Stochastic analysis of the interaction between excess fluid flow and soil deformation in heterogeneous deformable porous media

Since aquifers deform under applied stresses, it is important to understand the interaction between fluid flow and soil deformation, as the deformation of the solid matrix affects the storage of water in the void space and may reach an extent that causes land subsidence under certain conditions. Geological heterogeneity has a major influence on groundwater movement and can therefore affect the amount of compaction. The aim of this work is, therefore, to perform a stochastic analysis of the influence of the variability of hydraulic conductivity fields on the interaction between excess fluid flow and soil deformation in heterogeneous, deformable porous media. The stress equilibrium equation and the storage equation together form a pair of coupled constitutive equations to describe the interaction of deformation (volume strain) and excess pore fluid pressure head. Using the Fourier–Stieltjes representation approach and a perturbation approximation, the coupled equations are solved analytically in the Fourier space domain for the case of unidirectional excess mean flow. Based on these solutions and the representation theorem, results are obtained for the variances of excess pore fluid pressure head and volume strain. They serve as an index of variability quantification for the evaluation of the variability of the log conductivity field and the compressibility coefficient of the soil on the variability of pressure head and volume strain fields. An illustration of the application of the proposed stochastic theory to predict the excess pore pressure and volume strain under uncertainty is also given.