Unbonded Posttensioned Concrete Bridge Piers. II: Seismic Analyses

The seismic response characteristics of a proposed unbonded posttensioned concrete bridge-pier system are evaluated. Time-history analyses are carried out on prototype designs of single-column piers and two-column bents using detailed nonlinear finite-element (FE) models and equivalent single-degree-of-freedom (SDOF) systems embedded with phenomenological constitutive models. The phenomenological models are based on the hysteretic behavior of the prototype designs from cyclic analyses using nonlinear FE models, which have been calibrated and verified against experiments. The two modeling techniques are compared and evaluated for simulating the response of unbonded posttensioned bridge piers. Extensive time-history analyses are carried out on the SDOF models to study the influence of unbonded posttensioning on seismic response. To assess the adequacy of the proposed bridge-pier system, the seismic demands on the prototype designs are compared to their capacities as established in a companion paper. The applicability of current bridge design specifications to designing the proposed bridge-pier system is discussed.     

Modeling the Nonlinear Behavior of Concrete Masonry Walls Retrofitted with Steel Studs under Blast Loading

This paper presents the results of an analytical investigation of one-way unreinforced masonry (URM) walls retrofitted with externally anchored steel studs and subjected to blast loads. Using the wall geometrical and material properties, deflected shape, and crack pattern as input, a nonlinear model is developed to predict the inward force-displacement relationship of the retrofitted walls. In addition, using a rigid body analysis, a simple bilinear force-displacement relationship is developed to model the outward force-displacement relationship of the walls. Utilizing these two force-displacement relationships (resistance functions), a generalized single-degree-of-freedom (SDOF) model is developed to capture the nonlinear out-of-plane dynamic response of the retrofitted walls under blast loads. The SDOF model captured the experimentally observed displacement responses of the tested walls with reasonable accuracy. The model was also used to investigate the influence of block thickness, wall slenderness ratio, blast load intensity, and blast pulse shape on the out-of-plane dynamic response of retrofitted walls. The results demonstrated that anchored steel-stud systems could significantly enhance the out-of-plane capacity of the retrofitted walls by increasing their out-of-plane capacity and reducing their displacement.     

Unbonded Posttensioned Concrete Bridge Piers. I: Monotonic and Cyclic Analyses

The monotonic and cyclic behavior of a proposed unbonded, posttensioned concrete bridge pier system is studied using finite-element analyses. A procedure to evaluate seismic capacities based on results from the monotonic and cyclic analyses is described in the framework of a two-level approach considering functional- and survival-performance limits. A set of criteria to define functional-and survival-level displacement capacities for the system is developed. The proposed criteria represent improvements over existing criteria in that they are applicable to both conventional reinforced concrete structures and unbonded posttensioned structures. The monotonic and cyclic behavior of prototype single-column pier and two-column bent designs is presented. Monotonic analyses are performed to characterize the stiffness, strength, ductility, and limit-state behavior of these systems. Cyclic analyses are carried out to estimate energy dissipation capacity, residual displacements, and general hysteretic behavior. The influence of the degree of unbonded posttensioning on bridge pier behavior is examined. Using the finite-element results and the proposed criteria, seismic capacities of the prototype bridge pier systems are established.     

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.     

Refined Stick Model for Dynamic Analysis of Skew Highway Bridges

Stick models are widely employed in the dynamic analysis of bridges when only approximate results are desired or when detailed models are difficult or time-consuming to construct. Although the use of stick models for regular bridges has been validated by various researchers, the application of such models to skew highway bridges continues to present challenges. The conventional single-beam stick model used to represent the bridge deck often fails to capture certain predominant vibration modes that are important in obtaining the true dynamic response of the bridge. In this paper, a refined stick model is proposed for the preliminary dynamic analysis of skew bridges. The model utilizes a dual-beam stick representation of the bridge deck. The validity of the model is established by comparing results obtained from the proposed model with numerical solutions obtained for skew plates and a skew bridge. It is shown that this dual-beam stick model is superior to the conventional single-beam model in estimating the natural vibration frequencies and in predicting the predominant vibration modes of the bridge. Because of its simplicity and relative accuracy, this model is recommended for the preliminary dynamic analysis of skew highway bridges.     

