Analytical Solutions for the Construction of Circular Tunnel Accounting for Timedependent Characteristic of the Rheological Rock

Abstract:

The problems of lined circular tunnel construction subject to nonhydrostatic initial stresses were considered, accounting for crosssection excavation, longitudinal advancement, and any installation time of the elastic liner. In the derivation, linear viscoelastic models were adopted to simulate the rheological properties of the rock, time dependent excavation process and fictitious stresses were considered to simulate sequential excavation and tunnel advancement, respectively. According to the complex variable method and Laplace transform technique, the boundary and compatibility conditions were expressed by the two potentials, and the equations with respect to the coefficients in potentials were established afterwards. The analytical solutions for stress and displacement were then provided for the whole construction process after the determination of the coefficients by solving these equations. A good agreement between results from Finite Element Method and the analytical solutions had been obtained. Based on analytical solutions, a comprehensive parametrical analyses were then carried out to investigate the distribution discipline of displacements and stresses of the rock, as well as the influence of liner installation time on displacements and stresses of the rock. According to presented solutions, a fast predicting system for the mechanical state of the rock can be obtained and the ones provide much convenient way for preliminary design of tunnel construction.

Key words:tunnel; support; viscoelastic; sequential construction; analytical solution