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.     

Effect of Asynchronous Earthquake Motion on Complex Bridges. I: Methodology and Input Motion

Based on observed damage patterns from previous earthquakes and a rich history of analytical studies, asynchronous input motion has been identified as a major source of unfavorable response for long-span structures, such as bridges. This study is aimed at quantifying the effect of geometric incoherence and wave arrival delay on complex straight and curved bridges using state-of-the-art methodologies and tools. Using fully parametrized computer codes combining expert geotechnical and earthquake structural engineering knowledge, suites of asynchronous accelerograms are produced for use in inelastic dynamic analysis of the bridge model. Two multi-degree-of-freedom analytical models are analyzed using 2,000 unique synthetic accelerograms with results showing significant response amplification due to asynchronous input motion, demonstrating the importance of considering asynchronous seismic input in complex, irregular bridge design. The paper, Part 1 of a two-paper investigation, presents the development of the input motion sets and the modeling and analysis approach employed, concluding with sample results. Detailed results and implications on seismic assessment are presented in the companion paper: Effect of Asynchronous Motion on Complex Bridges. Part II: Results and Implications on Assessment.     

Effects of Pier and Deck Flexibility on the Seismic Response of Isolated Bridges

The seismic response of bridges isolated by elastomeric bearings and the sliding system is investigated under two horizontal components of real earthquake ground motions. The selected bridges consist of multispan continuous deck supported on the piers and abutments. Three different mathematical models of the isolated bridge are considered for the analytical seismic response by considering and ignoring the flexibility of the deck and piers. The mathematical formulation for seismic response analysis of various mathematical models of the bridges isolated by different isolation systems is presented. The accuracy and computational efficiency of various mathematical models of isolated bridges is investigated by comparing their responses under different system parameters and earthquake ground motions. The important parameters selected are the flexibility of deck, piers, and isolation systems. There was significant difference in the computational time required for different models, but it was observed that the seismic response of the bridges obtained from different equivalent mathematical models is quite comparable even for an unsymmetrical bridge. Thus, the earthquake response of a seismically isolated bridge can be effectively obtained by modeling it as a single-degree-of-freedom system (i.e., considering the piers and deck as rigid) supported on an isolation system in two horizontal directions.     

Seismic Response of Liquid Storage Tanks Incorporating Soil Structure Interaction

A frequency domain method is presented to compute the impulsive seismic response of circular surface mounted steel and concrete liquid storage tanks incorporating soil-structure interaction (SSI) for layered sites. The method introduces the concept of a near field region in close proximity to the mat foundation and a far field at distance. The near field is modeled as a region of nonlinear soil response with strain compatible shear stiffness and viscous material damping. The shear strain in a representative soil element is used as the basis for strain compatibility in the near field. In the far field, radiation damping using low strain soil response is used. Frequency dependent complex dynamic impedance functions are used in a model that incorporates horizontal displacement and rotation of the foundation. The focus of the paper is on the computation of the horizontal shear force and moment on the tank foundation to enable foundation design. Significant SSI effects are shown to occur for tanks sited on soft soil, especially tanks of a tall slender nature. SSI effects take the form of period elongation and energy loss by radiation damping and foundation soil damping. The effects of SSI for tanks are shown to reverse the trend of force and moment reduction under earthquake loading as is usually assumed by designers. The reasons for this important effect in tank design are given in the paper and relate to the very short period of most tanks, hence, period lengthening may result in load increase. A comparison is made with SSI effects evaluated using the code SEI/ASCE 7-02. Period elongation is found to be similar for relatively stiff soils when assessed by the code compared with the results of the dynamic analysis. For soft soils, the agreement is not as good. Code values of system damping are found to agree reasonably well with an assessment based on the dynamic analyses for the range of periods covered by the code. Energy loss by material damping and radiation damping is discussed. It is shown that energy loss may be computed using the complex dynamic impedance function associated with the viscous dashpot in the analytical model. The proportion of energy loss in the translation mode compared to that dissipated in the rotational mode is addressed as a function of the slenderness of the tank. Energy loss increases substantially with the volume of liquid being stored.     

