Simulation‐based characterization of the variability of earthquake risk to buildings in the near‐field

Recent advancements in high performance computing platforms and computational workflow for regional‐scale simulations are enabling unprecedented modeling of fault‐to‐structure earthquake processes. Regional simulations resolving ground motions at frequencies relevant to engineered systems are becoming computationally viable and provide a new capability to improve understanding of the geographical distribution and intensity of risk to buildings and critical infrastructure. As computational capabilities advance, it is essential to move beyond illustrative single rupture realizations for scenario earthquake events towards the development of a full suite of rupture realizations that appropriately characterize the range of risk to building systems. The work described in this article investigates the application of a suite of fault rupture realizations with the objective of assessing near‐fault, site‐specific seismic demand variability for building structures. A representative high‐performance regional‐scale computational model is utilized to execute ground motion and building response simulations based on 18 kinematic rupture realizations of an M7 strike‐slip scenario earthquake. The fault rupture models for the scenario earthquake are created by systematically perturbing the hypocenter location and stochastically generating rupture parameters (slip, rise time, rake angle) to represent a breadth of ground motion intensities resulting from the spatial and temporal variabilities of an earthquake rupture process. The resulting seismic demand variability for three‐story (short period) and forty‐story (long period) steel moment‐resisting frame buildings is characterized in terms of the median and distribution of peak inter‐story drift ratio for a range of near‐fault sites. The full suite of 18 fault rupture realizations and approximately 280,000 nonlinear dynamic building simulations indicate that the three‐story building undergoes higher median seismic demand and significantly greater variability of demand at a given site than the forty‐story building, which has important implications for the level of certainty in predicting building performance during an earthquake. The simulations performed provide deeper insight into the relationship between fault rupture parameterization and building response, which is essential information for developing a representative suite of rupture realizations for specific earthquake scenarios.


NOVELTY
• HPC simulations of ground motions and approximately 280,000 nonlinear building simulations provide an extensive synthetic dataset on near-field building response.• New information is provided on intra-and inter-event variability of risk through a suite of rupture simulations along with computed statistics of building response.This knowledge informs appropriate selection of the seismic design basis, and quantifies the potential variance from design basis for equally probable realizations of fault rupture.• For an established kinematic rupture model, the number of realizations required to quantify risk, in terms of median seismic demand and standard deviation, is explored for low-rise (high frequency) and tall (low frequency) buildings.
motions in seismic hazard and risk analysis is the ability to incorporate region-specific source and wave propagation effects that are not fully representable in empirical ground motion models. 31In addition, simulations can provide synthetic data with a desired spatial density and temporal resolution for understanding building response variability on a site-by-site basis from both intra-and inter-event earthquake realizations.However, a major challenge in utilizing physics-based simulations in earthquake risk evaluations is to identify and simulate a sufficient set of computationally intensive fault rupture realizations that can adequately capture and characterize the variability of the risk.This difficulty includes the challenges associated with pushing the reliability of simulations to higher frequencies of engineering interest where source mechanics and finer-scale geologic structure are still less well understood and constrained.
To demonstrate and compute seismic risk accounting for the aforementioned variabilities, a pair of recent studies 28,32 utilized a set of three fault rupture realizations employing an advanced pre-exascale (1 exaflop = 10 18 FLOPS) HPC earthquake simulation framework (EQSIM).McCallen et al. 32 employed a set of three stochastic fault rupture models accounting for the hypocenter locations only (i.e., same slip distributions), that demonstrated a clear trend in higher median and greater variability of a building's peak interstory drift (PID) ratio near the fault.The study also computed site-to-site PID ratios of two realizations to illustrate an inter-event variability of building response between the two simulations by changing the location of the hypocenter.Kenawy et al. 28 utilized a combination of one stochastic and two hybrid 34 source rupture models that accounted for changes in fault slip distribution on two representative reinforced concrete buildings and demonstrated a building's PID can vary up to eightfold within 1 km of the rupturing fault.
The research work described herein, employs a larger suite of fault rupture realizations to further explore and quantify site-to-site seismic demand variability of building systems as a consequence of changing the hypocenter location as well as slip distribution on the fault surface, which are two critical source parameters influencing the resulting ground motions.The utilization of a broader suite of fault rupture realizations provides a more comprehensive inspection of the inter-and intra-event variability in building seismic demand due to modeling uncertainty of the earthquake source rupture process.In addition, application of the wider range of source description permits evaluation of the distributions and expected median seismic demands of building systems at desired sites with greater confidence.Furthermore, this application enables to approximately quantify the number of rupture realizations required to inform simulation-based earthquake risk assessment.
With the simulation capabilities gained through recent computational advancements 27,33,35,36 a comprehensive exploration of earthquake source effects on building risk posed by a potential large magnitude earthquake event is computationally achievable.The practical removal of computational barriers through the EQSIM HPC simulation advancement has enabled the evaluation of multiple source rupture realizations and associated hundreds of thousands of building response simulations utilized in this study.The goal of the study is to characterize both intra-and inter-event seismic demand variability of a building at near-fault sites and quantify an adequate number of fault rupture realizations to that end.Building models employed in this study encompass high-frequency three story and low-frequency forty story steel moment-resisting frame buildings to capture a breadth of variability for both stiff and flexible structures.

