Search

This work aims at proposing the methodology on the basis of the extension of the famous reliability analysis, joining the Kriging and Monte Carlo Simulation (AK-MCS) metamodeling technique for analyzing the long-term stability of deep tunnel support constituted by two layers (a concrete liner covered with a compressible layer). A novel active learning function for selecting new training points enriches the Design of Experiment (DoE) of the built surrogate. This novel learning function, combined with an appropriate stopping criterion, improves the original AK-MCS method and significantly reduces the number of calls to the performance function. The efficiency of this modified AK-MCS method is demonstrated through two examples (a well-known academic problem and the case of a deep tunnel dug in the rock working viscoelastic Burgers model). In these examples, we illustrate the accuracy and performance of our method by comparing it with direct MCS and well-known Kriging metamodels (i.e., the classical AK-MCS and EGRA methods).

The sustainability of geotechnical infrastructures is closely linked with their long-time behavior. In fact, there is not a straightforward procedure to predict this behavior, and very often, the back analyses of observed data are the best tool to understand their long-time response. In-situ observations of drifts constructed in the Callovo-Oxfordian (COx) claystone, the potential host formation for geological radioactive waste disposal, in France exhibit a progressive convergence. These convergence measurements with quite significant dispersions reveal a considerable uncertainty of time-dependent behavior of this argillaceous rock that can strongly affect the transmit loading to liners, hence the long term stability of the drift. Consequently, the uncertain quantification of the creep behavior of COx claystone presents an important task before analyzing the safety of the waste disposal system. In this work, this challenge was conducted by using the well-known Bayesian inference technique. For this aim, on the one hand, the effectiveness of the classical and hierarchical Bayesian techniques to quantify the epistemic and aleatoric uncertainties of the time-dependent behavior of the host rock were investigated using synthetic data. On the other hand, we dealt with the uncertain quantification of the Lemaitre parameters that characterize the visco-plastic behavior of COx claystone thanks to the real data of in-situ convergence measurements of drifts.

Callovo-Oxfordian (COx) claystone has been considered as a potential host rock for geological radioactive waste disposal in France (Cigéo project). During the exploitation phase (100 years), the stability of drifts (e.g. galleries/alveoli) within the disposal is assured by the liner, which includes two layers: concrete arch segment and compressible material. The latter exhibits a significant deformation capacity (about 50%) under low stress (

Time-dependent rock behavior can significantly affect the design and the construction method of tunnel support lining. As an innovation, a concrete liner covered with a compressible layer is thus of great interest to reduce the underground space project costs. Indeed, the compressible material usually exhibits very high deformability under oedometric loading (30–60% volumetric deformation under a weak variation in axial stress). This helps to absorb the convergence of the excavated wall of the squeezing rock, and thus limit the transmission of stress to the inner concrete lining. This study firstly aims at deriving a closed-form solution for a deep-circular tunnel excavated within the viscoelastic Burger rock and supported by a double-layer concrete/compressible material. The inner concrete layer is assumed to be linear elastic, while the outer compressible layer is described by a tri-linear elastic model. The analytical solution is derived under the integral equation form. Secondly, the effects of uncertainty of time-dependent mechanical properties of host rock on the failure probability of tunnel for a period of 100 years are studied by introducing the closed-form solution into the well-known Kriging-based reliability analysis AK-MCS (Active learning reliability method combining Kriging and Monte Carlo Simulation) method. Notably, the benefit of the compressible layer is highlighted from the reliability analysis.

The determination of the optimal liner thickness is an important task in the design of tunnels. To take into account the heterogeneous characteristic in nature of the surrounding rock mass, the deterministic approach by using the factor of safety of different parameters involved in the design process has been largely chosen. However, this approach can overestimate or underestimate the support thickness, particularly in the case of highly heterogeneous rocks. As an improvement, the application of the probabilistic methods in the design process to optimize the liner thickness, known as the Reliability-Based Design Optimization (RBDO) has been intensively conducted in the last decade. In this context, the present contribution aims at optimizing the liner thickness of the deep tunnel excavated in a viscoelastic medium (Burgers rock) by performing the probabilistic method (Subset Simulation (SS)). This developed RBDO process allows considering the elapsed installation time of liner with respect to the excavation of the tunnel while the optimal liner thickness is determined from two failure modes, namely the support capacity criterion and the maximum tunnel convergence.

International audience; The behavior of deep tunnel is usually time dependent due to the sequential construction process as well as the rheological characteristic of the rock mass. Moreover, the uncertainty of different parameters such as the viscoelastic properties can play an essential role on the stability of tunnel and its supports. The reliability analysis based on the probabilistic approach, which has been largely applied in the last 2 decades to treat this kind of problems, presents an efficient tool but its application is usually limited in case of time-independent behavior of tunnel supported by a single liner. This study aims at assessment of time-dependent reliability of deep circular tunnel counting for rheological characteristic of rock mass and sequential construction of liners. Since the reliability analysis, using direct Monte Carlo Simulation and a FEM software could be very time-consuming, we establish firstly a closed form solution for the response of a deep tunnel excavated in the viscoelastic Burger rock accounting for the sequential installation of two liners. The validation of this analytical solution is performed by comparing the results of this solution with some previous existing analytical solutions as well as with numerical results obtained from the finite element simulation in some case studies. Once validated, this analytical solution is used as a fast tool for the time-dependent reliability analysis by direct Monte Carlo Simulation. The influence of different parameters on the probability of failure of a double liners tunnel in respect with its life service, by taking into account of the sequential construction, was discussed in the last part of the paper.

International audience