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.     

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.     

Evaluation of Site Factors for Seismic Bridge Design in New York City Area

Site factors for seismic bridge design in the New York metropolitan area are evaluated. Several profiles from Brooklyn, Queens, and Manhattan, matching soil categories D and E as defined in the recent New York City Department of Transportation and NEHRP provisions, are analyzed using 1D wave-propagation theory. Dynamic soil properties are derived using state-of-practice correlations with standard penetration resistance and compared to available in situ geophysical measurements. Three different rock motions are used, each modified from real records to match 500- and 2,500-year probabilistic spectra for the region. Results are presented in terms of dimensionless ratios of surface and rock response spectra. The effect of impedance contrast between soil and rock on soil amplification is examined. It is shown that, although seismic hazard in the area is moderate, large surface motions can be generated because of strong site amplification effects that exceed those in the western United States. Derived spectra are compared with current design spectra defined in the 1998 New York City Department of Transportation guidelines and the 1995 New York City Seismic Code. Three issues that are not sufficiently addressed in existing codes are discussed: (1) deep sites containing thick layers of high-plasticity clay; (2) shallow sites with thickness <30 m; and (3) amplification of vertical ground motions.     

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.     

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.     

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.     

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.     

Modified Topographic Amplification Factors for a Single-Faced Slope due to Kinematic Soil-Structure Interaction

In this paper, we evaluate the additive effects of topography, soil nonlinearity, and soil-structure interaction (SSI) along the crest of an idealized 40?m high cliff-type topographic feature with slope inclination 300, where excessive damage was observed during the Athens 1999 earthquake. The objective of this paper is to investigate the relative contribution of topographic amplification, and kinematic SSI as a function of the incident motion frequency content and geotechnical site conditions for a surface and an embedded structure located at the cliff crest. For this purpose, we perform elastic parametric and nonlinear site-specific two-dimensional finite element simulations using three profiles and six input motions. We illustrate the role of SSI in altering the response at the location of peak topographic amplification potential behind the crest, the effects of incident motion incoherency on the transient structural response, and the beneficial contribution of structural embedment. We finally suggest that empirical models for base-slab averaging of shallow foundations, developed as a function of site conditions, structural dimensions and center line location, could be combined with topographic amplification factors to predict realistic design spectra for structures located on irregular topographic features.     

Effect of Sediment Column on Weak-Motion Site Response for a Deep Basin Fill

Unique challenges arise when projecting dynamic site response in a deep, steep sided, irregularly shaped, sediment-filled basin. The influence of shallow sediments on site response was investigated for a 1-km-deep alluvial column in the Las Vegas Basin, subjected to weak ground motions. A one-dimensional equivalent-linear model was applied. Response analyses for deep deposits are complicated because dynamic material properties at depth are uncertain. To compensate, the model half space was placed well above the physical bottom of the sediment column. The depth to half space was selected by matching characteristics of projected surface response to measured data or expectations. Weak ground-motion datasets resulting from underground nuclear tests were considered. The best-match half space depth, 375?m, greatly exceeded the depth of the threshold shear wave velocity for engineering bedrock. The analysis captured site response over the period range 0.3–1.3?s. When the parameterization was tested for a weak-ground-motion earthquake dataset, projections were poorer but still instructive.     

Modeling Evapotranspiration of Two Land Covers Using Integrated Hydrologic Model

Modeling evapotranspiration (ET) distribution in shallow water table environments is of great importance for understanding and reproducing other hydrologic fluxes such as runoff and recharge. Unfortunately, ET distribution can be the most difficult hydrologic process to analyze. The partitioning of ET into upper zone ET, lower zone ET, and groundwater ET is complex because it depends on land cover and subsurface characteristics. One comprehensive distributed parameter model, integrated hydrologic model (IHM), builds on an improved understanding and characterization of ET partitioning between surface storages, vadose zone storage, and saturated groundwater storage. It provides a smooth transition to satisfy ET demand between the vadose zone and the deeper saturated groundwater. In this paper, the IHM was used to analyze ET contribution from different regions of the vadose zone and saturated zone. Rigorous testing was done on two distinct land covers, grass land and forest land, at a study site in West-Central Florida. Sensitivity analysis on the key parameters was investigated and influence of parameters on ET behavior was also discussed. Statistics with the root mean square error and mean bias error for forest total ET were about 1.46 and 0.04 mm/day, respectively, and 1.61 and 1.07 mm/day for grass total ET. Modeling results further proved that ET distributions from the upper and lower soil and water table, while incorporating field-scale variability of soil and land cover properties, can be predicted reasonably well using IHM model.     

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.     

Frequency-Dependent Amplification of Unsaturated Surface Soil Layer

This paper presents a study of the amplification of SV waves obliquely incident on a surface soil layer overlying rock formation. Special attention is placed on the influence of the saturation states of the soil layer and the bedrock on the amplification in both horizontal and vertical directions as well as on the amplitude ratios between the two directions at the surface, where the vertical and horizontal amplification and the amplitude ratios are expressed as functions of the frequency of incident waves. The analysis indicates that while the influence of the saturation state of the bedrock is insignificant, a change of the saturation state of the soil layer may have a marked impact on the vertical amplification. For typical seismic frequencies, an unsaturated soil layer can generate greater vertical amplification than a saturated layer; it can also cause larger amplitude ratios between vertical and horizontal components at the surface. The analysis further confirms the potential importance of the saturation condition of near-surface soils in site response analysis.     

