A performance‐based seismic loading protocol: The generated sequential ground motion

A realistic performance‐based seismic loading protocol called generated sequential ground motion (GSGM) has been developed in this paper. GSGM is a ground motion fabricated from segments of real recorded ground motions that could enable the introduction of performance‐based seismic assessment and design to experimental testing in setups such as shaking table testing. It can also significantly reduce the number of nonlinear time history analyses required in performance‐based seismic design. The protocol optimizes the behavioral information output of an experimental test or numerical analysis by incorporating dynamic demands corresponding to design limit states with different probabilities of exceedance (i.e. 10%, 5%, and 2% in 50 years) in a single record. In addition, since the segments are matched to relevant target spectra, the number of ground motions required to estimate the mean response is reduced. This paper presents the algorithm developed to produce the GSGM. The capability of the GSGM to replicate the structural responses produced by code‐compliant suites, and a suite of 100 ground motions as a more robust estimation of the actual response is investigated. The results of the case study bridge pier show that the drift variation of the GSGMs compared to code‐compliant suites is within 10%. Compared to the estimate of the actual response, the drift variation of GSGMs and the code‐compliant suites is 20% and 15%, respectively, and the damage variation is 30% and 15%, respectively. Furthermore, considering other relevant intensity measures when producing GSGMs can reduce these variations. This study suggests that the GSGM can replicate structural responses of the current code procedures.

of cycles applied to the structure under a series of two or three ground motions (e.g. corresponding to 10%, 5%, and 2% probability of exceedance in 50 years) are not realistic representations of a single ground motion representing a limit state corresponding to 2% in 50 years probability. Furthermore, since the nonlinear structural response is sensitive to the load path, this results in an unrealistic simulation of the damage endured by the structure in the final states.
In 1991, Seible et al. 21 proposed a test method called Generated Sequential Displacement (GSD) to address the difficulties associated with testing stiff multi-degree-of-freedom (MDOF) structures. The goal was to simulate realistic seismic loading for full-scale testing of stiff MDOF systems using PsD testing. The GSD test method used a selected sequence of segments of a recorded or generated seismic ground motion as input to perform a PsD test. The GSD consisted of four components: a selected sequence of recorded or generated seismic ground motion input segments, an analytical model and the numerical time integration scheme, the computer-controlled inner loop of the online servo-controlled actuator system, and the actuator and loading system itself with ramp generator and servo-control. 21 The motion input of this method allowed the structure to experience predetermined limit states by subjecting it to a selection of sequential seismic excitation input segments. Later Igarashi et al. 22 used the input motion to test a full-scale three-story masonry shear wall and provided more detail on the method in the U.S.-technical coordinating committee for masonry research (TCCMAR) project reports. [22][23][24] In this initial concept of GSD, a single ground motion (in this case, Imperial Valley 1979 earthquake, James Rd. station, 230 component) was broken down into different segments. Then, a specific sequence of the segments was selected and scaled based on expected response requirements. Therefore, segments of a single ground motion with different durations were used, and the order of the segments was altered to form the sequence. Also, there was no mention of scaling the windows to different acceleration target spectra; instead, they used scaling to achieve a certain drift level or limit state in the experiment. In this method, two segments could overlap and contain the same part of the ground motion, which meant the same cycles could be applied more than once.
Later, Seible et al. 25 modified the method. The idea of subjecting the building to a sequence of earthquake motion windows from various earthquake records rather than different segments of a single earthquake record was proposed by Kariotis in a correspondence letter to Seible on August 8th, 1991. Since limit states were defined based on the displacement demand applied to the structure in the initial method, each segment was looked at separately and independent of prior ones. So, the ground motion windows did not start at the beginning of the time history. However, in the final version of the method, the limit states represented specific design spectra rather than displacements. Hence, the accumulated frequency content from the start of the ground motion is considered to represent each limit state, which is more realistic. The GSD presented in the final method had four windows, each representing one of the four target spectral response levels: 0.1 g, 0.3 g, 0.4 g, and 0.6 g UBC S2 design response spectra. The windows were scaled to the UBC spectra (Code 1985) to represent the corresponding limit state. The windows in GSD were supposed to represent particular limit states; however, their response spectra showed significant deviations from the target spectra and were not closely matched to the target. More deviation meant less accuracy in the representation of the target spectrum. Moreover, the GSD was performed at a slower rate than that of the actual seismic event (rates of 1/2000 times the event) to allow for the numerical time integration scheme to be analyzed.
This study aims to fill the abovementioned gaps. It attempts to create a ground motion time history that possesses the characteristics of real ground motions and includes demands corresponding to different seismic performance levels. The method can extend PBEE to experimental testing or be used in NTHA to reduce the number of analyses required by the PBEE procedures presented in codes. To establish an accurate representation of performance levels, a protocol has been carefully developed by elaborating on the core idea behind the GSD method. This protocol, called the generated sequential ground motion (GSGM), is fabricated from segments of actual ground motions that subject the structure to increasing dynamic demands representing different design limit states. GSGM offers one of the economical and technical advantages of QST to shake table testing and PsD testing, that is characterizing the structure's behaviour in different limit states within a single test. It also has the added advantage of accounting for strain rate effects and maintaining the general characteristics of actual ground motion records. The method is simplified and uses information available to practicing engineers. The features and the step-by-step algorithm developed to produce the GSGM are presented in this study. The PBEE process relates the earthquake intensity to structural performance. In this process, GSGM is considered an alternative seismic input for the structural analysis step. In order to investigate the validity of this alternative input, its capability to capture the output of the structural engineering process should be assessed. The output of this process is the Engineering Demand Parameters (EDP), computed using structural analysis procedures such as NTHA. The maximum drift ratio is studied initially as a typical EDP for RC columns. Cumulative damage indices are also considered as EDPs. Therefore, to assess the validity of GSGM in replicating typical input ground motions, its ability to replicate the maximum drift ratio and damage endured by the structure must be evaluated. Initially, the validity of the GSGM in replicating responses produced by codecompliant ground motion suites is investigated. Then, GSGM and code-compliant ground motion suites are compared F I G U R E 1 Schematic of the generated sequential ground motion (GSGM). against a more robust estimation of the actual response. A suite of 100 ground motions is selected and scaled to estimate the actual response.

GENERATED SEQUENTIAL GROUND MOTION (GSGM) CONCEPT AND APPLICATION
The goal of producing the GSGM is to create a ground motion with the characteristics of real, not simulated ground motions, that optimizes the behavioral information output of seismic experimental tests using a single ground motion and test. The GSGM can be used as input for experimental testing in setups such as shaking table and PsD testing. To perform a single test that allows for the manifestation of different performance levels, GSGM is created from a series of six or more segments taken from actual earthquake ground motions that subject the structure to increasingly severe behavioral demands of different design limit states. The sequence of the six segments creates a ground motion that incorporates six windows. The first window (first segment) contains a low amplitude ground motion segment that exists at the beginning of all earthquake records. By adding segment 2 to segment 1, Window 2 is produced; by adding segment 3 to Window 2, Window 3 is created, and so forth. Hence, each window accounts for the accumulated demand from the beginning of the record. In this study, the second, third, and fourth windows closely match the site's 10%, 5%, and 2% in 50 years probability of exceedance target spectra in the period range specified by the codes. 2,26 Thus, windows 2 to 4, called performance windows, subject the structure to increasingly severe behavioral states associated with three seismic hazard levels, that is, probability of exceedance of 10%, 5%, and 2% in 50 years.
In addition, another performance window can be included. This additional window (Window 5 in Figure 1) includes what is called the collapse segment that aims to ensure the structure is taken to a desired nonlinearity level or target displacement, or experiences specific behavior such as collapse. This paper focuses on the three performance windows corresponding to specific code limit states and does not include the collapse window for simplicity. The final segment of the GSGM contains a low-amplitude tail-end ground motion segment which allows for monitoring the behavior of the structure following high nonlinearity states or failure, or can represent aftershocks. The initial and final segments are lowamplitude ground motion segments taken from the beginning and end of earthquake ground motions. These segments do not contain significant frequency content but are paramount in creating a realistic ground motion. A schematic of the GSGM and a description of different windows of this ground motion are depicted in Figure 1. The number of windows incorporated in GSGM is flexible. It can be defined by the user to include any number, sequence, and type of hazard levels or target demand. In a nutshell, the GSGM is established based on concepts such as performance levels, ground motion segment selection, spectral matching, connecting ground motion segments, and segment duration, which are discussed in detail hereafter.

