Blast Limits for Transmission Structures. I: Response Spectra Development

To develop a defense strategy to protect power transmission lines against blast-induced ground motions, an understanding of the dynamic responses of these structures must be first established. This paper presents the results from ground motion monitoring at two blast sites in southern United States. These studies are being conducted as part of a research effort to establish strong ground motion characteristics necessary for developing blast limits for power transmission systems. Ground movements caused by the surface mining blast and quarry blasting were recorded using geophones and wireless triaxial sensing units. The process of establishing the ground motion response spectra via analyzing actual ground motion measurements, including noise filtration and signal processing, is then described. These ground motion response spectra are the necessary inputs for spectrum analysis of structural responses that can be used to establish ground vibration limits.     

Response Spectrum Analysis of Suspension Bridges for Random Ground Motion

The response spectrum method of analysis for suspension bridges subjected to multicomponent, partially correlated stationary ground motion is presented. The analysis is based on the relationship between the power spectral density function and the response spectrum of the input ground motion and fundamentals of the frequency domain spectral analysis. The analysis duly takes into account the spatial correlation of ground motions between the supports, the quasi-static component of the response, and the modal correlation between different modes of vibration. A suspension bridge is analyzed under a set of important parametric variations in order to (1) compare between the responses obtained by the response spectrum method of analysis and the frequency domain spectral analysis; and (2) investigate the behavior of suspension bridges under seismic excitation. The parameters include the spatial correlation of ground motion, the angle of incidence of the earthquake, the ratio between the three components of ground motion, the number and nature of modes considered in the analysis, and the nature of the power spectral density function of ground motion. It is shown that the response spectrum method of analysis provides a fair estimate of responses under parametric variations considered in the study.     

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.     

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.     

Nonlinear Aeroelastic Simulation of a Full-Span Aircraft with Oscillating Control Surfaces

In this paper, the transonic and low-supersonic aeroelastic behavior of the generic fighter model was investigated in the time domain. The simulation of flutter flight test using forced harmonic motion of control surfaces including inertial coupling effects was conducted at the various conditions. The detailed dynamic aeroelastic responses are computed using a coupled time-marching method based on the effective computational structural dynamic and computational fluid dynamics techniques. The nonlinear aerodynamic effects due to an existing shock wave on the lifting surfaces were considered using a transonic small disturbance equation. A modal model obtained by a free vibration analysis was used for the structural model. The relations between the computed flutter boundary and the simulation results of the responses using the harmonic motions of control surfaces at various conditions were investigated.     

Effects of Space Distribution of Excitation on Seismic Response of Arch Dams

The effects of the ground motion spatial variation and of the canyon geometry on the dynamic response of arch dams during the event of an earthquake is studied in this paper. The seismic response of a dam subject to time harmonic longitudinal, shear, and Rayleigh waves impinging the dam site from different directions is analyzed. Several canyon and reservoir geometries are considered. A three-dimensional boundary element model which allows for the rigorous representation of the dynamic interaction between the dam, the foundation rock, and the water is used. The foundation rock is modeled as a uniform viscoelastic boundless domain where the incident traveling wave field is defined by its analytical expression, which may include any spatial variation. The obtained results show the importance of three-dimensional effects which are many times neglected.     

Seismic Vulnerability and Mitigation during Construction of Cable-Stayed Bridges

The implications of earthquake loading during balanced cantilever construction of a cable-stayed bridge are examined. Finite-element models of a cable-stayed bridge were developed and multiple ground motion time history records were used to study the seismic response at the base of the towers for six stages of balanced cantilever construction. Probabilistic seismic hazard relationships were used to relate ground motions to bridge responses. The results show that there can be a high probability of having seismic responses (forces/moments) in a partially completed bridge that exceed, often by a substantial margin, the 10%/50-year design level (0.21% per annum) for the full bridge. The maximum probability of exceedance per annum was found to be 20%. This occurs because during balanced-cantilever construction the structure is in a particularly precarious and vulnerable state. The efficacy of a seismic mitigation strategy based on the use of tie-down cables intended for aerodynamic stability during construction was investigated. This strategy was successful in reducing some of the seismic vulnerabilities so that probabilities of exceedance during construction dropped to below 1% per annum. Although applied to only one cable-stayed bridge, the same approach can be used for construction-stage vulnerability analysis of other long-span bridges.     

