On the relationship between water flux and hydraulic gradient for unsaturated and saturated clay

Experimental results indicate that the traditional form of Darcy’s law is not adequate for describing water flow processes in clay media because the observed relationship between water flux and hydraulic gradient can be highly non-linear. To capture this non-Darcian flow behavior, we propose a new relationship between water flux and hydraulic gradient by generalizing the currently existing relationships. The new relationship is shown to be consistent with experimental observations for both saturated and unsaturated conditions. In this paper, we also develop an empirical relationship between permeability and threshold hydraulic gradient, an important measure of non-Darcian behavior. The latter relationship is practically useful because it can reduce the number of parameters whose values need to be determined from experiment data in order to model non-Darcian behavior. How to incorporate the impacts of temperature and electrolyte concentrations into the proposed relationships needs further research.