Generalized Damped Wave Approach for Evaluating Seismic Shear Demands

This paper presents a new analytical approach for simple and explicit computation of the seismic base shear demand of structural systems that can be idealized by a uniform shear-beam model. The approach is based on a Green’s function representation for the relative displacement response that is assumed to be composed of exponentially decaying wave sequences. Explicit solutions for both the strain and displacement response are derived in terms of an effective ground velocity and displacement that can be computed incrementally from the ground acceleration. A physical interpretation for the damping mechanism is proposed. The method is further generalized to form a class of physically motivated shear-beam systems referred to as the continuous spring-dashpot (CSD) model. The response characteristics of three cases of the CSD model along with a shear beam equipped with a mass-proportional external damping are compared and discussed for the case of near-field earthquake excitation.     

Potential for Structural Failure in the Seismic Near Field

This study analyzes the possibility that large distortions and distortion rates due to wave-propagation phenomena within structures were responsible for unexpected cracking at connections of steel-frame buildings in the seismic near-field region during the Northridge (1994) and Kobe (1995) earthquakes. Since such internal wave propagation is characteristic of a structure with a continuous distribution of mass, the problem is studied by numerically simulating the structural response for both discrete and continuous models of a 20-story building, using ground motion time histories from the Northridge earthquake. The time histories are chosen from the far-field and near-field regions of the earthquake to determine if wave-propagation effects within the structure are especially significant in the near field. A truncated modal analysis is also performed using only the first vibrational mode to see if significantly lower response levels result. It is found that the continuous model gives higher response levels—indicating that wave propagation may have been a factor—but the discrepancy is not limited to the near field. Strain rates are higher from the continuous model than from the discrete model and much higher than from the truncated modal analysis, but the magnitudes are too low to be a significant factor in the observed damage. The explanation for the connection cracking may simply be high-intensity ground motion in the near field.     

Seismic Compression of Two Compacted Earth Fills Shaken by the 1994 Northridge Earthquake

Seismic compression is defined as the accrual of contractive volumetric strain in unsaturated soil during strong shaking by earthquakes. We document and analyze two case histories (denoted school site and site A) of ground deformation from seismic compression in canyon fills strongly shaken by the Northridge earthquake. Site A had ground settlements up to about 18 cm, which damaged a structure, while the school site had settlements up to about 6 cm. For each site, we perform decoupled analyses of shear and volumetric strain. Shear strain is calculated using one-dimensional and two-dimensional ground response analyses, while volumetric strain is evaluated from shear strain using material-specific models derived from simple shear laboratory testing that incorporates important effects of fines content and as-compacted density and saturation. Analyses are repeated using a logic tree approach in which weights are assigned to multiple possible realizations of uncertain model parameters. At the school site, predicted settlements appear to be unbiased. At site A, the analyses successfully predict the shape of the settlement profile along a section, but the weighted average predictions are biased slightly too low. We speculate that the apparent site A bias can be explained by limited resolution of the site stratigraphy, bias in laboratory-derived volumetric strain models, and/or uncertainty in the estimated earthquake-induced settlements.     

Nonlinear Identification of Lumped-Mass Buildings Using Empirical Mode Decomposition and Incomplete Measurement

Most structures exhibit some degrees of nonlinearity such as hysteretic behavior especially under damage. It is necessary to develop applicable methods that can be used to characterize these nonlinear behaviors in structures. In this paper, one such method based on the empirical mode decomposition (EMD) technique is proposed for identifying and quantifying nonlinearity in damaged structures using incomplete measurement. The method expresses nonlinear restoring forces in semireduced-order models in which a modal coordinate approach is used for the linear part while a physical coordinate representation is retained for the nonlinear part. The method allows the identification of parameters from nonlinear models through linear least-squares. It has been shown that the intrinsic mode functions (IMFs) obtained from the EMD of a response measured from a nonlinear structure are numerically close to its nonlinear modal responses. Hence, these IMFs can be used as modal coordinates as well as provide estimates for responses at unmeasured locations if the mode shapes of the structure are known. Two procedures are developed for identifying nonlinear damage in the form of nonhysteresis and hysteresis in a structure. A numerical study on a seven-story shear-beam building model with cubic stiffness and hysteretic nonlinearity and an experimental study on a three-story building model with frictional magnetoreological dampers are performed to illustrate the proposed method. Results show that the method can quite accurately identify the presence as well as the severity of different types of nonlinearity in the structure.     