Simplified Procedure for Estimating Earthquake-Induced Deviatoric Slope Displacements

A simplified semiempirical predictive relationship for estimating permanent displacements due to earthquake-induced deviatoric deformations is presented. It utilizes a nonlinear fully coupled stick-slip sliding block model to capture the dynamic performance of an earth dam, natural slope, compacted earth fill, or municipal solid-waste landfill. The primary source of uncertainty in assessing the likely performance of an earth/waste system during an earthquake is the input ground motion. Hence, a comprehensive database containing 688 recorded ground motions is used to compute seismic displacements. A seismic displacement model is developed that captures the primary influence of the system’s yield coefficient (ky), its initial fundamental period (Ts), and the ground motion’s spectral acceleration at a degraded period equal to 1.5Ts. The model separates the probability of “zero” displacement (i.e., ? 1?cm) occurring from the distribution of “nonzero” displacement, so that very low values of calculated displacement do not bias the results. The use of the seismic displacement model is validated through reexamination of 16 case histories of earth dam and solid-waste landfill performance. The proposed model can be implemented rigorously within a fully probabilistic framework or used deterministically to evaluate seismic displacement potential.     

Investigation of Foundation Vibrations Resting on a Layered Soil System

This paper presents an investigation of the dynamic response of foundations resting on a layered soil underlain by a rigid layer. Model block vibration test results are used for the investigation. For the analysis, two different methods, namely, the equivalent spring-mass-dashpot model and the cone model, are used. A simple method to estimate the equivalent stiffness of the foundations resting on any multilayered soil system is presented. Obtaining stiffness from the proposed method and using different values of the damping factor ranging between 1.5 and 10.0%, the dynamic response of a foundation resting on a layered soil system is computed. One-dimensional wave propagation in an elastic cone for the analysis of foundations resting on the elastic homogeneous half-space or layered soil is also used to compute dynamic responses of the foundations resting on different layered soil. Finally, results obtained from two analytical methods are compared with the test results. It has been observed from the comparison that the results obtained by the equivalent spring-mass-dashpot model with a damping factor of 1.5% matched well with the experimental results for all cases. Results obtained by the cone model match well with experimental results for the cases where the top layer is softer than the bottom layer.     

Data Reduction of Horizontal Load Full-Scale Tests on Bored Concrete Piles and Pile Groups

This paper proposes a new approach for data reduction of horizontal load full-scale tests on piles and pile groups. This approach has been developed on results from tests run on bored concrete piles embedded in homogeneous and nonhomogeneous ground. Due to nonlinear response of pile material and also to nonhomogeneous embedding ground, the problem of fitting reliable curves for representing strains along shafts is increased. It is suggested that B-splines fixed by a weighted least-squares algorithm should be used to overcome that problem. Taking advantage of the mathematical properties of B-splines, an algorithm for computing the internal force distribution amongst pile heads direct from test results is also proposed for pile groups. It is shown that the integration of the curvatures to compute pile movements should be done using natural boundary conditions instead of pile head measurements whenever possible. Despite the concrete crack, the distribution of bending moments can be computed from curvatures provided a reliable reinforced concrete model is used. Finally, it is proposed to compute the soil reactions by the integration of bending moments, solving an integral equation by again using B-spline functions.     

Site-Specific Validation of Random Vibration Theory-Based Seismic Site Response Analysis

Seismic site response analysis is typically performed using a suite of rock acceleration-time histories prescribed at the base of a soil column and propagated to the ground surface. To develop statistically stable estimates of the site response, a large number of input motions are required. Alternatively, random vibration theory (RVT) can be used to predict statistically stable estimates of the surface response spectrum in one analysis without the need to prescribe the input rock motion in the time domain. Thus, the critical and time consuming activity of choosing appropriate input ground motions and fitting them to a target spectrum is avoided. This paper describes the RVT approach, its analytical background and input requirements, and provides a site-specific validation of the procedure against traditional site response predictions. The single-corner frequency Brune source spectrum is used in the RVT procedure to describe the input motion in the frequency domain. RVT site response predictions using the Brune spectrum as input are compared with those from traditional site response analyses that incorporate different suites of input rock motions. Results indicate that RVT site response analysis can provide a response spectrum that is similar to the median response spectrum from analyses performed using a suite of input rock motions. However, the favorable comparison is obtained only when the seismological parameters used to describe the RVT input motion are carefully chosen to be consistent with the suite of input rock motions.     

