Considerations of Multimode Structural Response for Near-Field Earthquakes

This paper presents an investigation of multimode effects of tall buildings idealized as a continuous shear-beam model subjected to near-field pulse-like ground motion. The investigation is based on three analytical approaches: a damped wave solution approach, a fundamental-mode approach, and a modal summation approach. In the modal summation approach, all modal damping ratios are assumed to be equal and a set of Green’s functions for the shear strain response is explicitly derived. The multimode effects on the base-level shear strain/force demands are compared by using an effective response spectrum for shear-beam systems. The study results show that the occurrence of major spectral differences is conditioned on the ratio of the fundamental structural period to the duration of the predominant excitation pulse. Seismic analyses for a set of recorded near-field earthquake data indicate a strong correlation between the characteristics of effective response spectra and the ground pulse parameters.     

Seismic Performance of Hillside Fills

Permanent ground deformations in unsaturated, compacted hillside fills under seismic loading conditions are discussed, with emphasis given to fill performance during the 1994 Northridge earthquake. These movements represent a significant yet often unrecognized hazard to developed hillside areas, as relatively modest deformations induced widespread damage totaling hundreds of millions of dollars during the Northridge event. The development of grading standards in the Los Angeles area is reviewed to place the seismic fill deformation problem in context with other issues that have shaped design and construction practices for hillside fills. Field observational data on fill performance during the Northridge earthquake is presented, and typical ground distress patterns are found to include cracking near cut/fill contacts, lateral extension and settlement of fill pads, and bulging of fill slope faces. For most sites, the prevalent mechanism of permanent ground deformation responsible for the fill movements is contractive volumetric strain accumulation within the unsaturated fill soils during strong earthquake shaking (that is, seismic compression).     

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.     

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.     

Responses of Buried Corrugated Metal Pipes to Earthquakes

This study describes the results of field investigations and analyses carried out on 61 corrugated metal pipes (CMP) that were shaken by the 1994 Northridge earthquake. These CMPs, which include 29 small-diameter (below 107 cm) CMPs and 32 large-diameter (above 107 cm) CMPs, are located within a 10 km2 area encompassing the Van Norman Complex in the Northern San Fernando Valley, in Los Angeles, California. During the Northridge earthquake, ground movements were extensively recorded within the study area. Twenty-eight of the small-diameter CMPs performed well while the 32 large-diameter CMPs underwent performances ranging from no damage to complete collapse. The main cause of damage to the large-diameter CMPs was found to be the large ground strains. Based on this unprecedented data set, the factors controlling the seismic performance of the 32 large-diameter CMPs were identified and framed into a pseudostatic analysis method for evaluating the response of large diameter flexible underground pipes subjected to ground strain. The proposed analysis, which is applicable to transient and permanent strains, is capable of describing the observed performance of large-diameter CMPs during the 1994 Northridge earthquake. It indicates that peak ground velocity is a more reliable parameter for analyzing pipe damage than is peak ground acceleration. Results of this field investigation and analysis are useful for the seismic design and strengthening of flexible buried conduits.     

Response of an Earth Dam to Spatially Varying Earthquake Ground Motion

The stochastic response of the Santa Felicia earth dam, in southern California, to spatially varying earthquake ground motion (SVEGM) is analyzed. An SVEGM model that accounts for both incoherence and propagation of seismic waves is used, the results are compared with those for various simplified excitations, and the sensitivity of the responses to coherency models proposed by different researchers is investigated. A 3D inhomogeneous finite-element model is used to represent the dam. Finite element-based random vibration analysis is performed and the statistical moments of Cartesian displacement, stress, and strain responses are computed. Statistical moments of the maximum shear stress are computed using Monte Carlo simulation that utilizes results from the random vibration analysis. The results indicate that the stress response of stiff material near the base of the dam can be significantly increased due to SVEGM, and that the increase is sensitive to the low-frequency variation of ground motion coherency.     

