Dynamic interactions of groundwater flow and soil deformation in randomly heterogeneous porous media

The interaction of groundwater flow and soil deformation within porous media is a complicated process. Water movement or stress change in porous media result in both deformation and alteration in pore water pressure. In this study, the dynamic interactions of flow and deformation in randomly heterogeneous porous media are analyzed using the stochastic first-order second-moment (FOSM) method. Various flow boundaries are considered, including sudden starts and sudden stops of discharge and recharge. The stochastic model is first verified with the results from Monte Carlo simulations with a constant discharge. The patterns of mean, variance, and covariance solutions obtained using the FOSM method are the same as those obtained using Monte Carlo simulations. The results show that the mean behaviors of water pressure variation and deformation are well explained by the concept of effective stress. The second-moment solutions show monotonic increases in the variances of displacement and changes in pore water pressure with distance away from the prescribed boundary. The cross-covariance of log hydraulic conductivity and change in pore water pressure is initially negative and then becomes positive, whereas that of change in pore water pressure and displacement is initially positive and then becomes negative soon after discharge starts at the boundary. The initial behavior is opposite to that in the later period. This reversal of cross-covariance is attributed initially to stress and later to water flow, and it extends from the boundary and then diminishes quickly with time. The Rhade effect occurs for the mean change in pore water pressure in areas away from the discharge boundary when discharge suddenly stops. The reversal of cross-covariance is also found at various depths immediately after the stop of flow at the boundary for both discharge and recharge conditions due to the dynamic interactions of flow and deformation. The results also show that the strength of the dynamic interactions between groundwater flow and soil stress increases with decreasing mean hydraulic conductivity and average stiffness of randomly heterogeneous porous media. Neglecting the dynamic interactions of flow and deformation leads to misinterpretation of aquifer properties and increases estimation uncertainty.