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Evaluation of post-earthquake fire capacity of reinforced concrete elements
Soil Dynamics and Earthquake Engineering 128 (2020) 105900
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Soil Dynamics and Earthquake Engineering journal homepage: http://www.elsevier.com/locate/soildyn
Evaluation of post-earthquake fire capacity of reinforced concrete elements Hugo Vitorino a, Hugo Rodrigues b, *, Carlos Couto c a
Escola Superior de Tecnologia e Gest~ ao, Instituto Polit�ecnico de Leiria, Leiria, Portugal RISCO, Escola Superior de Tecnologia e Gest~ ao, Instituto Polit�ecnico de Leiria, Departamento de Engenharia Civil, Leiria, Portugal c RISCO, Departamento de Engenharia Civil, Universidade de Aveiro, Portugal b
A R T I C L E I N F O
A B S T R A C T
Keywords: Fire after earthquake Fire safety assessment Fire resistance Reinforced concrete structure Earthquake damage Seismic assessment
Large earthquakes may cause a chain of events, and one of which can be fire after an earthquake. The effects of fire after earthquake on urban areas can be even worse than the effects of the earthquake itself. Buildings are not adequately designed for fire after an earthquake since most standards ignore that possibility. The aim of the work is to evaluate the consequences of the damage introduced due to the seismic events on the fire resistance of reinforced concrete elements. Several numerical analyses were performed to reinforce concrete elements using the program SAFIR, considering the thermal and mechanical analysis of the structure. The main variables in the analysis were the type of damage in the elements and the type of loads. The thermal analysis was performed using the standard fire curve ISO 834. The results show that the damage imposed by earthquake on reinforced concrete structures reduces the fire resistance, especially if the cover of the elements is removed and the rein forcement is exposed to fire.
1. Introduction There is historical evidence that confirms the possible occurrence of fire after an earthquake event in the built urban environment. The consequences lead to an increase in the losses of lives and property. There are three main combined aspects that under normal circumstances allow a response to fires in buildings, both active and passive fire pro tection systems and manual fire-fighting by a fire brigade. It is necessary to have the availability of water supplies due to the difficulty of extin guishing the fire without water. The water distribution systems are susceptible to earthquake damage and failures are likely. The earth quakes can cause structural and non-structural damage which leads to failure of the passive protection systems, possibly creating openings that increase the ventilation in the compartments. These openings allow the movement of smoke and hot gases to different areas of the building. The active protection systems, such as detection, alarm and suppression systems, can also be damaged after an earthquake, leading to defective functioning, which can cause unnoticed ignitions resulting in larger fires that are more difficult to extinguish. It is possible that after a major earthquake the fire teams are faced with several problems that prevent them from rapidly proceeding the rescues and the put out of fires. Those problems can be related to reporting delays, impassable access routes,
traffic jams, loss of operational vehicles and loss of equipment. The firemen’s presence will be delayed due to the possible appearance of multiple simultaneous ignitions and insufficient resources for fire fighting [1,2]. After an earthquake, and given the higher number of occurrences, the rescue teams will be very solicited, and the response times will consequently be higher. This situation together with the eventual reduction of the fire resistance of the damaged reinforced concrete elements can lead to the loss of lives and structures. Thus, a better understanding of the fire behavior following an earthquake, particularly in major structures, is important so that it is possible to implement some prescriptive measures that can ensure better perfor mance of structures in those circumstances. 2. Post-earthquake fire – brief overview 2.1. Earthquake damages in buildings Earthquakes can cause different types of structural and nonstructural damage in buildings. In common reinforced concrete (RC) infilled buildings, the masonry walls normally are not considered as structural elements [3]. The masonry bricks usually have brittle behavior and can modify the structural response of the building by
* Corresponding author. Civil Engineering Department School of Technology and Management, Polytechnic Institute of Leiria, Campus 2 - Morro do Lena - Alto do Vieiro, Apartado, 4163-2411-901, Leiria, Portugal. E-mail addresses: [email protected] (H. Vitorino), [email protected] (H. Rodrigues), [email protected] (C. Couto). https://doi.org/10.1016/j.soildyn.2019.105900 Received 23 May 2019; Received in revised form 7 October 2019; Accepted 10 October 2019 Available online 18 October 2019 0267-7261/© 2019 Elsevier Ltd. All rights reserved.
