Geostatistical interpolation and simulation of RQD measurements

The application of geostatistics to strongly skewed data has always been problematic. The ordinary geostatistical methods cannot deal with highly skewed data very well. Multi-Indicator methods are potential candidates for the interpolation of this type of datasets, but the workload associated with them is sometimes intimidating. In this study, six geostatistical estimators, namely, ordinary kriging, simple kriging, universal kriging, trend-only kriging, lognormal kriging and indicator kriging, as well as two deterministic estimating techniques – inverse distance weighted and nearest neighbor – were applied to a highly negatively skewed RQD dataset to determine which one is more appropriate for interpolating a geotechnical model, based on their summary statistics. Universal kriging was identified to be the best method, with the trend being modeled by a quadratic drift item and the residual being estimated with simple kriging. Two simulators – sequential Gaussian and sequential indicator – were applied in this thesis for the purpose of identifying the probabilistic distribution at each location and joint-distribution for multiple locations. A transfer function was defined to transform each of the realizations to a single conceptual cost value for the sake of risk analysis, based on the relation between RQD and tunnel support specifications summarized by Merritt (1972). The distribution of the cost values corresponding to all of the realizations are quasi-normal and no estimators except KT produced a cost value that was less than two standard deviations away from the mean, once again proving the smoothing effect of all linear weighted estimators. If high values account for a dominant percentage in the sample dataset, the estimated RQD models are likely to be over-pessimistic compared with their simulated counterparts. GSLIB was used in this thesis, which in its original form does not impose a limit on the maximum number of samples coming from the same borehole when performing either estimation or simulation. It is recommended to customize the source code of GSLIB to implement this constraint to check what effect it would have on the results, if some commercial FORTRAN compiler can be made handy.Applied Science, Faculty ofMining Engineering, Keevil Institute ofGraduat