Simulating Seismic Response of Cantilever Retaining Walls

Many failures of retaining walls during earthquakes occurred near waterfront. A reasonably accurate evaluation of earthquake effects under such circumstance requires proven analytical models for dynamic earth pressure, hydrodynamic pressure, and excess pore pressure. However, such analytical procedures, especially for excess pore pressure, are not available and hence comprehensive numerical procedures are needed. This paper presents the results of a finite-element simulation of a flexible, cantilever retaining wall with dry and saturated backfill under earthquake loading, and the results are compared with that of a centrifuge test. It is found that bending moments in the wall increased significantly during earthquakes both when backfill is dry or saturated. After base shaking, the residual moment on the wall was also significantly higher than the moment under static loading. Liquefaction of backfill soil contributed to the failure of the wall, which had large outward movement and uneven subsidence in the backfill. The numerical simulation was able to model quite well the main characteristics of acceleration, bending moment, displacement, and excess pore pressure recorded in the centrifuge test in most cases with the simulation for dry backfill slightly better than that for saturated backfill.     

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.     

Seismic Fragility of Continuous Steel Highway Bridges in New York State

This paper presents the results of an analytical seismic fragility analysis of a typical steel highway bridge in New York State. The structural type and topological layout of this multispan I-girder bridge have been identified to be most typical of continuous bridges in New York State. The structural details of the bridge are designed as per New York State bridge design guidelines. Uncertainties associated with the estimation of material strength, bridge mass, friction coefficient of expansion bearings, and expansion-joint gap size are considered. To account for the uncertainties related to the bridge structural properties and earthquake characteristics, ten statistical bridge samples are established using the Latin Hypercube sampling and restricted pairing approach, and 100 ground motions are simulated numerically. The uncertainties of capacity and demand are estimated simultaneously by using the ratios of demands to capacities at different limit states to construct seismic fragility curves as a function of peak ground acceleration and fragility surfaces as a function of moment magnitude and epicentral distance for individual components using nonlinear and multivariate regressions. It has been observed that nonlinear and multivariate regressions show better fit to bridge response data than linear regression conventionally used. To account for seismic risk from multiple failure modes, second-order reliability yields narrower bounds than the commonly used first-order reliability method. The fragility curves and surfaces obtained from this analysis demonstrate that bridges in New York State have reasonably low likelihood of collapse during expected earthquakes.     

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 Response Modification Factors for Reinforced Masonry Structural Walls

The current North American design standards provide seismic force modification factors for the rectangular masonry structural walls category only; no similar provisions for flanged and end-confined masonry structural walls exist. This study demonstrates that seismic force reduction factor (R) values calculated for rectangular walls was close to 5.0, which is consistent with the value stipulated by the ASCE 7, and was 36 and 90% higher for the corresponding flanged and end-confined walls. The deflection amplification factor (Cd) values calculated for rectangular walls were higher than specified in the ASCE 7 for the special reinforced masonry wall category. Values of the ductility-related force modification factor (Rd) for flanged and end-confined walls were, respectively, at least 30 and 100% higher than those of rectangular walls specified in the National Building Code of Canada (NBCC). Quantification of the seismic response parameters within this study is expected to facilitate adoption of the flanged and end-confined wall categories in North American masonry codes as a cost-effective technique to enhance the seismic performance of masonry construction.     

Stress Reduction Coefficient and Amplification Factor for Seismic Response of Ground

Incorporating the increase of shear modulus with depth (z) by using a depth exponent p, the response of linear visco-elastic ground under steady state harmonic vibration was examined. The soil mass lying above the rigid base was discretized into a large number of horizontal layers. For a given vertical thickness (Hr) of the upper ground material in the first mode of resonance, it was noted that the resonant frequency (fr) as well as the values of amplification factor (Mf) and the stress reduction coefficient (Cd) at a given z/Hr can be computed as a function of p and D, where D is the damping ratio of the material. An increase in D leads to (1) an increase in Cd; (2) a very little increase in fr; and (3) a decrease in Mf. On the other hand, an increase in p causes: (1) an increase in fr; (2) a marginal increase in Mf; and (3) a decrease in Cd. It was evident that the values of Mf and Cd at a given depth will be affected significantly by changes in the chosen thickness of the soil deposit in resonance.     

