A model to assess the response of an arched roof of a lined tunnel

A model to analyze the response of an arched roof of a tunnel lining under a surface static loading is presented. It enhances a previous model by the authors, which is based on a discrete-continuous concept and is suitable for depths of burial at which ‘arching’ can develop. The current enhanced model takes into consideration the curvature of an arched roof of a lined tunnel. The proposed 2DOF system’s stiffness includes the influences of the soil side pressure as well as the arched geometry of the roof. For the case of zero curvature the analytical solution for the mid-roof deflection and average contact pressure that has been derived converges to the solution of a flat roof. The case of a relatively shallow buried structure has been calibrated and then verified against published experimental results.A case study shows that there is a certain opening angle of the roof at which the contact pressure has a maximum value. This angle coincides with the angle at which there is also a maximum value of the roof stiffness. However, it is also shown that approximately at this opening angle, the internal forces are minimal. It is therefore concluded that the average contact pressure is not necessarily the most important criterion for a design of an optimal shape of the roof. Furthermore, the angle that yields maximum contact pressure should be preferred for an optimal roof design. It is further shown that as the roof slenderness increases this optimal angle decreases.