Bayesian Inference of Grouted Anchors for Reliability Analyses

Bayesian analysis is a powerful tool to quantify uncertainty. Based on a prior estimate of a parameter distribution, and a likelihood function which ties together the simulated model response with the data, one estimates the posterior distribution. Therefore, this approach enables the calculation of the data distribution itself given prior knowledge and limited data. In geotechnical engineering, this asset is of special interest, since data in most applications is scarce.
There is limited knowledge about the bearing behavior of grouted anchors at design stage, which entails that in practice many anchor tests are conducted to ensure and verify that an anchor can provide its anticipated resistance. The design of an anchored structure is usually not altered unless several anchors fail the testing, thus apart from verification the testing data yields limited additional value.
This research introduces and compares different statistical models which allow failure probability estimation of individual grouted anchors and anchor groups. An analytical anchor-head displacement model is utilized to assess the anchor test data with a multivariate normal distribution as a likelihood function with weakly informative prior distributions. The soil parameters are treated as random variables. The statistical models are purely data-driven, meaning that no prior knowledge of the soil parameters is utilized, apart from upper limits. The individual statistical model allows the analysis of a single anchor for a specific load step by directly calculating posterior distributions for the uncertain soil parameters. Anchor groups are assessed using a hierarchical model formulation, where the distribution of uncertain parameters and the corresponding hyperparameters are treated as unknowns. These analyses allow inferences about probability of failure and expected resistance distributions.
The statistical models deliver failure probabilities, that are in line with the data distribution itself, and thereby provide a method for the reliability assessment of grouted anchors. A major influential factor in the reliability assessment is the modelling choice of the likelihood function's covariance. Furthermore, the quality of measurements taken is governing the quality of the inferred anchor's resistance estimation.

Keywords: Bayesian, Anchor, Reliability, Hierarchical, Probabilistic.