Seismic capacity and vulnerability assessment considering ageing effects. Case study: 2 Three local Portuguese RC buildings

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The Version of Record is available online at: [https://dx.doi.org/10.1007/s10518-020-00955-4]” Bulletin of Earthquake Engineering Seismic capacity and vulnerability assessment considering ageing effects.Case study: Three local Portuguese RC buildings --Manuscript Draft-- Manuscript Number: Full Title: Seismic capacity and vulnerability assessment considering ageing effects.Case study: Three local Portuguese RC buildings Article Type: S.I. : Recent Advances in Seismic Fragility and Vulnerability Keywords: RC buildings; Ageing effects; Performance-based seismic assessment; Non-linear static analyses; Fragility Curves Corresponding Author: Rita Bento, Ph.D CERIS, Instituto Superior Técnico, Universidade de Lisboa, Portugal Lisbon, PORTUGAL Corresponding Author Secondary Information: Corresponding Author's Institution: CERIS, Instituto Superior Técnico, Universidade de Lisboa, Portugal Corresponding Author's Secondary Institution: First Author: Rita Couto First Author Secondary Information: Order of Authors: Rita Couto Maria Victoria Requena-García-Cruz Rita Bento, Ph.D Antonio Morales-Esteban Order of Authors Secondary Information: Funding Information: Abstract: A high percentage of reinforced concrete (RC) buildings in Portugal were designed and built before the introduction of modern seismic codes. This research aims to assess the seismic capacity and vulnerability of RC buildings in the city of Lisbon. For that purpose, nonlinear static procedures have been used and fragility curves have been developed. These buildings are reaching the end of their nominal life. Therefore, ageing effects have been taken into account, as well as the presence of smooth rebar. To do so, a sensitivity analysis has been performed by considering the chlorideinduced corrosion of the reinforcement steel rebar and the degradation of the concrete cover. To illustrate the effects of ageing and the procedure adopted for the seismic fragility assessment of old RC structures, three RC buildings with masonry infills have been selected as case studies. They were all built between 1960 and 1980, and they are representative of the current building stock in Lisbon. The seismic capacity of the buildings has been determined by means of nonlinear static analyses of threedimensional numerical models. The N2 method and its extended version have been considered to determine the target displacement. The seismic safety of the buildings has been estimated in terms of the demand/capacity ratio (DCR) for each vertical structural element (columns and walls) according to the bending and the shear failures. Then, a set of fragility curves has been developed for all the buildings’ RC columns and walls to represent the probability of reaching or exceeding the significant damage state. Results have shown that the concrete strength degradation has had more influence than reduction of the rebar diameter in the seismic capacity. When considering steel corrosion, it has been demonstrated that the corrosion rate has reduced the capacity more than the time of exposure. It can be concluded that ageing affects the seismic behaviour of RC structures, increasing the vulnerability of these buildings. Powered by Editorial Manager® and ProduXion Manager® from Aries Systems Corporation Suggested Reviewers: Francisco Martínez-Álvarez, Dr Associate Professor, Pablo de Olavide University [email protected] Based in his expertise. He is an expert in seismic engineering, time series and data mining. Daniel Celarec Faculty of Civil and Geodetic Engineering, University of Ljubljana, Slovenia [email protected] He is an expert in seismic engineering assessment, modelling uncertainties and reinforced concrete buildings behavior. He has published several papers on the seismic performance of these buildings as well as the simulation of the ageing effects which have been considerably cited. Powered by Editorial Manager® and ProduXion Manager® from Aries Systems Corporation 1 Seismic capacity and vulnerability assessment considering ageing effects. Case study: 1 Three local Portuguese RC buildings 2 R. Couto1, M.V. Requena-García-Cruz2, R. Bento1(*), A. Morales-Esteban2 3 4 1CERIS, Instituto Superior Técnico, Universidade de Lisboa, Portugal, Address: Av. Rovisco Pais 1049-001 Lisbon, Portugal, 5 [email protected]t; [email protected] 6 2 Department of Building Structures and Geotechnical Engineering, University of Seville, Spain. Address: Av. Reina Mercedes, 2, 41012, Seville, Spain, 7 mrequena[email protected], [email protected] 8 (*) Corresponding Author – Rita Bento, [email protected], Tel: +351 218 418 205 9 10 Abstract (150-250 words) 11 A high percentage of reinforced concrete (RC) buildings in Portugal were designed and built before the introduction of modern 12 seismic codes. This research aims to assess the seismic capacity and vulnerability of RC buildings in the city of Lisbon. For that 13 purpose, nonlinear static procedures have been used and fragility curves have been developed. These buildings are reaching the 14 end of their nominal life. Therefore, ageing effects have been taken into account, as well as the presence of smooth rebar. To do 15 so, a sensitivity analysis