Is rocking motion predictable?

102

Summary This paper characterizes the ability of natural ground motions to induce rocking demands on rigid structures. In particular, focusing on rocking blocks of different size and slenderness subjected to a large number of historic earthquake records, the study unveils the predominant importance of the strong‐motion duration to rocking amplification (ie, peak rocking response 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 (intensity, frequency, duration, and/or energy‐based) scalar IMs 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. Lastly, the analysis shows that an IM that “efficiently” captures rocking amplification is not necessarily an “efficient” IM for predicting rocking overturning, which is dominated by the velocity characteristics (eg, peak velocity) of the ground motion.

Section: Introductionmentioning

confidence: 99%

Rocking amplification and strong‐motion duration

Giouvanidis

Dimitrakopoulos

2018

102

“…Several researchers have built on Housner's classical model, extending their analyses to rocking frames and three‐dimensional rocking structures . Although a precise prediction of the full response history of a rocking oscillator under a given ground motion may be impractical due to the strong nonlinearities involved (eg, negative stiffness) and the uncertainties associated with modelling impact phenomena, Housner's model has been shown capable of predicting the main statistics of the seismic response of rocking structures . In this regard, early studies recognized that rocking motion is highly sensitive to the velocity and acceleration characteristics of the ground motion .…”

Section: Introductionmentioning

confidence: 99%

Seismic protection of rocking structures with inerters

Thiers-Moggia

Mariotti

2018

Summary The seismic behaviour of a wide variety of structures can be characterized by the rocking response of rigid blocks. Nevertheless, suitable seismic control strategies are presently limited and consist mostly on preventing rocking motion all together, which may induce undesirable stress concentrations and lead to impractical interventions. In this paper, we investigate the potential advantages of using supplemental rotational inertia to mitigate the effects of earthquakes on rocking structures. The newly proposed strategy employs inerters, which are mechanical devices that develop resisting forces proportional to the relative acceleration between their terminals and can be combined with a clutch to ensure their rotational inertia is only employed to oppose the motion. We demonstrate that the inclusion of the inerter effectively reduces the frequency parameter of the block, resulting in lower rotation seismic demands and enhanced stability due to the well‐known size effects of the rocking behaviour. The effects of the inerter and inerter‐clutch devices on the response scaling and similarity are also studied. An examination of their overturning fragility functions reveals that inerter‐equipped structures experience reduced probabilities of overturning in comparison with uncontrolled bodies, while the addition of a clutch further improves their seismic stability. The concept advanced in this paper is particularly attractive for the protection of rocking bodies as it opens the possibility of nonlocally modifying the dynamic response of rocking structures without altering their geometry.

“…The well‐known coefficient of restitution, ratio of velocity just after impact by velocity right before it, is used to damp oscillations, and it is computed as n the conservation of angular momentum . Several experimental tests show that such analytical previsions usually underestimate energy dissipation . With specific reference to masonry and laboratory campaigns, for fired clay and tuff brickwork, the ratio of experimental to analytical coefficients of restitution was about 95%, and 2 double leaf masonry walls made of approximately dressed stone units with low quality mortar have shown corresponding mean values in the range 95% to 98% .…”

Section: Introductionmentioning

confidence: 99%

In situ free‐vibration tests on unrestrained and restrained rocking masonry walls

Giresini

Sassu

Sorrentino

2018

Summary In the out‐of‐plane assessment of rocking walls, a relevant and yet uncertain aspect is the influence of energy dissipated during motion due to impacts and restraints, such as a floor or tie rods. Therefore, in situ rocking tests on unrestrained and restrained unreinforced masonry walls, made of composite (rubble + blockwork) masonry, were performed and analyzed. The restraint is given by steel springs of assigned stiffness, simulating a floor connected to full‐scale (4 × 1 × 0.6 m3) specimens from a dismantling building. The specimens are displaced from a static equilibrium position and released, allowing to evaluate energy dissipation. The coefficient of restitution is estimated as the square root of consecutive peak velocities of the same sign, to take into account nonhomogeneities in walls. For unrestrained walls, experimental coefficients of restitution vary between 81 and 88% of analytical ones, confirming the latter as conservative. For restrained configurations, experimental coefficients of restitution are between 74% and 83% of analytical values of unrestrained walls. Hence, an additional energy damping can be ascribed to the springs. Equivalent viscous damping ratios of a nonlinear rocking system are calculated by considering a velocity logarithmic decrement, resulting between 6% and 8% (unrestrained condition) and between 8% and 10% (restrained condition). An analytical formula is proposed for estimating the coefficient of restitution for restrained walls if the dynamic properties of the unrestrained wall and the horizontal restraint are known. Finally, the relevance of a refined estimation of energy dissipation is discussed by means of numerical time history analyses.