Hierarchical Bayesian Framework for Estimating Autocorrelation Length in Data-Scarce Geotechnical Site Characterization

Random-field theory plays a vital role in characterizing spatial variability in geotechnical properties and in supporting reliability-based design and analysis in geotechnical and geoenvironmental engineering. However, accurate estimation of random-field parameters - particularly the spatial autocorrelation length - remains challenging, as it typically requires extensive site-specific measurements. This study presents a hierarchical Bayesian method for estimating the autocorrelation length by integrating sparse site-specific measurements with abundant data from nearby geotechnical sites exhibiting similar geological conditions. In the proposed framework, autocorrelation lengths of multiple sites are modeled as random variables drawn from a common underlying distribution, enabling robust inference even with limited site data. Markov chain Monte Carlo simulations are employed for Bayesian updating, producing posterior distributions that comprehensively quantify uncertainty. Numerical examples demonstrate that the method substantially improves estimation accuracy and reduces uncertainty compared to conventional single-site analyses. Sensitivity analyses examine the influence of both the number of site-specific measurements and the quantity of similar site data, highlighting the method's flexibility and robustness. Real-world applications involving cone penetration test and plasticity index data confirm the practical applicability of the approach. Compared to conventional Bayesian estimation, the proposed method reduced the estimation error relative to the true value from 308% to 4% and decreased uncertainty (in terms of standard deviation) by more than 70%. This study therefore provides a rigorous yet practical tool for estimating random-field parameters in routine geotechnical site characterization, particularly valuable for preliminary design, reliability assessment, and decision-making under data-limited conditions.