Anisotropic Damage Model for Concrete

In this paper, a damage constitutive model accounting for induced anisotropy and bimodular elastic response is applied to two-dimensional analysis of reinforced concrete structures. Initially, a constitutive model for the concrete is presented, where the material is assumed as an initial elastic isotropic medium presenting anisotropy and bimodular response (distinct elastic responses, whether tension or compression stress states, prevail) induced by damage. Two damage tensors govern the stiffness under prevailing tension or compression stress states. Criteria are then proposed to characterize the dominant states. Finally, the proposed model is used in plane analysis of reinforced concrete beams to show its potential for use and to discuss its limitations.     

Vehicle-Induced Dynamic Performance of FRP versus Concrete Slab Bridge

In the United States alone, about 30% of the bridges are classified as structurally deficient or functionally obsolete. To alleviate this problem, a great deal of work is being conducted to develop versatile, fully composite bridge systems using fiber-reinforced polymers (FRPs). To reduce the self-weight and also achieve the necessary stiffness, FRP bridge decks often employ hollow sandwich configurations, which may make the dynamic characteristics of FRP bridges significantly different from those of conventional concrete and steel bridges. Due to the geometric complexity of the FRP sandwich panels, dynamic analyses of FRP bridges are very overwhelming and rarely reported. The present study develops an analysis procedure for the vehicle-bridge interaction based on a three-dimensional vehicle-bridge coupled model. The vehicle is idealized as a combination of rigid bodies connected by a series of springs and dampers. A slab FRP bridge, the No-Name Creek Bridge in Kansas, is first modeled using the finite-element method to predict its modal characteristics, then the bridge and vehicle systems are integrated into a vehicle-bridge system based on the deformation compatibility. The bridge response is obtained in the time domain by using an iterative procedure employed at each time step, considering the deck surface roughness as a vertical excitation to the vehicle. The bridge dynamic response and the calculated impact factors are compared between the FRP slab bridge and a corresponding concrete slab bridge. Finally, the applicability of AASHTO impact factors to FRP bridges is discussed.     

海冰对单柱式桥墩非线性地震反应的影响

用简化的附加水质量模型考虑动水压力对桥墩的影响,用动冰力模型考虑冰与桥墩的相互作用,建立了冰水域单柱式桥墩地震反应的动力计算模型,并利用时程分析法研究了在不同类型地震作用下海冰对桥墩非线性地震反应的影响.桥墩的最不利反应一般发生在海冰质量为5×10⁶~5×10⁷kg,可作为桥墩设计时的海冰质量;且墩底截面出现最大曲率时对应的海冰质量随着水深的增大而变大.有冰时墩底截面曲率延性需求系数、墩顶最大位移和墩顶残余位移比无冰时增大数倍,墩底截面弯矩–曲率滞回曲线呈倒\     

Design Charts for Evaluating Impact Forces on Dissipative Granular Soil Cushions

This paper concerns the problem of designing standard artificial tunnels for rock boulder protection. The proposed approach consists in uncoupling the problem of the dynamic response of the granular dissipative soil cushion placed on the top of artificial tunnels from the dynamic response of the reinforced concrete structure underneath. An already conceived elasto-viscoplastic constitutive model capable of simulating the penetration process of the boulder within the soil stratum and reproducing the force acting on the boulder is briefly described. Its simplified one-dimensional formulation is outlined. A modified version of the model, taking into account large displacements occurring when either impacts on loose granular soils or high energetic content impacts on dense sand strata are considered, is also introduced. To validate the approach, some in situ test results are numerically simulated. A simplified numerical approach is proposed for obtaining the evolution with time of both impact force and boulder penetration, bypassing the use of the rheological model. This goal is achieved by introducing some abaci obtained numerically with reference to an ideal dense sand soil stratum of reference.     

