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Method for Ranking Pulse-like Ground Motions According to Damage Potential for Reinforced Concrete Frame Structures

Method for Ranking Pulse-like Ground Motions According to Damage Potential for Reinforced... buildings Article Method for Ranking Pulse-like Ground Motions According to Damage Potential for Reinforced Concrete Frame Structures 1 , 2 3 , 1 , 2 1 , 2 , 3 1 , 2 Qinghui Lai , Jinjun Hu * , Longjun Xu , Lili Xie and Shibin Lin State Key Laboratory of Precision Blasting, Jianghan University, Wuhan 430056, China; laiqinghui@jhun.edu.cn (Q.L.); xulj@jhun.edu.cn (L.X.); 18845117968@163.com (L.X.); shibinlin@gmail.com (S.L.) Hubei Key Laboratory of Blasting Engineering, Jianghan University, Wuhan 430056, China Key Laboratory of Earthquake Engineering and Engineering Vibration, Institute of Engineering Mechanics, China Earthquake Administration, Harbin 150080, China * Correspondence: hujinjun@iem.ac.cn Abstract: To rank the pulse-like ground motions based on the damage potential to different structures, the internal relationship between the damage potential of pulse-like ground motions and engineering demand parameters (EDPs) is analyzed in this paper. First, a total of 240 pulse-like ground motions from the NGA-West2 database and 16 intensity measures (IMs) are selected. Moreover, four reinforced concrete frame structures with significantly different natural vibration periods are established for dynamic analysis. Second, the efficiency and sufficiency of the IMs of ground motion are analyzed, and the IMs that can be used to efficiently and sufficiently evaluate the EDPs are obtained. Then, based on the calculation results, the principal component analysis (PCA) method is employed to obtain a comprehensive IM for characterizing the damage potential of pulse-like ground motions for specific building structures and EDPs. Finally, the pulse-like ground motions are ranked based on the selected IM and the comprehensive IM for four structures and three EDPs. The results imply that Citation: Lai, Q.; Hu, J.; Xu, L.; Xie, the proposed method can be used to efficiently and sufficiently characterize the damage potential of L.; Lin, S. Method for Ranking pulse-like ground motions for building structures. Pulse-like Ground Motions According to Damage Potential for Reinforced Concrete Frame Keywords: pulse-like ground motions; damage potential ranking; intensity measures; analysis of Structures. Buildings 2022, 12, 754. efficiency and sufficiency; principal component analysis https://doi.org/10.3390/ buildings12060754 Academic Editor: Eva O. 1. Introduction L. Lantsoght Ground motion damage to building structures is of two types: (1) cumulative damage, Received: 10 April 2022 which occurs due to ground motion at medium and faraway sites; (2) instantaneous damage, Accepted: 22 April 2022 which primarily occurs due to the destructive pulse-like ground motion. The mechanisms Published: 1 June 2022 of the two types of ground motion damage are different. The damage potential of pulse-like Publisher’s Note: MDPI stays neutral ground motions for building structures is more significant compared with that of ordinary with regard to jurisdictional claims in ground motions [1–4]. Therefore, the damage potential of pulse-like ground motions must published maps and institutional affil- be accurately evaluated for the seismic design of building structures. To estimate the iations. damage potential of ground motions for building structures, two intermediate variables are introduced—one represents structural performance and the other represents ground motion characteristics [5–8]. An intensity measure (IM) that has a strong correlation with the appropriate engineering demand parameter (EDP) must be selected. However, several Copyright: © 2022 by the authors. IMs can be used to predict structural responses by establishing a seismic demand model Licensee MDPI, Basel, Switzerland. between IMs and EDPs [3,9,10]. Yazdani and Yazdannejad [11] noted that the uncertainties This article is an open access article associated with the seismic demand model are related to uncertainties associated with distributed under the terms and ground motions. conditions of the Creative Commons A few studies have focused on commonly used IMs such as peak ground acceleration Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ (PGA), peak ground velocity (PGV), peak ground displacement (PGD), Arias intensity 4.0/). (AI), specific energy density (SED), and cumulative absolute velocity (CAV) [12]. However, Buildings 2022, 12, 754. https://doi.org/10.3390/buildings12060754 https://www.mdpi.com/journal/buildings Buildings 2022, 12, 754 2 of 18 these IMs are based only on ground motion characteristics, and the uncertainties associated with structural performance are not considered. The more ground motion information and structural information an IM contains, the better the correlation with EDPs is. Compared with the aforementioned IMs, the first-order spectral acceleration (S (T )) is the most a 1 extensively used IM in seismic risk analysis and structural seismic analysis [13–19]. S (T ) presents a high degree of correlation with the EDPs of structures with small natural vibration periods. However, several studies [20,21] have discovered that there is a low degree of correlation between the S (T ) and EDPs of super-high-rise buildings. To this a 1 end, some experts have selected relative displacement (S (T )) or input energy (Ei (T )) as d 1 1 the IMs for predicting structural responses [18,22]. A few studies have focused on achieving discreteness in vector IMs and EDPs [23,24]; the discreteness achieved in vector IMs and EDPs is smaller than that in scalar IMs. However, vector IMs are complex and thus not conducive to practical engineering applications. To avoid the complexities associated with the use of vector IMs, scalar IMs can be used instead, especially when the same capacity for predicting EDPs can be achieved using scalar IMs [25,26]. Significant uncertainties are prevalently associated with structural performance. How- ever, in some studies, only a few similar structures have been comprehensively analyzed via non-linear time-history analysis [9,20,26,27]; the results obtained in this direction are consistent. Ebrahimian [9] analyzed the prediction capacities of different IMs for the struc- tural responses of four-story and six-story isolated structures, which were subjected to pulse-like ground motions and ordinary ground motion. The results implied that the vector IMs related to S (T ) could be used to predict structural responses more efficiently and a 1 sufficiently. Dávalos and Miranda [26] analyzed the efficiency and sufficiency of FIV3 in predicting the structural responses of a four-story reinforced concrete (RC) frame. The results indicated that the novel FIV3 is a promising parameter that can be used for assessing structural collapse risks. Furthermore, some researchers have investigated the correlation between the IMs and structural responses of different structures. Palanci [28] analyzed the correlation between the average values of spectral displacement over different periods via the SDOF system involving different hysteretic models. However, in this study, the correlation between different IMs and the average values of EDPs of different structures is investigated to determine the prediction capacities of IMs, without considering the un- certainties associated with the structures. Note that the correlations between the EDPs and different IMs are significantly different for structures with different natural vibration periods [29–31]. Yakhachalian and Ghodrati [29] analyzed the discreteness of IMs and EDPs for low- and middle-rise structures via the strip method. The vector IM (S (T ), S a 1 a (T )/PGV) is proposed as an optimal IM for predicting the maximum inter-story drift ratio (MIDR) for low- and middle-rise RC moment-resisting frame structures. However, the aforementioned studies have only verified the prediction capacity of the selected IMs for different structures; meanwhile, few studies have used the obtained IMs to further analyze ground motion characteristics. The damage potential of ground motions for building structures can be determined based on different IMs. Notably, ground motions, especially pulse-like ground motions, have not been ranked based on the optimal IMs in the aforementioned studies. In this study, pulse-like ground motions are ranked based on their damage potential for different RC frame structures. 2. Technical Framework To rank the ground motions in predicting EDPs based on the damage potential, a method is proposed for ranking pulse-like ground motions according to their damage potential in this study; the method involves predicting EDPs based on ground motion IMs. The uncertainties associated with both ground motions and building structures are considered in the proposed method. The 16 selected IMs include amplitude, spectrum, and duration, which can be used to describe the uncertainties associated with ground motions. Meanwhile, four reinforced concrete (RC) frame structural models with signifi- cantly different natural vibration periods are established, and three EDPs are considered for Buildings 2022, 12, 754 3 of 18 evaluating the uncertainty of the established structures. The efficiency and sufficiency of IMs in predicting EDPs are analyzed to determine the optimal IMs for different structures. Furthermore, for multiple optimal IMs, the pulse-like ground motions are ranked by deter- mining the comprehensive IM via the principal component analysis (PCA) method. Finally, the pulse-like ground motions are ranked according to their damage potential using the selected optimal IM. The technical framework of this paper is illustrated in Figure 1. Figure 1. Technical framework. 