Probabilistic back analysis for improved reliability of geotechnical predictions considering parameters uncertainty, model bias, and observation error

The predicted performance of a geotechnical system may deviate from the in situ observation due to the uncertainties in the input geotechnical parameters, solution model, and observation error. A precise characterization of these uncertainties is a significant challenge primarily because of limited data availability. The Bayesian theory provides a means for updating these uncertainties by incorporating prior statistical information and observations. However, conventional Bayesian inference focuses on limited sources of uncertainties. This paper presents a probabilistic back analysis method for improved reliability of subsequent predictions that considers all the uncertainties. Three distinct features of this new method include: (1) multiple observations are incorporated into the Bayesian updating, (2) the statistical information of the uncertain variables is updated in a stage-by-stage manner, and (3) the posterior distributions of uncertain variables are derived with Markov Chain Monte Carlo (MCMC) simulation that is based on the Hamiltonian Monte Carlo (HMC) algorithm. Two case histories, including a braced excavation problem and a tunnel excavation problem, are analyzed to demonstrate the effectiveness of the new method. The advantages of this new back analysis method over the conventional Bayesian updating analyses are documented.