has been performed by considering the chloride-induced corrosion of the reinforcement steel rebar and the 16 degradation of the concrete cover. To illustrate the effects of ageing and the procedure adopted for the seismic fragility assessment 17 of old RC structures, three RC buildings with masonry infills have been selected as case studies. They were all built between 1960 18 and 1980, and they are representative of the current building stock in Lisbon. The seismic capacity of the buildings has been 19 determined by means of nonlinear static analyses of three-dimensional numerical models. The N2 method and its extended version 20 have been considered to determine the target displacement. The seismic safety of the buildings has been estimated in terms of the 21 demand/capacity ratio (DCR) for each vertical structural element (columns and walls) according to the bending and the shear 22 failures. Then, a set of fragility curves has been developed for all the buildings’ RC columns and walls to represent the probability 23 of reaching or exceeding the significant damage state. Results have shown that the concrete strength degradation has had more 24 influence than reduction of the rebar diameter in the seismic capacity. When considering steel corrosion, it has been demonstrated 25 that the corrosion rate has reduced the capacity more than the time of exposure. It can be concluded that ageing affects the seismic 26 behaviour of RC structures, increasing the vulnerability of these buildings. 27 28 Keywords (max 6): 29 RC buildings; Ageing effects; Performance-based seismic assessment; Non-linear static analyses; Fragility Curves. 30 31 32 1. Introduction 33 In recent years, reinforced concrete (RC) buildings with low seismic capacities have been seismically damaged in 34 earthquake-prone countries. Such is the case of the 1999 Kocaeli Earthquake, the 1999 Chi-chi Earthquake, the 2011 35 East Japan Earthquake, the 2011 Christchurch Earthquake and the 2017 Puebla Earthquake (Earthquake Engineering 36 Research Institute 2020). Moreover, previous studies stated that buildings constructed prior to seismic codes are likely 37 to be damaged due to an earthquake (Kam et al. 2011). This is because they have only been gravity load designed and 38 built with an inadequate lateral load resistance. In fact, they have been widely analysed and proved to be of limited 39 ductility capacity, i.e. seismically vulnerable (Arteta et al. 2019). Hence, this accounts for the need to propose reliable 40 seismic risk assessment and earthquake loss models for such structures. 41 42 A major issue of adequate seismic risk assessment and earthquake loss modelling is the proper characterisation of the 43 expected behaviour of these structures. In order to tackle this issue, models considering the performance of different 44 building classes (e.g. vulnerability functions, fragility functions, etc.) have been employed. Building class definitions 45 have followed no uniform rule. For instance, HAZUS-MH used between 190 and 5,300 classes (National Institute of 46 Building Sciences and Federal Emergency Management Agency (NIBS and FEMA) 2003), depending on how they 47 are counted. The Global Earthquake Model (GEM) proposed an innovative genetic taxonomy (Scawthorn et al. 2013) 48 that could classify buildings in unlimited ways. Some authors even developed models of the fragility or vulnerability 49 of different classes based on individual buildings (Maio and Tsionis 2016). In general, these buildings were chosen 50 due to their representativeness of a region of interest. In addition, in order to consider the variety of different features 51 of the classes, a probabilistic model of the building class was also established. 52 53 The deterioration effect of the structures during their lifetime has been commonly neglected in seismic vulnerability 54 assessment studies (Rossetto and Elnashai 2005; Tsionis et al. 2011; Caruso et al. 2019a). However, a considerable 55 number of old RC structures suffer from the ageing and the degradation of materials, which may adversely affect their 56 structural performance. Among different deterioration mechanisms, corrosion in reinforcement is one of the major 57 problems in the durability of existing RC structures. Previous studies showed that corrosion can affect the concrete 58 cover of the reinforcement (Al-Harthy et al. 2011), the mechanical behaviour of the reinforcement (Du et al. 2005) 59 Manuscript Click here to access/download;Manuscript;_BEE_AgingEffects_Structure_202 Click here to view linked References 2 and the bond between the concrete and the reinforcement (Lundgren 2007). These corrosion effects were studied in 60 old RC buildings subjected to seismic action (Celarec et al. 2011; Yalciner et al. 2015). Nonetheless, according to the 61 authors’ knowledge, there are few studies on the influence of ageing effects on the seismic performance of existing 62 RC buildings. In fact, there is a distinct lack of studies that focus on sensitively analysing the influence of these 63 different parameters (the corrosion rate of the reinforcement, the time for corrosion initiation, the spalling of the 64 concrete cover and the affected structural elements) while considering the fragility level. 