Parameter estimation of an overconsolidated aquitard subjected to periodic hydraulic head variations within adjacent aquifers

摘要

Extensometers provide long-term records of deformation over a depth interval of interest. An overconsolidated aquitard usually undergoes elastic deformation if the hydraulic head within adjacent aquifers remains higher than the preconsolidation head within the aquitard. The vertical hydraulic conductivity (K-v) and elastic skeletal specific storage (S-ske) are two critical parameters that control the deformation behavior of an overconsolidated aquitard, and they could be interpreted from valuable extensometer data. An analytical solution for the elastic aquitard deformation caused by periodic hydraulic head variations (PHHV) within adjacent aquifers is derived using the separation of variables method based on Euler's formula. The phase difference in PHHV between adjacent aquifers is found to reduce the amplitude of periodic aquitard deformation. Meanwhile, the phase difference is found to cause no influence on the growth pattern of the phase shift, which is between the periodic aquitard deformation and PHHV, versus the period. A new parameter estimation method is further proposed to interpret aquitard K-v and S-ske from periodic aquitard deformation data. This new method yields robust K-v and S-ske estimates of a moderately thick aquitard, whose deformation history has been recorded by an extensometer, located in Shanghai, China. The field study confirms that the phase difference in PHHV between the aquifers adjacent to the overconsolidated aquitard of interest cannot be ignored.