DESCRIPTION OF THE EARTHQUAKE SOURCE RUPTURE MODELS
Ground motions (0-5 Hz) are simulated for an M7.0 strike-slip crustal earthquake by employing a fully deterministic wave propagation modeling approach, and the kinematic rupture generator 37 of Graves and Pitarka (GP, hereafter).The simulations are performed under the US Department of Energy Exascale Computing Project 32,33 and employ an advanced HPC tool to compute ground motions in a 100 km × 40 km idealized regional-scale domain (see Figure 1) with resolved frequencies up to 5 Hz at a total of 3861 locations spaced at 1 km.A fourth order 3D finite difference code 38 SW4 that includes topography, anelastic attenuation, and mesh refinement and a 600 m deep canonical basin velocity model with a flat free surface, 26,28 illustrated in Figure 1, is used in ground motion simulations.The 3D velocity model is designed to produce wave propagation effects that are typical for a shallow basin structure, including trapping, focusing and scattering of waves in the basin sediments, while including velocity contrast between the basin and surrounding rock.The rock consists of layers representing a gradual increase in velocity, starting with a thin layer with a relatively low velocity near the free surface.The seismic properties in the top layer of the rock model represent the properties of the weathered layer commonly observed at basin-bounding rock sites.Although, similar to the eastern part of the San Francisco Bay Area basin model, 39 the canonical basin model used in this study is not designed to mimic any particular structure.Instead, it is designed to incorporate simple but realistic basin properties in the interest of producing realistic wave propagation effects while facilitating the interpretation of these effects on simulated ground motion.The numerical model solves the wave equation for an anelastic medium in which the dimensionless attenuation factors Q p and Q s are modeled as follows: Basin sedimentary layer: For a minimum shear wave velocity of 320 m/s, a minimum grid spacing of 12.5 m adopted in the geologic model is selected in order to achieve the numerical accuracy required to model wave propagation up to a target frequency of 5 Hz.The resulting computational grid contained approximately 30 billion grid points.The velocity model does not include small-scale variations.The high-frequency modeling of such variations, which can be represented by correlated stochastic velocity perturbations, 40 is beyond the scope of this paper.
A physics-based kinematic fault rupture modeling approach 37 that utilizes correlated kinematic rupture parameters constrained by empirical relationships and dynamic rupture modeling, 34,41 is used to generate the fault rupture realizations.The GP rupture model 37 is heterogeneous with correlated random perturbations at different scale lengths.The resulting rupture model incorporates depth-dependent multi-scale spatial variations of slip, slip rate, slip rake, and rupture velocity that allow for reproducing observed characteristics of near-fault ground motion on a broad frequency range.For example, the long rise time at shallow depths and shorter rise time at greater depths are designed to correctly represent the depth-dependent frequency content of the generated seismic energy on a broad frequency range.Details about the rupture model can be found in GP 2016, 37 and validations of the generated ground motions are available in Pitarka et al. 34,42,43 and Rodgers et al. 44 The vertical planar fault used in the rupture models has a length of 62.6 km, and width of 16 km.It is located 10 km away from the rock edge at the rock-basin interface at a depth of 0.2 km.The rupture velocity is set to 80% of the local shear wave velocity in accordance with observed rupture velocity values found for shallow crustal earthquakes on mature faults.The earthquake focal mechanism is assumed to be predominantly of strike-slip type.The average rake angle is set to 0 degree with spatially correlated random perturbations, computed  following the GP method.Based on rupture models of earthquakes with similar magnitude, 45 the hypocenter was located at a depth of 8 km from the free surface in all rupture scenarios.Along the strike direction the hypocenter was in the center for the bilateral rupture, and it was located at 10 km from the fault edge in the cases of the unilateral rupture models.
A suite of 18 fault rupture models is utilized to characterize variability in ground motions at each site of the computational domain and evaluate the resulting variability in site-to-site building seismic demand.Figure 2 illustrates nine of the 18 rupture models where the hypocenter is chosen to be located either in the center (ruptures 5, 7, 9) or near the fault edges (ruptures 1, 2, 3, 4, 6, 8).As a result of the symmetry created by the horizontally uniform geology, an additional six rupture realizations with hypocenters right-of-center can be generated by mirroring the left-of-center hypocenter realizations about a fault-normal section passing through the fault center.For those cases having hypocenters located at the fault center, the mirroring action does not change their hypocenter locations but reflects the resulting change in the slip distribution, thus still providing three additional albeit different source rupture realizations.The mirroring action thus conducted allows for consistent representation of the realizations with the hypocenters located left, center, and right of the fault plane with equal weight.Each of these fault rupture models differs either in rupture initiation (hypocenter location) or in slip distribution on the fault.The selected rupture initiation locations produce unilateral as well as bilateral ruptures allowing representation of rupture directivity effects with various strengths.For the sake of generality, rupture models with deterministic large-scale features, are not considered in this study.
Figure 3 illustrates the simulated ground motion variability at a given near-fault site (1 km off the fault) resulting from the 18 rupture realizations.The peak ground acceleration (PGA), velocity (PGV), and displacement (PGD) are indicated next to the individual time histories for all realizations.Inter-event variability is observed to be somewhat larger for the PGA than for the PGV.Furthermore, the time histories of the ground velocity are distinguished by the long-period, single-and double-sided high-amplitude pulses that often characterize near-fault motions observed during damaging large earthquakes.Although to a lesser extent, the simulated PGD is also highly variable.As expected, due to the predominantly strike-slip mechanism the PGDs are larger on the FP component of motion than on the FN component.Additionally, permanent ground displacements including fling steps are noticeable in the FP component of It is noted that the PGA amplitudes illustrated here are bounded by the resolved frequencies (0-5 Hz) utilized in the study, but investigations informed that the higher frequencies do not affect the building systems analyzed herein.Figure 4 shows the corresponding acceleration, velocity, and displacement response spectra.FN spectral acceleration indicates higher amplitudes in the short period range, which suggests a higher response susceptibility for stiffer buildings.Spectral velocity demonstrates a similar response, except for a few realizations that exhibit an increased response at longer periods, which mainly affects taller buildings.Spectral displacement exhibits similar behavior trend to the spectral velocity.
Ground motions for the nine source rupture realizations (see Figure 2) are evaluated by plotting the median spectral response of all sites lying within 10 km of the fault (830 for each realization) against 38 selected pulse-like ground motions 46 and demonstrated in Figure 5. Due to symmetry, the median ground motions for the additional nine rupture models are the same and not included in the figure.The real record database utilized in this comparison and the details of the evaluation procedure are explained in McCallen et al. 32 Figure 5 illustrates that median spectral acceleration and +/−1 standard deviation for the real data entirely encapsulates all the median simulated motions at all periods.The synthetic data demonstrate somewhat higher spectral amplitudes at the short period range (∼0.4-0.8 s) and slightly lower spectral amplitudes in the intermediate-long period range (∼2-6 s) in the fault normal component.Figure 6 demonstrates spectral comparison with GMPE 47 at three different near-fault sites (1, 5, and 10 km off the fault) for a strike-slip M7 event with consistent source parameters and site conditions.Such comparisons are illustrated in Figure 6A-C, respectively.Overall, median RotD50 spectra from simulations demonstrate slightly greater spectral amplitudes than the median GMPE but otherwise they agree strongly at all periods and all three distances.Individual spectral scatter from the 18 realizations falls mostly within the +/− 1 SD of the median GMPE at the period range of interest for this study, providing confidence of F I G U R E 4 Spectral response variability at the selected site (see Figure 3) from 18 rupture realizations.utilizing these realizations in building response simulations.It is also worth noting that spectral scatter at 1 km exhibits greater variability than that predicted by the empirical model, which is expected due to near-fault phenomena discussed in the literature not necessarily well represented by the GMPE, particularly for near-fault sites from an M7 event for which the database of observed motions is very limited.

