Probabilistic Seismic Demand Models and Fragility Estimates for Reinforced Concrete Highway Bridges with One Single-Column Bent

In performance-based seismic design, general and practical seismic demand models of structures are essential. This paper proposes a general methodology to construct probabilistic demand models for reinforced concrete (RC) highway bridges with one single-column bent. The developed probabilistic models consider the dependence of the seismic demands on the ground motion characteristics and the prevailing uncertainties, including uncertainties in the structural properties, statistical uncertainties, and model errors. Probabilistic models for seismic deformation, shear, and bivariate deformation-shear demands are developed by adding correction terms to deterministic demand models currently used in practice. The correction terms remove the bias and improve the accuracy of the deterministic models, complement the deterministic models with ground motion intensity measures that are critical for determining the seismic demands, and preserve the simplicity of the deterministic models to facilitate the practical application of the proposed probabilistic models. The demand data used for developing the models are obtained from 60 representative configurations of finite-element models of RC bridges with one single-column bent subjected to a large number of representative seismic ground motions. The ground motions include near-field and ordinary records, and the soil amplification due to different soil characteristics is considered. A Bayesian updating approach and an all possible subset model selection are used to assess the unknown model parameters and select the correction terms. Combined with previously developed capacity models, the proposed seismic demand models can be used to estimate the seismic fragility of RC bridges with one single-column bent. Seismic fragility is defined as the conditional probability that the demand quantity of interest attains or exceeds a specified capacity level for given values of the earthquake intensity measures. As an application, the univariate deformation and shear fragilities and the bivariate deformation-shear fragility are assessed for an example bridge.     

Wave Passage and Ground Motion Incoherency Effects on Seismic Response of an Extended Bridge

This paper investigates the implications of ground motion spatial variability on the seismic response of an extended highway bridge. An existing 59-span, 2,164-meter bridge with several bearing types and irregularity features was selected as a reference structure. The bridge is located in the New Madrid Seismic Zone and supported on thick layers of soil deposits. Site-specific bedrock input ground motions were selected based on a refined probabilistic seismic hazard analysis of the bridge site. Wave passage and ground motion incoherency effects were accounted for after propagating the bedrock records to the ground surface. The results obtained from inelastic response-history analyses confirm the significant impact of wave passage and ground motion incoherency on the seismic behavior of the bridge. The amplification in seismic demands exceeds 150%, whereas the maximum suppression of these demands is less than 50%. The irregular and unpredictable changes in structural response owing to asynchronous earthquake records necessitate in-depth seismic assessment of major highway bridges with advanced modeling techniques to realistically capture their complex seismic response.     

Experimental Study of Seismic Behaviors of As-Built and Carbon Fiber Reinforced Plastics Repaired Reinforced Concrete Bridge Columns

In order to reliably obtain seismic responses of as-built and repaired reinforced concrete bridge columns under near-fault ground motions, pseudodynamic testing of two bridge columns with a reduced scale of 2/5 was performed. Pseudodynamic test results reveal that a ductile member may have no chance to entirely develop its ductile behavior to dissipate seismic energy, because it may suddenly be destroyed by a significant pulse-like wave. The seismic performance of the two damaged bridge columns can be recovered after repair with carbon fiber reinforced plastics composite sheets. It is also experimentally confirmed that the flexural failure moment obtained from the pseudodynamic test is in good agreement with the plastic moment predicted by the ACI 318 code. As pseudodynamic test results are believed to be more accurate than numerical solutions, they can be considered as reference solutions in developing a finite-element model. An identical specimen was tested under cyclic loading to estimate basic properties of these columns, such as shear strength, flexural strength, and ductility, so that the seismic responses obtained from pseudodynamic tests can be thoroughly discussed. Furthermore, its hysteretic response may also be used to match a mathematical model to simulate the very complicated load-displacement relation for analysis.     

Investigation of effect of near-fault motions on substandard bridge structures

The objective of this study was to investigate the effects of near-fault ground motions on substandard bridge columns and piers. To accomplish these goals, several large scale reinforced concrete models were constructed and tested on a shake table using near- and far-field ground motion records. Because the input earthquakes for the test models had different characteristics, three different measures were used to evaluate the effect of the input earthquake. These measures are peak shake table acceleration, spectral acceleration at the fundamental period of the test specimens, and the specimen drift ratios.For each measure, force-displacement relationships, strains, curvatures, drift ratios, and visual damage were evaluated.Results showed that regardless of the measure of input or response, the near-fault record generally led to larger strains,curvatures, and drift ratios. Furthermore, residual displacements were small compared to those for columns meeting current seismic code requirements.     