Random Plastic Analysis Using a Constitutive Model to Predict the Evolutionary Stress-Related Responses and Time Passages to Failure

The random vibration analyses of gradually yielding shear-frame buildings are considered using a recently proposed constitutive model that is used to calculate the detailed degradation of the stiffness of structures which permits the prediction of their global responses, as well as the states of stress in their members. It is shown that the detailed stress degradation model can also be used in connection with a global force-displacement model, such as the Bouc and Wen model, to predict the time evolution of the various stress-related variables and time passages to failure. The two models are applied in separate analyses and are exemplified using both a single-story building and a four-story building subjected to artificial ground motions. The corresponding probability density functions of the various stress-related responses, including the strains and plastic hinge lengths, and the first time passages to failure are presented and discussed.     

Effects of Mine Blasting on Residential Structures

Blasting is common in the coal industry to remove rock overburden so that the exposed coal can be mechanically excavated. The ground vibrations and air blast produced by blasting are often felt by residents surrounding the mines. There has been a trend for regulatory authorities, especially those concerned with the environment, to impose low limits on blast vibration levels in response to community pressure, based on human perception and response to vibration. This paper reports the findings of an extensive study on a house which was located adjacent to a coal mine. The house was monitored for over 1?year and was subjected to ground peak particle velocity (PPV) ranging from 1.5?to?222?mm/s. The house was instrumented with accelerometers to measure its dynamic response due to blasting and it was also monitored for cracks before and after each blast. Based on this study, ground motion amplifications along the height of the structure have been established. A simplified methodology presented in this paper has been used to estimate the ground PPV at which cracking is likely.     

Generalized Bouc–Wen Model for Highly Asymmetric Hysteresis

Bouc–Wen class models have been widely used to efficiently describe smooth hysteretic behavior in time history and random vibration analyses. This paper proposes a generalized Bouc–Wen model with sufficient flexibility in shape control to describe highly asymmetric hysteresis loops. Also introduced is a mathematical relation between the shape-control parameters and the slopes of the hysteresis loops, so that the model parameters can be identified systematically in conjunction with available parameter identification methods. For use in nonlinear random vibration analysis by the equivalent linearization method, closed-form expressions are derived for the coefficients of the equivalent linear system in terms of the second moments of the response quantities. As an example application, the proposed model is successfully fitted to the highly asymmetric hysteresis loops obtained in laboratory experiments for flexible connectors used in electrical substations. The model is then employed to investigate the effect of dynamic interaction between interconnected electrical substation equipment by nonlinear time-history and random vibration analyses.     

轧机主传动系统的扭振分析与建模

利用拉格朗日方程建立了传动系统扭转振动分析的通用数学模型,进行了系统固有模态分析;依据动力学理论知识,求解不同的加载方式下系统的动态响应,获得了扭转振动的扭矩放大倍数,并对系统进行了灵敏度分析。在此基础上,以某轧机的主传动系统为例,求解出系统的扭振特性的关键参数,并与试验结果作对比分析。计算表明,应用该方法分析系统的扭振特性是行之有效的。     

Numerical Modeling of Seismic Response of Rigid Foundation on Soft Soil

A numerical model was developed to simulate the response of two instrumented, centrifuge model tests on soft clay and to investigate the factors that affect the seismic ground response. The centrifuge tests simulated the behavior of a rectangular building on 30?m uniform and layered soft soils. Each test model was subjected to several earthquakelike shaking events at a centrifugal acceleration level of 80g. The applied loading involved scaled versions of an artificial western Canada earthquake and the Port Island ground motion recorded during the 1995 Kobe Earthquake. The centrifuge model was simulated with the three-dimensional finite-difference-based fast Lagrangian analysis of continua program. The results predicted with the use of nonlinear elastic–plastic model for the soil are shown to be in good agreement with measured acceleration, soil response, and structural behavior. The validated model was used to study the effect of soil layering, depth, soil–structure interaction, and embedment effects on foundation motion.     

