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Investigating the source of hysteresis in the soil–water characteristic curve using the multiphase lattice Boltzmann method

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Abstract

The soil–water characteristic curve (SWCC) is the most fundamental relationship in unsaturated soil mechanics, relating the amount of water in the soil to the corresponding matric suction. From experimental evidence, it is known that SWCC exhibits hysteresis (i.e., wetting/drying path dependence). Various factors have been proposed as contributors to SWCC hysteresis, including air entrapment, contact angle hysteresis, ink-bottle effect, and change of soil fabric due to swelling and shrinkage; however, the significance of their contribution is debated. From our pore-scale numerical simulations, using the multiphase lattice Boltzmann method, we see that, even when controlling for all these factors, SWCC hysteresis still occurs, indicating that there is some underlying source that is not accounted for in these factors. We find this underlying source by comparing the liquid/gas phase distributions for simulated wetting and drying experiments of 2D and 3D granular packings. We see that during wetting (i.e., pore filling) many liquid bridges expand simultaneously and join together to fill the pores from the smallest to the largest, allowing menisci with larger radii of curvature (lower matric suction). Whereas, during drying (i.e., pore emptying), only the limited existing gas clusters can expand, which become constrained by the size of the pore openings surrounding them and result in menisci with smaller radii of curvature (higher matric suction).

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Data availability

The datasets generated and analyzed during the current study are available from the corresponding author on reasonable request.

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Authors and Affiliations

  1. Department of Civil, Architectural, and Environmental Engineering, The University of Texas at Austin, 301 E Dean Keaton, Austin, TX, 78731, USA

    Reihaneh Hosseini & Krishna Kumar

  2. IATE, Université Montpellier, CIRAD, INRAE, Montpellier SupAgro, Montpellier, France

    Jean-Yves Delenne

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  1. Reihaneh Hosseini
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  2. Krishna Kumar
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Appendix: Hysteresis due to the ink-bottle effect

Appendix: Hysteresis due to the ink-bottle effect

Consider the pore structure in Fig. 26, consisting of three chambers connected with throats. Starting from point A, if the suction is monotonically increased, the meniscus will move downward to point b and then c, to take the higher curvature required. At point c, the meniscus has reached the narrowest part of the throat. If the suction is again increased, the meniscus cannot find equilibrium at any height inside of the middle chamber, because all curvatures will be smaller than required. Therefore, the meniscus has to drop to the next throat at point d, which results in a sudden emptying of the middle chamber. Now, if the process is reversed and suction is monotonically decreased, the meniscus will start moving upwards from d to e to f. At point f, it reaches the widest part of the chamber. If suction is further decreased, the chamber cannot provide the required lower curvature, therefore, the meniscus jumps up to the next chamber, resulting in the sudden filling of the middle chamber. This difference in the pore emptying versus pore filling processes causes SWCC hysteresis as shown in the \(S-\Delta P\) plot in Fig. 26, and is known as the ink-bottle effect. The ink-bottle effect occurs when the suction monotonically increases or decreases, such as in pressure-controlled tests. If instead, the test is performed as volume-controlled, meaning that a certain amount of liquid is drained or injected and system is allowed to take any desired suction at equilibrium, then the meniscus will slowly move up or down without any sudden emptying or filling, taking the path a–b–c–f–e–d during drying and the exact reverse during wetting. These paths are shown with red arrows in Fig. 26. In such case, the drying and wetting curves will coincide and there will be no hysteresis.

Fig. 26
figure 26

Schematic representation of the ink-bottle effect

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Hosseini, R., Kumar, K. & Delenne, JY. Investigating the source of hysteresis in the soil–water characteristic curve using the multiphase lattice Boltzmann method. Acta Geotech. (2024). https://doi.org/10.1007/s11440-024-02295-y

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