Probabilistic Assessment of Slope Stability That Considers the Spatial Variability of Soil Properties

In this paper, a numerical procedure for probabilistic slope stability analysis is presented. This procedure extends the traditional limit equilibrium method of slices to a probabilistic approach that accounts for the uncertainties and spatial variation of the soil strength parameters. In this study, two-dimensional random fields were generated based on a Karhunen-Loève expansion in a fashion consistent with a specified marginal distribution function and an autocorrelation function. A Monte Carlo simulation was then used to determine the statistical response based on the generated random fields. This approach makes no assumption about the critical failure surface. Rather, the critical failure surface corresponding to the input random fields of soil properties is searched during the process of analysis. A series of analyses was performed to verify the application potential of the proposed method and to study the effects of uncertainty due to the spatial heterogeneity on the stability of slope. The results show that the proposed method can efficiently consider the various failure mechanisms caused by the spatial variability of soil property in the probabilistic slope stability assessment.     

Parametric Studies on the Behavior of Reinforced Soil Retaining Walls under Earthquake Loading

The finite element procedures are extremely useful in gaining insights into the behavior of reinforced soil retaining walls. In this study, a validated finite element procedure was used for conducting a series of parametric studies on the behavior of reinforced soil walls under construction and subject to earthquake loading. The procedure utilized a nonlinear numerical algorithms that incorporated a generalized plasticity soil model and a bounding surface geosynthetic model. The reinforcement layouts, soil properties under monotonic and cyclic loadings, block interaction properties, and earthquake motions were among major variables of investigation. The performance of the wall was presented for the facing deformation and crest surface settlement, lateral earth pressure, tensile force in the reinforcement layers, and acceleration amplification. The effects of soil properties, earthquake motions, and reinforcement layouts are issues of major design concern under earthquake loading. The deformation, reinforcement force, and earth pressure increased drastically under earthquake loading compared to end of construction.     

Three-Dimensional Linear and Simplified Nonlinear Soil Response Methods Based on an Input Wave Field

We propose three-dimensional linear and simplified nonlinear soil response methods based on an input seismic wave field. An input wave field is employed to treat seismic surface waves excited by a deep structure in a shallow soil model. First, the linear method is applied to a hard- and a soft-soil site located in Mexico City, and soil responses excited by S-, surface-, and whole-wave fields reproduce the input waves fields well. Then, the linear method is applied to estimate soil responses for three large earthquakes at two soft-soil sites located in the reclaimed zone of Tokyo Bay, and again it works well. Finally, we attempt to perform nonlinear and liquefaction soil response analyses in the reclaimed zone, on the basis of an input wave field modified according to varied soil properties. The nonlinear method seems to provide reasonable nonlinear and liquefaction soil responses.     

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.     

Reliability of VS,30 Evaluation from Surface-Wave Tests

The reliability of surface-wave tests for the evaluation of VS,30 in seismic site characterization is assessed with respect to both uncertainty and accuracy. The discussion of uncertainty is mainly focused on the implications of solution nonuniqueness in inverse problems; only the inversion uncertainty is considered within this work, omitting other possible issues such as nontrivial geological settings (e.g., lateral variations) or the influence of different processing procedures. A Monte?Carlo?approach has been used to select, through a statistical test, a set of shear-wave velocity models that can be considered equivalent with respect to fitting the experimental dispersion curve according to the information content (dispersion velocities and frequency range) and the experimental uncertainties. This set of equivalent solutions is then used to evaluate the uncertainty in the determination of VS,30. Moreover, comparisons between the results obtained by surface-wave tests and invasive seismic methods are reported to assess the accuracy of VS,30 evaluation by using surface-wave methods. It is shown that, given an adequate investigation depth, the solution nonuniqueness is not a major concern and that the results are comparable in most situations with the results of invasive tests providing an accurate estimate of VS,30, even with simplified approaches.     

Liquefaction Resistance of Soils from Shear-Wave Velocity

A simplified procedure using shear-wave velocity measurements for evaluating the liquefaction resistance of soils is presented. The procedure was developed in cooperation with industry, researchers, and practitioners and evolved from workshops in 1996 and 1998. It follows the general format of the Seed-Idriss simplified procedure based on standard penetration test blow count and was developed using case history data from 26 earthquakes and >70 measurement sites in soils ranging from fine sand to sandy gravel with cobbles to profiles including silty clay layers. Liquefaction resistance curves were established by applying a modified relationship between the shear-wave velocity and cyclic stress ratio for the constant average cyclic shear strain suggested by R. Dobry. These curves correctly predicted moderate to high liquefaction potential for >95% of the liquefaction case histories and are shown to be consistent with the standard penetration test based curves in sandy soils. A case study is provided to illustrate application of the procedure. Additional data are needed, particularly from denser soil deposits shaken by stronger ground motions, to further validate the simplified procedure.     

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.