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A novel equation for simulating the bimodal soil–water retention curve of unsaturated soils

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Abstract

Unsaturated soils with bimodal pore structures, such as many residual and colluvial soils, are widespread in nature. Bimodal pore structures can noticeably influence their soil–water retention behaviour. Estimating the bimodal soil–water retention curve (SWRC) accurately has become critical in both theoretical research and engineering practice. In this paper, a novel equation to simulate the bimodal SWRC of unsaturated soils is proposed. The proposed bimodal SWRC equation not only provides higher simulation accuracy for bimodal SWRCs compared to other equations, but it also shows good agreement with experimental data from different types of soils. Moreover, the relationships between bimodal SWRC variables (i.e., air entry value, inflection point, and slopes at transition zone) and the best fitting parameters are presented. Finally, a practical approach is developed to estimate the bimodal relative permeability of unsaturated soils based on the proposed bimodal SWRC equation. The results are convincingly demonstrated that there is good agreement between the predicted and measured relative permeability coefficients of unsaturated soils in the literature.

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References

  1. Burger CA, Shackelford CD (2001) Evaluating dual porosity of pelletized diatomaceous earth using bimodal soil–water characteristic curve functions. Can Geotech J 38(1):53–66

    Article  Google Scholar 

  2. Burton GJ, Pineda JA, Sheng DC, Airey D (2015) Microstructural changes of an undisturbed, reconstituted and compacted high plasticity clay subjected to wetting and drying. Eng Geol 193:363–373

    Article  Google Scholar 

  3. Burton GJ, Sheng D, Campbell C (2014) Bimodal pore size distribution of a high-plasticity compacted clay. Geotech Lett 4(2):88–93

    Article  Google Scholar 

  4. Cai GQ, Zhou AN, Liu Y, Xu RZ, Zhao CG (2020) Soil water retention behavior and microstructure evolution of lateritic soil in the suction range of 0–286.7 MPa. Acta Geotech 15:3327–3341

    Article  Google Scholar 

  5. Chen H, Feng SJ (2023) A simple water retention model of dual-porosity soils based on self-similarity of bimodal pore size distribution. Comput Geotech 162:105684

    Article  Google Scholar 

  6. Chen RP, Liu P, Liu XM, Wang PF, Kang X (2019) Pore-scale model for estimating the bimodal soil-water characteristic curve and hydraulic conductivity of compacted soils with different initial densities. Eng Geol 260:105199

    Article  Google Scholar 

  7. Costa MBA, Cavalcante ALB (2021) Bimodal soil-water retention curve and k-function model using linear superposition. Int J Geomech 21(7):04021116

    Article  Google Scholar 

  8. Delage P (2010) A microstructure approach to the sensitivity and compressibility of some Eastern Canada sensitive clays. Geotechnique 60(5):353–368

    Article  Google Scholar 

  9. Dexter AR, Czyż EA, 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

    Article  ADS  Google Scholar 

  10. Fredlund DG, Rahardjo H (1993) Soil mechanics for unsaturated soils. Wiley, New York

    Book  Google Scholar 

  11. Fredlund DG (2006) Unsaturated soil mechanics in engineering practice. J Geotech Geoenviron 132(3):286–321

    Article  Google Scholar 

  12. Fredlund DG, Xing A (1994) Equation for the soil–water characteristic curve. Can Geotech J 31(4):521–532

    Article  Google Scholar 

  13. Fredlund DG, Xing A, Huang S (1994) Predicting the permeability function for unsaturated soils using the soil–water characteristic curve. Can Geotech J 31(4):533–546

    Article  Google Scholar 

  14. Gallipoli D, Wheeler S, Karstunen M (2003) Modelling the variation of degree of saturation in a deformable unsaturated soil. Geotechnique 53(1):105–112

    Article  Google Scholar 

  15. Gao Y, Li Z, Cui WJ, Sun DA, Yu HH (2023) Tensile strength behaviour of unsaturated fine-grained soil with different initial void ratios. Acta Geotech 07:01–14

    Google Scholar 

  16. Gao Y, Sun DA (2017) Soil–water retention behavior of compacted soil with different densities over a wide suction range and its prediction. Comput Geotech 91:17–26

    Article  Google Scholar 

  17. Gao Y, Sun DA, Zhou AN (2016) Hydromechanical behaviour of unsaturated soil with different specimen preparations. Can Geotech J 53(6):909–917