65 66 The scope of this study is to investigate the seismic capacity and vulnerability of RC buildings in the city of Lisbon 67 through non-linear static analyses and the development of fragility curves. These buildings are reaching the end of 68 their nominal life. Therefore, ageing effects have been taken into account. To do so, a sensitivity analysis has been 69 performed by considering the chloride-induced corrosion of the reinforcement steel rebar and the degradation of the 70 concrete cover. To illustrate the effects of ageing and the procedure adopted for the seismic fragility and vulnerability 71 assessment of old RC structures, three RC buildings with masonry infills have been selected as case studies. They 72 were all built between 1960 and 1980, and they are representative of the current building stock in Lisbon. 73 74 75 2. Case Studies of Building Structures 76 In Portugal, according to the 2011 Census Survey (Instituto Nacional de Estatística (INE) 2012), RC buildings 77 represent about 50% of the total building stock in the country. Moreover, 49% of these buildings were constructed 78 without adequate seismic provisions and based on early seismic codes (pre–1983). According to Silva et al. (2014), in 79 2011, RC buildings in Portugal hosted 60% of the national population, i.e. 6,342,000 people. Furthermore, the seismic 80 hazard in Portugal has been widely proved to be of considerable importance (Campos Costa et al. 2008). Recent 81 studies (Amaro-Mellado et al. 2017a; Amaro-Mellado et al. 2017b) have shown that the maximum recorded magnitude 82 in the area is 6.6 and the fault’s maximum magnitude is 6.5, which shows an outstanding seismic risk. 83 84 In Portugal, the first design codes that proposed some provisions regarding seismic action were the RSCCS (Diário 85 do Governo 1958) and the RSEP (Diário do Governo 1961). In 1983, the design code RSA (Diário do Governo 1983) 86 was introduced to finally establish adequate and restrictive seismic performance requirements. In this study, the 87 classification proposed by Silva et al. (2014) has been followed; buildings constructed before 1958 have been 88 classified as pre-code (PC), buildings constructed between 1958 and 1983 have been categorised as mid-code (MC), 89 and finally, the ones built after 1983 have been categorised as post-code (C). 90 91 In the case of Lisbon, according to the 2011 Census Survey, there are 52,496 buildings and 42% of them are RC 92 buildings, of which 71% are PC. In this work, a survey in the area of “Alvalade” (Fig. 1(a)) has been carried out to 93 characterise the existing buildings, focusing on the number, date of construction and their RC structural configuration. 94 This area is limited by the “Avenida do Brasil”, the “Avenida Almirante Gago Coutinho”, the “Avenida do Campo 95 Grande” and the train line (Fig. 1(b)). 96 97 98 (a) (b) 99 Fig. 1. Plan of Lisbon (a) indicating Alvalade’s area and (b) limits. 100 101 This assessment included 2,249 buildings, of which 28% have an RC structure and 71% have a mixed masonry- 102 concrete structure. The latter buildings are very common in Lisbon (and Portugal in general) and they were constructed 103 3 between 1930 and 1960. Their seismic performance was broadly analysed in different studies (Milosevic et al. 2018, 104 2019). The other 1% represents the Gaioleiro buildings (Simões et al. 2019a, b), garages and some unknown buildings 105 (due to the lack of data). The assessment has been carried out by analysing and gathering the data from the blueprints 106 available at the “Arquivo Municipal do Lisboa” in ArcGIS (Environmental Systems Research Institute (ESRI) 2011). 107 108 Regarding the RC structures, the structural configuration of 88% of them has been identified: 46% are framed and 109 42% are wall-frame. Fig. 2(a) shows the distribution of the RC structures identified in the area of Alvalade according 110 to their structural configuration: framed in blue, wall-frame in red and unknown in yellow. Most of the RC buildings 111 were built before 1980 (97% of all of them), while 70% of these were constructed between 1950 and 1970 (when RC 112 structures started to be built) (Fig. 2(b)). 113 114 115 (a) (b) 116 Fig. 2. Distribution of RC buildings in Alvalade regarding (a) construction date in 3D view and (b) identification of 117 their structural configuration in graph format. 118 119 The number of storeys has been identified as one of the main parameters to classify the buildings in typologies. Fig. 120 3(a) shows the distribution of the RC buildings according to their structural configuration and the number of storeys 121 in Alvalade. The majority of the framed structures (51%) are medium-height buildings of three to five storeys. In the 122 case of the wall-frame structures, most of them (49%) are tall buildings of more than nine storeys (Fig. 3(b)). A high 123 percentage of all the RC buildings presents irregularities in elevation: 57% and 67% of the framed and wall-frame 124 buildings, respectively. The wall-frame buildings (62%) are also characterised by the presence of soft storeys. This 125 has been proved to be one of the typical vulnerabilities that increase seismic damage in buildings (Ruiz-Pinilla et al. 126 2016). Also, the cross-section of the columns in 30% of the buildings of both structural configurations decreases in 127 height. 