Analytical Seismic Assessment of a Tall Long-Span Curved Reinforced-Concrete Bridge. Part II: Structural Response

The seismic assessment of special bridges, even under the hypothesis of full knowledge of site conditions, structural characteristics, and seismic activity at their location, is not an easy and straightforward task due to the complexities and uncertainties related to the finite-element modeling approaches, structural loading scenarios, and seismic analysis methodologies. In this article, a series of nonlinear static and dynamic finite-element analyses on the Mogollon Rim Viaduct are performed with consideration of both uniform and conditionally simulated non-uniform seismic motions. The failure modes of the bridge using different numerical modeling approaches are discussed, and the degree of sensitivity of its response to the different seismic assessment strategies is evaluated. The effect of the multi-component, multi-support and multi-directional excitations of ground motions on the design and response are studied, and the pros and cons of the commonly used structural analysis methodologies of bridges are also addressed. The numerical results of the present study provide a deeper insight into the nonlinear behavior of curved reinforced-concrete bridges, and suggest practice-oriented approaches for their seismic assessment.     

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.     

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.     

A Checking Method for Multiple Seismic Performance Objectives of Bridge Piers Designed According to Code Provisions

Seismic bridge design codes require that bridge piers designed according to prescribed design rules should attain specified multiple seismic performance objectives. However, design codes do not explicitly require checking the attainment of specified performance objectives for designed bridge piers. In this article, seismic performance levels have been correlated with engineering damage parameters. A checking method for multiple seismic performance objectives of bridge piers has been outlined and validated with experimental results. The application of the method has been demonstrated by checking the performance of a bridge pier designed according to a code provision for a wide range earthquake ground motions.     

Response Sensitivity of Highway Bridges to Randomly Oriented Multi-Component Earthquake Excitation

In two-dimensional and single axis three-dimensional finite element analyses, the ground motion incidence angle can play a significant role in structural response. The effect of incidence angle for three-dimensional excitation and response is investigated in this paper for response of highway bridges. Single-degree-of-freedom elastic and inelastic mean spectra were computed from various orientation techniques and found indistinguishable for combinations of orthogonal horizontal components. Probabilistic seismic demand models were generated for the nonlinear response of five different bridge models. The negligible effect of incidence angle on mean ensemble response was confirmed with a stochastic representation of the ground motions.     

A Fast and Efficient Simulation of the Far-Fault and Near-Fault Earthquake Ground Motions Associated with the June 17 and 21, 2000, Earthquakes in South Iceland

The two M_w 6.5 earthquakes on June 17 and 21, 2000, respectively, in the populated South Iceland Seismic Zone (SISZ) significantly augmented the Icelandic database of strong ground motions, and several strong velocity pulses were recorded at near-fault sites. The strong motions are interpreted via the Specific Barrier Model (SBM) and a mathematical model of near-fault velocity pulses. The data indicates self-similar source scaling and significantly greater attenuation of seismic waves than in other interplate regions. Through inversion of the data a new attenuation function for the SISZ has been adopted, which results in unbiased simulations. For the first time, the characteristics of the recorded near-fault pulses have been identified and compared to the worldwide database of such records. The SBM and the near-fault pulse model combine naturally in a fast and efficient synthesis of realistic, broad-band strong ground motions in the far-fault and near-fault region. Such simulations are showcased for the June 2000 earthquakes and indicate that the modeling approach adopted in this study is an effective tool for the estimation of realistic earthquake ground motions in the SISZ.     

Shake Table Test and Numerical Analysis of a Bridge Model Supported on Elastomeric Pad Bearings

Elastomeric pad bearings are widely applied in short- to medium-span girder bridges in China, with the superstructure restrained by reinforced concrete (RC) shear keys in the transverse direction. Field investigations after the 2008 Wenchuan earthquake reveal that bearing systems had suffered the most serious damage, such as span falling, bearing displaced, and shear key failure, while the piers and foundations underwent minor damage. As part of a major study on damage mechanism and displacement control method for short- to medium-span bridges suffered in Wenchuan earthquake, a 1:4 scale, two-span bridge model supported on elastomeric pad bearings were recently tested on shake tables at Tongji University, Shanghai. The bridge model was subjected to increasing levels of four seismic excitations possessing different spectral characteristics. Two restraint systems with and without the restraint of RC shear keys were tested. A comprehensive analytical modeling of the test systems was also performed using OpenSees. The experimental results confirmed that for the typical bridges on elastomeric pad bearings without RC shear keys, the sliding effect of the elastomeric pad bearings plays an important role in isolation of ground motions and, however, lead to lager bearing displacement that consequently increases the seismic risk of fall of span, especially under earthquakes that contain significant mid-period contents or velocity pulse components. It is suggested from the test results that RC shear keys should be elaborately designed in order to achieve a balance between isolation efficiency and bearing displacement. Good correlation between the analytical and the experimental data indicates that the analytical models for the bearing and RC shear key as well as other modeling assumptions were appropriate.     

