Constructing a Site-Specific Multivariate Probability Distribution Using Sparse, Incomplete, and Spatially Variable (MUSIC-X) Data
Publication: Journal of Engineering Mechanics
Volume 146, Issue 7
Abstract
It is important to be able to construct a site-specific multivariate probability density function (PDF) of soil parameters based on limited and incomplete site-specific investigation data alone. This allows the unique features of each site (in the well-known geotechnical context that local correlations between soil parameters are different from site to site) to be captured to the extent permitted by inevitable statistical uncertainties. A method that handles Multivariate, Uncertain and unique, Sparse, and InComplete (MUSIC) data was proposed recently, but the site-specific data were assumed independent at different depths, and the typical spatial correlation among depths was not addressed. In other words, this MUSIC method cannot deal with densely sampled data with a sampling interval less than the scale of fluctuation or spatially correlated data. This study generalizes the existing method to handle spatially correlated data. The proposed new method (called the MUSIC-X method, where “X” denotes the spatial/time dimension) is more complete in the sense that it makes predictions based on all available information, by conditioning on different test results at roughly the same depth and at roughly the same location using parameter cross correlation as well as by conditioning on the data measured at nearby depths in roughly the same location where the vertical correlation is appreciable and potentially other locations where the horizontal spatial correlation is appreciable. This MUSIC-X method is also capable of simulating conditional random fields for all soil parameters within the depth range where observations are made. The MUSIC-X method is examined by numerical examples and a real case study in Taipei. It is shown that the 95% confidence interval for the depth profile of the target design parameter is generally smaller when both cross correlation and spatial correlation are incorporated into the estimation.
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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 first author would like to thank the gracious support from the Ministry of Science and Technology of Taiwan (106-2221-E-002-084-MY3 and 107-2221-E-002-053-MY3). The authors would like to thank the members of the TC304 Committee on Engineering Practice of Risk Assessment & Management of the International Society of Soil Mechanics and Geotechnical Engineering for developing the 304dB database (http://140.112.12.21/issmge/Database_2010.htm) used in this study and making it available for scientific inquiry.
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Published In
Journal of Engineering Mechanics
Volume 146 • Issue 7 • July 2020
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©2020 American Society of Civil Engineers.
History
Received: Nov 20, 2018
Accepted: Jan 2, 2020
Published online: Apr 23, 2020
Published in print: Jul 1, 2020
Discussion open until: Sep 23, 2020
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