Active Confinement of Reinforced Concrete Bridge Columns Using Shape Memory Alloys

This paper presents experimental and analytical work conducted to explore the feasibility of using an innovative technique for seismic retrofitting of RC bridge columns using shape memory alloys (SMAs) spirals. The high recovery stress associated with the shape recovery of SMAs is being sought in this study as an easy and reliable method to apply external active confining pressure on RC bridge columns to improve their ductility. Uniaxial compression tests of concrete cylinders confined with SMA spirals show a significant improvement in the concrete strength and ductility even under small confining pressure. The experimental results are used to calibrate the concrete constitutive model used in the analytical study. Analytical models of bridge columns retrofitted with SMA spirals and carbon fiber-reinforced polymer (CFRP) sheets are studied under displacement-controlled cyclic loading and a suite of strong earthquake records. The analytical results proves the superiority of the proposed technique using SMA spirals to CFRP sheets in terms of enhancing the strength and effective stiffness and reducing the concrete damage and residual drifts of retrofitted columns.     

Dynamic Behavior of Nonlinear Cable System. IV

A suitable filter response is defined that allows studies of the effects of excitation bandwidth on the responses of geometrically nonlinear dynamic systems. For such a random excitation, as the bandwidth approaches zero, the mean square displacement response of a linear single-degree-of-freedom (SDOF) system approaches the mean square response to harmonic excitation. Studies of mean square responses of a nonlinear SDOF model of a cable system are presented. The set of nonlinear equations for the response moments are truncated using Gaussian closure and solved using continuation techniques as implemented in the program AUTO. Surfaces of turning point loci are computed in the parameter space of excitation bandwidth, excitation central frequency, and system damping. These surfaces provide values of the three parameters that separate regions with multiple mean square responses from regions with unique mean square responses. Response time histories are computed by simulation to illustrate system behavior in regions with multiple stable mean square responses.     

Long-Term Response Prediction of Integral Abutment Bridges

The importance of long-term behavior in integral abutment (IA) bridges has long been recognized. This paper presents an analytical, long-term, response prediction methodology using finite-element (FE) models and compares results to measured response. Three instrumented Pennsylvania IA bridges have been continuously monitored since November 2002, November 2003, and September 2004 to capture bridge response. An evaluation of measured responses indicates that bridge movement progresses year to year with long-term response being significant with respect to static predictions. Both two-dimensional and three-dimensional FE models were developed using ANSYS to determine an efficient and accurate analysis level. Seasonal cyclic ambient temperature and equivalent temperature derived from time-dependent strains using the age adjusted effective modulus method were employed as major loads in all FE models. The elastoplastic p-y curve method, classical earth pressure theory, and moment-rotation relationships with parallel unloading paths were used to model hysteretic behavior of soil-pile interaction, soil-abutment interaction, and abutment-to-backwall connection. Predicted soil pressures obtained from all FE models are similar to the measured response. Predicted abutment displacements and corresponding design forces and moments at the end of the analytically simulated 100-year period indicate the significance of long-term behavior that should be considered in IA bridge design.     

Validity of SDOF Models for Analyzing Two-Way Reinforced Concrete Panels under Blast Loading

The combined manual TM 5-1300/NAVFAC P-397/AFR 88-22, Structures to Resist the Effects of Accidental Explosions, published by the joint departments of the Army, the Navy, and the Air Force, has been used in all NATO countries for the past 50 years for protective design applications. The manual was recently reformatted to meet the Department of Defense Unified Facility Criteria (UFC). As a first step, the current production of the new document, UFC 3-340-02, focused on making the original TM 5-1300 available in a more functional format so that future technical updates can be facilitated. In this study, a single-degree-of-freedom (SDOF) model, based on the guidelines of the UFC 3-340-02, was used to formulate a FORTRAN code to predict the response of SDOF systems under blast. The code was used to generate pressure-impulse (P-I) diagrams for a series of two-way reinforced concrete (RC) panels with different dimensions, aspect and reinforcement ratios, and support conditions. The P-I diagram predictions were compared to the results of experimentally validated nonlinear explicit finite-element (FE) analyses and significant differences in deflection and shear predictions were observed. The general trend of results and the major characteristics of the P-I diagrams were discussed in terms of the discrepancies between the SDOF and the FE predictions. The work presented in this paper is expected to contribute to improving the modeling provisions of the two-way RC panels in the future edition of the UFC 3-340-02 by understanding the limitations of SDOF models using advanced FE analysis techniques.     