SEISMIC ENERGY DEMAND IN STEEL MOMENT FRAMES

The present paper investigates the seismic energy demand in steel moment-resisting frames. The frames, with 3, 6 and 10 storeys, and 4 and 8 spans, are designed according to current seismic code provisions. The energy response (energy quantities and their distributions) in the frames subjected to an ensemble of six earthquake ground motions recorded on different soil conditions, is investigated by nonlinear time history analysis. The study concludes that (1) the results of energy response can be developed into a rational method of seismic evaluation and design for steel moment-resisting frames; (2) the energy concept based on the single-degree-of-freedom has limitations when extended to the realistic structural system for design purposes; and (3) it is necessary to develop the energy-based approach for seismic evaluation and design based on the seismic response of a realistic multi-degree-of-freedom structural system.     

SEISMIC AMPLIFICATION AT A SOFT SOIL SITE WITH LIQUEFIABLE LAYER

It is well known that local soil conditions play a key role in the amplification of earthquake waves. In particular, a liquefiable shallow soil layer may produce a significant influence on ground motion during strong earthquakes. In this paper, the response of a liquefiable site during the 1995 Kobe earthquake is studied using vertical array records, with particular attention on the effects of nonlinear soil behaviour and liquefaction on the ground motion. Variations of the characteristics of the recorded ground motions are analysed using the spectral ratio technique, and the nonlinearity occurring in the shallow liquefied layer during earthquake is identified. A fully coupled, inelastic finite element analysis of the response of the array site is performed. The calculated stress-strain histories of soils and excess pore water pressures at different depths are presented, and their relations to the characteristics of the ground motions are addressed.     

A PROCEDURE FOR COMBINING VERTICAL AND HORIZONTAL SEISMIC ACTION EFFECTS

The vertical component of earthquake ground motion has generally been neglected in the earthquake-resistant design of structures. This is gradually changing due to the increase in near-source records obtained recently, coupled with field observations confirming the possible destructive effect of high vertical vibrations.

In this paper, simple procedures are suggested for assessing the significance of vertical ground motion, indicating when it should be included in the determination of seismic actions on buildings. Proposals are made for the calculation of elastic and inelastic vertical periods of vibration incorporating the effects of vertical and horizontal motion amplitude and the cross-coupling between the two vibration periods. Simplified analysis may then be used to evaluate realistic vertical forces by employing the vertical period of vibration with pertinent spectra without resorting to inelastic dynamic analysis.

Finally, a procedure is suggested for combining vertical and horizontal seismic action effects which accounts for the likelihood of coincidence, or otherwise, of peak response in the two directions.     

Reconnaissance Report on Damage of Bridges in 2008 Wenchuan,China, Earthquake

This is a reconnaissance report on the damage to bridges during the 2008 Wenchuan, China, earthquake. Site investigation was conducted by the authors on August 10–14, 2008. Presented is a detailed discussion of the damage to 12 bridges as well as possible damage mechanisms. Characteristics of two near-field ground accelerations and Chinese seismic bridge design practices are also presented. An investigation of the damage finds insufficient intensity of seismic design force, inadequate structural detailing for enhancing the ductility capacity, and an absence of unseating prevention devices.     

Simplification and Assessment of Modal-Based Story Damage Index for Reinforced Concrete Frames Subjected to Seismic Excitations

Different relations have been represented for the local damage index of structures to date, while the same application is defined for them as can be an indicator of relative sustained damage by the components or stories. Since different force-resisting systems subjected to the ground motions can behave differently, some well-known story damage indices are evaluated for the reinforced concrete frames with regards to their operation during nonlinear time history analysis. Two general concepts of story damage determination are selected for this purpose. SDI is a modal-based story damage index, which is calculated by the modal frequency and mode shapes. The behavior of this local index is evaluated during the seismic excitations. The results were compared with Park-Ang and modal flexibility story damage indices. Based on analytical study on seismic responses of some RC frames subjected to a suit of earthquake records a new story damage index has been developed. It has been derived from a simple global damage equation (softening index) using a normalized ratio of inelastic story shear to its drift. A procedure is recommended to use the proposed equation without any requirement to perform nonlinear dynamic analysis, which can significantly reduce the computational efforts. Distribution of the new represented SDI along the structural height shows a good agreement with damaged state of the RC frames after seismic excitations.     

