Seismic Displacement Demands on Skewed Bridge Decks Supported on Elastomeric Bearings

The unseating of decks is one of the most prevalent failure modes of bridges after earthquake events, as observed in the 2010 Chile Earthquake. Damaged bridges in Chile often had skew angles and were supported on elastomeric bearings. Similar bridge construction practices with decks supported on elastomeric bearings are also common in the central and eastern U.S. (CEUS). The seismic displacement demands on skewed bridges are more complicated than those on bridges without skew angles due to the coupling of translational modes with the rotational mode of vibration. The study presented in this article seeks to understand the seismic response of skewed bridge decks supported on elastomeric bearings. The scope of the study is limited to one- and two-span bridges, which constitute a large portion of bridge inventory in the CEUS. The vibration modes of skewed bridge decks are derived in closed form and the modes are compared when the gaps between the bridge deck and the abutment are open and when one of the gaps is closed due to seismic excitation. Nonlinear response history analyses are carried out to understand the effects of vertical ground motion, skew angles, aspect ratios, and different ground motion types on the seismic displacement demand in these cases. Amplification factors that approximate the increase in the displacement demand due to the skew angle are proposed.     

Modification of Ductility Reduction Factor for Strength Eccentric Structures Subjected to Pulse-Like Ground Motions

This article investigates the ductility reduction factors for RC eccentric frame structures subjected to pulse-like ground motions. The structural models are with the strength eccentricities which are much disadvantageous than the stiffness eccentricities during the inelastic response range. A method to determine the ductility reduction factors of the strength eccentric structures is suggested by modifying those of reference symmetric structures through an eccentricity modification factor. The four factors of strength eccentricity ratio, ductility ratio, story number and velocity pulse of ground motions, are investigated to gain insight into this modification factor. It shows that the ductility reduction factors of the eccentric structures are clearly smaller than those of the symmetric structures. The eccentricity modification factor is mainly affected by the strength eccentricity and the ductility ratio, decreasing with the increment of the eccentricity or the decrement of the ductility ratio in a medium eccentricity range. The earthquake pulse-like effect and the eccentricity have coupling influence on the modification factor, while the effect of story number is not apparent. Based on the results of a comprehensive statistical study a simplified expression is suggested, which can estimate the eccentricity modification factors for both pulse-like and nonpulse-like ground motion cases.     

Probabilistic Performance Assessment of Retrofitted Skewed Multi Span Continuous Concrete I-girder Bridges

The unique dynamic response of skewed bridges causes them to experience more noticeable damage compared to straight bridges during seismic events. The effectiveness of different retrofit strategies on the fragility of skewed bridges can change with the skew angle. This article assesses the impact of skew angle and various retrofit strategies on the fragility of multi span continuous concrete I-girder bridges. The results indicate that the level of effectiveness of a retrofit strategy is highly dependent on the skew angle and damage state of interest and an appropriate retrofit strategy should be chosen based on the vulnerability of the components.     

EVALUATION OF ACCIDENTAL ECCENTRICITY IN BUILDINGS DUE TO ROTATIONAL COMPONENT OF EARTHQUAKE

This study adopts a random procedure in the evaluation of the effect of the rotational component of earthquake on the accidental eccentricity of symmetric and asymmetric buildings. The spectral density function of the rotational component of earthquake acceleration (about the vertical axis) is obtained on the basis of the spectral density function of the horizontal component of earthquake acceleration. The rotational component of an earthquake can increase the response of the structure. The degree of the increase is highly dependent upon the dynamic characteristics of the system and the rotational component of the earthquake. To bring this increase under consideration, seismic codes represent a parameter referred to as accidental eccentricity, as a part of the design eccentricity. The purpose of the present study is to estimate the value of this increase and to make appropriate suggestions based on frequency domain analysis.     

Impact of Vertical Ground Excitation on a Bridge with Footing Uplift

Ground motions recorded in the epicentral region of an earthquake often have a strong vertical component with dominant high frequencies. Damage to bridges in near-source regions due to strong vertical ground motion has been reported. The beneficial effects of footing uplift on structural performance in form of reduction of seismic response of structural members have been confirmed in previous research. The uplift of bridge piers has been utilised in a very limited number of bridge structures, e.g., the South Rangitikei railway bridge in New Zealand. However, the near-fault seismic behaviour of bridges with footing uplift has been even less addressed. In this study shake table investigations were carried out on the response of a single-span bridge model with footing uplift subjected to simultaneous vertical and horizontal excitations. Near-fault ground motions recorded in the Canterbury earthquake sequences of 2010 and 2011 were used. The experimental results show that inclusion of vertical ground motions produce stronger axial force in the pier and larger bending moment in the deck. Concurrent horizontal and vertical excitations may also cause more frequent footing uplift than the solely horizontal excitations.     

