Estimation of missing borehole data from physically-bounded multi-task Bayesian compressive sensing

The Cone Penetration Test (CPT) is one of the most important in-situ methods for geotechnical site investigation. To address issues encountered in engineering practice, such as localized data gaps and significant variations in CPT measurements due to probe malfunctions and abrupt changes in soil properties at stratigraphic interfaces, this paper proposes a physics-Bounded Multi-Task Bayesian Compressive Sensing (B-MTBCS) methodology. This approach establishes an information fusion mechanism for multiple CPT soundings within a Bayesian framework. By incorporating physical constraints—specifically, the non-negativity of CPT responses—as boundary conditions for predicted data, it allows for accurate estimation of missing CPT measurements. Validation through numerical simulations and real-world engineering case studies demonstrates the method’s effectiveness in recovering missing CPT data under complex geological conditions. Compared to the conventional Multi-Task Bayesian Compressive Sensing (MTBCS) approach, the proposed method reduces prediction errors by over 34%. These research findings provide substantial support for critical geotechnical applications, including parameter inversion, foundation bearing capacity evaluation, and liquefaction potential assessment in sandy soils.