Analytical Modeling, System Identification, and Tracking Performance of Uniaxial Seismic Simulators

This technical note presents a simplified approach to reproducing historical earthquake records using uniaxial seismic simulators. Although complex, real-time feedback control systems may be utilized to control such simulators, it is shown herein that the application of a simple, off-line correction procedure is adequate for producing reasonable reproductions of historical earthquakes. An analytical model which describes the dynamic properties of a uniaxial seismic simulator is formulated in the frequency domain and calibration of the analytical model is performed via experimental system identification testing. It is shown that the model and identified properties are valid over a practical range of frequencies of motion. The analytical model is subsequently utilized in the implementation of an off-line correction procedure to improve the dynamic tracking performance of the seismic simulator. The effectiveness of the procedure is demonstrated by comparing motion of the simulator using both uncorrected and corrected command signals that correspond to historical earthquake records. The results show that the analytical model developed is adequate for describing the dynamic behavior of the seismic simulator and that the application of a simple, off-line correction procedure improves the dynamic tracking performance of the simulator.     

Effect of Asynchronous Earthquake Motion on Complex Bridges. I: Methodology and Input Motion

Based on observed damage patterns from previous earthquakes and a rich history of analytical studies, asynchronous input motion has been identified as a major source of unfavorable response for long-span structures, such as bridges. This study is aimed at quantifying the effect of geometric incoherence and wave arrival delay on complex straight and curved bridges using state-of-the-art methodologies and tools. Using fully parametrized computer codes combining expert geotechnical and earthquake structural engineering knowledge, suites of asynchronous accelerograms are produced for use in inelastic dynamic analysis of the bridge model. Two multi-degree-of-freedom analytical models are analyzed using 2,000 unique synthetic accelerograms with results showing significant response amplification due to asynchronous input motion, demonstrating the importance of considering asynchronous seismic input in complex, irregular bridge design. The paper, Part 1 of a two-paper investigation, presents the development of the input motion sets and the modeling and analysis approach employed, concluding with sample results. Detailed results and implications on seismic assessment are presented in the companion paper: Effect of Asynchronous Motion on Complex Bridges. Part II: Results and Implications on Assessment.     

Seismic Design of Flexible Cantilevered Retaining Walls

In this paper, the seismic behavior of embedded cantilevered retaining walls in a coarse-grained soil is studied with a number of numerical analyses, using a nonlinear hysteretic model coupled with a Mohr-Coulomb failure criterion. Two different seismic inputs are used, consisting of acceleration time histories recorded at rock outcrops in Italy. The numerical analyses are aimed to investigate the dynamic behavior of this class of retaining walls, and to interpret this behavior with a pseudostatic approach, in order to provide guidance for design. The role of the wall stiffness on the dynamic response of the system is investigated first. Then, the seismic performance of the retaining walls under severe seismic loading is investigated, exploring the possibility of designing the system in such a way that during the earthquake the strengths of both the soil and the retaining walls are mobilized. In this way, an economic design criterion may be developed, that relies on the ductility of the system, as it is customary in the seismic design of structures.     

Dynamic Behavior of Steel Deck Tension-Tied Arch Bridges to Seismic Excitation

The dynamic responses of steel deck, tension-tied, arch bridges subjected to earthquake excitations were investigated. The 620 ft (189 m) Birmingham Bridge, located in Pittsburgh, was selected as an analytical model for the study. The bridge has a single deck tension-tied arch span and is supported by two bridge piers, which in turn are supported by the pile foundations. Due to the complex configuration of the deck system, two analytical models were considered to represent the bridge deck system. Using the normal mode method, seismic responses were calculated for two bridge models and the results were compared with each other. Three orthogonal records of the El Centro 1940 earthquake were used as input for the seismic response analysis. The modal contributions were also checked in order to obtain a reasonable representation of the response and to minimize computational cost. Displacements and stresses at the panel points of the bridge are calculated and presented in graphical form.     

Ground motion spatial variability effects on seismic response control of cable-stayed bridges

The spatial variability of input ground motion at supporting foundations plays a key role in the structural response of cable-stayed bridges (CSBs); therefore, spatial variation effects should be included in the analysis and design of effective vibration control systems. The control of CSBs represents a challenging and unique problem, with many complexities in modeling, control design and implementation, since the control system should be designed not only to mitigate the dynamic component of the structural response but also to counteract the effects of the pseudo-static component of the response. The spatial variability effects on the feasibility and efficiency of seismic control systems for the vibration control of CSBs are investigated in this paper. The assumption of uniform earthquake motion along the entire bridge may result in quantitative and qualitative differences in seismic response as compared with those produced by uniform motion at all supports. A systematic comparison of passive and active system performance in reducing the structural responses is performed, focusing on the effect of the spatially varying earthquake ground motion on the seismic response of a benchmark CSB model with different control strategies, and demonstrates the importance of accounting for the spatial variability of excitations.     