Calibration of Soil Constitutive Models with Spatially Varying Parameters

Soil constitutive models are frequently calibrated from laboratory tests that utilize global boundary measurements, which necessarily relegate soil response to that of a homogenized equivalent medium. This paper demonstrates the applicability of advanced experimental technologies to enhance the state of model-based predictions in soil mechanics by taking into account the possibility of material heterogeneity during model calibration. By utilizing the full-field displacement measurement technique of three-dimensional digital image correlation, displacements of the surfaces of deforming triaxial sand specimens are measured throughout deformation. These displacements are assimilated into finite-element (FE) models of the test specimen through solution of an inverse problem. During optimization, in which the difference between measured and predicted displacements across the specimen surface form the basis for the objective function, model parameters are allowed to vary spatially throughout the specimen volume. FE models allowing three different levels of spatial variability are tested. Results indicate that accommodating consideration of material heterogeneity during calibration leads to more accurate predictions of global stress-strain behavior that are more faithful to observed full-field response.     

Identification of a Distribution of Stiffness Reduction in Reinforced Concrete Slab Bridges Subjected to Moving Loads

The method for identifying arbitrary stiffness reduction in damaged reinforced concrete slab bridges under moving loads is proposed and dynamic signals measured at several points are used as response data to reflect the properties of the moving loads sensitivity. In particular, the change in stiffness in each element before and after damage, based on the system identification method, is described and discussed by using a modified bivariate Gaussian distribution function. The proposed method in this work is more feasible than the conventional element-based damage detection method from the computational efficiency because the procedure of finite-element analysis coupled with microgenetic algorithm using six unknown parameters irrespective of the number of elements are considered. The validity of the technique is numerically verified using a set of dynamic data obtained from a simulation of the actual bridge modeled with a three-dimensional solid element. The numerical calculations show that the proposed technique is a feasible and practical method that can prove the exact location of a damaged region as well as inspect the complex distribution of deteriorated stiffness, although there is a modeling error between actual bridge results and numerical model results as well as a measurement error like uncertain noise in the response data.     

Uncertainty Analysis of Creep and Shrinkage Effects in Long-Span Continuous Rigid Frame of Sutong Bridge

The long-term behavior of long-span prestressed concrete continuous rigid-frame bridges is significantly sensitive to creep and shrinkage. Therefore, it is important to accurately estimate creep and shrinkage effects. This paper presents modified prediction models that are based on the creep and shrinkage models in the existing bridge code. These modified prediction models match well with the test results of the high-strength concrete used in the continuous rigid frame of the Sutong Bridge in China. Results indicate that the accuracy in predicting creep and shrinkage can be enhanced greatly by measuring short-term creep and shrinkage on the given concrete and by modifying the prediction model parameters accordingly. Subsequently, the probabilistic analysis method of structural creep and shrinkage effects was studied. Uncertainty analysis of time-dependent effects in the given bridge was performed using the modified model, and results were compared with field-test data. Two approaches for mitigating deflections that were used in the continuous rigid frame of the Sutong Bridge are introduced. Finally, the time-dependent deflection at the midspan attributable to creep and shrinkage was analyzed.     

