Influence of Input Motion and Site Property Variabilities on Seismic Site Response Analysis

Seismic site response analysis evaluates the influence of local soil conditions on earthquake ground shaking. There are multiple sources of potential uncertainty in this analysis; the most significant pertaining to the specification of the input motions and to the characterization of the soil properties. The influence of the selection of input ground motions on equivalent-linear site response analysis is evaluated through analyses performed with multiple suites of input motions selected to fit the same target acceleration response spectrum. The results indicate that a stable median surface response spectrum (i.e., within ±20% of any other suite) can be obtained with as few as five motions, if the motions fit the input target spectrum well. The stability of the median is improved to ±5 to 10% when 10 or 20 input motions are used. If the standard deviation of the surface response spectra is required, at least 10 motions (and preferably 20) are required to adequately model the standard deviation. The influence of soil characterization uncertainty is assessed through Monte Carlo simulations, where variations in the shear-wave velocity profile and nonlinear soil properties are considered. Modeling shear-wave velocity variability generally reduces the predicted median surface motions and amplification factors, most significantly at periods less than the site period. Modeling the variability in nonlinear properties has a similar, although slightly smaller, effect. Finally, including the variability in soil properties significantly increases the standard deviation of the amplification factors but has a lesser effect on the standard deviation of the surface motions.     

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.     

Use of Exact Solutions of Wave Propagation Problems to Guide Implementation of Nonlinear Seismic Ground Response Analysis Procedures

One-dimensional nonlinear ground response analyses provide a more accurate characterization of the true nonlinear soil behavior than equivalent-linear procedures, but the application of nonlinear codes in practice has been limited, which results in part from poorly documented and unclear parameter selection and code usage protocols. In this article, exact (linear frequency-domain) solutions for body wave propagation through an elastic medium are used to establish guidelines for two issues that have long been a source of confusion for users of nonlinear codes. The first issue concerns the specification of input motion as “outcropping” (i.e., equivalent free-surface motions) versus “within” (i.e., motions occurring at depth within a site profile). When the input motion is recorded at the ground surface (e.g., at a rock site), the full outcropping (rock) motion should be used along with an elastic base having a stiffness appropriate for the underlying rock. The second issue concerns the specification of viscous damping (used in most nonlinear codes) or small-strain hysteretic damping (used by one code considered herein), either of which is needed for a stable solution at small strains. For a viscous damping formulation, critical issues include the target value of the viscous damping ratio and the frequencies for which the viscous damping produced by the model matches the target. For codes that allow the use of “full” Rayleigh damping (which has two target frequencies), the target damping ratio should be the small-strain material damping, and the target frequencies should be established through a process by which linear time domain and frequency domain solutions are matched. As a first approximation, the first-mode site frequency and five times that frequency can be used. For codes with different damping models, alternative recommendations are developed.     

Seismic Site Response for Near-Fault Forward Directivity Ground Motions

Forward directivity effects in the near-fault region produce pulse-type motions that differ significantly from ordinary ground motions that occur at greater distances from the causative fault. Current code site factors are based on empirical observations and analyses involving less intense nonpulse ordinary ground motions. Nonlinear site response analyses with bidirectional shaking are performed using representative site profiles to quantify seismic site response effects for intense near-fault motions resulting from forward directivity. Input rock motions are represented with simplified velocity pulses that characterize the amplitude and period of forward directivity motions. Results indicate that site response affects both the amplitude and period of forward directivity pulses, and hence, local site conditions should be considered when evaluating seismic designs in the near-fault region. Stiff soil sites tend to amplify the peak ground velocity and increase the period of pulse-type motions, particularly, when the period of the rock motion coincides with the degraded period of the site. Amplification is limited at soft soil sites by the dynamic strength of the weak soil, so attenuation occurs for intense input motions. This nonlinearity is not reflected in the site factors in current building codes. Guidance is provided for estimating the amplitude and pulse period for velocity pulses at soil sites.     

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.     

Site Response at Treasure and Yerba Buena Islands, California

A variety of methods are utilized to reinvestigate the physical relationship between the seismic response of Treasure Island (TI) and Yerba Buena Island (YBI) in California. These islands are a soil (TI) and rock (YBI) site pair separated by 2 km. The site pair has been used previously by researchers to identify soil response to earthquake shaking. Linear regime ground motions (MW4.0–MW4.6 and PGA: 0.014–0.017 g) recorded in the TI vertical array indicate a coherent wavefield in the sediments and an incoherence between the rock and sediments. Our analyses show that the greatest change in the wavefield occurred between the rock and soil layers, corresponding to a significant impedance contrast. The waveforms change very little as they propagate through the sediments, indicating that the site response is a cumulative effect of the entire soil structure and not a result of wave propagation within individual soil layers. In order to highlight the complexity of the site response, correlation analysis was used to demonstrate that the rock and soil ground motions were not highly coherent between the two sites. YBI was, therefore, shown to be an inappropriate reference site for TI. One-dimensional (1D) vertical wave propagation and inverse techniques were used to differentiate between 1D site response and more complex site behavior. Both 1D methods (vertical wave propagation and inverse transfer functions) proved incapable of capturing the site response at TI beyond the initial four seconds of motion. Finite difference waveform modeling, based on a two-dimensional velocity structure of the northern San Francisco Bay was needed to explain the linear site response at TI as horizontally propagating surface waves trapped in the bay sediments. A simplified velocity structure for the San Francisco Bay including a single 100 m basin layer (constant shear-wave velocity of 400 m/s) over a 1.5 km/s layer of Franciscan bedrock was able to trap energy in the basin and produce surface waveform ringing similar to that observed in the TI data. Due to surface waves propagating in the San Francisco Bay sediments, any 1D model will not fully characterize site response at TI. All 1D models will fail to produce the late arriving energy observed in the ground motions.     