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instance, the likelihood of several simultaneous ignitions, detection delays, reporting delays and water supplies reduced or exhausted. The widespread effects of earthquakes can generate several simultaneous ignitions. The post-earthquake fires have the opportunity to grow and spread and are more difficult to extinguish when compared to fires that happen at any other time. The difficulty to extinguish the fire arises from the insufficient fire service resources after an earthquake. Damage in detectors or distracted observers can lead to detection delays but the time of discovery of post-earthquake fire is usually not different from the time of discovery of any other fire. The failure of communications sys tems and the overload from high usage levels lead to reporting delays [1, 7]. The main ignition sources of post-earthquake fire are electrical or gas-related. Other sources can also be, open flames, hot surfaces, exothermic chemical reactions from spilled chemicals and fires inten tionally lit [1,2]. The earthquake shaking can stress the electrical wiring which leads to short-circuits that can cause ignitions. The earthquake shaking can also cause damage to gas appliances and gas supply lines which can be ignited by electrical sources or flames present in the ap pliances. Certain electrical appliances (e.g. cookers, gas-fueled water heaters, and solid-fueled burners) that are not properly restrained can topple and their residual heat may initiate fires if brought in contact with combustible materials. The restoration of electrical and gas sup plies to damaged appliances and wiring can also cause fires. If some preventive practices and installation procedures are performed it is possible to reduce the fire risk after a major earthquake. The main ac tions to reduce the post-earthquake fire sources are the education of the population to minimize the risk of fire and the adequate design of the gas networks including an automatic valve that reduces the gas quantities in case of damage in the network. These automatic valves are placed in the pipe after the gas meter; with these, after an earthquake, the amount of gas inside the house is reduced. The electric power networks usually have a security device that shuts off the network for several seconds after the beginning of a big earthquake [1]. The effects of fire after an earthquake on the RC buildings are not very well known. In the past years, there were developed several numerical and experimental studies regarding the post-earthquake fire to be able to better understand the phenomenon. Some experimental studies developed in frames showed that using a standard fire curve may not be very accurate since different elements can have different temperature profiles [8–11]. In the same studies, the cracks that appeared in the different elements of the analyzed structure indicate that the detailing of reinforcement has consequences on the global behavior of the structure when exposed to fire. In the majority of the structural members, the temperatures in the RC frame with nonductile detailing were much higher than those with ductile detailing [10,11]. It was observed that the brick infill walls provide insulation to the RC structural elements and slow the trans mission of heat to these elements. This shows the beneficial effect that the masonry walls have on the columns and beams integrated into the masonry walls, and this beneficial effect should be considered while designing the columns and beams [8]. The position of the openings in the compartments and the resulting movement of fire plume and hot gases have also an influence in terms of the evolution of temperatures in the structural sections. This situation may or may not lead to an overlap between the locations of the damage caused by the earthquake and the damage caused by the fire [9]. Some numerical and experimental studies were also developed regarding the fire resistance of CFRP-strengthened reinforced concrete elements [12,13]. The results show that the fire resistance of the specimens subjected to life safety (LS) and collapse prevention (CP) damage levels are about 32 and 15 min and for the CFRP-strengthened specimen is about 43 and 23 min, respectively. This solution represents a 25% increase at LS level and 35% increase at the CP level [12]. Also, regarding the use of CFRP, using this solution to relo cate plastic hinges of the beams away from the columns improve the post-earthquake fire resistance of the frames [14]. Beyond the research of post-earthquake fire on RC buildings, there are also works developed regarding the post-earthquake fire on steel structures. In some works,
changing the structural stiffness, attracting forces to structural elements not designed to resist such forces. This situation can be avoided with more ductile masonry walls. There is also the structural damage in the RC elements like beams, columns, walls, slabs and even foundations. To assure proper structural behavior under an earthquake action it is important to have structural elements with proper strength, stiffness, and ductility but it is also important that the beam-column joints are well connected and with proper ductile behavior. The poor detailing of the reinforcing steel is a common deficit in the existing structures, especially on old reinforced concrete structures, designed without seismic concerns. There are several cases reported related to the poor detail, namely related to the confinement reinforcement not correctly placed at the beam-column joints, deficiency of transverse reinforce ment in the columns with wide spacing of the ties and poor confinement of the concrete core. The short lap splices and incorrect end hook angle are also examples of poor detailing of the reinforcing steel. The use of smooth reinforcing bar that creates a weaker bond between concrete and steel can also be observed in some cases [4]. There are other cases that lead to a poor behavior of the structures to the seismic action, such as, poor concrete quality, damage related with strong beam-weak column, soft stories at the first-floor level, and defects in the workmanship [5,6]. 