Probability Distributions for Hydraulic Conductivity of Compacted Soil Liners
Publication: Journal of Geotechnical Engineering
Volume 119, Issue 3
Abstract
This paper describes an analysis of hydraulic conductivity data collected from 57 landfill liners and covers throughout North America. Statistical characteristics of the data are summarized, and goodness‐of‐fit analyses are performed on each set to determine a distributional form that can be used to describe spatial variability of hydraulic conductivity. The statistics of hydraulic conductivity are shown to vary widely. The mean varied from to , the coefficient of variation varied between 27 and 767, the coefficient of skewness between −0.23 and 7.7, and the coefficient of kurtosis from 1.75 to 58. Goodness‐of‐fit tests show that the two‐parameter log‐normal hypothesis is often rejected. The traditional two‐parameter log‐normal distribution is compared to four alternative distributions: the three‐parameter log‐normal, generalized extreme value (GEV), the three‐parameter gamma, and inverse Gaussian. The analyses show that the three‐parameter log‐normal and GEV result in superior fits to the data.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Anderson, R. L. (1942). “Distribution of the serial correlation coefficient.” J. Royal Statistical Soc. B, 105(1), 1–13.
2.
Ang, A., and Tang, W. (1975). Probability concept in engineering planning and design, volume I‐Basic principles, John Wiley and Sons, New York, N.Y.
3.
Baker, F., and Bouma, J. (1976). “Variability of hydraulic conductivity in two suburface horizons of two silt loam soils.” J. Soil Sci. Soc. of Amer., 40(2), 219–222.
4.
Boutwell, G., and Hedges, C. (1989). “Evaluation of waste‐retention liners by multivariate statistics.” Proc., Twelfth Int'l Conf. on Soil Mech. and Found. Engrg., Int. Soc. for Soil Mech. and Found. Engrg., 2, 815–818.
5.
Benson, C., and Charbeneau, R. (1991). “Reliability analysis for time of travel in compacted soil liners.” Proc., ASCE Geotech. Cong. 1991, Boulder, Colo., GSP. No. 28, 1, 456–467.
6.
Blom, G. (1958). Statistical estimates and transformed beta‐variables. John Wiley and Sons, New York, N.Y.
7.
Bogardi, I., Kelly, W. E., and Bardossy, A. (1989). “Reliability model for soil liners: Initial design.” J. Geotech. Engrg., ASCE, 115(5), 658–669.
8.
Cunanne, C. (1989). “Statistical distributions for flood frequency analysis.” Operational Hydrol. Rep. No. 718, World Meteorological Organization, A3.1–A3.5.
9.
Donald, S. B. (1990). “Stochastic analysis of compacted clay landfill liners,” M.S. thesis, University of Waterloo, Waterloo, Ontario, Canada.
10.
Estimating probabilities of extreme floods—Methods and recommended research. (1988). Committee on Techniques for Estimating Probabilities of Extreme Floods, Water Sci. and Tech. Board, Nat. Res. Council, Washington, D.C.
11.
Filliben, J. (1975). “The probability plot correlation coefficient test for normality.” Technometrics, 17(1), 111–117.
12.
Folks, J., and Chhikara, R. (1978). “The inverse Gaussian distribution and its statistical application—A review.” J. Royal Statistical Soc. B, 40(3), 263–289.
13.
Freeze, R. A. (1975). “A stochastic‐conceptual analysis of one‐dimensional ground‐water flow in non‐uniform homogeneous media.” Water Resour. Res., 11(5), 725–741.
14.
Greenwood, J., and Durand, D. (1960). “Aids for fitting the gamma distribution by maximum likelihood.” Technometrics, 2(1), 55–65.
15.
Haan, C. T. (1977). Statistical methods in hydrology. Iowa State Univ. Press, Ames, Iowa.
16.
Hoeksema, R., and Kitanidis, P. (1985). “Analysis of spatial structure of selected aquifers.” Water Resour. Res., 21(4), 563–572.
17.
Hosking, J. R. M. (1986). “The theory of probability weighted moments.” Res. Rep. #54860, IBM T. J. Watson Res. Ctr., Math. Sci. Dept., Yorktown Heights, N.Y.
18.
Hosking, J. R. M. (1990). “L‐moments: Analysis and estimation of distributions using linear combinations of order statistics.” J. Royal Statistical Soc. B, 52(1), 105–124.
19.
Hosking, J. R. M., et al. (1985). “Estimation of generalized extreme‐value distribution by the method of probability‐weighted moments.” Technometrics, 27(3), 251–261.
20.
Johnson, G., Crumbley, W. S., and Boutwell, G. P. (1990). “Field verification of clay liner hydraulic conductivity.” Waste containment systems: Construction, regulation, and performance, ASCE, 226–245.
21.
Krapac, I. G., Panno, S. V., Rehfeldt, K. R., Herzog, B. L., Hensel, B. R., and Cartwright, K. (1989). “Hydraulic properties of an experimental soil liner: Preliminary results.” Proc. 12th Ann. Madison Waste Conf., Univ. of Wisconsin Extension, 395–411.
22.
Larsen, R., and Marx, M. (1986). Mathematical statistics and its applications. Prentice‐Hall, Englewood Cliffs, N.J.
23.
Lumb, P. (1966). “The variability of natural soils.” Canadian Geotech. J., 3(2), 74–97.
24.
Pearson, E. S., and Hartley, H. O., eds. Biometrika (1966). Biometrika tables for statisticians, Cambridge Univ. Press, Cambridge, England, 1, 207–208.
25.
Smirnov, N. (1948). “Table for estimating goodness‐of‐fit of empirical distributions.” The Annals of Math. Statistics, XIX(2), 279–281.
26.
Stedinger, J. (1980). “Fitting log normal distributions to hydrologic data.” Water Resour. Res., 16(3), 481–490.
27.
Thom, H. (1958). “A note on the gamma distribution.” Monthly Weather Rev., 86(4), 117–122.
28.
Vogel, R. (1986). “The probability plot correlation coefficient test for the normal, log‐normal, and gumbel distribution hypotheses.” Water Resour. Res., 22(4), 587–590.
Information & Authors
Information
Published In
Journal of Geotechnical Engineering
Volume 119 • Issue 3 • March 1993
Pages: 471 - 486
Copyright
Copyright © 1993 American Society of Civil Engineers.
History
Received: Jun 20, 1991
Published online: Mar 1, 1993
Published in print: Mar 1993
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.