Model Development and Validation for a Seismic Isolation System for Lightweight Structures

A low-cost seismic isolation system for lightweight structures, consisting of concrete concave plates and elastomeric deformable rolling balls, has been recently tested on a shake table using test models with realistic mass distribution and high-intensity tri-axial ground motions. The tests demonstrated that the system is very effective in the horizontal direction, whereas it does not isolate vertically, and it may magnify the vertical ground motion. The tests showed that these isolators exhibit a complex behavior with fluctuating shear stiffness and strength due to changes in the rolling ball's shape caused by the gravity load and the additional dynamic axial load due to the overturning moment and vertical ground motion. A model of the behavior of the isolator is presented in this paper. The model uses a combination of mechanics-based and phenomenological elements and requires calibration based on individual isolator testing. In the vertical direction, the model employs a phenomenological Kelvin–Voigt element with velocity-dependent damping and displacement-dependent stiffness. A biaxial hysteretic element with displacement-dependent elastic force derived from a mechanical analog of the rolling oval-shaped ball is used in the horizontal direction. The mechanical analog uses an initially assumed shape of the rolling ball to obtain the force when the ball rocks and rolls. The model emulates reasonably well the behavior observed during testing, including the fluctuating stiffness and strength, stiffening at large displacements, uplift, and horizontal and vertical impact. Comparisons of analytical and experimental results show that the analytical model predicts horizontal isolator displacements and structural accelerations with acceptable accuracy.