2.1
Performance levels GSGM can represent any type and sequence of structural demand. One common type of demand is the hazard levels used in PBSD. The number and type of hazard levels can be selected in accordance with any PBSD code and can vary based on the structure. The most common seismic hazard levels used in the design of bridges are associated with a probability of exceedance of 10%, 5%, and 2% in 50 years. Windows 2, 3, and 4 of the GSGM represent the aforementioned seismic hazard levels. The collapse window is optional and can be used to ensure the failure of the structure, a specific nonlinearity or displacement target, near collapse limit states, or an amplified target spectrum is reached. In cases where a specific target displacement is to be reached, an iterative process must be performed to find a scale factor that takes the structural response to that target. In experimental testing, it is also possible to incorporate a time lag or pause between the performance windows and the collapse segment to make a more educated estimation of what amplification factor or segment to use for the collapse segment to lead the structure to the desired target displacement. This more comprehensive and elaborate form of GSGM can be investigated in future studies. In this paper, each performance window in GSGM represents one of the three aforementioned seismic hazard levels. Hence, one record represents three different ground motion levels. In addition, since each performance window is matched to a specific target spectrum, each performance level represents numerous ground motions. In order to be able to use a response spectrum for analysis of an event in a specific location/region that has not yet happened, a design response spectrum is used. The design response spectrum can be seen as an envelope over all known and anticipated earthquakes in a specific geographical region. Uniform Hazard Spectrum (UHS) is the most common design spectrum used in current codes. An alternative to the UHS as the target spectrum is the Conditional Mean Spectrum (CMS). 27,28 Using CMS creates a more realistic target spectrum and thus GSGM; however, hazard disaggregation information is required to compute it. Even though USGS provides a tool to directly download a Conditional Mean Spectrum (CMS) for a given site in the US, such a tool is not available for sites in other countries, such as Canada. Since GSGM aims to be simple by using information available to practicing engineers, UHS is used in this paper. Additionally, Since GSGM aims to use a single ground motion to match the target spectrum and cannot account for the variance on its own, UHS is a better choice for the target spectrum since it has already accounted for variance. 29 Baker and Cornel 29 also explained that since UHS is always higher than individual CMS spectra, UHS would be a safer choice for target spectrum when expensive analyses or experiments on structures with many sensitive periods are of interest.

Selection of initial ground motion segment
One of the main characteristics of the GSGM is that it is created from segments of actual ground motions rather than artificial records. This helps keep the frequency content distribution and general ground motion characteristics close to that of real ground motions. Therefore, real earthquake ground motion segments roughly close to the target spectrum must be selected first. Later, spectral matching will be performed to create a closer match. When using this method, great attention must be paid to selecting ground motion segments that closely match the target spectra. This minimizes the need for aggressive spectral matching and reduces unnecessary manipulation of the original ground motion. To find suitable ground motion segments for each window, segments must be selected from a vast database of ground motion segments to allow for a wide range of response spectra to select from. To this end, an algorithm is developed in MATLAB 30 that breaks down real ground motions into segments and finds the segments with the least amount of misfit from the target spectrum. Different measures of error or misfit, such as the sum of squared differences between the response spectrum of the segment and the response target spectrum in the period range of interest, as suggested by relevant PBSD codes, can be used.
To reduce the run time of the selection algorithm and simplify the method, instead of finding different segments for each performance level, that is, segments that match 10%, 5%, and 2% spectra, only segments that match one target spectrum (for example, 10% spectrum) are found. Since the shape of most target spectra for different probabilities is similar, applying a scale factor to that segment can create a rough match to the other target spectra (5% and 2%). Then, scale factors for the selected segment are chosen so that windows 3 and 4 would match the 5% and 2% target spectra, respectively. The selection algorithm selects segments from more than a thousand ground motion segments by applying scale factors to the segments to find the closest match to the target spectrum. It is essential that the range of scale factors used to find the ideal segments be limited to avoid excessive scaling of recorded ground motions. This is important as the excessive scaling of ground motions can produce bias in the results of seismic response analysis of structures. 31,32 Therefore, the range of scale factors for all segments is suggested to be kept within 0.5-5.0, which falls within the range suggested by Baker et al. 33 and Chandramohan et al. 34 In this study, this limit is even more stringent, and the scale factors are limited to a maximum of 4.5 instead. This is to avoid scaling of high and low-intensity records by small and large factors, respectively. The user can select the total range of scale factors based on the level of bias acceptable to them, following studies such as Baker. 35 This range will then determine the scale factor range for segment selection based on the hazard level used for selection and the factors required to scale this segment up or down for other considered hazard levels. For all segments, including the Collapse segment, scale factors must be carefully selected to avoid bias. This is especially important for the Collapse segment, as larger scale factors are required to produce such strong demand. Therefore, it is suggested that the same selected segment for the hazard windows not be scaled and used for the Collapse segment. Instead, a stronger ground motion segment that requires a smaller scale factor be used. Finding such a segment is not difficult as the response spectrum of the Collapse segment is not required to match any target spectrum.

Spectral matching
Current performance-based seismic design guidelines use a suite of ground motions to account for the record-to-record variability of ground motions. However, the average of that suite is used in the design procedure and not the variability. Therefore, producing a ground motion replicating the suite's average could potentially replace the suite. This can be done using spectral matching. Response-spectrum matching is a method that modifies a real recorded earthquake ground motion (the frequency content of the ground motion) so that its response spectrum matches the desired target spectrum across a range of periods. The use of spectrum-matched records in nonlinear analysis reduces the record-to-record variability of the input, which also reduces the variability in the response of the structure. 36 To elaborate more, it is known that spectrum-compatible time series reduces the number of time series required to be run in the engineering analyses, that is, one spectrum-compatible record is worth three scaled records. 31 Due to lower variability in the mean of the nonlinear responses, the spectrum-compatible ground motion suites require a smaller number of ground motions than scaled ground motion suites to result in the same accuracy for the mean response. 37 Hancock et al. 38 also showed that one or two spectrum-matched records could estimate the response within ±5% for a 64% confidence level for measures such as drift. Hence, the hypothesis that a single ground motion that is closely matched to a target spectrum provides sufficient accuracy as a suite of scaled ground motions is backed by previous studies and will also be studied here. Therefore, as each performance window of GSGM is matched to a target spectrum associated with a specific performance level, each performance window represents a suite of ground motions typically used to represent that limit state. Since it would be almost impossible to find a segment from a real ground motion that closely matches a target spectrum, spectral matching is used to more closely match the response spectrum to the target. Hence, the selected segments are used as seed ground motions, and loose spectral matching is performed to represent the target spectra better. Modifications due to spectral matching may seem insignificant, but the fact that it results in a more accurate representation of performance levels is fundamental to the concept of using a single ground motion. Spectral matching has been controversial for two reasons. Here, we discuss the reasons and justify why these drawbacks are irrelevant to the proposed method. First, it is well known that the design spectra provided by codes are an envelope of many ground motion response spectra rather than a single earthquake event. Therefore, it is presumed unrealistic to have a time series that matches an entire design spectrum and represent multiple earthquakes rather than one. This is true and typically considered a disadvantage, but in the GSGM method, our primary goal is to represent performance levels representing many ground motions. Additionally, the response spectra of spectrum-compatible time series are smooth, which is unrealistic compared to real earthquake response spectra with large peaks and troughs. However, that would be the price to pay for having a single ground motion representing numerous records. Secondly, to closely match a record to a target spectrum, the ground motion would have to be altered to the extent it would not resemble the original record. This would mean we are no longer working with real earthquake ground motions. To avoid such significant alteration, thousands of segments are scanned to find the closest match so that loose spectral matching can be performed.
Current guidelines have little to offer on acceptance and acceptability criteria for spectrally matched ground motions and how to assess if a ground motion may be considered realistic for use in response history analysis. Since the objective of time history analyses is an unbiased estimation of peak structural response quantities, acceptance criteria can be based on the effect of matching on the nonlinear response rather than preserving every cycle of the original motion. 39 Nevertheless, studies on the effect of matching on nonlinear response suggest visual observations of the changes in the time domain of the record as the only means of drawing conclusions about the acceptability of matched ground motions. A qualitative visual check on one or more of the acceleration, velocity, or displacement ground motion histories, and the Husid plot, 40 which shows the growth of Arias Intensity 41 over time (see recommendations in reference 42 ), must be performed.