INTRA-EVENT BUILDING RESPONSE VARIABILITY
To analyze the response characteristics of engineered structures with a range of frequency sensitivities, two canonical steel moment resisting 2D frames 32,48 consisting of a high-frequency (stiff) three-story building and a low-frequency (flexible) forty-story building are selected.The frames were designed for combined gravity and seismic load according to the ASCE provisions 49 in the San Francisco Bay Area with a soil site class C. All beam-to-column joints are rigid moment connections for both buildings.All columns employ ASTM A913 Grade 65 with Fy = 65 ksi and Fu = 80 ksi and all beams utilize ASTM A992, Grade 50 with Fy = 50 ksi and Fu = 65 ksi.A bilinear elasto-plastic fiber-based beam element is utilized to characterize cyclic stress-strain curve with a post-yield stiffness ratio of 0.5.A nonlinear finite element code NEVADA is utilized to simulate the structural response. 50The periods of the first Eigen modes are 0.61 and 3.76 s for the three and the forty-story buildings, respectively.
To illustrate the potential variability of a building's seismic demand for a specific fault rupture realization, the distribution of the three-story building PID along the blue line parallel to, and 1 km off the fault, is illustrated in Figure 7.The computational domain, geologic structure and shear-wave velocity illustrated in Figure 1 are utilized for this simulation.The hypocenter for this scenario case is located toward the left end of the fault line and at a depth of 5 km below the ground surface (see rupture realization 4 in Figure 2).The vertical strike-slip fault surface is illustrated (below Figure 7A by a stochastic representation of a heterogeneous slip distribution.The contour plot in the bottom (Figure 7B) demonstrates a snapshot of the ground velocity at a time of 25 seconds after the initiation of the rupture.The color codes represent the intensity of the velocity magnitudes, with the warmer colors portraying the higher magnitudes.For this particular fault rupture realization where the hypocenter is located on the left, the velocity contour plot clearly demonstrates the rupture directivity effect manifested by the increased magnitude towards the right end of the fault.
Figure 7C illustrates the three-story building PID evaluated at every kilometer along the locations lying on the blue line.Despite these sites being equidistant from the fault strike, the building response is found to be highly variable from site Building PID (%) Building PID (%) Building PID (%) Building PID (%)