Aerodynamic Coupling Effects on Flutter and Buffeting of Bridges

The effects of aerodynamic coupling among modes of vibration on the flutter and buffeting response of long-span bridges are investigated. By introducing the unsteady, self-excited aerodynamic forces in terms of rational function approximations, the equations of motion in generalized modal coordinates are transformed into a frequency-independent state-space format. The frequencies, damping ratios, and complex mode shapes at a prescribed wind velocity, and the critical flutter conditions, are identified by solving a complex eigenvalue problem. A significant feature of this approach is that an iterative solution for determining the flutter conditions is not necessary, because the equations of motion are independent of frequency. The energy increase in each flutter motion cycle is examined using the work done by the generalized aerodynamic forces or by the self-excited forces along the bridge axis. Accordingly, their contribution to the aerodynamic damping can be clearly identified. The multimode flutter generation mechanism and the roles of flutter derivatives are investigated. Finally, the coupling effects on the buffeting response due to self-excited forces are also discussed.     

Damping in Shear Beam Structures and Estimation of Drift Response

Under pulse-type ground motions modal analysis is not quite efficient for estimating the elastic response of multi-degree-of-freedom systems, in particular when the effects of higher modes are significant. This paper first shows that the assumption of nondispersive damped waves for shear beams leads to inconsistent response estimation. Subsequently, a closed form time domain dispersive damped wave solution to the partial differential equation of motion is presented and it is verified with frequency domain solutions. Finally, using the solutions to the differential equation of motion, the response of frame structures with energy dissipating devices is studied.     

On-Site Nonlinear Hysteresis Curves and Dynamic Soil Properties

Strong motion records at five vertical array sites in Japan are used to examine soil shear modulus and material damping as a function of shear strain during large earthquakes. Acceleration data from the sites are processed directly for evaluation of site shear stress-strain hysteresis curves for different time windows of the record. Results of the analysis demonstrate a significant nonlinear ground response at the sites with surface peak ground accelerations exceeding 90 gal. The results of shear stress-strain hysteresis curves are also used to estimate variation of soil shear modulus and material damping characteristics with shear strain amplitude at each site. The identified shear modulus-shear strain and damping ratio-shear strain relationships are in general agreement with published laboratory results. These response interpretations are also compared with the results of a frequency-domain analysis by using the spectral ratio (uphole∕downhole) technique. There is general agreement between the time- and frequency-domain results. The results illustrate the significance of the site nonlinearity during strong ground motions as well as the accuracy of the dynamic soil properties obtained from laboratory tests.     

Determination of Nonlinear Softening Behavior at FRP Composite/Concrete Interface

For concrete beams and slabs, the bonding of fiber reinforced plastic (FRP) plates to the bottom surface is an effective and efficient technique for flexural strengthening. Failure of strengthened members often occurs due to stress concentrations at the FRP/concrete interface. For debonding failure initiated at the bottom of shear or shear/flexural cracks in the concrete, experimental results clearly indicate a progressive failure process accompanied by gradual reduction in shear transfer capability at the interface. Several existing models for FRP debonding have taken interfacial shear softening into account. However, the assumed shear stress versus slip relations employed in the models have never been properly measured. In this investigation, a combined experimental/theoretical approach for the extraction of interfacial stress versus slip relation is developed. With loading applied to a bonded FRP plate, strain is measured at various points along its length. Based on the strain measurements, the interfacial softening curve is derived from a finite element analysis. The present paper will present the proposed approach in detail, demonstrate its application to typical experimental data, and discuss the implications of the results.     