2.4
Connecting ground motion segments GSGM is created by assembling segments of recorded ground motions. Two techniques can be used to add segments and create the GSGM; adding displacement histories of segments or adding acceleration histories of segments. To make adding segments possible, each displacement/acceleration segment is truncated so that the displacement/acceleration at the start and end of the segments is zero. This way, when the segments are added, they all connect at a value of zero and do not produce unrealistic ground motion cycles. Each technique demonstrates certain complications that will be discussed herein.
One way is to assemble displacement histories of the segments to create the record. The generated displacement time history is then differentiated twice to get to the acceleration time history of the GSGM. The slope and curvature of the displacement curve are the velocity and acceleration of the time history. Thus, the acceleration time history of the produced ground motion is sensitive to the curvature of the displacement time history. If the slope and curvature of the displacement curve on the two sides of the connecting point change drastically, large-amplitude pulses appear in the velocity and acceleration time histories at the connecting point. Therefore, attention must be paid to the displacement pulses at the connecting point of the two segments. To avoid unrealistic acceleration spikes, the slope and polarity of the pulses on the two sides of the connecting point must complement each other to create a smooth displacement cycle, which is difficult to obtain. If medium acceleration spikes are formed, the acceleration time history can be smoothed at the connecting point using the smooth command in MATLAB. 30 However, removing large spikes can manipulate the acceleration time history and response spectrum. Considering these issues, the displacement technique will not be used to create the GSGM.
Conversely, acceleration histories of the segments can be assembled to create the record, that is, GSGM. Since the assembled segments were truncated to start and end at zero acceleration naturally, the assembled acceleration history contains realistic cycles of actual ground motion, and no unrealistic spikes are produced. This way, all acceleration values and cycles before and after the connecting point are that of a real recorded motion. At the connecting point, the acceleration value of both segments is naturally zero. Therefore, no severe acceleration changes are produced due to connecting the segments. The only manipulation is that segments have been rearranged, which can be deemed negligible, as earthquake cycles are inherently random. Finally, to calculate the displacement time history of the record, double integration is used. The acceleration and velocity paths affect the calculated displacement when double integration is performed. Since acceleration segments are taken from different parts of a ground motion, the acceleration and velocity paths do not match the original record. As a result, this technique results in unrealistic residual displacements at the end of each window and the entire displacement time history. To resolve this issue, baseline correction can be used, which removes the bogus residual displacement. This applies in the case of far-fault or near-fault scenarios when no fling step is expected. Baseline correction can be applied at the end of each generated window. However, this results in a skewed total displacement time history. Finally, it was found that it is best to perform baseline correction on each segment and then add the baseline-corrected segments to create the GSGM. This method results in a realistic ground motion in terms of displacement and acceleration history. The example shown in the next sections will illustrate this more.
Baseline correction removes the spurious baseline trends created in the displacement time history by double integration. 43 Polynomials of 0 to 3rd degree, that is, constant, linear, quadratic, and cubic baseline correction, can be employed. In the production of GSGM, the order used for baseline correction of the segments can be selected based on whichever order gives the closest displacement values to the displacement time history of the actual ground motion. It was seen that a 3rd order baseline correction gave the best results for the selected segments in the GSGM method. The literature shows that, when correcting complete recorded ground motions, high polynomial orders have no physical justification and are inadequate for intermediate and long accelerograms. 44 However, Hudson et al. 44 showed that parabolic baseline correction minimally manipulates the velocity and displacement histories when performed on short records with zero initial conditions. Therefore, since the segments in GSGM are considered short, it would be adequate to use higher orders, such as quadratic and cubic, to correct the record if needed.

Segment duration
It is known that the strong motion duration of the ground motion could significantly affect the damage and nonlinear response of structures. Hence, producing unrealistic ground motions in terms of duration can impose unrealistic demands on the structure. For the GSGM to resemble the qualities of real ground motions consistent with a scenario, the duration must also conform to that expected from the actual ground motions of that scenario. Ground motion duration definitions such as uniform, 45 structural response, 46 bracketed, 47 significant, 48 or effective duration 49 have been used in the literature. It is proposed here that the average duration of a suite of ground motions associated with the specific site or scenario be chosen as the duration of the GSGM. This total duration then dictates the duration of each segment. Producing GSGM falls within a general seismic hazard assessment, which requires the window of significant shaking of ground motion Step-by-step procedure of GSGM.
accelerograms to be identified. Hence, the uniform and structural response durations are eliminated. In addition, the bracketed duration is highly sensitive to the selected threshold levels, making it insufficient. 49 Significant duration is based on the energy in the record. However, it uses relative criteria for the cut-off energy levels. Effective duration, on the other hand, has the advantage of using the energy in the record as well as using absolute thresholds for arias intensity. These features make effective duration the most suitable duration definition for building GSGM. Nonetheless, more research can be performed to assess different ground motion duration definitions and find the most appropriate duration definition and cut-off threshold for producing GSGMs.

GENERATED SEQUENTIAL GROUND MOTION (GSGM) STEP-BY-STEP PROCEDURE
The step-by-step procedure and algorithm developed to create the GSGM are presented here. This method consists of six steps, shown in the flowchart in Figure 2, which are explained in detail herein.

3.1
Step 1: Input The input of the GSGM procedure is the number of windows (N w ), specific hazard levels and target spectra of the site, the period of the structure, a ground motion database with versatile frequency content consistent with the seismicity of the site, and ground motion duration. The number of required windows and hazard levels are specified per the PBSD code. It is at least five if the start and end windows and three performance windows are included for design purposes. Site location and, consequently, nearby seismic sources can determine ground motion duration, target spectra, fault mechanism, the distance of the site from seismic sources, and the magnitude of possible earthquakes. The design spectra (UHS) for the 10%, 5%, and 2% probability of exceedance in 50 years associated with the site where the structure is located are derived either from design codes or by producing site-specific target spectra. A large ground motion database (more than 100) representative of the site must be selected from databases such as the PEER ground motion database, 50 providing a diverse frequency content database to select from. The selection is based on magnitude (M), radius (R), etc. Nonetheless, the selection criteria regarding spectral matching are not as stringent as for scaling because spectral matching modifies the frequency content of the ground motion. 36 So, in cases where ground motions are scarce, criteria such as soil type can be lenient since the frequency content will be tampered with eventually. As discussed previously, effective ground motion duration is selected and calculated from the average of a selected suite from the database consistent with the scenario. As scaling ground motions would affect the effective duration, the selected suite is scaled and matched to the 2% probability of exceedance target spectra. The average effective duration of this suite represents the duration of strong motion for a 2% probability of exceedance in 50 years scenario. In GSGM, the 2% probability of exceedance scenario is represented by Window 3 of the GSGM. Hence, the effective duration of Window 3 is assumed to be commensurate with the average effective duration of the suite, corresponding to a 2% probability of exceedance in 50 years scenario. In the specific case where the GSGM contains only three performance levels, that is, 10%, 5%, and 2%, the entire GSGM represents the 2% scenario, which is the case in this paper. Since GSGM contains two segments (first and last) that do not count as strong ground motion, the contribution of those two segments to the effective duration would be minimal and thus ignored for simplicity. Moreover, it is a reasonable assumption that only the performance segments containing strong ground motion would contribute to the effective duration of the produced GSGM. As a result, the approximate effective duration of GSGM is assumed to be the duration of the performance segments it contains, which is three. Therefore, the suite's effective duration is divided by the number of GSGM performance segments (three) to estimate segment duration ( ). Equation (1) shows the formula for :

