Nonlinear Coupled Seismic Sliding Analysis of Earth Structures

Earthquake-induced sliding displacements of earth structures are generally evaluated using simplified sliding block analyses that do not accurately model the seismic response of the sliding mass nor the seismic forces along the slide plane. The decoupled approximation introduced to capture each of these effects separately is generally believed to be conservative. However, recent studies using linear viscoelastic sliding mass models have revealed instances where the decoupled approximation is unconservative. In this paper, a coupled analytical model that captures simultaneously the fully nonlinear response of the sliding mass (necessary for intense motions) and the nonlinear stick-slip sliding response along the slide plane is presented. The proposed sliding model is validated against shaking table experiments of deformable soil columns sliding down an inclined plane. The effect of sliding on the response of earth structures is evaluated, and comparisons are made between sliding displacements calculated using coupled and decoupled analytical procedures with linear and nonlinear material properties. Nonlinearity resulting from stick-slip episodes is often the dominant source of nonlinearity in this problem. The decoupled approximation was unconservative primarily for intense ground motions for systems with low values of ky, larger values of ky∕kmax, and high period ratios (Ts∕Tm). Results indicate that a decoupled analysis is adequate for earth structures that are not expected to experience intense, near-fault motions. However, for projects undergoing intense, near-fault ground motions, a fully nonlinear, coupled stick-slip analysis is recommended.     

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.     

Effect of Near-Fault Vertical Ground Motions on Seismic Response of Highway Overcrossings

Results of comprehensive nonlinear response history analyses on a range of configurations representing typical highway overcrossings subjected to combined effects of vertical and horizontal components of near-fault ground motions are reported. Current seismic design guidelines in California neglect the vertical components of ground motions for peak ground accelerations less than 0.6?g and provide rather simplistic measures to account for vertical effects when they need to be incorporated in the design. Results from the numerical simulations show that the vertical components of ground motions cause significant amplification in the axial force demand in the columns and moment demands in the girder at both the midspan and at the face of the bent cap. Axial capacity of the columns and moment capacity of the girder at the face of the bent cap were generally found to be sufficient to resist the amplification in the respective demands due to vertical effects. However, midspan moments in negative bending due to vertical motions are found to exceed the capacity of the girder. The amplified midspan moments lead to yielding of the top reinforcement resulting in average peak strains on the order of 1%. It is concluded that seismic demand analysis of ordinary highway bridges in general and overcrossings in particular should incorporate provisions for considering the adverse vertical effects of near-fault ground 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.     

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.     

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.     

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.     

Equivalent Number of Uniform Stress Cycles for Soil Liquefaction Analysis

The seismic demand on potentially liquefiable soils can be approximated by a series of uniform shear stress cycles. Procedures are reviewed for converting an arbitrary acceleration time history to a series of uniform cycles with amplitude = 0.65 of the peak. The number of cycles (N) at this amplitude is evaluated so as to represent a seismic demand for liquefaction triggering equivalent to that of the accelerogram. An assumed relationship between N and magnitude (m) underlies so-called magnitude scaling factors used to adjust the liquefaction resistance of soil for the effects of duration∕magnitude. Scaling factors can alternatively be related directly to N, which enables the effects of factors other than m (for example, site-source distance r) to be quantified. We develop empirical models for N that are applicable to active tectonic regions and find a strong dependence on m and r and a weaker dependence on site condition and near-fault rupture directivity effects. The model for N is used to develop new scaling factors for soil liquefaction resistance that are distance-dependent and have a defined level of uncertainty.     

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.     

Evaluation of Peak Ground Velocity as a “Good” Intensity Measure for Near-Source Ground Motions

This paper investigates the “goodness” of peak ground velocity as a dependable intensity measure for the earthquake shaking of civil structures. The paper stresses the importance of distinguishing between acceleration pulses and velocity pulses, and identifies two classes of near-source ground motions: those where the peak ground velocity is the integral of a distinguishable acceleration pulse and those where the peak ground velocity is the result of a succession of high-frequency, one-sided acceleration spikes. It is shown that the shaking induced by the former class is in general much more violent than the shaking induced by the latter class of motions even when motions that belong to the former class may be generated by significantly smaller-magnitude earthquakes. Building on the dimensional analysis introduced in the companion papers this paper shows that both linear and nonlinear structural responses from a variety of records which exhibit distinguishable pulses scale better with the peak pulse acceleration than with the peak pulse velocity, indicating that the peak pulse acceleration is a more representative intensity measure of the earthquake shaking. This conclusion is further supported from the response analysis of linear and bilinear single-degree-of-freedom oscillators subjected to selected records from the 1999 Chi-Chi Taiwan earthquake that exhibit unusually high and long period velocity pulses. The paper shows that these high velocity pulses alone do not impose unusual demands on most civil structures. What is more detrimental are local, distinguishable acceleration pulses that override the long period velocity pulses.     

