A Hierarchical Bayesian Model for Static Pile Load Testing-Article

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The paper presents a hierarchical Bayesian framework for interpreting static pile load tests that stop before failure. Rather than treating the maximum test load as the pile’s capacity, the method treats each successful test as a right-censored observation: capacity is known only to exceed the applied load.<br /><br />Pile capacities are modeled as lognormal. The framework jointly estimates a site-level mean, between-pile variability, and residual capacity scatter, using partial pooling to share information across tested piles. Survival likelihoods incorporate the exceedance outcomes, and Markov chain Monte Carlo produces posterior estimates and predictions for future piles.<br /><br />The method is illustrated using eight driven piles in Queens, New York, each tested to 672 kips without reaching the defined failure condition. The results indicate a posterior mean site median capacity of about 1,012 kips and a 92% probability that a future pile would exceed 672 kips. However, the tests do not reveal how far capacities exceed the test load, so uncertainty remains substantial. In particular, the variability parameters are only partly identifiable and are sensitive to prior assumptions.<br /><br />The paper concludes that this approach can support risk-informed design by expressing test results as probabilities of exceeding relevant loads, rather than as simple pass/fail outcomes. Its current limitation is that it uses only exceedance information, not measured load–settlement behavior. Incorporating displacement data, tests to failure, or information from multiple sites could improve estimation of capacity and variability.

Keywords

hierarchical Bayesian framework

static pile load tests

right-censored observation

pile capacity

lognormal distribution

partial pooling

survival likelihood

Markov chain Monte Carlo

posterior estimates

risk-informed design