3. Selection of Pulse-like Ground Motions and IMs 3.1. Selected Pulse-like Ground Motions Compared with that of ordinary ground motions, the damage potential of pulse-like ground motions is typically higher. Pulse-like ground motions involve the release of significant amounts of instantaneous energy, thereby causing impact damage in building structures. Figure 2 depicts the velocity time-histories of two ground motions, (a) pulse-like ground motion and (b) non-pulse-like ground motion, which are significantly different from each other. In this study, the damage potential of 240 pulse-like ground motions is analyzed; the ground motions are selected according to the method proposed by Zhai [32]. An energy- based significant velocity half-cycle is used as a reference for distinguishing pulse-like ground motions. Note that these pulse-like ground motions are extensively studied [33]. Figure 3 illustrates the station distribution of pulse-like ground motions, which is mainly distributed in the United States, Japan, the Middle East, and Taiwan Province of China. Figure 4 shows the distributions of V , magnitude (M), and epicentral distance (R). The s30 values of M range from 5.21 to 7.62, and those of V are mainly < 1000 m/s. Pulse-like s30 ground motions can be generated not only in the near field, but also in the relative far field (R > 100 km). Buildings 2022, 12, 754 4 of 18 Figure 2. Velocity time-history of pulse-like and non-pulse-like ground motions. (a) Pulse-like ground motion; (b) non-pulse-like ground motion. Figure 3. Station distribution of selected pulse-like ground motions. Figure 4. Distribution ranges of M, R, and V of the selected pulse-like ground motions. (a) Vs30-M; s30 (b) Vs30-R. 3.2. Selected IMs The main causes of structural damage caused by ground motion are included in the whole ground motion time-history. The time-history characteristics of ground motion are Buildings 2022, 12, 754 5 of 18 indicated by various IMs. In this study, a novel method is employed for predicting the damage potential of ground motion for building structures; the method involves adopting 16 commonly used IMs, including amplitude, duration, spectrum, and energy parameters, based on previous studies. The selected IMs are shown in Table 1, and their physical significance and calculation methods are mentioned in the relevant literature [32,34,35]. Table 1. Selected IMs.. Note Ground Motion IMs Expression IM Peak ground acceleration (PGA) PG A = maxja(t)j IM Peak ground velocity (PGV) PGV = maxjn(t)j IM Peak ground displacement (PGD) PGD = maxjd(t)j IM Bracketed duration (D ) D = max(t) min(t) 4 b b IM Uniform duration (D ) D = H a(t) a dt (j j ) 5 u u 0 IM Significant duration (D ) D = t t 6 s s 95 5 IM Effective peak acceleration (EPA) EPA = S /2.5 7 a IM Effective peak velocity (EPV) EPV = S /2.5 8 v 2.5 IM Housner intensity (SI) S I = S (x, T)dT z v 0.1 t +1 IM Cumulative absolute velocity (CAV) C AV(t) = W j A(t)jdt 10 å i i IM Maximum incremental velocity (MIV) - IM Maximum incremental displacement (MID) - Spectral acceleration at the first mode period IM - of vibration (S (T )) a 1 Spectral velocity at the first mode period of IM - vibration (S (T )) v 1 Spectral displacement at the first mode IM - period of vibration (S (T )) d 1 Relative input energy at the first mode R IM 16 E(T ) = 2 a vdt 1 g period of vibration E (T ) i 1 4. Selection of Structural Models and EDPs 4.1. Structural Models To comprehensively analyze the destruction mechanism of different structures caused by pulse-like ground motions, four representative structural models with quite different natural vibration periods are established and used for comprehensively analyzing the damage caused by pulse-like ground motions in different structures. The structural models are designed according to Zhai et al. [35] and Li et al. [36]. The four frame structures are of different types—short-period, short- and middle-period, middle- and long-period, and long-period—with 2, 5, 8, and 15 stories, respectively. These buildings are symmetric. The finite element software IDARC-2D is used to analyze the four frame structures [37]. The natural vibration period (T ) of each structure is shown in Table 2. The four structural models are based on four ordinary RC frame structures, with seismic fortification intensity of seven degrees. The four structures are modeled considering a class II site. The improved I-K trilinear hysteretic model is used for the four structures [38,39], and Figure 5 shows the hysteretic skeleton curve of the model. The four buildings use C30 concretes, and the live load is 0.4 kN/m . Figure 6 illustrates the plan and elevation of the four representative structures. Tables 3 and 4 show the sectional dimensions, concrete grades, and steel rebars of the beams and columns of the structures. The yielding strength f of the main yk reinforcement rebars is 400 MPa, and the yielding strength f of the stirrups is 300 MPa. yk During calculations, the stiffness in the floor plane is considered infinite. The stiffness degradation coefficient a, strength degradation coefficient b, and pinch effect coefficient g determine the hysteretic responses of the structures. The values 8.0, 0.1, and 0.5 are selected for the parameters a, b, and g, respectively, for the analysis using the IDARC-2D software. Centralized plasticity is considered as the plasticity type. Buildings 2022, 12, 754 6 of 18 Table 2. Natural vibration periods and types of structures. Building Structures Natural Vibration Period T Structure Types 2-story 0.20 s Short period 5-story 0.89 s Short and middle period 8-story 1.73 s Middle and long period 15-story 2.73 s Long period Figure 5. Backbone curve for improved I-K hysteretic model. Figure 6. Cont. Buildings 2022, 12, 754 7 of 18 Figure 6. Elevation of four representative reinforced concrete frame structures (unit: mm). Table 3. Beam section properties of four RC frame buildings. 2 2 Section Size (mm  mm) Area of Longitudinal Reinforcement (mm )/Stirrup (mm ) Story Structure Side Column Middle Column Side Column Middle Column 2-story 1–2 600  300 600  300 1313/'8@100 1313/'8@100 1–4 500  250 400  250 1008/'8@100 763/'8@200 5-story 5 500  250 400  250 763/'8@200 603/'8@200 1–4 500  250 500  250 1296/'8@100 710/'8@200 8-story 5–6 500  250 500  250 1015/'8@100 710/'8@200 7–8 500  250 500  250 710/'8@100 710/'8@200 1–7 600  250 450  250 1964/'8@100 935/'8@100 8–10 600  250 450  250 1742/'8@100 833/'8@100 15-story 11–12 600  250 450  250 1520/'8@100 833/'8@100 13–14 600  250 450  250 1250/'8@100 833/'8@100 15 600  250 450  250 942/'8@100 755/'8@100 The yielding strength f of main reinforcement rebars is 400 MPa, and the yielding strength f of stirrups is yk yk 300 MPa. Table 4. Column section properties for four RC frame buildings. 2 2 Section Size (mm  mm) Area of Longitudinal Reinforcement (mm )/Stirrup (mm ) Story Structure Side Column Middle Column Side Column Middle Column 2-story 1–2 700  700 700  700 2330/'8@100 2330/'8@100 5-story 1–5 500  500 500  500 2512/'8@100 2512/'8@100 1–5 550  550 550  550 2733/'8@100 2733/'8@100 8-story 6–8 500  500 600  600 2035/'8@100 2035/'8@100 1–5 650  650 650  650 4560/'10@100 4560/'10@100 15-story 6–10 600  600 600  600 3807/'10@100 3807/'10@100 11–15 550  550 550  550 3411/'8@100 3411/'8@100 The yielding strength f of main reinforcement rebars is 400 MPa, and the yielding strength f of stirrups is yk yk 300 MPa. 4.2. Selected EDPs The degree of damage in the structures due to pulse-like ground motions is comprehen- sively evaluated by selecting several EDPs, as shown in Table 5: (1) MIDR is the maximum Buildings 2022, 12, 754 8 of 18 inter-story drift ratio (drift normalized by the story height) over all stories/closely re- lated to local damage, instability, and story collapse; (2) MFA is the maximum value of floor absolute acceleration for all stories and indicates the level of non-structural damage; (3) OSDI denotes the degree of overall damage in the structure and is determined by the peak displacement and hysteretic energy consumption of the structure. Table 5. Engineering demand parameters considered in the study. Num Notation Name 1 MIDR Maximum inter-story drift ratio 2 MFA Maximum floor acceleration 3 OSDI Overall structural damage index 5. Prediction and Analysis of EDPs Based on IMs The capacity of an IM for predicting EDPs is primarily determined via analyzing the efficiency and sufficiency of the IM. In traditional methods [32,35], the numerical values of IMs and EDPs are typically assumed to have linear or logarithmic distribution, as shown in Equations (1) and (2). The aim of this study is to rank pulse-like ground motions based on their damage potential. To this end, a new data-processing method is proposed. The IMs that can be used to efficiently and sufficiently predict EDPs are positively correlated with EDPs. IMs and EDPs are separately used to rank ground motions, which are ranked based on IMs and EDPs, respectively, and the relationship between the two ranking results (R IM and R ) is shown in Equation (3). The efficiency and sufficiency of an IM is determined EDP by the ability of the IM to predict EDP. h = b + b I M (1) Dj I M 0 1 lnh = b + b ln I M (2) Dj I M 0 1 R = b + b R (3) EDP 0 1 I M where b and b are regression coefficients, R is the ranking obtained using an IM, and 0 1 IM R is the ranking obtained using an EDP. EDP 5.1. Efficiency of the IMs Efficiency is an important metric for assessing the quality of a selected IM. There are two commonly used statistical parameters that can be used to describe the efficiency of IMs [9,40]. The first parameter is the determination coefficient (R ), as shown in Equation (4). A value of R is closer to one; the efficiency of the IM increases with the decrease in the discreteness of IM ranking and EDP ranking fitting. The second statistical parameter is the standard deviation b . The greater the value of b , the smaller the D|IM D|IM dispersion, which means that the regression model is more efficient for characterizing the structural response. Either of the statistical parameters can be used to effectively measure the efficiency of IMs. R is used as the criterion in this study. å (R R ) EDP EDP 2 k=1 R = (4) (R R ) EDP k EDP k=1 where n denotes the number of ground motion data points; R denotes the response EDP fitting ranking based on the IM ranking; R is the average ranking of EDP; R is the EDP EDP EDP ranking. The efficiencies of the IMs are analyzed based on the structural responses of the four structures, and the calculation results are shown in Figures 7–9. Notably, the uncertain- ties associated with ground motion and building structure should be considered while analyzing the damage potential of ground motion for building structures. There are no- Buildings 2022, 12, 754 9 of 18 table differences between the discreteness of the same IM and the same EDP for different structures. Furthermore, the discreteness of the same IM and different EDPs may also be different for the same structure. These results indicate the uncertainties associated with structure. However, in many studies, only similar structures have been analyzed, and the results are inconsistent with the findings of this study [9,26]. Figure 7. R of IMs and MIDR, obtained via the cloud analysis of four typical structures subjected to pulse-like ground motions. Figure 8. R of IMs and MFA, obtained via the cloud analysis of four typical structures subjected to pulse-like ground motions. Figure 9. R of IMs and OSDI, obtained via the cloud analysis of four typical structures subjected to pulse-like ground motions. In addition, there are significant differences between the R values of different IMs and EDPs for the same structure; this indicates the uncertainties associated with ground motion. The uncertainties associated with ground motion and building structure are considered in this study for analyzing the ability of IMs to predict EDPs accurately and to determine Buildings 2022, 12, 754 10 of 18 the optimal IMs for describing the damage potential of ground motion. Three IMs with the largest R for EDP prediction are selected for the different structural types and EDPs. The results are shown in Table 6. The results indicate that even for the same EDP, the most efficient IMs are different for different structural types. When MIDR is selected as the EDP, the most efficient IMs are different