Constructing a Site-Specific Multivariate Probability Distribution Using Sparse, Incomplete, and Spatially Variable (MUSIC-X) Data

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.