1. Home
  2. Vol 11, No 2 (2025)
  3. Gómez

A Theoretical Pore Network Model for the Soil–Water Characteristic Curve and Hysteresis in Unsaturated Soils

Angela V. Gómez

Abstract


This study presents a novel approach to modeling the soil–water characteristic curve in unsaturated soils, employing Monte Carlo simulations to capture the complex behavior of the pore network. The primary objective is to develop an alternative method to represent the hysteretic nature of the soil–water characteristic curve, which is critical for understanding unsaturated soil behavior in various engineering applications. The proposed approach conceptualizes soil as a network of interconnected pores, where each pore interacts with its nearest neighbors. Monte Carlo simulations are used to model the pore-filling distribution as a function of pressure differences during drying and wetting cycles. The model effectively reproduces the characteristic hysteresis curves associated with the hydraulic and mechanical processes in unsaturated soils. A key finding is that the simulated soil–water characteristic curve captures the impact of pore-scale interactions and reflects the complex hysteresis effects observed in experimental data. The novelty of this work lies in integrating pore network modeling with Monte Carlo simulations, addressing limitations of traditional models and offering a more accurate representation of unsaturated soil behavior. While the model has not yet undergone experimental validation, it provides valuable insights into the dynamics of soil moisture retention and serves as a foundation for future experimental testing and refinement of soil–water models.

 

Doi: 10.28991/CEJ-2025-011-02-021

Full Text: PDF


Keywords


Unsaturated Soil; Hysteresis; Monte Carlo; Statistics; Ising Model.

References


Fredlund, D. G. (1995). The scope of unsaturated soil problems. Proceedings of the First International Conference on Unsaturated Soils, UNSAT'95, 6-8 September, Paris, France.

Rahardjo, H., Kim, Y., & Satyanaga, A. (2019). Role of unsaturated soil mechanics in geotechnical engineering. International Journal of Geo-Engineering, 10(1), 1–23. doi:10.1186/s40703-019-0104-8.

Vanapalli, S. K., Fredlund, D. G., Pufahl, D. E., & Clifton, A. W. (1996). Model for the prediction of shear strength with respect to soil suction. Canadian Geotechnical Journal, 33(3), 379–392. doi:10.1139/t96-060.

Zhu, S., Zhang, L., & Wu, L. (2024). Simulation of hydro-deformation coupling problem in unsaturated porous media using exponential SWCC and hybrid improved iteration method with multigrid and multistep preconditioner. Acta Geotechnica, 19(10), 7011–7029. doi:10.1007/s11440-024-02414-9.

Yang, H., Rahardjo, H., Leong, E. C., & Fredlund, D. G. (2004). Factors affecting drying and wetting soil-water characteristic curves of sandy soils. Canadian Geotechnical Journal, 41(5), 908–920. doi:10.1139/T04-042.

Azizi, A., Jommi, C., & Musso, G. (2017). A water retention model accounting for the hysteresis induced by hydraulic and mechanical wetting-drying cycles. Computers and Geotechnics, 87, 86–98. doi:10.1016/j.compgeo.2017.02.003.

Fu, Y., Xu, L., & Liao, H. (2024). Quantitative experimental study on the apparent contact angle of unsaturated loess and its application in soil–water characteristics curve modeling. Vadose Zone Journal, 23(6), 20376. doi:10.1002/vzj2.20376.

Brooks, R. H. (1965). Hydraulic properties of porous media. PhD Thesis, Colorado State University, Fort Collins, United States.

Brooks, R. H., & Corey, A. T. (1966). Properties of Porous Media Affecting Fluid Flow. Journal of the Irrigation and Drainage Division, 92(2), 61–88. doi:10.1061/jrcea4.0000425.

Lyu, H., Fan, L., Gu, J., Huang, J., Chen, G., Shi, Z., & Zhang, J. (2024). Characterization of pore water distribution in unsaturated soils during drying process with NMR and soil-water characteristic curves. Transportation Geotechnics, 49, 101440. doi:10.1016/j.trgeo.2024.101440.

Liu, H., Rahardjo, H., Satyanaga, A., & Du, H. (2023). Use of osmotic tensiometers in the determination of soil-water characteristic curves. Engineering Geology, 312, 106938. doi:10.1016/j.enggeo.2022.106938.

Yan, G., Bore, T., Bhuyan, H., Schlaeger, S., & Scheuermann, A. (2022). The Technical Challenges for Applying Unsaturated Soil Sensors to Conduct Laboratory-Scale Seepage Experiments. Sensors, 22(10), 3724. doi:10.3390/s22103724.

Kumar, A., Azizi, A., & Toll, D. G. (2022). Application of Suction Monitoring for Cyclic Triaxial Testing of Compacted Soils. Journal of Geotechnical and Geoenvironmental Engineering, 148(4), 4022009. doi:10.1061/(asce)gt.1943-5606.0002766.