for different building types: EPA, S (T ), and S (T ) are a 1 1 the most efficient IMs for two-story buildings; SI, EPV, and S (T ) are the most efficient IMs a 1 for five-story buildings; PGV, S (T ), and E(T ) are the most efficient IMs for eight-story d 1 1 buildings, and PGD, MID, and S (T ) are selected as the most efficient IMs for 15-story d 1 buildings. The IMs that can be used to predict OSDI and MIDR are the same in most cases. Some IMs related to acceleration can be used to efficiently characterize MFA, such as PGA, EPA, and S (T ). Table 6. The most efficient IMs for different typical structures. Models MIDR MFA OSDI 2-story EPA, S (T ), S (T ) EPA, S (T ), S (T ) EPA, S (T ), S (T ) a a a 1 d 1 1 d 1 1 d 1 5-story SI, EPV, S (T ) PGA, EPA, EPV SI, S (T ), S (T ) a a 1 1 d 1 8-story PGV, S (T ), E (T ) PGA, EPA, EPV PGV, S (T ), E(T ) 1 1 1 1 d i d 15-story PGD, MID, S (T ) PGA, EPA, SI PGD, MID, S (T ) 1 1 d d 5.2. Sufficiency of the Selected IMs In addition to efficiency, sufficiency is important for assessing the quality of IMs. An IM is sufficient when the probability distribution of an EDP is independent from ground motion characteristics, such as epicenter distance, magnitude, and the ground motion parameter epsilon (#) [41]. Zelaschi et al. [40] obtained p-values for the residuals of EDP and ln h with magnitude and epicenter distance of the ground motion when they proved Dj I M that an IM is sufficient. Similar methods [20,29,42] have been used in relevant studies to demonstrate the sufficiency of IMs. However, the method proposed by Zelaschi et al. is unreasonable because the calculated p-values are closely related to the number of samples, as noted in relevant studies [40,43]. It becomes more difficult to accept the null hypothesis with an increasing number of samples. The sufficiency of an IM can also be verified based on relative entropy, a concept in seismic engineering proposed by Jalayer [27]. In this study, based on the concept of relative entropy, a simple quantitative measure is introduced; it is called the relative sufficiency measure, which is selected as a parameter to measure the relative sufficiency of one IM with respect to another. Therefore, the relative sufficiency measure is used to verify the sufficiency of the selected IMs. The simplified and approximate formulation of relative sufficiency is shown in Equation (5). 0 1 lny lnh ( I M ) 2,K k Dj I M n b B b C Dj I M Dj I M 2 B C I(Dj I M j I M )  log   (5) 2 1 å 2@ A lny lnh ( I M ) n b k Dj I M 2,K Dj I M k=1 2 1 Dj I M where b is the conditional standard deviation, which serves as a quantitative measure D|IM for the prediction efficiency of the IMs; y is the R ; lnh is the fitting function; n is k EDP D|IM the number of samples. The above equation was derived by Jalayer [27] and Ebrahimian [9]. The reference intensity (i.e., IM in Equation (5)) is considered to be S (T ) for the structural response, 1 a 1 mainly because S (T ) is a better characterization parameter for the structural response a 1 and is extensively used in earthquake engineering. The sufficiency is measured for each candidate IM relative to S (T ). If (IM |IM ) has a positive value, the candidate IM is more sufficient than S (T ). 2 1 a 1 Similarly, if I (IM |IM ) has a negative value, the candidate IM is less sufficient than S (T ) 2 1 1 for predicting EDPs. Buildings 2022, 12, 754 11 of 18 The obtained results, as shown in Figures 10–12, indicate that one or more IMs are more sufficient than S (T ) for characterizing the EDPs in most cases. However, when analyzing MFA and MIDR for a two-story structure, all I( I M j I M ) values are not positive, 2 1 which indicates that S (T ) is the most sufficient among all parameters. Finally, all the a 1 most sufficient IMs for characterizing the EDPs are obtained, as shown in Table 7. Figure 10. I (IM jIM ) between IMs and MIDR, obtained via the cloud analysis of four typical 2 1 structures subjected to pulse-like ground motions. Figure 11. I (IM jIM ) between IMs and MFA, obtained via the cloud analysis of four typical structures 2 1 subjected to pulse-like ground motions. Figure 12. I (IM jIM ) between IMs and OSDI, obtained via the cloud analysis of four typical 2 1 structures subjected to pulse-like ground motions. Buildings 2022, 12, 754 12 of 18 Table 7. The most sufficient IMs for different structures. Building Structure MIDR MFA OSDI 2-story S (T ) S (T ) EPA a 1 a 1 5-story SI, EPV PGA, EPA, EPV, S (T ) SI v 1 8-story PGV, S (T ), E (T ) PGA, D , EPA, EPV, SIMIV, S (T ), S (T ) PGV, S (T ), E (T ) d 1 i 1 s v 1 d 1 d 1 i 1 15-story PGD, MID PGA, D , EPA, EPV, SI PGD, MID, S (T ) d 1 5.3. Comprehensive Analysis of the Selected IMs The efficiency and sufficiency of 16 IMs are analyzed to determine the optimal IMs for accurately describing the damage potential of ground motions. The ground motion IMs that satisfy the requirements of both efficiency and sufficiency are determined by comparing the analysis results for efficiency and sufficiency, as shown in Table 8. For a short-period structure (for example, two-story) and MFA as the EDP, the acceleration-related IMs can be used to efficiently and sufficiently characterize the EDPs. For MIDR or OSDI as the EDP and a medium-period structure (for example, eight-story), the velocity-related IMs can be used to efficiently and sufficiently characterize the EDPs. Finally, the displacement-related IMs can be used to efficiently and sufficiently characterize the MIDR or OSDI for a long-period structure (for example, 15-story). Table 8. The most efficient and sufficient IMs for different buildings. Building Structure MIDR MFA OSDI 2-story S (T ) S (T ) EPA a 1 a 1 5-story SI, EPV PGA, EPA, EPV SI 8-story PGV, S (T ), E(T ) PGA, EPA, EPV PGV d 1 1 15-story PGD, MID PGA, EPA PGD, MID 6. Establishing the Pulse-like Ground Motion Rankings To describe the destructive capacity of ground motion more accurately and rank the pulse-like ground motions based on the optimal IMs, the efficiency and sufficiency of 16 IMs are analyzed by four different structures. However, there are two cases based on the number of IMs, as shown in Table 8: (1) only one optimal IM is obtained, and the pulse-like ground motions are ranked directly based on this IM, which is the damage potential ranking result of the pulse-like ground motions; the ranking depicts the ranking in which the ground motions can damage a building structure—the most unfavorable to the most favorable; (2) multiple IMs are obtained. However, further analysis is necessary for developing a ranking method in the case of multiple IMs. A novel method is proposed for combining multiple IMs into one comprehensive IM. The method involves reducing the dimensions of the variables via PCA. Subsequently, the damage potential of pulse-like ground motion is comprehensively evaluated according to the principal component. The results are highly interpretable [44–46]. 6.1. Comprehensive IM Determination Based on the PCA The proposed method is a multivariate statistical method that involves dimensional reduction and the transformation of multiple indicators into a few comprehensive indica- tors, while ensuring minimal loss of data or information. Generally, the comprehensive IM generated via transformation is called the principal component, which is a linear combina- tion of original variables. Based on the principal component, the main contradictions can be identified and the collinearity problem between variables can be avoided, and thus the efficiency of the IM can be improved. For example, there are n samples, and each sample contains p variables. A strong correlation exists among these p variables, which is denoted by X = (x , x , . . . , x )’ after 1 2 p Buildings 2022, 12, 754 13 of 18 standardization. The mathematical model of PCA is shown in Equation (6). A is an orthogonal matrix as shown in Equation (7). y = a x + a x + + a x > 1 11 1 12 2 1 p y = a x + a x + + a x 2 22 2 2 p p 21 1 (6) > . y = a x + a x + + a x p p1 1 p2 2 p p p 2 3 a a  a 11 12 1 p 6 7 a a  a 21 22 2 p 6 7 A = 6 7 (7) . . . . . . . . 4 5 . . . . a a  a p1 p2 p p where y , y , . . . , y are the principal components. The determination steps of the compre- 1 2 p hensive IM based on PCA are as follows. Step 1: The correlation coefficient matrix is calculated to test whether the variables to be analyzed are suitable for PCA. According to the results in Table 8, there are seven cases for which PCA can be applied: (1) MIDR of 5-story, (2) MFA of 5-story, (3) MIDR of 8-story, (4) MFA of 8-story, (5) MIDR of 15-story, (6) MFA of 15-story, and (7) OSDI of 15-story. The correlation coefficients for IMs under all conditions are depicted in Table 9. Notably, when a high degree of correlation exists between the two IMs under all cases, PCA can be performed. Table 9. Correlation coefficients for related parameters (p < 0.05). Correlation Coefficients PGA PGV PGD EPV S (T = 1.73 s) d 1 MID - - 0.99 - - EPA 0.93 - - 0.68 - EPV 0.73 - - - - SI - - - 0.92 - S (T = 1.73 s) - 0.73 - - - d 1 E (T = 1.73 s) - 0.73 - - 0.97 i 1 Step 2: The characteristic values of the correlation coefficient matrix are calculated under seven cases, and the calculation results are shown in Figure 13. Figure 13. Characteristic values of different components. Step 3: The number of principal components is determined. There are two situations associated with the determination of the principal component: (1) the cumulative contri- bution rate of the principal component reaches a certain probability; (2) the characteristic Buildings 2022, 12, 754 14 of 18 value is greater than one. The second situation is applied to this study. Based on the characteristic values shown in Figure 13, the number of principal components obtained is one. Therefore, only one principal component f can be used to characterize the damage potential of ground motions. Step 4: The pulse-like ground motions are ranked based on the principal components. The pulse-like ground motions can be ranked directly based on the first principal compo- nent f . Each principal component need not be added to determine the comprehensive score. Table 10 shows the correlation coefficients and component score coefficients between the principal component f and IMs under the same case. Note that the principal compo- nent is highly correlated with other parameters. The principal component f is calculated as shown in Equation (8). f = c I M + c I M + + c I M (8) n n 1 1 1 2 2 where c , c , . . . , c are the score coefficients of different IMs; n is the number of IMs. 1 2 Table 10. Correlation coefficients and score coefficients between principal component f and corre- sponding values. Correlation Coefficient Score Building Structure EDP IM (p < 0.05) Coefficient SI 0.98 0.51 MIDR EPV 0.98 0.51 5-story PGA 0.96 0.38 EPA 0.95 0.37 MFA EPV 0.86 0.34 PGV 0.87 0.33 S (T ) 0.97 0.37 MIDR 1 E (T ) 0.97 0.37 8-story PGA 0.96 0.38 EPA 0.95 0.37 MFA EPV 0.86 0.34 PGD 1.00 0.50 MIDR MID 1.00 0.50 PGA 0.98 0.51 15-story MFA EPA 0.98 0.51 PGD 1.00 0.50 OSDI MID 1.00 0.50 6.2. Ranking of Pulse-like Ground Motions According to Damage