Locations along strike parallel Locations along strike parallel Locations along strike parallel
F I G U R E 8 Three-story building PID demands at 1, 5, and 10 km off the fault for nine rupture realizations (see Figure 2)-FN motions (top three rows) and FP motions (bottom three rows).
to site with a maximum PID of 5% and minimum PID of approximately 1%.The plot demonstrates very large differential response towards the right end of the fault.These simulated instances of building response demonstrate significant differences from the expected response obtained through traditionally utilized building code approaches, where equidistant buildings from the fault are assumed to experience nearly similar seismic demands.Current building codes 51 (e.g., ASCE  7) based on the combined use of site-specific uniform hazard spectra and ground-motion records do yield some variability at equidistant sites, yet cannot capture the variability estimated through the utilization of simulated motions.For this particular rupture realization, the range between maximum and minimum PIDs along the strike parallel line situated 1 km off the fault is approximately five, indicative of the breadth of seismic demand variability and presenting a challenge for the structural engineers to select an appropriate earthquake induced demand for use in the design of a building.Furthermore, Building PID (%) Building PID (%) Building PID (%) Building PID (%) Building PID (%)

Locations along strike parallel Locations along strike parallel Locations along strike parallel
F I G U R E 9 Forty-story building PID demands at 1, 5, and 10 km off the fault for nine rupture realizations (see Figure 2)-FN motions (top three rows) and FP motions (bottom three rows).
despite having some constraints on the magnitude of a potential earthquake scenario that will occur in a certain region, the causative fault rupture mechanism is never well enough constrained to employ a single source rupture model in the structural risk evaluation.Therefore, depending on the rupture model parameterization in deterministically-simulated earthquake realizations, the seismic demand can exhibit large intra-event variability for the same scenario earthquake.The building design in such a seismically active near-fault region must therefore be informed by the statistics of the building's seismic demands estimated from a suite of rupture realizations that account for the aleatory uncertainty of the source rupture process.Figures 8 and 9 illustrate site-to-site variability of PID for the three and the forty story buildings for the nine rupture realizations (see Figure 2) at three different strike-parallel sections, that is, 1, 5, and 10 km off the fault.The observed drifts indicate that building response from both FN (top three rows) and FP (bottom three rows) motions is generally higher at locations closer to the fault.The drift values also demonstrate localized spikes in PID response at the closer distances especially at 1 km for both components of ground motion.This behavior is indicative of relatively higher site-to-site ground motion variability occurring at locations closer to the source than at more distant sites (e.g., at 5 and 10 km).Site-to-site PID ratios for the three-story building are mostly higher than the corresponding PID ratios for the forty-story building along all the three strike parallel sections, indicating a greater response sensitivity in the case of the shorter building in all nine earthquake realizations.This can be attributed to the fact that the three-story building being stiffer, as opposed to the more flexible forty-story building, is more responsive to higher frequency ground motion waveforms in the near-fault region.
The intra-event PID variability plots provide insight on highly localized building response at the near-fault sites.For instance, two neighboring sites (see plot 4 for FN motions at 68 and 70 km along the fault plane in Figure 8) spaced at just 2 km apart exhibit building PID seismic demands of approximately 1.8% and 5%, respectively.Ground motion and corresponding building response at these two sites are illustrated in Figure 10 in detail.The PGAs at both sites are observed to be nearly equal with an amplitude of 1.5 g.However, the computed ground motion at site B possesses two large pulses in its acceleration time history in contrast to one large pulse observed in site A. These pulses are noticed more clearly in their velocity and displacement time histories where more pronounced double-sided pulse-like waveforms are observed, especially for site B. As discussed in the literature, these pulse-like, high amplitude velocity or displacement waveforms can be especially damaging to buildings.Inspection of the permanent roof displacement and interstory drift comparison at site A and B demonstrates the building response at site A exhibits some plastic behavior whereas the building response at site B exhibits very large plastic deformation in the steel buildings.This significant difference in nonlinear building performance, despite relatively minor differences in their ground motions, has been observed in evaluations of real buildings. 52Based on their analysis of a number of existing buildings, Malley and Pekelnicky noted that when a building undergoes significant nonlinearity, a 10% increase in ground motion magnitude can result in a change of the predicted seismic performance of a building from a condition of immediate occupancy to a condition of collapse.
Table 1 lists the ratio of maximum to minimum PIDs for both three-and forty-story buildings for all sites along the three different strike-parallel sections for nine rupture realizations.The ratios for the remaining nine symmetric realizations are the same and not shown in the table.The computed ratios demonstrate the range of a building's seismic demand variability by identifying the two sites that experience the lowest and highest seismic demands along the equidistant strike parallel section.The maximum intra-event variability is observed to be 12.5, 5.3, and 4.6 for the three-story building, TA B L E 1 Ratio of maximum to minimum PIDs at three strike parallel sections and distances off the fault.and 8.5, 4.3, and 5.1 for the forty-story building for sites 1, 5, and 10 km off the fault, respectively.It is noted that nearly all maximum intra-event variability ratios result from the FP motions (except for the forty-story building at 10 km) for both buildings, indicating a greater motion variability than the FN components at all three distances off the fault.Both three-and forty-story buildings demonstrate an approximately twofold decrease in variability moving from 1 to 5 km off the fault.The average ratios computed from all the ruptures and ground motion components indicate that this variability tends to become similar for both buildings at distances beyond 5 km.

