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Modelling Particle-Size Distribution and Estimation of Soil–water Characteristic Curve utilizing Modified Lognormal Distribution function

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Abstract

In unsaturated soil mechanics, the soil–water characteristic curve (SWCC) is the most fundamental soil attribute. All seepage analyses require SWCC to generate the pore-water pressure and water content distribution within the soil layers. SWCC is often determined using laboratory procedures. However, the expensive cost, long testing time, and difficulty of the SWCC tests hinder the use of unsaturated soil mechanics in engineering practice. Models for predicting SWCC have been proposed in the literature; however, the equations cannot be applied to soils of a wide variety, and their parameters lack physical significance. This work used a modified lognormal distribution function to generate the equations that best suit the grain-size distribution (GSD) and the model that estimates SWCC for a wide range of soil types. The parameters of the proposed GSD equation have well-defined physical meanings. The model for estimating SWCC was established based on the link between soil pore-size distribution and dry density, void ratio, and saturated water content. The air-entry value of coarse-grained soil is a function of inflection point of SWCC and percentage of coarse particle. The air-entry value of fine-grained soil is a function of saturated water content. Experiments were carried out as part of this study to evaluate the proposed equation as well as its model. The proposed model to estimate SWCC was compared with other models. The proposed model is better than other models in the estimation of SWCC from GSD.

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References

  • Alves RD, Gitirana GFN, Vanapalli SK (2020) Advances in the modeling of the soil–water characteristic curve using pore-scale analysis. Comput Geotech 127:103766

    Article  Google Scholar 

  • Amadi AA, Osinubi KJ, Okoro JI (2023) Hydraulic conductivity of unsaturated specimens of lateritic soil-bentonite mixtures. Geotech Geol Eng. https://doi.org/10.1007/s10706-023-02524-3

    Article  Google Scholar 

  • Arya LM, Paris JF (1981) A physicoempirical model to predict the soil moisture characteristic from particle-size distribution and bulk density data. Soil Sci Soc Am J 45:1023–1030

    Article  Google Scholar 

  • ASTM D0422–63R07 (2009), Test Method for Particle-Size Analysis of Soils, Annual Book of ASTM Standards, Vol. 04.08, ASTM International, West Conshohocken, PA.

  • ASTM D2487–10 (2010) Standard Practice for Classification of Soils for Engineering Purposes (Unified Soil Classification System), Annual Book of ASTM Standards, Vol. 04.08, ASTM International, West Conshohocken, PA.

  • ASTM D4318–10 (2010) Standard Test Methods for Liquid Limit, Plastic Limit, and Plasticity Index of Soils, Annual Book of ASTM Standards, Vol. 04.08, ASTM International, West Conshohocken, PA.

  • ASTM D854–06E01 (2009) Standard Test Methods for Specific Gravity of Soil Solids by Water Pycnometer, Annual Book of ASTM Standards, Vol. 04.08, ASTM International, West Conshohocken, PA.

  • ASTM D2487-06E01 (2010) Standard Practice for Classification of Soils for Engineering Purposes (Unified Soil Classification System)

  • Buchan GD (1989) Applicability of the simple lognormal model to particle size distribution in soils. Soil Sci 147:155–161

    Article  Google Scholar 

  • Brooks RH, Corey AT (1964) Hydraulic properties of porous media. Colorado state university, Fort Collins, pp 24–37

  • Chen X, Hu K, Chen J, Zhao W (2018) Laboratory investigation of the effect of initial dry density and grain size distribution on soil-water characteristic curves of wide-grading gravelly soil. Geotech Geol Eng 36:885–896

    Google Scholar 

  • Chen Y, Sun X, Yan T, Yao D, Duan R (2020) Experimental study on micron-sized sand particles transport in the water flow path of hydrates production wellbore. J Nat Gas Sci Eng 73:103088

    Article  Google Scholar 

  • Dane JH (1983) Physical characteristics of soils of the southern region: Troup and Lakeland series, Southern Coop. Series Bull. No. 262, Auburn Univ., Alabama Agric. Exp. Sta, Auburn, Alabama.

  • Fredlund DG, Rahardjo H (1993) Soil mechanics for unsaturated soils. John Wiley and Sons Inc, New York

    Book  Google Scholar 

  • Fredlund DG, Xing A (1994) Equations for the soil-water characteristic curve. Can Geotech J 31:533–546

    Article  Google Scholar 

  • Fredlund MD, Fredlund DG, Wilson GW (2000) An Equation to represent grain-size distribution. Can Geotech J 37:817–827

    Article  Google Scholar 

  • Fredlund MD, Wilson GW, Fredlund DG (2002) Use of the grain-size distribution for estimation of the soil-water characteristic curve. Can Geotech J 39:1103–1117

    Article  Google Scholar 

  • Fredlund DG, Rahardjo H, Fredlund MD (2012) Unsaturated soil mechanics in engineering practice, John Wiley & Sons, Inc., New York, 926 pages.

