Seismic Fragility And Post-Earthquake Reparability of Concrete Frame With Low-Bond High-Strength Rebar Reinforced Concrete Column

To further study the global seismic behaviour and post-earthquake reparability of RC building frames 21 with the proposed self-centring columns with low-bond high-strength reinforcements (LBHSRs), 22 incremental dynamic analysis (IDA) of five-floor and ten-floor frame archetypes under excitation by 23 twenty ground motions (GMs) was performed. First, the pushover results indicated that the use of 24 LBHSR could substantially improve the yield and ultimate lateral drift of both the archetypes, although 25 the archetype had a smaller longitudinal reinforcement ratio (LR) of the LBHSR and similar seismic 26 resistance. The dynamic response results indicated that the archetype with LBHSRs exhibited a smaller 27 residual story lateral drift although the effectiveness of the use of LBHSR to reduce seismic response was 28 not apparent for the archetype subjected to a low-intensity earthquake. The seismic fragility results 29 showed that LBHSR was more effective for preventing seismic collapse than for attaining the immediate 30 occupancy (IO), life safety (LS), and collapse prevention (CP) limit states. Furthermore, the higher the 31 LR, the lower was the likelihood of seismic collapse. The fragility curves of the residual story lateral 32 drifts indicate that the use of LBHSR can significantly mitigate the residual deformation in the DS1, DS2, 33 and DS3 damage states. Moreover, the effectiveness increases with the increase in the LR and earthquake 34 intensity. Comparisons of residual story lateral drifts between the predicted results and IDA results 35 indicated that the present calculation models are not suitable for predicting residual deformation. The 36 model needs to be studied further.

seismic design method proposed in the Japanese code (AIJ, 2016). 48 The design concept for preventing engineering structures from collapsing to protect human lives is 49 effective. Human casualties in the recent earthquakes in Japan were significantly less than those in earlier 50 earthquakes. However, these design methods result in significant seismic damage of engineering 51 structures in the form of plastic hinge. Engineering structures that sustain severe seismic damage incur 52 substantial post-earthquake repair expense. Occasionally, a structure that does not undergo seismic 53 collapse needs to be demolished because of the substantial repair cost. This substantially hinders the 54 rehabilitation of society and human life because the repair of infrastructure including buildings and 55 bridges is highly time-consuming and requires substantial socio-economic resources. Therefore, scholars 56 have indicated that engineering structures should satisfy the traditional design objective of ensuring 57 human safety as well as limit the seismic damage and residual deformation to aid the repair of the 58 structure after an earthquake (Kawashima 1997). Furthermore, the residual deformation after an 59 earthquake also poses a risk to structural safety during post-earthquake fires . 60 "Resilient City" should become the next research emphasis for seismic-resistant engineering structures. 61 Since 1963, Housner (1963 determined that structures did not sustain severe seismic damages in the 62 1960 Chile earthquake because the connection between the main structure and foundation had been 63 bond-strength reinforcements. Furthermore, the seismic damage of the proposed RC columns was 136 marginal (see Fig.3). This further reduced the difficulty and cost of post-earthquake repair. 137 The seismic behaviours of beam-column joint assembly reinforced by either PDHSRs or normal steel 138 rebars were experimentally investigated (Wang 2021). The results indicated that the use of PDHSR in the 139 columns was favourable to the improvement of the ductility of beam-column joints. Meanwhile, the use 140 of both beams and columns with PDHSRs can substantially improve the seismic behaviours of beam-141 column joints, including their seismic resistance, ductility, and residual deformation. This prevents the 142 deterioration of the seismic behaviours of the RC frame with the proposed columns because of the use of 143

PDHSR. 144