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.     

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.     

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.     

Site specific probabilistic seismic hazard analysis at Dubai Creek on the west coast of UAE

A probabilistic seismic hazard analysis (PSHA) was conducted to establish the hazard spectra for a site located at Dubai Creek on the west coast of the United Arab Emirates (UAE). The PSHA considered all the seismogenic sources that affect the site, including plate boundaries such as the Makran subduction zone, the Zagros fold-thrust region and the transition fault system between them; and local crustal faults in UAE. PSHA indicated that local faults dominate the hazard. The peak ground acceleration (PGA) for the 475-year return period spectrum is 0.17 g and 0.33 g for the 2,475-year return period spectrum. The hazard spectra are then employed to establish rock ground motions using the spectral matching technique.     

Seasonally Frozen Soil Effects on the Seismic Site Response

Several large-magnitude earthquakes, including the Prince William Sound earthquake of March 1964 and the Denali earthquake of November 2002, occurred in the state of Alaska and caused considerable damages to its transportation system, including damage to several highway bridges and related infrastructure. Some of these damages are related to frozen soil effects. However, only limited research has been carried out to investigate the effects of frozen soils on seismic site responses. A systematic investigation of seasonally frozen soil effects on the seismic site response has been conducted and is presented in this paper. One bridge site in Anchorage, Alaska, was selected to represent typical sites with seasonally frozen soils. A set of input ground motions was selected from available strong-motion databases and scaled to generate an ensemble of hazard-consistent input motions. One-dimensional equivalent linear analysis was adopted to analyze the seismic site response for three seismic hazard levels, i.e., maximum considered earthquake (MCE), AASHTO design, and service design level hazards. Parametric studies were conducted to assess the sensitivity of the results to uncertainties associated with the thickness and shear-wave velocity of seasonally frozen soils. The results show that the spectral response of ground motions decreases as the thickness of seasonally frozen soil increases, and the results are insensitive to the shear-wave velocity of seasonally frozen soils. In conclusion, it is generally conservative to ignore the effects of seasonally frozen soils on seismic site response in the design of highway bridges.     

Effect of Nonlinear Soil Behavior on Inelastic Seismic Response of a Structure

The characteristics of the earthquake motions at the base of a structure are affected by the properties of the underlying soil through the soil amplification and soil–structure interaction phenomena. In this paper the effect of nonlinear soil behavior on the elastic and inelastic response spectra of the motions that would be recorded at the free surface of a soft soil deposit or at the base of each structure is investigated. The analyses are conducted for a soil layer by itself and for a complete soil structure system using a finite element discretization of the soil in cylindrical coordinates and an approximate linear iterative procedure to simulate nonlinear behavior. Studies are conducted for structures, with a constant base and variable height modeled as equivalent linear or nonlinear single degree of freedom systems and an input motion at the base of the soil deposit representative of rock outcrop motions. Both mat and pile foundations are considered. The results illustrate clearly the importance of the nonlinear soil behavior.     

Probabilistic Seismic Demand Model for California Highway Bridges

A performance-based seismic design method enables designers to evaluate a graduated suite of performance levels for a structure in a given hazard environment. The Pacific Earthquake Engineering Research Center is developing a framework for performance-based seismic design. One component of this framework is a probabilistic seismic demand model for a class of structures in an urban region with a well-defined seismic hazard exposure. A probabilistic seismic demand model relates ground motion intensity measures to structural demand measures. It is formulated by statistically analyzing the results of a suite of nonlinear time-history analyses of typical structures under expected earthquakes in the urban region. An example of a probabilistic seismic demand model for typical highway bridges in California is presented. It was formulated using a portfolio of 80 recorded ground motions and a portfolio of 108 bridges generated by varying bridge design parameters. The sensitivity of the demand models to variation of bridge design parameters is also discussed. Trends derived from this sensitivity study provide designers with a unique tool to assess the effect of seismicity and design parameters on bridge performance.     

