application of hyperstatic reaction method for designing of tunnel permanent lining, part i: 2d numerical modelling

the increase of bored tunnels in the entire world has raised the question how to design the tunnel structure in an efficient way. this paper proposes a numerical approach to the hyperstatic reaction method (hrm) for analysing permanent tunnel linings. the permanent tunnel lining is known as main structure of tunnel maintenance during the time. the hrm is one of the analysis methods for tunnel lining in long term. in this paper, two dimensional numerical modelling is performed by considering hyperstatic reaction concepts. loading is done after the calculation of long term loads, and ground reaction is simulated by springs. designing is done for manjil-rudabar freeway project, tunnel no. 2. the numerical analyses were performed for operational design earthquake (ode) and maximum design earthquake (mde) loading conditions. a new simplified approach is used for considering the effect of earthquake loading on the tunnel lining. then, an interaction diagram between axial force and bending moment used for investigating the capacity of tunnel lining. the thickness of tunnel lining and armature are calculated for three sections based on induced forces in tunnel lining. these forces were different in every section according to the load combinations, rock mechanics properties, lining properties, and overburden. the numerical results showed that the forces in tunnel lining for mde condition is approximately 50% more than ode condition in earthquake loading. this numerical processing presented that the hrm is a proper, fast, and practical method for designing and analysing the tunnel lining.