Effects of Pier and Deck Flexibility on the Seismic Response of Isolated Bridges

The seismic response of bridges isolated by elastomeric bearings and the sliding system is investigated under two horizontal components of real earthquake ground motions. The selected bridges consist of multispan continuous deck supported on the piers and abutments. Three different mathematical models of the isolated bridge are considered for the analytical seismic response by considering and ignoring the flexibility of the deck and piers. The mathematical formulation for seismic response analysis of various mathematical models of the bridges isolated by different isolation systems is presented. The accuracy and computational efficiency of various mathematical models of isolated bridges is investigated by comparing their responses under different system parameters and earthquake ground motions. The important parameters selected are the flexibility of deck, piers, and isolation systems. There was significant difference in the computational time required for different models, but it was observed that the seismic response of the bridges obtained from different equivalent mathematical models is quite comparable even for an unsymmetrical bridge. Thus, the earthquake response of a seismically isolated bridge can be effectively obtained by modeling it as a single-degree-of-freedom system (i.e., considering the piers and deck as rigid) supported on an isolation system in two horizontal directions.     

Variational Solutions for Externally Induced Sloshing in Horizontal-Cylindrical and Spherical Vessels

A mathematical model is developed for calculating linear sloshing effects in the dynamic response of horizontal-cylindrical and spherical liquid containers under external excitation, with emphasis on earthquake excitation. The velocity potential is expressed in a series form, where each term is the product of a time function and the associated spatial function. Because of the configuration of the containers, the associated spatial functions are nonorthogonal and the problem is not separable, resulting in a system of coupled nonhomogeneous ordinary linear differential equations of motion. The solution can be obtained through either direct integration or modal analysis. Particular emphasis is given on the rate of convergence of the solution. The cases of half-full cylinders and spheres are examined in detail, where explicit expressions for the coefficients of the governing equations are derived. Using the proposed methodology, sloshing frequencies and masses are calculated rigorously for arbitrary liquid height of horizontal-cylindrical or spherical containers, and the response under two characteristic seismic events is obtained. The results describe the linear dynamic response of such containers and can be used for an efficient seismic analysis and design of industrial pressure vessels.     

某尾矿坝三维动力响应分析

针对尾矿坝的动力响应问题,基于完全非线性动力分析理论,采用Flac3D软件,分析计算了某尾矿库1#副坝地震响应,获得了该尾矿坝在地震作用下的加速度放大系数、动位移及库区液化的动力响应特性。结果表明:在动力荷载作用下,坝体竖直方向和水平方向加速度放大系数分别为1. 47和2. 91,具有较大的安全储备;坝体水平方向位移变化不大,且液化范围较小,不影响尾矿坝的整体稳定性。     

Assessment of seismic design response factors of concrete wall buildings

To verify the seismic design response factors of high-rise buildings, five reference structures, varying in height from 20- to 60-stories, were selected and designed according to modem design codes to represent a wide range of concrete wall structures. Verified fiber-based analytical models for inelastic simulation were developed, considering the geometric nonlinearity and material inelasticity of the structural members. The ground motion uncertainty was accounted for by employing 20 earthquake records representing two seismic scenarios, consistent with the latest understanding of the tectonic setting and seismicity of the selected reference region (UAE). A large number of Inelastic Pushover Analyses (IPAs) and Incremental Dynamic Collapse Analyses (IDCAs) were deployed for the reference structures to estimate the seismic design response factors. It is concluded that the factors adopted by the design code are adequately conservative. The results of this systematic assessment of seismic design response factors apply to a wide variety of contemporary concrete wall buildings with various characteristics.     

Seismic Earth Pressures on Cantilever Retaining Structures

An experimental and analytical program was designed and conducted to evaluate the magnitude and distribution of seismically induced lateral earth pressures on cantilever retaining structures with dry medium dense sand backfill. Results from two sets of dynamic centrifuge experiments and two-dimensional nonlinear finite-element analyses show that maximum dynamic earth pressures monotonically increase with depth and can be reasonably approximated by a triangular distribution. Moreover, dynamic earth pressures and inertia forces do not act simultaneously on the cantilever retaining walls. As a result, designing cantilever retaining walls for maximum dynamic earth pressure increment and maximum wall inertia, as is the current practice, is overly conservative and does not reflect the true seismic response of the wall-backfill system. The relationship between the seismic earth pressure increment coefficient (ΔKAE) at the time of maximum overall wall moment and peak ground acceleration obtained from our experiments suggests that seismic earth pressures on cantilever retaining walls can be neglected at accelerations below 0.4 g. This finding is consistent with the observed good seismic performance of conventionally designed cantilever retaining structures.     

