Reliability analysis of slopes from sparse measurements considering sites similarity

This paper proposes a hierarchical Bayesian method(HBM) combined with Markov Chain Monte Carlo (MCMC) to address the challenges of large statistical uncertainty in geotechnical experimental data，inaccurate probability distribution of geotechnical parameters，and unreasonable slope reliability analysis under small sample-sized conditions. The HBM comprehensively incorporates information from multiple similar geotechnical sites and integrates it with the limited measurements from the target site. This approach enables a more reasonable characterization of the probability distribution of geotechnical parameters under small sample conditions. The proposed method is validated using real datasets from several loess sites in northern Shaanxi Province，China. Based on these datasets，a reliability analysis of a loess slope is conducted to demonstrate the practical application of the HBM. The results indicate that，compared to the independent parameter model(IPM)，which does not utilize information from similar geotechnical sites，the failure probability of the loess slope is reduced from 11.6% to 4.8% when using the HBM. Additionally，extensive numerical simulations are carried out to further verify the accuracy of the HBM compared to traditional methods. The results show that，compared to IPM，the HBM improves the accuracy of geotechnical statistics by 33% to 53% and reduces uncertainty by approximately 19% to 53%.