2.2. Fire action Fire is a combustion characterized by the appearance, conservation and propagation of flame, heat release, gas emission, and smoke production. During the natural development of a fire, from the beginning until the extinction, there are several important stages, namely: ignition, growth, flashover, burning, and decay [8]. The fire evolution from the ignition until the flashover depends on several factors, some related to the fuel and oxidizer, others related to the local characteristics of the place where the fire develops. The main factors are: (i) type and quantity of available fuel, (ii) quantity of oxidizer (oxygen) available, that de pends on the compartment ventilation conditions and the dimensions of the openings, (iii) compartment geometry, (iv) type of pavements, walls and coatings, and (v) atmospheric conditions (temperature, wind di rection, etc). After the ignition, the fire starts to develop according to the fuel available in the place, releasing heat that leads to the temperature increase. In this phase, the fire can conclude due to the lack of fuel material (fire controlled by the fuel), or by oxidizer deficit (fire controlled by ventilation). If there is sufficient fuel and oxidizer and no outside intervention, the temperature in the compartment continuous to increase. This situation leads to the ignition of materials that until that moment had not initiated the combustion process yet. The flashover establishes the transition to the burning phase. The burning phase takes place when all the fuel in the compartment is involved in the fire. The temperature inside a compartment where a fire is developing is not uniform, near the ceiling the temperature is higher when compared with the flooring and lower places of the walls. The hot gases produced during the fire go to the higher part of the compartment and the flames elongate towards the ceiling [1]. Not all the fires have a complete development, due to direct intervention (firefighters’ action or auto matic extinguishing systems, for example), or due to the compartment characteristics (lack of oxidizer, for example), the fire can be extin guished before reaching the burning phase [8]. 2.3. Post-earthquake fire The urban fires will normally follow several stages, ignition, growth, detection, report, response, suppression activities and extinguishment (due to the suppression activities or due to the exhaustion of the fuel). The development of post-earthquake fires will be similar to fires that occur at any other time. The main difference is related to the response of rescue teams, that will probably be disrupted during and after a major earthquake. The disruption can happen due to several factors, for 2
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the focus is the analysis of the behavior of steel frames to post-earthquake fire [15]. There are studies where the aim is to analyze the impact that the earthquake has on the passive fire protection of the steel structures. Some materials that are used as passive fire protection have a brittle behavior and suffer damage due to the seismic action, leading to a lower fire resistance of the steel structures [16,17]. There is also research regarding the behavior of the joints and connections of the steel frames. The results show that severe damage to the connections lead to reduced fire resistance capacities [18,19].
structure is calculated, based on the geometry, support conditions, loads and the strength of the materials. The increase in temperature changes the strength of the materials and leads to thermal elongation. The reduction of the strength and stiffness combined with the thermal elongation leads to an increase in the displacements until the collapse of the structure. The mechanical behavior is directly influenced by the loss of strength, stiffness and thermal elongation which is the result of the temperature increase. In SAFIR, the numerical analysis will stop at the time specified by the user (240 min), or if it finds numerical problems at the material level, or when it cannot converge to a state of equilibrium [25,26]. The first procedure performed was the creation of different sections for the beam and column, with different types of damage and number of fire frontiers. A thermal analysis was developed in the sections to determine the influence of the damage and fire frontiers in the tem perature of the reinforcing steel bars. Subsequently, the different sec tions were incorporate in the RC elements to be able to develop a structural analysis of the beams and columns. The materials properties used in the analysis of the beam and column are the same. The damage in the sections was simulated by reducing the thickness of the cover. The damage D0/D1 corresponds to an intact section or a section with minor cracks, the damage D2 corresponds to the slight damage with some concrete spalling, traduced in the removal of the exterior fibers in the numerical model and damage D3 corresponds major damage level, corresponding to the large concrete spalling, traduced in the removal of the entire cover, leaving the reinforcement steel exposed in the nu merical model. In the beam cross-section, the damage was considered in the bottom and sides and in the columns the damage is considered in all the column cross-section sides. It was considered that the damages represented in the R.C elements (D0/D1, D2 and D3) correspond to the structural performance levels presented in FEMA356. In the Immediate Occupancy (IO) level is observed minor damage in the structural ele ments, which in the following analysis corresponds to damage D0/D1. In the Life Safety (LS) level is observed extensive damage to beams and spalling of cover and shear cracking for ductile columns, which in the following analysis corresponds to damage D2. Regarding the collapse prevention (CP) level, it is observed extensive spalling in columns and beams, which corresponds to damage D3 in the following analysis [27, 28]. The fire curve used was ISO 834 [29]. For the section of the beams, the fire frontiers were considered on the bottom and