Estimation for Stochastic Soil Models
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 125, Issue 6
Abstract
Although considerable theory exists for the probabilistic treatment of soils, the ability to identify the nature of spatial stochastic soil variation is almost nonexistent. We all know that we could excavate an entire site and there would be no doubt about the soil properties. However, there would no longer be anything to rest our structure on, and so we must live with uncertainty and attempt to quantify it rationally. Twenty years ago the mean and variance was sufficient. Clients are now demanding full reliability studies, requiring more sophisticated models, so that engineers are becoming interested in rational soil correlation structures. Knowing that soil properties are spatially correlated, what is a reasonable correlation model? Are soils best represented using fractal models or finite-scale models? What is the difference? How can this question be answered? Once a model has been decided upon, how can its parameters be estimated? These are questions that this paper addresses by looking at a number of tools that aid in selecting appropriate stochastic models. These tools include the sample covariance, spectral density, variance function, variogram, and wavelet variance functions. Common models, corresponding to finite scale and fractal models, are investigated, and estimation techniques are discussed.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Anderson, T. W. ( 1971). “The statistical analysis of time series.” Probability and mathematical statistics, Wiley, New York.
2.
Beran, J. ( 1994). “Statistics for long-memory processes.” Monographs on statistics and applied probability, Chapman & Hall, New York.
3.
Brockwell, P. J., and Davis, R. A. ( 1987). Time series: Theory and methods. Springer, New York.
4.
Cressie, N. A. C. ( 1993). Statistics for spatial data, 2nd Ed., Wiley, New York.
5.
Dahlhaus, R. ( 1989). “Efficient parameter estimation for self-similar processes.” Ann. Statist., 17, 1749–1766.
6.
DeGroot D. J., and Baecher, G. B. (1993). “Estimating autocovariance of in-situ soil properties.”J. Geotech. Engrg., ASCE, 119(1), 147–166.
7.
Fenton, G. A. (1994). “Error evaluation of three random field generators,”J. Engrg. Mech., ASCE, 120(12), 2478–2497.
8.
Fenton, G. A. (1999). “Random field modeling of CPT data.”J. Geotech. and Geoenvir. Engrg., ASCE, 125(6), 486–498.
9.
Fenton, G. A., and VanMarcke, E. H. (1990). “Simulation of random fields via local average subdivision,”J. Engrg. Mech., ASCE, 116(8), 1733–1749.
10.
Journel, A. G., and Huijbregts, Ch. J. ( 1978). Mining geostatistics . Academic, New York.
11.
Marple, S. L., Jr. ( 1987). Digital spectral analysis. Prentice-Hall, Englewood Cliffs, N.J.
12.
Mandelbrot, B. B., and Ness, J. W. ( 1968). “Fractional Brownian motions, fractional noises and applications.” SIAM Rev., 10(4), 422–437.
13.
Matheron, G. ( 1962). “Traite de Geostatistique Appliquee, Tome I,” Memoires du Bureau de Recherches Geologiques et Minieres, 14, Editions Technip, Paris (in French).
14.
Priestley, M. B. ( 1981). Spectral analysis and time series. Vol. 1, Univariate Series, Academic, New York.
15.
Strang, G., and Nguyen, T. ( 1996). Wavelets and filter banks. Wellesley-Cambridge, New York.
16.
VanMarcke, E. H. ( 1984). Random fields: Analysis and synthesis, MIT Press, Cambridge, Mass.
17.
Wornell, G. W. ( 1996). Signal processing with fractals: A wavelet based approach. Prentice-Hall, Englewood Cliffs, N.J.
18.
Yajima, Y. ( 1989). “A central limit theorem of Fourier transforms of strongly dependent stationary processes.” J. Time Ser. Anal., 10, 375–383.
Information & Authors
Information
Published In
History
Received: May 27, 1998
Published online: Jun 1, 1999
Published in print: Jun 1999
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.