A scaling method for temperature distribution in tunnel linings under fire based on equivalent thermal boundary conditions

Tunnel fires generate extreme temperatures that threaten the structural safety of lining, and laboratory tests based on scaled models are crucial for revealing their thermal response. However, the high thermal inertia of concrete creates a scaling conflict between internal conduction and surface heat transfer, making conventional methods unable to reproduce the prototype's true temperature gradients. To address this, a fire-curve scaling method for concrete structures is proposed. Based on the criteria of “similarity of cumulative heat input” and “similarity of surface temperature,” the method constructs scaled-model fire curves by jointly adjusting the duration and temperature amplitude, and adopts a simplified heat conduction strategy during the cooling phase. Considering the temperature-dependent nonlinear thermal properties of concrete, the standard HC and RABT curves are selected as representative scenarios to perform scaling calculations. Typical scaling schemes are presented, and scaling errors are quantitatively assessed. Numerical calculations and comparative validation show that, within the furnace heating capacity, the proposed method can limit the temperature errors at the heated surface and in the region close to the surface to within 10% during the heating and temperature holding stages of the scaled model. Once the scaled fire curve reaches the furnace temperature limit, the heat input during model heating becomes insufficient, and temperature similarity gradually decreases as the scale ratio decreases. For the RABT fire curve containing a cooling stage, the simplified treatment of cooling alters the heat dissipation process near the heated surface, resulting in an evolution of temperature error during cooling that differs from that during heating. More specifically, under some conditions with insufficient heat input, this effect can reduce the difference between the final temperature distributions of the model and prototype, thereby improving the similarity of the final thermal response. This study provides a practical methodology to achieve thermal similarity in scaled concrete structures, establishing a foundation for the design of thermo-mechanical coupled tunnel fire tests.