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Probability Distribution for Mobilized Shear Strengths of Saturated Undrained Clays Modeled by 2-D Stationary Gaussian Random Field - A 1-D Stochastic Process View

Published online by Cambridge University Press:  13 March 2014

J. Ching  and
C.-J. Lin
J. Ching*
Affiliation:
Department of Civil Engineering, National Taiwan UniversityTaipei, Taiwan 10617, R.O.C.
C.-J. Lin
Affiliation:
Department of Civil Engineering, National Taiwan UniversityTaipei, Taiwan 10617, R.O.C.
*
jyching@gmail.com
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Abstract

This paper shows that the mobilized shear strength of a two-dimensional (2-D) spatially variable saturated undrained clay is closely related to the extreme value of a one-dimensional (1-D) continuous stationary stochastic process. This 1-D stochastic process is the integration of the 2-D spatially variable shear strength along potential slip curves. Based on this finding, a probability distribution model for the mobilized shear strength of the 2-D clay is developed based on a probability distribution model for the extreme value of the 1-D stochastic process. The latter (the model for the 1-D extreme value) has analytical expressions. With the proposed probability distribution model, the mobilized shear strength of a 2-D clay can be simulated without the costly random field finite element analyses.

Keywords

Random fieldSoil spatial variabilityClay shear strengthProbability distributionContinuous stochastic process
Type
Research Article
Information
Journal of Mechanics , Volume 30 , Issue 3 , June 2014 , pp. 229 - 239
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2014 

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References

REFERENCES

1.Ching, J. and Phoon, K. K., “Mobilized Shear Strength of Spatially Variable Soils Under Simple Stress States,” Structural Safety, 41, pp. 20–28 (2013).Google Scholar
2.Ching, J., Phoon, K. K. and Kao, P. H., “Mean and Variance of the Mobilized Shear Strengths for Spatially Variable Soils under Uniform Stress States,” Journal of Engineering Mechanics, ASCE (2013).Google Scholar
3.Fenton, G. A. and Griffiths, D. V., “Bearing Capacity Prediction of Spatially Random c-φ Soils,” Canadian Geotechnical Journal, 40, pp. 54–65 (2003).CrossRefGoogle Scholar
4.Breysse, D., Niandou, H., Elachachi, S. and Houy, L., “A Generic Approach to Soil-Structure Interaction Considering the Effects of Soil Heterogeneity,” Geotechnique, 55, pp. 143–150 (2005).CrossRefGoogle Scholar
5.Soubra, A. H., Youssef Abdel Massih, D. S. and Kalfa, M.Bearing Capacity of Foundations Resting on a Spatially Random Soil. Geocongress 2008: Geosustainability and Geohazard Mitigation, Geotechnical Special Publication, ASCE, 178, pp. 66–73 (2008).Google Scholar
6.Vanmarcke, E. H., “Probabilistic Modeling of Soil Profiles,” Journal of Geotechnical Engineering Division, ASCE, 103, pp. 1227–1246 (1977).Google Scholar
7.Phoon, K. K., Quek, S. T. and An, P., “Identification of Statistically Homogeneous Soil Layers Using Modified Bartlett Statistics,” Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 129, pp. 649–659 (2003).CrossRefGoogle Scholar
8.Ditlevsen, O., “Extremes of Realizations of Continuous Time Stationary Stochastic Processes on Closed Intervals,” Journal of Mathematical Analysis and Applications, 14, pp. 463–474 (1966).Google Scholar
9.Ching, J. and Phoon, K. K., “Effect of Element Sizes in Random Field Finite Element Simulations of Soil Shear Strength,” Computers and Structures, 126, pp. 120–134 (2013).CrossRefGoogle Scholar
10.Jha, S. K. and Ching, J., “Simulating Spatial Averages of Stationary Random Field Using Fourier Series Method,” Journal of Engineering Mechanics, ASCE, 139, pp. 594–605 (2013).Google Scholar
11.Mollon, G., Phoon, K. K., Dias, D. and Soubra, A.-H., “Validation of a New 2D Mechanism for the Stability Analysis of a Pressurized Tunnel Face in Spatially Varying Sand,” Journal of Engineering Mechanics, ASCE, 137, pp. 8–21 (2011).Google Scholar