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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2501.00661 |
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| _version_ | 1866915087493627904 |
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| author | Hosseini, Reihaneh Kumar, Krishna |
| author_facet | Hosseini, Reihaneh Kumar, Krishna |
| contents | 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, $S_r$; however, they have not been able to justify the particular shapes of the $χ$-$S_r$ curves. Theoretical solutions express $χ$ as a function of $S_r$ and the air-water interfacial area, $a_{wn}$; however, $a_{wn}$ 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 $χ$-$S_r$ curve over a full hydraulic cycle for a synthetic 3D granular soil column with immobile grains. We find that $χ=1$ at $S_r=1$ and $χ=0$ at $S_r=0$, while $χ>S_r$ for all other saturations. The maximum divergence of $χ$ from $S_r$ happens at the transition from/to the pendular regime. We also observe that the $χ$-$S_r$ curve is hysteretic; $χ$ is larger during wetting (imbibition) compared to drying (drainage) due to larger contribution of surface tension forces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_00661 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Measuring the effective stress parameter using the multiphase lattice Boltzmann method and investigating the source of its hysteresis Hosseini, Reihaneh Kumar, Krishna Soft Condensed Matter 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, $S_r$; however, they have not been able to justify the particular shapes of the $χ$-$S_r$ curves. Theoretical solutions express $χ$ as a function of $S_r$ and the air-water interfacial area, $a_{wn}$; however, $a_{wn}$ 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 $χ$-$S_r$ curve over a full hydraulic cycle for a synthetic 3D granular soil column with immobile grains. We find that $χ=1$ at $S_r=1$ and $χ=0$ at $S_r=0$, while $χ>S_r$ for all other saturations. The maximum divergence of $χ$ from $S_r$ happens at the transition from/to the pendular regime. We also observe that the $χ$-$S_r$ curve is hysteretic; $χ$ is larger during wetting (imbibition) compared to drying (drainage) due to larger contribution of surface tension forces. |
| title | Measuring the effective stress parameter using the multiphase lattice Boltzmann method and investigating the source of its hysteresis |
| topic | Soft Condensed Matter |
| url | https://arxiv.org/abs/2501.00661 |