Seismic behavior of rocking bridges exhibiting negative stiffness

Abstract

Rocking structures with negative lateral stiffness are a promising solution for enabling the use of precast elements in the substructure of bridges constructed in seismically active regions. Such structural systems are resilient, presenting minimal or no residual displacements and damages after an earthquake; and they potentially reduce the forces transmitted to the foundation, and consequently reduce its size. Nevertheless, despite its advantages, such design concept has not found widespread implementation, mainly because of the limited number of experimental studies on their seismic performance, and because of the absence of established simplified design methods. This dissertation is an effort to bring such systems closer to practice. It provides both a simplified design method for systems with negative lateral stiffness, as well as experimental evidence of their seismic resilience. The simplified design method presented herein was developed based on the observation that, when the rocking motion is described in terms of horizontal displacements (not rotations), the response of the system depends mainly on its uplift force and not on its displacement capacity. Thus, by disregarding the displacement capacity term, a unique spectrum for systems with same uplift force, but different displacement capacity can be constructed. Two approaches were explored for estimating the displacement demand of a given system using the proposed spectrum: the equal displacement rule and the equal energy rule. Case studies comparing the results given by the proposed method and time history analyses reveal that equal energy rule is more conservative than the equal displacement rule. In all studied cases, the proposed design method returned displacement demands with a maximum of 40% deviation from the displacement demand predicted by the time history analysis, which suggests its adequacy for preliminary design calculations. A uniform risk spectrum (URS), which introduces the uncertainties of seismic actions into the previously proposed spectrum, was also presented in this dissertation. After discussing the methodology for its construction, site-specific uniform risk spectra constructed using the geomean of the peak ground acceleration (PGA) and peak ground velocity (PGV) as intensity measures are presented for six different locations in Europe. Bootstrapping analysis were employed to indirectly investigate the efficiency of each intensity measure. It was concluded that PGV is the optimal intensity measure for predicting the peak rocking response, while PGA is optimal for predicting rocking initiation. Finally, analytical approximations of the PGV-based spectra, which facilitate their implementation in practice, were also offered. In addition, an experimental campaign comprising quasi-static cyclic tests and shaking table tests on restrained rocking systems with negative lateral stiffness was performed. The specimens consisted of rocking columns simply standing on the ground and only connected to a cap-beam or slab through unbonded tendons in series with springs. At the quasi-static tests, the rocking piers were subjected to drift ratios of up to 16%, presenting almost no damage and no residual displacements, an indication of the resilience of the system. Furthermore, the system response agreed reasonably well with the response of a rigid body model. The seismic resilience of the system was also confirmed by shaking table tests. The specimen was subjected to 181 excitations, scaled to two different levels of the peak ground velocity, and the only observed damage was the abrasion of the edges of the column ends. The slab experienced torsion, which was caused by small imperfections in the system. The system collapsed during the last excitation due to premature failure of the tendons. This highlights that the tendons should be designed with a large safety factor. The dissertation concludes with the statistical validation of a 3D rigid body model against the experimental data from the shaking table tests. Despite the simplicity of the model, which disregards a number of physical mechanisms observed in the tests, the numerical empirical cumulative distribution functions (CDF) were within the 95% confidence interval of the experimental empirical CDF, giving a first indication that the numerical model can be considered a good descriptor for the tested system.