The seismic behaviours of RC columns with LBSHSRs or PDHSRs subjected to lateral cyclic loading 145 have been investigated extensively and comprehensively through experiment and evaluation (Wang et al. 146 2019; ; Wang et al. 2021). Further study is required to better comprehend the influence 147 of the proposed SC columns with LBHSRs on the seismic responses of an entire RC frame. This paper 148 presents the time-history analysis results of five-floor and ten-floor building frame archetypes with 149 concrete columns reinforced by steel rebars with different bond properties. Nonlinear numerical models 150 considering steel-bond slip were proposed in OpenSees (2018), and incremental dynamic analysis (IDA) 151 was performed to obtain seismic responses of the designed building frame archetypes based on twenty 152 earthquake ground motions. The results were used to determine 1) seismic fragility curves for evaluating 153 seismic collapse 2) and residual drift curves for estimating the post-earthquake reparability of the 154 designed building archetypes. Furthermore, the residual story lateral drifts obtained from the IDA were 155 evaluated using the equations proposed in the FEMA and JRA codes. The works of this study provide a 156 better understanding of the proposed RC column application for designing an inexpensive SC-RC frame 157 by using simple techniques. 158 159 2 Numerical models of concrete frame with LBHSR reinforced columns 160

Design of building frame archetypes 161
Five-floor and ten-floor RC building frames were designed to represent the expected design variation 162 of short and medium-rise buildings. Fig. 4 shows the plan view and elevation of the building frames. Each 163 floor contains many moment resisting frames (MRFs) in both horizontal and vertical directions. There are 164 four and seven bays in the vertical and horizontal directions, respectively. It is assumed that the building 165 frames has identical story height and bay width of 3.2 m and 4.0 m, respectively. The intermediate MRF 166 was selected to perform the time-history analysis. The columns of the first floor were assumed to fix the 167 foundation. It was assumed that the width of the slabs was 4.0 m, and the membrane element was used to 168 model the slabs. Live loads of 2.0 kN/m 2 were assigned to all the building floors. The dead load was 169 calculated according to the self-weights of all the members including the columns, beams, and slabs. 170 The building archetypes were assumed to be located in Dongchuan District, Kunming City, Yunnan 171 Province of China. It is in the southwestern of China and is one of the areas that are highly vulnerable to 172 earthquake. The latitudes and longitudes are 102° 47′-103° 18′ and 25° 57′-26° 32′, respectively. 173 According to the seismic design code of China (GB 50011-2010), the building archetypes satisfy the 174 Seismic design category (SDC) 9, which is the highest seismic vulnerability. The maximum considered 175 earthquake (MCE) spectral acceleration Sa was 0.4g. The soil was assumed to be of Class II. The natural 176 eigenperiod Tg is 0.55 s. The first modes of the building archetypes were considered in the nonlinear 177 time-history analysis. The fundamental periods T1 of the five-floor and ten-floor archetypes were 0.5 s 178 and 1.0 s, respectively. These were calculated by Eq. (1) proposed in the ASCE 7 code (ASCE/SEI 7-10,  Table 1. The design earthquake accelerations of the building  184   archetypes were calculated from their fundamental periods using the equations for calculating earthquake  185   acceleration proposed in the seismic design code of China (GB 50011-2010). 186 The compressive strength of the concrete was assumed to be 36.0 MPa, and the confinement ratio of 187 the column section was assumed to be 1.22. Meanwhile, the beam section did not consider the 188 confinement to concrete. The dimensions of the column and beam are shown in Fig.4  HBNSRs or LBHSRs with a diameter of 25 mm was designed to reinforce the column section to yield a 198 longitudinal reinforcement ratio (LR) of 3.14%. However, owing to the higher yield strength of LBHSR, 199 the seismic base force resistances of the building archetypes with LBHSRs was higher than those for the 200 archetypes with HBNSRs with identical LR (see Fig.10). To eliminate the effect of the yield strength of 201 LBHSR and further study the influence of the bond property of longitudinal reinforcement on the seismic 202 responses of building archetypes, 12 D22 and 4 D12 LBHSRs (to yield a lower LR of 2.09%) was 203 assumed to reinforce the columns of another building archetype scenario for providing a seismic base 204 force resistance similar to that of the building archetype scenario with 16 D25 HBNSRs (see Table 1). 205 The damping ratio of both the archetypes was assumed to be 5.0%. 206 207

Ground motions 208
Twenty ground motions (GMs) including ten far-field (FF), five near-field pulse (NFP), and five near-209 field no-pulse (NFNP) GMs summarized by FEMA P695 (FEMA 2009) were selected to perform the 210 nonlinear time-history analysis. The acceleration data of these GMs were downloaded from 'PEER 211 Strong Ground Motion Database'. The basic information including locations, years, magnitude, peak 212 ground acceleration (PGA), and duration are shown in Table 2. The corresponding acceleration spectral 213 with a damping ratio of 5.0% is shown in

Considerations of column sectional confinement and steel-bond slip of LBHSR 233
