Fast non-parametric simulation of 2D multi-layer cone penetration test (CPT) data without pre-stratification using Markov Chain Monte Carlo simulation

Cone penetration test (CPT) is one of the most commonly used in-situ methods for characterizing spatial variability of soil properties in geotechnical site characterization. It provides almost continuous soil responses when a cone is pushed into the ground at a constant rate. With the almost continuous CPT data, many geotechnical and geological engineering problems, such as evaluation of liquefaction potential and subsurface soil stratification, may be properly addressed. Although CPT provides almost continuous soil responses along the depth direction, the number of CPT soundings along a horizontal direction is usually small for a specific site, due to time, resources, or technical constraints. In these cases, interpolation or stochastic simulations are often needed to estimate CPT data at un-sampled locations. Several methods have been developed to address this issue, such as random field approach, geo-statistical methods, among others. However, determination of the parameters needed in random field theory and geo-statistical methods often requires a relatively large number of CPT soundings along horizontal directions, which is often not available in practice. Moreover, subsurface soils often contain multiple soil layers with spatially varying and unknown layer boundaries, and therefore CPT data are often non-stationary, leading to the difficulty in dealing with non-stationary CPT data due to different soil layers. This paper proposes a new and fast method that combines Bayesian compressive sensing with Markov Chain Monte Carlo (MCMC) simulation. The proposed method is data-driven, non-parametric, and directly applicable to non-stationary CPT data without pre-stratification of subsurface soils. In addition, to improve computational efficiency of MCMC simulation, a sequential updating technique is developed using Kronecker product. Both numerical and real-life examples are used to illustrate the proposed method. The results show that the proposed method is robust and performs well.