128 129 130 (a) (b) 131 Fig. 3. Distribution of RC buildings in Alvalade regarding (a) the number of storeys in 3D view and (b) identification 132 of their structural configuration in graph format. 133 134 Three case studies of buildings have been selected as the most representative of their structural configurations in the 135 area of Alvalade (Fig. 4): one framed (Model C) and two wall-frame buildings (Models A and B). They are MC 136 4 buildings constructed with typical design details of pre-70s RC buildings in Lisbon as well as with smooth rebar. The 137 analysis of the blueprints has revealed that reinforcement is not adequate in the joints since: i) the spacing and the 138 ratio of the stirrups is not enough in columns and beams, leading to shear failures and plastic hinge generation; ii) the 139 longitudinal ratio is insufficient in the bottom part of the beams; iii) the longitudinal reinforcement was designed to 140 resist code-based moments; and iv) the section of the columns decreases in height which reduces the stiffness of the 141 system. A typical constructive detail of the beam-column or wall-beam joints is shown in Fig. 5. In Table 1, the 142 variation of the reinforcement ratios of the structural elements of each model is listed. Moreover, the three buildings 143 only have infills in the upper storeys, which leads to the generation of soft-storey mechanisms in the ground floor 144 (Models A and B) and in the first floor (Model C). 145 146 147 Fig. 4. Structural schemes and plans of the three models. 148 149 150 Fig. 5. Typical constructive detail of the beam-column or wall-beam joints. 151 152 Table 1. Geometrical properties and minimum and maximum reinforcement for the structural elements of each model. 153 (T and B refer to top and bottom beam reinforcements, respectively). 154 155 Characteristic Columns Beams Walls Models A B C A B C A B C Dimensions (cm) 12.7x11.3- 28.6x27.2 23x25- 25x87 20x31- 30x40 10x31- 40x45 13x31- 25x68 10x40- 20x60 300x15- 400x25 250x25 - 5 Cross-section (cm2) 143.5-777.9 575-2175 558-1240 310-1800 403-1700 440-1380 4500- 1000 6250 - Longitudinal rebar (cm2) 4.04-61.68 0.63-7.29 0.31-38.79 T: 3.30-12.26 T:2.26-29.76 T: 0.63-16.46 3.41 15.78 - B:4.28-16.04 B: 3.93-33.58 B: 1.42-11.10 - Transversal rebar (cm2) 3.18 0.18-0.71 1.58 3.2-10.0 1.48 2.11-2.47 2.45 3.15 - Spacing of stirrups (cm) 20 5-19 15 20 20-50 15-18 25 15 156 For each building, the mass of the structures has been divided into dead and live loads. The dead loads have included 157 the self-weight of the RC elements, masonry infills and coatings, i.e. 8 kN/m2. The live loads have been defined 158 according to Part-1 of Eurocode 8 (EC8-1) (European Union 2004). The total mass and height of the buildings are 159 shown in Table 2, as well as the fundamental period of vibration of each of the models for the initial situation (without 160 corrosion, and herein called “IS”). 161 162 Table 2. Geometrical characteristics of the buildings: mass, height and fundamental period of vibration for the IS. 163 Total mass (ton) Total height (m) Fundamental period of vibration (IS) (s) X Y Model A 3677 24.6 0.90 0.87 Model B 720 15.4 0.31 0.41 Model C 1507 17.02 0.51 0.54 164 Model A was built in the 1960s and it is an eight-storey RC wall-frame, with a total height of 24.6 m. All storeys are 165 3.0 m high, except for the ground floor, which is 3.6 m high. The structure has three main frames in the X direction, 166 with all the columns oriented in this direction. In the Y direction, the structure has RC walls on the stairs and a lift 167 core. Therefore, the horizontal loads in X direction are resisted by the frames, while in the Y direction they are mainly 168 resisted by the walls. The ground floor has a soft storey configuration. 169 170 Model B was built in the 1950s and it is a five-storey RC wall-frame, with a total height of 15.5 m. All storeys have 171 the same height of 3.0 m; except for the ground floor, which is 3.5 m high. It has three and five frames in the X and 172 Y direction, respectively. The stairs and the lift are included in the centre of the building, surrounded by a shear wall 173 in the X direction. Similar to Model A, the ground floor has a soft storey configuration. 174 175 Model C was built in the 1960s and it is a six-storey framed RC building, with a total height of 17.0 m. The height of 176 all floors is irregular. Even between the ground and first floor, a significant irregularity in height can be found, which 177 leads to the generation of short columns. In the plan, the structural configuration is considerably symmetrical in the X 178 direction but significantly irregular in the Y direction. Moreover, the columns are all oriented with their strong axis in 179 the X direction. It also includes a staircase in the centre of the building, as well as internal partitions of considerable 180 thickness and a soft storey mechanism in the ground floor. 181 182 183 3. Building Structural Modelling 184 The three buildings have been analysed with the OpenSees software (McKenna et al. 2000). The columns, beams and 185 shear walls have been modelled with force-based fibre elements. The behaviour of the cover and core concrete fibres 186 has been simulated employing the model proposed by Popovics (Concrete04 material in OpenSees) (Popovics 1973). 