Efficient Longitudinal Seismic Fragility Assessment of a Multispan Continuous Steel Bridge on Liquefiable Soils

The increased failure potential of aging U.S. highway bridges and their susceptibility to damage during extreme events necessitates the development of efficient reliability assessment tools to prioritize maintenance and rehabilitation interventions. Reliability communication tools become even more important when considering complex phenomena such as soil liquefaction under seismic hazards. Currently, two approaches are widely used for bridge reliability estimation under soil failure conditions via fragility curves: liquefaction multipliers and full-scale two- or three-dimensional bridge-soil-foundation models. This paper offers a computationally economical yet adequate approach that links nonlinear finite-element models of a three-dimensional bridge system with a two-dimensional soil domain and a one-dimensional set of p-y springs into a coupled bridge-soil-foundation (CBSF) system. A multispan continuous steel girder bridge typical of the central and eastern United States along with heterogeneous liquefiable soil profiles is used within a statistical sampling scheme to illustrate the effects of soil failure and uncertainty propagation on the fragility of CBSF system components. In general, the fragility of rocker bearings, piles, embankment soil, and the probability of unseating increases with liquefaction, while that of commonly monitored components, such as columns, depends on the type of soil overlying the liquefiable sands. This component response dependence on soil failure supports the use of reliability assessment frameworks that are efficient for regional applications by relying on simplified but accepted geotechnical methods to capture complex soil liquefaction effects.     

Orthogonal Effects in Seismic Analysis of Skewed Bridges

In seismic analysis of bridges, the designer chooses the direction of the applied earthquake forces arbitrarily. This paper investigates the effects of seismic force direction on the responses of slab-girder skewed bridges in response spectrum and time history linear dynamic analyses. The combination rules for orthogonal earthquake effects, such as the 100/30, 100/40?percentage rules and the SRSS method are also examined. It is concluded that either the SRSS or the 100/40?percentage rule in the skew direction should be used in the response spectrum analysis of skewed bridges. For time history analysis none of the combination rules provide conservative results. In this case, the application of paired acceleration time histories in several angular directions is recommended.     

Cyclic Softening of Low-Plasticity Clay and Its Effect on Seismic Foundation Performance

During the 1999 Chi-Chi Earthquake (Mw = 7.6), significant incidents of ground failure occurred in Wufeng, Taiwan, which experienced peak accelerations ～ 0.7?g. This paper describes the results of field investigations and analyses of a small region within Wufeng along an E–W trending line 350?m long. The east end of the line has single-story structures for which there was no evidence of ground failure. The west end of the line had three to six-story reinforced concrete structures that underwent differential settlement and foundation bearing failures. No ground failure was observed in the free field. Surficial soils consist of low-plasticity silty clays that extend to 8–12?m depth in the damaged area (west side), and 3–10?m depth in the undamaged area (east side). A significant fraction of the foundation soils at the site are liquefaction susceptible based on several recently proposed criteria, but the site performance cannot be explained by analysis in existing liquefaction frameworks. Accordingly, an alternative approach is used that accounts for the clayey nature of the foundation soils. Field and laboratory tests are used to evaluate the monotonic and cyclic shear resistance of the soil, which is compared to the cyclic demand placed on the soil by ground response and soil–structure interaction. Results of the analysis indicate a potential for cyclic softening and associated strength loss in foundation soils below the six-story buildings, which contributes to bearing capacity failures at the edges of the foundation. Similar analyses indicate high factors of safety in foundation soils below one-story buildings as well in the free field, which is consistent with the observed field performance.     

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.     

Rotation Response of a Rigid Body under Seismic Excitation

After the 1994 Sanriku-Haruka-Oki, Japan, earthquake, rotation of tombstones along the vertical axis occurred in a graveyard about 34?m from the Japan Meteorological Agency Hachinohe Observatory where strong motion was recorded. The properties of seismic motion that make a rigid rectangular solid body rotate are discussed. Shaking table tests were conducted to reproduce the rotation response of Japanese-style tombstones which typically consist of several stone blocks whose shapes are rectangular solids. Data obtained from those tests were used to calibrate a numerical model by the three-dimensional distinct element method. Results of the shaking tests and numerical analyses showed that rotation of a rigid rectangular solid body may be caused by the combination of the rocking of the body and particle motion of the input acceleration. Rotation behavior of an actual tombstone was simulated based on the observed accelerogram. Findings show that one or two cycles of particle motion near peak acceleration caused the rotation.     