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.     

Investigation of effect of near-fault motions on substandard bridge structures

The objective of this study was to investigate the effects of near-fault ground motions on substandard bridge columns and piers. To accomplish these goals, several large scale reinforced concrete models were constructed and tested on a shake table using near- and far-field ground motion records. Because the input earthquakes for the test models had different characteristics, three different measures were used to evaluate the effect of the input earthquake. These measures are peak shake table acceleration, spectral acceleration at the fundamental period of the test specimens, and the specimen drift ratios.For each measure, force-displacement relationships, strains, curvatures, drift ratios, and visual damage were evaluated.Results showed that regardless of the measure of input or response, the near-fault record generally led to larger strains,curvatures, and drift ratios. Furthermore, residual displacements were small compared to those for columns meeting current seismic code requirements.     

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.     

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.     

Application of Seismic Refraction Tomography in Karst Terrane

Seismic refraction tomography field data were collected on several bridge foundation sites in Pennsylvania, in close proximity to geotechnical boring locations. Profiles determined from these field measurements were plotted against drilling data, and these comparisons revealed the ability of seismic wave velocities to differentiate overburden soil from rock. In addition, foundation construction data were collected at each of the sites and compared with refraction test results determined prior to construction. In particular, top of rock revealed by an excavation, and pile tip elevations at driving refusal, were compared with refraction test results. From these data it appears that seismic wave tomograms can characterize the soil/rock interface, and that it is possible to predict expected design pile lengths based upon a measured P-wave velocity tomogram. It can be concluded from these site comparisons that geophysical techniques such as seismic refraction tomography can provide important additional information to site characterization for bridge foundations in karst terrane. However, these techniques should not be viewed as a replacement, but should be conducted during design stage site investigation to aid selection of borehole locations and other testing needs.     

Rocking Response of Anchored Blocks under Pulse-Type Motions

This paper examines the transient rocking response of anchored blocks subjected to physically realizable horizontal pulse-type motion. Restrainers with elastic-brittle and elastic-plastic behavior are considered. Under one-sine pulse, anchored blocks can overturn with two distinct modes of overturning: (1) by exhibiting one impact; and (2) without exhibiting any impact. It is found that restrainers are more efficient in preventing overturning of small slender blocks subjected to low frequency pulses. This study uncovers that, although for most of the frequency range anchored blocks survive higher accelerations than free-standing blocks, there is a finite frequency range where the opposite happens. This paper examines this counterintuitive behavior and explains the destructive effect that increased strength and increased ductility of restrainers have on the rocking stability of rigid structures when excited by certain ground motions.     

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.     

Probabilistic Seismic Demand Models and Fragility Estimates for Reinforced Concrete Highway Bridges with One Single-Column Bent

In performance-based seismic design, general and practical seismic demand models of structures are essential. This paper proposes a general methodology to construct probabilistic demand models for reinforced concrete (RC) highway bridges with one single-column bent. The developed probabilistic models consider the dependence of the seismic demands on the ground motion characteristics and the prevailing uncertainties, including uncertainties in the structural properties, statistical uncertainties, and model errors. Probabilistic models for seismic deformation, shear, and bivariate deformation-shear demands are developed by adding correction terms to deterministic demand models currently used in practice. The correction terms remove the bias and improve the accuracy of the deterministic models, complement the deterministic models with ground motion intensity measures that are critical for determining the seismic demands, and preserve the simplicity of the deterministic models to facilitate the practical application of the proposed probabilistic models. The demand data used for developing the models are obtained from 60 representative configurations of finite-element models of RC bridges with one single-column bent subjected to a large number of representative seismic ground motions. The ground motions include near-field and ordinary records, and the soil amplification due to different soil characteristics is considered. A Bayesian updating approach and an all possible subset model selection are used to assess the unknown model parameters and select the correction terms. Combined with previously developed capacity models, the proposed seismic demand models can be used to estimate the seismic fragility of RC bridges with one single-column bent. Seismic fragility is defined as the conditional probability that the demand quantity of interest attains or exceeds a specified capacity level for given values of the earthquake intensity measures. As an application, the univariate deformation and shear fragilities and the bivariate deformation-shear fragility are assessed for an example bridge.     

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.