Rocking amplification and strong‐motion duration

Summary Rocking isolation has been increasingly studied as a promising design concept to limit the earthquake damage of civil structures. Despite the difficulties and uncertainties of predicting the rocking response under individual earthquake excitations (due to negative rotational stiffness and complex impact energy loss), in a statistical sense, the seismic performance of rocking structures has been shown to be generally consistent with the experimental outcomes. To this end, this study assesses, in a probabilistic manner, the effectiveness of using rocking isolation as a retrofit strategy for single‐column concrete box‐girder highway bridges in California. Under earthquake excitation, the rocking bridge could experience multi‐class responses (eg, full contacted or uplifting foundation) and multi‐mode damage (eg, overturning, uplift impact, and column nonlinearity). A multi‐step machine learning framework is developed to estimate the damage probability associated with each damage scenario. The framework consists of the dimensionally consistent generalized linear model for regression of seismic demand, the logistic regression for classification of distinct response classes, and the stepwise regression for feature selection of significant ground motion and structural parameters. Fragility curves are derived to predict the response class probabilities of rocking uplift and overturning, and the conditional damage probabilities such as column vibrational damage and rocking uplift impact damage. The fragility estimates of rocking bridges are compared with those for as‐built bridges, indicating that rocking isolation is capable of reducing column damage potential. Additionally, there exists an optimal slenderness angle range that enables the studied bridges to experience much lower overturning tendencies and significantly reduced column damage probabilities at the same time.

\frac{f_{r} italicPGV}{g tan α}

. This study utilizes a different approach, ie, the machine learning framework with the logistic regression method, but also identifies that

ln ((), \frac{f_{italicr} PGV}{g tan α})

is the best predictor among various parameters.…”

Section: Conditional Probability Damage Models Of the Rocking Bridgesmentioning

confidence: 99%

Section: Conditional Probability Damage Models Of the Rocking Bridgesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Seismic fragilities of single‐column highway bridges with rocking column‐footing

Xie

Zhang

DesRoches

et al. 2019

“…Since then, a plethora of papers on rocking structures has been published studying these structures theoretically [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] and experimentally. Their systematic study started after the 1960 Chilean earthquake, when Housner published his seminal paper 1 on the behavior of "inverted pendulum structures."…”

Section: Introductionmentioning

confidence: 99%

Rolling and rocking of rigid uplifting structures

Bachmann

Vassiliou

Stojadinović

2019

Summary Allowing structures to uplift modifies their seismic response; uplifting works as a mechanical fuse and limits the forces transmitted to the superstructure. However, engineers are generally reluctant to construct an unanchored structure because the system could overturn due to lacking redundancy. Using a safety factor for the design of a flat rocking foundation, ie, designing it wider, goes against the main idea of this seismic modification method as the force demand for the structure increases. We propose to extend the flat base of a rocking block with curved extensions to better protect the block from overturning, yet not prevent its uplifting. After investigating the seismic response of such rocking blocks, we extend the study to investigate the seismic response of rolling and rocking frames comprising columns with curved base extensions. The equations of motion are derived, time history analyses are performed, and rocking spectra are constructed. We draw two important conclusions: (a) the response of a class of rocking oscillators with curved base extensions is equivalent to the response of a flat‐base rocking oscillators of the same slenderness, yet larger size; (b) the rotation demand on two negative stiffness rocking and rolling oscillators with the same uplifting acceleration and the same size is roughly the same as long as the rocking oscillators are not close to overturning. The above findings can serve as a basis for the rational seismic design of structures supported on rocking columns with curved bases, a system that has been used since the 1960s.

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.