Earthquake Spectra

We provide a methodology that seamlessly integrates national seismic hazard models across the Canada-U.S. border to provide earthquake risk managers with updated and consistent seismic hazard science and technology in the two countries. Consistent with our U.S. hazard model, we developed a new Canadian model that incorporates (1) spatially varying seismicity for the major metropolitan areas of southeastern and southwestern Canada and the United States, (2) a comprehensive probabilistic model for the Cascadia subduction zone that includes M 8.0–9.2 interface earthquakes, (3) a consistent set of ground motion prediction equations across eastern and western North America, and (4) a soil-based attenuation (SBA) methodology that mitigates uncertainty in the conversion of earthquake motions from rock to soil, on which the majority of exposure is located. NEHRP site conditions are mapped for all of Canada from existing geological data, and NEHRP site factors are used to account for local site conditions.

Ground motion prediction equations (GMPEs) relate ground motion intensity measures to variables describing earthquake source, path, and site effects. From many available GMPEs, we select those models recommended for use in seismic hazard assessments in the Global Earthquake Model. We present a GMPE selection procedure that evaluates multidimensional ground motion trends (e.g., with respect to magnitude, distance, and structural period), examines functional forms, and evaluates published quantitative tests of GMPE performance against independent data. Our recommendations include: four models, based principally on simulations, for stable continental regions; three empirical models for interface and in-slab subduction zone events; and three empirical models for active shallow crustal regions. To approximately incorporate epistemic uncertainties, the selection process accounts for alternate representations of key GMPE attributes, such as the rate of distance attenuation, which are defensible from available data. Recommended models for each domain will change over time as additional GMPEs are developed.

Current seismic design practice often relies on the use of the uniform hazard response spectrum (UHRS), which implicitly includes motions from multiple earthquake sources and envelops possible spectra, yet does not represent a single event. Seismic hazard analyses at the site of a major Mississippi River crossing near St. Louis, Missouri, showed bimodal seismic hazard dominated by small, nearby earthquakes at short periods and large, distant earthquakes in the New Madrid seismic zone at long periods. UHRS motions resulted in large seismic demands and predictions of pervasive liquefaction that were inconsistent with historical and geologic records. UHRS-compatible conditional mean spectra (CMS) were developed to bridge deterministic and probabilistic seismic hazard evaluations, and used to evaluate liquefaction, lateral spreading, and settlement potential. The computed response was consistent with the historical and geologic record. CMSs offer hazard-compatible alternatives to the UHRS and result in seismic demand consistent with historical and geologic evidence.

In this study, the effects of implementing stochastic finite fault ground motion simulations in earthquake hazard and risk assessment are evaluated. The investigations are conducted for the city of Dehradun (Indian Himalayas). We compare two ground motion estimation techniques: a ground motion prediction equation–based technique and a simulation-based technique. The comparison focuses on the differences the techniques imply on earthquake damage and loss estimates. Ground motion simulations are first calibrated against the instrumental recordings of the 1991 M_w 6.8 Uttarkashi earthquake. Afterward, a number of events are considered with different magnitude, distance, and azimuth to the source. Results indicate large differences between ground motion and loss estimates derived by the two methods, especially in the direction of rupture propagation, which persist to 2–2.5 fault lengths distance. It is therefore strongly recommended to consider rupture kinematics and orientation to the test bed when providing ground motion estimates for near-field earthquake loss assessment studies.

Nonlinear dynamic analysis is often used to develop fragility curves within the framework of seismic risk assessment and performance-based earthquake engineering. In the present article, fragility curves are derived from randomly generated clouds of structural response results by using least squares and sum-of-squares regression, and maximum likelihood estimation. Different statistical measures are used to estimate the quality of fragility functions derived by considering varying numbers of ground motions. Graphs are proposed that can be used as guidance regarding the number of calculations required for these three approaches. The effectiveness of the results is demonstrated by their application to a structural model. The results show that the least-squares method for deriving fragility functions converges much faster than the maximum likelihood and sum-of-squares approaches. With the least-squares approach, a few dozen records might be sufficient to obtain satisfactory estimates, whereas using the maximum likelihood approach may require several times more calculations to attain the same accuracy.

