Semi-analytical solutions for land subsidence due to groundwater withdrawal

Abstract

This paper introduces novel semi-analytical models tailored for estimating land subsidence resulting from groundwater extraction in confined aquifers. These models offer high scalability, allowing them to be applied to various well configurations and pumping schedules. Their development involves the numerical integration of two key analytical solutions: the “nucleus of strain” (NoS) (Mindlin and Chen, 1950), which represents a localised zone within the aquifer where a unit change in pore pressure leads to deformation and subsequent surface displacement, and the classic Theis equation (Theis, 1935) for the pore pressure changes induced by a constant-rate well pumping from a laterally unbounded aquifer. These integrations yield surface displacement components, both horizontal and vertical, expressed as functions of two dimensionless spatial–temporal variables, which encompass aquifer depth, thickness, well placement, pumping schedules, and critical hydro-geomechanical parameters like hydraulic conductivity, porosity, vertical compressibility, and water compressibility. Proposed are two distinct modelling approaches: one employing a lookup table (LT) derived from numerical integration results, and the other providing direct closed-form surface displacement solutions by fitting LT data with “hinge models”, which use piecewise-linear functions linked by sigmoidal curves for computational efficiency. In both cases, surface displacement components are estimated by plugging in the dimensionless variables. Conditions of variable pumping from multiple wells can be addressed by applying superposition of solutions. In essence, these semi-analytical models offer swift computational capabilities for understanding and forecasting land subsidence dynamics. Their scalability makes them adaptable to a wide array of well configurations and scheduling scenarios, rendering them valuable for numerous applications. They are particularly significant for providing preliminary estimates of the impacts of groundwater development, conducting “what-if” tests, and performing sensitivity analyses to identify key factors affecting land subsidence risk. This underscores the importance of these models in sustainable groundwater resource management and in mitigating land subsidence and its associated consequences.