UC Berkeley

The technology of base isolating a structure using laminated rubber bearings to protect the structure and the contents of the structure from earthquake damage has been proven effective. This technology has evolved since it was first discovered in the 1980’s. More buildings have been constructed using this technology to ensure that the contents are well protected during the event of an earthquake and more importantly, the structure can continue to operate after an earthquake. This advantage is particularly important for critical structures such as hospitals and emergency centers, and sensitive structures such as nuclear power plants. The use of high damping rubber isolation system has the advantage over most of other isolation systems mainly due to the presence of moderate damping in the material that could help with displacement control without significantly exciting the higher modes response in the structure. In addition, the simplicity in the installation does not require additional installation for supplementary energy dissipating mechanisms.

High damping rubber has been known for the uniqueness in terms of the dynamic and mechanical properties. In addition, this material is rather complex mainly due to the nonlinearity in the force-displacement relationship and several other dependencies such as strain and temperature. Due to the complexity of the material, the development of the phenomenological model to represent this material often resulted with complicated model, which could potentially make the implementation in structural analyses difficult. In this study, with the aim of simplicity, a phenomenological model for high damping rubber isolator was developed while capturing as many important dynamic properties of the material as possible. The calibration of the high damping rubber isolator model was based on the laboratory test results on double shear test piece with high damping rubber material tested up to 500% shear strain. The final model in this study exhibits the characteristic of nonlinearity of the material due to varying shear strain and the change in dynamic properties such as the effective shear modulus and effective damping ratio with shear strain. The dynamic properties of the developed model were observed to closely follow the distribution of the properties observed through laboratory test results. In addition, the relationship between the energy dissipation and shear strain was found to be close to the actual material.

On the other hand, in dynamics, damping is critical for system responding near the resonance frequency. Damping is also known as a mechanism to reduce peak displacement response as observed from the displacement spectra with different damping values. However, it is often overlooked that too much damping in a system, particularly base isolation system, would excite higher mode response. This adverse effect from damping could lead to the damage of vibration sensitive equipment housed in the structure.

Study on bilinear model was included in this work. The definition and implementation of bilinear model based on the ASCE 7-16 design document were studied and outlined. Three typical design scenarios were established and the associated bilinear models were developed. The dynamic properties of these models were evaluated before dynamic analyses were carried out using the two-degree-of-freedom base isolated system. The effectiveness of each isolator model was evaluated using the roof floor response spectra. The results showed that each design scenario has resulted in highly damped isolation system and as a result, higher mode response was excited.

The work concluded with a comparison of the dynamic analyses results using three isolator models, the high damping rubber isolator model, bilinear model, and a model with linear spring model and linear viscous damper. The bilinear model was developed based on the laboratory test results of double shear test piece with high damping rubber material and in accordance to the procedure outlined in the design document. The dynamic properties of the model were calibrated at 100% shear strain, consistent with the calibration of the high damping rubber isolator model. The responses of the two-degree-of-freedom base isolated model using all isolator models subjected to ground motions with different intensities were compiled for comparison. The results showed that the bilinear model overestimated the damping at shear strain less than the design shear strain while underestimated the damping for shear strains beyond the design shear strain. The linear spring model with linear viscous damper exhibited the opposite trend as the model has constant damping ratio independent of shear strain.

With the proper amount of damping modelled in the isolator model and the stiffening effect, the high damping rubber isolator model has shown to be able to control the peak displacement of the system without significantly exciting the higher mode response of the system. Unlike the nature of the bilinear model, the presence of high amount of damping at the small shear strain range has the potential to excite the higher mode response when the system is subjected to weak ground motions.

A simple three-element high damping rubber isolator model has been developed from this study and the dynamic properties were found to closely follow the distribution of the dynamic properties of the material obtained through laboratory test. More thorough analyses would be carried out to ensure the consistency of the procedure in developing this model based on laboratory test results. One of the elements of this model was based on the mathematical model developed using unfilled rubber. Studies can be carried out to investigate the accuracy of this model when used for high damping rubber isolator model, which is a filled rubber. In addition, the arbitrary model used as one of the energy dissipation mechanisms could be improved to better capture the mechanisms for the material.