DFI Journal - The Journal of the Deep Foundations Institute
Volume 20, Issue 1, August 2026
DOI: 10.37308/DFIJnl.20260315.347
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A Hierarchical Bayesian Model for Static Pile Load Testing
Article Type: Research Paper
E. Hoomaan
Abstract
Geotechnical engineers often use static pile load tests to reduce uncertainty in deep foundation design. In many load testing programs, tests are stopped at a target load without reaching failure, so the observations are right-censored and should be treated as exceedance events rather than measured capacities. This paper presents a hierarchical Bayesian framework for interpreting non-failure load tests and updating site-level capacity parameters for censored data. Pile capacity is modeled on the log scale with a site-level log-mean and variance components representing between-pile variability and residual log-capacity scatter, and the load test outcomes are incorporated directly through survival (exceedance) likelihoods. The model was implemented in Python/PyMC. The interpretation is illustrated through prior-posterior comparisons and posterior predictive exceedance probabilities at design-relevant load levels. Results show that multiple successful non-failure load tests can strongly constrain exceedance probability at the test load and can shift inferred site-level central tendency, while the margin above the test load and the variance components remain only partially identifiable from exceedance-only data. Sensitivity analyses highlight the role of variability assumptions in posterior inference and predictive performance, supporting risk-informed design decisions based on explicit exceedance probabilities.
Keywords:
right-censored observations, proof-load interpretation, bayesian updating