Thermal-Structural Modeling and Temperature Control of Roller Compacted Concrete Gravity Dam

A coupled thermal-structural analysis is carried out using both a two- and a three-dimensional finite-element method. The computer program ANSYS is used and simulates the construction process of a roller compacted concrete (RCC) dam. Thermally induced stresses are computed for the 60 m high RCC Tannur Dam in Jordan. The actual temperature distribution in the body of the dam measured by thermocouples is compared with that obtained by ANSYS; generally, a good agreement is obtained. The study demonstrates that detailed thermal stress analysis should be performed for large RCC dams to provide a basis to minimize and control the occurrence of thermal cracking.     

Kinematic Soil-Structure Interaction from Strong Motion Recordings

Earthquake strong motion recordings from 29 sites with instrumented structures and free-field accelerographs are used to evaluate variations between foundation-level and free-field ground motions. The focus of the paper is on buildings with surface and shallowly embedded foundations. The foundation/free-field ground motion variations are quantified in terms of frequency-dependent transmissibility function amplitude ∣H∣. Procedures are developed to fit to ∣H∣ analytical models for base slab averaging for the assumed conditions of a rigid base slab and a vertically propagating, incoherent incident wave field characterized by ground motion incoherence parameter κ. The limiting assumptions of the model are not strictly satisfied for actual structures, and the results of the identification are apparent κ values (denoted κa) that reflect not only incoherence effects, but also possible foundation flexibility and wave inclination effects. Nonetheless, a good correlation is found between κa values and soil shear wave velocity for sites with stiff foundation systems. Based on these results, recommendations are made for modifying free-field ground motions to estimate base slab motions for use in response analyses of buildings.     

Active Control of Flexural Vibrations in Beams

The feasibility of using piezoelectric actuators to control the flexural oscillations of large structures in space is investigated. Piezoelectric actuators have the advantage of exerting localized bending moments. In this way, vibration is controlled without exciting rigid body modes in the structure. The actuators are used in collocated sensor∕driver pairs to form a feedback control system. The sensor produces a voltage that is proportional to the dynamic stress at the sensor location, and the driver produces a force that is proportional to the voltage applied to it. The analog control system amplifies and phase shifts the sensor signal to produce the voltage signal that drives the driver piezoelectric. The feedback control system is demonstrated to increase the first mode damping in a cantilever beam by up to 85%, depending on the amplifier gain. An analytical model of the control system is developed. The estimated and measured vibration control compare favorably. A simulated free‐free beam is fabricated and instrumented with a distribution of piezoelectric sensor∕driver pairs. The purpose is to evaluate the damping efficiency of the control system when the piezoelectrics are not optimally positioned at points of high stress in the beam. The control system is found to reduce the overall vibration response to impact by a factor of two.     

Earth Dam on Liquefiable Foundation and Remediation: Numerical Simulation of Centrifuge Experiments

A series of four dynamic centrifuge model tests was performed to investigate the effect of foundation densification on the seismic performance of a zoned earth dam with a saturated sand foundation. In these experiments, thickness of the densified foundation layer was systematically increased, resulting in a comprehensive set of dam-foundation response data. Herein, Class-A and Class-B numerical simulations of these experiments are conducted using a two-phase (solid and fluid) fully coupled finite element code. This code incorporates a plasticity-based soil stress–strain model with the modeling parameters partially calibrated based on earlier studies. The physical and numerical models both indicate reduced deformations and increased crest accelerations with the increase in densified layer thickness. Overall, the differences between the computed and recorded dam displacements are under 50%. At most locations, the computed excess pore pressure and acceleration match the recorded counterparts reasonably well. Based on this study, directions for further improvement of the numerical model are suggested.