Probabilistic Back Analysis Based on Adam, Bayesian and Multi-output Gaussian Process for Deep Soft-Rock Tunnel

The uncertainty of surrounding rock mechanical parameters has much great influence on design, construction and stability evaluation for tunnel engineering. However, the traditional deterministic back analysis cannot consider the uncertainty of surrounding rock parameters. In the paper, we proposed a novel probabilistic back analysis method integrating adaptive momentum (Adam) stochastic optimization algorithm, Bayesian method and multi-output Gaussian process (MOGP)—Adam–Bayesian-based MOGP (ABMOGP), and implemented it in Python. The proposed method adopts MOGP to build the nonlinear mapping relationships between displacements and mechanical parameters of surrounding rock, and utilizes Adam algorithm to optimize the hyperparameters of MOGP model, and employs Bayesian method to deal with the uncertainty of mechanical parameters of surrounding rock. The proposed method was applied to a deep-buried soft-rock highway tunnel. At the tunnel, the uncertainty of elastic modulus, Poisson’s ratio, internal friction angle and cohesion of surrounding rock was modeled as random variables. Based on the mechanical parameters of surrounding rock identified by the proposed method, the calculated value of displacement agreed closely with the field measured value of displacement. The results show that the ABMOGP can present the uncertainty of surrounding rock mechanical parameters reasonably, and has great advantages over neural networks and support vector regression method. The proposed method provides an important novel approach for the probabilistic back analysis to determine surrounding rock mechanical parameters.