Predicting the Seismic Response of Capacity-Designed Structures by Equivalent Linearization

An equivalent linearization procedure is developed for predicting the inelastic deformations and internal forces of capacity-designed structures under earthquake excitations. The procedure employs response spectrum analysis, and mainly consists of the construction of an equivalent linear system by reducing the stiffness of structural members that are expected to respond in the inelastic range. These members are well defined in structures designed with capacity principles. Maximum modal displacement demands of the equivalent linear system are determined either from the equal displacement rule, or from independent nonlinear response history analysis of SDOF systems representing inelastic modes.

Predictions obtained from the proposed equivalent linearization procedure are evaluated comparatively by using the results of nonlinear response history analysis as benchmark, linear elastic response spectrum analysis and conventional pushover analysis. The deformations and capacity controlled actions of a 12-story symmetrical plan concrete frame and a 6-story unsymmetrical plan concrete frame are obtained by each method under 96 strong ground motions. It is observed that the proposed procedure results in better accuracy in estimating the inelastic seismic displacement response parameters and capacity controlled forces than the other two approximate methods.     

ENGINEERING EVALUATION OF THE 1 OCTOBER 1995 DİNAR EARTHQUAKE (ML = 5.9)

In 1995, a swarm of earthquakes affected the city of Dinar, Turkey, which is located in Southwest Anatolia and has a population of 35 000. The mainshock having a local magnitude of 5.9 occurred on 1 October 1995. It was preceded by foreshocks in the previous four days, the largest one with a magnitude of 4.7. These foreshocks initiated structural damage in many buildings, which was then severely aggravated by the mainshock and a strong aftershock two hours later, with a magnitude of 5.0. Numerous aftershocks were recorded throughout the following three months. Strong ground motions were recorded within the city. The mainshock produced peak horizontal accelerations of 0.28 g and 0.29 g. The Dinar earthquake caused a death toll of 92 and more than 200 injuries. The economic losses due to structural damage alone are estimated at 250 million USD.     

Analytical Collapse Study of Lightly Confined Reinforced Concrete Frames Subjected to Northridge Earthquake Ground Motions

Review of older non seismically detailed reinforced concrete building collapses shows that most collapses are triggered by failures in columns, beam-column joints, and slab-column connections. Using data from laboratory studies, failure models have previously been developed to estimate loading conditions that correspond to failure of column components. These failure models have been incorporated in nonlinear dynamic analysis software, enabling complete dynamic simulations of building response including component failure and the progression of collapse. A reinforced concrete frame analytical model incorporating column shear and axial failure elements was subjected to a suite of near-fault ground motions recorded during the 1994 Northridge earthquake. The results of this study show sensitivity of the frame response to ground motions recorded from the same earthquake, at sites of close proximity, and with similar soil conditions. This suggests that the variability of ground motion from site to site (so-called intra-event variability) plays an important role in determining which buildings will collapse in a given earthquake.     

Seismic Evaluation and Retrofit of Asymmetric Multi-Story Wood-Frame Building

The presented research focuses on large-scale seismic testing under multi-directional ground motion of a three-story high, wood-frame residential building representing late 1960's California construction. Earthquake lateral resistance is provided by plywood shear walls around the perimeter of the building with an open front in the first story for tuck-under parking. Accordingly, the as-built structural configuration is asymmetric in plan and discontinuous in elevation with tendency to twist about a vertical axis and to form a weak story mechanism. The test results confirm this tendency. They also reveal the sensitivity of the response to multi-direction ground motion. Asymmetric damage patterns are induced by the multi-component motions in the walls oriented perpendicular to the open front for the as-built test structure, with or without finish materials. However, the observed damage remained noncritical as far as structural integrity is concerned even for ground accelerations exceeding 120% of that recorded during Northridge earthquake. This is viewed as a consequence of the better construction of the test building compared to actual construction. Investigated retrofit includes adding a welded moment resisting steel frame around of the garage opening and strengthening the diaphragm to header beam connections. The study indicates that the retrofit significantly reduced the maximum story drift in the open front. Moreover, the finish material and the retrofit greatly reduce the maximum rotation of the building about the vertical axis.     