187 The reinforcement steel fibres have been modelled by using the uniaxial Giuffre-Menegotto-Pinto model (Steel02 188 material in OpenSees) (Filippou et al. 1983). Table 3Error! Reference source not found. provides the mean values 189 of the properties of the materials adopted in this study. It should be mentioned that the concrete tensile strength has 190 been simulated as 10% of the compressive strength. 191 192 Table 3. Structural material properties. 193 Concrete fc (MPa) ɛc (‰) ɛcu (‰) Ec (GPa) Cover 28 2 200 30 Core 28 2 4 30 Steel fy (MPa) fu (MPa) ɛsu (‰) Es (GPa) 6 Ribbed rebar 370 36 240 210 Smooth rebar 222 216 168 126 Masonry Gw (GPa) α τcr (MPa) Ew (GPa) Infills 1240 0.05 280 4092 fc -compressive maximum strength; ɛc - strain at maximum strength; ɛcu - ultimate strain; Ec - modulus of elasticity for concrete; fy - yielding strength; 194 fu - ultimate strength; ɛsu - ultimate strength; and Es - modulus of elasticity for steel; Gw - elastic shear modulus; α - post-capping degrading branch 195 coefficient; τcr - shear cracking stress; Ew - modulus of elasticity of the masonry. 196 197 The effects of the smooth rebar have been taken into account by modifying the steel constitutive law as proposed by 198 Caruso et al. (2019c). Infills can worsen the seismic behaviour of buildings if they are not regularly distributed. In the 199 cases under study, they are slightly heterogeneously distributed in plan and elevation. Therefore, the infill panels have 200 been considered and modelled by assuming the two-diagonal truss approach established in Celarec et al. (2012). Also, 201 the concrete slabs present significant stiffness in all the buildings as shown in Fig. 5. Therefore, their effects have 202 been simulated by connecting the RC beams by a rigid diaphragm at each floor level. Then, the masses have been 203 applied at the centre of each floor. 204 205 206 4. Damage Limit States 207 Seismic demand has been defined according to the EC8-1 elastic response spectrum for soil type A and the provisions 208 established in the Portuguese EC8-3 Annex (Instituto Português da Qualidade 2017). As established in this document, 209 the return periods to consider in the assessment of existing buildings are: 73, 308 and 975 years for the damage 210 limitation (DL), the significant damage (SD) and the near-collapse (NC) limit states, respectively. According to each 211 of the limit states, the reference ground acceleration (agR) is then multiplied by a coefficient. Only the response 212 spectrum for the Type 1 seismic action has been taken into account, therefore, the PGA defined for Lisbon (Zone 1.3) 213 is 0.15g (Instituto Português da Qualidade 2017). 214 215 Seismic safety of the buildings has been estimated in terms of the demand/capacity ratio (DCR) for each vertical 216 structural element (columns and walls). The procedures established in Part 3 of Eurocode 8 (EC8-3) (European Union 217 2005) have been followed to determine the limit states. The SD state has been used for the seismic assessment, as 218 required in the EC8-3 Portuguese Annex for residential buildings. It has been assumed that the most critical vertical 219 element, considering a ductile or fragile failure, controls the state of the structure. To do so, the bending and shear 220 capacities for the SD limit state have been obtained through Equation A.1 and A.12 from the EC8-3. Then, as 221 established in the document, the ultimate chord rotation (θu) has been multiplied by 0.75 and 0.58 to determine the 222 failure in columns and walls, respectively. Moreover, the reduction coefficients provided by the EC8-3 have been used 223 to take into account the smooth rebar. 224 225 Several methods were proposed to take into account the degradation of the capacity of buildings over time, i.e. the 226 ageing effects (Berto et al. 2009). They have been considered by means of: i) the reduction of the longitudinal and the 227 transversal rebar section; ii) the reduction of the ultimate rebar deformation; and iii) the degradation of the concrete 228 cover. In this study, the reduction of the ultimate rebar deformation has been neglected due to the negligible values 229 obtained in experimental tests (Celarec et al. 2011). Therefore, only two approaches have been followed: the simplified 230 model to take into account the corrosion of the longitudinal and transverse reinforcement in the exterior (i.e. exposed) 231 elements; and the model to simulate the spalling and degradation of the concrete cover. It has only been assumed that 232 the corrosion influences the diameter of the steel rebar, even though it can also affect the bond stress between the 233 concrete and the steel. 