Step 2: Selection algorithm
The selection algorithm aims to find a ground motion segment that best matches a specific target spectrum. A dynamic segment generation algorithm is devised for breaking ground motions into segments. This method will produce higher numbers of segments and broader frequency content alternatives for the selected ground motion segment to be chosen from. In this method, each ground motion is broken down into segments with a duration of t s that starts from t = 0. The start time is then shifted by 0.5 s to produce the next segment. This goes on until the end of the shifted segment reaches the end of the ground motion. This way, a 10-s-long ground motion will produce a total of 11 5-s segments (0-5, 0.5-5.5, 1−6, . . . , and 5−10). Then, the algorithm developed will select the best match from this pool of segments. The best segment for one of the performance levels is selected based on the least deviation from the target spectrum. The deviation is measured through the sum of squared differences (SSD) between the response spectrum of the segment and the response target spectrum in the 0.2T to 1.5T period range, T being the fundamental period of the structure. The user also defines acceptable ranges for scale factors to be used in the selection algorithm. Based on this range and the ratio of the target spectra of all hazard levels, the algorithm finds the acceptable scale factor range for each hazard level which is used to find the best-scaled match. Stringent criteria are considered in the selection of ground motion segments so that refinements required by spectral matching to match the segment to the target spectra would be minimized. The algorithm's output in this step is the segment of a ground motion that best matches the target spectrum, called the selected segment. The selected segment is scaled for other hazard levels and used to create the GSGM. The ground motion from which the best segment is selected is called the selected ground motion. The selection algorithm exports the top 20 selected segments, the start and end segments corresponding to each selected ground motion and the selected ground motion. An essential part of the selection algorithm is that it truncates all the segments at both ends so that they start and end with acceleration values of zero. This is important as these acceleration segments will finally be connected to form one single ground motion. This way, all segments start and end at zero acceleration and can be easily assembled. If the acceleration segments start and end with random non-zero values, unreal acceleration pulses would form in the produced acceleration time history.

Step 3: Spectral matching
In this step, the selected segment signal exported in the previous step is used as seed ground motion for spectral matching. Any spectral matching software can be used in this step to loosely match the selected segment to the 10% target spectrum. All criteria for visual inspection of spectral matching must be considered. These inspections make sure that the general characteristics of the initial time series (acceleration, velocity, and displacement) have been preserved throughout the spectral matching process. This means that the amplitude and timing can be slightly off while ensuring no phase change in the response peak has occurred and no secondary peaks have become critical. Checks of the build-up of Arias intensity should also demonstrate that the energy distribution within the record is similar to the original ground motion and that the total energy content has not been changed by more than 10%. After performing these checks, the initially selected segment is discarded if a suitable match cannot be made, and the next best selection is adopted to perform spectral matching.
Step 3 is then repeated with a new segment until a segment is found that produces a close match to the target spectrum while maintaining all spectral matching inspection criteria.

Step 4: Baseline correction
The procedure developed in this paper is based on connecting acceleration segments. However, since acceleration segments are taken from different parts of the ground motion, the acceleration path does not match that of the original record. Hence, unrealistic residual displacements appear at the end of each window and the entire displacement time history. Therefore, baseline correction is performed for all segments to avoid such bogus residual displacement. In this step, the selected segment that was previously matched and exported in step 3 and the start and end segments exported in step 1 are subjected to baseline correction to correct the displacement deviations of the segments. This means that all segments start and end at a displacement of zero as well as an acceleration of zero. If segments without baseline correction were used, the produced GSGM would end up with a large unrealistic residual displacement. The order of the polynomial used for baseline correction, that is, 0, 1st, 2nd, or 3rd order, can be selected so that the corrected segment would result in displacement values closer to that of the original ground motion in the range of the selected segment. In most cases, a 3rd order polynomial baseline correction gave the best displacement values. The academic version of SeismoSignal software 51 has been used in this paper to perform baseline correction.

Step 5: Create windows
This step produces windows 1 through N w -1 of the GSGM. An algorithm has been developed that scales and adds the segments to create the windows. Window 1 only consists of the starting segment. The truncated matched selected segment is then scaled and added to Window 1 to create Window 2. The scale factor is selected, so the created window has a close response spectrum to the target spectrum. Here, visual inspection is performed on the acceleration time history of Window 2 to ensure segment 1 has a substantially lower amplitude than segment 2. The scale factor of segment 1 can be manipulated to ensure segment 1 will not affect the response spectra of Window 2. Similarly, the selected segment is scaled and added to Window 2 to create Window 3. The scale factor for the selected segment is chosen so that Window 3 closely matches the 5% target spectra. The same procedure is done to create a Window 4 that best matches the 2% spectrum.

3.6
Step 6: Create the final window Segment N w of GSGM is the end segment of the selected ground motion produced in step 1. By adding the truncated end segment to Window 4, Window 5 is created. This allows the test to provide information on how the structure behaves following failure or severe nonlinear demands. Applying aftershocks at the end of GSGM is also feasible. The acceleration time history of GSGM in its entirety is produced in this step. The algorithm then uses integration to produce the velocity and displacement time histories of GSGM as well. Visual inspection is performed to make sure all time histories are realistic. Finally, the response spectra of all performance levels are plotted to do a final check on the adequacy of the match of all performance levels.

