Uncertainties in LU decomposition-based random field modelling of soil spatial variability

This paper presents a comprehensive statistical analysis to evaluate the uncertainties inherited in the lower–upper matrix (LU) decomposition-based random field theory, which is commonly used in geotechnical engineering to model the random spatial variability of soil properties. To facilitate this study, several realisations of Monte Carlo simulation coupled with LU decomposition-based random field theory are made for varying values of input statistical parameters. Thereafter, the statistical parameters are estimated for each simulated random field using the method of maximum likelihood. The results obtained in this study indicate that the LU decomposition-based random field theory does not yield the random field as it is anticipated to be for given input parameters. Ideally, the statistical parameters estimated from the simulated random fields should be nearly equal to the values of input parameters; however, there is significant randomness in the statistical parameters of the simulated random fields. Furthermore, this paper also presents the analysis to evaluate the factors affecting the uncertainties in the random fields simulated by LU decomposition-based theory by varying the input statistical and geometrical parameters.