Seismic Site Response for Near-Fault Forward Directivity Ground Motions

Forward directivity effects in the near-fault region produce pulse-type motions that differ significantly from ordinary ground motions that occur at greater distances from the causative fault. Current code site factors are based on empirical observations and analyses involving less intense nonpulse ordinary ground motions. Nonlinear site response analyses with bidirectional shaking are performed using representative site profiles to quantify seismic site response effects for intense near-fault motions resulting from forward directivity. Input rock motions are represented with simplified velocity pulses that characterize the amplitude and period of forward directivity motions. Results indicate that site response affects both the amplitude and period of forward directivity pulses, and hence, local site conditions should be considered when evaluating seismic designs in the near-fault region. Stiff soil sites tend to amplify the peak ground velocity and increase the period of pulse-type motions, particularly, when the period of the rock motion coincides with the degraded period of the site. Amplification is limited at soft soil sites by the dynamic strength of the weak soil, so attenuation occurs for intense input motions. This nonlinearity is not reflected in the site factors in current building codes. Guidance is provided for estimating the amplitude and pulse period for velocity pulses at soil sites.     

Nonlinear Coupled Seismic Sliding Analysis of Earth Structures

Earthquake-induced sliding displacements of earth structures are generally evaluated using simplified sliding block analyses that do not accurately model the seismic response of the sliding mass nor the seismic forces along the slide plane. The decoupled approximation introduced to capture each of these effects separately is generally believed to be conservative. However, recent studies using linear viscoelastic sliding mass models have revealed instances where the decoupled approximation is unconservative. In this paper, a coupled analytical model that captures simultaneously the fully nonlinear response of the sliding mass (necessary for intense motions) and the nonlinear stick-slip sliding response along the slide plane is presented. The proposed sliding model is validated against shaking table experiments of deformable soil columns sliding down an inclined plane. The effect of sliding on the response of earth structures is evaluated, and comparisons are made between sliding displacements calculated using coupled and decoupled analytical procedures with linear and nonlinear material properties. Nonlinearity resulting from stick-slip episodes is often the dominant source of nonlinearity in this problem. The decoupled approximation was unconservative primarily for intense ground motions for systems with low values of ky, larger values of ky∕kmax, and high period ratios (Ts∕Tm). Results indicate that a decoupled analysis is adequate for earth structures that are not expected to experience intense, near-fault motions. However, for projects undergoing intense, near-fault ground motions, a fully nonlinear, coupled stick-slip analysis is recommended.     

Seismic Fragility of Continuous Steel Highway Bridges in New York State

This paper presents the results of an analytical seismic fragility analysis of a typical steel highway bridge in New York State. The structural type and topological layout of this multispan I-girder bridge have been identified to be most typical of continuous bridges in New York State. The structural details of the bridge are designed as per New York State bridge design guidelines. Uncertainties associated with the estimation of material strength, bridge mass, friction coefficient of expansion bearings, and expansion-joint gap size are considered. To account for the uncertainties related to the bridge structural properties and earthquake characteristics, ten statistical bridge samples are established using the Latin Hypercube sampling and restricted pairing approach, and 100 ground motions are simulated numerically. The uncertainties of capacity and demand are estimated simultaneously by using the ratios of demands to capacities at different limit states to construct seismic fragility curves as a function of peak ground acceleration and fragility surfaces as a function of moment magnitude and epicentral distance for individual components using nonlinear and multivariate regressions. It has been observed that nonlinear and multivariate regressions show better fit to bridge response data than linear regression conventionally used. To account for seismic risk from multiple failure modes, second-order reliability yields narrower bounds than the commonly used first-order reliability method. The fragility curves and surfaces obtained from this analysis demonstrate that bridges in New York State have reasonably low likelihood of collapse during expected earthquakes.     

Probabilistic Seismic Demand Models and Fragility Estimates for Reinforced Concrete Bridges with Two-Column Bents