Summary of SAC Case Study Building Analyses

Summarized in this paper are the major findings from analytical studies of nine steel moment frame buildings conducted under Phase 1 of the SAC Steel Project. The buildings range in height from two to seventeen stories and most of them experienced damage to welded beam-column connections during the Northridge earthquake of 1994. Elastic response spectrum, inelastic static pushover, and elastic and inelastic time-history analyses were conducted using ground motion data representative of the Northridge earthquake to establish the loading∕deformation demands that the buildings experienced. The primary performance indices obtained from the analyses were demand-to-capacity ratios, interstory drift ratios, and inelastic hinge rotations. Maximum ratios of elastic member force demands to plastic strengths ranged between 1.0 and 2.0; maximum inelastic hinge rotations were 0.005–0.010 rad; and maximum interstory drift ratios were from 1 to 2%. These damage indices increased by 50%–150% under more severe ground motions recorded during the Northridge earthquake at the Sylmar site. Accuracy of the analyses is shown to be sensitive to a number of modeling parameters including finite joint size, joint panel behavior, composite beam action, strain hardening, second-order (P-Δ) effects, and three-dimensional response. Overall, there was only modest correlation between the frame performance indices and the observed connection damage, due largely to the fact that significant aspects of the connection fracture behavior are not captured in the frame analyses.     

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.     

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.     

Temporal aN and aT in Earthquake Ground Motion at a Single Point

This paper describes a continued study on three-dimensional temporal characteristics of earthquake ground motions at a single point. Based on an instantaneous tangential and normal acceleration decomposition of ground acceleration trajectory, a ground motion can be partitioned into a finite sequence of staggered time intervals of acceleration and deceleration. A formulation is developed to estimate speed and angular changes over a partitioned interval in terms of rates of positive and negative tangential and normal acceleration. Based on these concepts, general ground motion properties, peak ground acceleration, peak ground velocity, and peak ground displacement are examined. Several Northridge earthquake records are studied in detail. It is found that the highest peak of ground acceleration in these records corresponds to a high peak of deceleration, and a velocity maximum often precedes the peak of acceleration.     

Wave Passage and Ground Motion Incoherency Effects on Seismic Response of an Extended Bridge

This paper investigates the implications of ground motion spatial variability on the seismic response of an extended highway bridge. An existing 59-span, 2,164-meter bridge with several bearing types and irregularity features was selected as a reference structure. The bridge is located in the New Madrid Seismic Zone and supported on thick layers of soil deposits. Site-specific bedrock input ground motions were selected based on a refined probabilistic seismic hazard analysis of the bridge site. Wave passage and ground motion incoherency effects were accounted for after propagating the bedrock records to the ground surface. The results obtained from inelastic response-history analyses confirm the significant impact of wave passage and ground motion incoherency on the seismic behavior of the bridge. The amplification in seismic demands exceeds 150%, whereas the maximum suppression of these demands is less than 50%. The irregular and unpredictable changes in structural response owing to asynchronous earthquake records necessitate in-depth seismic assessment of major highway bridges with advanced modeling techniques to realistically capture their complex seismic response.     

Equivalent Modal Damping of Short-Span Bridges Subjected to Strong Motion

In this paper four different methods are investigated for estimating the equivalent modal damping ratios of a short-span bridge under strong ground motion by considering the energy dissipation at the boundary. The Painter Street Overcrossing (PSO) is investigated because of seismic data availability. Computed responses using the response-spectrum method with the equivalent damping ratios estimates are compared with the recorded responses. The results show that the four methods provide reasonable estimation of equivalent modal damping ratios and that neglecting off-diagonal elements in the damping matrix is the most efficient and practical method. The equivalent damping ratio of the PSO was nearly 25% under an earthquake with peak ground acceleration of 0.55g, which is much higher than the conventional assumption of 5%.     

Ground Response in Lotung: Total Stress Analyses and Parametric Studies

Previous papers have reported on the performance of a recently developed nonlinear ground response analysis code, SPECTRA, with reference to the prediction of the free-field response at a Large-Scale Seismic Test site in Lotung, Taiwan during the M6.5 earthquake of May 20, 1986. Two more major earthquakes of different characteristics shook this test site later that same year, a M6.2 earthquake that occurred on July 30 and a M7.0 earthquake that occurred on November 15. The present article analyzes the free-field responses recorded by a downhole array from these latter two events using the code SPECTRA and a widely used equivalent linear analysis code SHAKE. The studies focus on the relative accuracy and sensitivity of the two codes with respect to the variations of the input material parameters, using time histories, acceleration response spectra, Fourier acceleration amplitude spectra, and Arias intensities as criteria for the comparison. The two codes captured the general wave form of the acceleration histories well, but there was a general tendency for both codes (particularly SHAKE) to underpredict the Arias intensities of the earthquakes.     

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 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.     

