The effect of pore geometry in constitutive hysteretic models for unsaturated water flow

Water flow in porous media is strongly controlled by the microscale structure of the pore space. Therefore, understanding the dynamics at pore scale is fundamental to better estimate and describe the hydraulic properties and phenomena associated to water flow which are observed in a macroscale such as field or laboratory experiments. Pore geometry plays a key role since its variations cause modifications in hydraulic behaviour at the macroscale. In this study, we develop a new analytical model which represents the pore space of a medium as a bundle of tortuous sinusoidal capillary tubes with periodic pore throats and a fractal pore-size distribution. This model is compared with a previous model of straight constrictive capillary tubes in order to analyze the effect of pore geometry on hydraulic properties under partially saturated conditions. The comparison of the constitutive models shows that macroscopic hydraulic properties, porosity and permeability, present the strongest differences due to changes in the pore geometry. Nonetheless, no variations are observed in the relative hydraulic properties, effective saturation and relative permeability. The new model has been tested with experimental data consisting on sets of porosity-permeability, water content-pressure head, conductivity-pressure head, and hysteretic water content-pressure values. In all cases, the model is able to satisfactorily reproduce the data. This new analytical model presents an improvement over the previous model since the smoother variation of the pore radii allows a more realistic representation of the porous medium.