Homogenization framework for three-dimensional elastoplastic finite element analysis of a grouted pipe-roofing reinforcement method for tunnelling

摘要

This paper deals with the grouted pipe-roofing reinforcement method that is used in the construction of tunnels through weak grounds. This system consists on installing, prior to the excavation of a length of tunnel, an array of pipes forming a kind of 'umbrella' above the area to be excavated. In some cases, these pipes are later used to inject grout to strengthen the ground and 'connect' the pipes. This system has proven to be very efficient in reducing tunnel convergence and water inflow when tunnelling through weak grounds. However, due to the geometrical and mechanical complexity of the problem, existing finite element frameworks are inappropriate to simulate tunnelling using this method. In this paper, a mathematical framework based on a homogenization technique to simulate 'grouted pipe-roofing reinforced ground' and its implementation into a 3-D finite element programme that can consider stage construction situations are presented. The constitutive model developed allows considering the main design parameters of the problem and only requires geometrical and mechanical properties of the constituents. Additionally, the use of a homogenization approach implies that the generation of the finite element mesh can be easily produced and that re-meshing is not required as basic geometrical parameters such as the orientation of the pipes are changed. The model developed is used to simulate tunnelling with the grouted pipe-roofing reinforcement method. From the analyses, the effects of the main design parameters on the elastic and the elastoplastic analyses are considered.