Civil infrastructures, such as highway bridges, located in seismically active regions are often subjected to multiple earthquakes, including multiple main shocks during their service life or main shock–aftershock sequences. Repeated seismic events result in reduced structural capacity and may lead to bridge collapse, causing disruption in the normal functioning of transportation networks. This study proposes a framework to predict damage accumulation in structures subjected to multiple shock scenarios after developing damage index prediction models and accounting for the probabilistic nature of the hazard. The versatility of the proposed framework is demonstrated on a case-study highway bridge located in California for two distinct hazard scenarios: (1) multiple main shocks during the service life and (2) multiple aftershock earthquake occurrences following a single main shock. Results reveal that in both cases there is a significant increase in damage index exceedance probabilities due to repeated shocks within the time window of interest.

This paper proposes a reliability estimation methodology which utilizes system identification results obtained from vibration measurements. A series of earthquake and white noise excitations are imposed to a three-bent reinforced concrete bridge by three-shaking tables, simultaneously. Progressive structural damage is measured and observed, in accordance with increasing intensities of damaging events. Response measurements are obtained by accelerometers located on the deck and the columns of the bridge. Finite element models for non-updated and updated cases were obtained with and without considering acceleration measurements, respectively. Afterwards, damage detection and reliability estimation were carried out for these two cases using fragility curves. Consequently, it is shown that fragility curves of updated models significantly differ from fragility curves of non-updated models. The distinction stems from the difference between stiffness and especially damping parameters of updated and non-updated models. Such difference becomes more prominent at the extreme levels of damage.

The development of fragility relations is an important step in the application of performance-based earthquake engineering. Data from 69 tests were collected and reviewed to develop fragility relations for new slab-column frame construction. Damage states were defined and fragility relations were developed for reinforced and post-tensioned concrete connections, both with and without shear reinforcement. Test results were reviewed to determine the likelihood and type of repair for various damage states. Derived empirical fragilities were incorporated into the ATC-58 loss estimation software Performance Assessment Calculation Tool (PACT). Nonlinear pushover analyses were conducted on test specimens and findings were compared to test results to assess bias in common modeling approaches. Comparisons indicate that the values of median model to test ratios vary between 0.9 and 1.25 for displacements corresponding to yield and for models with column stiffness based on ASCE 41-06 median stiffness at low axial loads of 0.2EI_gross.

A direct displacement-based design (DDBD) methodology is described for propped rocking walls (PRWs). PRWs represent a novel seismic force-resisting system that combines passive supplemental damping devices with unbonded post-tensioned concrete rocking walls. The key aspect of the proposed design procedure is the closed-form derivation of the stabilized hysteretic response of PRWs under reverse cyclic loading. This allows the direct application of the DDBD procedure to satisfy desired displacement performance objectives under prescribed levels of seismic intensity. Nonlinear response analyses are conducted on a prototype PRW structure, designed according to the proposed DDBD procedure to evaluate its performance under strong ground shaking.

Results from a previous experimental program demonstrated that loading rate, strength mechanisms associated with the failure mode, low-cycle fatigue, and cumulative values of displacement, and dissipated energy strongly affect the degradation properties of reinforced concrete (RC) walls for low-rise housing. Thus, data obtained from quasi-static (QS) cyclic tests should not immediately be assumed to represent a conservative lower bound on a specimen's capacity. Aimed at numerically correlating results measured during dynamic and QS-cyclic testing, this paper proposes a strength degradation model. The model is readily applicable to seismic design or assessment of performance of existing and new structures. A seismic demand model is also proposed for correlating the intensity and duration of a given earthquake-induced movement to parameters that define the degradation model. Correlations are deemed useful for interpreting the results of QS-cyclic tests and for calibrating hysteretic and behavioral analytical models obtained from QS testing.

Unreinforced masonry buildings, constructed with stones or bricks, are common in the northern areas of Pakistan. In the October 2005 Kashmir earthquake, the seismic performance of stone masonry buildings was found to be poor, which was the primary source of fatalities. Unreinforced brick masonry (URBM) buildings, however, performed well even in severely jolted areas. The performance of URBM could have been much better if the affected buildings were constructed by using proper guidelines. Taking lessons from the disaster, an experimental investigation, based on typical geometry and precompression levels of the URBM shear walls in the affected region, was conducted to evaluate their seismic performance. Twelve walls were tested in the in-plane direction using quasi-static cyclic loading. First-story drift ratios for various performance levels in URBM buildings are proposed. The influences of relative precompression level and aspect ratio on the damage pattern, ultimate drift ratio, and equivalent viscous damping of the walls are examined.