sides. For the section of the columns, it was considered three different dispositions of fire frontiers, with one, three and four fire frontiers. The standard fire curve ISO 834 represents the time-temperature evolution during an actual fire, from flashover to the full development of the fire. Fires in buildings have a heating phase followed by a cooling phase, which is not represented in the standard fire curve ISO 834. The mechanical prop erties of R.C structures after the fire can be lower or higher than during the fire. Usually, the load-bearing capacity of a structure continues to decrease in the cooling phase, reaching the lowest load-bearing capacity followed by a partial or complete recovery when the structure is back to ambient temperature. This situation brings a threat that is not consid ered when the standard fire curve ISO 834 is used, the possibility of structural failure a period of time after the maximum temperature in the compartment [30,31]. This situation is important and deserves more study to be able to better understand the materials and structures behavior under decreasing temperatures. However, this aspect was not considered in the following numerical analysis, and the collapse of the R. C structural elements coincide with the highest temperature. In Table 1 are represented all the material properties for the RC el ements used in the numerical analysis. The concrete compression strength and the reinforcing steel yield strength evolution with tem perature will be according to EN 1992-1-2 [32]. There are several con crete parameters introduced in the model, the aggregate type (siliceous or calcareous), Poisson’s ratio, compressive strength and tensile strength. It is also necessary to indicate in the model if the transient creep is treated implicitly or explicitly. The implicit formulation
2.4. Review of historical data Throughout history is possible to find several examples of postearthquake fires, for instance, the Hokkaido Nansei-Oki earthquake, Northern Japan in 1993. In this earthquake 246 people were dead or missing, 190 houses and buildings were consumed by fire over an 11-h period [17]. The town of Aonae was destroyed by conflagration following earthquake and tsunami. Building-to-building fire spread was accelerated by externally stored propane and kerosene tanks used for cooking and heating. Another example is the 1994 earthquake in Northridge, San Fernando Valley in Southern California. This earth quake had 58 fatalities (none from fire) and 1500 serious injuries. There were 30–50 significant fires initially following the earthquake, and after less than 8 h the total number of fires was about 110. The principal cause was gas leaks from natural gas pipelines and appliances. The restoration of gas and power after a few days caused a significant number of fires [1, 2]. There is also a different perspective for the post-earthquake fire when the fire does not start immediately after the earthquake. The Great East Japan Earthquake, which occurred on 11 March 2011 was one of the largest earthquakes in recent Japanese history and resulted in the gen eration of large amounts of disaster waste. It was necessary the creation of outdoor storage areas to deposit disaster waste. In these areas, in the Tohoku region, more than 40 fires occurred. One probable cause of the fire is thought to have been the heat generated by fermentation of mi croorganisms. The microorganisms can thrive easily in those conditions, and the heat created can lead to spontaneous ignition. The materials deposited in the outdoor storage areas have a huge influence on this process, it is expected that the presence of wood will most likely lead to more ignitions than the presence of concrete, for instance. A study performed in this topic revealed that the heat generated during fermentation of wood chips and rotten tatami was most likely the trigger of the spontaneous ignition. This situation only serves as an example that the post-earthquake fires can appear from different causes and maybe in places where not initially expected [20,21]. 3. Research methodology The numerical analysis was developed with SAFIR, a computer program for the analysis of structures under ambient temperature and elevated temperature conditions. The program is based on the Finite Element Method (FEM) and can be used to study the behavior of one, two and three-dimensional structures. SAFIR can perform thermal and mechanical analysis. They are performed separately and subsequently. The temperature distribution will deeply influence the mechanical response, but the opposite is not currently handled by the software. There is no influence of the cracking of the concrete determined in the analysis of the thermal conductivity that is used in the thermal analysis [22,23]. Some studies showed that there is no significant increase or decrease in the thermal propagation through concrete with tensile cracking where the cracks are up to the order of 101 mm at the heated surface. This situation shows that performing sequentially thermal then me chanical analysis of heated structures is a valid approach [24]. The gas temperatures produced by the fire are entered as input data in the SAFIR. With these, SAFIR will calculate the evolution of the temperatures in the structure. After that, the mechanical behavior of the 3
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Table 1 – Concrete and reinforcing steel properties used in the numerical analysis. Concrete properties Concrete model Specific mass of concrete Water content Coefficient of convection on heated surfaces Coefficient of convection on unheated surfaces Emissivity Compression strength Tensile strength Poisson’s ratio Reinforcing Steel properties Steel model Modulus of elasticity Yield strength Poisson’s ratio Coefficient of convection on heated surfaces Coefficient of convection on unheated surfaces Emissivity Reinforcing Steel diameter
rho w hh hc
ε
fc fct v
Es fy v hh hc
ε Φs
Siliceous aggregate [32] 2300 kg/m3 46 kg/m3 25 W/m2K 4 W/m2K 0,7 30 MPa Zero 0,2
Hot rolled, class B [32,36] 210 GPa 500 MPa 0,3 25 W/m2K 4 W/m2K 0,7 25 mm
Fig. 2. – Beam section.
