Hyperstatic Reaction Method for the Design of U-Shaped Tunnel Supports

This paper presents a numerical hyperstatic reaction method (HRM) for analyzing U-shaped (with inverted arch) tunnel structures. A comparison of the results obtained from two different load conditions, i.e., with and without considering the change in depth of external loads under the effect of a gravity field, is presented. The parameters that have an effect on the design of the support structures are presented. The calculation code was developed by using the finite element method (FEM) framework. This code considers the effective geometry of the support, the horizontal and vertical loads, and enables analysis of the ground mass-structure interaction in detail. The proposed numerical HRM model is validated by using a finite difference model. The numerical results obtained show that the proposed HRM model can be used to effectively design inverted U-shaped tunnel supports. Also discussed is the influence of different parameters on the support structures, which make it possible to verify their influence on the dimensioning of the support structures.