Point-to-Surface Pounding of Highway Bridges with Deck Rotation Subjected to Bi-Directional Earthquake Excitations

Post-earthquake survey of several strong earthquakes demonstrated that pounding between the neighboring civil infrastructures, such as building and highway bridge, would induce significant structural damage, even collapse, of the structures. This article presents a pounding experiment of highway bridge, especially focused on the point-to-surface pounding of bridge decks due to torsional rotation, when subjected to extreme bi-directional earthquake excitations. To experimentally investigate the point-to-surface pounding between the neighboring bridge segments, a base-isolated highway bridge model, in which the mass centers of the bridge decks do not strictly coincide with the corresponding stiffness centers, is manufactured. A series of shaking table tests of the highway bridge model are carried out for the structural model with large and small separations of the expansion joint to investigate the dynamic responses of the bridge model with and without including the pounding effects, respectively. An analytical model of the highway bridge, in which the point-to-surface pounding is represented by using a modified contact-friction element, is also established based on the lump mass model with three degrees of freedom for each segment. Based on the test results, the model parameters of the modified contact-friction element are identified, and the analytical responses of the highway bridge model with pounding effects are compared with the experimental data. The results show that the highway bridge is vulnerable to the deck rotation, and point-to-surface pounding should be considered in the structural design to lighten the pounding damage of the highway bridge under strong earthquake excitations.     

SIMPLE EXPRESSION OF THE DYNAMIC STIFFNESS OF GROUPED PILES IN SWAY MOTION

A simplified expression is derived for the dynamic stiffness of grouped piles subjected to lateral loading. A computer program, based on the Thin Layered Element Method, is used for this purpose. The results of the program are compared with rigorous solutions. The simplified expression of the dynamic stiffness of grouped piles, where the mass, damping and stiffness parameters are frequency invariant, will be particularly useful for an equivalent linear analysis of the interaction between nonlinear soil and grouped piles in real time.     

Sensitivity Analysis for Soil-Structure Interaction Phenomenon Using Stochastic Approach

This article analyses 1.36 million realistic soil-structure interaction (SSI) scenarios in a systematic fashion to define the correlation between soil, structural, and system parameters and interaction effects on the structural response. In the analyses, a soil-shallow foundation-structure model that satisfies design building code requirements is utilized. It has been identified that soil shear wave velocity, shear wave velocity degradation ratio, structure-to-soil stiffness ratio, and structural aspect ratio combined with the system stiffness are the key parameters whose variation significantly affects variation in structural response. The critical range of variation of these parameters resulting in a detrimental SSI effects is also defined.     

Natural Frequency of Single Pier Bridges Considering Soil-Structure Interaction

Because of the crucial role of free vibration frequency of a structure (e.g., a bridge) in design procedure, more realistic estimation of the frequency ends up in safer and more optimized design. As obtaining the free vibration frequencies of a bridge, considering soil-pile group-structure interaction, provide more realistic values, development of an analytical model to obtain such free vibration frequencies is studied in this research work. Most researchers have studied models with a single pile foundation. The purpose of this study is to assess soil-structure interaction (SSI) effects on dynamic performance of pile group supported bridges. A new analytical model is proposed to predict seismic analysis of these bridges. Applying the dynamic equations of motion for the system, SSI effects have been estimated. Based on the suggested analytical model, a new approximate equation is proposed for calculating natural frequency of pile group supported bridges. Equation accuracy has been investigated by comparing the results with those achieved by previous studies. Most periods calculated by the approximate equation are similar to those given for other case studies, indicating that the model could be applicable to other projects. Since the proposed model is very similar to real soil-pile-pier systems, this approximate equation can be used in preliminary seismic design of bridges.     

SEISMIC RESPONSE CONTROL OF CABLE-STAYED BRIDGE USING DIFFERENT CONTROL STRATEGIES

The goal of this research is to study the effect of cable vibration through a number of control cases of a cable-stayed bridge. In order to consider the complicated dynamic behaviour of the full-scale bridge, a three-dimensional numerical model of the MATLAB-based analysis tool has been developed by the complete simulation of the Gi-Lu bridge. The dynamic characteristics of cables in the cable-stayed bridge are verified between the field experiment and the result from numerical simulation using geometrically nonlinear beam elements in MATLAB program. Three types of control devices are selected to reduce the response of the bridge deck which includes: actuators, viscous-elastic dampers with large capacity, and base isolations. Moreover, two types of control devices, MR dampers and viscous dampers, are installed either between the deck and cables and/or between two neighbouring cables for controlling the cable vibration. A modified bi-viscous model combined with convergent rules is used to describe the behaviour of MR dampers. Finally, through evaluation criteria the control effectiveness on the cable-stayed bridge using different control strategies is examined.     