Transient Dynamics of Stochastically Parametered Beams

The problem of determining the statistics of the transient response of randomly inhomogeneous beams is formulated. This is based on the use of stochastic dynamic stiffness coefficients in conjunction with the fast Fourier transform algorithm. The dynamic stiffness coefficients, in turn, are determined using a stochastic finite-element formulation that employs frequency-dependent shape functions. The approach is illustrated by analyzing the response of a random rod subject to a boxcar type of axial impact and, also, by considering the flexural response of a randomly inhomogeneous beam resting on a randomly varying Winkler's foundation and subjected to the action of a moving force. A discussion on the treatment of system property random fields as being non-Gaussian in nature is presented. Also discussed are the methods for handling nonzero initial conditions within the framework of the frequency domain response analysis employed in the study. Satisfactory comparisons between the analytical results and simulation results are demonstrated.     

Effect of Asynchronous Earthquake Motion on Complex Bridges. II: Results and Implications on Assessment

Nonuniform seismic excitation has been shown through previous analytical studies to adversely affect the response of long-span bridge structures. To further understand this phenomenon, this study investigates the response of complex straight and curved long-span bridges under the effect of parametrically varying asynchronous motion. The generation process and modeling procedures are presented in a companion paper. A wide-ranging parametric study is performed aimed at isolating the effect of both bridge curvature and the two main sources of asynchronous strong motion: geometric incoherence and the wave-passage effect. Results from this study indicate that response for the 344?m study structure is amplified significantly by nonsynchronous excitation, with displacement amplification factors between 1.6 and 3.4 for all levels of incoherence. This amplification was not constant or easily predicable, demonstrating the importance of inelastic dynamic analysis using asynchronous motion for assessment and design of this class of structure. Additionally, deck stiffness is shown to significantly affect response amplification, through response comparison between the curved and an equivalent straight bridge. Study results are used to suggest an appropriate domain for consideration of asynchronous excitation, as well as an efficient methodology for analysis.     

Numerical Evaluation of Adaptive Base-Isolated Structures Subjected to Earthquake Ground Motions

In this study, the seismic response of a scale-model, base-isolated, multistory structure is numerically investigated. At the isolation level, the structure is equipped with isolation bearings combined with adaptive (semiactive) fluid dampers. The behavior of the dampers is controlled according to an H∞ optimal feedback control algorithm which utilizes a fuzzy logic approach to establish weighting functions. Numerical simulations are performed to evaluate the dynamic response of the isolated test structure when different damping mechanisms (passive, semiactive, or active) are incorporated within the isolation system. The numerical simulations indicate that, in comparison to an isolation system with high passive damping, an isolation system with semiactive damping can be effective in simultaneously controlling the response of the structure while limiting the isolation system response.     

Dynamic Behavior of Reinforced Concrete Beams Strengthened with Composite Materials

The dynamic behavior of reinforced concrete (RC) beams strengthened with externally bonded composite materials is analytically investigated. The analytical model is based on dynamic equilibrium, compatibility of deformations between the structural components (RC beam, adhesive, composite material) and the concept of the high order approach. The equations of motion along with the boundary and continuity conditions are derived using Hamilton’s variational principle and the kinematic relations of small deformations. The mathematical formulation also includes the constitutive laws that are based on beam and lamination theories, and the two-dimensional elasticity representation of the adhesive layer including the closed form solution of its stress and displacement fields. The Newmark time integration method, which is directly applied to the resulting set of coupled partial differential equations, is adopted. This procedure yields a set of ordinary differential equations, which are analytically or numerically solved in every time step. The response of a strengthened beam to different dynamic loads that include impulse load, harmonic load, and seismic base excitation is numerically investigated. The numerical study highlights some of the phenomena associated with the dynamic response and explores the capabilities of the proposed model. The paper closes with a summary and conclusions.     