The confined concrete compressive strength was used to simulate the FRP-confined column section. 234 The confinement ratio was calculated using Eq. (2) of the model proposed by Lam and Teng (2003). 235 Meanwhile, Eq. (3) proposed by Sun and Sakino (1996)    responses of the test columns are shown in Fig.9. As is evident from the figure, the proposed OpenSees 273 element models shown in Fig.8 can be used to predict the seismic behaviours (including the stiffness, 274 seismic resistance, ductility, and residual lateral drift) of test columns reinforced by longitudinal reinforcements (PDHSRs, LBSHSRs, HBHSRs) with good accuracy. As indicated, the experimentally 276 determined early stiffness in the negative direction of the specimen columns PPD0, PPD4, and PPD6 277 differed marginally from the predicted results. This was attributed to the seismic damage in the negative 278 direction initiated when the test column was thrust in the positive direction. It should be noted that the 279 experimentally determined seismic behaviours of the test columns FATSB and FATUS in the negative 280 direction did not agree with the predicted results. This was attributed to the fact that the capacity of the 281 hydraulic jack during the testing was smaller than the seismic resistance capacity of these two test 282 columns. The maximum lateral drift cycles were up to 3.5% and 2.0% for FATSB and HBNSRs and LBHSRs are shown in Fig. 10. It is evident from the figure that both five-archetype and 10-289 archetype with an identical LR (= 3.14%) of LBHSRs displayed better seismic responses (including 290 higher seismic resistance and higher deformability) compared with the archetypes with HBNSRs. The 291 lateral drifts at the peak lateral forces of the two archetypes with LBHSRs were 180% and 241%, 292 respectively, higher than those of the archetypes with HBNSRs. When the LR of LBHSRs was decreased 293 from 3.14% to 2.09%, the seismic base shear forces of the building archetypes were similar to those of the 294 archetype reinforced with HBNSRs having an LR of 3.14%. However, the peak lateral drifts of the five-295 floor and ten-floor archetypes with LBHSRs were increased by 139% and 222%, respectively, compared 296 with the archetypes with HBNSRs. For the two LRs of LBHSR (3.14% and 2.09%), both the archetypes 297 had reduced stiffness compared with that for HBNSRs (LR = 3.14%) from a certain lateral drift level, 298 moreover, lower the LR, lower was the stiffness (see Fig.10). These observation were consistent with the 299 experimental results shown in the references (Wang et al. 2019; Wang et al. 2021). This can be attributed 300 to the fact that the low-bond property of LBHSR delayed the development of the yielding process of the 301 longitudinal reinforcement. Thereby, the archetypes with LBHSRs had larger yield roof lateral drifts, Ry,eff 302 (see Table 1). When the LR of LBHSR was 3.14%, the Ry,eff of the archetypes with LBHSRs was 2.81 and 303 1.88 times, respectively, that of the archetypes with HBNSRs. Meanwhile, because the LR was 2.09%, 304 the Ry,eff values were still increased by 48.6% and 3.3%, respectively, for the five-floor and ten-floor 305 archetypes. 306 The over-strength factor Ω and period-based ductility μT were used to quantify the seismic behaviour of 307 the building frame archetypes (see Table 1). The average yield displacement of the calculated results of 308 three methods including first yield, the geometric graphic method, and the equivalent elastoplastic energy 309 method defined by Park (1989) was used in this study to calculate the period-based ductility. Meanwhile, 310 the point of 20% strength loss (0.8V) was considered as the ultimate displacement. As shown in Table 1, 311 the Ωs of both five-floor and ten-floor archetypes were similar when the LRs of HBNSR and LBHSR 312 were 3.14% and 2.09%, respectively. Consequently, the use of LBHSR can reduce the amount of 313 longitudinal reinforcement. However, when the LR of LBHSR was 3.14%, the Ωs were larger by 31% 314 and 16%, respectively, compared with the archetypes with HBNSRs. As shown in Table 1, the μT of the 315 five-floor archetypes with LBHSRs was marginally smaller compared with that attained with HBNSRs. 316 Meanwhile, the ten-floor archetypes with LBHSRs had larger μT compared with the ten-floor archetypes 317 with HBNSRs. 