Probabilistic models are developed to predict the deformation and shear demands due to seismic excitation on reinforced concrete (RC) columns in bridges with two-column bents. A Bayesian methodology is used to develop the models. The models are unbiased and properly account for the predominant uncertainties, including model errors, arising from a potentially inaccurate model form or missing variables, measurement errors, and statistical uncertainty. The probabilistic models developed are akin to deterministic demand models and procedures commonly used in practice, but they have additional correction terms that explicitly describe the inherent systematic and random errors. Through the use of a set of “explanatory” functions, terms that correct the bias in the existing deterministic demand models are identified. These explanatory functions provide insight into the underlying behavioral phenomena and provide a means to select ground motion parameters that are most relevant to the seismic demands. The approach takes into account information gained from scientific/engineering laws, observational data from laboratory experiments, and simulated data from numerical dynamic responses. The demand models are combined with previously developed probabilistic capacity models for RC bridge columns to objectively estimate the seismic vulnerability of bridge components and systems. The vulnerability is expressed in terms of the conditional probability (or fragility) that a demand quantity (deformation or shear) will be greater than or equal to the corresponding capacity. Fragility estimates are developed for an example RC bridge with two-column bents, designed based on the current specifications for California. Fragility estimates are computed at the individual column, bent, and bridge system levels, as a function of the spectral acceleration and the ratio between the peak ground velocity and the peak ground acceleration.     

Seismic Response of Multiple Span Steel Bridges in Central and Southeastern United States. II: Retrofitted

Part I of this two-part paper evaluated the seismic response of typical multispan simply supported (MSSS) and multispan continuous steel girder bridges in the central and southeastern United States. The results showed that the bridges were vulnerable to damage resulting from impact between decks, and large ductility demands on nonductile columns. Furthermore, fixed and expansion bearings were likely to fail during strong ground motion. In this paper, several retrofit measures to improve the seismic performance of typical multispan simply supported and multispan continuous steel girder bridges are evaluated, including the use of elastomeric bearings, lead-rubber bearings, and restrainer cables. It is determined that lead-rubber bearings are the most effective retrofit measure for reducing the seismic vulnerability of typical bridges. While isolation provided by elastomeric bearings limits the forces into the columns, the added flexibility results in pounding between decks in the MSSS steel girder bridges. Restrainer cables, which are becoming a common retrofit measure, are effective in reducing the hinge opening in MSSS bridges with steel bearings. However, when used with elastomeric bearings, the restrainer cables negate the isolation effect of the bearings.     

Role of Shear Keys in Seismic Behavior of Bridges Crossing Fault-Rupture Zones

This paper examines the role of shear keys at bridge abutments in the seismic behavior of “ordinary” bridges. The seismic responses of bridges subjected to spatially uniform and spatially varying ground motions for three shear-key conditions—nonlinear shear keys that break off and cease to provide transverse restraint if deformed beyond a certain limit; elastic shear keys that do not break off and continue to provide transverse restraint throughout the ground shaking; and no shear keys—are examined. Results show that seismic demands for a bridge with nonlinear shear keys can generally be bounded by the demands of a bridge with elastic shear keys and a bridge with no shear keys for both types of ground motions. While ignoring shear keys provides conservative estimates of seismic demands in bridges subjected to spatially uniform ground motion, such a practice may lead to underestimation of some seismic demands in bridges in fault-rupture zones that are subjected to spatially varying ground motion. Therefore, estimating the upper bounds of seismic demands in bridges crossing fault-rupture zones requires analysis for two shear-key conditions: no shear keys and elastic shear keys.     

Seasonally Frozen Soil Effects on the Seismic Site Response

Several large-magnitude earthquakes, including the Prince William Sound earthquake of March 1964 and the Denali earthquake of November 2002, occurred in the state of Alaska and caused considerable damages to its transportation system, including damage to several highway bridges and related infrastructure. Some of these damages are related to frozen soil effects. However, only limited research has been carried out to investigate the effects of frozen soils on seismic site responses. A systematic investigation of seasonally frozen soil effects on the seismic site response has been conducted and is presented in this paper. One bridge site in Anchorage, Alaska, was selected to represent typical sites with seasonally frozen soils. A set of input ground motions was selected from available strong-motion databases and scaled to generate an ensemble of hazard-consistent input motions. One-dimensional equivalent linear analysis was adopted to analyze the seismic site response for three seismic hazard levels, i.e., maximum considered earthquake (MCE), AASHTO design, and service design level hazards. Parametric studies were conducted to assess the sensitivity of the results to uncertainties associated with the thickness and shear-wave velocity of seasonally frozen soils. The results show that the spectral response of ground motions decreases as the thickness of seasonally frozen soil increases, and the results are insensitive to the shear-wave velocity of seasonally frozen soils. In conclusion, it is generally conservative to ignore the effects of seasonally frozen soils on seismic site response in the design of highway bridges.     

