Using covariance function to investigate the reverse phenomena under groundwater pumping

The reverse behavior caused by a groundwater pumping was observed in the field for decades. The mechanism is believed in the difference of the propagation velocity between mechanic pass and fluid flow under a coupled system. This coupled behavior can be well described by the poroelastic theory. In the physical viewpoint, the reverse behavior indicates an anomaly relationship between displacement and pore pressure, and it can be, theoretically, explained by the covariance function of displacement and pore pressure. Therefore, a stochastic approach called the first-order second-moment (FOSM) method is adopted to construct a stochastic poroelastic model. The second moment solution is used to describe the reverse behavior of Noordbergum and Rhade effects. This is the first time to use a one-dimensional stochastic poroelastic model to explain the reverse phenomena. The results show that the one-dimensional FOSM stochastic poroelastic model ca n easily detect the reverse phenomena under both a constant discharge and a sudden stop of discharge conditions. The reverse phenomena are dominant under a small hydraulic conductivity and Young's modulus and depend on both the spatial and temporal scales. The results also imply that one-dimensional poroelastic model under a constant discharge condition could be a coupled system. The proposed FOSM method provides an approach to detect the reverse phenomena under discharge conditions. This phenomenon can be used in parameter inverse in the pumping test.