This work presents mechanics, tests, and finite element analyses of a novel steel dual-core self-centering brace (SCB) with flag-shaped re-centering responses. The axial deformation capacity of the brace is doubled with respect to the SCED brace by serial deformations of two sets of parallel tensioning elements when both braces use the same tensioning elements. The mechanics of the brace is first explained; six tensioning elements and four dual-core SCBs are tested to evaluate their cyclic performance. The braces exhibit excellent performance up to a drift of 2% with a maximum axial force around 1,400 kN. The braces also survive 15 low-cycle fatigue tests at a drift of 1.5%. Tensioning elements fail when the braces are overloaded to 2.5–3% drift. Finite element analysis is conducted to further verify hysteretic responses of the dual-core SCB in cyclic tests. A design procedure for the proposed dual-core SCB is also included in the paper.

Spray-applied fire-resistive material (SFRM) is prone to debonding, cracking, and spalling in steel moment-frame plastic hinge regions during inelastic seismic response. To evaluate the effect of experimentally observed earthquake-induced SFRM spall patterns on building sidesway response during an ensuing fire, an analytical case study is developed for a steel special moment-frame building with a seismic hazard representative of coastal California. Response data from numerical earthquake simulations indicate that damage to SFRM insulation in beam hinge regions should be anticipated following ground shaking representative of the maximum considered seismic hazard. Thermomechanical post-earthquake fire simulations demonstrate that earthquake-induced SFRM spalling significantly increases thermal degradation in the affected beam hinge regions during fire exposure, leading to pronounced softening of moment-rotation response for the beam-column assemblies. This temperature-induced moment-frame connection softening increases the flexibility of the structural system for sidesway motion and exacerbates drift demands under the action of residual destabilizing forces.

A reduced-scale, planar, two-story by two-bay reinforced concrete frame with weak beam-column joints was subjected to earthquake simulations on a shaking table. The beam-column joints did not contain transverse reinforcement, as is typical in older construction designed without attention to detail for ductile response. A series of linear and nonlinear analytical models of the frame were developed in accordance with American Society of Civil Engineers standards and subjected to the input base motions. The goodness of fit between analytical and measured results depended on the details of the analytical model. Reasonably accurate reproduction of the measured response was obtained only by modeling the inelastic responses of both columns and beam-column joints. The results confirm the importance of modeling nonlinear joint behavior in older concrete buildings with deficient beam-column joints.

In this paper, new formulations to calculate equivalent damping ratios used in equivalent linear analysis of seismic-isolated structures, specifically isolated with lead-rubber bearings (LRBs), are proposed. These formulations are capable of incorporating the variation in LRB hysteretic behavior due to reduced bearing strength as a function of lead core heating. To quantify the accuracy of the proposed equations in predicting the maximum isolator displacements (MIDs), MIDs obtained from an extensive number of nonlinear time history analyses (NTHAs) were compared with predicted ones. NTHAs were conducted with two sets of near-field ground motions recorded at different soil conditions. It was found that different formulations are needed to calculate the equivalent LRB damping ratios for the two considered ground motion sets. It was also found that the proposed equations result in highly accurate MID estimations, regardless of isolator characteristics, soil properties, or seismicity levels.

Masonry-infilled reinforced concrete (RC) frames are popular structural systems; however, there is much uncertainty in their response under seismic loads. Using the data from past experimental studies, a simple force-deformation model with three control points was developed. The effect of the model parameters on the ductility reduction factor (DRF) and ductility demand (DD) was examined. Statistical tests indicated that the ratio of residual strength to peak strength was the most significant parameter. The traditional approach to determining DRF ordinates through iteration for an assumed value of ductility may result in inappropriate DRF values because of the nonmonotonic relationship between DRF and DD. Constant ductility charts were developed to appropriately account for nonmonotonicity. It was found that the allowable DRF may be much higher if relatively weaker infill compared to the strength of the frame is used, which underscores the need for modifying code provisions because they allow relatively strong infill.