318 12 was approximately 2.0%, whereas the value for the archetype with LBHSRs was higher than 2.0% for 325 LRs of 3.14% and 2.09%. However, for the high-intensity earthquake GM 13, the maximum story lateral 326 drift of the archetype with HBNSRs (LR = 3.14%) was approximately 10.0%. It could be assumed to be a 327 collapse. However, the values of the archetypes with LBHSRs were decreased to 6.42% and 8.23% for 328 LRs of 3.14% and 2.09%, respectively. As shown in Fig.11 (b), when subjected to GM12, the base shear 329 force of the archetype with LBHSRs was smaller than that of the archetype with HBNSRs. For GM 13, 330 the archetype with LBHSRs having an LR of 3.14% displayed larger base shear force, whereas the base 331 shear forces of the archetypes with HBNSRs having an LR of 3.14% and those with LBHSRs having an 332 LR of 2.09% were equal. Furthermore, the stiffness of the archetype with LBHSRs was also smaller than 333 that of the archetype with HBNSRs when the lateral drift entered the large deformation stage. These 334 observations were in agreement with the static pushover results shown in Fig.10. It was also observed that 335 the residual lateral drifts of the archetypes with three longitudinal reinforcement scenarios were similar 336 when subjected to GM12. Meanwhile, the archetypes with LBHSRs having LRs of 3.14% and 2.09% 337 displayed smaller residual lateral drifts compared with the archetypes with HBNSRs (LR = 3.14%) 338 subjected to GM13. Furthermore, larger the LR of LBHSR, smaller was the residual lateral drift (see 339 Fig.11(a)). The dynamic responses shown in Fig.11 indicate that the only apparent effect of the use of 340 LBHSR is the reduction in the seismic dynamic responses of structures subjected to a high-intensity 341 earthquake. 342 The lateral drift responses in conjunction with the height of the archetype are shown in Fig.12. 343 Identical to the observations in Fig.11, the maximum story lateral drift response of the archetype 344 subjected to the relatively moderate or low-intensity earthquake G12 was significantly smaller compared 345 with that for GM 13. However, regardless of the earthquake intensity, LBHSR was remarkably effective 346 in reducing the residual story lateral drift, as shown in Fig.12 (b). Similar conclusions were obtained from 347 comparisons of the dynamic responses of the ten-floor archetypes reinforced by LBHSRs and HBNSRs. 348 IDA was performed to capture the entire seismic response of the designed building frame archetype. 349 The time-history analysis was conducted repeatedly through amplitude-scaling of each GM until the 350 archetypes were assumed as the failure. The time-history analysis was terminated when the inter-story 351 drift ratio exceeded 10%. Fig.13 shows the relationships between the earthquake intensities at period T1 This rule was also adopted in this study. 373 Fig.14 shows the seismic fragility probabilities of the exceedances of the IO, LS, CP, and collapse limit 374 states of both five-floor and ten-floor archetypes. As indicated, for the IO and LS limit states, the 375 possibility curves of the five-floor archetypes with LBHSRs were larger than those of the five-floor 376 archetypes with HBNSRs. Moreover, the median collapse capacity SCT representing half of the GMs 377 caused the limit state of the five-floor archetypes with HBNSRs to be the largest. Comparing the CP and 378 collapse limit states, it was observed that the possibility of the archetype with HBNSRs was the highest. 379 This implies that the use of LBHSR could reduce the likelihood of CP and seismic collapse limit states. 380 Furthermore, larger the LR, lower is the likelihood. The above statements indicate that the use of LBHSR 381 had no apparent effect on the resistance to the marginal seismic limit states such as IO and LS. However, 382 it was favourable to the CP and seismic collapse limit states. Furthermore, higher the LR of LBHSR, 383 lower is the likelihood of seismic collapse. A similar conclusion can be obtained by observing the 384 possibility curves of the ten-floor archetypes. Comparing the probability curves of the IO, LS, and CP 385 limit states, the possibility curves of the ten-floor archetype with LBHSRs (LR = 3.14% and 2.09%) were 386 larger than that of the ten-floor archetype with HBNSRs having an LR of 3.14%. However, the possibility 387 curves of the seismic collapse limit state of the ten-floor archetypes with LBHSRs (LR = 3.14% and 388 2.09%) were significantly smaller compared with the HBNSR scenario. Moreover, the advantage of using 389 LBHSR was more apparent for the IO, LS, and CP limit states of the five-floor archetype than for those 390 of the ten-floor archetype. However, a comparison of the difference in the possibility curves of the 391 archetypes with HBNSRs and LBHSRs revealed that the application of LBHSR in the ten-floor archetype 392 was more effective for resisting the collapse limit state. The collapse margin ratio (CMR) is used to 393 represent seismic safety and is defined as the ratio of the SCT to the 5%-damped spectral acceleration of 394 the MCE GMs at the fundamental period, Sa(T1) (FEMA 2009). The CMRs of all the building archetypes 395 with different longitudinal reinforcement scenarios at four SDCs of Chinese seismic code (GB 50011-396 2010) are shown in Table 1. As is evident, although