Optimum Design of Bridge Abutments under Seismic Conditions: Reliability-Based Approach

The paper focuses on the reliability-based design optimization of gravity wall bridge abutments when subjected to active condition during earthquakes. An analytical study considering the effect of uncertainties in the seismic analysis of bridge abutments is presented. Planar failure surface has been considered in conjunction with the pseudostatic limit equilibrium method for the calculation of the seismic active earth pressure. Analysis is conducted to evaluate the external stability of bridge abutments when subjected to earthquake loads. Reliability analysis is used to estimate the probability of failure in three modes of failure viz. sliding failure of the wall on its base, overturning failure about its toe (or eccentricity failure of the resultant force) and bearing failure of foundation soil below the base of wall. The properties of backfill and foundation soil below the base of abutment are treated as random variables. In addition, the uncertainties associated with characteristics of earthquake ground motions such as horizontal seismic acceleration and shear wave velocity propagating through backfill soil are considered. The optimum proportions of the abutment needed to maintain the stability are obtained against three modes of failure by targeting various component and system reliability indices. Studies have also been made to study the influence of various parameters on the seismic stability.     

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.     

Nonlinear Soil–Abutment–Bridge Structure Interaction for Seismic Performance-Based Design

Current seismic design of bridges is based on a displacement performance philosophy using nonlinear static pushover analysis. This type of bridge design necessitates that the geotechnical engineer predict the resistance of the abutment backfill soils, which is inherently nonlinear with respect to the displacement between soil backfill and the bridge structure. This paper employs limit-equilibrium methods using mobilized logarithmic-spiral failure surfaces coupled with a modified hyperbolic soil stress–strain behavior (LSH model) to estimate abutment nonlinear force-displacement capacity as a function of wall displacement and soil backfill properties. The calculated force-displacement capacity is validated against the results from eight field experiments conducted on various typical structure backfills. Using LSH and experimental data, a simple hyperbolic force-displacement (HFD) equation is developed that can provide the same results using only the backfill soil stiffness and ultimate soil capacity. HFD is compatible with current CALTRANS practice in regard to the seismic design of bridge abutments. The LSH and HFD models are powerful and effective tools for practicing engineers to produce realistic bridge response for performance-based bridge design.     

Allowable Bearing Pressures of Bridge Sills on GRS Abutments with Flexible Facing

Compared to geosynthetic-reinforced soil (GRS) retaining walls, GRS abutment walls are generally subjected to much greater intensity surface loads that are fairly close to the wall face. A major issue with the design of GRS abutments is the allowable bearing pressure of the bridge sill on the abutments. The allowable bearing pressure of a bridge sill over reinforced soil retaining walls has been limited to 200?kPa in the current NHI and Demo 82 design guidelines. A study was undertaken to investigate the allowable bearing pressures of bridge sills over GRS abutments with flexible facing. The study was conducted by the finite element method of analysis. The capability of the finite element computer code for analyzing the performance of GRS bridge abutments with modular block facing has been evaluated extensively prior to this study. A series of finite element analyses were carried out to examine the effect of sill type, sill width, soil stiffness/strength, reinforcement spacing, and foundation stiffness on the load-carrying capacity of GRS abutment sills. Based on the results of the analytical study, allowable bearing pressures of GRS abutments were determined based on two performance criteria: A limiting displacement criterion and a limiting shear strain criterion, as well as the writers’ experiences with GRS walls and abutments. In addition, a recommended design procedure for determining the allowable bearing pressure is provided.     

Assessment of Shear Forces on Bridge Abutments: Simplified Method

The conventional application of reduction factors to response spectrum analysis results is inappropriate for the abutment shear forces, which are based on elastic action. On the other hand, adopting the unreduced values from the elastic dynamic analysis does not achieve equilibrium among the abutment shear forces, deck inertia forces, and reduced pier forces. A simplified method is here proposed for the assessment of the shear on the abutments, documented by comparison with response spectrum and time history nonlinear analyses for several bridge configurations. For the analyzed configuration of the bridge with an internal movement joint, the response spectrum analysis underestimates the shear on the abutment for low values of the abutment flexibility and overestimates it when the stiffness of the abutments becomes higher than that of the piers. In all the case studies analyzed, the proposed method approximates the time history results better than the response spectrum.     