Full-Scale Tests of Bridge Steel Pedestals

Overheight vehicle collisions can cause major damage to bridges. To address the issue of limited vertical clearance heights and reduce the likelihood of impact damage, the Georgia Department of Transportation has implemented a program to elevate major highway bridges using very short columns referred to as steel pedestals. The process to elevate the bridges and install the steel pedestals is cost effective and efficient, resulting in minimum disruption to highway traffic. However, in practice, these pedestals are not detailed to provide end fixity, so they add considerable flexibility to the superstructure supports and potentially make the bridge more susceptible to instability and damage from seismic loads. Therefore, there is a need to evaluate how these steel pedestals will perform under the low-to-moderate earthquakes expected in this region. A full-scale 12.2?m (40?ft) dual steel girder simply supported bridge elevated with 500?mm (19?in.) and 850?mm (33?1/2?in.) steel pedestals is constructed based on typical field procedures. The full-scale bridge specimen is subjected to quasistatic unidirectional reversed cyclic loads to determine the strength and deformation capacity of the steel pedestals and overall system performance. The kinematics, mechanisms, and load–displacement hysteretic relationships of the bridge steel pedestals and its components are presented. Results show that the steel pedestals undergo kinematic rigid body motion, dissipate energy, and demonstrate reasonable deformation and strength capacities when subjected to quasistatic, reversed cyclic loads.     

Examination of Level of Analysis Accuracy for Curved I-Girder Bridges through Comparisons to Field Data

To evaluate the accuracy of different levels of analysis used to predict horizontally curved steel I-girder bridge response, a field test was performed on a three-span structure. Collected strain data were reduced to determine girder vertical and bottom flange lateral bending moments. Experimental moments were compared to numerical moments obtained from three commonly employed levels of analysis. Level 1 analysis includes two manual calculation methods: a line girder analysis method described in the AASHTO Guide Specification for Horizontally Curved Highway Bridges, and the V-load method. Grillage models represent Level 2 and were created using three commercially available computer programs: SAP2000, MDX, and DESCUS. Level 3 consists of three-dimensional (3D) finite element models created using SAP2000 and the BSDI 3D system. Responses obtained from each level are compared and discussed for a single radial cross section of the structure, and the compared results involve truck loads and placement schemes that do not represent those used for bridge design. The field test and numerical data presented are used solely to determine the accuracy of each level of analysis for predicting structure response to a specific live load at a specific cross section. Results showed that Level 2 and Level 3 analyses predict girder vertical bending moment distributions more accurately than Level 1 analyses throughout the tested cross section. The comparisons indicate that Level 3 girder vertical bending moment distributions offered no appreciable increase in accuracy over Level 2 analyses. The study also indicates that both Level 1 and Level 3 analyses provide bottom flange lateral bending moment distributions that do not correlate well with field test results for the studied bridge cross section.     

Evaluation of Site Factors for Seismic Bridge Design in New York City Area

Site factors for seismic bridge design in the New York metropolitan area are evaluated. Several profiles from Brooklyn, Queens, and Manhattan, matching soil categories D and E as defined in the recent New York City Department of Transportation and NEHRP provisions, are analyzed using 1D wave-propagation theory. Dynamic soil properties are derived using state-of-practice correlations with standard penetration resistance and compared to available in situ geophysical measurements. Three different rock motions are used, each modified from real records to match 500- and 2,500-year probabilistic spectra for the region. Results are presented in terms of dimensionless ratios of surface and rock response spectra. The effect of impedance contrast between soil and rock on soil amplification is examined. It is shown that, although seismic hazard in the area is moderate, large surface motions can be generated because of strong site amplification effects that exceed those in the western United States. Derived spectra are compared with current design spectra defined in the 1998 New York City Department of Transportation guidelines and the 1995 New York City Seismic Code. Three issues that are not sufficiently addressed in existing codes are discussed: (1) deep sites containing thick layers of high-plasticity clay; (2) shallow sites with thickness <30 m; and (3) amplification of vertical ground motions.     

Static Pushover Analyses of Pile Groups in Liquefied and Laterally Spreading Ground in Centrifuge Tests

Monotonic, static beam on nonlinear Winkler foundation (BNWF) methods are used to analyze a suite of dynamic centrifuge model tests involving pile group foundations embedded in a mildly sloping soil profile that develops liquefaction-induced lateral spreading during earthquake shaking. A single set of recommended design guidelines was used for a baseline set of analyses. When lateral spreading demands were modeled by imposing free-field soil displacements to the free ends of the soil springs (BNWF_SD), bending moments were predicted within ?8% to +69 (16th to 84th percentile values) and pile cap displacements were predicted within ?6 to +38%, with the accuracy being similar for small, medium, and large motions. When lateral spreading demands were modeled by imposing limit pressures directly to the pile nodes (BNWF_LP), bending moments and cap displacements were greatly overpredicted for small and medium motions where the lateral spreading displacements were not large enough to mobilize limit pressures, and pile cap displacements were greatly underpredicted for large motions. The effects of various parameter relations and alternative design guidelines on the accuracy of the BNWF analyses were evaluated. Sources of bias and dispersion in the BNWF predictions and the issues of greatest importance to foundation performance are discussed. The results of these comparisons indicate that certain guidelines and assumptions that are common in engineering design can produce significantly conservative or unconservative BNWF predictions, whereas the guidelines recommended herein can produce reasonably accurate predictions.     