Expressions for the expected value of the first mode damping ratio are derived by using 122 seismic responses from concrete buildings and 81 from steel. The results include dissipation at the soil-structure interface and are appropriate for situations in which this source of dissipation is not included in the model. Comparisons between models of different complexity indicate the appropriateness of using a single regressor, for which the building height is used. It is shown that the Fisher information about damping increases with the number of response cycles; this result is used to define weights for the residuals of the regression. The effective damping in steel buildings, with the exception of very tall structures, is found to be larger than the 2% typically used in practice, whereas the 5% assigned to concrete proves to be similar to the mean of the data set.

The endurance time method (ET) is a dynamic analysis procedure in which intensifying dynamic excitations are used as the loading function. Seismic performance is evaluated over the entire range of equivalent seismic intensities of interest in each response history analysis, considerably reducing computational demand. In this paper, a general methodology for performance-based retrofitting of typical steel frames by the ET method is discussed. A baseline steel moment-resisting frame is considered, and its seismic performance is evaluated by the ET method, considering viscous dampers and shear wall panels as strengthening alternatives. Each retrofitting option includes several design alternatives as well. The versatility of the ET method for this category of seismic design problems is demonstrated. Seismic performance, in conjunction with life-cycle costs, is employed to select the most appropriate alternative.

A simple prismatic Timoshenko beam model with soil-structure interaction (SSI) is developed to approximate the dynamic linear elastic behavior of buildings. A closed-form solution with complete vibration modes is derived. It is demonstrated that building properties, including mode shapes, can be derived from knowledge of the natural frequencies of the first two translational modes in a particular direction and from the building dimensions. In many cases, the natural frequencies of a building's first two vibrational modes can be determined from data recorded by a single seismometer. The total building's vibration response can then be simulated by the appropriate modal summation. Preliminary analysis is performed on the Caltech Millikan Library, which has significant bending deformation because it is much stiffer in shear.

Liquid sloshing causes severe damage to the floating roofs of storage tanks. Liquid–roof interaction imposes a complicated distribution of out-of-plane deformation in a single deck floating roof (SDFR), which is the primary source of high seismic stress. This paper proposes a new seismic design procedure for evaluating the seismic stress of an SDFR. This method revises the relationship between vertical deformation of the deck plate and the radial shrinkage of the pontoon, and estimates the nonlinear behavior of the free surface. Moreover, the attenuation of the sloshing wave height attributable to the presence of an SDFR is analytically evaluated. A design flowchart according to the new method is suggested. This method emphasizes the nonlinear effects of large amplitude wave for smaller capacity tanks, and the seismic stress caused by the second sloshing mode for broad tanks.

An approach is proposed to evaluate the confidence factor implicit in structures over an interval of time, considering that the structural capacity and structural demand vary simultaneously over time. A new closed-form mathematical expression of the confidence factor over a time interval is used, assuming that the structural capacity degradation is represented by a second degree polynomial function in the total interval. This formulation is made in accordance with the demand and capacity factor design format. Confidence factors at the ends of different time intervals are evaluated for an old ten-story building. The confidence factors and their confidence levels, calculated under the assumption that the structural capacity degradation follows a linear function, and alternatively, a polynomial function, are compared. The maximum difference between confidence factors assuming both types of functions is 5% after 100 years of structure construction, which represents a small difference for the engineering practice.

This study addresses the responses of idealized building clusters during earthquakes, their effects on ground motion, and the ways individual buildings interact with the soil and with each other. We simulate the ground motion during the 1994 Northridge earthquake and focus on the coupled responses of multiple simplified building models located within the San Fernando Valley. Numerical results show that the soil-structure interaction (SSI) effects vary with the number and dynamic properties of the buildings, their separation, and their impedance with respect to the soil. These effects appear as: (i) an increased spatial variability of the ground motion; and (ii) significant reductions in the buildings’ base motion at high frequencies, changes in the higher natural frequencies of the building-foundation systems, and variations in the roof displacement, with respect to those of the corresponding rigid-base and single SSI models.