Bearing and Shear Failure of Pipe-Pin Hinges Subjected to Earthquakes

Pipe-pin rotational two-way column hinges were developed by bridge designers at the California Department of Transportation. An extensive experimental and analytical study was undertaken to understand the behavior of pipe-pin hinges and develop design guidelines. As part of the study, six 1:3.5?scale push-off tests were carried out to assess the bearing capacity of the concrete against the pipe. The tests showed that the bearing strength of concrete is as high as twice the concrete compressive strength because of the confining effect of the concrete and reinforcement. In addition, to determine the shear capacity of the concrete-filled steel pipe, six concrete-filled pipe specimens were tested in pure shear, and an empirical design equation was developed to assess their shear strength. In the analytical studies, ABAQUS finite-element (FE) package was used to perform a series of detailed nonlinear analyses. The results showed that the FE models accurately simulated the behavior of the push-off specimens and the observed modes of failure.     

Shake Table Studies of a Concrete Bridge Pier Utilizing Pipe-Pin Two-Way Hinges

Pipe-pin two-way hinge details were recently developed by California Department of Transportation (Caltrans) to eliminate moments while transferring shear and axial loads from integral bridge bent caps to reinforced concrete bridge columns. The hinges consist of a steel pipe that is anchored in the column with an extended segment into the cap beam. There is no specific design guideline for these hinges, and the current design method is primeval and only controls shear failure of the steel pipe. In this study, a rational method is proposed on the basis of the possible limit states to obtain the lateral capacity of these hinges. To validate the proposed method, a large-scale two-column bridge pier model utilizing pipe-pin hinges was tested on a shake table. The model was subjected to increasing levels of one of the Sylmar-Northridge 1994 earthquake records. A comprehensive analytical modeling of the pier was also performed using OpenSees; for this purpose, a macro model was developed for pipe-pin hinges in this study. The experimental results confirmed that the hinges designed on the basis of the proposed guideline remain elastic with no damage. The good correlation between the analytical and experimental data indicated that the macro model and other modeling assumptions were appropriate.     

Simulating the Behavior of GRS Bridge Abutments

Geosynthetic-reinforced soil (GRS) bridge-supporting abutments are similar in principle to GRS retaining walls, except that GRS abutments are typically subjected to a much higher area load, and that the loads are close to the wall face. The GRS abutment technology is relatively new, but it has great potential, and it has been gaining some popularity in recent years. This paper describes the finite element analyses of two full-scale loading tests of GRS bridge abutments referred to as the “National Cooperative Highway Research Program (NCHRP) experiment.” The analysis was carried out using the computer program Dyna3d, developed at the Lawrence Livermore National Laboratory. The finite element analysis of the NCHRP experiment will help with the understanding of the complex behavior of GRS structures in general, and the behavior of GRS bridge abutments with modular block facing in particular. The analysis of the two full-scale loading tests allows the loading conditions that are of greatest concern in the design of the bridge abutments to be examined rationally. The analysis shows that the performance of a GRS abutment, resulting from the complex interaction among the various components, while subject to a service load or a limiting failure load can be simulated in a reasonably accurate manner. In addition, a parametric study was conducted to investigate the performance of the modular block facing GRS bridge abutments subjected to live and dead loads from a bridge superstructure. This study investigated the performance of the GRS bridge abutments as they are affected by backfill properties, reinforcement stiffness properties, and reinforcement vertical spacing.     

Evaluation of As-Built, Retrofitted, and Repaired Shear-Critical Hollow Bridge Columns under Earthquake-Type Loading

The objective of this research is to investigate the seismic performance of as-built, retrofitted, and repaired hollow bridge columns with insufficient shear strength. Two as-built full-scale columns were first tested and repaired using carbon-fiber-reinforced polymer composites (CFRP) jackets and dog-bone-shaped bars and then retested. Another two columns having the same reinforcement as the as-built columns were retrofitted with CFRP jackets. In addition to the tests, the repairability of the failed hollow columns was investigated by analytical evaluation. The test results and analysis of the retrofitted columns showed that CFRP composites can effectively strengthen shear-critical hollow bridge columns and can successfully transform the failure mode from shear to flexure. The test results of the repaired circular columns show that dog-bone-shaped bars successfully repaired the flexural damage caused by the fractured longitudinal bars.     

