Earthquake Spectra

This paper presents the results of a study investigating the correlation between the anticipated seismic performance of an ASCE 7 code-compliant steel building with special moment frames and its predicted performance as quantified using ASCE 41 analysis procedures and structural performance metrics. Analytical results based on component-level performances at the collapse prevention structural performance level indicate that special moment frames designed in accordance with ASCE 7, and its referenced standards, have difficulty satisfying the acceptance criteria in ASCE 41 for an existing building intended to be equivalent to a new building.

Chimney behavior is studied via computer simulations to quantify the effects of specific parameters, including chimney height above roof, masonry flexural tensile strength, chimney section dimensions, vertical steel reinforcement, and chimney-house anchorage strength. All of these parameters are found to affect performance. Damage functions are formulated relating peak ground acceleration to the likelihood of extensive chimney damage. The functions offer a practical way to inform fragility curves, thereby better reflecting an individual chimney as well as chimney inventories in regions of interest.

A set of tests on 17 large-scale, nominally identical, beam specimens with variations in loading protocol, loading rate, and restraint to axial elongation are described. Three specimens were also repaired by epoxy injection following an initial damaging earthquake loading. This paper provides a detailed description of the test program, and the corresponding data are made available at Design-Safe (DOI: 10.17603/DS2SQ2K). While the primary goal of the test program was to improve the state of knowledge regarding the post-earthquake residual capacity of reinforced concrete plastic hinges in beams, the data are useful for modeling approaches that consider loading rate, plastic hinge elongation, cyclic degradation, and flexure–shear–axial interaction, in addition to investigating the effectiveness of post-earthquake repair techniques by epoxy injection of cracks.

Monuments, equipment, chimneys, and older intake structures for dams all may rock during strong ground motions. These and other rocking objects are vulnerable to overturning, leading to potential economic loss and disruption to affected communities. The need for methods to estimate rocking response is supported by the breadth of structures susceptible to overturning and their prevalence in the built environment. Previous research on the development of numerical tools for the simulation of rocking behavior in response to earthquake motions has shown that simulation results are highly sensitive to input parameters, and that data from experimental tests are needed to calibrate these tools. To provide such test data, 312 experiments were conducted on unanchored concrete blocks on an earthquake simulator. The tests were instrumented using accelerometers and a three-dimensional (3-D), noncontact optical tracking system. All data are available online and can be accessed via DOI: 10.4231/R7FB513S and in interactive form at datacenterhub.org/resources/14255. Two simple examples are provided to show how the data may be used. Readers are encouraged to use the data as a means for evaluating more detailed methods to evaluate rocking response.

Deep (typically > 1,000 m) shear wave velocity (V _S ) profiles were developed across the Canterbury region of New Zealand at nine strong-motion stations using a combination of active and passive surface wave methods. A multimode, multimethod joint inversion process, which included Rayleigh and Love wave dispersion and horizontal-to-vertical spectral ratio data, was used to develop the V _S profiles at each site. A priori geologic information was used in defining preliminary constraints on the complex geologic layering of the deep basin underlying the region, including velocity reversals in locations where interbedded terrestrial gravels and marine sediments are present. Shear wave profiles developed as part of this study had characteristics comparable to the profiles from 14 Christchurch sites detailed in a separate study. The profiles developed in the two studies were combined to form region-specific V _S profiles for typical deposits, which can be used to improve the accuracy of current three-dimensional (3-D) crustal velocity models of the region.

