Statistical interpretation of soil property profiles from sparse data using Bayesian compressive sampling

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, q_c). The q_c profile and the associated uncertainty are reasonably reconstructed and quantified from sparse q_c data points. Furthermore, as the number of measured q_c points increases, the statistical uncertainty in the interpreted q_c profile reduces substantially. When all q_c points are measured, the associated statistical uncertainty reduces to almost zero.