The principal purpose of this work consists in optimizing the support system of a deep tunnel accounting for the uncertainty of the time-dependent behaviour of the surrounding rock, which is described by the rheological Burger law. The stochastic approach is chosen for this aim. On one hand the Quantile Monte Carlo (QMC) simulation is used to determine the optimal design variables (i.e., the thickness of two liners). On the other hand, the well-known Kriging metamodeling technique is undertaken to approximate the limit state function in the augmented reliability space (i.e., the tensor product between the random variable space and the design variable space). The adopted optimization process allows to derive the optimal tunnel support that verifies two failure modes, namely the support capacity criterion and the maximum tunnel convergence.
The optimization in the design process of the deep tunnel with respect to the uncertainty in input mechanical parameters is one of the most critical issues in the rock engineering field. The conservative design of the support element has been usually conducted based on the deterministic approach using the factor of safety of different parameters involved. Although the robustness thanks to its simplicity in the engineering application, such an approach does not permit us to understand the effect of the uncertainty in ground properties, particularly in the case of highly heterogeneous formations and can induce an overestimated result of the support elements.
In the last decade, many scholars attempt to account for the uncertainty in the analysis and the design process of tunnel by using rational statistical treatment. Especially, the performance of some well-known probabilistic methods such as the direct Monte Carlo Simulation (MCS), the Response Surface Method (RSM) in combination with the First or Second-Order Reliability Method (FORM/SORM) or the Kriging metamodeling technique in the optimization of tunnel supports was demonstrated in many contributions. However, this procedure, known as the Reliability-based optimization design (RBOD) was mostly limited in case of time-independent behaviour, while many experimental studies in the field revealed a significant time-dependent response of a large range of rock formations. Due to the time-dependent characteristics of the studied problem, the application of Monte Carlo Simulations (MCS) becomes time-consuming and its combination with the metamodeling technique such as the Kriging method is preferred. This latter will be chosen in this work to optimize the thickness of the tunnel support system constructed in the rheological rock which verifies at the same time two failure modes, namely the support capacity criterion and the maximum tunnel convergence.