Abstract
Probabilistic models of geotechnical phenomena, based on the concept of random fields of variation of soil properties, require knowledge of the field statistics, which must be derived from sample data. A frequently adopted assumption in these models is that the pattern of variation consists of stationary random zero-mean gaussian fluctuations, superposed on a deterministic average trend. This paper shows how to estimate the trend and the covariance function of the fluctuations from sample data of the pattern of variation. Stochastic interpolation techniques can be used as a method of verification of these estimates. The kriging approach and the approach based on conditional probability density distributions lead to identical expressions for stochastic interpolation, when gaussian fluctuations are assumed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alonso, A.A., 1976, “Risk Analysis of Slopes and its Application to Slopes in Canadian Sensitive Clays”, Geotechnique 26, no 3.
Calle, E.O.F. and W.J. Heijnen, 1982, “Considerations on Safety of Piled Raft Foundations”, Proc. ESOPT I I Amsterdam, Publ. A.A. Balkema, Rotterdam.
Calle, E.O.F., J. van Heteren and M.P. Quaak, 1987, “Experimental Verification by Field Measurements of Covariance Models for a Geotechnical Property”, Proc. Int. Conf. Appl. Stat. and Prob. in Soil and Struct. Eng., Vancouver.
Dagan, G., 1982, “Stochastic Modeling of Groundwater Flow by unconditional and conditional Probabilities”, Water Resour. Res., 18.
Delfiner, P., 1976, “Linear Estimation of Non-stationary Phenomena”, in Guarascio et al., Advanced Geostatistics in the Mining Industry, D. Reidel Publ., Dordrecht-Holland.
Feinerman, E., G. Dagan and E. Bresler, 1986, “Statistical Inference of Spatial Random Functions”, Water Resour. Res., Vol$122 no. 6., pp 935–942.
Journel, A.G. and Ch. J. Huijbregts, 1978, Mining Geostatistics, Academic Press London.
Kitanidis, P.K. and E.G. Vomvoris, 1983, “A Geostatistical Approach to the Inverse Problem in Groundwater Modeling (Steady State) and Onedimensional Simulations”, Water Resour. Res., Vol. 19, pp 677–690.
Tang, W.H., 1979, “Probabilistic Evaluation of Penetration Resistances”, ASCE Journ. of the Geot. Eng. Div., GT10.
Vanmarcke, E.H., 1977, “Probabilistic Modeling of Soil Profiles”, ASCE Journ. Of the Geot. Eng. Div., GT11. “Reliability of Earth Slopes”, same volume.
Vrouwenvelder A. and E. Calle, 1988, “Measuring Spatial Correlation of Soil Properties”, paper submitted to Structural Safety.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Calle, E.O.F., van Heteren, J. (1989). Statistical Inference of Trend and Covariance of a Random Field with Nonstationary Mean and Stationary Covariance Properties. In: Armstrong, M. (eds) Geostatistics. Quantitative Geology and Geostatistics, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-6844-9_18
Download citation
DOI: https://doi.org/10.1007/978-94-015-6844-9_18
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-015-6846-3
Online ISBN: 978-94-015-6844-9
eBook Packages: Springer Book Archive