Simulating Seismic Response of Cantilever Retaining Walls

Many failures of retaining walls during earthquakes occurred near waterfront. A reasonably accurate evaluation of earthquake effects under such circumstance requires proven analytical models for dynamic earth pressure, hydrodynamic pressure, and excess pore pressure. However, such analytical procedures, especially for excess pore pressure, are not available and hence comprehensive numerical procedures are needed. This paper presents the results of a finite-element simulation of a flexible, cantilever retaining wall with dry and saturated backfill under earthquake loading, and the results are compared with that of a centrifuge test. It is found that bending moments in the wall increased significantly during earthquakes both when backfill is dry or saturated. After base shaking, the residual moment on the wall was also significantly higher than the moment under static loading. Liquefaction of backfill soil contributed to the failure of the wall, which had large outward movement and uneven subsidence in the backfill. The numerical simulation was able to model quite well the main characteristics of acceleration, bending moment, displacement, and excess pore pressure recorded in the centrifuge test in most cases with the simulation for dry backfill slightly better than that for saturated backfill.     

Sensitivity of Seismic Applications to Different Shape Memory Alloy Models

Shape memory alloys (SMAs) are known for their superelastic properties, which have been exploited in numerous applications in the biomedical, aerospace, and commercial fields. More recently, these materials have been evaluated for applications in the area of earthquake engineering. One key question that arises when using these materials is the appropriate constitutive material model to use to capture the highly nonlinear behavior of SMAs. This paper explores the effect of using different SMA constitutive models on the resulting response of systems using SMAs. A sensitivity analysis is conducted by using three SMA models with various levels of complexity. The models are implemented in a single-degree-of-freedom system and subjected to three groups of earthquake records with various characteristics. Considering a more accurate trend in modeling incomplete cycles in SMAs has little impact on the structural response. The strength degradation and residual deformation seem to be of more importance than the sublooping behavior. The response is more sensitive to the cyclic effects in the case of records with long durations or large intensities.     

Dynamic Response of a Highway Bridge Subjected to Moving Vehicles

Several full-scale load tests were performed on a selected Florida highway bridge. The bridge was dynamically excited by two fully loaded trucks, and the strain, acceleration, and displacement at selected points were recorded for the investigation of the bridge’s dynamic response. Experimental data were compared with simplified vehicle and bridge finite-element models. The vehicle was represented as a three-dimensional mass–spring–damper system with 11?degrees of freedom, and the bridge was modeled as a combination of plate and beam elements that characterize the slab and girders, respectively. The equations of motion were formulated with physical components for the vehicle and modal components for the bridge. The coupled equations were solved using a central difference method. It was found that the numerical analysis matched well with the experimental data and was used to successfully explain critical dynamic phenomena observed during the testing. Impact factors for this tested bridge were thoroughly investigated by using these models.     

Numerical Study of Reinforced Soil Segmental Walls Using Three Different Constitutive Soil Models

A numerical finite-difference method (FLAC) model was used to investigate the influence of constitutive soil model on predicted response of two full-scale reinforced soil walls during construction and surcharge loading. One wall was reinforced with a relatively extensible polymeric geogrid and the other with a relatively stiff welded wire mesh. The backfill sand was modeled using three different constitutive soil models varying as follows with respect to increasing complexity: linear elastic-plastic Mohr-Coulomb, modified Duncan-Chang hyperbolic model, and Lade’s single hardening model. Calculated results were compared against toe footing loads, foundation pressures, facing displacements, connection loads, and reinforcement strains. In general, predictions were within measurement accuracy for the end-of-construction and surcharge load levels corresponding to working stress conditions. However, the modified Duncan-Chang model which explicitly considers plane strain boundary conditions is a good compromise between prediction accuracy and availability of parameters from conventional triaxial compression testing. The results of this investigation give confidence that numerical FLAC models using this simple soil constitutive model are adequate to predict the performance of reinforced soil walls under typical operational conditions provided that the soil reinforcement, interfaces, boundaries, construction sequence, and soil compaction are modeled correctly. Further improvement of predictions using more sophisticated soil models is not guaranteed.