A Methodology for the Analysis of Tunnel Intersections Using Two-dimensional Numerical Modeling

Intersections of tunnels are an integral component of most underground applications. The design and construction of tunnel intersections can be the most technically challenging element of a tunnel project. Yet, there are relatively few publications and methods regarding tunnel intersection design. Tunnel intersections are essentially a three-dimensional problem. However, 3D models require significantly longer time for solving and interpreting, greater computer resources, and higher user expertise. Hence, there is a great incentive to develop simpler and quicker analysis methods for tunnel intersections. In this paper, a methodology is developed so that a 3D tunnel intersection problem can be modelled using an equivalent 2D numerical model. For this purpose, it is proposed that the main tunnel cross section is modelled with an additional horizontal expansion component that represents the cross tunnel. Multiple 3D and 2D models were computed for the purpose of finding the expansion distances in the 2D models that yield similar deformations to the 3D models. Based on the results, regression analysis was employed to derive a formula relating the ratio of equivalent diameters of the main to cross tunnel to the proper expansion distance. This formula provides a useful and practical tool for preliminary tunnel intersection design. The current work relies on a number of assumptions, mainly that the rock mass is elastic. More work can be carried out to extend and modify the proposed method for more complex conditions.