Scale of Fluctuation for Spatially Varying Soils: Estimation Methods and Values
This article has been corrected.
VIEW CORRECTIONPublication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 6, Issue 4
Abstract
Spatial variability is one of the major sources of uncertainty in geotechnical applications. This variability is characterized customarily by the scale of fluctuation. Scale of fluctuation describes the distance over which the parameters of a soil or rock are similar or correlated. The scale of fluctuation is required in order to best characterize and to simulate a spatially variable field. This paper first provides an overview of the various methods available for estimating the scale of fluctuation from cone penetration test (CPT) data, along with two examples for comparing the methods. The first part reveals some issues with two popular estimation methods, namely the method of moments and the maximum-likelihood method (MLE). The method of moments is less sensitive to the choice of the autocorrelation function (ACF), but it could be less precise and may be based on a correlation estimator that does not produce a positive definite autocorrelation matrix. MLE can be very sensitive to the choice of the classical one-parameter ACF. It is not uncommon to assume such an ACF, rather than to identify the ACF from actual soil data with a more general two-parameter Whittle–Matérn (WM) model. This practice may not be robust. Nonetheless, a literature survey is useful if these caveats are kept in mind. The second part of this paper provides a database table of horizontal and vertical scale of fluctuation values in different locations and for different materials, collected from published case studies, which can be used as a reference when field data are not readily available. The probable range of values as a function of soil type is provided to inform sensitivity analysis and to guide the selection of a prior distribution for Bayesian analysis.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The authors thank Professor Bilal Ayyub for his encouragement to prepare this review paper for the ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering. The authors also are grateful to Richard J. Bathurst, Nezam Bozorgzadeh, Zijun Cao, Reza Jamshidi Chenari, Jinsong Huang, Shadi Najjar, Qiujing Pan, and Yutao Pan for their invaluable comments and generous assistance in the preparation of this paper. In addition, Dr. Zijun Cao assisted in clarifying the limitations of the method in Fig. 1 and corrected errors in Table 2. Dr. Zijun Cao and Yuxin Lu independently verified the results in Tables 5 and 6. Dr. Yutao Pan provided additional data on cement-mixed soils (Table 9). We thank them for their substantial efforts to improve this paper. The third author extends his appreciation to the Institute for Risk and Reliability, Leibniz University, and the funding from the Alexander von Humboldt Foundation for providing the support to complete this paper. The authors Brigid Cami and Sina Javankhoshdel would like to extend their appreciation to Rocscience for their encouragement in the preparation of this paper.
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ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 6 • Issue 4 • December 2020
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© 2020 American Society of Civil Engineers.
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Published online: Jul 31, 2020
Published in print: Dec 1, 2020
Discussion open until: Dec 31, 2020
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