Thermal Scaling Effects in Lead Rubber Bearing Tests: A New Approach for Temperature-Compensated Scaled Testing

Lead rubber bearings (LRBs) generate heat during deformation, causing temperature rise in the lead core that affects their restoring force characteristics. In scaled model tests of LRBs, thermal effects pose significant challenges due to the fundamental scaling conflict: heat generation is proportional to volume (length³) while heat dissipation is proportional to surface area (length²). This study investigates the thermal effects in scaled LRB tests where the lead yield stress depends on both strain rate and temperature according to the formulation developed in the author’s previous study, which is based on the Arrhenius law. Three similarity conditions are examined: strain rate matching, velocity matching, and temperature matching. However, since LRB behavior depends simultaneously on both strain rate and temperature, it is impossible to achieve perfect similarity between full-scale and scaled specimens. This fundamental constraint creates an inherent limitation in scaled testing. Thermal analysis using simplified one-dimensional heat diffusion theory reveals that strain rate matching conditions underestimate temperature rise in smaller specimens, while temperature matching conditions result in different strain rates between specimens. To address this issue, a new testing method is proposed where the excitation frequency is adjusted during testing to match the average temperature of the lead core between full-scale and scaled specimens. The proposed method enables estimation of full-scale stress by applying correction factors based on strain rate differences. While this approach requires knowledge of the LRB constitutive law, it provides a practical first-order approximation for evaluating full-scale LRB performance even when the constitutive law contains uncertainties.