Approximation of Nonlinear Unloading Effects in the Strain Rate Dependent Deformation Analysis of Polymer Matrix Materials Utilizing a State Variable Approach

An experimental and analytical program is carried out to explore key behaviors in the loading and unloading behavior of polymers. Specifically, the effects of strain rate and hydrostatic stresses on the nonlinear portions of the deformation response are examined. Tension, compression, and shear load only and load/unload tests are conducted on a representative polymer across a range of strain rates, and key features of the experimental results are identified. To conduct a preliminary exploration of how the key features of the deformation response could be simulated analytically, a previously developed set of constitutive equations, which were developed to analyze the strain rate dependent, nonlinear deformation of polymers including the effects of hydrostatic stresses, were modified in order to approximate key features of the nonlinear unloading behavior observed in the polymer. The constitutive relations are based on state variable constitutive equations originally developed for metals. The nonlinear unloading observed in the experiments is approximated by reducing the unloading modulus of the material as the effective inelastic strain is increased. The effects of the hydrostatic stress state on the unloading modulus are also simulated analytically. To examine the revised formulation, the loading and load/unload responses of the representative polymer in tension, compression, and shear are examined at several strain rates. Results computed using the developed constitutive equations were found to correlate reasonably well with the experimental data.     

Learning of Dynamic Soil Behavior from Downhole Arrays

An increasing number of downhole arrays are deployed to measure motions at the ground surface and within the soil profile. Measurements from these arrays provide an opportunity to improve site response models and to better understand underlying dynamic soil behavior. Parametric inverse analysis approaches have been used to identify constitutive model parameters to achieve a better match with field observations. However, they are limited by the selected material model. Nonparametric inverse analysis approaches identify averaged soil behavior between measurement locations. A novel inverse analysis framework, self-learning simulations (SelfSim), is employed to reproduce the measured downhole array response while extracting the underlying soil behavior of individual soil layers unconstrained by prior assumptions of soil behavior. SelfSim is successfully applied to recordings from Lotung and La Cienega. The extracted soil behavior from few events can be used to reliably predict the measured response for other events. The field extracted soil behavior shows dependencies of shear modulus and damping on cyclic shear strain level, number of loading cycles, and strain rate that are similar qualitatively to those reported from laboratory studies but differ quantitatively.     

Flow Resistance over Mobile Bed in an Open-Channel Flow

This paper deals with the underlying mechanism of flow resistance in an alluvial channel: The effects of sidewall and bed form on flow resistance, Einstein’s divided hydraulic radius approach and Engelund’s energy slope division approach are reexamined. These two approaches assume that the shear stress on a mobile bed is the summation of shear stresses caused by skin friction and bed form. Using a different approach, this paper presents a theoretical relationship between the total bed shear stress with grain and bed-form shear stresses. The contribution of sidewall on the total bed shear stress is also discussed. The writers found that the size of bed form plays a significant role for the flow resistance, and developed relevant expressions for the length of the separation zone behind the bed forms. In addition, a systematical approach has been developed to compute the flow velocity in an alluvial channel. This approach is tested and verified against 5,989 flume and field measurements. The computed and measured discharge/velocity are in good agreement and 83.0% of all data sets fall within the ±20% error band.     

Quantification of Cable Deformation with Time Domain Reflectometry—Implications to Landslide Monitoring

Time domain reflectometry (TDR) technology has become a valuable tool for detecting displacements and locating shear planes in rock or soil slopes. It is based on transmitting an electromagnetic pulse into a coaxial cable grouted in rock or soil mass and watching for reflections of this transmission due to cable deformity induced by the ground deformation. Early detection of localized shear deformation in soft soils and quantifying the shear displacement using TDR remains a challenging work. The TDR response due to localized shear deformation is affected by cable resistance, soil-grout-cable interaction, and shear bandwidth. A comprehensive TDR wave propagation model considering cable resistance is introduced to model TDR response to cable deformity. Effects of the influencing factors on the relationship between the reflection spike and the shear displacement are investigated through laboratory tests and numerical simulations. The implications to enhancing TDR response and quantifying shear displacement are stressed. Practical suggestions are made, including procedure for correcting resistance effect, selection of cable and grout, and how to quantify shear displacement using TDR.     

