Interpretation of soil property profile from limited measurement data: a compressive sampling perspective

Variation of soil properties with depth, i.e., the soil property profile, is a key input in geotechnical design and analysis, and it is determined during geotechnical site characterization. Determination of such a soil property profile requires extensive measurement data points from site characterization. However, the number of measurement data points from geotechnical site characterization is usually sparse and limited. As such, determining the soil property profile from a limited number of measurement points remains a challenge to geotechnical engineers. In engineering practice, the soil property profile is frequently determined with the assistance of engineering experience and judgment or statistical methods when only limited measurement data are available. Because both methods inevitably involve either subjectivity or assumptions that might contradict reality, the derived profile might not reflect the real variation of soil properties with depth. This paper aims to address this problem and develop an objective and rational approach to interpret the soil property profile from limited measurement data. The proposed approach is based on a novel sampling theory, called compressive sampling (or compressive sensing, CS), in mathematics and signal processing. Using compressive sampling, a high-resolution signal (e.g., a soil property profile in this study) can be reconstructed from a limited number of measurement data points. The reconstructed soil property profile is nearly continuous and has a resolution as high as cone penetration test (CPT) data. As it contains a large number of data points, conventional statistical methods can be applied easily. In this paper, the proposed approach is illustrated and validated using a set of real CPT data (i.e., tip resistance, q(c)). The results show that the proposed approach reasonably reconstructs the complete qc profiles from a limited number of q(c) data points.