The variations of identified wave velocities of vertically propagating waves through the structure are investigated for a 54-story steel-frame building in downtown Los Angeles, California, over a period of 19 years since construction (1992–2010), using records of six earthquakes. The set includes all significant earthquakes that shook this building, which produced maximum transient drift ∼0.3% and caused no reported damage. Wave velocity profiles β(z) are identified for the NS, EW, and torsional responses by fitting layered shear beam/torsional shaft models in the recorded responses, by waveform inversion of pulses in impulse response functions. The results suggest variations larger than the estimation error, with a coefficient of variation about 2–4.4%. About 10% permanent reduction of the building stiffness is detected, caused mainly by the Landers and Big Bear earthquake sequence of 28 June 1992, and the Northridge earthquake of 17 January 1994. Permanent changes of comparable magnitude were identified also in the first two apparent modal frequencies, f_1;app, and f_2;app, which were identified from the peaks of the transfer-function amplitudes.

On 23 October 2011, and then on 9 November 2011, two earthquakes struck the province of Van in eastern Turkey. One month after the first earthquake, between 25 November and 27 November 2011, a reconnaissance team from the Middle East Technical University, Disaster Management Implementation and Research Center (METU DMC) visited the region. The team focused on disaster management activities such as emergency relief, damage assessment, psychosocial support, and economic impacts. Field observations and personal interviews concluded that deficits in mitigation led to shortcomings in the response and rehabilitation operations in Van. Although search and rescue activities were evaluated as satisfactory, there were problems in the organization of support services, temporary accommodation, and delivery of basic needs. This paper presents a reconnaissance report outlining the observations of the interdisciplinary team in the field. It suggests some policies for improvement in the disaster management system in the future.

This paper describes two large, high-quality experimental data sets of ground motions collected with locally dense arrays of seismometers deployed on steep mountainous terrain with varying slope angles and topographic features. These data sets were collected in an area of central-eastern Utah that experiences frequent and predictable mining-induced seismicity as a means to study the effects of topography on small-strain seismic ground motions. The data sets are freely available through the George E. Brown, Jr. Network for Earthquake Engineering Simulation data repository (NEEShub.org) under the DOI numbers 10.4231/D34M9199S and 10.4231/D3Z31NN4J. This paper documents the data collection efforts and metadata necessary for utilizing the data sets, as well as the availability of supporting data (e.g., high-resolution digital elevation models). The paper offers a brief summary of analyses conducted on the data sets thus far, in addition to ideas about how these data sets may be used in future studies related to topographic effects and mining seismicity.

The purpose of the Bayesian approach is to integrate multiple sources of information into one final best-estimate with a unique algorithm, and a few applications have been developed for a variety of studies. This technical note provides two Bayesian algorithms for earthquake studies: the development of earthquake source-to-site distance distributions and the smoothing of earthquake rates in a region. In addition to the derivations, this note also provides demonstrations on the basis of real earthquake data to provide a better explanation of the two Bayesian algorithms proposed.

Estimation of fragility functions using dynamic structural analysis is an important step in a number of seismic assessment procedures. This paper discusses the applicability of statistical inference concepts for fragility function estimation, describes appropriate fitting approaches for use with various structural analysis strategies, and studies how to fit fragility functions while minimizing the required number of structural analyses. Illustrative results show that multiple stripe analysis produces more efficient fragility estimates than incremental dynamic analysis for a given number of structural analyses, provided that some knowledge of the building's capacity is available prior to analysis so that relevant portions of the fragility curve can be approximately identified. This finding has other benefits, given that the multiple stripe analysis approach allows for different ground motions to be used for analyses at varying intensity levels, to represent the differing characteristics of low-intensity and high-intensity shaking. The proposed assessment approach also provides a framework for evaluating alternate analysis procedures that may arise in the future.

A risk prioritization procedure is developed for deficient concrete public buildings within the scope of a seismic risk reduction program. The main purpose is identifying public buildings with high damage risk in a region for efficient retrofit investments. Regularity of structural systems and repeatability of deficiencies in public buildings provide opportunities for developing simple and reliable assessment procedures. The proposed procedure is based on calculating a risk index from the comparison of lateral load demand to lateral load capacity at the critical story of a building, and then prioritize the buildings in accordance with their risk index. Final decision for retrofitting is made with reference to the ratio of retrofitting cost versus demolishing and rebuilding cost. It has been shown on a sample of 70 retrofitted public buildings that the retrofitting cost ratio of deficient buildings is independent of risk level, age, height, floor area and concrete quality.