Seismic Response of Multiple Span Steel Bridges in Central and Southeastern United States. I: As Built

The seismic response of typical multispan simply supported (MSSS) and multispan continuous steel girder bridges in the central and southeastern United States is evaluated. Nonlinear time history analyses are conducted using synthetic ground motion for three cities for 475 and 2,475-year return period earthquakes (10 and 2% probability of exceedance in 50 years). The results indicate that the seismic response for the 475-year return period earthquake would lead to an essentially linear response in typical bridges. However, the seismic response for a 2,475-year return period earthquake resulted in significant demands on nonductile columns, fixed and expansion bearings, and abutments. In particular, pounding between decks in the MSSS bridge would result in significant damage to steel bearings and would lead to the toppling of rocker bearings, which may result in unseating of the bridge deck.     

Probabilistic Characterization of Live Load Using Visual Counts and In-Service Strain Monitoring

It has been argued that the AASHTO LRFD design code for maximum live loads on highway bridges is overly conservative. In an attempt to determine the level of conservativeness, if any, the writers developed a methodology incorporating real-time visual data collection from traffic cameras coupled with structural strain response of girder bridges. Average daily truck traffic along with frequency of multiple presences (same lane as well as adjacent lanes) and lane-wise truck traffic distribution were estimated for a steel-girder highway bridge on I-95 in Delaware. These data compared well with predictions from a Poisson process based model developed for this study. Statistical properties of girder moments in single and multiple presence conditions were determined as well. In this particular example, the girder design moment on the 24.6?foot approach span according to AASHTO specifications was found to be about 3.5 times higher than that estimated from the in-service data.     

Saturation Effects of Soils on Ground Motion at Free Surface Due to Incident SV Waves

A study is presented of saturation effects of subsoil on seismic motions at the free surface of a half space due to an inclined (SV) wave. By treating the soil as a partially water-saturated porous medium that is characterized by its degree of saturation, porosity, permeability, viscosity, and compressibility, a theoretical formulation is developed for the computation of free-surface amplitudes in both the horizontal and vertical components, which are defined as a function of the degree of saturation, the angle of incidence, and the frequency. Numerical results are presented using typical sand properties. It is shown that even a slight decrease of full saturation may lead to a substantial influence on the free-surface amplitudes in both the components and the amplitude ratios between them, and this influence is dependent on the angle of incidence. Significant phase shift between the horizontal and vertical components may also occur due to this slight change in saturation. At small incident angles, partial saturation of subsoil generally may cause a greater vertical-to-horizontal ratio compared with a fully saturated model. It is suggested that one may need to carefully take into account the saturation condition in the interpretation of field observations on seismic ground motions.     

Elastic-Plastic Seismic Behavior of Long Span Cable-Stayed Bridges

This paper investigates the elastic-plastic seismic behavior of long span cable-stayed steel bridges through the plane finite-element model. Both geometric and material nonlinearities are involved in the analysis. The geometric nonlinearities come from the stay cable sag effect, axial force-bending moment interaction, and large displacements. Material nonlinearity arises when the stiffening steel girder yields. The example bridge is a cable-stayed bridge with a central span length of 605 m. The seismic response analyses have been conducted from the deformed equilibrium configuration due to dead loads. Three strong earthquake records of the Great Hanshin earthquake of 1995 in Japan are used in the analysis. These earthquake records are input in the bridge longitudinal direction, vertical direction, and combined longitudinal and vertical directions. To evaluate the residual elastic-plastic seismic response, a new kind of seismic damage index called the maximum equivalent plastic strain ratio is proposed. The results show that the elastic-plastic effect tends to reduce the seismic response of long span cable-stayed steel bridges. The elastic and elastic-plastic seismic response behavior depends highly on the characteristics of input earthquake records. The earthquake record with the largest peak ground acceleration value does not necessarily induce the greatest elastic-plastic seismic damage.