Seismic Retrofit of Hollow Rectangular Bridge Columns

The seismic performance of rectangular hollow bridge columns is a significant issue of the high-speed rail project in Taiwan. The flexural ductility and shear capacity of such columns with the configuration of lateral reinforcement used in Taiwan have been studied recently. This paper reports that hollow rectangular bridge columns retrofitted with fiber-reinforced polymer (FRP) sheets were tested under a constant axial load and a cyclically reversed horizontal load to investigate their seismic behavior, including flexural ductility, dissipated energy, and shear capacity. An analytical model was also developed to predict the moment-curvature curve of sections and the load-displacement relationship of columns. Based on the test results, the seismic behavior of such columns will be presented. The test results were also compared to the proposed analytical model. It was found that the ductility factors of the tested piers are in the range from 3.4 to 6.3, and the proposed analytical model can predict the load-displacement relationship of such columns with acceptable accuracy. All in all, FRP sheets can effectively improve both the ductility factor and shear capacity of hollow rectangular bridge columns.     

Full-Scale Tests of Seismic Cable Restrainer Retrofits for Simply Supported Bridges

Many parts of the central and southeastern United States have recently begun initiating seismic retrofit programs for bridges on major interstate highways. One of the most common retrofit strategies is to provide cable restrainers at the intermediate hinges and abutments in order to reduce the likelihood of collapse due to unseating. To evaluate the force-displacement behavior of the cable restrainer retrofits, a full-scale bridge setup was constructed based on an existing multispan, simply supported steel girder bridge in Tennessee, that has been considered for seismic retrofit using cable restrainers. Seismic cable restrainers were connected to the bridge pier using steel bent plates, angles, and undercut anchors embedded in the concrete as specified by typical bridge retrofit plans. The full-scale bridge model was subjected to monotonic loading to test the capacity of the cable restrainer system and to determine the modes of failure. The results showed that the primary modes of failure are in the connection elements of the pier and girders, and they occur at force levels much lower than the strength of the cable. Modifications to the connection elements were designed and tested. The new connections resulted in a higher strength and deformation capacity of the cable restrainer assembly.     

Shear Retrofit of Hollow Bridge Piers with Carbon Fiber-Reinforced Polymer Sheets

Hollow bridge piers are currently being used in high-speed rail and highway projects in Taiwan. The flexural ductility and shear capacity of such piers with the configuration of lateral reinforcement used in Taiwan has recently been studied.?This paper reports that circular and rectangular hollow bridge piers retrofitted by carbon fiber-reinforced polymer (CFRP) sheets were tested under a constant axial load and a cyclic reversed horizontal load to investigate their seismic behavior, including flexural ductility, dissipated energy, and shear capacity. An analytical model is also developed to predict the moment-curvature relationship of sections and the lateral load-displacement relationship of piers. Based on the test results, the seismic behavior of such piers is presented. The test results are also compared with the proposed analytical model. It was found that the ductility factors of the tested piers ranged from 3.3 to 5.5 and that the proposed analytical model could predict the lateral load-displacement relationship of such piers with reasonable accuracy. All in all, CFRP sheets can effectively improve both the ductility factor and the shear capacity of hollow bridge piers.     

Strengthening of Short Shear Span Reinforced Concrete T Joists with Fiber-Reinforced Plasic Composites

In this work, the results of an experimental study conducted in a 1964-vintage building are presented. Twelve reinforced concrete (RC) T-joists strengthened with fiber-reinforced plastic (FRP) composites were loaded until failure in a short shear span configuration. Different strengthening schemes, including different FRP materials and a new FRP anchorage system, were adopted in order to compare the performance of the different installations. Carbon FRP and aramid FRP sheets in an epoxy matrix were bonded to the RC joists using the wet layup technique. All of the joists were loaded close to one end support and showed similar cracking patterns at failure. The design calculations were based on experimental results. All of the unanchored FRP strengthened beams showed failure due to peeling, while the anchored FRP strengthened members showed failure due to anchor pullout at higher load values. It was found that an increase in the amount of FRP did not result in a proportional increase in the shear capacity, as expected by design equations, but all of the beams showed a considerable increase in stiffness. The experimental results are compared with the results expected by analytical models in order to discuss the structural behavior of FRP strengthened beams tested in a real building with a short shear span. It was found that theoretical calculations resulted in nonconservative results for the tested specimens.     