INTER-EVENT BUILDING RESPONSE VARIABILITY
The spatial distributions of PIDs computed for the three-and the forty-story buildings at 3,861 sites in the entire domain, and for the nine center-to-left hypocenter earthquake realizations are illustrated in Figures 11 and 12, respectively.The contour scale is constructed based on the four limit states associated with building damage set by the American Society of Civil Engineers Standard 49 [ASCE 41 -19] to express various levels of inelastic deformation in the steel moment frames.The plots illustrate the distribution of the buildings' peak drift obtained from each of the nine rupture realizations (see Figure 2) for an M7.0 scenario earthquake.All FN plots demonstrate a narrow band of large PID concentrated in the vicinity of the fault, whereas large PID due to the FP motion extends to larger distance from the fault.Overall, the three-story building demonstrates higher inelastic response behavior than the forty-story building for both FN (higher concentration of inelastic PIDs around the fault) and FP (larger spread of inelastic PIDs across the domain) motions.The yellow zones in the FP plots that are located at the farthest distance in the domain indicate that sites as far as 30 km away from the earthquake source can experience some inelastic deformation.Median PID limit state distribution plots are constructed for both three-and forty-story buildings by aggregating building PIDs from all 18 realizations and are illustrated in Figure 13.The median is calculated based on the lognormal distribution of the building PID data.Median PID limit state plots demonstrate a similar trend of building response distribution in the domain to that of the individual realizations.However, since PID data from a total of 18 realizations is aggregated, the median plots illustrate a smoothed variation of the building response distribution compared to the F I G U R E 1 1 PID limit states distribution for the three-story building and nine fault rupture realizations (see Figure 2)-FN motions (top three rows) and FP motions (bottom three rows).individual realizations.Median PID limit state plots are symmetric about a FN plane passing through the center of the fault due to the horizontally homogeneous geology and mirroring of the rupture realizations.Expressing building response in terms of median PID is key information for earthquake design considerations of the buildings since each earthquake source realization is equally probable.However, it is also desirable to understand the degree to which a building's PID demand at a given site for any individual rupture realization can exceed the building's median demand.This provides insight on the potential exceedance of the design basis (if, e.g., median demand is selected as the design basis) for any one equally probable rupture realization.
For demonstration of inter-event building response variability, site-to-site ratios of building PID between a given rupture realization and the median PIDs are calculated for each component of ground motion.For example, ratios of individual PIDs between rupture realization no. 5 (selected randomly) and the medians are shown for the two buildings and two components of the motion in Figure 14.All four spatial distributions indicate that this ratio primarily varies between 1 and 2 with a few localized areas of significantly higher values.The maximum ratio occurring at any site within 10 km off the fault is identified and labeled with its corresponding magnitude for each case.The maximum ratio is 2.9 for the three-story building in the case of FP motion.The maximum PID ratios for both buildings and motion components for all rupture realizations are computed and listed in Table 2 (due to symmetry maximum ratios for the remaining nine realizations are identical).The maximum values for the three and the forty story buildings are found to be 5.2 (#R8), and 3.1 (#R7), respectively.For an equally probable realization for an M 7.0 scenario earthquake, these values indicate a demand of nearly five and three times higher than the respective medians or expected seismic demands for the two buildings.The building PID ratios listed in Tables 1 and 2 demonstrate both the largest intra-event (12.5, ratio of PIDs  F I G U R E 1 2 PID limit states distribution for the forty-story building and nine fault rupture realizations (see Figure 2)-FN motions (top three rows) and FP motions (bottom three rows).See legend description in Figure 11.relative to one site to the other) and inter-event (5.2, ratio relative to the median PID) variability occurs in the case of FP motions of realization no. 8.