The 2008 M_w 7.9 Wenchuan, earthquake caused naturally deposited ravelly soils to liquefy over a wide area. Although liquefaction of gravely soils is recognized by the geotechnical profession, observations of liquefaction and nonlique-faction case histories within the literature are few. Through several years of systematic study following the 2008 Wenchuan earthquake (M_w 7.9), 92 locations of gravel liquefaction were identified, described, and mapped. These locations lie within an approximately 3,000 km² area of the Chengdu Plain. Peak ground accelerations estimated at the sites range from 0.15 g to 0.49 g. Taken collectively, these studies reveal the necessary conditions for liquefaction triggering in gravelly materials. Grain size analyses indicates that the ejecta was much finer than the gravels that liquefied. Gravel contents of liquefied soils ranged from 5% to more than 85%. The liquefied gravelly soils were loose, but their measured shear wave velocities range from 133 m/s to 267 m/s, with corrected values ranging from 154 m/s to 31 4m/s. The unique depositional conditions under Chengdu Plain provide favorable conditions for extensive liquefaction of gravelly soils. The shallow soil profiles consist of a 0.5 m to 5.5 m impermeable soil (i.e., the capping layer) overlying gravels ranging in thickness from a few meters to hundreds of meters.

Current practice in seismic design often assumes free-field conditions for the estimation of liquefaction-induced building settlement. This is inaccurate, as a structure places additional stresses on the soil, resulting in changes to the spatial and temporal occurrence of liquefaction, accelerations, and deformations. Further complications arise in dense urban environments where closely spaced structures may interact through structure-soil-structure interaction (SSSI). Previous studies have shown that SSSI may have positive or negative effects on the response of adjacent structures in terms of permanent settlement, rotation, and flexural deformations. However, little is known regarding how to maximize the benefits of SSSI with minimal risk of adverse consequence. In this study, centrifuge tests were conducted on both isolated and closely spaced structures to identify how the building separation and ground motion characteristics affect the response of adjacent structures founded on a layered, liquefiable soil profile. Results indicate that properly planned configurations and interactions may be employed in combination with traditional mitigation strategies to improve the settlement-rotation response of adjacent structures, while also reducing the demand imposed on the superstructure.

There is no scientific consensus on how finite virtual faults should be modeled in the probabilistic seismic hazard analysis of diffuse seismicity. Often pragmatic implementation decisions are made as a matter of convenience or computational efficiency. To better understand how differences in modeling virtual faults impact seismic hazard, we evaluated several methods of modeling such faults. For our preferred model, we test the sensitivity of the hazard to differences in fault discretization density, number of random azimuths, and cutoff distance. We propose a new computationally efficient method of modeling the random orientation of virtual faults by holding the fault plane fixed in space and rotating a virtual site around the source grid point. We show that there can be relatively large differences in seismic hazard, depending on how virtual faults are modeled, and provide guidance on how virtual-fault parameters should be selected in order to achieve a specified degree of accuracy.

Deep dynamic site characterization and a site-specific ground motion response analysis (SSGMRA) were conducted for a bridge site in Monette, Arkansas. The SSGMRA indicated the design acceleration response spectrum determined using the American Association of State Highway and Transportation Officials (AASHTO) general seismic procedure could be reduced by one third for the short-period range due to attenuation of the short-period ground motions. The steel girder pile-bent bridge, originally designed using the AASHTO general seismic design procedure, was redesigned using the updated seismic demands estimated from SSGMRA. A cost-savings analysis was then conducted to determine the potential savings associated with conducting the SSGMRA. By designing based on the results of the SSGMRA, a potential gross savings of $205,000, or 7% of the original bridge construction cost, could be achieved for the study bridge. Items that contributed most to the cost savings were the pile and embankment construction.

This paper presents a ground motion prediction model (GMPM) for estimating medians and standard deviations of the random horizontal component of the peak inelastic displacement of 5% damped single-degree-of-freedom (SDOF) systems, with bilinear hysteretic behavior and 3% postelastic stiffness ratio, directly as a function of the earthquake magnitude and the distance to the source. The equations were developed using a mixed effects model, with 1,662 recorded ground motions from 63 seismic events. In the proposed model, the median is computed as a function of the vibration period and the normalized strength of the system, as well as the event magnitude and the Joyner-Boore distance to the source. The standard deviation of the model is computed as a function of the vibration period and the normalized strength of the system. The proposed model has the advantage of not requiring an auxiliary elastic GMPM to predict the median and dispersion of peak inelastic displacement.

