The highly compressible nature of some aquitards leads to nonlinear consolidation where the groundwater flow parameters are stress-dependent. The case is further complicated by the heterogeneity of the hydrogeologic and geotechnical properties of the aquitards. To adequately model land subsidence in these systems, we develop a modeling approach to couple a nonlinear 1-D groundwater flow and consolidation model with a data assimilation scheme based on ensemble Kalman filter. This modeling approach allows to estimate the ensemble mean distribution of state variables and stress-dependent parameters, such as hydraulic conductivity (K), pore-pressure and total settlement. Zapata-Norberto et al. (2017) have shown that in randomly heterogeneous highly compressible aquitards under 1-D vertical flow, the parameter with largest impact on ensemble total settlement and its variance is K. We therefore consider the case where only K is randomly heterogeneous. We consider cases where pore-pressure and/or K measurements are available at given time intervals. We test our approach by solving the nonlinear flow and consolidation problem on a generated 1-D realization of lnK with exponential spatial correlation. These results are taken as our “true” solution. We take pore-pressure and/or lnK “measurements” at different times from this “true” solution. The ensemble Kalman filter method is then employed to estimate ensemble mean distribution of lnK, pore-pressure and total settlement based on the sequential assimilation of those measurements. The ensemble-mean estimates from this procedure closely approximate those from the “true” solution. This procedure can be easily extended to other random variables such as compression index and void ratio.
Zapata-Norberto B., Morales-Casique E. & Herrera G.S. Hydrogeology Journal (2017). https://doi.org/10.1007/s10040-017-1698-6
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