Potential The pulse-like ground motions are ranked according to the selected IMs under different cases, as shown in Table 11. If only one IM is obtained in certain cases, the pulse-like ground motions can be ranked directly based on that IM. In addition, the pulse-like ground motions are ranked according to the principal component f . Furthermore, the ranking results are obtained for the damage potential of pulse-like ground motions for different structures. The ranking results are shown in Appendix A. Due to the large number of ground motion data points, only a few of the ranked ground motion data points are given. The remaining data points are entered in an MS Excel spreadsheet. Buildings 2022, 12, 754 15 of 18 Table 11. Ranking of pulse-like ground motions based on optimal IMs under different cases. Type of Structures Representative Structures MIDR MFA OSDI Low period 2-story S (T ) S (T ) EPA a 1 a 1 Low and middle period 5-story f f SI 1, (SI, EPV) 1, (PGA, EPA, EPV) Middle and tall period 8-story f f PGV 1, (PGV, Sa (T1), E(T1)) 1, (PGA, EPA, EPV) Tall period 15-story f f f 1, (PGD, MID) 1, (PGA, EPA) 1, (PGD, MID) 7. Discussion It is well known that the damage potential of pulse-like ground motions is greater than that of ordinary ground motions. However, previous studies have not yet quantitatively measured the damage potential of pulse-like ground motions for different structures. To solve this challenge, this study proposed a new method to rank pulse-like ground motions based on the damage potential. The method was developed based on 240 pulse-like ground motions and 16 IMs. IMs were employed to describe the damage potential of ground motions, and EDPs were used to characterize the damage state of structures. The relationship between the IMs and EDPs was analyzed based on four representative RC frame structures to cover a wide range of natural vibration periods, which can better represent the variety of actual structures than the traditional studies with close natural vibration periods. The results of this study indicate that there are notable differences between the discreteness of the IMs and the EDPs for the RC frame structures with different natural vibration periods. When MFA is used as the EDP, the acceleration-related IMs can be used to efficiently and sufficiently characterize MFA for all four structures. When MIDR or OSDI is used as the EDP, the acceleration-related, velocity-related, and displacement- related IMs can be used to efficiently and sufficiently characterize EDP for short-period structures (e.g., two-story), medium-period structures (e.g., eight-story), and long-period structures (e.g., fifteen-story), respectively. In addition, the two cases on the selected IMs shown in Table 8 indicate that: (1) only one optimal IM was obtained for the structures with different natural vibration periods and EDPs, respectively; (2) multiple IMs were obtained, the PCA method was employed to obtain a comprehensive IM to characterize the damage potential of pulse-like ground motions for specific building structures and EDPs. The pulse-like ground motions were ranked based on the selected IM and the comprehensive IM for four structures and three EDPs, respectively. The proposed method can quantitatively evaluate the damage potential of pulse-like ground motions for RC frame structures. Note that the proposed ranking method was validated for four representative RC-frame structures, and the feasibility of the method for more types of structures needs further investigation. 8. Conclusions In this paper, a new method of ranking pulse-like ground motions based on the damage potential was proposed. Four ordinary representative RC frame structures with different natural vibration periods were built, based on which the IMs that could predict the damage potential of ground motions for structures were analyzed and obtained. Then, the efficiency and sufficiency of the obtained IMs were verified. Finally, the pulse-like ground motions were ranked according to their damage potential. The conclusions of the study are as follows. (1) The ground motion IMs that can be used to efficiently and sufficiently predict the EDPs of different structures are obtained by analyzing the efficiency and sufficiency of 16 IMs. First, when the MFA is selected as the EDP, the acceleration-related IMs can efficiently determine the EDP. Second, when MIDR or OSDI is selected as the EDP, the acceleration-related, velocity-related, and displacement-related IMs can be used to effectively determine the EDPs of short-period structures (for example, two-story), medium-period structures (for example, eight-story), and long-period structures (for example, 15-story), respectively. Buildings 2022, 12, 754 16 of 18 (2) The PCA method is used to reduce the variable dimensions of the IMs selected under seven conditions, and the principal component f is selected as the comprehensive IM that can reflect the damage potential of multiple IMs. (3) The pulse-like ground motions are ranked based on the selected IMs and the compre- hensive IM under different cases. Finally, the damage-potential-based ranking of the pulse-like ground motions is completed. The damage potential ranking method proposed in this study can quantitatively evaluate the damage potential of pulse-like ground motions. The ranking results of 240 pulse-like ground motions provide a database for selecting ground motions in seismic design of RC-frame structures. Author Contributions: Conceptualization, Q.L. and J.H.; methodology, L.X. (Lili Xie); software, Q.L.; validation, Q.L., J.H., L.X. (Lili Xie) and L.X. (Longjun Xu); formal analysis, L.X. (Longjun Xu) and S.L.; investigation, S.L.; resources, S.L.; data curation, Q.L.; writing—original draft preparation, Q.L.; writing—review and editing, J.H.; visualization, J.H.; supervision, L.X. (Lili Xie); project administration, L.X. (Longjun Xu); funding acquisition, L.X. (Longjun Xu). All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Natural Science Foundation of China, grant number [U2139207; U1939210]. Additionally, the APC was funded by [U2139207]. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Acknowledgments: The work is supported by the National Natural Science Foundation of China (Grant No. U2139207; U1939210). The support is gratefully acknowledged. The authors would also like to thank the NGA-West2 database for providing the strong ground motion data. Conflicts of Interest: The authors declare no conflict of interest. Appendix A Table A1. Damage potential ranking of pulse-like ground motions. 2-Story 5-Story 8-Story 15-Story Ranking MIDR and MIDR and Number OSDI MIDR MFA OSDI MIDR MFA OSDI MFA MFA OSDI 1 GBZ000 GBZ000 H-E03140 H-E05140 SKR090 SKR090 H-E05140 TCU059-N TCU059-N H-E05140 6 PUL194 PUL194 SCE288 DZC270 SCE288 YPT330 DZC270 TCU057-W TCU057-W DZC270 11 H-E03230 H-E03230 WPI046 PAR--T WPI046 TCU060-W PAR–T SCR090 TCU026-W H-E03230 16 H-E11230 H-E11230 LDM334 TCU068-N H-E10320 TCU115-W TCU068-N A-BIR180 SHI000 SCR090 21 DZC180 DZC180 CPM000 H-E06140 WPI316 DZC270 H-E06140 SCE288 TCU046-W H-ECC002 26 TAK090 TAK090 TCU060-W TCU057-W TCU059-W H-E11230 TCU057-W TCU115-W TCU065-W TCU057-W 31 H-E06140 H-E06140 ERZ-NS CPM000 ERZ-NS ERZ-NS CPM000 CHY002-N TCU056-N SKR090 36 LCN000 LCN000 MUL279 D-TSM270 CNP196 TCU116-W D-TSM270 SHI000 TCU029-N WPI316 41 ORR090 ORR090 WVC000 SCE018 WVC000 WPI316 SCE018 CPM000 TCU076-N LDM334 46 A-OR2010 A-OR2010 ORR090 TCU128-W H-E04230 LDM334 TCU128-W H-E11230 CHY101-W SCE018 51 CPM000 CPM000 H-HVP225 SPV270 D-TSM270 H-HVP315 SPV270 TCU103-W TCU045-W TCU111-W 56 LDM334 LDM334 D-TSM360 DZC180 STN110 H-ECC002 DZC180 TCU057-N CHY029-N SCS142 61 GOF090 GOF090 TCU120-W RIO270 TCU063-N ORR090 RIO270 TCU063-N TCU047-N TCU059-W 66 HSP000 HSP000 40I07EW MUL279 H-BRA315 A-OR2010 MUL279 WVC000 TCU094-W UNI005 71 STG000 STG000 A-ZAK360 MVH135 H-E08140 SPV270 MVH135 TCU087-W TCU100-W TCU038-W 76 40E01EW 40E01EW YER270 NAS270 H-BRA225 40I07EW NAS270 TCU049-W TCU064-N TCU068-W 81 TCU059-N TCU059-N MU2035 WWT180 LOS000 TRI090 WWT180 TCU096-W ILA037-N H-BRA225 86 CPM090 CPM090 H-AGR273 H-HVP225 TCU095-N TCU060-N H-HVP225 A-OR2010 TCU070-N ERZ-NS 91 40I01EW 40I01EW CPM090 D-PVY045 DZC180 TCU026-W D-PVY045 H-BRA315 TCU098-N D-PVY045 96 UNI005 UNI005 TCU055-N TCU057-N TCU068-N TCU103-W TCU057-N H-E06140 HSP000 H-E10050 101 SCS052 SCS052 A-BAG270 TAB-LN CYC285 TCU076-N TAB-LN TCU095-N TCU095-W ARC090 106 WWT270 WWT270 40E01EW WVC270 D-OLC270 TCU136-E WVC270 TCU026-W CHY006-E WVC270 111 TCU115-W TCU115-W TCU052-W TCU116-W NPS210 40E01EW TCU116-W TCU068-N YPT330 BOL090 116 TCU045-N TCU045-N SPG360 40E01EW G01090 TCU040-N 40E01EW TCU039-N A02043 A-ZAK360 121 TCU031-W TCU031-W A02043 TCU040-N H-QKP085 TCU045-N TCU040-N JEN022 H-AGR273 TCU040-N 126 TCU049-N TCU049-N MUL009 TAZ000 TCU048-N TCU049-W TAZ000 TCU076-N A02133 TCU117-W Buildings 2022, 12, 754 17 of 18 Table A1. Cont. 2-Story 5-Story 8-Story 15-Story Ranking MIDR and MIDR and Number OSDI MIDR MFA OSDI MIDR MFA OSDI MFA MFA OSDI 131 STG090 STG090 TCU049-N STG000 GAZ000 MU2035 STG000 MU2035 TCU064-W STG000 136 TCU117-W TCU117-W H-AGR003 TCU105-N TCU109-W G01090 TCU105-N PAC265 TCU075-W KJM090 141 TCU046-W TCU046-W TCU104-N H-E11140 GOF090 H-BRA225 H-E11140 TCU051-W 40I01EW H-BRA315 146 S2330 S2330 TCU026-W TCU100-N TCU128-N C02065 TCU100-N TCU042-W H-HVP315 TCU045-N 151 KJM090 KJM090 TAB-TR HVR240 ARC090 TCU039-W HVR240 TCU076-W WPI316 HVR240 156 PAC175 PAC175 TCU034-W TCU098-N TCU018-W TCU017-W TCU098-N H-E06230 H-E03140 TAZ090 161 A02133 A02133 FOR000 A02133 TCU046-W STG000 A02133 LGP000 CHY002-N H-QKP085 166 G06090 G06090 TAZ000 TCU055-N H-AEP045 TCU083-W TCU055-N TCU036-N GOF090 TAB-TR 171 TCU083-W TCU083-W TCU031-W TCU104-N TCU105-W TCU105-W TCU104-N TCU070-N NAS270 TCU095-N 176 TCU048-N TCU048-N TCU050-N TCU039-N SCS052 TCU017-N TCU039-N DZC180 PAR–L NSY-N 181 TCU050-W TCU050-W STG000 TCU103-W TCU003-W CHY101-N TCU103-W TCU048-N TAK000 TCU109-W 186 PRS090 PRS090 TCU067-W H-FRN044 PAC175 D-OLC270 H-FRN044 KJM090 PRS090 TCU029-N 191 TCU104-W TCU104-W TCU015-W TCU087-W TCU050-W MUL009 TCU087-W 40I07EW CNP196 H-FRN044 196 TCU064-W TCU064-W TCU076-N TCU015-W TCU104-W H-QKP085 TCU015-W TCU067-N G06230 TCU015-W 201 TCU105-W TCU105-W TCU083-W TCU010-W TCU083-W TCU064-W TCU010-W TCU053-N MU2035 TCU104-W 206 CHY080-N CHY080-N TCU029-N TCU083-W TCU051-W TCU036-N TCU083-W G06090 CYC195 TCU065-W 211 TCU029-W TCU029-W TCU047-N TCU096-W CHY101-N TCU089-N TCU096-W TCU095-W GAZ000 TCU095-W 216 JEN292 JEN292 TCU098-W TCU064-W TCU089-N PAC175 TCU064-W H-QKP085 H-BRA225 TCU064-W 221 GAZ090 GAZ090 S2330 TCU076-N TCU075-W CHY029-N TCU076-N H-FRN044 H-E08140 TCU053-W 226 TCU-E TCU-E TCU029-W CHY080-W TCU064-N CHY028-W CHY080-W PAC175 CPM090 CHY080-W 231 CHY080-W CHY080-W TCU087-N CHY029-N TCU-E H-ECC092 CHY029-N CHY029-N H-E07140 CHY029-N 236 TCU067-N TCU067-N TCU067-N TCU067-N TCU067-N 40I01EW TCU067-N TCU067-W LDM064 TCU067-N Note: 1. 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Method for Ranking Pulse-like Ground Motions According to Damage Potential for Reinforced Concrete Frame Structures

Lai, Qinghui; Hu, Jinjun; Xu, Longjun; Xie, Lili; Lin, Shibin