234 235 236 5. Sensitivity Analysis 237 The capacity of each of the models considered in the study has been obtained by means of non-linear static analyses 238 using the OpenSEEs software and handling their outputs in Matlab (The MathWorks Inc. 2018). First, a modal analysis 239 has been carried out to obtain the periods of vibration. Then, a displacement-control integrator has been used to scale 240 the forces to reach a displacement. The analyses have been obtained for the ±X and ±Y directions, and two load 241 patterns have been considered: modal, proportional to the fundamental mode of vibration; and uniform, proportional 242 to the masses of the floors. As in Requena-García-Cruz et al. (2019), only the results corresponding to the modal 243 pattern have been taken into account, since they have been more restrictive. Despite the slight asymmetry in the Y 244 direction of all models, no significant differences have been obtained between the positive and the negative 245 13 configuration: there are four walls in the Y direction and only two in the X direction. In the case of Model B, this 442 influence has been more probable due to the walls’ corrosion capacity and the modal pattern adopted for the 443 distribution of lateral forces. In the X direction, the modal pattern has been more restrictive for the intermediate 444 storeys, which cannot be corroded. In the Y direction, the modal pattern is more demanding for the walls on the ground 445 floor, which are those that can be affected by corrosion. According to Fig. 14. Comparison between Simulation A and 446 Simulation D for Models A and B (only models including walls) in the (a) X and (b) Y directions.Fig. 14, Model B 447 does not comply with the EC8-1 provisions in any of the simulations. Furthermore, considering the different corrosion 448 rates, the difference obtained is about 1% in the X direction for both models and in the Y direction 4% and 3% for 449 Model A and Model B, respectively. 450 451 452 (a) (b) 453 Fig. 13. Normalised pushover curves for Simulation D in the (a) X and (b) Y directions. 454 455 456 (a) 457 458 (b) 459 Fig. 14. Comparison between Simulation A and Simulation D for Models A and B (only models including walls) in 460 the (a) X and (b) Y directions. 461 462 Fig. 15(a) and (b) show the distribution of damage for the initial situation in the vertical elements in the X and Y 463 directions, respectively. Different levels have been determined according to the DCR for the flexural and shear 464 failures. It has been assumed that the significant damage limit state is attained when the storey shear (Vdemand) or the 465 storey chord rotation (θdemand) is equal to or greater than 1 (Vdemand/VR ≥ 1 and θdemand/θum,SD≥1, respectively). For the 466 flexural damage, two more levels have been determined to visualise the elements that almost reached the DCR for the 467 14 SD limit state (θdemand/θy>0.9) and the elements that already exceeded the chord for yielding (θdemand/θy>1). In the case 468 of Model A, most of the walls will be damaged due to flexural failure. In both directions, the walls in the intermediate 469 floors will be considerably damaged. Even in the Y direction, most of them will collapse due to flexural failure. In 470 addition, all the columns will be close to yielding. In the case of Model B, in the X direction, the intermediate walls 471 will collapse due to flexural failure while the ground floor wall will collapse due to shear failure. In the Y direction, 472 only the ground floor elements will be damaged, and some will even collapse due to both flexural and shear failures. 473 Most of the damaged elements are in the ground floor due to the soft storey mechanism. In the case of Model C, in 474 the X direction, the columns of the soft storey floor will reach and exceed the yielding. In the Y direction, some of the 475 columns will be damaged due to flexural yielding and shear failure. It should be mentioned that the ageing effects do 476 not modify the element’s type of collapse. Moreover, it has been verified that, for every single simulation, the types 477 of failure and the more vulnerable elements have not changed compared to the initial situation. 478 479 480 (a) 481 482 (b) 483 Fig. 15. Damage in vertical elements for the initial situation in the X (a) and Y (b) directions. 484 485 Finally, the fragility curves for the most demanding simulation and the worst direction have been obtained for each 486 model. Fig. 16 shows the fragility curves in the Y direction for Models A (b), B (c) and C (d). For Models A and B, 487 the fragility curves have been obtained for Simulation D; while for Model C, Simulation A has been considered. In 488 Fig. 16(a), every curve has been plotted to compare the results. For the following figures, each model’s fragility curve 489 has been presented with an appropriate scale. The curves with the ageing effect have 20% more probability of 490 exceedance for Model A and Model B, and only 0.7% for Model C. These curves lead to the same conclusions as 491 previously mentioned: i) the vulnerability of Model B is considerable; ii) Model A has presented the best seismic 492 behaviour of all the cases; and iii) for Model C, the influence of corrosion has been barely observed. 493 15 Nevertheless, it is worth highlighting that if higher values of dispersion had been adopted for the structures where 494 corrosion was considered, with higher amounts of b ds as the time interval Δt and the levels of the corrosion rate 495 increase, the seismic performance of the RC buildings could become much worse. 496 497 498 (a) (b) 499 500 501 (c) (d) 502 Fig. 16. Fragility curves for the most demanding simulation and for the worst direction. 503 504 505 8. Conclusions 506 This paper has focused on the assessment of the seismic vulnerability of RC buildings in the city of Lisbon through 507 the definition of analytical damage fragility curves. The ageing effects have been taken into account, as well as the 508 presence of smooth rebar. To do so, a sensitivity analysis has been performed by considering the chloride-induced 509 corrosion of the rebar and the degradation of the concrete cover. To illustrate the effects of ageing and the procedure 510 adopted in this study, three RC buildings with masonry infills have been selected as case studies. They were all built 511 between 1960 and 1980, and they are representative of the current building stock of Lisbon. 