    Article  Google Scholar 

  18. Kuhn OV, Lopes BCFL, Caicedo B, Cordao NMP (2021) Micro-structural and volumetric behaviour of bimodal artificial soils with aggregates. Eng Geol 288:106139

    Article  Google Scholar 

  19. Lebeau M, Konrad JM (2010) A new capillary and thin film flow model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour Res 46(12):W12554

    Article  ADS  Google Scholar 

  20. Lei H, Xu Y, Jiang M, Jiang Y (2020) Deformation and fabric of soft marine clay at various cyclic load stages. Ocean Eng 195:106757

    Article  Google Scholar 

  21. Leong EC, Rahardjo H (1997) Review of soil–water characteristic curve equations. J Geotech Geoenviron 123(12):1106–1117

    Article  Google Scholar 

  22. Li D, Wang SJ, Li X, Chen HK, Liang GC, Jiang WJ (2021) Soil–water characteristic curve of sandy clayey purple soil under different overburden pressures. Chin J Geotech Eng 43(10):1950–1956

    Google Scholar 

  23. Li P, Pan ZH, Xiao T, Wang JD (2023) Effects of molding water content and compaction degree on the microstructure and permeability of compacted loess. Acta Geotech 18(2):921–936

    Article  CAS  Google Scholar 

  24. Liu S, Yasufuku N, Liu Q, Omine K, Hemanta (2013) Bimodal and multimodal descriptions of soil–water characteristic curves for structural soils. Water Sci Technol 67(8):1740–1747

    Article  PubMed  Google Scholar 

  25. Li X, Li JH, Zhang LM (2014) Predicting bimodal soil–water characteristic curves and permeability functions using physically based parameters. Comput Geotech 57:85–96

    Article  CAS  Google Scholar 

  26. Li X, Zhang LM, Fredlund DG (2009) Wetting front advancing column test for measuring unsaturated hydraulic conductivity. Can Geotech J 46(12):1431–1445

    Article  Google Scholar 

  27. Li X, Zhang LM, Li JH (2009) Development of a modified axis translation technique for measuring SWCCs for gravel soils at very low suctions. Geotech Test J 32(6):478–488

    CAS  Google Scholar 

  28. Li Y, Vanapalli SK (2021) A novel modeling method for the bimodal soil–water characteristic curve. Comput Geotech 138:104318

    Article  Google Scholar 

  29. Li Z, Gao Y, Yu HH, Chen B (2022) Soil water retention and hysteresis behaviors of different clayey soils at a high suction range. Geomech Eng 30(4):373–382

    Google Scholar 

  30. Peng F, Sun DA, Yao YP, Tan YZ (2024) Effect of granular structure and initial suction on shear strength of GMZ bentonite for deep geological disposal. Appl Clay Sci 249:107249

    Article  CAS  Google Scholar 

  31. Ng CWW, Akinniyi DB, Zhou C (2020) Influence of structure on the compression and shear behaviour of a saturated lateritic clay. Acta Geotech 15:3433–3441

    Article  Google Scholar 

  32. Ng CWW, Sadeghi H, Jafarzadeh F (2017) Compression and shear strength characteristics of compacted loess at high suctions. Can Geotech J 54(5):690–699

    Article  Google Scholar 

  33. Niu G, Sun DA, Wei CF, Yan RT, Hen JT, Yu MB (2016) Water retention behaviour of complete-intense weathering mudstone and its prediction. Chin J Geotech Eng 38(2):216–221

    Google Scholar 

  34. Oliveira AD, Pelaquim FGP, Zanin RFB, de Melo TR, Filho JT, Andrello AC, Teixeira RS (2022) The structure of tropical lateritic soils as an impacting factor in the shape of soil–water characteristic curves. Soils Rocks 45(2):1–13

    Article  Google Scholar 

  35. Otalvaro IF, Neto MPC, Delage P, Caicedo B (2016) Relationship between soil structure and water retention properties in a residual compacted soil. Eng Geol 205:73–80

    Article  Google Scholar 

  36. Perdomo CV, Nogueira LC, Miguel MG, Ladeira FSB (2021) Analysis of water retention in soil horizons of two open trenches on a slope of Serra do Mar, Brazil, susceptible to landslides. MATEC Web Conf 337(7):03015

    Article  Google Scholar 

  37. Qian JG, Lin ZQ, Shi ZH (2022) Experimental and modeling study of water-retention behavior of fine-grained soils with dual-porosity structures. Acta Geotech 17(8):3245–3258