Buildings , Volume 12 (6) – Jun 1, 2022
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buildings Article Method for Ranking Pulse-like Ground Motions According to Damage Potential for Reinforced Concrete Frame Structures 1 , 2 3 , 1 , 2 1 , 2 , 3 1 , 2 Qinghui Lai , Jinjun Hu * , Longjun Xu , Lili Xie and Shibin Lin State Key Laboratory of Precision Blasting, Jianghan University, Wuhan 430056, China; laiqinghui@jhun.edu.cn (Q.L.); xulj@jhun.edu.cn (L.X.); 18845117968@163.com (L.X.); shibinlin@gmail.com (S.L.) Hubei Key Laboratory of Blasting Engineering, Jianghan University, Wuhan 430056, China Key Laboratory of Earthquake Engineering and Engineering Vibration, Institute of Engineering Mechanics, China Earthquake Administration, Harbin 150080, China * Correspondence: hujinjun@iem.ac.cn Abstract: To rank the pulse-like ground motions based on the damage potential to different structures, the internal relationship between the damage potential of pulse-like ground motions and engineering demand parameters (EDPs) is analyzed in this paper. First, a total of 240 pulse-like ground motions from the NGA-West2 database and 16 intensity measures (IMs) are selected. Moreover, four reinforced concrete frame structures with significantly different natural vibration periods are established for dynamic analysis. Second, the efficiency and sufficiency of the IMs of ground motion are analyzed, and the IMs that can be used to efficiently and sufficiently evaluate the EDPs are obtained. Then, based on the calculation results, the principal component analysis (PCA) method is employed to obtain a comprehensive IM for characterizing the damage potential of pulse-like ground motions for specific building structures and EDPs. Finally, the pulse-like ground motions are ranked based on the selected IM and the comprehensive IM for four structures and three EDPs. The results imply that Citation: Lai, Q.; Hu, J.; Xu, L.; Xie, the proposed method can be used to efficiently and sufficiently characterize the damage potential of L.; Lin, S. Method for Ranking pulse-like ground motions for building structures. Pulse-like Ground Motions According to Damage Potential for Reinforced Concrete Frame Keywords: pulse-like ground motions; damage potential ranking; intensity measures; analysis of Structures. Buildings 2022, 12, 754. efficiency and sufficiency; principal component analysis https://doi.org/10.3390/ buildings12060754 Academic Editor: Eva O. 1. Introduction L. Lantsoght Ground motion damage to building structures is of two types: (1) cumulative damage, Received: 10 April 2022 which occurs due to ground motion at medium and faraway sites; (2) instantaneous damage, Accepted: 22 April 2022 which primarily occurs due to the destructive pulse-like ground motion. The mechanisms Published: 1 June 2022 of the two types of ground motion damage are different. The damage potential of pulse-like Publisher’s Note: MDPI stays neutral ground motions for building structures is more significant compared with that of ordinary with regard to jurisdictional claims in ground motions [1–4]. Therefore, the damage potential of pulse-like ground motions must published maps and institutional affil- be accurately evaluated for the seismic design of building structures. To estimate the iations. damage potential of ground motions for building structures, two intermediate variables are introduced—one represents structural performance and the other represents ground motion characteristics [5–8]. An intensity measure (IM) that has a strong correlation with the appropriate engineering demand parameter (EDP) must be selected. However, several Copyright: © 2022 by the authors. IMs can be used to predict structural responses by establishing a seismic demand model Licensee MDPI, Basel, Switzerland. between IMs and EDPs [3,9,10]. Yazdani and Yazdannejad [11] noted that the uncertainties This article is an open access article associated with the seismic demand model are related to uncertainties associated with distributed under the terms and ground motions. conditions of the Creative Commons A few studies have focused on commonly used IMs such as peak ground acceleration Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ (PGA), peak ground velocity (PGV), peak ground displacement (PGD), Arias intensity 4.0/). (AI), specific energy density (SED), and cumulative absolute velocity (CAV) [12]. However, Buildings 2022, 12, 754. https://doi.org/10.3390/buildings12060754 https://www.mdpi.com/journal/buildings Buildings 2022, 12, 754 2 of 18 these IMs are based only on ground motion characteristics, and the uncertainties associated with structural performance are not considered. The more ground motion information and structural information an IM contains, the better the correlation with EDPs is. Compared with the aforementioned IMs, the first-order spectral acceleration (S (T )) is the most a 1 extensively used IM in seismic risk analysis and structural seismic analysis [13–19]. S (T ) presents a high degree of correlation with the EDPs of structures with small natural vibration periods. However, several studies [20,21] have discovered that there is a low degree of correlation between the S (T ) and EDPs of super-high-rise buildings. To this a 1 end, some experts have selected relative displacement (S (T )) or input energy (Ei (T )) as d 1 1 the IMs for predicting structural responses [18,22]. A few studies have focused on achieving discreteness in vector IMs and EDPs [23,24]; the discreteness achieved in vector IMs and EDPs is smaller than that in scalar IMs. However, vector IMs are complex and thus not conducive to practical engineering applications. To avoid the complexities associated with the use of vector IMs, scalar IMs can be used instead, especially when the same capacity for predicting EDPs can be achieved using scalar IMs [25,26]. Significant uncertainties are prevalently associated with structural performance. How- ever, in some studies, only a few similar structures have been comprehensively analyzed via non-linear time-history analysis [9,20,26,27]; the results obtained in this direction are consistent. Ebrahimian [9] analyzed the prediction capacities of different IMs for the struc- tural responses of four-story and six-story isolated structures, which were subjected to pulse-like ground motions and ordinary ground motion. The results implied that the vector IMs related to S (T ) could be used to predict structural responses more efficiently and a 1 sufficiently. Dávalos and Miranda [26] analyzed the efficiency and sufficiency of FIV3 in predicting the structural responses of a four-story reinforced concrete (RC) frame. The results indicated that the novel FIV3 is a promising parameter that can be used for assessing structural collapse risks. Furthermore, some researchers have investigated the correlation between the IMs and structural responses of different structures. Palanci [28] analyzed the correlation between the average values of spectral displacement over different periods via the SDOF system involving different hysteretic models. However, in this study, the correlation between different IMs and the average values of EDPs of different structures is investigated to determine the prediction capacities of IMs, without considering the un- certainties associated with the structures. Note that the correlations between the EDPs and different IMs are significantly different for structures with different natural vibration periods [29–31]. Yakhachalian and Ghodrati [29] analyzed the discreteness of IMs and EDPs for low- and middle-rise structures via the strip method. The vector IM (S (T ), S a 1 a (T )/PGV) is proposed as an optimal IM for predicting the maximum inter-story drift ratio (MIDR) for low- and middle-rise RC moment-resisting frame structures. However, the aforementioned studies have only verified the prediction capacity of the selected IMs for different structures; meanwhile, few studies have used the obtained IMs to further analyze ground motion characteristics. The damage potential of ground motions for building structures can be determined based on different IMs. Notably, ground motions, especially pulse-like ground motions, have not been ranked based on the optimal IMs in the aforementioned studies. In this study, pulse-like ground motions are ranked based on their damage potential for different RC frame structures. 2. Technical Framework To rank the ground motions in predicting EDPs based on the damage potential, a method is proposed for ranking pulse-like ground motions according to their damage potential in this study; the method involves predicting EDPs based on ground motion IMs. The uncertainties associated with both ground motions and building structures are considered in the proposed method. The 16 selected IMs include amplitude, spectrum, and duration, which can be used to describe the uncertainties associated with ground motions. Meanwhile, four reinforced concrete (RC) frame structural models with signifi- cantly different natural vibration periods are established, and three EDPs are considered for Buildings 2022, 12, 754 3 of 18 evaluating the uncertainty of the established structures. The efficiency and sufficiency of IMs in predicting EDPs are analyzed to determine the optimal IMs for different structures. Furthermore, for multiple optimal IMs, the pulse-like ground motions are ranked by deter- mining the comprehensive IM via the principal component analysis (PCA) method. Finally, the pulse-like ground motions are ranked according to their damage potential using the selected optimal IM. The technical framework of this paper is illustrated in Figure 1. Figure 1. Technical framework. 