Abeykoon, T., Udukumburage, R. S., Gallage, C., & Uchimura, T. (2017). Comparison of direct and indirect measured soil-water characteristic curves for a silty sand. International Journal of GEOMATE, 13(39), 9–16. doi:10.21660/2017.39.170519.

Fredlund, D. G., & Anqing Xing. (1994). Equations for the soil-water characteristic curve. Canadian Geotechnical Journal, 31(4), 521–532. doi:10.1139/t94-061.

van Genuchten, M. T. (1980). A Closedâ€form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils. Soil Science Society of America Journal, 44(5), 892–898. doi:10.2136/sssaj1980.03615995004400050002x.

Rossi, C., & Nimmo, J. R. (1994). Modeling of soil water retention from saturation to oven dryness. Water Resources Research, 30(3), 701–708. doi:10.1029/93WR03238.

Assouline, S., Tessier, D., & Bruand, A. (1998). A conceptual model of the soil water retention curve. Water Resources Research, 34(2), 223–231. doi:10.1029/97WR03039.

Aubertin, M., Mbonimpa, M., Bussière, B., & Chapuis, R. P. (2003). A model to predict the water retention curve from basic geotechnical properties. Canadian Geotechnical Journal, 40(6), 1104–1122. doi:10.1139/t03-054.

Leong, E. C., & Rahardjo, H. (1997). Review of Soil-Water Characteristic Curve Equations. Journal of Geotechnical and Geoenvironmental Engineering, 123(12), 1106–1117. doi:10.1061/(asce)1090-0241(1997)123:12(1106).

Dexter, A. R., Czyz, E. A., Richard, G., & Reszkowska, A. (2008). A user-friendly water retention function that takes account of the textural and structural pore spaces in soil. Geoderma, 143(3–4), 243–253. doi:10.1016/j.geoderma.2007.11.010.

Omuto, C. T. (2009). Biexponential model for water retention characteristics. Geoderma, 149(3–4), 235–242. doi:10.1016/j.geoderma.2008.12.001.

Khlosi, M., Cornelis, W. M., Douaik, A., van Genuchten, M. T., & Gabriels, D. (2008). Performance Evaluation of Models That Describe the Soil Water Retention Curve between Saturation and Oven Dryness. Vadose Zone Journal, 7(1), 87–96. doi:10.2136/vzj2007.0099.

Cao, Y., Zhang, K., Liu, S., & Wang, Y. (2024). A review of advancements in the theory and characterization of soil macropore structure. PeerJ, 12(11), 18442. doi:10.7717/peerj.18442.

Daneshian, B., Habibagahi, G., & Nikooee, E. (2021). Determination of unsaturated hydraulic conductivity of sandy soils: a new pore network approach. Acta Geotechnica, 16(2), 449–466. doi:10.1007/s11440-020-01088-3.

Sharma, S., Rathor, A. P. S., & Sharma, J. K. (2025). Prediction of soil water characteristic curve of unsaturated soil using machine learning. Multiscale and Multidisciplinary Modeling, Experiments and Design, 8(1), 1–17. doi:10.1007/s41939-024-00664-4.

He, X., Cai, G., & Sheng, D. (2025). Indirect models for SWCC parameters: reducing prediction uncertainty with machine learning. Computers and Geotechnics, 177, 106823. doi:10.1016/j.compgeo.2024.106823.

Lee, T. D., & Yang, C. N. (1952). Statistical theory of equations of state and phase transitions. II. Lattice gas and ISING model. Physical Review, 87(3), 410–419. doi:10.1103/PhysRev.87.410.

Hopfield, J. J. (2018). Neural networks and physical systems with emergent collective computational abilities. Feynman and Computation, 7–19. doi:10.1201/9780429500459.

Strogatz, S. H. (2001). Exploring complex networks. Nature, 410(6825), 268–276. doi:10.1038/35065725.

Goh, S., Choi, M. Y., Lee, K., & Kim, K. M. (2016). How complexity emerges in urban systems: Theory of urban morphology. Physical Review E, 93(5), 523091. doi:10.1103/PhysRevE.93.052309.

Louf, R., Roth, C., & Barthelemy, M. (2014). Scaling in transportation networks. PLoS ONE, 9(7), 102007. doi:10.1371/journal.pone.0102007.

Xu, J., & Louge, M. Y. (2015). Statistical mechanics of unsaturated porous media. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 92(6), 0624051–06240517. doi:10.1103/PhysRevE.92.062405.

Du, X., Du, C., Radolinski, J., Wang, Q., & Jian, J. (2022). Metropolis-Hastings Markov Chain Monte Carlo Approach to Simulate van Genuchten Model Parameters for Soil Water Retention Curve. Water (Switzerland), 14(12), 1968. doi:10.3390/w14121968.