Description of the prototype bridge pier and validation of the FE model
The case study column used in this study is the middle column of a two-span concrete bridge with two 18 m long spans. The bridge deck is placed on elastomeric bearings at both ends and the column. The single column with a height of 5500 mm is the only lateral resisting component of the bridge. The bridge deck width and weight per meter are 120 kN/m and 10 m, respectively, making the dead load of the column equal to 2700 kN and the seismic weight 4185 kN. Soil is assumed to be very dense soil and soft rock (type C) with a shear wave velocity range of 360−760 m/s. The column is assumed to be located on a site in Vancouver and far from active faults. For simplicity, it is assumed that the only seismic source in the site's vicinity creates crustal earthquakes, neglecting other sources such as subduction earthquakes. In addition, a magnitude 7.0 earthquake occurring on a strike-slip fault 50 km from the fault is assumed for the earthquake scenario. The case study column was designed according to performance-based design regulations of CHBDC Code. 2 The designed column diameter is 1000 mm with 18 52 This column was modeled in OpenSees 53 as a two-dimensional cantilevered reinforced concrete (RC) circular column with a structural height of 7320 mm, which is the free height from the top of the footing to the center of mass of the superstructure. A diameter of 1220 mm and a concrete cover of 51 mm were used. The results of material tests performed by Schoettler et al. 52 showed a concrete compression strength of 41.9 MPa, concrete elastic modulus of 23000 MPa, compressive strain at the maximum strength of 0.0026, steel yield strength of 518 MPa, and steel elastic modulus of 196 GPa. 18 #11 bars and double #5 spirals spaced at 152 mm were used as longitudinal and transverse reinforcement. Strain corresponding to initial strain hardening, tangent stiffness at initial strain hardening, and ultimate strain for the longitudinal reinforcement are 0.011, 5515.5, and 0.0122 MPa, respectively. Concrete02 material model was employed. In order to capture the damage endured by the structure, the Concrete07 material model was used within the plastic hinge length in the FE model. Concrete07 is a simplified version of the model proposed by Chang and Mander, 54 which results in closer to a true estimation of concrete response under inelastic dynamic loading compared to Concrete01 and Con-crete02. The effective plastic hinge length (L p ) was estimated to be 1000 mm using the expression proposed by Paulay and Priestley, 55 which is consistent with experimental observations. In addition, the ReinforcingSteel material model was used, which is based on Chang and Mander 54 uniaxial steel model. The fatigue model adopted uses material constants Cf and Cd. Fatigue parameter values reported by Brown and Kunnath 56 were used here; C f = 0.26, C d = 0.389, and α = 0.506. These values were obtained from experimental data for bars with a slenderness of 6.0. Since the slenderness of the column in this study is less than 6.0, the results of the experiment can be extended and used here. The buckling model proposed by Dhakal and Maekawa 57 was used within the ReinforcingSteel material to model the buckling of reinforcing bars. The model is based on slenderness ratio (l sr ) and adjustment constant (α). The slenderness ratio is equal to the ratio of the spacing between transverse rebars to the longitudinal rebar diameter. The adjustment constant was assumed to be 0.95 as the steel material in this specimen showed a significant strain hardening range.
Fiber sections were implemented for the core and cover concrete as well as the rebars. The cross sections were discretized with 1080 fibers. The FE model was generated using seven dispBeamColumn elements with five integration points. Strain penetration was modeled using a zeroLengthSection element at the base of the column, and equations proposed by Zhao and Sritharan 58 were used to calculate slip parameters. A total mass of 247 N.s 2 /mm was considered to account for the effective mass of the pier and the lumped mass. The proportional vertical load was applied at the top node. A tangent stiffness-proportional viscous damping model with a damping coefficient of 0.01 was employed through the Rayleigh damping command in OpenSees. 53 The test specimen's geometry, reinforcement layout of the section, discretized fiber section, and the FE model diagram is shown in Figure 3.
In the experiment, a time history consisting of six records was applied to the model, each simulating a target displacement ductility of 1, 2, 4, 2, 8, and 4. 52 Ground motions 1−4 and 6 are from the Loma Prieta earthquake of 1989, with a magnitude of 6.9. The stations for these ground motions are Agnew state hospital (090), Corralitos (090), LGPC(000), Corralitos (090), and LGPC (000) and the scale factor was 1.0 for all. Ground motion 5 is the Takatori station (000) record of the Kobe earthquake of 1995 with a magnitude of 6.9. The scale factor for this ground motion was −0.8. The same ground motions were used to perform nonlinear time history analyses here, yet only ground motions 1, 3, and 5 were presented for validation here. Validation of the FE model with experimental results is shown in Figure 4. for ground motions 1, 3, and 5, and good agreement is seen between the experimental and FE analysis results.

Producing site-specific GSGMs
The step-by-step procedure presented previously is used to produce a GSGM associated with the case study column. In step 1, the input of the procedure is gathered. This paper aims to investigate hazard-specific performance levels in comparison with design codes. Hazard levels of interest for this case study bridge pier as per CHBDC 2 are associated with 10%, 5%, and 2% probability of exceedance. Therefore, considering the start and end segments, the number of windows of the GSGM ( ) is equal to five. The 10%, 5%, and 2% probability of exceedance target spectra for the site located in Vancouver are downloaded from the UNBC website. The period of the designed column is 0.94 s. Next, the following search parameters corresponding to the earthquake scenario were considered to assemble a ground motion database consistent with the case study. Since the assumed scenario in this study is 50 km, an R range of 30−100 km is considered. The source mechanism is strike-slip but can be ignored as a selection criterion for far-fault records, allowing for more ground motions. In addition, a magnitude range of 6.4-7.4 was assumed. Finally, the site is located in type C soil; hence, a wave velocity range of 360−760 is considered. These search parameters were used to select and assemble a ground motion database comprising 100 ground motion records from the PEER database. 50 Finally, segment duration must be determined. First, a suite of 11 ground motions is selected and scaled to match the site's 2% probability of exceedance target spectrum. Next, the average effective duration of the suite is calculated. An AI 0 value of 0.01 m/s and an AI f value of 0.15 m/s are used for calculating the effective duration. 49 With these values, the average effective duration of the selected suite is 20.6 s. Hence, the duration of each performance segment is = 20.6 3 = 6.7 ≈ 7 . In step 2, the selection algorithm was run to break down the ground motions of the database into 7-s segments and choose the segment closest to the 5% target spectra in the 0.05-1.9 s period range. Based on the acceptable scale factor range mentioned in section 2.2 (0.5-4.5), the scale factor range for the level 2 segment is estimated as 0.7-3. This segment would have to be multiplied by 0.7 and 1.37 to roughly match the 10% and 2% target spectra, respectively. This makes the range of factors used for levels 1 and 3 to be 0.5-2.1 and 0.96-4.1, making the scale factor range for all three performance levels to be 0.5-4.1. The top 20 selected segments are found through the selection algorithm. With each selection, the selected segment, the start segment, and the end segment of that ground motion were truncated and exported. Figure 5 shows the output of step 2: the truncated selected segment, truncated start segment, and truncated end segment.
In step 3, spectral matching is performed on the selected segment using SeismoMatch. 59 Visual inspection was performed on the displacement, velocity, and acceleration time histories. Since the acceleration time histories saw a significant shift in the peak acceleration, it was concluded that this segment did not offer a good match without significantly changing the acceleration signal. This was the case for the first five selected segments. Finally, the sixth selection provided the best match without significantly altering the signal (see Figure 6) and was selected to create the GSGM. In step 4, the matched selected segment, the start segment, and the end segment were subjected to baseline correction to correct the bogus displacement deviations of the segments. Now all segments start and end at a displacement of zero as well as an acceleration of zero. Figure 6A shows that the original and matched segment acceleration time histories are not significantly different. The displacement and velocity time histories have also been checked, and the match is acceptable. Figure 6B shows a bogus residual displacement of more than 1 m. Figure 6C shows that the response spectrum of the matched segment is very close to the target spectrum within the 0.05-1.9 s period range. Figure 6D and F shows that the effect of baseline correction on the acceleration time history and response spectrum is negligible, which is expected. However, Figure 6E shows that the baseline correction has removed the unrealistic displacement values.
In step 5, the selected segment, which was previously matched and baseline corrected, was added to the start segment to produce Window 2. Next, the selected segment was scaled by a scale factor of 1.33 and added to Window 2 to match the 5%, creating Window 3. Then, the same procedure was repeated using a scale factor of 1.9 and Window 3, creating Window 4. Figure 7 shows windows 2 and 4 created in step 5.   In step 6, the end segment of the selected ground motion was added to the last window created in the previous step, Window 4, to create the entire GSGM. This GSGM is referred to as GSGM I. Then, the same procedure was repeated for selected segment 10 to produce another GSGM for this scenario, referred to as GSGM II. Figures 8 and 9 show the acceleration, velocity, and displacement time histories of GSGM I and GSGM II. In addition, the response spectra of windows 2, 3, and 4 of both GSGSMs are also shown in the figures. More information on the ground motions used to create these GSGMs is presented in Table 2.

