Fast stratification of geological cross-section from CPT results with missing data using multitask and modified Bayesian compressive sensing

Since cone penetration test (CPT) is reasonably rapid, affordable, and repeatable, it has been widely used in situ for subsurface soil stratification and classification in geological and geotechnical engineering practice. When used for soil stratification across a 2D geological cross-section, however, it is often observed that some CPTs probe deeper than others, and that some CPT soundings may contain missing data due to presence of gravel-sized particles or intentional bypassing of gravelly soil layers. Arguments above and frequently encountered problem of a small number of CPT soundings in practice pose a great challenge for 2D soil stratification, especially for nonstationary CPT within multilayers. While certain methods have been proposed hoping to address these concerns, they are frequently constrained by either stationary assumption of data, autocorrelation function forms, or computational issues. This study introduces a data-driven multitask Bayesian compressive sensing (MTBCS) method to estimate missing data for CPT sounding of interest, and then develops a modified 2D BCS method for fast interpolation for horizontal locations without CPT soundings. The proposed method is demonstrated and validated using both numerical and real-world CPT data. Results show that proposed method is both efficient and robust in terms of missing data estimation in each CPT sounding and soil stratification for a 2D geological cross-section.