Estimation of Strong Ground Motions in Southwest Western Australia with a Combined Green's Function and Stochastic Approach

As only a very limited number of earthquake strong ground motion records are available in southwest Western Australia (SWWA), it is difficult to derive a reliable and unbiased strong ground motion attenuation model based on these data. To overcome this, in this study a combined approach is used to simulate ground motions. First, the stochastic approach is used to simulate ground motion time histories at various epicentral distances from small earthquake events. Then, the Green's function method, with the stochastically simulated time histories as input, is used to generate large event ground motion time histories. Comparing the Fourier spectra of the simulated motions with the recorded motions of a ML6.2 event in Cadoux in June 1979 and a ML5.5 event in Meckering in January 1990, provides good evidence in support of this method. This approach is then used to simulate a series of ground motion time histories from earthquakes of varying magnitudes and distances. From the regression analyses of these simulated data, the attenuation relations of peak ground acceleration (PGA), peak ground velocity (PGV), and response spectrum of ground motions on rock site in SWWA are derived.     

Seismic Vulnerability Analysis of RC Bridges Based on Kriging Model

This paper presents a Kriging model-based method for seismic vulnerability analysis of reinforced concrete (RC) bridges. It aims at reducing the computational effect when the Monte Carlo technique is used for establishing the structural vulnerability curves. The general procedure of the proposed method is put forward firstly. In the procedure, the uncertainties existing in the structures and ground motions are both taken into account, and the uniform design (UD) technique is adopted for generating the random samples. The reliability of the proposed method is demonstrated by the vulnerability analysis of an single degree of freedom (SDOF) system using the Latin hypercube simulation (LHS) method. Vulnerability analysis of an RC bridge system is then carried out using the proposed method. The vulnerability curves of the bridge obtained by the Kriging model-based method are compared with those obtained by the LHS method. Additionally, three simulation schemes adopting different UD tables are employed to investigate the convergence and stability of the proposed method. The results show that the proposed method used for the seismic vulnerability analysis of RC bridges can reduce the computational effort and time to a large extent without much compromise on the accuracy.     

Seismic Response of Bridges Subjected to Different Earthquake Types Using IDA

Incremental Dynamic Analysis (IDA) was used to evaluate the seismic response of straight, continuous 4-span bridges with different sub-structure configurations. Three different record sets were chosen to represent three different earthquake types which can occur for a site such as Vancouver (i.e., crustal, subduction interface, and subduction inslab earthquakes). Seventy eight records were considered in each set (i.e., a total of 234 records) and the capacities of the bridges were evaluated using a fast IDA algorithm. A simplified method to account for the effects of spectral shapes was used. Different subsets of the records with specific characteristics were also used in the IDA. The bridges were designed and evaluated for two different design force modification factors and bridges with different degrees of irregularity were studied. Comparisons of the IDA results obtained indicated that in most of the cases the interface record sets resulted in lower median collapse capacities and hence were the most critical of the ground motions studied.     

Transverse Seismic Behavior Studies of a Medium Span Cable-Stayed Bridge Model with Two Concrete Towers

Due to lack of investigation on nonlinear seismic behavior of cable-stayed bridges under strong earthquake excitation, the concrete towers, as the main gravity-carrying component, are usually required to remain nearly elastic. However, in order to achieve this high seismic performance objective, the reinforcement ratio of the tower legs and the tower struts need to be greatly increased in addition to its static loading requirement. To study the potential plastic region and possible failure mode of the cable-stayed bridge, a 1/20-scale full bridge model from a typical medium span concrete cable-stayed bridge was designed, constructed and tested on 4 linear shake tables using a site specific artificial wave in the transverse direction. Test results showed that the damage characteristics of the bridge model were as follows: (1) the severe damage was observed at the upper strut, with several steel bars fractured at both ends; (2) the repairable damage was observed at tower legs at the bottom and the middle part, with concrete cover spalling and exposure of steel bars; (3) the minimal damage was observed at the lower strut and the both sides of the side bents, with only slightly concrete spalling; and (4) no damage was observed at the auxiliary bents, the superstructure and the cables. Numerical results and test results were further compared and showed good agreement in low amplitudes of excitations. The test also proved that the bridge system was stable in flexural failure of upper struts, and had the negligible residual displacement subjected to high amplitudes of excitations.