Selection of ground motion suites
The main purpose of this study is to evaluate the ability of the GSGM, as an alternative input to code-based ground motion suites, in predicting structural behavior. To do this, the average response of suites of ground motion compliant with code criteria must be obtained. Even though a suite of 11 ground motions is what the codes suggest, the variability of 11 ground motions is still questionable and cannot be assumed as the point of comparison for the actual response. In the PEER GMSM study, 60 points of comparison were used as benchmarks for the structural response. The point of comparison was estimated by carrying out hundreds of NTHA, recording the responses, and developing a regression model to predict the response. 60 Later Whittaker et al. 39 used the median of the response of the suite of ground motion selected per the algorithm suggested by Jayaram et al. 61 as the point of comparison, which showed good agreement with the results of the regression analyses. Therefore, a suite of 100 ground motions is selected to create a more accurate estimation of the real response, creating a point of comparison for both the GSGM method and ground motion suites compliant with the code procedure. This suite is called U1 herein, and the same criteria mentioned before are used to select the suite. The results show that this suite's mean and median are close. Hence, since CMS was not used as the target spectrum in this paper, the mean of the response subjected to a suite of 100 ground motions will be used as the point of comparison instead of the median. The faulting mechanism is ignored in the selection criteria of Suite U1. However, a suite of 28 strike-slip ground motions, consistent with the scenario, was also considered to assess the assumption of ignoring the fault mechanism in far-fault scenarios. This suite is called Suite U2, and the average of this suite is also used as a second estimation for the point of comparison. The suites were selected from the PEER database 29 consistent with the assumed scenario and the same search parameters mentioned in the GSGM production procedure. As per CSA-S6-19, 2 the suites are selected and scaled in accordance with the guidelines of the 2019 National Building Code of Canada 62 using the 2% in 50 years probability target spectrum. The period range for scaling for the prototype bridge pier is 0.05-1.9 s based on the structural period of 0.95 s. The suites selected for the 2% probability spectrum will also be scaled to match the target spectra for 5% and 10% probability of exceedance in 50 years. The scale factors for the 2% suites are initially limited in a way that ground motion scale factors for all levels would fall within a reasonable range (0.7-4.2). Information on Suite U1 and Suite U2 ground motions is summarized in Table 1.
To be able to compare the structural responses yielded by the GSGMs with that of the code, two suites of 11 ground motions (Suites I and II) were also selected from the PEER database 50 consistent with the assumed scenario and the same search parameters, and as per the same criteria mentioned for Suite U1. Table 2 provides information about both ground motion suites. Figure 10 shows the response spectra for individual records and the mean response spectra for Suite U1, Suite U2, Suite I, and Suite II for a 2% probability of exceedance in 50 years. Figure 11 shows the mean response spectra for all three levels for Suite U1, Suite U2, Suite I, and Suite II.

SEISMIC RESPONSE EVALUATION OF THE CASE STUDY BRIDGE PIER
In this section, 452 nonlinear time-history analyses (NTHA) were conducted on the case study bridge pier in OpenSees. 53 There were four ground motion suites consisting of 100, 28, 11, and 11 records each. Each suite and the corresponding scale Manjil Iran 7.37 strike slip 1  factors for the three intensity levels (10%, 5%, and 2% probability of exceedance) were used to perform a total of 450 NTHA. Two analyses were also performed using the two GSGMs. Structural responses are presented in terms of maximum drift ratios, here called drift, and damage in terms of damage indices for all seismic levels (with 10%, 5%, and 2% probability of exceedance). In the case of the ground motion suites, the average of the maximum responses of the case study bridge pier subjected to each ground motion suite is calculated. For GSGM I and GSGM II, the maximum response of the structure within the windows corresponding to the 10%, 5%, and 2% probability of exceedance is calculated as the maximum response for seismic levels 1, 2, and 3. For example, the maximum drift within Window 2 (0-13.45 s of GSGM I and 0-13.65 s of GSGM II) is recorded as the maximum response for level 1, corresponding to a 10% probability of exceedance probability. In addition, the damage index calculated within that window is recorded as the damage index for level 1. The maximum drift and damage index for other levels are calculated similarly, considering the window corresponding to that earthquake level.

Evaluating GSGM drift responses against code-compliant suites
Initially, the response of GSGMs is compared to code-based ground motion suites. The maximum drift responses of the code-based suites and GSGMs for different earthquake levels are shown in Figure 12. Figure 12 shows that the drift responses produced by GSGM fall within 10% of the drift for code-compliant suites (Suite I or Suite II). However, it is also evident that even the two suites selected based on the same code criteria produced different demands, with a drift TA B L E 2 Ground motion record information for GSGM I, GSGM II, Suite I, and Suite II. variation of 10%, 6%, and 23% in Levels 1, 2, and 3, respectively. Hence, a 20% drift variation for different ground motion suites is anticipated; therefore, such a variation for the GSGMs response is also reasonable.

Evaluating GSGM and code-compliant suite drift responses against the point of comparison
In the end, all the responses must be assessed compared to the actual response of the structure. As mentioned in the previous section, the point of comparison is taken as the mean of Suite U1, which consists of 100 ground motions. The median and mean of Suite U1 were the same for levels 1 and 2 and within 8% for level 3. In addition, Suite U2 and Suite U1's means for all levels are very close (1.39, 2.04, and 2.86 for U2 and 1.4, 1.96, and 2.87 for U1), increasing our confidence in taking the mean of Suite U1 as the point of comparison. Drift responses for individual records of Suite U1, mean of Suite U1, and 16th and 84th percentiles of Suite U1 are presented in Figure 13A. Suite U1 showed to have a normal distribution, and thus the 16th and 84th percentiles were used to show one standard deviation below and above the mean. The mean drift of Suite U2, Suite I, and Suite II as well as the drift of GSGM I and GSGM II, are also shown in Figure 13A. To be able to better compare the results to the point of comparison, all drift responses were normalized by the mean drift value of Suite U1 for each earthquake level. These normalized values are shown in Figure 13A-C for earthquake levels 1, 2, and 3, respectively. This figure also shows the drift for 100 individual records of Suite U1. The mean, 16th, and 84th percentiles of Suite U1 are also shown. Collapses are not plotted in this figure. It is evident that in level 1, code-compliant suites render responses close to the point of comparison. At this level, GSGMs can either overestimate or underestimate the response by 5−10%. This variation can be associated with the discrepancy of PGV of the GSGM with Suite U1. By controlling PGV when producing GSGM, this variation can be minimized. In nonlinear levels (levels 2 and 3), the code-compliant suites can overestimate the maximum drift by as large as 15%. The two suites can also result in as large as a 10% discrepancy in the drift response compared to one another. In the nonlinear levels, the initial GSGMs overestimate the drift by 20%. However, it is evident that after taking PGA into consideration when producing GSGMs, this variation is reduced to less than 5% in level 2 and less than 10% in level 3. This means that if relevant IMs such as PGA and PGV are considered, GSGMs can provide a better estimate of the average response than suites of ground motion selected per code requirements. The normalized values show that the response estimated through the code-based suites (Suite I and Suite II) is within 12% of the point of comparison for all levels. GSGM I also provides a drift response variation of 6.5% with respect to the point of comparison. GSGM II, however, shows a variation of 11%, 20%, and 16% from the point of comparison for levels 1, 2, and 3, respectively. Looking at the response spectra for the two GSGMs within the specified period range shown in Figures 8  and 9, no significant difference is observed. This variation could still be acceptable. However, more investigation will be done to find the source of the variation in the drift response.