Empirical Formulation for Estimating the Fundamental Frequency of Slender Masonry Structures

The fundamental frequency of a structure enables better assessment of its seismic demand for an efficient design and planning of its maintenance and retrofit strategy. The frequency is independent of the type of external loads, however, depends on structural stiffness, mass, damping and boundary conditions. In the case of slender masonry structures such as towers, minarets chimneys, and pagoda temples, it is influenced by mass and stiffness distribution, connection to adjacent structures, material properties, aspect ratio and slenderness ratio. In this present article, the data collected from various literature reviews on the slender masonry structures regarding dynamic, geometrical, and mechanical characteristics have been correlated to identify the major parameters influencing the fundamental frequency of such structures. The database has been used for developing an empirical formulation for predicting the fundamental frequency of such structures. The comparison between the experimental fundamental frequencies and the estimated fundamental frequencies are carried out in order to define reliability and accuracy of these empirical formulae.     

Impact Stiffness of the Contact-Element Models for the Pounding Analysis of Highway Bridges: Experimental Evaluation

For the requirement of pounding analysis of highway bridges, how to properly choose the impact stiffness has become a primary issue for an achieving accurate result. This article presents an evaluation test of the impact stiffness of four types of contact-element models based on the shaking table test results of a steel highway bridge model. The analytical results indicate that the theoretical impact parameters are significantly larger than the identified values because the assumptions for deriving those models cannot match the actual impact conditions. The possible reasons causing those differences are discussed at the end of this study.     

Critical Assessment of Intensity Measures for Seismic Response of Italian RC Bridge Portfolios

The seismic assessment of a road network depends largely on the characterization of the fragility of its bridge components. The accuracy of bridge seismic demand estimates and the use of proper intensity measures (IM) will significantly influence such task. The available literature has mainly focused on buildings or a limited number of bridge configurations and IMs, which may not be representative for bridge portfolio assessment studies. In this paper, the correlation quality between a larger pool of traditional and innovative IMs and the nonlinear dynamic response of typical Italian RC bridges is investigated to identify the best-performing IMs.     

The Strength Reduction Factors for Seismic-Isolated Bridges Characterized by SDOF Bilinear Systems in Far-Fault Areas

This article presents a statistical study on strength reduction factors for seismic-isolated bridges in far-fault areas. 1410 ground motions are selected and modified to be compatible with the recommended response spectra. Then, they are divided into 60 groups to investigate the effects of PGA/PGV ratios, soil conditions and post-to-pre-yield stiffness ratio. Results show that reduction factors are significantly affected by the PGA/PGV ratio, while the latter two items are not as important as the first one. Finally, an improved equation to estimate the reduction factor is proposed, and the accuracy of the equation is verified by additional records.     

INTEGRATED PASSIVE-ACTIVE SYSTEM FOR SEISMIC PROTECTION OF A CABLE-STAYED BRIDGE

This paper presents an integrated passive-active (i.e. hybrid) system for seismic response control of a cable-stayed bridge. Since multiple control devices are operating, a hybrid control system could alleviate some of the restrictions and limitations that exist when each system is acting alone. Lead rubber bearings are used as passive control devices to reduce the earthquake-induced forces in the bridge and hydraulic actuators are used as active control devices to further reduce the bridge responses, especially deck displacements. In the proposed hybrid control system, a linear quadratic Gaussian control algorithm is adopted as a primary controller. In addition, a secondary bang-bang type (i.e. on-off type) controller according to the responses of lead rubber bearings is considered to increase the controller robustness. Numerical simulation results show that control performances of the integrated passive-active control system are superior to those of the passive control system and are slightly better than those of the fully active control system. Furthermore, it is verified that the hybrid control system with a bang-bang type controller is more robust for stiffness perturbation than the active controller with a μ-synthesis method, and there are no signs of instability in the over-all system whereas the active control system with linear quadratic Gaussian algorithm shows instabilities in the perturbed system. Therefore, the proposed hybrid protective system could effectively be used for seismically excited cable-stayed bridges.     

