Solution of the one-dimensional consolidation theory equation with a pseudospectral method

The one-dimensional consolidation theory equation is solved for an aquifer system using a pseudospectral method. The spatial derivatives are computed using Fast Fourier Transforms and the time derivative is solved using a fourth-order Runge-Kutta scheme. The computer model calculates compaction based on the void ratio changes accumulated during the simulated periods of time. Compactions and expansions resulting from groundwater withdrawals and recharges are simulated for two observation wells in Santa Clara Valley and two in San Joaquin Valley, California. Field data previously published are used to obtain mean values for the soil grain density and the compression index and to generate depth-dependent profiles for hydraulic conductivity and initial void ratio. The water-level plots for the wells studied were digitized and used to obtain the time dependent profiles of effective stress.