Curved Sandwich Panels Subjected to Temperature Gradient and Mechanical Loads

The results of a detailed study of the nonlinear response of curved sandwich panels with composite face sheets, subjected to a temperature gradient through the thickness combined with mechanical loadings, are presented. The analysis is based on a first-order shear-deformation Sanders-Budiansky-type theory, including the effects of large displacements, moderate rotations, transverse shear deformation, and laminated anisotropic material behavior. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the panel. The nonlinear displacements, strain energy, principal strains, transverse shear stresses, transverse shear strain energy density, and their hierarchical sensitivity coefficients are evaluated. The hierarchical sensitivity coefficients measure the sensitivity of the nonlinear response to variations in the panel parameters, the effective properties of the face sheet layers and the core, and the micromechanical parameters. Numerical results are presented for cylindrical panels subjected to combined pressure loading, edge shortening or extension, edge shear, and a temperature gradient through the thickness. The results show the effects of variations in the loading and the panel aspect ratio, on the nonlinear response, and its sensitivity to changes in the various panel, effective layer, and micromechanical parameters.     

Active Vibration Damping of Composite Beam using Smart Sensors and Actuators

This paper discusses active vibration control of an E-glass/epoxy-laminated composite beam using smart sensors and actuators. The smart sensors and actuators used in this study are piezoelectric ceramic patches. The composite beam is in a cantilevered configuration. Both theoretical and numerical (finite-element analysis) studies of the laminated composite beam are conducted to reveal the beam’s fundamental modal frequencies and modal shapes. The results based on the theoretical predication and numerical simulation are then compared with those from experimental modal testing, and a good correlation is obtained. Utilizing results from the model analysis and experimental modal testing, two control algorithms, namely, positive position feedback control and strain rate feedback control, are designed. Both single-mode vibration suppression and multimode vibration suppression are studied. An experimental apparatus has been developed to implement the control algorithms. The apparatus consists of a voltage amplifier and a data acquisition and real-time control system, in addition to the composite beam with bonded piezoelectric ceramic sensors and actuators. Experiments show that the proposed controllers can achieve active vibration damping of the composite beam.     

Stress-Strain Responses of Block Samples of Compressible Chicago Glacial Clays

This paper presents the results and analysis of a laboratory investigation of the behavior of lightly overconsolidated compressible Chicago glacial clays over a wide strain range. Each specimen was trimmed from high quality block samples taken from an excavation in Evanston, Illinois. Specimens were instrumented with three sets of bender elements and local LVDTs. After K0 consolidation to the in situ vertical effective stress of the block, drained stress probe tests were conducted. Results of bender elements tests obtained prior to stress probing show that compressible Chicago glacial clay initially is cross anisotropic. Propagation velocities measured by bender elements in axial direction after K0 reconsolidation and drained creep agrees well with the in situ shear wave velocity measured by seismic cone penetration tests. Results of drained stress probe tests are analyzed in terms of shear, volumetric and coupled stiffness, stiffness degradation, and direction of loading. The significant variability of shear, bulk and cross-coupling response depending on stress path direction and strain level provide experimental evidence that the Chicago clays are incrementally nonlinear at the strain levels investigated.     

Online Earthquake Response Test for Stratified Layers of Clay and Sand

Artificial islands often consist of layers of alluvial clay and reclaimed soil of varying order and thickness. Soft clay layers have nonlinear characteristics and can both amplify and attenuate earthquake ground motions. Liquefied ground impedes propagation of shear waves and thus attenuates the earthquake accelerations. Online testing is a method of feeding soil response characteristics directly from soil samples into a modeling algorithm. The effects of the layer thickness, configuration, and degree of consolidation on the earthquake response characteristics of alternating layers of clay and sand have been investigated. The degree of liquefaction and strain generated in sand adjacent to clay layers increased with the degree of consolidation. Clay layers attenuate the motions of sand layers for short period vibrations but amplify the long period motions, increasing the strain in overlying liquefied sand layers. Clay layers which were closer to the ground surface or of greater thickness tended to increase the surface accelerations. Normalized cumulative energy loss was larger in clay than in sand increasing with a decreasing degree of consolidation.     

