One‐dimensional simulation of aquifer system compaction near Pixley, California: 2. Stress‐Dependent Parameters

A major problem facing hydrologists is how to predict land subsidence. A key to this problem is the development of a reliable method for evaluating aquitard parameters. For assumed values of hydraulic conductivity and storage, vertical compaction and expansion of idealized aquitards can be computed (predicted) by an appropriate diffusion equation from known (projected) water level changes in adjacent aquifers. If water levels within the aquifers are observed and the resulting field compaction and expansion are measured, the parameters themselves can be evaluated. Such field measurements are available at a site near Pixley, California, for the composite behavior of a series of 21 doubly draining aquitards. By means of a linear partial differential equation with constant coefficients within one digital model, average hydraulic conductivity for idealized aquitards was evaluated from the field data to be 3 × 10 −3 ft yr −1 (2.9 × 10 −9 cm s −1 ), and average nonrecoverable specific storage was evaluated to be 2.3 × 10 −4 ft −1 (7.5 × 10 −4 m −1 ). A second model allows parameters of nonrecoverable compaction to be stress dependent by assuming for any single material that the product of hydraulic conductivity and an incremental effective stress is a constant and that the product of nonrecoverable specific storage and past maximum effective stress is a constant. The latter assumption is a standard simplification of laboratory consolidation data; the former is introduced in the present paper. This second model improved simulation of observed compaction and expansion severalfold with virtually no increase in computer time. By using a double transformation of applied stress within the second model to linearize the nonlinear partial differential equation, hydraulic conductivity was evaluated to decrease by more than an order of magnitude during 12 years of record from 3.4 × 10 −3 ft yr −1 (3.3 × 10 −9 cm s −1 ) near the midplane of an idealized aquitard to 3.0 × 10 −4 ft yr −1 (2.9 × 10 −10 cm s −1 ) near the drainage faces of the idealized aquitard. Average nonrecoverable specific storage was evaluated to decrease from 2.3 × 10 −4 ft −1 to 1.9 × 10 −4 ft −1 (7.6 × 10 −4 m −1 to 6.2 × 10 −4 −1 ). In both models the average recoverable specific storage was evaluated to be 4.6 × 10 −6 ft −1 (1.5 × 10 −5 m −1 ).