Tests of RC Deck Girders with 1950s Vintage Details

Large numbers of conventionally reinforced concrete (CRC) bridges in the national bridge inventory built during the 1950s are lightly reinforced for shear. Inspections revealed many of these bridges exhibit diagonal cracks resulting in load postings, monitoring, emergency shoring, repairs, and unscheduled bridge replacements. A research program was conducted to investigate the behavior and capacity of CRC bridge girders with vintage details. Laboratory tests of large-size girders representative of 1950s design and construction practice were carried out. Various steel reinforcement configurations were tested. Loading conditions were varied to reproduce girder behavior at different positions in a bridge and various loading protocols were considered. Test results provide a comprehensive data set for comparison of analysis methods and repair strategies; and indicated that anchorage of flexural steel was key to developing higher ultimate capacity, initial crack damage may not necessarily contribute to the final failure mode, and crack width alone may not indicate the level of damage to the beam.     

Frequency of Discharge Causing Abutment Scour in South Carolina

The purpose of this study is to evaluate the adequacy of the 100-year discharge along with the Froehlich bridge abutment scour equation adopted by the U.S. Federal Highway Administration (FHwA) in predicting abutment scour for bridge design purposes in South Carolina streams. The analysis utilized bridge properties, stream cross-sectional and hydraulic data, local flood frequency equations, a one-dimensional steady river flow computer model (WSPRO), and procedures recommended by the FHwA for predicting abutment scour. A method was developed to identify the single stream-discharge at each bridge that can cause the abutment scour that was observed at 73 bridge abutments. Analysis of the results revealed that for one-third of the abutments in the sandy soil region of South Carolina, the flow rates required to produce the observed scour depths had return periods greater than 100?years. Although for bridges in the region dominated by clay soil, the return periods were significantly smaller than 100?years.     

Lateral Performance of Full-Scale Bridge Abutment Wall with Granular Backfill

Bridge abutments typically contain a backwall element that is designed to break free of its base support when struck by a bridge deck during an earthquake event and push into the abutment backfill soils. Results are presented for a full-scale cyclic lateral load test of an abutment backwall configured to represent the dimensions (1.7?m height), boundary conditions, and backfill materials (compacted silty sand) that are typical of California bridge design practice. An innovative loading system was utilized that operates under displacement control and that assures horizontal wall displacement with minimal vertical displacement. The applied horizontal displacement ranged from null to approximately 11% of the wall height (0.11H). The maximum earth pressure occurred at a wall displacement of 0.03H and corresponded to a passive earth pressure coefficient of Kp = 16.3. The measured force distribution applied to the wall from hydraulic actuators allowed the soil pressure distribution to be inferred as triangular in shape and the mobilized wall-soil interface friction to be evaluated as approximately one-third to one-half of the soil friction angle. Post-test trenching of the backfill showed a log-spiral principal failure surface at depth with several relatively minor shear surfaces further up in the passive wedge. The ultimate passive resistance is well estimated by the log-spiral method and a method of slices approach. The shape of the load-deflection relationship is well estimated by models that produce a hyperbolic curve shape.     

Validated Simulation Models for Lateral Response of Bridge Abutments with Typical Backfills

Abutment-backfill soil interaction can significantly influence the seismic response of bridges. In the present study, we provide numerical simulation models that are validated using data from recent experiments on the lateral response of typical abutment systems. Those tests involve well-compacted clayey silt and silty sand backfill materials. The simulation methods considered include a method of slices approach for the backfill materials with an assumed log-spiral failure surface coupled with hyperbolic soil stress-strain relationships [referred to as “log-spiral hyperbolic (LSH) model”] as well as detailed finite-element models, both of which were found to compare well with test data. Through parametric studies on the validated LSH model, we develop equations for the lateral load-displacement backbone curves for abutments of varying height for the two aforementioned backfill types. The equations describe a hyperbolic relationship between lateral load per unit width of the abutment wall and the wall deflection and are amendable to practical application in seismic response simulations of bridge systems.     