Nonlinear Response of Deep Immersed Tunnel to Strong Seismic Shaking

Critical for the seismic safety of immersed tunnels is the magnitude of deformations developing in the segment joints, as a result of the combined longitudinal and lateral vibrations. Analysis and design against such vibrations is the main focus of this paper, with reference to a proposed 70?m-deep immersed tunnel in a highly seismic region, in Greece. The multisegment tunnel is modeled as a beam connected to the ground through properly calibrated interaction springs, dashpots, and sliders. Actual records of significant directivity-affected ground motions, downscaled to 0.24 g peak acceleration, form the basis of the basement excitation. Free-field acceleration time histories are computed from these records through one-dimensional wave propagation equivalent-linear and nonlinear analyses of parametrically different soil profiles along the tunnel; they are then applied as excitation at the support of the springs, with a suitable time lag to conservatively approximate wave passage effects. The joints between the tunnel segments are modeled realistically with special nonlinear hyperelastic elements, while their longitudinal prestressing due to the great (7?bar) water pressure is also considered. Nonlinear dynamic transient analysis of the tunnel is performed without ignoring the inertia of the thick-walled tunnel, and the influence of segment length and joint properties is investigated parametrically. It is shown that despite ground excitation with acceleration levels exceeding 0.50 g and velocity of about 80?cm/s at the base of the tunnel, net tension and excessive compression between the segments can be avoided with a suitable design of joint gaskets and a selection of relatively small segment lengths. Although this research was prompted by the needs of a specific project, the dynamic analysis methods, the proposed design concepts, and many of the conclusions of the study are sufficiently general and may apply in other immersed tunneling projects.     

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.     

ONDA: Computer Code for Nonlinear Seismic Response Analyses of Soil Deposits

This paper describes a newly developed computer code for performing one-dimensional nonlinear dynamic analysis (ONDA) of soil deposits. The code has been developed by revisiting the 1982 work by Ohsaki with the purpose of simulating the ground response to an earthquake of moderate intensity (i.e., values of peak ground acceleration on stiff soil on the order of 0.15 to 0.25g, which are typical of many sites in Italy). In the Ohsaki model a horizontally stratified soil deposit is idealized as a discrete mechanical system composed of a finite number of lumped masses connected with a series of springs and dashpots. Nonlinearity is modeled by assuming (1) a “backbone” curve that describes the initial monotonic loading of the stress-strain curve, and (2) a “rule” that simulates the unloading-reloading paths and stiffness degradation undergone by soil as seismic excitation progresses. Typically, the backbone curve is obtained from conventional cyclic undrained loading laboratory tests. The rule generally used is the so-called Masing criterion, which assumes that the unload-reload branches of the stress-strain curve have the same shape as the initial loading curve but are affected by a scale factor (n) equal to 2. In this work, the Masing criterion has been modified by assuming a scale factor (n) not necessarily equal to 2. It turns out that a factor n greater than 2 allows the simulation of cyclic hardening, while cyclic softening can be modeled by assuming decreasing values of n even smaller than 2. Pyke proposed in 1979 to use a scale factor (n) lower than 2 to simulate cyclic degradation. According to Pyke, the n parameter is a function of the mobilization factor. The generalization of the Masing criterion allows ONDA to properly simulate the phenomena of soil hardening and soil degradation, giving it the capability to compute the permanent strains developed during a seismic event. The procedure required to evaluate the model parameters is also described in the paper. Note that the laboratory tests examined gave values of n between 2 and 6 for a strain level not greater than 0.3%. In ONDA the numerical solution of the nonlinear equations of motion is obtained using the unconditionally stable Wilson θ algorithm (with θ ≥ 1.37). The new method has been used to predict the seismic response at two sites in Italy. For these case studies, the maximum input acceleration was not greater than 0.3g and the computed shear strains were less than 0.2%. The ONDA results have been compared with those computed with SHAKE, EERA (equivalent-linear analysis), and NERA (nonlinear analysis).