ASSESSMENT OF MULTIPLE RUPTURE REALIZATIONS FOR BUILDING RISK
To realize the full potential of high-performance earthquake simulations, it will be necessary to gain deeper insight into the number of rupture realizations required to define the risk to specific building systems.In this section, the building response variability from the 18 rupture realizations is investigated at a near-fault site to assess the variability of seismic demand with an increasing number of representative rupture realizations.As illustrated in Figure 15A, the site is located   1 km off the fault and was selected due to its relatively high inter-event building response variability (max PID 4.76% and min PID 0.72%).Figure 15B demonstrates variability of the three-story building PID statistics in terms of median and standard deviation (SD), computed for the FP motions and plotted against the number of realizations.Black circles indicate median PIDs (lognormal) computed from the corresponding number of rupture realizations and the shaded grey area indicates the ±1 SD from the median value.The red and blue dashed lines indicate the maximum and minimum PIDs obtained at that site from the total 18 rupture realizations.The PID statistics indicate that if this building is designed for the median PID of 1.59% then there could be a realization of the same scenario earthquake for which a PID of 4.76% or nearly three times more seismic demand can occur at the site of inspection.If the median plus one SD (2.52%) is used for the design criterion, there could still be approximately twice as much demand caused by that specific rupture realization.As demonstrated in Figure 15B, the median PID fluctuates with each added rupture realization.As more realizations are added, the median value starts to exhibit a stability with respect to the addition of more realizations.For the site illustrated in Figure 15A, and within the context of the rupture models utilized here, the number of rupture realizations to achieve stability of the median PID is around 12. The standard deviation value demonstrates a similar behavior trend as the median with a slight decrease with the number of realizations.The fluctuation trend of the median PID and its standard deviation may depend on the order in which the realizations are used in the analysis.
Figure 15B illustrates only one such randomly selected ensemble containing 18 PID values from 18 rupture realizations.The total number of randomly ordered ensemble of cases will include the permutations of these 18 realizations yielding a large probability space to potentially be considered.However, for practical purposes, using a fraction of that number will yield a reasonable approximation of all realization sequences.Figure 16 illustrates nine random ensembles of PID statistics for the same site inspected in Figure 15.A number of plots were generated and inspected manually for maximum variations of the statistics in selecting these nine plots.These ensembles demonstrate variable trends of PID statistics with the addition of rupture realizations eventually converging to the final median and SD magnitudes at 18 realizations.The careful inspection of these random ensemble cases reveals that within 10 to 12 realizations, reasonably stable PID statistics can be approximated for the site.To gain more insight into the requirement of rupture realizations, multiple near-fault sites with large PID variability were inspected and shown in Appendix A. For each site a plot is selected such that the ordering of the corresponding ensemble results in greater median variability.It was found that within 10 to 12 realizations the statistics for those sites come to a reasonably stable state.It was concluded that a minimum of 12 rupture realizations is required to capture the median PID demand and its standard deviation at a near-fault site for the scope of rupture models considered.These trends are specific to the limited rupture models and parametric variations considered here, but the analysis approach is extendable to more complexities in the rupture model, for example, the inclusion of deterministic rupture patches at randomly selected locations.