    Article  Google Scholar 

  38. Rudiyanto MB, Shah RM, Setiawan BI, van Genuchten MT (2020) Simple functions for describing soil water retention and the unsaturated hydraulic conductivity from saturation to complete dryness. J Hydrol 588:125041

    Article  Google Scholar 

  39. Sasanian S, Newson TA (2013) Use of mercury intrusion porosimetry for microstructural investigation of reconstituted clays at high water contents. Eng Geol 158:15–22

    Article  Google Scholar 

  40. Satyanaga A, Bairakhmetov N, Kim JR, Moon SW (2022) Role of bimodal water retention curve on the unsaturated shear strength. Appl Sci 12(3):1266

    Article  CAS  Google Scholar 

  41. Satyanaga A, Rahardjo H, Leong EC (2016) The unsaturated shear strength of dual porosity Soil. Geo-Chicago 271:688–697

    Google Scholar 

  42. Satyanaga A, Rahardjo H, Leong EC, Wang JY (2013) Water characteristic curve of soil with bimodal grain-size distribution. Comput Geotech 48:51–61

    Article  Google Scholar 

  43. Satyanaga A, Rahardjo H (2019) Unsaturated shear strength of soil with bimodal soil–water characteristic curve. Geotechnique 69(9):828–832

    Article  Google Scholar 

  44. Seki K (2007) SWRC fit-a nonlinear fitting program with a water retention curve for soils having unimodal and bimodal pore structure. Hydrol Earth Syst Sci 4(1):407–437

    Google Scholar 

  45. Sun DA, Gao Y, Zhou AN, Sheng DC (2016) Soil–water retention curves and microstructures of undisturbed and compacted Guilin lateritic clay. B Eng Geol Environ 75:781–791

    Article  Google Scholar 

  46. Sun WJ, Cui YJ (2020) Determining the soil–water retention curve using mercury intrusion porosimetry test in consideration of soil volume change. J Rock Mech Geotech 12(5):1070–1079

    Article  Google Scholar 

  47. Thom R, Sivakumar R, Sivakumar V, Murray EJ, Mackinnon P (2007) Pore size distribution of unsaturated compacted kaolin: the initial states and final states following saturation. Geotechnique 57(5):469–474

    Article  Google Scholar 

  48. Van Genuchten MT (1980) A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci Soc Am J 44(5):892–898

    Article  Google Scholar 

  49. Wijaya M, Leong EC (2016) Equation for unimodal and bimodal soil–water characteristic curves. Soils Found 56(2):291–300

    Article  Google Scholar 

  50. Zhai Q, Rahardjo H, Satyanaga A (2017) Effect of bimodal soil–water characteristic curve on the estimation of permeability function. Eng Geol 230:142–151

    Article  Google Scholar 

  51. Zhai Q, Rahardjo H (2012) Determination of soil–water characteristic curve variables. Comput Geotech 42:37–43

    Article  Google Scholar 

  52. Zhang LM, Chen Q (2005) Predicting bimodal soil–water characteristic curves. J Geotech Geoenviron 131(5):666–670

    Article  Google Scholar 

  53. Zhou AN, Huang RQ, Sheng DC (2016) Capillary water retention curve and shear strength of unsaturated soils. Can Geotech J 53(6):974–987

    Article  Google Scholar 

  54. Zhou AN, Sheng DC, Carter JP (2012) Modelling the effect of initial density on soil–water characteristic curves. Geotechnique 62(8):669–680

    Article  Google Scholar 

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Acknowledgements

The authors express their gratitude for the Grants provided by the National Natural Science Foundation of China (No. 42272312), the China Postdoctoral Science Foundation Funded Project (Grant No. 2023M732252), the Zhejiang Provincial Xinmiao Talents Program (No. 2022R405B076).

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Authors and Affiliations

  1. School of Civil & Environmental Engineering and Geography Science, Ningbo University, 818, Fenghua Road, Ningbo, 315211, China

    You Gao & Yuchen Fu

  2. Department of Civil Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    You Gao & Jinjian Chen

  3. Department of Civil Engineering, Shanghai University, 149, Yanchang Road, Shanghai, 200444, China

    De’an Sun

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  1. You Gao
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  2. Yuchen Fu
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Gao, Y., Fu, Y., Chen, J. et al. A novel equation for simulating the bimodal soil–water retention curve of unsaturated soils. Acta Geotech. (2024). https://doi.org/10.1007/s11440-024-02233-y

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