512 513 Results have shown that the number of walls and the orientation of the columns are decisive in determining the 514 capacity of RC buildings. In addition, this is related to the premature brittle shear collapse, as was clearly identified 515 at the beginning of the pushover curves in all cases. Therefore, a retrofitting scheme focused on solving the shear 516 problems should be taken into account to improve the seismic performance of these RC buildings. Besides, the 517 influence of the infills has been more critical in the case of the model without walls, i.e. in the framed building. This 518 is because, for the other models, the buildings’ behaviour basically depends on the shear walls. Concerning the models’ 519 behaviour, Model B has presented the worst behaviour, followed by Model A and then C. This is not only due to the 520 structural configuration of the buildings, but also due to the total number of elements exposed to the exterior 521 environment and therefore affected by ageing. 522 523 By considering the ageing effects, the seismic performance of these buildings can worsen by up to 20%, as concluded 524 by the fragility analysis. Among the aspects analysed, it has been observed that concrete strength degradation has 525 significantly reduced the capacity of all the models when compared to the reduction of the rebar diameter, i.e. steel 526 16 corrosion approach. Moreover, in the hypothesis of the steel corrosion approach, corrosion rate has had more influence 527 than the time of exposure. In conclusion, ageing affects the seismic behaviour of RC structures, increasing the 528 vulnerability of these buildings. 529 530 531 Acknowledgments 532 The first author would like to acknowledge the financial support of Fundação para a Ciência e a Tecnologia (FCT, 533 Ministério da Educação e Ciência, Portugal) through the scholarship BL105/2019 by the FCT Research Program: 534 MitRisk - Framework for seismic risk reduction resorting to cost-effective retrofitting solutions, POCI-01-01456- 535 Feder-031865. In addition, the scholarship provided by the VI-PPI of the University of Seville is acknowledged. 536 537 538 References 539 Al-Harthy AS, Stewart MG, Mullard J (2011) Concrete cover cracking caused by steel reinforcement corrosion. 540 63:655–667. https://doi.org/10.1680/macr.2011.63.9.655 541 Amaro-Mellado JL, Morales-Esteban A, Asencio-Cortés G, Martínez-Álvarez F (2017a) Comparing seismic 542 parameters for different source zone models in the Iberian Peninsula. Tectonophysics 717:449–472. 543 https://doi.org/10.1016/J.TECTO.2017.08.032 544 Amaro-Mellado JL, Morales-Esteban A, Martínez-Álvarez F (2017b) Mapping of seismic parameters of the Iberian 545 Peninsula by means of a geographic information system. Cent Eur J Oper Res. https://doi.org/10.1007/s10100- 546 017-0506-7 547 Arteta CA, Carrillo J, Archbold J, et al (2019) Response of Mid-Rise Reinforced Concrete Frame Buildings to the 548 2017 Puebla Earthquake. Earthq Spectra 35:1763–1793. https://doi.org/10.1193/061218EQS144M 549 Berto L, Vitaliani R, Saetta A, Simioni P (2009) Seismic assessment of existing RC structures affected by degradation 550 phenomena. Struct Saf 31:284–297. https://doi.org/10.1016/j.strusafe.2008.09.006 551 Campos Costa A, Sousa ML, Carvalho A (2008) Seismic Zonation for Portuguese National Annex of Eurocode 8. 8– 552 15 553 Caruso C (2019) Seismic retrofit options for an old RC wall-frame building in Lisbon: impact on loss estimation and 554 cost-benefit analysis. Istituto Técnico Superior, Universidade de Lisboa, Portuga 555 Caruso C, Bento R, Castro JM (2019a) A contribution to the seismic performance and loss assessment of old RC wall- 556 frame buildings. Eng Struct 197:109369. https://doi.org/10.1016/j.engstruct.2019.109369 557 Caruso C, Bento R, Castro JM (2019b) Seismic risk assessment of an old RC frame-wall building. In: Symposium 558 Guimarães 2019 Towards a Resilient Built Environment–Risk and Asset Managem (IABSE2019). Guimarães, 559 Portugal, pp 1480–1487 560 Caruso C, Bento R, Sousa R, Correia AA (2019c) Modelling strain penetration effects in RC walls with smooth steel 561 bars. Mag Concr Res 71:894–906. https://doi.org/10.1680/jmacr.18.00052 562 Celarec D, Ricci P, Dolšek M (2012) The sensitivity of seismic response parameters to the uncertain modelling 563 variables of masonry-infilled reinforced concrete frames. Eng Struct 35:165–177. 564 https://doi.org/10.1016/j.engstruct.2011.11.007 565 Celarec D, Vamvatsikos D, Dolšek M (2011) Simplified estimation of seismic risk for reinforced concrete buildings 566 with consideration of corrosion over time. Bull Earthq Eng 9:1137–1155. https://doi.org/10.1007/s10518-010- 567 9241-3 568 Diário do Governo (1958) Regulamento de Segurança das Construções Contra os Sismos (RSCCS), Decreto-Lei 569 n◦41658, Lisbon, Portugal [In Portuguese] 570 Diário do Governo (1961) Regulamento de Solicitações em Edifício e Pontes (RSEP), Decreto-Lei n. 44041, Lisbon, 571 Portugal [In Portuguese]. 