3. Selection of Pulse-like Ground Motions and IMs 3.1. Selected Pulse-like Ground Motions Compared with that of ordinary ground motions, the damage potential of pulse-like ground motions is typically higher. Pulse-like ground motions involve the release of significant amounts of instantaneous energy, thereby causing impact damage in building structures. Figure 2 depicts the velocity time-histories of two ground motions, (a) pulse-like ground motion and (b) non-pulse-like ground motion, which are significantly different from each other. In this study, the damage potential of 240 pulse-like ground motions is analyzed; the ground motions are selected according to the method proposed by Zhai [32]. An energy- based significant velocity half-cycle is used as a reference for distinguishing pulse-like ground motions. Note that these pulse-like ground motions are extensively studied [33]. Figure 3 illustrates the station distribution of pulse-like ground motions, which is mainly distributed in the United States, Japan, the Middle East, and Taiwan Province of China. Figure 4 shows the distributions of V , magnitude (M), and epicentral distance (R). The s30 values of M range from 5.21 to 7.62, and those of V are mainly < 1000 m/s. Pulse-like s30 ground motions can be generated not only in the near field, but also in the relative far field (R > 100 km). Buildings 2022, 12, 754 4 of 18 Figure 2. Velocity time-history of pulse-like and non-pulse-like ground motions. (a) Pulse-like ground motion; (b) non-pulse-like ground motion. Figure 3. Station distribution of selected pulse-like ground motions. Figure 4. Distribution ranges of M, R, and V of the selected pulse-like ground motions. (a) Vs30-M; s30 (b) Vs30-R. 3.2. Selected IMs The main causes of structural damage caused by ground motion are included in the whole ground motion time-history. The time-history characteristics of ground motion are Buildings 2022, 12, 754 5 of 18 indicated by various IMs. In this study, a novel method is employed for predicting the damage potential of ground motion for building structures; the method involves adopting 16 commonly used IMs, including amplitude, duration, spectrum, and energy parameters, based on previous studies. The selected IMs are shown in Table 1, and their physical significance and calculation methods are mentioned in the relevant literature [32,34,35]. Table 1. Selected IMs.. Note Ground Motion IMs Expression IM Peak ground acceleration (PGA) PG A = maxja(t)j IM Peak ground velocity (PGV) PGV = maxjn(t)j IM Peak ground displacement (PGD) PGD = maxjd(t)j IM Bracketed duration (D ) D = max(t) min(t) 4 b b IM Uniform duration (D ) D = H a(t) a dt (j j ) 5 u u 0 IM Significant duration (D ) D = t t 6 s s 95 5 IM Effective peak acceleration (EPA) EPA = S /2.5 7 a IM Effective peak velocity (EPV) EPV = S /2.5 8 v 2.5 IM Housner intensity (SI) S I = S (x, T)dT z v 0.1 t +1 IM Cumulative absolute velocity (CAV) C AV(t) = W j A(t)jdt 10 å i i IM Maximum incremental velocity (MIV) - IM Maximum incremental displacement (MID) - Spectral acceleration at the first mode period IM - of vibration (S (T )) a 1 Spectral velocity at the first mode period of IM - vibration (S (T )) v 1 Spectral displacement at the first mode IM - period of vibration (S (T )) d 1 Relative input energy at the first mode R IM 16 E(T ) = 2 a vdt 1 g period of vibration E (T ) i 1 4. Selection of Structural Models and EDPs 4.1. Structural Models To comprehensively analyze the destruction mechanism of different structures caused by pulse-like ground motions, four representative structural models with quite different natural vibration periods are established and used for comprehensively analyzing the damage caused by pulse-like ground motions in different structures. The structural models are designed according to Zhai et al. [35] and Li et al. [36]. The four frame structures are of different types—short-period, short- and middle-period, middle- and long-period, and long-period—with 2, 5, 8, and 15 stories, respectively. These buildings are symmetric. The finite element software IDARC-2D is used to analyze the four frame structures [37]. The natural vibration period (T ) of each structure is shown in Table 2. The four structural models are based on four ordinary RC frame structures, with seismic fortification intensity of seven degrees. The four structures are modeled considering a class II site. The improved I-K trilinear hysteretic model is used for the four structures [38,39], and Figure 5 shows the hysteretic skeleton curve of the model. The four buildings use C30 concretes, and the live load is 0.4 kN/m . Figure 6 illustrates the plan and elevation of the four representative structures. Tables 3 and 4 show the sectional dimensions, concrete grades, and steel rebars of the beams and columns of the structures. The yielding strength f of the main yk reinforcement rebars is 400 MPa, and the yielding strength f of the stirrups is 300 MPa. yk During calculations, the stiffness in the floor plane is considered infinite. The stiffness degradation coefficient a, strength degradation coefficient b, and pinch effect coefficient g determine the hysteretic responses of the structures. The values 8.0, 0.1, and 0.5 are selected for the parameters a, b, and g, respectively, for the analysis using the IDARC-2D software. Centralized plasticity is considered as the plasticity type. Buildings 2022, 12, 754 6 of 18 Table 2. Natural vibration periods and types of structures. Building Structures Natural Vibration Period T Structure Types 2-story 0.20 s Short period 5-story 0.89 s Short and middle period 8-story 1.73 s Middle and long period 15-story 2.73 s Long period Figure 5. Backbone curve for improved I-K hysteretic model. Figure 6. Cont. Buildings 2022, 12, 754 7 of 18 Figure 6. Elevation of four representative reinforced concrete frame structures (unit: mm). Table 3. Beam section properties of four RC frame buildings. 2 2 Section Size (mm  mm) Area of Longitudinal Reinforcement (mm )/Stirrup (mm ) Story Structure Side Column Middle Column Side Column Middle Column 2-story 1–2 600  300 600  300 1313/'8@100 1313/'8@100 1–4 500  250 400  250 1008/'8@100 763/'8@200 5-story 5 500  250 400  250 763/'8@200 603/'8@200 1–4 500  250 500  250 1296/'8@100 710/'8@200 8-story 5–6 500  250 500  250 1015/'8@100 710/'8@200 7–8 500  250 500  250 710/'8@100 710/'8@200 1–7 600  250 450  250 1964/'8@100 935/'8@100 8–10 600  250 450  250 1742/'8@100 833/'8@100 15-story 11–12 600  250 450  250 1520/'8@100 833/'8@100 13–14 600  250 450  250 1250/'8@100 833/'8@100 15 600  250 450  250 942/'8@100 755/'8@100 The yielding strength f of main reinforcement rebars is 400 MPa, and the yielding strength f of stirrups is yk yk 300 MPa. Table 4. Column section properties for four RC frame buildings. 2 2 Section Size (mm  mm) Area of Longitudinal Reinforcement (mm )/Stirrup (mm ) Story Structure Side Column Middle Column Side Column Middle Column 2-story 1–2 700  700 700  700 2330/'8@100 2330/'8@100 5-story 1–5 500  500 500  500 2512/'8@100 2512/'8@100 1–5 550  550 550  550 2733/'8@100 2733/'8@100 8-story 6–8 500  500 600  600 2035/'8@100 2035/'8@100 1–5 650  650 650  650 4560/'10@100 4560/'10@100 15-story 6–10 600  600 600  600 3807/'10@100 3807/'10@100 11–15 550  550 550  550 3411/'8@100 3411/'8@100 The yielding strength f of main reinforcement rebars is 400 MPa, and the yielding strength f of stirrups is yk yk 300 MPa. 4.2. Selected EDPs The degree of damage in the structures due to pulse-like ground motions is comprehen- sively evaluated by selecting several EDPs, as shown in Table 5: (1) MIDR is the maximum Buildings 2022, 12, 754 8 of 18 inter-story drift ratio (drift normalized by the story height) over all stories/closely re- lated to local damage, instability, and story collapse; (2) MFA is the maximum value of floor absolute acceleration for all stories and indicates the level of non-structural damage; (3) OSDI denotes the degree of overall damage in the structure and is determined by the peak displacement and hysteretic energy consumption of the structure. Table 5. Engineering demand parameters considered in the study. Num Notation Name 1 MIDR Maximum inter-story drift ratio 2 MFA Maximum floor acceleration 3 OSDI Overall structural damage index 5. Prediction and Analysis of EDPs Based on IMs The capacity of an IM for predicting EDPs is primarily determined via analyzing the efficiency and sufficiency of the IM. In traditional methods [32,35], the numerical values of IMs and EDPs are typically assumed to have linear or logarithmic distribution, as shown in Equations (1) and (2). The aim of this study is to rank pulse-like ground motions based on their damage potential. To this end, a new data-processing method is proposed. The IMs that can be used to efficiently and sufficiently predict EDPs are positively correlated with EDPs. IMs and EDPs are separately used to rank ground motions, which are ranked based on IMs and EDPs, respectively, and the relationship between the two ranking results (R IM and R ) is shown in Equation (3). The efficiency and sufficiency of an IM is determined EDP by the ability of the IM to predict EDP. h = b + b I M (1) Dj I M 0 1 lnh = b + b ln I M (2) Dj I M 0 1 R = b + b R (3) EDP 0 1 I M where b and b are regression coefficients, R is the ranking obtained using an IM, and 0 1 IM R is the ranking obtained using an EDP. EDP 5.1. Efficiency of the IMs Efficiency is an important metric for assessing the quality of a selected IM. There are two commonly used statistical parameters that can be used to describe the efficiency of IMs [9,40]. The first parameter is the determination coefficient (R ), as shown in Equation (4). A value of R is closer to one; the efficiency of the IM increases with the decrease in the discreteness of IM ranking and EDP ranking fitting. The second statistical parameter is the standard deviation b . The greater the value of b , the smaller the D|IM D|IM dispersion, which means that the regression model is more efficient for characterizing the structural response. Either of the statistical parameters can be used to effectively measure the efficiency of IMs. R is used as the criterion in this study. å (R R ) EDP EDP 2 k=1 R = (4) (R R ) EDP k EDP k=1 where n denotes the number of ground motion data points; R denotes the response EDP fitting ranking based on the IM ranking; R is the average ranking of EDP; R is the EDP EDP EDP ranking. The efficiencies of the IMs are analyzed based on the structural responses of the four structures, and the calculation results are shown in Figures 7–9. Notably, the uncertain- ties associated with ground motion and building structure should be considered while analyzing the damage potential of ground motion for building structures. There are no- Buildings 2022, 12, 754 9 of 18 table differences between the discreteness of the same IM and the same EDP for different structures. Furthermore, the discreteness of the same IM and different EDPs may also be different for the same structure. These results indicate the uncertainties associated with structure. However, in many studies, only similar structures have been analyzed, and the results are inconsistent with the findings of this study [9,26]. Figure 7. R of IMs and MIDR, obtained via the cloud analysis of four typical structures subjected to pulse-like ground motions. Figure 8. R of IMs and MFA, obtained via the cloud analysis of four typical structures subjected to pulse-like ground motions. Figure 9. R of IMs and OSDI, obtained via the cloud analysis of four typical structures subjected to pulse-like ground motions. In addition, there are significant differences between the R values of different IMs and EDPs for the same structure; this indicates the uncertainties associated with ground motion. The uncertainties associated with ground motion and building structure are considered in this study for analyzing the ability of IMs to predict EDPs accurately and to determine Buildings 2022, 12, 754 10 of 18 the optimal IMs for describing the damage potential of ground motion. Three IMs with the largest R for EDP prediction are selected for the different structural types and EDPs. The results are shown in Table 6. The results indicate that even for the same EDP, the most efficient IMs are different for different structural types. When MIDR is selected as the EDP, the most efficient IMs are different for different building types: EPA, S (T ), and S (T ) are a 1 1 the most efficient IMs for two-story buildings; SI, EPV, and S (T ) are the