STATISTICAL EVALUATION OF SITE-TO-SITE INTER-EVENT VARIABILITY
To demonstrate site-to-site seismic demand variability from a suite of fault rupture simulations, PID distributions from the 18 realizations for the three-story and the forty-story buildings located 1 km off the fault are shown in Figure 17.Each site on these plots includes a PID distribution resulting from 18 realizations.The maximum and minimum PID values of the distribution at a given site are represented with the top and the bottom black circles, respectively.The median PID is computed based on a lognormal distribution at each site and represented with a red circle.The shaded grey region signifies the span between ±1 SD from the median PID.An inspection of the distributions across the domain demonstrates more pronounced site-to-site peak magnitude differences in the three-story seismic demands than the forty-story, indicating a higher site-to-site, inter-event PID variability in the three-story building.The simulated site-to-site medians as well as standard deviations indicate an increased variability in the building response from FP motions compared to FN components.However, there is no major difference between the average medians (summed across all the stations along the length of the fault) between the two components.A small number of locations in the three-story FP plot demonstrate PID demands in excess of 8% which are indicative of building extreme damage or potential collapse.The collapse mechanism is not represented by a failure criterion in the nonlinear steel frame models and is beyond the scope of this study.At sites along the fault, the average median PID seismic demand for the three-story building is approximately 1.9% and approximately 1.6% for the forty-story building, both lying in the 'moderate permanent distortion' range according to the ASCE 41-19 limit states. 49To add understanding to the observed inter-event variability, maximum and minimum building responses from the 18 rupture realizations at a specific site, illustrated in Figure 17B, are investigated in detail.This site is chosen based on its large building response variability.The maximum and minimum PIDs occurring at this site are labeled by corresponding realization numbers from Figure 2. Rupture realization number 5 (R5) provides the maximum building PID ratio of 4.76% while realization number seven (R7) provides the minimum PID ratio of 0.72%.
Appendix B compares the fault-parallel component of ground motion and building response at the selected site obtained from the rupture realizations R5 and R7, respectively.It is important to note that despite their identical locations of rupture initiation, the two rupture realizations produce significantly different ground motion and building response.A close inspection of the slip characteristics of the rupture area between the hypocenter and this specific site reveals that in the case of realization R5, the rupture propagates through high slip patches near the building site, thus generating higher seismic energy and higher amplitude ground motion.In this case, the rupture directivity effect at the site is manifested by the pulse-like ground velocity and displacement, which are particularly damaging to buildings.In contrast, in the case of realization R7, because the rupture propagates through areas of relatively low slip, the seismic energy directed toward the site is low and consequently the ground motion is comparatively low.Since the site is located very close to the fault and the geologic medium is horizontally homogeneous, the ground motion differences illustrated here are indicative of the differences that might be expected due to variations in the specific fault rupture evolution for the same scenario earthquake.
Figure 18 and Appendix C illustrate distribution plots for the two buildings at 5 km (top) and 10 km (bottom), respectively, demonstrating the attenuation of building seismic response with distances farther off the fault.Comparing these plots with those in Figure 17, it is observed that median PID for the three-story FN case decreases from 1.9% to 1.0% to 0.55% with increasing distances of 1 to 5 to 10 km off the fault, respectively.Median PIDs for the three-story FP case are slightly higher for the similar distances off the fault.Median FN PIDs for the forty-story building range from 1.6% to 0.9% to 0.5% for 1, 5, and 10 km distances off the fault.Comparison of the median PID magnitude decay between the two buildings indicates that in moving from 1 to 5 km off the fault, the three-story exhibits sharper reduction in its seismic demands than the forty-story.This finding was also observed from the PID ratio summary in Table 1.Nearly a uniform median PID of 0.5% is observed at 10 km off the fault in the FN motions across the domain span for both three story and forty story buildings indicating little or no variability and essentially linear elastic behavior of the steel frames.
The simulation results presented here indicate significant intra-and inter-event variability for representative scenarioconsistent earthquake rupture realizations.The analysis approach for evaluation of site-specific variability investigated here can be augmented by using rupture realizations with additional deterministic rupture complexities such as large slip patches and a broader range of rupture velocity.

