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.
In geotechnical engineering, the number of measurement data obtained from in situ or laboratory tests is usually sparse, especially for projects of small or medium size. Interpretation from such sparse measurement data is challenging and may result in significant statistical uncertainty, which refers to inaccuracy of the statistical inference results caused by a limited number of data used in the statistical inferences. Consider, for example, a soil property profile (i.e. variation of a soil property with depths), which is usually interpreted from sparse measurement data and unavoidably contains significant uncertainty. Geotechnical design and analysis results are greatly affected by the interpreted soil property profile and its uncertainty. Quantification of the uncertainty contained in the interpreted soil property profile is therefore essential, especially for probability-based design and analysis. This paper aims to address this problem using a Bayesian compressive sampling (BCS) method. The proposed approach is able not only to provide a rational and objective interpretation of the soil property profile from a relatively limited number of measurement data, but also to quantify the associated statistical uncertainty simultaneously. The quantified uncertainty provides an objective and explicit measure on the accuracy and reliability of the interpreted soil property profile. An important novelty of the proposed approach is that it depicts the quantitative evolution of statistical uncertainty in the interpreted profile as the number of measurement data increases. The proposed approach is illustrated using two sets of real cone penetration test data (i.e. tip resistance, qc). The qc profile and the associated uncertainty are reasonably reconstructed and quantified from sparse qc data points. Furthermore, as the number of measured qc points increases, the statistical uncertainty in the interpreted qc profile reduces substantially. When all qc points are measured, the associated statistical uncertainty reduces to almost zero.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.