Free Out-of-Plane Vibrations of Masonry Walls Strengthened with Composite Materials

The natural frequencies and the out-of-plane vibration modes of one-way masonry walls strengthened with composite materials are studied. Due to the inherent nonlinear behavior of the masonry wall, the dynamic characteristics depend on the level of out-of-plane load (mechanical load or forced out-of-plane deflections) and the resulting cracking, nonlinear behavior of the mortar material, and debonding of the composite system. In order to account for the nonlinearity and the accumulation of damage, a general nonlinear dynamic model of the strengthened wall is developed. The model is mathematically decomposed into a nonlinear static analysis phase, in which the static response and the corresponding residual mechanical properties are determined, and a free vibration analysis phase, in which the dynamic characteristics are determined. The governing nonlinear differential equations of the first phase, the linear differential eigenvalue problem corresponding to the second phase, and the solution strategies are derived. Two numerical examples that examine the capabilities of the model and study the dynamic properties of the strengthened wall are presented. The model is supported and verified through comparison with a step-by-step time integration analysis, and comparison with experimental results of a full-scale strengthened wall under impulse loading. The results show that the strengthening system significantly affects the natural frequencies of the wall, modifies its modes of vibration, and restrains the deterioration of the dynamic properties with the increase of load. The quantification of these effects contributes to the understanding of the performance of damaged strengthened walls under dynamic and seismic loads.     

Decoupling Criteria for Inelastic Irregular Primary/Secondary Structural Systems Subject to Seismic Excitation

The present work deals with the dynamic response of structures that are irregular in height, consisting of two parts, a lower part made of concrete and an upper part made of steel. Irregularity is due to different dynamic responses of the two parts, here expressed by their different damping ratios and inelastic material laws. The seismic design of such structures is not satisfactorily covered by current design codes, especially if a decoupled procedure is chosen for the analysis, where the lower part is excited first and its response is used as excitation for the upper part. The present paper aims at contributing toward better understanding of the interaction between the two parts and at proposing improved decoupling criteria for the seismic analysis of inelastic primary-secondary systems. Toward that goal, each part is modeled as a one-degree-of-freedom system, and the maximum responses of coupled and decoupled inelastic time history analyses are compared over a wide range of dynamic characteristics and strength levels of the two parts. The results are presented in the form of error levels between the two alternative analysis procedures.     

Dynamic and Seismic Analysis of Foundations based on Free Field B-Spline Characteristic Response Histories

A direct time domain formulation for the analysis of unbounded media and foundations is developed that treats dynamic excitations and ground motion in a uniform manner. The method uses the boundary element method with higher order B-Spline fundamental solutions to compute the characteristic responses of the surface of the elastodynamic domain. Subsequently, time histories of the system response to general excitations are computed by a mere superposition scheme that accommodates in a uniform manner arbitrary time histories of external loads and/or ground motion. The characteristic responses are computed in the form of time dependent flexibility matrices of the medium that are sparse due to the finite duration of the B-Spline excitation signal and the characteristics of the wave propagation. The duration of the B-Spline impulse response is limited to only a few time steps. Consequently, significant savings in computing time and storage requirements are achieved. Furthermore, the characteristic responses do not depend on the type or wave form of the actual external excitations and the presence of rigid foundations. This is a significant advantage when the response of a system to excitations of long duration is to be computed. In addition, the proposed approach significantly reduces the size of the problems under consideration and yet fully considers the effects of the free field. The significance of nonrelaxed boundary conditions and correct representation of the free field is established. The method is demonstrated and validated through applications pertaining to the analysis of foundations and inclusions subjected to transient loads and seismic excitations.     

Property Modification Factors for Seismically Isolated Bridges

An analytical study investigating how changes in the mechanical properties of individual seismic isolators affect the response of isolated bridge structures subjected to earthquake excitation is summarized. Nonlinear response-history analyses are conducted utilizing bins of recorded earthquake ground motion pairs. Twenty bilinear isolation systems are considered so that the results of this study are broadly applicable to the design of seismic isolation systems in the United States. Variations in the mechanical properties are considered using a property modification factor, λ, to modify the appropriate bilinear isolator parameter. The results of analyses considering nominal and modified isolation systems are used to systematically identify changes in system response as a function of the property modification factor. These results are used to determine threshold values of the property modification factor that should aid engineers in the preliminary design and assessment of an isolation system prior to performing the bounding analysis now required by bridge and building design codes.     

Special Studies for Vasco da Gama Bridge

The importance and structural characteristics of the Vasco da Gama Bridge led to the development of some special studies to achieve a more detailed analysis of its structural behavior. The studies reported in this paper concern the following subjects: (1) Analysis of the behavior of the deck under a “design ship fire”; (2) study of an elastoplastic damping system to control the seismic response; and (3) analysis of the aerodynamic behavior of the bridge (computational fluid dynamics analysis of the deck and dynamic analyses of the structure to assess the effects of wind gusts). These studies gave technical support to some important decisions that were undertaken, such as the installation of two vertical baffles under the deck to improve the aerodynamic stability and eight hysteretic damping devices in the connections between the deck and the towers to reduce the seismic displacements.