Vertically Loaded Single Piles in Gibson Soil

The available closed-form solutions for vertically loaded piles have been, strictly speaking, limited to homogeneous soil, or nonhomogeneous soil with the shear modulus as a power of depth. The latter solutions—based on a zero shear modulus at ground surface—are generally sufficiently accurate for normally consolidated soil. For overconsolidated soil, however, there is generally a nonzero shear modulus at the surface, which may affect pile response. In this note, rigorous closed-form solutions are established to account for the nonhomogeneity of soil profile with nonzero shear modulus at ground surface. The solutions are developed using a load transfer approach, and are shown to give satisfactory results in comparison with a more rigorous continuum-based numerical approach, when the proposed load transfer factors are adopted.     

Durability Evaluation of Glass Fiber Reinforced-Polymer-Concrete Bonded Interfaces

In this investigation, 90-cm-long plain concrete beam specimens reinforced with externally bonded wet-laid glass fiber reinforced-polymer sheets are investigated. The specimens are precracked with a three point flexural load, subjected to a constant four point flexural load of about 25% of the initial ultimate moment, and placed into different environmental conditions. The four environmental conditions under investigation are indoor laboratory, outdoor, elevated temperature/dry, and freeze/thaw. By varying the exposure time in different environments and using the photoelastic coating method to evaluate strain distributions, the durability of the externally reinforced concrete beams is evaluated. An innovative approach based on fracture mechanics and local bond shear stress-slip relationships is proposed to explain the degradation mechanism. This approach is capable of qualitatively and quantitatively characterizing the environmental effect in terms of the parameters of the shear stress-slip law. Four one-dimensional shear stress-slip relationships are evaluated in terms of their ability to model the environment-dependent strain distribution and debond data obtained in the present investigation.     

Sampling Disturbance Effects in Normally Consolidated Clays

The effects of sampling disturbance are investigated by performing single element triaxial tests in which specimens of normally consolidated resedimented Boston blue clay are disturbed according to the “perfect sampling approach” (PSA) and the “ideal sampling approach” (ISA). The effects of PSA and ISA disturbance on the compression and undrained shear behavior of the soil are quantified by comparison with the intact behavior. The results indicate that the release of shear stress associated with PSA disturbance causes a modest change in the engineering properties of the soil. The effects of ISA disturbance are, on the other hand, very significant and increase systematically with the amplitude of the strain imposed. An increase in disturbance causes a decrease in the compression ratio, a decrease in the undrained strength, and an increase in the strain at failure and the recompression ratio, but has a minor effect on the preconsolidation pressure. These effects derive from the decrease in effective stress and from the damage to the soil fabric that occur as a result of sampling. The loss in undrained strength is primarily controlled by the decrease in effective stress and the post-disturbance strength ratio (cu/σs′) may be related to the “induced” overconsolidation ratio (IOCR = σvc′/σs′) through a SHANSEP equation.     

A planar simple shear test and flow behavior in a superplastic Al-Mg alloy

Superplasticity is generally studied by performing tensile and gas-pressure-bulge tests. In formed parts, however, a variety of strain states, including in-plane shear, are encountered. The understanding of the mechanical response in shear is helpful in the study of superplastic metal forming. In this study, a device for a planar simple shear test was designed and used to perform tests on a superplastic Al-Mg alloy sheet at the elevated temperatures of 500 °C (773K) and 550 °C (823K). In such a test, the incremental rotation of the principal strain axes and specimen-end effects during deformation can complicate the determination of true mechanical response. The possible approximations regarding the strain state in the specimen gage have been investigated. The σ _e -ε _e curves developed based on a simple-shear assumption show a lower flow stress than that under uniaxial tension, and strain hardening is related to dynamic grain growth. The rate of strain hardening at a fixed _e level is essentially the same for both uniaxial tension and shear, but the difference in the effective stress between uniaxial tension and shear depends upon strain rate and temperature. This study marks the first known attempt to characterize large strain response for superplastic metals under conditions of simple shear.