Rocking of Non-symmetric Rigid Blocks in Buildings Considering Effects Associated with Dynamic Soil-Structure Interaction

A dynamic model for the estimation of the rocking and/or overturning response of a free-standing non-symmetric rigid block considering rotational and horizontal excitation is proposed. The block is situated at different levels of a building with flexible base subjected to earthquakes. Base flexibility introduces the rotational component of the excitation due to dynamic soil-structure interaction (DSSI). The model is used to assess the influence of the dynamic soil-structure interaction on the behavior of the block. An illustrative example of the proposed model for non-symmetric rigid blocks in 5-, 10-, and 15-story buildings located in soft soils considering earthquakes from different seismic sources is presented. Results show that it is important to consider kinematic effects as well as inertial effects of DSSI in the dynamic response of contents. The influence of base flexibility depends on the change of spectral intensities associated to the increase of the building structural period and is larger for higher building levels.     

GROUND MOTION DOMINANT FREQUENCY EFFECT ON THE DESIGN OF MULTIPLE TUNED MASS DAMPERS

Utilising the Kanai-Tajimi and Clough-Penzien spectrums and the pseudo-excitation algorithm in the frequency domain, parametric study is performed to examine the effect of the dominant frequency of ground motion on the optimum parameters and effective-ness of multiple tuned mass dampers (MTMD) with identical stiffness and damping coefficient but with unequal mass. The examination of the optimum parameters is con-ducted through the minimisation of the minimum values of the maximum displacement and acceleration dynamic magnification factors of the structure with the MTMD. The optimum parameters of the MTMD include the optimum frequency spacing reflecting the robustness, the average damping ratio and the tuning frequency ratio. Minimisation of the minimum values of the maximum displacement and acceleration dynamic mag-nification factors, nondimensionalised respectively by the maximum displacement and acceleration dynamic magnification factors of the structure without the MTMD, is used to measure the effectiveness of the MTMD. The results indicate that in the two cases where both the total mass ratio is below 0.02 and the total mass ratio is above 0.02, but the dominant frequency ratio of ground motion is below unity (including unity), the earthquake ground motion can be modelled by a white noise. It is worth noting, however, that for the total mass ratio above 0.02, the Kanai-Tajimi Spectrum or Clough-Penzien spectrum needs to be employed to design the MTMD for seismic structures in situations where the dominant frequency ratio of ground motion is beyond unity.     

Analytical Seismic Assessment of a Tall Long-Span Curved Reinforced-Concrete Bridge. Part I: Numerical Modeling and Input Excitation

The seismic response of bridges is affected by a number of modeling considerations, such as pier embedment, buried pile caps, seat-type abutments, pounding, bond slip and architecturally flared part of piers, and loading considerations, such as non-uniform ground excitations and orientation of ground motion components, which are not readily addressed by design codes. This article addresses a methodology for the nonlinear static and dynamic analysis of a tall, long-span, curved, reinforced-concrete bridge, the Mogollon Rim Viaduct. Various modeling scenarios are considered for the bridge components, soil-structure interaction system, and materials, i.e., concrete and reinforcing steel, covering all its geotechnical and structural aspects based on recent advances in bridge engineering. Various analysis methodologies (nonlinear static pushover, time history response to uniform and spatially variable seismic excitations, and incremental dynamic analyses) are performed. For the dynamic analyses, a suite of nine earthquake accelerograms are selected and their characteristics are investigated using seismic intensity parameters. A recently developed approach for the generation of non-uniform seismic excitations, i.e., spatially variable simulations conditioned on the recorded time series, is used. Methods for the evaluation of structural performance are discussed and their limitations addressed. The numerical results of the seismic assessment of the Mogollon Rim Viaduct are presented in the companion article (Part II). The sensitivity of the bridge response to the adopted modeling, loading and analyzing strategies, as well as the correlation between structural damage and seismic intensity parameters are examined in detail.     

Regional Seismic Risk Assessment of Bridge Network in Charleston,South Carolina

This article presents the results of a seismic risk assessment of the bridge network in Charleston, South Carolina and the surrounding counties to support emergency planning efforts, and for prioritization of bridge retrofit. This study includes an inventory analysis of the approximately 375 bridges in the Charleston area, and convolution of the seismic hazard with fragility curves analytically derived for classes of bridges common to this part of the country. State-of-the-art bridge fragility curves and replacement cost estimates based on region-specific data are used to obtain economic loss estimates. The distribution of potential bridge damage and economic losses are evaluated for several scenario events in order to aid in the identification of emergency routes and assess areas for investment in retrofit. This article also evaluates the effect of uncertainty on the resulting predicted economic losses. The findings reveal that while the risk assessment is very sensitive to both the assumed fragility curves and damage ratios, the estimate of total expected economic losses is more sensitive to the vast differences in damage ratio models considered.