572 Diário do Governo (1983) Regulamento de Segurança e Acções para Estruturas de Edifícios e Pontes (RSA), Decreto- 573 Lein. 235/83, Lisbon, Portugal [In Portuguese] 574 Dolšek M, Fajfar P (2005) Simplified non-linear seismic analysis of infilled reinforced concrete frames. Earthq Eng 575 Struct Dyn 34:49–66. https://doi.org/10.1002/eqe.411 576 Du YG, Clark LA, Chan AHC (2005) Residual capacity of corroded reinforcing bars. Mag Concr Res 57:135–147. 577 https://doi.org/10.1680/macr.2005.57.3.135 578 Earthquake Engineering Research Institute (2020) Learning from Earthquakes Reconnaissance Archive. 579 https://www.eeri.org/projects/learning-from-earthquakes-lfe/lfe-reconnaissance-archive/ 580 Environmental Systems Research Institute (ESRI) (2011) ArcGIS Desktop: Release 10 581 European Union (2004) Eurocode 8: Design of structures for earthquake resistance. Part 1: General rules, seismic 582 17 actions and rules for buildings. Belgium 583 European Union (2005) Eurocode-8: Design of structures for earthquake resistance. Part 3: Assessment and retrofitting 584 of buildings. Belgium 585 Filippou FE, Popov EP, Bertero V V (1983) Effects of bond deterioration on hysteretic behavior of reinforced concrete 586 joints. Berkeley, California 587 Instituto Nacional de Estatística (INE) (2012) “Censos 2011 Resultados Definitivos - Portugal” , I.P. Lisboa [In 588 Portuguese]. http://censos.ine.pt/ 589 Instituto Português da Qualidade (2017) Eurocódigo 8: Projeto de estruturas para resisteência aos sismos. Parte 3: 590 Avaliaçao e reabilitaçao de edificios 591 Kam WY, Pampanin S, Elwood K (2011) Seismic performance of reinforced concrete buildings in the 22 February 592 Christchurch (Lyttelton) earthquake. Bull New Zeal Soc Earthq Eng 44:239–278. 593 https://doi.org/10.5459/bnzsee.44.4.239-278 594 Lundgren K (2007) Effect of corrosion on the bond between steel and concrete: an overview. Mag Concr Res 59:447– 595 461. https://doi.org/10.1680/macr.2007.59.6.447 596 Maio R, Tsionis G (2016) Seismic fragility curves for the European building stock: Review and evaluation of 597 analytical fragility curves 598 McKenna F, Fenves GL, Scott MH (2000) OpenSees: Open system for earthquake engineering simulation 599 Milosevic J, Cattari S, Bento R (2018) Sensitivity analysis of the seismic performance of ancient mixed masonry-RC 600 buildings in Lisbon. Int J Mason Res Innov 3:108–154. https://doi.org/10.1504/IJMRI.2018.092459 601 Milosevic J, Cattari S, Bento R (2019) Definition of fragility curves through nonlinear static analyses: procedure and 602 application to a mixed masonry-RC building stock. Bull Earthq Eng. https://doi.org/10.1007/s10518-019- 603 00694-1 604 National Institute of Building Sciences and Federal Emergency Management Agency (NIBS and FEMA) (2003) 605 Multi-hazard Loss Estimation Methodology, Earthquake Model, HAZUS MH Technical Manual, Federal 606 Emergency Management Agency. Washington, D. C. 607 Pantazopoulou SJ, Papoulia KD (2001) Modeling Cover-Cracking due to Reinforcement Corrosion in RC Structures. 608 J Eng Mech 127:342–351. https://doi.org/10.1061/(ASCE)0733-9399(2001)127:4(342) 609 Popovics S (1973) A numerical approach to the complete stress-strain curve of concrete. Cem Concr Res 3:583–599. 610 https://doi.org/10.1016/0008-8846(73)90096-3 611 Requena-García-Cruz MV, Morales-Esteban A, Durand-Neyra P, Estêvão JMC (2019) An index-based method for 612 evaluating seismic retrofitting techniques. Application to a reinforced concrete primary school in Huelva. PLoS 613 One 14:e0215120. https://doi.org/10.1371/journal.pone.0215120 614 Rossetto T, Elnashai A (2005) A new analytical procedure for the derivation of displacement-based vulnerability 615 curves for populations of RC structures. Eng Struct 27:397–409. https://doi.org/10.1016/j.engstruct.2004.11.002 616 Ruiz-Pinilla JG, Adam JM, Pérez-Cárcel R, et al (2016) Learning from RC building structures damaged by the 617 earthquake in Lorca, Spain, in 2011. Eng Fail Anal 68:76–86. 618 https://doi.org/10.1016/J.ENGFAILANAL.2016.05.013 619 Scawthorn C, Charleson A, Allen L, et al (2013) GEM global earthquake model GEM Building Taxonomy Version 620 2.0 exposure modelling 621 Silva V, Crowley H, Varum H, et al (2014) Investigation of the characteristics of Portuguese regular moment-frame 622 RC buildings and development of a vulnerability model. Bull Earthq Eng 13:1455–1490. 623 https://doi.org/10.1007/s10518-014-9669-y 624 Simões AG, Bento R, Lagomarsino S, et al (2019a) Seismic assessment of nineteenth and twentieth centuries URM 625 buildings in Lisbon: structural features and derivation of fragility curves. Bull Earthq Eng. 626 https://doi.org/10.1007/s10518-019-00618-z 627 Simões AG, Bento R, Lagomarsino S, et al (2019b) Fragility Functions for Tall URM Buildings around Early 20th 628 Century in Lisbon. Part 1: Methodology and Application at Building Level. Int J Archit Herit 1–24. 629 https://doi.org/10.1080/15583058.2019.1618974 630 The MathWorks Inc. (2018) MATLAB and Statistics Toolbox Release 2018b 631 Tsionis G, Papailia A, Fardis M (2011) Analytical Fragility Functions for Masonry Buildings and Building Aggregates 632 – UPAT methodology 633 Yalciner H, Sensoy S, Eren O (2015) Seismic Performance Assessment of a Corroded 50-Year-Old Reinforced 634 Concrete Building. J Struct Eng 141:05015001. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001263 635 636