  • Gardner WR (1956) Representation of soil aggregate size distribution by a logarithmic-normal distribution. Proc Soil Sci Soc Am 20:151–153

    Article  Google Scholar 

  • Gitirana GFN Jr, Fredlund DG (2004) Soil-water characteristic curve equation with independent properties. J Geotech Geoenviron Eng ASCE 130(2):209–212

    Article  Google Scholar 

  • Haverkamp R, Bouraoui F, Zammit C, Angulo-Jaramillo R (1999) Soil properties and moisture movement in the unsaturated zone, Handbook of Groundwater Engineering, Edited by J.W. Delleur, CRC Press New York, 5.1–5.47.

  • Haverkamp R, Parlange JY (1986) Predicting the water retention curve from particle size distribution: 1. Sandy Soils without Org Matter, Soil Sci 142:325–339

    Google Scholar 

  • Hilf JW (1956) An investigation of pore–water pressure in compacted cohesive soils. PhD Dissertation, Tech. Memo. No. 654, U. S. Department of the Interior, Bureau of Reclamation, Design and Construction Div., Denver, CO, pp 654

  • Huang C-Y, Hendrix PF, Fahey TJ, Bohlen PJ, Groffman PM (2010) A simulation model to evaluate the impacts of invasive earthworms on soil carbon dynamics. Ecol Model 221(20):2447–2457

    Article  CAS  Google Scholar 

  • Hwang SI, Lee KP, Lee DS, Powers SE (2002) Models for estimating soil particle-size distributions. Soil Sci Soc Am J, 66:1143–1150

    Article  CAS  Google Scholar 

  • Hwang S, Powers SE (2003) Using particle-size distribution models to estimate soil hydraulic properties. Soil Sci Soc Am J 67:1103–1112

    Article  CAS  Google Scholar 

  • Jiang X, Wu L, Wei Y (2020) Influence of fine content on the soil-water characteristic curve of unsaturated soils. Geotech Geol Eng 38:1371–1378

    Article  Google Scholar 

  • Khoshghalb A, Pasha AY, Khalili N (2015) A fractal model for volume change dependency of the water retention curve. Géotechnique 65(2):141–146

    Article  Google Scholar 

  • Kim Y, Satyanaga A, Rahardjo H, Park H, Sham AWL (2021) Estimation of effective cohesion using artificial neural networks based on index soil properties: a Singapore case. Eng Geol 289:106163

    Article  Google Scholar 

  • Kosugi K (1997) A new model to analyze water retention characteristics of forest soils based on soil pore radius distribution. J for Res 2(1):1–8

    Article  Google Scholar 

  • Leong EC, Wijaya M (2023) Laboratory Tests for Unsaturated Soils. CRC Press

    Book  Google Scholar 

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

    Article  Google Scholar 

  • Likos WJ, Jaafar R (2013) Pore-scale model for water retention and fluid partitioning of partially saturated granular soil. J Geotech Geoenviron Eng 139(5):724–737

    Article  Google Scholar 

  • Mendes RM, Marinho FAM (2020) Soil water retention curves for residual soils using traditional methods and MIP. Geotech Geol Eng 38:5167–5177

    Article  Google Scholar 

  • Nistor MM, Rahardjo H, Satyanaga A, Koh ZH, Qin X, Sham AWL (2020) Investigation of groundwater table distribution using borehole piezometer data interpolation: case study of Singapore. Eng Geol 271:105590

    Article  Google Scholar 

  • Quisenbeny VL, Cassel DK, Dane JH, Parker JC (1987) Physical characteristics of soils of the Southern Region—Norfolk, Dothan, Wagram, and Goldsboro Series. South. Coop. Ser. Bull. 263, South Carolina Agric. Exp. Stat., Clemson University, Clemson, SC

  • Rahardjo H, Satyanaga A, Mohamed H, Ip., C.Y., Rishi, S.S. (2019) Comparison of soil-water characteristic curves from conventional testing and combination of small-scale centrifuge and dew point methods. J Geotech Geol Eng 37(2):659–672

    Article  Google Scholar 

  • Raheem AM (2023) Developing a new soil-water characteristic model using nondestructive electrical properties for unsaturated soil. Geotech Geol Eng 41:1589–1601

    Article  Google Scholar 

  • Rawls WJ, Brakensiek DL (1989) Estimation of soil-water retention and hydraulic properties, In: Morel-Seytoux HJ (ed), Unsaturated flow in hydrologic modeling theory and practice, Kluwer, Beltsville, MD, pp 275–300.

