Direct simulation of random field samples from sparsely measured geotechnical data with consideration of uncertainty in interpretation

Random field theory has been increasingly used in probabilistic geotechnical analyses over the past few decades, where a random field generator with random field parameters is needed to simulate random field samples (RFSs) of interest. Estimation of random field parameters, particularly correlation functions or correlation length, generally requires extensive measurements. However, the data gathered from site characterizations are usually sparse, particularly for small or medium sized projects. Therefore, it is difficult to provide an accurate estimation on random field parameters, and the random field parameters estimated and subsequently used in RFS generation might contain significant uncertainty. This leads to a challenge of properly simulating RFSs in consideration of such uncertainty. This paper aims to address this challenge by developing a novel random field generator, which is capable of directly generating RFSs from sparse measurements obtained during site characterization and properly accounting for uncertainty associated with interpretation of sparse data. The proposed generator is based on Bayesian compressive sampling (BCS) and Karhunen–Loève (KL) expansion, and it is denoted as BCS–KL generator. The proposed BCS–KL generator is illustrated and validated through both simulated data and 30 sets of cone penetration test data measured throughout the world.