most efficient IMs a 1 for five-story buildings; PGV, S (T ), and E(T ) are the most efficient IMs for eight-story d 1 1 buildings, and PGD, MID, and S (T ) are selected as the most efficient IMs for 15-story d 1 buildings. The IMs that can be used to predict OSDI and MIDR are the same in most cases. Some IMs related to acceleration can be used to efficiently characterize MFA, such as PGA, EPA, and S (T ). Table 6. The most efficient IMs for different typical structures. Models MIDR MFA OSDI 2-story EPA, S (T ), S (T ) EPA, S (T ), S (T ) EPA, S (T ), S (T ) a a a 1 d 1 1 d 1 1 d 1 5-story SI, EPV, S (T ) PGA, EPA, EPV SI, S (T ), S (T ) a a 1 1 d 1 8-story PGV, S (T ), E (T ) PGA, EPA, EPV PGV, S (T ), E(T ) 1 1 1 1 d i d 15-story PGD, MID, S (T ) PGA, EPA, SI PGD, MID, S (T ) 1 1 d d 5.2. Sufficiency of the Selected IMs In addition to efficiency, sufficiency is important for assessing the quality of IMs. An IM is sufficient when the probability distribution of an EDP is independent from ground motion characteristics, such as epicenter distance, magnitude, and the ground motion parameter epsilon (#) [41]. Zelaschi et al. [40] obtained p-values for the residuals of EDP and ln h with magnitude and epicenter distance of the ground motion when they proved Dj I M that an IM is sufficient. Similar methods [20,29,42] have been used in relevant studies to demonstrate the sufficiency of IMs. However, the method proposed by Zelaschi et al. is unreasonable because the calculated p-values are closely related to the number of samples, as noted in relevant studies [40,43]. It becomes more difficult to accept the null hypothesis with an increasing number of samples. The sufficiency of an IM can also be verified based on relative entropy, a concept in seismic engineering proposed by Jalayer [27]. In this study, based on the concept of relative entropy, a simple quantitative measure is introduced; it is called the relative sufficiency measure, which is selected as a parameter to measure the relative sufficiency of one IM with respect to another. Therefore, the relative sufficiency measure is used to verify the sufficiency of the selected IMs. The simplified and approximate formulation of relative sufficiency is shown in Equation (5). 0 1 lny lnh ( I M ) 2,K k Dj I M n b B b C Dj I M Dj I M 2 B C I(Dj I M j I M )  log   (5) 2 1 å 2@ A lny lnh ( I M ) n b k Dj I M 2,K Dj I M k=1 2 1 Dj I M where b is the conditional standard deviation, which serves as a quantitative measure D|IM for the prediction efficiency of the IMs; y is the R ; lnh is the fitting function; n is k EDP D|IM the number of samples. The above equation was derived by Jalayer [27] and Ebrahimian [9]. The reference intensity (i.e., IM in Equation (5)) is considered to be S (T ) for the structural response, 1 a 1 mainly because S (T ) is a better characterization parameter for the structural response a 1 and is extensively used in earthquake engineering. The sufficiency is measured for each candidate IM relative to S (T ). If (IM |IM ) has a positive value, the candidate IM is more sufficient than S (T ). 2 1 a 1 Similarly, if I (IM |IM ) has a negative value, the candidate IM is less sufficient than S (T ) 2 1 1 for predicting EDPs. Buildings 2022, 12, 754 11 of 18 The obtained results, as shown in Figures 10–12, indicate that one or more IMs are more sufficient than S (T ) for characterizing the EDPs in most cases. However, when analyzing MFA and MIDR for a two-story structure, all I( I M j I M ) values are not positive, 2 1 which indicates that S (T ) is the most sufficient among all parameters. Finally, all the a 1 most sufficient IMs for characterizing the EDPs are obtained, as shown in Table 7. Figure 10. I (IM jIM ) between IMs and MIDR, obtained via the cloud analysis of four typical 2 1 structures subjected to pulse-like ground motions. Figure 11. I (IM jIM ) between IMs and MFA, obtained via the cloud analysis of four typical structures 2 1 subjected to pulse-like ground motions. Figure 12. I (IM jIM ) between IMs and OSDI, obtained via the cloud analysis of four typical 2 1 structures subjected to pulse-like ground motions. Buildings 2022, 12, 754 12 of 18 Table 7. The most sufficient IMs for different structures. Building Structure MIDR MFA OSDI 2-story S (T ) S (T ) EPA a 1 a 1 5-story SI, EPV PGA, EPA, EPV, S (T ) SI v 1 8-story PGV, S (T ), E (T ) PGA, D , EPA, EPV, SIMIV, S (T ), S (T ) PGV, S (T ), E (T ) d 1 i 1 s v 1 d 1 d 1 i 1 15-story PGD, MID PGA, D , EPA, EPV, SI PGD, MID, S (T ) d 1 5.3. Comprehensive Analysis of the Selected IMs The efficiency and sufficiency of 16 IMs are analyzed to determine the optimal IMs for accurately describing the damage potential of ground motions. The ground motion IMs that satisfy the requirements of both efficiency and sufficiency are determined by comparing the analysis results for efficiency and sufficiency, as shown in Table 8. For a short-period structure (for example, two-story) and MFA as the EDP, the acceleration-related IMs can be used to efficiently and sufficiently characterize the EDPs. For MIDR or OSDI as the EDP and a medium-period structure (for example, eight-story), the velocity-related IMs can be used to efficiently and sufficiently characterize the EDPs. Finally, the displacement-related IMs can be used to efficiently and sufficiently characterize the MIDR or OSDI for a long-period structure (for example, 15-story). Table 8. The most efficient and sufficient IMs for different buildings. Building Structure MIDR MFA OSDI 2-story S (T ) S (T ) EPA a 1 a 1 5-story SI, EPV PGA, EPA, EPV SI 8-story PGV, S (T ), E(T ) PGA, EPA, EPV PGV d 1 1 15-story PGD, MID PGA, EPA PGD, MID 6. Establishing the Pulse-like Ground Motion Rankings To describe the destructive capacity of ground motion more accurately and rank the pulse-like ground motions based on the optimal IMs, the efficiency and sufficiency of 16 IMs are analyzed by four different structures. However, there are two cases based on the number of IMs, as shown in Table 8: (1) only one optimal IM is obtained, and the pulse-like ground motions are ranked directly based on this IM, which is the damage potential ranking result of the pulse-like ground motions; the ranking depicts the ranking in which the ground motions can damage a building structure—the most unfavorable to the most favorable; (2) multiple IMs are obtained. However, further analysis is necessary for developing a ranking method in the case of multiple IMs. A novel method is proposed for combining multiple IMs into one comprehensive IM. The method involves reducing the dimensions of the variables via PCA. Subsequently, the damage potential of pulse-like ground motion is comprehensively evaluated according to the principal component. The results are highly interpretable [44–46]. 6.1. Comprehensive IM Determination Based on the PCA The proposed method is a multivariate statistical method that involves dimensional reduction and the transformation of multiple indicators into a few comprehensive indica- tors, while ensuring minimal loss of data or information. Generally, the comprehensive IM generated via transformation is called the principal component, which is a linear combina- tion of original variables. Based on the principal component, the main contradictions can be identified and the collinearity problem between variables can be avoided, and thus the efficiency of the IM can be improved. For example, there are n samples, and each sample contains p variables. A strong correlation exists among these p variables, which is denoted by X = (x , x , . . . , x )’ after 1 2 p Buildings 2022, 12, 754 13 of 18 standardization. The mathematical model of PCA is shown in Equation (6). A is an orthogonal matrix as shown in Equation (7). y = a x + a x + + a x > 1 11 1 12 2 1 p y = a x + a x + + a x 2 22 2 2 p p 21 1 (6) > . y = a x + a x + + a x p p1 1 p2 2 p p p 2 3 a a  a 11 12 1 p 6 7 a a  a 21 22 2 p 6 7 A = 6 7 (7) . . . . . . . . 4 5 . . . . a a  a p1 p2 p p where y , y , . . . , y are the principal components. The determination steps of the compre- 1 2 p hensive IM based on PCA are as follows. Step 1: The correlation coefficient matrix is calculated to test whether the variables to be analyzed are suitable for PCA. According to the results in Table 8, there are seven cases for which PCA can be applied: (1) MIDR of 5-story, (2) MFA of 5-story, (3) MIDR of 8-story, (4) MFA of 8-story, (5) MIDR of 15-story, (6) MFA of 15-story, and (7) OSDI of 15-story. The correlation coefficients for IMs under all conditions are depicted in Table 9. Notably, when a high degree of correlation exists between the two IMs under all cases, PCA can be performed. Table 9. Correlation coefficients for related parameters (p < 0.05). Correlation Coefficients PGA PGV PGD EPV S (T = 1.73 s) d 1 MID - - 0.99 - - EPA 0.93 - - 0.68 - EPV 0.73 - - - - SI - - - 0.92 - S (T = 1.73 s) - 0.73 - - - d 1 E (T = 1.73 s) - 0.73 - - 0.97 i 1 Step 2: The characteristic values of the correlation coefficient matrix are calculated under seven cases, and the calculation results are shown in Figure 13. Figure 13. Characteristic values of different components. Step 3: The number of principal components is determined. There are two situations associated with the determination of the principal component: (1) the cumulative contri- bution rate of the principal component reaches a certain probability; (2) the characteristic Buildings 2022, 12, 754 14 of 18 value is greater than one. The second situation is applied to this study. Based on the characteristic values shown in Figure 13, the number of principal components obtained is one. Therefore, only one principal component f can be used to characterize the damage potential of ground motions. Step 4: The pulse-like ground motions are ranked based on the principal components. The pulse-like ground motions can be ranked directly based on the first principal compo- nent f . Each principal component need not be added to determine the comprehensive score. Table 10 shows the correlation coefficients and component score coefficients between the principal component f and IMs under the same case. Note that the principal compo- nent is highly correlated with other parameters. The principal component f is calculated as shown in Equation (8). f = c I M + c I M + + c I M (8) n n 1 1 1 2 2 where c , c , . . . , c are the score coefficients of different IMs; n is the number of IMs. 1 2 Table 10. Correlation coefficients and score coefficients between principal component f and corre- sponding values. Correlation Coefficient Score Building Structure EDP IM (p < 0.05) Coefficient SI 0.98 0.51 MIDR EPV 0.98 0.51 5-story PGA 0.96 0.38 EPA 0.95 0.37 MFA EPV 0.86 0.34 PGV 0.87 0.33 S (T ) 0.97 0.37 MIDR 1 E (T ) 0.97 0.37 8-story PGA 0.96 0.38 EPA 0.95 0.37 MFA EPV 0.86 0.34 PGD 1.00 0.50 MIDR MID 1.00 0.50 PGA 0.98 0.51 15-story MFA EPA 0.98 0.51 PGD 1.00 0.50 OSDI MID 1.00 0.50 6.2. Ranking of Pulse-like Ground Motions According to Damage Potential The pulse-like ground motions are ranked according to the selected IMs under different cases, as shown in Table 11. If only one IM is obtained