  • Richards L. (1965). Physical condition of water in soil. Methods of Soil Analysis: Part 1 Physical and Mineralogical Properties, Including Statistics of Measurement and Sampling 9: 128–152

  • Rocha BP, Rodrigues RA, Giacheti HL (2021) The flat dilatometer test in an unsaturated tropical soil site. Geotech Geol Eng 39:5957–5969

    Article  Google Scholar 

  • Rouault Y, Assouline S (1998) A probabilistic approach towards modeling the relationship between particle and pore size distributions: the multicomponent sphere pack case. Powder Technol 96:33–41

    Article  CAS  Google Scholar 

  • Satyanaga A, Rahardjo H, Zhai Q (2017) “Estimation of unimodal water characteristic curve for gap-graded soil”. Soils and Foundations, 57(5): 789–801. https://doi.org/10.1016/j.sandf.2017.08.009

    Article  Google Scholar 

  • Satyanaga A, Rahardjo H, Koh ZH, Mohamed H (2019) Measurement of a soil-water characteristic curve and unsaturated permeability using the evaporation method and the chilled-mirror method. J Zhejiang Univ-Sci a 20(5):368–375

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  • Schaap MG, Leij FJ (1998) Database-related accuracy and uncertainty of pedo-transfer functions. Soil Sci 163:765–779

    Article  CAS  Google Scholar 

  • Shirazi MA, Boersma L (1984) A unifying quantitative analysis of soil texture. Soil Sci Soc Am J 48:142–147

    Article  Google Scholar 

  • Sweijen T, Hassanizadeh SM, Aslannejad H, Leszczynski S (2017) Grain-scale modelling of swelling granular materials using the discrete element method and the multi-sphere approximation. In Poromechanics VI. (pp. 329– 336).

  • Teiwes K (1988) Einfluß von Bodenbearbeitung und Fahrverkehr auf physikalische Eigenschaften schluffreicher Ackerb¨oden, PhD Thesis.

  • Udukumburage RS, Gallage C, Dawes L (2019) Oedometer based estimation of vertical shrinkage of expansive soil in a large instrumented soil column. Heliyon 5(9):e02380

    Article  CAS  Google Scholar 

  • Udukumburage RS, Gallage C, Dawes L, Gui Y (2020) Determination of the hydraulic conductivity function of grey Vertosol with soil column test. Heliyon 6:e05399

    Article  CAS  Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

  • Wijaya M, Leong EC, Rahardjo H (2015) Effect of shrinkage on air-entry value of soils. Soils Found 55(1):166–180

    Article  Google Scholar 

  • Zhai Q, Rahardjo H (2012) Determination of soil–water characteristic curve variables. Comput Geotech 42: 37–43. https://doi.org/10.1016/j.compgeo.2011.11.010

    Google Scholar 

  • Zhai Q, Rahardjo H, Satyanaga A (2017) Uncertainty in the estimation of hysteresis of soil–water characteristic curve. Environ Geotech 6(4):204–213

    Article  Google Scholar 

  • Zhai, Q., Rahardjo, H., & Satyanaga, A.,. (2019). “Estimation of air permeability function from soil-water characteristic curve”. Can Geotech J 56(4): 505–513. https://doi.org/10.1139/cgj-2017-0579

    Article  Google Scholar 

  • Zhai Q, Rahardjo H, Satyanaga A, Dai G (2020a) Estimation of the soil-water characteristic curve from the grain-size distribution of coarse-grained soils. Eng Geol 267:105502

    Article  Google Scholar 

  • Zhai Q, Rahardjo H, Satyanaga A, Dai G, Du YJ (2020c) Estimation of the wetting scanning curves for sandy soils. Eng Geol 272:105635

    Article  Google Scholar 

  • Zhai W, Rahardjo H, Satyanaga A, Zhu Y, Dai G, Zhao X (2021) Estimation of wetting hydraulic conductivity function for unsaturated sandy soil. Eng Geol 285:106034

    Article  Google Scholar 

  • Zhai Q, Rahardjo H, Satyanaga A, Dai G, Zhuang Y (2020b) Framework to estimate the soil-water characteristic curve for soils with different void ratios, Bulletin of Engineering Geology and the Environment (Accepted in Apr 2020b) https://doi.org/10.1007/s10064-020-01825-8

  • Zhang T, Zhang J, Jiang T, Wang X, Jia H, Wang L (2019) SWCCs of silt in Yudong zone and its prediction under different drying-wetting cycle conditions. Geotech Geol Eng 37:1977–1986

    Article  Google Scholar 

  • Zhao Y, Rahardjo H, Satyanaga A, Zhai Q, He J (2023) A general best-fitting equation for the multimodal soil-water characteristic curve. Geotech Geol Eng 41:3239–3252

    Article  Google Scholar 

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Acknowledgements

This research was supported by the Nazarbayev University Research Fund under Grants 11022021CRP1512 and 11022021CRP1508. The authors are grateful for this support. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the Nazarbayev University

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Nazarbayev University, 53 Kabanbay Batyr Ave, 010000, Nur-Sultan, Kazakhstan

    Alfrendo Satyanaga, Sung-Woo Moon & Jong Kim

  2. School of Civil and Environmental Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, Singapore

    Harianto Rahardjo

  3. Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education, Southeast University, Nanjing, 210096, China

    Qian Zhai

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  1. Alfrendo Satyanaga
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Correspondence to Alfrendo Satyanaga.

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Satyanaga, A., Rahardjo, H., Zhai, Q. et al. Modelling Particle-Size Distribution and Estimation of Soil–water Characteristic Curve utilizing Modified Lognormal Distribution function. Geotech Geol Eng 42, 1639–1657 (2024). https://doi.org/10.1007/s10706-023-02638-8

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