Sciences de l'ingénieur; dimensional analysis; hydraulic conductivity; particle size distribution
Abstract :
[en] Estimating hydraulic conductivity from particle size distribution (PSD) is an important issue for various engineering problems. Classical models such as Hazen model, Beyer model, and Kozeny-Carman model usually regard the grain diameter at 10% passing (d10) as an effective grain size and the effects of particle size uniformity (in Beyer model) or porosity (in Kozeny-Carman model) are sometimes embedded. This technical note applies the dimensional analysis (Buckingham's π theorem) to analyze the relationship between hydraulic conductivity and particle size distribution (PSD). The porosity is regarded as a dependent variable on the grain size distribution in unconsolidated conditions. It indicates that the coefficient of grain size uniformity and a dimensionless group representing the gravity effect, which is proportional to the mean grain volume, are the main two determinative parameters for estimating hydraulic conductivity. Regression analysis is then carried out on a database comprising 431 samples collected from different depositional environments and new equations are developed for hydraulic conductivity estimation. The new equation, validated in specimens beyond the database, shows an improved prediction comparing to using the classic models.
Disciplines :
Civil engineering
Author, co-author :
Wang, Ji-Peng
François, Bertrand ; Université de Liège - ULiège > Urban and Environmental Engineering
Lambert, Pierre
Language :
English
Title :
Equations for hydraulic conductivity estimation from particle size distribution: A dimensional analysis
Alyamani, M. S., and Z. Sen (1993), Determination of hydraulic conductivity from complete grain-size distribution curves, Ground Water, 31(4), 551–555, doi:10.1111/j.1745-6584.1993.tb00587.x.
American Society for Testing and Materials (2006), Standard Test Method for Permeability of Granular Soils, ASTM Standard D2434–68, Am. Soc. for Test. and Mater., West Conshohocken, Pa.
Beyer, W. (1964), Zur Bestimmung der Wasserdurchlassigkeit von Kieson und Sanduen aus der Kornverteilung, Wasserwirt. Wassertech., 14, 165–169.
Buckingham, E. (1914), On physically similar systems; illustrations of the use of dimensional equations, Phys. Rev., 4(4), 345–376, doi:10.1103/PhysRev.4.345.
Cabalar, A. F., and N. Akbulut (2016), Evaluation of actual and estimated hydraulic conductivity of sands with different gradation and shape, Springerplus, 5(1), 820, doi:10.1186/s40064-016-2472-2.
Carman, P. (1937), Fluid flow through granular beds, Trans. Chem. Eng., 15, 150–166.
Carman, P. C. (1956), Flow of Gases Through Porous Media, Butterworth Sci. Publ., London.
Cheng, Y.-T., and C.-M. Cheng (2004), Scaling, dimensional analysis, and indentation measurements, Mater. Sci. Eng. R, 44(4–5), 91–149, doi:10.1016/j.mser.2004.05.001.
Harleman, D., P. Mehlhorn, and R. Rumer (1963), Dispersion-permeability correlation in porous media, J. Hydraul. Div. Am. Soc. Civ. Eng., 89(2), 67–85.
Hazen, A. (1892), Physical Properties of Sands and Gravels With Reference to Their Use Infiltration, Massachusetts State Board of Health, Boston, Mass.
Kozeny, J. (1927), Über kapillare leitung des wassers im boden: (aufstieg, versickerung und anwendung auf die bewässerung), Hölder-Pichler-Tempsky, 136, 271–306.
Kozeny, J. (1953), Das Wasser im Boden. Grundwasserbewegung, in Hydraulik, edited by J. Kozeny, pp. 380–445, Springer, Vienna.
Lu, C., X. Chen, C. Cheng, G. Ou, and L. Shu (2012), Horizontal hydraulic conductivity of shallow streambed sediments and comparison with the grain-size analysis results, Hydrol. Processes, 26(3), 454–466, doi:10.1002/hyp.8143.
Riva, M., X. Sanchez-Vila, and A. Guadagnini (2014), Estimation of spatial covariance of log conductivity from particle size data, Water Resour. Res., 50, 5298–5308, doi:10.1002/2014WR015566.
Rosas, J., O. Lopez, T. M. Missimer, K. M. Coulibaly, A. H. A. Dehwah, K. Sesler, L. R. Lujan, and D. Mantilla (2014), Determination of hydraulic conductivity from grain-size distribution for different depositional environments, Ground Water, 52(3), 399–413, doi:10.1111/gwat.12078.
Song, J., X. Chen, C. Cheng, D. Wang, S. Lackey, and Z. Xu (2009), Feasibility of grain-size analysis methods for determination of vertical hydraulic conductivity of streambeds, J. Hydrol., 375(3–4), 428–437, doi:10.1016/j.jhydrol.2009.06.043.
Vienken, T., and P. Dietrich (2011), Field evaluation of methods for determining hydraulic conductivity from grain size data, J. Hydrol., 400(1–2), 58–71, doi:10.1016/j.jhydrol.2011.01.022.
Vignaux, G. (1992), Dimensional analysis in data modelling, in Maximum Entropy and Bayesian Methods, edited by C. R. Smith, G. J. Erickson and P. O. Neudorfer, pp. 121–126, Springer, Netherlands.
Vukovic, M., and A. Soro (1992), Determination of Hydraulic Conductivity of Porous Media From Grain-Size Composition, Water Resour. Publ., Littleton, Colo.
Wang, J.-P., N. Hu, B. François, and P. Lambert (2017), Estimating water retention curves and strength properties of unsaturated sandy soils from basic soil gradation parameters, Water Resour. Res., 53, 6069–6088, doi:10.1002/2017WR020411.
Wenzel, L. (1942), Methods for determining permeability of water-bearing materials, with special reference to discharging-well methods, with a section on direct laboratory, U.S. Geol. Surv. Water- Supply Pap. 887.
Wiebenga, W. A., W. R. Ellis, and L. Kevi (1970), Empirical relations in properties of unconsolidated quartz sands and silts pertaining to water flow, Water Resour. Res., 6(4), 1154–1161, doi:10.1029/WR006i004p01154.