5.2.1
Effect of different IMs on the drift response of the case study column In order to find the source of variation of the case study column's drift response for the GSGMs compared to Suite U1, a total of 20 intensity measures (IMs) such as Peak Ground Acceleration (PGA), Peak Ground Velocity (PGV), Peak Ground Displacement (PGD), spectral acceleration at the fundamental period of the structure S a (T 1 ), S a (2T 1 ), and S a (3T 1 ) are calculated for the GSGMs and the suites. All the considered IMs have been commonly used in the literature except for S a (3T 1 ). Whittaker et al. 39 suggested using 3T 1 as the upper bound of the period range for spectrum matching of tall moment frames that were taken to large nonlinearities. In this study, the period of the case study structure elongated to 2.72 s in most level 3 earthquakes, which is three times the fundamental period. Therefore, S a (3T 1 ) was also included in the study. To make the investigation more reliable, more GSGMs were created by manipulating the scale factors used in the GSGM procedure. Thus, different versions of GSGM I and GSGM II were created (i.e., GSGM Ia, GSGM Ib, GSGM IIa, GSGM IIb, etc.). NTHA of the bridge pier is performed subjected to these GSGMs, and drift responses are recorded. Finally, the 20 IMs and maximum drift responses were calculated for Suite U1 and Suite U2, Suite I and Suite II, and all GSGMs. The drift and the IMs for all GSGMs were normalized by the mean drift and mean IMs of Suite U1 (as the point of comparison). The normalized curves for drift and each of the 20 IMs were then plotted and studied at different levels. When more than one IM seemed to contribute to the response, a weighted average of the two IMs that showed a closer correlation with the response was then plotted. Figure 14 shows these normalized curves for the most significant IM combinations for each level. Figure 14A and B shows that in levels 1 and 2, the drift response strongly correlates with PGA and S a (2T 1 ). This is reasonable as with higher nonlinearity levels, the structure becomes nonlinear, and period elongation occurs. Figure 14C shows that in level 3, PGD and S a (2T 1 ) are relevant; however, S a (3T 1 ) shows a better correlation than S a (2T 1 ). This is because at this level, the structure is further in nonlinearity levels, and the period has elongated to 2.72 s, which is close to 3T 1 . Therefore, at such high nonlinearity levels, the elongated period of 3T 1 is more representative of the structure. It should also be mentioned that IMs such as Acceleration Spectrum Intensity (ASI) and Velocity Spectrum Intensity (VSI) were also studied and turned out to be significant IMs. However, the intention was to use more simple IMs that could easily be calculated in the process of producing GSGM, and thus they were not included here.
This simple study of IMs against the drift response showed that in levels 1 and 2, S a (2T 1 ) and PGA showed the same trend as drift. In level 3, mainly PGD, PGV, and subsequently S a (3T 1 ) were the significant IMs. Looking at the time histories for the two main GSGMs, GSGM I and GSGM II, in Figures 8 and 9, it is evident that while the PGA of GSGM I is larger than that of GSGM II in all earthquake levels, the PGV and PGD of GSGM II are larger. It is also observed that while the response spectra for both GSGMs seem to be similar within the code-defined period range, spectral acceleration at 3T in level 3 for GSGM II is 0.18 g, while it is 0.15 g and 0.166 g for GSGM I and Suite U1. Spectral acceleration curves within specific period ranges are commonly used to determine the severity of seismic events at a site. However, different IMs can be used to quantify seismic hazards at particular sites. Here the selection of suites and production procedure of the GSGMs were performed based on spectral acceleration as per code procedures. This is because GSGM attempts to replicate code procedures. This part of the study showed the sensitivity of the estimated response using GSGMs to other IMs compared to the suites. Therefore, in order to increase the accuracy of the GSGM in capturing structural responses, significant IMs for the structure can be identified from the literature and used as a controlling parameter when creating the GSGM. This can be done by approximately matching IMs such as the PGA and PGD of the GSGM to the mean of a ground motion suite or the IM values estimated from attenuation equations.

Evaluating structural damage under GSGM and code-compliant suites against the point of comparison
The performance-based methodology requires the assessment of structural damage. Therefore, the capability of GSGM to simulate damage correctly is investigated here. To quantify the damage endured by the structure, damage indices are used. Williams and Sexsmith 63 presented a state-of-art review of available damage models for RC components. Damage models use damage rules to calculate damage indices based on force, displacement, energy, or a combination of them. In this research, three damage indices are used. The widely used combined damage model proposed by Park and Ang 64 and two of its variations are used. Equations (2) and (3) show the two variations of the damage formulation for the Park-Ang damage model. 64 These two damage indices are called Park-Ang DI 1 and Park-Ang DI 2.
In these equations, is the maximum deformation under an earthquake, is the ultimate deformation capacity under monotonic loading, F y is the calculated yield strength (the smaller value of the yield strength and ultimate strength, is the incremental absorbed energy, ( ) is the accumulated energy per loading cycle for the current displacement, is the yield displacement, and and are the calibration parameters for cyclic damage. is assumed to be 0.1, and is assumed as 1.0 based on Altoonash. 65 Pushover analysis of the column was performed to calculate . Valles et al. 66 proposed the ultimate capacity point to be chosen as the point where either the ultimate compressive strain of the concrete is reached or the ultimate strength of one of the rebars. The pushover curve was approximated by a bilinear relation as per ASCE, 67 based on which the and are estimated. The Kratzig damage model 68 which is based on dissipated energy contributions is also used here. This model is a complex energy formulation that divides the cycles experienced by the structure into two categories of primary and follower half-cycles. A primary half-cycle (PHC) is defined as the first halfcycle of loading at a given displacement amplitude. All subsequent half-cycles are termed followers (FHC) unless they exceed the previous maximum displacement amplitude. In this model, the cumulative damage parameter for the positive deformation half-cycles is defined based on Equation (4): in which E pi is the energy in a PHC, E i is the energy in an FHC, and E f is the maximum energy at the failure point under monotonic loading used as the calibrating parameter. The same parameter is calculated for the negative half-cycles (D − ), and the overall damage index is then defined in Equation (5): The damage indices were calculated and normalized by the corresponding damage index of Suite U1 and presented in Figure 15. Figure 15A-C shows the normalized damage indices for Park-Ang DI 1, Park-Ang DI 2, and Kratzig DI, respectively. It can be seen that the DI of code-based suites falls within 15% of the point of comparison. When considering Park-Ang DI 1 and Park-Ang DI 2, the estimated DI for GSGM I also falls within 15% of the point of comparison. The DI estimated by GSGM II shows a maximum error of 30%. In the case of the Kratzig DI, however, the maximum variation is 40% and 76% for GSGM I and GSGM II, respectively. Since the DI proposed by Kratzig is energy-based, and the number of earthquake cycles within each GSGM window is evidently less than that of an entire earthquake ground motion, regardless of how strong the cycles are, it is expected for the Kratzig DI of the GSGMs to be significantly less than the average of the suites. Even though this model accounts for deformation damage by giving more significance to PHCs, it is still very sensitive to the number of cycles. Kunnath et al. 49 calculated several damage indices for a number of RC columns that were tested under different loading paths. In all cases, the Kratzig DI reached a value close to 1.0, hundreds of cycles before other damage indices such as the Park and Ang or fatigue models. The Kratzig DI is, therefore, not an accurate estimate of the damage endured by the structure. Other combined damage indices, such as the Park-Ang DI 2, offer more accurate estimates by taking into account both the maximum displacements and the energy dissipated by the structure.