A damage assessment survey of 169 low-rise reinforced concrete buildings was conducted following the 16 April 2016 Ecuador earthquake. Forty-four percent of the buildings surveyed sustained severe structural damage. Using the collected data, seismic vulnerability indices were calculated to examine their correlation with damage observations. It was found that 92% of the buildings with observed severe structural damage had calculated wall and column index pairs (WI, CI) that satisfied the relation WI+CI/2 < 0.2%. The frequency of damage was lower for higher-priority index values, defined as the sum of CI+WI. Furthermore, frequency of damage in buildings with captive columns was observed to decrease with window height-to-column height ratios of more than 20%.

With the rapid development of remote sensing technology, satellite or aerial images from the disaster area become available within 24 hours after an earthquake. The collapsed buildings can be easily identified from these images. In this work, a framework for near real-time seismic loss estimation for regional buildings is proposed, which improves the accuracy of nonlinear time-history analysis (THA)-based loss estimations by taking advantage of the identified building collapse scene of the disaster area. Specifically, a series of THA are performed for the target regional buildings, thereby generating a number of simulation results. Those simulation results that bear strong similarities to the identified collapse scene are identified as the optimal solutions, which will be used to estimate the seismic loss. The simulation results of the case studies signify that the use of the identified building collapse scene leads to much closer estimations to actual economic losses.

Post-earthquake recovery models can be used as decision support tools for pre-event planning. However, due to a lack of available data, there have been very few opportunities to validate and/or calibrate these models. This paper describes the use of building damage, permitting, and repair data from the 2014 South Napa Earthquake to evaluate a stochastic process post-earthquake recovery model. Damage data were obtained for 1,470 buildings, and permitting and repair time data were obtained for a subset (456) of those buildings. A “blind” prediction is shown to adequately capture the shape of the recovery trajectory despite overpredicting the overall pace of the recovery. Using the mean time to permit and repair time from the acquired data set significantly improves the accuracy of the recovery prediction. A generalized model is formulated by establishing statistical relationships between key time parameters and endogenous and exogenous factors that have been shown to influence the pace of recovery.

Large inelastic tensile strains and wide horizontal cracks primarily caused by in-plane loading, may lead to local out-of-plane deformations of the end regions of reinforced concrete (RC) walls within a buckled zone that comprises the plastic hinge length. Critical parameters that influence the onset of this failure mode have been studied through past experimental tests on RC prisms subjected to axial loading, which simulates the response of end regions of RC walls under in-plane demands. Missing from those studies is the effect of bidirectional loading protocols and the effect of the longitudinal reinforcement ratio on the hysteretic response. Therefore, 12 RC prisms with 3 longitudinal steel ratios representative of prototype boundary elements of typical special RC walls and piers walls were tested. The experimental results showed that the longitudinal steel content and the in-plane loading demands mainly govern the onset of out-of-plane buckling instability of planar RC walls.

This study presents a beam-based modeling approach for the analysis of reinforced concrete (RC) frame members under cyclic loads that can capture the effect of inelastic buckling and rupture of reinforcing steel bars. The approach uses force-based elements with a fiber-section model and a corotational formulation to account for the geometric nonlinearity effect on the response of columns. A recently proposed phenomenological uniaxial model for steel reinforcement, capable of simulating inelastic buckling and rupture due to low-cycle fatigue, is used for the reinforcing steel fibers. Numerical simulation models also account for strain penetration effects in the analyses. The modeling approach is validated with the results of experimental tests on RC columns under cyclic loads. A sensitivity study is also pursued to elucidate the impact of bar buckling and strain penetration on the analytical results.