in certain cases, the pulse-like ground motions can be ranked directly based on that IM. In addition, the pulse-like ground motions are ranked according to the principal component f . Furthermore, the ranking results are obtained for the damage potential of pulse-like ground motions for different structures. The ranking results are shown in Appendix A. Due to the large number of ground motion data points, only a few of the ranked ground motion data points are given. The remaining data points are entered in an MS Excel spreadsheet. Buildings 2022, 12, 754 15 of 18 Table 11. Ranking of pulse-like ground motions based on optimal IMs under different cases. Type of Structures Representative Structures MIDR MFA OSDI Low period 2-story S (T ) S (T ) EPA a 1 a 1 Low and middle period 5-story f f SI 1, (SI, EPV) 1, (PGA, EPA, EPV) Middle and tall period 8-story f f PGV 1, (PGV, Sa (T1), E(T1)) 1, (PGA, EPA, EPV) Tall period 15-story f f f 1, (PGD, MID) 1, (PGA, EPA) 1, (PGD, MID) 7. Discussion It is well known that the damage potential of pulse-like ground motions is greater than that of ordinary ground motions. However, previous studies have not yet quantitatively measured the damage potential of pulse-like ground motions for different structures. To solve this challenge, this study proposed a new method to rank pulse-like ground motions based on the damage potential. The method was developed based on 240 pulse-like ground motions and 16 IMs. IMs were employed to describe the damage potential of ground motions, and EDPs were used to characterize the damage state of structures. The relationship between the IMs and EDPs was analyzed based on four representative RC frame structures to cover a wide range of natural vibration periods, which can better represent the variety of actual structures than the traditional studies with close natural vibration periods. The results of this study indicate that there are notable differences between the discreteness of the IMs and the EDPs for the RC frame structures with different natural vibration periods. When MFA is used as the EDP, the acceleration-related IMs can be used to efficiently and sufficiently characterize MFA for all four structures. When MIDR or OSDI is used as the EDP, the acceleration-related, velocity-related, and displacement- related IMs can be used to efficiently and sufficiently characterize EDP for short-period structures (e.g., two-story), medium-period structures (e.g., eight-story), and long-period structures (e.g., fifteen-story), respectively. In addition, the two cases on the selected IMs shown in Table 8 indicate that: (1) only one optimal IM was obtained for the structures with different natural vibration periods and EDPs, respectively; (2) multiple IMs were obtained, the PCA method was employed to obtain a comprehensive IM to characterize the damage potential of pulse-like ground motions for specific building structures and EDPs. The pulse-like ground motions were ranked based on the selected IM and the comprehensive IM for four structures and three EDPs, respectively. The proposed method can quantitatively evaluate the damage potential of pulse-like ground motions for RC frame structures. Note that the proposed ranking method was validated for four representative RC-frame structures, and the feasibility of the method for more types of structures needs further investigation. 8. Conclusions In this paper, a new method of ranking pulse-like ground motions based on the damage potential was proposed. Four ordinary representative RC frame structures with different natural vibration periods were built, based on which the IMs that could predict the damage potential of ground motions for structures were analyzed and obtained. Then, the efficiency and sufficiency of the obtained IMs were verified. Finally, the pulse-like ground motions were ranked according to their damage potential. The conclusions of the study are as follows. (1) The ground motion IMs that can be used to efficiently and sufficiently predict the EDPs of different structures are obtained by analyzing the efficiency and sufficiency of 16 IMs. First, when the MFA is selected as the EDP, the acceleration-related IMs can efficiently determine the EDP. Second, when MIDR or OSDI is selected as the EDP, the acceleration-related, velocity-related, and displacement-related IMs can be used to effectively determine the EDPs of short-period structures (for example, two-story), medium-period structures (for example, eight-story), and long-period structures (for example, 15-story), respectively. Buildings 2022, 12, 754 16 of 18 (2) The PCA method is used to reduce the variable dimensions of the IMs selected under seven conditions, and the principal component f is selected as the comprehensive IM that can reflect the damage potential of multiple IMs. (3) The pulse-like ground motions are ranked based on the selected IMs and the compre- hensive IM under different cases. Finally, the damage-potential-based ranking of the pulse-like ground motions is completed. The damage potential ranking method proposed in this study can quantitatively evaluate the damage potential of pulse-like ground motions. The ranking results of 240 pulse-like ground motions provide a database for selecting ground motions in seismic design of RC-frame structures. Author Contributions: Conceptualization, Q.L. and J.H.; methodology, L.X. (Lili Xie); software, Q.L.; validation, Q.L., J.H., L.X. (Lili Xie) and L.X. (Longjun Xu); formal analysis, L.X. (Longjun Xu) and S.L.; investigation, S.L.; resources, S.L.; data curation, Q.L.; writing—original draft preparation, Q.L.; writing—review and editing, J.H.; visualization, J.H.; supervision, L.X. (Lili Xie); project administration, L.X. (Longjun Xu); funding acquisition, L.X. (Longjun Xu). All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Natural Science Foundation of China, grant number [U2139207; U1939210]. Additionally, the APC was funded by [U2139207]. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Acknowledgments: The work is supported by the National Natural Science Foundation of China (Grant No. U2139207; U1939210). The support is gratefully acknowledged. The authors would also like to thank the NGA-West2 database for providing the strong ground motion data. Conflicts of Interest: The authors declare no conflict of interest. Appendix A Table A1. Damage potential ranking of pulse-like ground motions. 2-Story 5-Story 8-Story 15-Story Ranking MIDR and MIDR and Number OSDI MIDR MFA OSDI MIDR MFA OSDI MFA MFA OSDI 1 GBZ000 GBZ000 H-E03140 H-E05140 SKR090 SKR090 H-E05140 TCU059-N TCU059-N H-E05140 6 PUL194 PUL194 SCE288 DZC270 SCE288 YPT330 DZC270 TCU057-W TCU057-W DZC270 11 H-E03230 H-E03230 WPI046 PAR--T WPI046 TCU060-W PAR–T SCR090 TCU026-W H-E03230 16 H-E11230 H-E11230 LDM334 TCU068-N H-E10320 TCU115-W TCU068-N A-BIR180 SHI000 SCR090 21 DZC180 DZC180 CPM000 H-E06140 WPI316 DZC270 H-E06140 SCE288 TCU046-W H-ECC002 26 TAK090 TAK090 TCU060-W TCU057-W TCU059-W H-E11230 TCU057-W TCU115-W TCU065-W TCU057-W 31 H-E06140 H-E06140 ERZ-NS CPM000 ERZ-NS ERZ-NS CPM000 CHY002-N TCU056-N SKR090 36 LCN000 LCN000 MUL279 D-TSM270 CNP196 TCU116-W D-TSM270 SHI000 TCU029-N WPI316 41 ORR090 ORR090 WVC000 SCE018 WVC000 WPI316 SCE018 CPM000 TCU076-N LDM334 46 A-OR2010 A-OR2010 ORR090 TCU128-W H-E04230 LDM334 TCU128-W H-E11230 CHY101-W SCE018 51 CPM000 CPM000 H-HVP225 SPV270 D-TSM270 H-HVP315 SPV270 TCU103-W TCU045-W TCU111-W 56 LDM334 LDM334 D-TSM360 DZC180 STN110 H-ECC002 DZC180 TCU057-N CHY029-N SCS142 61 GOF090 GOF090 TCU120-W RIO270 TCU063-N ORR090 RIO270 TCU063-N TCU047-N TCU059-W 66 HSP000 HSP000 40I07EW MUL279 H-BRA315 A-OR2010 MUL279 WVC000 TCU094-W UNI005 71 STG000 STG000 A-ZAK360 MVH135 H-E08140 SPV270 MVH135 TCU087-W TCU100-W TCU038-W 76 40E01EW 40E01EW YER270 NAS270 H-BRA225 40I07EW NAS270 TCU049-W TCU064-N TCU068-W 81 TCU059-N TCU059-N MU2035 WWT180 LOS000 TRI090 WWT180 TCU096-W ILA037-N H-BRA225 86 CPM090 CPM090 H-AGR273 H-HVP225 TCU095-N TCU060-N H-HVP225 A-OR2010 TCU070-N ERZ-NS 91 40I01EW 40I01EW CPM090 D-PVY045 DZC180 TCU026-W D-PVY045 H-BRA315 TCU098-N D-PVY045 96 UNI005 UNI005 TCU055-N TCU057-N TCU068-N TCU103-W TCU057-N H-E06140 HSP000 H-E10050 101 SCS052 SCS052 A-BAG270 TAB-LN CYC285 TCU076-N TAB-LN TCU095-N TCU095-W ARC090 106 WWT270 WWT270 40E01EW WVC270 D-OLC270 TCU136-E WVC270 TCU026-W CHY006-E WVC270 111 TCU115-W TCU115-W TCU052-W TCU116-W NPS210 40E01EW TCU116-W TCU068-N YPT330 BOL090 116 TCU045-N TCU045-N SPG360 40E01EW G01090 TCU040-N 40E01EW TCU039-N A02043 A-ZAK360 121 TCU031-W TCU031-W A02043 TCU040-N H-QKP085 TCU045-N TCU040-N JEN022 H-AGR273 TCU040-N 126 TCU049-N TCU049-N MUL009 TAZ000 TCU048-N TCU049-W TAZ000 TCU076-N A02133 TCU117-W Buildings 2022, 12, 754 17 of 18 Table A1. Cont. 2-Story 5-Story 8-Story 15-Story Ranking MIDR and MIDR and Number OSDI MIDR MFA OSDI MIDR MFA OSDI MFA MFA OSDI 131 STG090 STG090 TCU049-N STG000 GAZ000 MU2035 STG000 MU2035 TCU064-W STG000 136 TCU117-W TCU117-W H-AGR003 TCU105-N TCU109-W G01090 TCU105-N PAC265 TCU075-W KJM090 141 TCU046-W TCU046-W TCU104-N H-E11140 GOF090 H-BRA225 H-E11140 TCU051-W 40I01EW H-BRA315 146 S2330 S2330 TCU026-W TCU100-N TCU128-N C02065 TCU100-N TCU042-W H-HVP315 TCU045-N 151 KJM090 KJM090 TAB-TR HVR240 ARC090 TCU039-W HVR240 TCU076-W WPI316 HVR240 156 PAC175 PAC175 TCU034-W TCU098-N TCU018-W TCU017-W TCU098-N H-E06230 H-E03140 TAZ090 161 A02133 A02133 FOR000 A02133 TCU046-W STG000 A02133 LGP000 CHY002-N H-QKP085 166 G06090 G06090 TAZ000 TCU055-N H-AEP045 TCU083-W TCU055-N TCU036-N GOF090 TAB-TR 171 TCU083-W TCU083-W TCU031-W TCU104-N TCU105-W TCU105-W TCU104-N TCU070-N NAS270 TCU095-N 176 TCU048-N TCU048-N TCU050-N TCU039-N SCS052 TCU017-N TCU039-N DZC180 PAR–L NSY-N 181 TCU050-W TCU050-W STG000 TCU103-W TCU003-W CHY101-N TCU103-W TCU048-N TAK000 TCU109-W 186 PRS090 PRS090 TCU067-W H-FRN044 PAC175 D-OLC270 H-FRN044 KJM090 PRS090 TCU029-N 191 TCU104-W TCU104-W TCU015-W TCU087-W TCU050-W MUL009 TCU087-W 40I07EW CNP196 H-FRN044 196 TCU064-W TCU064-W TCU076-N TCU015-W TCU104-W H-QKP085 TCU015-W TCU067-N G06230 TCU015-W 201 TCU105-W TCU105-W TCU083-W TCU010-W TCU083-W TCU064-W TCU010-W TCU053-N MU2035 TCU104-W 206 CHY080-N CHY080-N TCU029-N TCU083-W TCU051-W TCU036-N TCU083-W G06090 CYC195 TCU065-W 211 TCU029-W TCU029-W TCU047-N TCU096-W CHY101-N TCU089-N TCU096-W TCU095-W GAZ000 TCU095-W 216 JEN292 JEN292 TCU098-W TCU064-W TCU089-N PAC175 TCU064-W H-QKP085 H-BRA225 TCU064-W 221 GAZ090 GAZ090 S2330 TCU076-N TCU075-W CHY029-N TCU076-N H-FRN044 H-E08140 TCU053-W 226 TCU-E TCU-E TCU029-W CHY080-W TCU064-N CHY028-W CHY080-W PAC175 CPM090 CHY080-W 231 CHY080-W CHY080-W TCU087-N CHY029-N TCU-E H-ECC092 CHY029-N CHY029-N H-E07140 CHY029-N 236 TCU067-N TCU067-N TCU067-N TCU067-N TCU067-N 40I01EW TCU067-N TCU067-W LDM064 TCU067-N Note: 1. 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Journal

Buildings – Multidisciplinary Digital Publishing Institute

Published: Jun 1, 2022

Keywords: pulse-like ground motions; damage potential ranking; intensity measures; analysis of efficiency and sufficiency; principal component analysis

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