Scaling laws for shaking table testing of reinforced concrete tunnels accounting for post-cracking lining response

This paper proposes a new set of scaling laws for the study of the post-cracking behaviour of lightly reinforced concrete tunnel linings during 1g shaking table testing. The post-cracking behaviour scaling laws are formulated using two non-dimensional parameters: the brittleness number s, which governs the fracturing phenomenon for unreinforced concrete elements and N-p, which plays a primary role for the stability of the process of concrete fracture and steel plastic flow in reinforced concrete elements. The proposed laws allow for the development of an "adequate" experimental model and are validated using numerical analyses of a reinforced tunnel in rock, in both prototype and 1:30 model scale. The adopted experimental set-up is inspired by an existing 1g physical testing campaign on the seismic response of a concrete tunnel in rock and the postulated laws are shown to grant satisfactory similitude between the cracking behaviour of the model and prototype tunnel under two examined earthquake records. The potential of using the proposed laws in 1g tests for Class A predictions of evolving crack patterns in reinforced concrete tunnels is highlighted. The proposed laws are examined under three possible boundary conditions, indicating that both rigid and laminar boxes can still change the behaviour significantly compared to an envisaged free field boundary model. The analysis shows though that for larger soil to lining stiffness ratios, boundary artefacts could be greatly reduced. The present study provides useful recommendations for future 1g tests that did not exist to date, while the proposed scaling laws allow for versatility in the design of novel tunnel lining model test materials.