轻质混凝土拼装墙板填充钢框架协同抗震性能试验研究

为了研究墙板与钢框架结构之间的协同抗震性能,对采用不同墙框连接节点的轻质混凝土拼装墙板填充钢框架进行了低周往复荷载试验。通过对比试件的承载力、滞回性能、刚度、耗能以及延性性能,探讨了轻质混凝土拼装墙板及其整体性对结构抗震性能的影响。结果表明:填充墙板钢框架结构的最终破坏形态以墙板挤压开裂,框架梁柱端部翼缘屈曲为主;轻质混凝土拼装墙板与钢框架协同工作,有利于提高结构整体的承载力和变形能力,减轻钢框架在平面内的屈曲破坏;与刚性节点相比,采用柔性节点连接墙板与钢框架对结构的承载力、层间刚度和耗能能力更为有利;增强拼装墙板的整体性,有助于提高结构整体刚度、变形和耗能能力。研究结果可为轻质混凝土拼装墙板填充钢框架结构的抗震设计提供参考。      

Implications of Design Assumptions on Capacity Estimates and Demand Predictions of Multispan Curved Bridges

The paper presents a detailed seismic performance assessment of a complex bridge designed as a reference application of modern codes for the Federal Highway Administration. The assessment utilizes state-of-the-art assessment tools and response metrics. The impact of design assumptions on the capacity estimates and demand predictions of the multispan curved bridge is investigated. The level of attention to detail is significantly higher than can be achieved in a mass parametric study of a population of bridges. The objective of in-depth assessment is achieved through investigation of the bridge using two models. The first represents the bridge as designed (including features assumed in the design process) while the second represents the bridge as built (actual expected characteristics). Three-dimensional detailed dynamic response simulations of the investigated bridge, including soil-structure interaction, are undertaken. The behavior of the as-designed bridge is investigated using two different analytical platforms for elastic and inelastic analysis, for the purposes of verification. A third idealization is adopted to investigate the as-built bridge’s behavior by realistically modeling bridge bearings, structural gaps, and materials. A comprehensive list of local and global, action and deformation performance indicators, including bearing slippage and inter-segment collision, are selected to monitor the response to earthquake ground motion. The comparative study has indicated that the lateral capacity and dynamic characteristics of the as-designed bridge are significantly different from the as-built bridge’s behavior. The potential of pushover analysis in identifying structural deficiencies, estimating capacities, and providing insight into the pertinent limit state criteria is demonstrated. Comparison of seismic demand with available capacity shows that seemingly conservative design assumptions, such as ignoring friction at the bearings, may lead to an erroneous and potentially nonconservative response expectation. The recommendations assist be given to design engineers seeking to achieve realistic predictions of seismic behavior and thus contribute to uncertainty reduction in the ensuing design.     

Performance-Based Seismic Retrofit Strategy for Existing Reinforced Concrete Frame Systems Using Fiber-Reinforced Polymer Composites

The feasibility and efficiency of a seismic retrofit intervention using externally bonded fiber-reinforced polymer composites on existing reinforced concrete frame systems, designed prior to the introduction of modern standard seismic design code provisions in the mid-1970s, are herein presented, based on analytical and experimental investigations on beam-column joint subassemblies and frame systems. A multilevel retrofit strategy, following hierarchy of strength considerations, is adopted to achieve the desired performance. The expected sequence of events is visualized through capacity-demand curves within M-N performance domains. An analytical procedure able to predict the enhanced nonlinear behavior of the panel zone region, due to the application of CFRP laminates, in terms of shear strength (principal stresses) versus shear deformation, has been developed and is herein proposed as a fundamental step for the definition of a proper retrofit solution. The experimental results from quasi-static tests on beam-column subassemblies, either interior and exterior, and on three-storey three-bay frame systems in their as-built and CFRP retrofitted configurations, provided very satisfactory confirmation of the viability and reliability of the adopted retrofit solution as well as of the proposed analytical procedure to predict the actual sequence of events.