Chandler, D. (1987) Introduction to Modern Statistical Mechanics. Oxford University Press, Oxford, United Kingdom.

Staple, W. J. (1962). Hysteresis Effects in Soil Moisture Movement. Canadian Journal of Soil Science, 42(2), 247–253. doi:10.4141/cjss62-033.

Šimůnek, J., Kodešová, R., Gribb, M. M., & Van Genuchten, M. T. (1999). Estimating hysteresis in the soil water retention function from cone permeameter experiments. Water Resources Research, 35(5), 1329–1345. doi:10.1029/1998WR900110.

Fatt, I., & Dykstra, H. (1951). Relative Permeability Studies. Journal of Petroleum Technology, 3(09), 249–256. doi:10.2118/951249-g.

Mualem, Y. (1973). Modified approach to capillary hysteresis based on a similarity hypothesis. Water Resources Research, 9(5), 1324–1331. doi:10.1029/WR009i005p01324.

Mualem, Y. (1974). A conceptual model of hysteresis. Water Resources Research, 10(3), 514–520. doi:10.1029/WR010i003p00514.

Mualem, Y. (1984). A modified dependent-domain theory of hysteresis. Soil Science, 137(5), 283–291. doi:10.1097/00010694-198405000-00001.

Mualem, Y., & Dagan, G. (1975). A dependent domain model of capillary hysteresis. Water Resources Research, 11(3), 452–460. doi:10.1029/WR011i003p00452.

Klute, A., & Heermann, D. F. (1974). Soil water profile development under a periodic boundary condition. Soil Science, 117(5), 265–271. doi:10.1097/00010694-197405000-00005.

Hoa, N. T., Gaudu, R., & Thirriot, C. (1977). Influence of the hysteresis effect on transient flows in saturated-unsaturated porous media. Water Resources Research, 13(6), 992–996. doi:10.1029/WR013i006p00992.

Scott, P. S., Farquhar, G. J., & Kouwen, N. (1983). Hysteretic Effects on Net Infiltration. American Society of Agricultural Engineers, Michigan, United States.

Kool, J. B., & Parker, J. C. (1987). Development and evaluation of closedâ€form expressions for hysteretic soil hydraulic properties. Water Resources Research, 23(1), 105–114. doi:10.1029/WR023i001p00105.

Kool, J. B., & Parker, J. C. (1988). Analysis of the inverse problem for transient unsaturated flow. Water Resources Research, 24(6), 817–830. doi:10.1029/WR024i006p00817.

Pot, V., Peth, S., Monga, O., Vogel, L. E., Genty, A., Garnier, P., Vieublé-Gonod, L., Ogurreck, M., Beckmann, F., & Baveye, P. C. (2015). Three-dimensional distribution of water and air in soil pores: Comparison of two-phase two-relaxation-times lattice-Boltzmann and morphological model outputs with synchrotron X-ray computed tomography data. Advances in Water Resources, 84, 87–102. doi:10.1016/j.advwatres.2015.08.006.

Kaestner, A., Lehmann, E., & Stampanoni, M. (2008). Imaging and image processing in porous media research. Advances in Water Resources, 31(9), 1174–1187. doi:10.1016/j.advwatres.2008.01.022.

Schlüter, S., Sheppard, A., Brown, K., & Wildenschild, D. (2014). Image processing of multiphase images obtained via X-ray microtomography: A review. Water Resources Research, 50(4), 3615–3639. doi:10.1002/2014WR015256.

Chandler, R., Koplik, J., Lerman, K., & Willemsen, J. F. (1982). Capillary displacement and percolation in porous media. Journal of Fluid Mechanics, 119, 249–267. doi:10.1017/S0022112082001335.

Brush, S. G. (1967). History of the Lenz-Ising model. Reviews of Modern Physics, 39(4), 883–893. doi:10.1103/RevModPhys.39.883.

Christensen, K., & Moloney, N. R. (2005). Complexity and Criticality. Imperial College Press Advanced Physics Texts, World Scientific Publishing Company, Singapore. doi:10.1142/p365.

Ng, C. W. W., & Pang, Y. W. (2000). Influence of Stress State on Soil-Water Characteristics and Slope Stability. Journal of Geotechnical and Geoenvironmental Engineering, 126(2), 157–166. doi:10.1061/(asce)1090-0241(2000)126:2(157).

Roy, S., & Rajesh, S. (2018). Influence of Confining Pressure on Water Retention Characteristics of Compacted Soil. Indian Geotechnical Journal, 48(2), 327–341. doi:10.1007/s40098-017-0265-3.


Full Text: PDF

DOI: 10.28991/CEJ-2025-011-02-021

Refbacks

  • There are currently no refbacks.


Bookmark and Share


Copyright (c) 2025 Angela Viviana Gómez

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
x
Message