DISCUSSION AND SUMMARY
The advancement of massively parallel computer platforms and enhanced models of earthquake processes is providing an unprecedented simulation capability for advancing earthquake science and engineering knowledge through physicsbased, regional-scale simulations.Given the severe limitations of the existing database of ground motions in the nearfield of large earthquakes, simulation-based exploration provides a unique opportunity to increase understanding of the variability and statistics of ground motions and structural response in the near-fault region.The study conducted herein explored this problem space further by investigating the relationship between the earthquake source rupture parameters and building earthquake demands.The simulations evaluated site-dependent building seismic demand variability resulting from multiple scenario earthquake rupture realizations that were characterized by the Graves and Pitarka kinematic rupture model and provided preliminary insight into the number of rupture models required to fully characterize earthquake demand to buildings.Using the EQSIM earthquake simulation framework, ground motion simulation from a total of 18 rupture realizations of an M7.0 strike-slip scenario earthquake were conducted using idealized yet realistic seismological and geological features, followed by approximately 280,000 nonlinear building time history simulations of three and forty story steel moment frame buildings.Seismic demand was quantified in terms of a building's PID for each site location in a 100 km × 40 km regional-scale domain.
The building PID data from 18 fault ruptures were used to characterize both intra-and inter-event seismic demand variability.Intra-event variability was characterized by the building maximum seismic demand, relative to the minimum seismic demand experienced by an identical building for sites with the same distance from the fault.The intra-event variability for a three-story building (ratio of maximum PID to the minimum PID) was found to range between 12.5 and 4.6 at distances of 1 and 10 km from the fault, respectively.The corresponding range for the forty-story building was determined to be between 8.5 and 5.1, respectively, indicating a relatively lower variability than the three-story building near the fault.This was indicative of identical buildings, sited equally distant from the fault, having seismic demands that vary by an order of magnitude for a specific fault rupture event.
The inter-event variability was defined as the seismic demand experienced by a building at a given site relative to the median seismic demand computed from the 18 ruptures for that site.The inter-event variability ratios for the three-and forty-story buildings were computed to be 5.2 and 3.1, respectively.These ratios suggested that for a single, equally probable rupture occurrence, the three-and forty-story buildings could experience approximately five and three times their expected median demands at those given sites, respectively.If the design criteria were chosen, for example, as the median building demands, these ratios would provide insight into the potential beyond design basis demands that could result if the worst-case rupture realization happened to occur.
Site-to-site PID demands for the full suite of rupture realizations were combined to form distributions and compute statistics of building seismic demands.It was found that at a given site the three-story building experienced a somewhat greater median PID with significantly greater variability than the forty-story building.Analysis of these distributions also indicated that for a given site, a building could experience significantly different PID demands due to two different rupture characterizations of the same scenario earthquake.Similarly, identical buildings, located at two adjacent sites, might also experience such dramatically different seismic demands as informed by the intra-event variability analysis.It was found that the nonlinear response of these buildings, in terms of building drifts, was very sensitive to small changes in the ground motion amplitude.As noted in the text, this behavior was also recently observed by the building design community.Given the uncertainties in ground motion predictions, this finding could have major implications for the assurance of adequate building seismic response and needs further investigations.
Finally, in the interest of providing insight into the minimum number of rupture realizations needed for seismic design and risk analysis, building PID variability from the 18 rupture realizations was utilized at several near-fault locations.Within the limited context of the source models and parametric variations employed in this study, the simulation results indicated that at least twelve rupture realizations could provide a stable estimation of median and standard deviation of earthquake demand on building systems.The rupture model parameter space used in this study was by no means a complete description of the source rupture process and did not span the entire range of possible rupture cases (e.g., the underrepresentation of the earthquake slip distribution associated with patches and the restriction to simple fault geometry).Additional investigation using a broader suite of rupture realizations will be the subject of future work.

A C K N O W L E D G M E N T S
U R E 1 (A) The idealized computational domain (100 km × 40 km × 30 km) with its (B) geologic structure and seismic velocity profile.

F I G U R E 2
Nine stochastic earthquake source rupture model realizations generated based on GP 37 method-number on the top right of each panel indicates the rupture realization number.The contour lines on each slip distribution panel indicate the rupture front at 2 s time intervals.

F I G U R E 3
Ground (A) acceleration (B) velocity and (C) displacement at the indicated (D) site (1 km off the fault) from 18 rupture realizations, demonstrating a large variability in both FN and FP motions.

5
Comparison of the nine rupture (see Figure2) simulations (black traces) with recorded near-fault motions (red traces) extracted from an existing database,46 (A) FN component and (B) FP component.Median simulated spectra for the remaining nine ruptures are identical and not included in the plots.

6 7
Comparison of median RotD50 simulations (blue line) and median GMPE (red solid line) for three near-fault sites-(A) 1 km, (B) 5 km, and (C) 10 km away from the fault.Gray lines indicate simulated RotD50 data from individual realizations.Max PID / Min PID = 5/1 Ground motion and building response simulations from a single earthquake realization-(A) plan view of the domain with the fault, hypocenter location and slip distribution, (B) ground velocity snapshot at time 25 s, and (C) 3-story building PID distribution (FN motion) at 1 km off the fault.

1 0
Demonstration of intra-event variability of ground motion (A and B) and building response (C and D) at two near-fault sites (E) for FN component of motion, obtained through rupture realization R4.

3
Three (top panels) and forty (bottom panels) story building median PID limit states contours-each computed from a PID aggregate of 18 realizations.The black line indicates the fault location.Same legend description applies as in Figure11.

4
Individual realization-to-median ratios of building PIDs between rupture realization 5 and the corresponding median PIDs -3-story (top) and 40-story (bottom); FN motions (left) and FP motions (right).White rectangles contain sites within 10 km off the fault.TA B L E 2 Maximum ratios of PIDs between individual realizations and the medians within 10 km of fault.

5
(A) Location of an inspected site in the computational domain (black triangle); (B) three-story building PID statistics at that site in the FP component.

6
Nine random statistical ensembles of three-story building median PIDs and SDs for the selected near-fault site (FP motion).

7
Statistical distributions of site-to-site building seismic demands computed along a strike parallel line and at 1 km off the fault-(A) three story FN, (B) three story FP, (C) forty story FN, and (D) forty story FP.

8
Statistical distributions of site-to-site building seismic demands computed along a strike parallel line and 5 km off the fault-FN (left) and FP (right).
This research was supported by the Exascale Computing Project (ECP), Project Number: 17-SC-20-SC, a collaborative effort of two US Department of Energy (DOE) organizations-the Office of Science and the National Nuclear Security