Analytical solutions considering face advance and time-dependent behavior for back-analysis of convergence measurements in deep circular tunnels under isotropic initial stress state

A methodology is presented for the back-analysis of convergence measurements in deep tunnels to determine the constitutive parameters of the surrounding rock mass. Since increasing deformations and stresses with time are due to both the face advance and the time-dependent behavior of the ground, the two effects must be considered during the excavations. To that end, an analytical solution assuming an unlined circular tunnel excavated in a homogeneous isotropic ground under an initial isotropic stress field and assuming a fractional viscoelastic plastic behavior is developed. A second closed-form solution is also derived assuming an instantaneous excavation. Additionally, combining the developed analytical solution that takes into account the progressive face advance and an empirical approach, convergences are back-analyzed based on a least-squares optimization method to calibrate the constitutive parameters of the ground. The presented methodology aims to characterize the long-term behavior of tunnels and offers the advantage of being directly applicable during the excavation phase as soon as convergence measurements are available. Finally, the method is illustrated by two case studies related to the Fréjus road tunnel and the Saint-Martin-la-Porte access gallery (SMP2). • New analytical solutions for deep tunnels in viscoelastic plastic rocks are derived. • Both the face advance and the viscosity of the ground are considered simultaneously. • The time-dependent behavior is modeled using a fractional viscoelastic law. • Convergences are back-analyzed to determine the constitutive parameters of the rock. • The proposed methodology is applied to two different case studies.