Small-Strain Behavior of Granular Soils. II: Seismic Response Analyses and Model Evaluation

Using the recorded response at two vertical array sites, the SimSoil model presented in the companion paper is evaluated. The SimSoil model, which describes the small strain nonlinear behavior of granular materials, is implemented as a material model in AMPLE2000, a nonlinear, one-dimensional site response analysis code. Shear wave velocity profiles and laboratory test data available for both the La Cienega site, which was instrumented over 250?m, and the Lotung site, which was instrumented over 47?m, were used to determine SimSoil model parameters. Predictions from AMPLE2000 are compared with the measured response at several elevations for earthquakes that resulted in both nonlinear and nearly linear soil behavior. Using the available laboratory data and known input motions, the predictions of the response at these sites matched the recorded response well for varied magnitudes of shaking with a single set of parameters for each site.     

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.     

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.     

Numerical Modeling of Site Effects at San Giuliano di Puglia (Southern Italy) during the 2002 Molise Seismic Sequence

The seismic sequence that occurred in October and November 2002 in the Molise region (Southern Italy) was characterized by two Mw = 5.7 earthquakes within 24 h followed by one month long aftershocks series. The mainshocks caused substantial structural damage in the village of San Giuliano di Puglia. The damage distribution was highly non uniform. Heavy and widespread damage was observed to all buildings constructed in the recently developed part of the village, where subsoil conditions are characterized by a bowl-shaped basin filled with stiff clays, whereas in the historical center, built on an adjacent rock outcrop, many buildings showed no or light damage. Several accelerograms were recorded during the aftershocks sequence by a temporary network installed on two sites in the San Giuliano village, located on rock and soil, respectively. The geological, seismological, geotechnical, and structural relevant information of the earthquakes are presented in the first part of the paper. The second part of the paper investigates the possible role of site effects in the observed pattern of damage by one-dimensional (1D) and two-dimensional (2D) numerical site response analyses. First, the computed ground surface motions were compared to the aftershocks recordings. It was found that 1D analyses considerably underpredicted dynamic response while 2D modeling provided a better understanding of the amplification phenomena. Further, based on the calibration site response study performed with the aftershock records, the ground response simulation of October 31, 2002, mainshock was carried out. The results of 2D numerical analyses led to average ground surface motion characteristics consistent with the observed distribution of damage throughout the village.     

Boundary Finite-Element Method Coupling Finite-Element Method for Steady-State Analyses of Dam-Reservoir Systems

The boundary finite-element method (BFEM) is extended for steady-state analyses of dam-reservoir system problems. In this study, the dam is assumed to be rigid and subjected to horizontal ground motions, and the liquid in the reservoir is assumed to be semiinfinite. The semiinfinite reservoir domain is partitioned into two subdomains: a near-field domain and a far-field domain. In it, the near-field domain is modeled by using the finite-element method (FEM), whereas the far-field domain is modeled by BFEM and is treated as a layered semiinfinite fluid domain. A BFEM/FEM coupling procedure is employed to solve the steady-state response of the reservoir. The coupling procedure is easy to implement and suitable for all frequencies, be it real or complex. The BFEM/FEM coupling procedure is validated in the frequency domain. Numerical results that are based on the present procedure are in good agreement with analytical and other available numerical solutions.     

Energy Balance Assessment of Base-Isolated Structures

This paper explores the use of energy concepts in the analysis of base-isolated structures subject to severe earthquake ground motions. We formulate the energy balance equations in moving- and fixed-base coordinate frames and provide new physical insight into the time-dependent behavior of individual terms. Conventional wisdom in earthquake engineering circles is that systems with base isolation devices should be economically competitive and designed to: (1) minimize input energy, and (2) maximize the percentage of input energy dissipated by damping and inelastic mechanisms. Through the nonlinear time-history analysis of a base-isolated mass-spring system subject to an ensemble of severe ground motion inputs, we demonstrate that improvements in objective (2) often need to be balanced against increases in input energy. Hence, by itself, objective (1) presents an overly simplified view of desirable behavior.     

Role of Shear Keys in Seismic Behavior of Bridges Crossing Fault-Rupture Zones

This paper examines the role of shear keys at bridge abutments in the seismic behavior of “ordinary” bridges. The seismic responses of bridges subjected to spatially uniform and spatially varying ground motions for three shear-key conditions—nonlinear shear keys that break off and cease to provide transverse restraint if deformed beyond a certain limit; elastic shear keys that do not break off and continue to provide transverse restraint throughout the ground shaking; and no shear keys—are examined. Results show that seismic demands for a bridge with nonlinear shear keys can generally be bounded by the demands of a bridge with elastic shear keys and a bridge with no shear keys for both types of ground motions. While ignoring shear keys provides conservative estimates of seismic demands in bridges subjected to spatially uniform ground motion, such a practice may lead to underestimation of some seismic demands in bridges in fault-rupture zones that are subjected to spatially varying ground motion. Therefore, estimating the upper bounds of seismic demands in bridges crossing fault-rupture zones requires analysis for two shear-key conditions: no shear keys and elastic shear keys.