TECHNICAL NOTES
Mar 1, 1986

Probability Distribution of Strength Parameters in Uniform Soils

Publication: Journal of Engineering Mechanics
Volume 112, Issue 3

Abstract

Statistical tests on the cohesional and frictional components of shear strength of soils have repeatedly identified these parameters to be more adequately modeled by the beta distribution than by any of the other common two parameter distributions. The beta distribution is theoretically derived as the natural probability law governing the variations of c and tanϕ. The development is based completely on physical understanding on the particulate nature of soils.

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References

1.
Athanasiou‐Grivas, D., and Harr, M. E., “Stochastic Propagation of Rupture Surfaces Within Slopes,” Application of Statistics and Problems in Soil and Structural Engineering, Proceedings, 2nd International Conference, Aachen, Germany, Vol. 2, 1975, pp. 33–53.
2.
Athanasiou‐Grivas, D., and Harrop‐Williams, K., “Joint distribution of the components of soil strength,” Proceedings, Application of Statistics and Problems in Soil and Structural Engineering, 3rd International Conference, Sydney, Australia, 1979, pp. 189–197.
3.
Benjamin, J. R., and Cornell, C. A., Probability, Statistics and Decision for Civil Engineers, McGraw Hill Book Co., New York, NY, 1970.
4.
Harr, M. E., “Mechanics of Particulate Media—A Probabilistic Approach,” McGraw Hill Book Co., New York, NY, 1977.
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Hooper, J. A., and Butler, F. G., “Some numerical results concerning the shear strength of London clay,” Geotechnique, Vol. 16, No. 4, 1966, pp. 282–304.
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Johnson, N., and Kotz, S., Continuous Univariate Distributions, Houghton Mifflin, New York, NY, 1970.
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Lumb, P., “Variability of natural soils,” Canadian Geotechnical Journal, Vol. 3, No. 2, May, 1966.
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Lumb, P., “Safety factors and probability distribution of soil strength,” Canadian Geotechnical Journal, Vol. 7, No. 3, Aug., 1970.
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Lumb, P., “Precision and accuracy of soil tests,” International Conference on Statistics and Problems in Civil Engineering, Hong Kong, 1972.
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McGuffey, V., et al., “Statistical geotechnical properties of Lockport clays,” Annual Meeting of the Transportation Research Board, Washington, DC, Jan., 1981.
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Parzen, E., “Stochastic Processes,” Holden‐Day, Inc., San Francisco, CA, 1962.
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Schultze, E., “Frequency distribution and correlations of soil properties,” Statistics and Probability in Civil Engineering, Hong Kong University Press, 1972.
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Singh, A., and Lee, K. L., “Variability in Soil Parameters,” 8th Annual Symposium on Engineering Geology and Soils Engineering, Idaho State Univ., Apr., 1974.
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Wilks, S. S., Mathematical Statistics, John Wiley and Sons, New York, NY, 1962.

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Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 112Issue 3March 1986
Pages: 345 - 350

History

Published online: Mar 1, 1986
Published in print: Mar 1986

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Authors

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Kingsley Harrop‐Williams, M. ASCE
Staff Member, The BDM Corp., McLean, VA 22102

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