Numerical Modelling of the Time-Dependent Behaviour of Tunnels in Squeezing Ground

Abstract

During tunnel excavation in high stressed and weak rock masses, excessive deformation is often encountered characterized by squeezing. The squeezing phenomenon is referred to as the large timedependent convergence which occurs during excavation and continues over time, essentially associated with the creep mechanism. This time-dependent behavior is usually not identified at the feasibility stage of tunnel development. Consequently, leads to high cost in rock reinforcement and support installation as well as time-consuming and unsafe rehabilitation to keep tunnels in operation. Prediction of the timedependent deformation associated with squeezing at an early stage is of great significance for stable tunnel excavation and design. The depiction of this tunnel response requires analytical and numerical techniques, in numerical techniques, it is made possible by employing constitutive models. However, literature outlines the limitations of these conventional constitutive models in estimating time-dependent deformation in squeezing ground. Hence, this study makes three major contributions to the understanding of the 3-phase creep mechanism and presentation of efficient tools for its description. The first major contribution is the derivation and presentation of the closed-form analytical solutions which can estimate the confining stress-dependent and time-dependent response of tunnels excavated in squeezing ground. These solutions address the deficiencies encountered when employing the conventional analytical solution in the realistic estimation of the ground reaction attributed to squeezing. The second major contribution is the presentation of a fractional-order derivative viscoelastic viscoplastic (FDVP) constitutive model capable of estimating delayed deformations characterized by squeezing. Its equations are derived as an extension to the Burgers model and adjusted Perzyna overstress function with an associated viscoplastic flow rule. It addresses the deficiencies experienced by the conventional integer-order derivative constitutive models in describing the power-law mechanism of materials. The model is calibrated using experimental data obtained from literature and verified by monitored tunnel convergence data. Thereafter, implemented in a finite volume numerical code to simulate the timedependent tunnel response. The third major contribution is the presentation of an elasto-viscoplastic with isotropic damage (EVPD) constitutive model that explicitly describes the 3-phase creep mechanism. This model is an enhancement of the FDVP constitutive equations considering the isotropic damage effect characterized by the accelerated creep phase. Its derived constitutive equations are based on fractal-order derivatives obtained by applying scaling transformations on integer-order derivatives. These derived constitutive equations are also calibrated using literature attained experimental data and numerically implemented in a finite volume code to simulate the time-dependent response of a tunnel excavated in squeezing ground. In this study, these major contributions are presented and elaborated; includes the limitation that they address, their derivation, and applicability in the estimation of time-dependent tunnel deformations.