the seismic resistance of the archetype with LBHSRs 397 having a lower LR of 2.09% was similar to that of the archetype with HBNSRs having an LR of 3.14%, 398 the CMRs of the former at each SDC were increased by 6.7% and 13.75% compared with the latter for 399 the five-floor archetype and ten-floor archetype, respectively. Furthermore, when the LR of LBHSR was 400 increased from 2.09% to 3.14%, the increase ratio was enhanced further to 26.51% and 33.75% for the 401 five-floor archetype and ten-floor archetype, respectively. Hence, it was concluded that the global seismic 402 response of an RC building frame is substantially affected by the use of LBHSR. The effect of LBHSR is 403 more apparent when the building frame experiences a large deformation level such as the collapse limit 404 state. 405 406 5. Post-earthquake reparability and evaluation of residual story lateral drift of archetype 407

Analysis of fragility of residual story lateral drift 408
Residual deformation has been used as an index to estimate the post-earthquake damage of buildings, 409 bridges, and other infrastructure. FEMA P 58-1 (FEMA 2012) defined four damage states (DSi) ranging 410 from the onset of damage of nonstructural components to near-collapse of the structure. The residual 411 story drift ratios Δ / h of DS1, DS2, and DS3 are defined as 0.2%, 0.5%, and 1.0%, respectively. 412 Meanwhile, the Δ / h of the DS4 damage state for limited, moderate, and high ductility systems are 1.0%, 413 2.0%, and 4.0%, respectively. DS1 represents the state wherein no structural realignment is necessary for 414 structural stability, and the adjustment and repair of only certain nonstructural and mechanical 415 components that are sensitive to elevator rails, curtain walls, and doors are required. DS2 represents a 416 realignment of the structural frame and related structures are need to be maintained, limited degradation 417 in structural stability is permitted to occur in nonstructural and mechanical components. DS3 represents 418 the scenario where significant structural realignment is required to restore the margin-of-safety for lateral 419 stability. Furthermore, the repair of the structure is not economically or practically feasible. DS4 420 represents the scenario wherein the structure is in danger of collapse after an earthquake owing to an 421 excessive residual drift. 422 The relationships between earthquake intensity and the residual story lateral drift of archetypes with 423 HBNSRs and LBHSRs are shown in Fig.15. As is evident from the figure, the increase in the stiffness of 424 the fragility curves of the archetypes with LBHSRs was larger than that for the archetypes with HBHSRs. 425 This was particularly so for identical LR. Moreover, the number of residual story lateral drifts higher than 426 2.0% of the archetype with LBHSRs having an LR of 3.14% is not adequate for a residual drift fragility 427 analysis similar to the one for the other two longitudinal reinforcement scenarios. As shown in Fig.10, the 428 pushover curves of both archetypes indicate that the building frame could be assumed to be a moderate 429 ductility system. Consequently, only the DS1, DS2, and DS3 damage states of the archetypes were 430 compared in this study. 431 The comparisons of the possibility curves of three damage states of the archetypes with HBNSRs and 432 LBHSRs are shown in Fig.16. As is evident from the figure, regardless of the damage states, both five-433 floor and ten-floor archetypes with LBHSRs generally exhibited significantly smaller probability 434 compared with that for the archetypes with HBNSRs. Although the archetypes with HBNSRs having an 435 LR of 3.14% and LBHSRs having an LR of 2.09% had similar seismic resistance (see Fig.10), the 436 possibility curve of the archetype with LBHSRs having an LR of 2.09% was smaller than that of the 437 archetype with HBNSRs having an LR of 3.14%. Moreover, when the LR of LBHSR was increased from 438 2.09% to 3.14%, the possibility curve of the archetype was decreased further, as shown in Fig.16. This 439 implies that the low-bond property of longitudinal reinforcement influences the reduction in the residual 440 deformation of building frames. A closer inspection reveals that the LBHSR is more effective for 441 mitigating the residual drift for the low-rise five-floor building archetype. Furthermore, the possibility 442 curves of archetypes are similar at marginal earthquake intensity regardless of the type and LR of 443 longitudinal reinforcement. In addition, the difference in the possibility curves is increased with the 444 increase in the earthquake intensity. It can be concluded that the use of LBHSR is highly effective for 445 reducing the residual deformation of an RC building frame. Furthermore, it is more effective when the 446 building is subjected to a large earthquake.