COUPLED 2025

Darcy's Law in Coupled Geomechanics and Multiphase Flow

  • Nachum, Shay (BRAUDE)

Please login to view abstract download link

Coupled geomechanics and multiphase flow in porous media is one of the fundamental problems in geotechnical engineering. Soil behavior is typically described mathematically as a constitutive law including strain and stress tensors as well as soil parameters and water content. Water equations are necessary where water is neither uniform nor constant in time. The basic flow equation for rigid soils is based on Darcy's law, Darcy's law was developed by Darcy on the basis of empirical evidence for saturated flows; however, the law has also been applied to unsaturated flow and to non-rigid soil - when solids move along with liquids. Changes in soil volume affect the flow equation, which results in coupled problems. Darcy's law was applied by replacing the hydraulic head, H, with the soil's water potential, ψ, which is a measure of the potential energy of water in the soil compared to that of water in a reference state. The water potential can reach thousands of kPa, so for obtaining a reasonable water flux, the water potential must be multiplied by permeability values near zero. However, for calculating a value of 1, multiplying thousand by thousandth may not be the best approach. This paper illustrates why Darcy's law is problematic for coupled geomechanics and multiphase flow, and emphasizes that alternative mathematical frameworks must be developed.