Conventional (code-based) seismic design aims to provide the structure the necessary strength and ductility to withstand seismic forces. A strong earthquake, though, might be accompanied by irreversible structural deformation and therefore damage. The aftermath of recent severe earthquakes (e.g., the 2010 Canterbury, the 2011 Tohoku, as well as, the 2016 Central Italy and Kaikoura among others) highlighted the need for alternative design methodologies that can limit structural damage and guarantee post-earthquake serviceability. Rocking behavior isolates the structure from the ground to withstand strong seismic forces. Rocking allows the structure to uplift and pivot around predefined points relieving it from deformation, stresses and ultimately damage. Consequently, rocking beh...[ Read more ]

Conventional (code-based) seismic design aims to provide the structure the necessary strength and ductility to withstand seismic forces. A strong earthquake, though, might be accompanied by irreversible structural deformation and therefore damage. The aftermath of recent severe earthquakes (e.g., the 2010 Canterbury, the 2011 Tohoku, as well as, the 2016 Central Italy and Kaikoura among others) highlighted the need for alternative design methodologies that can limit structural damage and guarantee post-earthquake serviceability. Rocking behavior isolates the structure from the ground to withstand strong seismic forces. Rocking allows the structure to uplift and pivot around predefined points relieving it from deformation, stresses and ultimately damage. Consequently, rocking behavior is currently resurging.

Due to the increasing demand to predict the response of various rocking configurations, the present study sheds light to major challenges of rocking dynamics. As a first approach, it investigates, analytically and numerically, the seismic performance of a rocking frame which is either freestanding or hybrid i.e., supplemented with re-centering and energy dissipation devices exhibiting flag-shaped hysteretic behavior. This work establishes the equations of motion for the hybrid (and the freestanding) rocking frame following principles of analytical dynamics and examines its seismic behavior under both mathematical (pulse-type) and historic ground excitations. Throughout the analysis, the deformation of the structural members and sliding between the contacting bodies are ignored. The study introduces dimensionless design parameters which control the flag-shaped hysteretic loop and reveals their influence on the seismic performance of the hybrid rocking frame. The results unveil that prestressing the tendons could be beneficial mostly for small rocking rotations. For large rocking rotations, the prestressing force becomes progressively detrimental as the size of the columns increases. This study also compares hybrid rocking frames with negative, zero and/or positive post-uplift lateral stiffness. The analysis shows that increasing the stiffness of the frame does not necessarily lead to superior performance. Further, (hybrid) rocking frames with negative stiffness yield the lowest hysteretic energy demands, whereas positive stiffness frames might mitigate the response but at the expense of higher energy demands by the dissipaters; making the examined rocking frames sensitive to the characteristics of the ground motion. Consequently, the hybrid rocking frame could outperform the freestanding or the opposite.

Further, this study thoroughly investigates the contact phenomenon during rocking motion. Specifically, it revisits analytically and numerically the contact process adopting a nonsmooth dynamics approach assuming impacts behave as unilateral contacts. To validate the proposed methodology, it examines both rigid and flexible structures, specifically, the archetypal rigid rocking block and the flexible rocking oscillator. The present work treats impact and uplifting events by introducing a system of inequalities, which is known as the linear complementarity problem. Impact is considered to be instantaneous and is described by contact laws (i.e., Newton’s and/or Poisson’s). These set-valued laws capture the behavior in the normal direction of the (unilateral) contact. In the tangential direction, sliding is prevented either by designing the contact points to act as shear keys or by sufficient friction coefficient. This study demonstrates the ability of the proposed methodology to capture the impact behavior during rocking and liberates from the need for additional ad-hoc assumptions. The analysis further verifies pertinent analytical results from other methodologies for both examined structures, and proves that a given rocking oscillator might display different post-impact state i.e., bouncing, full contact, or immediate rocking, depending on its flexural deformation at the time of impact. In addition, the proposed response-history analysis of the flexible rocking oscillator is also validated with numerical and experimental results from literature.

Finally, due to the sensitivity of the rocking behavior to the characteristics of the ground motion, this work investigates the ability of (natural) earthquake records to induce rocking demands on different rigid structures. Focusing on freestanding rocking configurations of different size and slenderness subjected to a large number of historic earthquake records, this study unveils the predominant importance of the strong-motion duration to rocking amplification (i.e., rocking without overturning). It proposes original dimensionless intensity measures (IMs) which capture the total duration (or total impulse accordingly) of the time-intervals during which the ground motion is capable of triggering rocking motion. The results show that the proposed duration-based IMs outperform all other examined scalar IMs which hinge on intensity, frequency-content, duration and/or energy-input characteristics of the ground excitation in terms of both “efficiency” and “sufficiency”. Further, the pertinent probabilistic seismic demand models offer a prediction of the peak rocking demand which is adequately “universal” and of satisfactory accuracy.

Author keywords: rocking, analytical dynamics, overturning, linear complementarity problem, nonsmooth dynamics, impact, uplifting, intensity measures, strong-motion duration, probabilistic seismic demand models