Bayesian updating for improving the accuracy and precision of pile capacity predictions

To estimate and obtain the correct capacities of piles bored in the field, plenty of different formulas have been developed to solve this problem. Theoretical equations and empirical or semi-empirical methods have been applied to obtain the pile capacity including the static and dynamic methods. Developing and obtaining these predictions are particularly complex. Overcoming the complications of predicting pile capacity is mainly due to the correlation methods that are applied to standard penetration tests (SPT), cone penetration tests (CPT), and pressure meter tests. Although these tests reflect to some extent the natural soil conditions, they also include many limitations. However, these tests may provide good predictions if correlated with load test data on a regional basis. Because of the limitations from correlations obtained with the in situ tests, many empirical formulas have been developed based on load test results to provide quick and easy methods to estimate pile capacity. The most widely used empirical methods are proposed by Meyerhof (1976), Coyle and Castello (1981), Briaud et al. (1989), the American Petroleum Institute (RP2A, 1993), SPT97 (1995). Use of these methods has shown that they either oversimplify or improperly consider the effects of residual stresses, actual soil parameters, and the stress history. Therefore, it is necessary to develop an alternative method using the appropriate inputs to predict the pile capacity. The design of pile foundations and the estimation of static pile capacities based on measured soil properties have improved considerably over the years. Neural network paradigms are used to develop suitable computational models for calculating pile foundations, and it uses only simple geotechnical soil parameters and pile properties as the necessary inputs. In this study, the model of Artificial Neural Network used for predicting pile capacity, includes Back-Propagation Neural Networks (BPNN) and Generalized Regression Neural Networks (GRNN). Using the prior and likelihood distribution to deal with the question of updating the pile capacity. Bayesian technique is applied to updates of the predictions of axial pile capacity. The updated posterior probability values present the best estimation of pile capacity.