The assessment of the seismic performance of reinforced concrete (RC) frame structures using the equivalent linearization approach requires comprehensive insight into the nonlinear response of the system, and most previous researches focused on the analysis of a single-degree-of-freedom (SDOF) system. To describe the hysteretic behavior of a multi-degree-of-freedom (MDOF) system accurately, monotonic and cyclic pushover analyses for 88 RC frames structures with various configurations and design parameters are carried out and a unified hysteresis loop expression modeling the cyclic pushover results of RC frame system is developed. Then, a global equivalent damping based on Jacobsen's approach is derived, and comparisons between the displacements obtained by nonlinear static analysis (NSA) utilizing the derived global equivalent damping and those obtained by nonlinear time history analysis (NTHA) are made. Finally, a modified global equivalent damping is presented by calibrating the derived Jacobsen's equivalent damping through NTHA results. Based on the modified equivalent damping, the statistical analysis of the ratios of the results obtained by NTHA to those obtained by NSA is implemented to predicate the probabilistic seismic displacement demands of RC frame structures.

This paper aims at investigating the seismic fragility of confined masonry (CM) structures in Lima, Peru, which can be used to perform earthquake scenarios at urban scale. A database describing the geometric properties (walls density, building area, height) of this type of structure was developed using data from field surveys. This information was complemented with results from experimental tests to compute a large set of capacity curves using a mechanical procedure. These models were tested against a set of ground motion records using the displacement-based earthquake loss assessment (DBELA) procedure, and the structural responses were used to derive fragility functions for four building classes. The resulting fragility curves were convoluted with seismic hazard curves to evaluate the annualized expected loss ratio and annual collapse probability.

The earthquake performance of retrofitted clay brick masonry substation buildings was investigated from a multidisciplinary perspective that included structural, economic, and social considerations. One-hundred-fifteen single-story double-leaf clay-brick masonry substation buildings located within the wider Christchurch, New Zealand, region were investigated in detail. In the mid-1990s, these substation buildings were seismically retrofitted using a system of simple and cost-effective steel elements as part of a natural disaster improvement program, with an overall cost of N.Z. $6 million (approximately U.S. $4 million). Rapid assessment evaluation was conducted following the 2010/2011 Canterbury earthquakes with the determination that 82% of these clay-brick masonry substation buildings sustained minor damage, and 15% had moderate damage. Meanwhile, one substation building suffered significant damage, and two substation buildings experienced heavy damage. Investment in the seismic improvement program resulted in cost savings of approximately N.Z. $60 million (U.S. $44 million) and contributed to heritage building preservation.

Methods for the seismic design of base connections in steel moment frames are well-developed and routinely utilized by practicing engineers. However, design loads for these connections are not verified by rigorous analysis. This knowledge gap is addressed through nonlinear time history simulations using design-level seismic excitation that interrogate demands in column base connections in 2-, 4-, 8-, and 12-story steel moment frames, featuring base connections that reflect current U.S. practice. The results indicate that: (1) for exposed base plate connections, lower bound (rather than peak) estimates of axial compression are suitable for design because higher axial forces increase connection strength by delaying base plate uplift; (2) even when designed as pinned (as in low-rise frames), base connections carry significant moment, which can be estimated only through accurate representation of base flexibility; and (3) the failure of embedded base connections is controlled by moment, which may be estimated either through overstrength or capacity-based calculations.

Building-specific loss assessment methodologies use component fragility curves to compute expected losses in the aftermath of earthquakes. Such curves are not available for steel columns assuming they remain elastic because of capacity design considerations. Nonetheless, first-story steel columns in moment-resisting frames (MRFs) are expected to experience damage through flexural yielding and formation of geometric instabilities. This paper uses an experimental database that was recently assembled to develop two sets of univariate drift-based column fragility curves that consider the influence of loading history. Ordinal logistic regression is also employed to develop multivariate fragility curves that capture geometric and loading parameters that affect column performance. The implications of the proposed fragility curves for building-specific loss assessment are demonstrated using an eight-story office building with steel MRFs. It is shown that structural repair costs in this case may increase by 10%, regardless of seismic intensity, when column damage is considered. Similarly, the contribution of structural component repairs to expected annual losses may double over the building's life span.