Evaluating sequences of ground motions against individual ground motions
The need for GSGM was based on the hypothesis that the execution of multiple shake table tests on the same specimen to get to the higher hazard levels is unrealistic and may induce significant structural damage to the specimen and influence its performance, especially for the most severe damage states. This hypothesis will be discussed and investigated here in brief. Performance-based design codes 2,3 as well as the PBEE framework methodology developed by the Pacific Earthquake Engineering Research Center (PEER), treat each hazard level separately and have developed acceptance criteria for each individual hazard level, that is, not a sequence of hazard-level events. Therefore, the realistic representation of these demands would be if the hazard levels were imposed independently. The PBEE framework methodology consists of four stages; hazard analysis, structural analysis, damage analysis, and loss analysis. In the hazard analysis part, a hazard curve is produced that describes the annual frequency with which seismic excitation, that is an IM, is estimated to exceed various levels. In the structural analysis, NTHA is performed to obtain EDPs for each specific IM, that is each hazard level, not a sequence of hazard levels. In probabilistic terms, NTHA are performed, and EDPs are calculated given IM when IM is equal to IM n , where IM n is one of the IMs of interest corresponding to a specific hazard level. Hence, the estimate of the real response for each hazard level should be independent of the others. In addition, from a probabilistic point of view, it is unrealistic to assume a structure would be subjected to three major earthquakes in its life span (e.g., 10%, 5%, and 2% in 50 years probability of exceedance events). Thus, as per the guidelines put forward by performance-based design codes, the demands of each hazard level must be investigated independently from other levels.
Having said this, an alternative to GSGMs for implementing PBEE in experimental testing is applying a sequence of ground motions scaled to represent different hazard levels in PBEE. However, the input energy and damage imposed by the number of cycles of three full ground motions is an unrealistic representation of the damage endured at the final hazard level. To put this to the test, in this section, the input energy and some structural demand parameters of hazard level 3 will be investigated for two scenarios. The first scenario is to perform NTHA using a single ground motion in level 3. The second scenario requires performing NTHA using a sequence of ground motions from levels 1-3. These two scenarios are implemented using the 100 ground motions in Suite U1, and the suite average is used for comparison. Each ground motion in the suite has three scale factors corresponding to the three hazard levels used in this study. In the first scenario, the bridge pier is subjected to each individual ground motion of the suite with the scale factor corresponding to hazard level 3. In the second scenario, the bridge pier is subjected to the sequence of the three amplified versions of each ground motion successively (hazard levels 1-3). The average input energy and demand parameters in level 3 for these two scenarios and the GSGM are then calculated and compared.
Kalkan and Kunnath 69 showed that the difference between relative and absolute energy is insignificant for far fault records. Thus, the relative energy formulation shown in Equation (6) is used to calculate the seismic input energy for the bridge pier (SDOF system).
In this formula, m and k are the mass and stiffness of the structure, u is the displacement of the structure relative to the ground,̇is the velocity of the structure relative to the ground, and̈is the ground acceleration. Based on this formula, the average relative input energy for the single ground motion scenario in level three is 363.38 kJ; however, for the sequence scenario, it is 618.09 kJ, almost double. On the other hand, the input energy for the GSGMs ranges between 251.35 and 376.60 kJ. The data verify that applying a sequence of ground motions can result in applying as much as twice the input energy when a single ground motion is applied. Regarding structural demand parameters such as maximum and residual drift ratios, no significant difference was seen between the average of the two scenarios (single vs. sequence). However, in terms of damage, a 25% increase was seen in Park-Ang DI 2 for the sequence scenario.
Even though the maximum and residual drift for the 100 ground motions of suite U1 showed no significant variation for the two scenarios, this was not the case for each individual ground motion of this suite. By investigating each of the 100 ground motions, it was evident that the consequence of using a sequence compared to a single ground motion was different for each ground motion. In some cases, not much difference was seen in the response history. In other cases, the response history and maximum response were significantly altered, either increasing or decreasing the maximum response. This contrast can be attributed to the fact that different ground motions take the structure to different nonlinearity levels causing different damage levels in the structure, which then affect the structure's response when subjected to the following ground motions. Investigation of individual ground motions of Suite U1 showed that these increases and decreases cancelled each other out, resulting in similar average values. However, the fact that the averages remained the same does not mean the two scenarios are equivalent. To illustrate this, the time history of the top displacement and hysteresis of the pier subjected to the two scenarios for one of the ground motions of Suite U1 is shown in Figure 16. It can be seen that for level 3, the displacement history and, more importantly, the maximum displacement are different for the two cases. For this specific ground motion, the sequence scenario increased the maximum drift by 31%. The Park-Ang DI 1 also saw a 34% increase.

CONCLUSION
This study introduces a performance-based seismic loading protocol called generated sequential ground motion (GSGM) that extends using PBEE to experimental testing. The protocol optimizes the behavioral information output of an experimental test or numerical analysis by incorporating dynamic demands corresponding to design limit states with probabilities of exceedance of 10%, 5%, and 2% in 50 years in a single record. In addition, since the protocol is matched to the target spectra, the average response can be sufficiently represented by a single ground motion instead of a suite of F I G U R E 1 6 (A) Comparison of the displacement time history, and (B) hysteresis for the single and sequence scenarios for a single ground motion from Suite U1.
ground motions. Furthermore, GSGM is created from segments of real recorded ground motions rather than artificial. Therefore, it maintains the general characteristics of actual ground motion records. In the performance-based methodology, GSGM is considered an alternative seismic input to suites of ground motion for the structural analysis step. In order to investigate the validity of this alternative input, its capability to capture the output of the structural engineering process should be assessed. For this purpose, two structural demand parameters, namely, maximum drift and damage index, were studied. The step-by-step procedure to produce GSGM was presented and used to create two GSGMs consistent with the assumed earthquake scenario and the designed case study bridge pier. Since the protocol claims to replicate demand parameters corresponding to demands of three code limit states, that is, 10%, 5%, and 2% in 50 years probability of exceedance, two sets of 11 ground motions were selected and scaled as per the Canadian code. Additionally, two sets of ground motions consisting of 100 and 28 ground motions (Suite U1 and Suite U2, respectively) were selected and scaled to develop a more robust estimation of the actual response. Suite U1 did not include fault mechanism as a search criterion since a far-fault scenario is assumed. However, Suite U2 consisted of strike-slip earthquakes consistent with the assumed faulting mechanism. The mean and median drift reported by both suites were close; thus, the average of Suite U1 was selected as the real response, called the point of comparison.
The validated finite element model of the case study bridge pier was subjected to the ground motion suites and GSGMs. A comparison of the results reported by the GSGM with that of the two code-compliant suites showed a difference of up to 10% in maximum drift. This is while the two code-compliant suites showed a difference of 23% in drift. Compared to the point of comparison, the drift reported by code-compliant suites fell within 12% of the real response, while one of the GSGMs reported a drift deviation of 20% compared to the point of comparison. Twenty IMs were investigated, and it was found that other IMs, such as PGA and PGD, could affect the drift response. Since record-to-record variability cannot be considered in GSGM, in order to have a GSGM that more realistically represents a suite of ground motions, other IMs may be considered in addition to spectral acceleration when producing GSGMs. Finally, to study the damage, three damage indices were studied. The results showed that when the two Park and Ang damage indices were used to model damage, GSGM could predict the damage with a maximum variation of 30% from the point of comparison. Given that every ground motion is replaced by a ground motion segment in the GSGM, this variation could be acceptable.
The principal finding of this work is that the proposed loading protocol, GSGM, can extend performance-based seismic assessment and design of bridge piers to experimental testing and reduce the computational time of numerical performance-based design. This study is limited to investigating the capability of GSGM to replicate code-compliant responses for one case study bridge pier for a far-fault earthquake scenario. Hence, more comprehensive studies, including a broader range of bridge piers and other structural systems, could further assess the validity of the protocol. Nonetheless, for the case study and earthquake scenario assumed here, this study suggests that the GSGM can sufficiently replicate the responses reported by the current code procedure.
GSGM is a simulated ground motion that can be used as the input for experimental testing in setups such as shaking table or PsD testing. Such setups are restricted to experimental testing of SDOF and MDOF systems, such as the case study bridge pier in this study. The GSGM cannot, however, be used for experimental testing of structural elements outside of the structural system, such as beams, columns (with no mass), or braces in a setup similar to quasi-static testing. Nonetheless, testing of such elements would be possible if the sub-structuring technique is used to model the mass numerically, for example, in a sub-structured PsD setting. Despite this, the authors recognize the limitations of testing facilities and the ease of using loading histories through servo-hydraulic actuators in a quasi-static fashion. In this regard, future studies focusing on producing displacement protocols from GSGMs could help extend performance-based design through simpler testing equipment. In addition, in its current form, the GSGM does not include white noise to allow for dynamic identification of the structure after each hazard level. Therefore, white noise can only be included at the end of the GSGM to perform dynamic identification after the last performance level. It is, however, possible to change the basic form of the GSGM to include white noise at the end of each window to remedy this limitation.

A C K N O W L E D G E M E N T S
The financial contribution of the Natural Sciences and Engineering Research Council (NSERC) of Canada through the Discovery Grant was critical to conduct this research and has been gratefully acknowledged.

D ATA AVA I L A B I L I T Y S TAT E M E N T
Data will be made available upon a reasonable request from the corresponding author.