Consistent Finite-Element Response Sensitivity Analysis

This paper examines the important issue of response sensitivities of dynamic models of structural systems to both material and (discrete) loading parameters. Plasticity-based finite-element models of structural systems subjected to base excitation such as earthquake loading are considered. The two methods for computing the response sensitivities, namely, (1) discretizing in time the time continuous-spatially discrete response equations and differentiating the resulting time discrete-spatially discrete response equations with respect to sensitivity parameters, and (2) differentiating the time continuous-spatially discrete response equations with respect to sensitivity parameters and discretizing in time the resulting time continuous-spatially discrete response sensitivity equations, are clearly distinguished. The discontinuities in time of the response sensitivities arising due to material state transitions in the plasticity models, and their propagation from the quadrature point level to the global structural response level are discussed using a specific one-dimensional plasticity model. The procedure to obtain the exact sensitivities of the numerical nonlinear finite-element response, including proper capture of their discontinuities, is formalized. Application examples illustrating the concepts are presented at the end.     

Bayesian State Estimation Method for Nonlinear Systems and Its Application to Recorded Seismic Response

The focus of this paper is to demonstrate the application of a recently developed Bayesian state estimation method to the recorded seismic response of a building and to discuss the issue of model selection. The method, known as the particle filter, is based on stochastic simulation. Unlike the well-known extended Kalman filter, it is applicable to highly nonlinear systems with non-Gaussian uncertainties. The particle filter is applied to strong motion data recorded in the 1994 Northridge earthquake in a seven-story hotel whose structural system consists of nonductile reinforced-concrete moment frames, two of which were severely damaged during the earthquake. We address the issue of model selection. Two identification models are proposed: a time-varying linear model and a simplified time-varying nonlinear degradation model. The latter is derived from a nonlinear finite-element model of the building previously developed at Caltech. For the former model, the resulting performance is poor since the parameters need to vary significantly with time in order to capture the structural degradation of the building during the earthquake. The latter model performs better because it is able to characterize this degradation to a certain extent even with its parameters fixed. For this case study, the particle filter provides consistent state and parameter estimates, in contrast to the extended Kalman filter, which provides inconsistent estimates. It is concluded that for a state estimation procedure to be successful, at least two factors are essential: an appropriate estimation algorithm and a suitable identification model.     

1D Time-Domain Solution for Seismic Ground Motion Prediction

A full time-domain solution for predicting earthquake ground motion based on the 1D viscoelastic shear-wave equation is presented. The derivation results in a time-domain equation in the form of an infinite impulse response filter. A solution in the time domain has several advantages including causality, direct modeling of impulsive and transient processes, and ease of inclusion of nonlinear soil behavior. The method is applicable to any arbitrarily layered silhouette presented as SH-wave velocity, damping coefficient, and mass density profiles for designated soil intervals. For nonlinear evaluations, an equivalent-linear formulation is incorporated and the standard modulus and damping degradation curves become part of the input set. Input motion can be either rock-outcrop or body-wave motions measured or estimated at the bottom of the geologic profile, and the output is the estimated ground motion time history. Application of the method to vertical array strong motion records from Garner Valley, and Wildlife Site, Calif., shows that predicted surface (and interval) ground motion is virtually identical to that measured. The differences between the results of linear and nonlinear analyses are negligible for most cases. A comparison of the time-domain model with SHAKE shows that SHAKE fails to accurately predict time histories in some situations, whereas the time-domain solution always yields satisfactory predicted surface ground motions.     

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.     

Substructure Simulation of Inhomogeneous Track and Layered Ground Dynamic Interaction under Train Passage

The vibrations in track and ground induced by train passages are investigated by the substructure method with due consideration to dynamic interaction between an inhomogeneous track system comprising continuous rails and discrete sleepers, and the underlying viscoelastic layered half space ground. Initially, the total system is divided into two separately formulated substructures, i.e., the track and the ground. The rail is described by introducing the Green function for an infinite long Euler beam both for moving axle loads action from a train and for reactions from sleepers. The ground is formulated by the layer transfer matrix approach for wave propagation along the depth. Subsequently, these substructures are integrated to meet the displacement compatibility and force equilibrium via inertia of sleepers and stiffness of railpad springs. The dynamic equations are solved in the frequency–wave-number domain by applying the Fourier transform procedure. Based on the assumption of a constant train speed, the time domain response is evaluated from the inverse Fourier transform computation. The dispersive characteristics of the layered ground and the moving axle loads lead to significantly different response features, depending on the train speed. The response is classified as quasistatic for a low speed, whereas it is dynamic for a high-speed situation. An illustrative case study is presented for Swedish X-2000 train track properties and ground profile.