A controlled spine frame system consists of moment frames and spine frames with concentrated energy-dissipating members. This system guarantees the continuous usability of buildings against Japanese Level-2 earthquake events (similar to DBE events in California), and the authors have confirmed its excellent performance in preventing damage concentration in low-rise buildings. This study further investigates the effect of diverse structural properties on the seismic performance of controlled spine frames applied in high-rise buildings. The effect of building height, yield drift of dampers, spine-to-moment frame stiffness ratio, and damper-to-moment frame stiffness ratio are illustrated in detail, and optimal values are discussed. Also, a segmented spine frame system is proposed for high-rise buildings. The simple evaluation procedure proposed by the authors for low-rise buildings, based on equivalent linearization techniques and response spectrum analyses, was modified to include higher-mode effects for high-rise buildings based on modal analysis. The modified evaluation method was verified by modal pushover and time-history analyses.

In this study, a computational seismic design routine is proposed based on a generalized response spectrum analysis for highly indeterminate structures with energy-dissipation members, such as viscous or elasto-plastic dampers. Complex stiffness terms are introduced to account for displacement-dependent damping, and a three-dimensional (3-D) element stiffness matrix with complex axial stiffness is proposed for elasto-plastic dampers. A modified complete quadratic combination method previously developed for real symmetric damped systems is extended to complex asymmetric damped systems, based on a theoretical analysis of eigenvalue equations. The response is evaluated by iteratively conducting complex eigenvalue analysis and modal combination. The accuracy is confirmed through comparison to nonlinear response history analysis of 2-D frame models. Finally, an example application is presented of a 3-D truss tower seismically retrofitted by replacing the braces with viscoelastic and then elasto-plastic dampers. The proposed design routine is used to rapidly identify novel and efficient damper arrangements and sizing distributions, avoiding computationally intensive nonlinear response history analysis.

In many seismically active countries, there is a high level of earthquake risk because of the presence of large stocks of earthquake-prone buildings. The typically high cost of earthquake retrofit and the difficulties associated with satisfying the interests of multiple stakeholders within a meaningful time frame potentially result in building demolition as the default seismic risk reduction solution. The Heritage Evaluation Framework (HEF) is a multidisciplinary decision-making tool to guide proposed seismic retrofit design by gathering inputs from all project stakeholders and to evaluate a particular seismic retrofit design against client expectations. The performance of the HEF is demonstrated for two retrofit projects using input data acquired via interviews, site walkthroughs, and regular meetings with project teams and clients. Results show that the HEF accommodates conceptual designs and provides useful feedback while encouraging early multidisciplinary collaboration.

A major concern about chlorinated polyvinyl chloride (CPVC) pipes is the large swing of branch lines during earthquake-induced motions. National Fire Protection Association (NFPA) 13 defines spacing requirements for braces and restraints, based on pipe-bending strength, but does not limit the swing. Shake table tests and numerical simulations show that the swing of CPVC branch lines can be limited to an acceptable level if the ends are braced and the spacing of restraints follows the NFPA 13 requirements for CPVC, or if restraint spacing is reduced to about half of that currently allowed in NFPA 13.

Power transformers and bushings are key pieces of substation equipment and are vulnerable to the effects of earthquake shaking. The seismic performance of a 1,100 kV bushing, used in an ultra-high voltage (UHV) power transformer, is studied using a combination of physical and numerical experiments. The physical experiments utilized an earthquake simulator and included system identification and seismic tests. Modal frequencies and shapes are derived from white noise tests. Acceleration, strain, and displacement responses are obtained from the uniaxial horizontal seismic tests. A finite element model of the 1,100 kV bushing is developed and analyzed, and predicted and measured results are compared. There is reasonably good agreement between predicted and measured responses, enabling the finite element model to be used with confidence for seismic vulnerability studies of transformer-bushing systems. A coupling of the experimental and numerical simulations enabled the vertically installed UHV bushing to be seismically qualified for three-component ground shaking with a horizontal zero-period acceleration of 0.53 g.