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A Hysteresis Model Based on an Explicit Domain-Dependence Function¹

ABSTRACT

A quantitative model of hysteresis is proposed, assuming the pore-water blockage against air entry to be a direct function of the volume of pore domains located in the completely-filled region of the state diagram. The relative volume of the porewater domains _o, evaluated from the history of the capillary head assuming the domains are independent, is employed in a dependency correction function P*_d(_o). For calibration, this model requires only the main loop of hysteresis and one drying scanning curve. The merit of this "Model III_expl" compared with Model III (Y. Mualem, 1974b, Y. Mualem and G. Dagan, 1975) is that any hysteretic process of wetting and drying is expressed analytically in explicit form. This property simplifies the computational procedure and saves computer time in practical application.

The overall agreement between predicted and measured hysteretic behavior is acceptable. However, the study reveals that in the range of the air entry value the model does not reproduce the main drying curve accurately if it diverges considerably from the drying scanning curve. This deficiency may reflect the less physical ground for Model III_expl compared to the implicit Model III.

¹ Contribution from the Hydrology and Water Resource Program, Faculty of Civil Engineering, Colo. State Univ., Fort Collins, CO 80523. Supported by funds provided by the National Science Foundation under Grant ENG7800845.

² Research Associate Professor, Colorado State University, and Professor, University of Wisconsin-Madison, respectively.

Received for publication December 4, 1978. Accepted for publication June 30, 1979.

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