The effective stress parameter, χ, is essential for calculating the effective stress in unsaturated soils. Experimental measurements have captured different relationships between χ and the degree of saturation, Sr; however, they have not been able to justify the particular shapes of the χ-Sr curves. Theoretical solutions express χ as a function of Sr and the air-water interfacial area, awn; however, awn is difficult to predict, limiting further investigation of χ variation. We seek an alternative approach for studying χ by simulating the pore-scale distribution of the two fluid phases in unsaturated soils using the multiphase lattice Boltzmann method (LBM). We develop an algorithm for measuring χ based on the suction and surface tension forces applied to each grain. Using this algorithm, we simulate the χ-Sr curve over a full hydraulic cycle for a synthetic 3D granular soil column with immobile grains. We find that χ=1 at Sr=1 and χ=0 at Sr=0, while χ>Sr for all other saturations. The maximum divergence of χ from Sr happens at the transition from/to the pendular regime. We also observe that the χ-Sr curve is hysteretic; χ is larger during wetting (imbibition) compared to drying (drainage) due to larger contribution of surface tension forces.
Cite
Hosseini, R., & Kumar, K. (2024). Measuring the effective stress parameter using the multiphase lattice Boltzmann method and investigating the source of its hysteresis. arXiv preprint arXiv:2501.00661.
BibLaTeX
@article{hosseini2024measuring,
title={Measuring the effective stress parameter using the multiphase lattice Boltzmann method and investigating the source of its hysteresis},
author={Hosseini, Reihaneh and Kumar, Krishna},
journal={arXiv preprint arXiv:2501.00661},
year={2024}
}