to the serviceability and resilience of coastal infrastructure (e.g., slopes). In tropical and subtropic areas, rainfall events often cause seasonal wetting and drying of surface unsaturated soils, leading to variations in the shear strength and deformation of slopes. The most fundamental unsaturated soil property that governs the hydro-mechanical behaviour of slopes is the soil-water characteristic curve (SWCC). In practice, high-quality soil samples are often collected from sites, and the SWCC curves are obtained from laboratory tests on those samples. The testing process can be time consuming. Alternatively, some studies are dedicated to inversely determining the SWCC based on extensive monitoring data. It is common practice to assume the SWCC follows a given parametric function form and to estimate associated hyperparameters using probabilistic methods. However, this is a nontrivial task, particularly when only limited site-specific measurements are available. To explicitly address this challenge, in this study, an ensemble learning framework is proposed to estimate the SWCC from limited site-specific data. A physics-informed neural network is adopted to solve the partial differential equation (PDE) governing unsaturated seepage. Instead of adhering to a single parametric function form, the SWCC is assumed to be aweighted summation of a series of SWCC bases. The adopted bases consist of representativeSWCC curves derived from empirical relationships, and each base follows a different deterministic function. Therefore, the estimation of a suitable SWCC function evolves into the determination of appropriate weight coefficients. The performance of the proposed framework is demonstrated using a synthetic slope example. Results indicate that the proposed methodcan predict arbitrary SWCC curves, such as bimodal SWCC, with high accuracy.

Keywords: Soil slope, Ensemble learning, Data-driven, Parameter estimation, Water flow, Pore water pressure.