different types of damage can be seen in Fig. 3. The damage D0/D1 corresponds to an intact section or a section with small cracks, the damage D2 corresponds to the removal of the exterior fibers and damage D3 corresponds to the removal of the entire cover, leaving the rein forcement visible. The fibers on the top side were not removed. This assumption is consistent with the expected earthquake damage. There is also no fire frontier on the top side of the beam, it was considered that the fire develops below the beam (see Fig. 3). There were developed three different beams in SAFIR to better un derstand the fire after earthquake phenomenon. Table 2 shows the description and the location of the damage in each beam. In beam A1 all the 60 elements have the section with damage D0/D1, and in beams A2 and A3 the damage is in the 6 elements closer to the fixed supports, simulating the earthquake damage the expected beam areas. All the elements not mentioned in Table 2 have a section with damage D0/D1.
corresponds to the model in the Eurocode. The explicit formulation is a refinement of the Eurocode that is calibrated to yield the same response as the Eurocode model but is also able to consider the non-reversibility of transient creep strain when the stress and/or temperature is decreasing [33,34]. The beam element was used in the FEM simulation. The position of the beam element is defined with three nodes, two end nodes and a node that defines the position of the local y-axis of the beam. A fiber model is used to define the geometry of the cross-section. It is possible to create composite sections by defining different materials in different fibers. There are some assumptions considered in the beam element: the cross-section remains plane under bending moments, the plasticization is only considered in the longitudinal direction of the member and the non-uniform torsion is considered [35].
4.2. Thermal analysis In Figs. 4 and 5 are presented the evolution of the temperature in the beam reinforcing steel bars. The evolution of the temperature in the steel bars is compared with the fire curve ISO 834. For the section with damage D0/D1 and D2, the bottom steel bars present a higher temper ature. For the section with damage D3, with the steel bars directly exposed to the fire, the temperature of the bottom and top steel bars is the same. In the section with damage D3, the temperature of the steel bars is similar to the temperature of the fire curve ISO 834. In Figs. 4 and 5 are also represented three temperature lines (500, 600 and 700 � C) that can be associated with the effective yield strength (k) of the rein forcing steel bars [32]. These temperature lines allow a comparison between the sections with different damage. For example, in Fig. 4, the reinforcement steel bar reaches a temperature of 700 � C in 180 min for the section with damage D0/D1, 90 min for the section with damage D2 and about 15 min for the section with damage D3. This comparison shows the huge impact of the damage on the evolution of the temper atures in the sections.
4. Post-earthquake fire analysis on RC beams 4.1. Introduction The schematic of the beam used in the numerical analysis is repre sented in Fig. 1. The beam has fixed supports and a continuous load of 45 kN/m is applied. It is also represented the characterization of the finite element mesh used in SAFIR. The beam with 6 m was divided into 60 elements, each element with 10 cm. In Fig. 2 is represented the section of the beam without damage and the location of the reinforcement (4Φ25). There were considered three different beam sections, each one with different simulated damage. The
Fig. 1. – Beam with fixed supports: (a) Beam length and load applied; (b) Characterization of the finite element mesh.
Fig. 3. – Different sections of the beam according to the type of damage. The fire frontiers are also represented. 4
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reaches higher axial forces sooner than the beam with damage D2 and the beam with damage D2 reaches higher axial forces sooner than the beam with damage D0/D1. One possible explanation for this is related to the thermal elongation of the steel bars. The effect of the temperature happens earlier in the beam with damage D3 because the steel bars are exposed. For the other beams, the idea is the same, the steel bars in the beam A1 are more protected than the steel bars in the beam A2 and that leads to the later thermal elongation of the steel bars. Since the beams have fixed supports there is no horizontal displacement in the beam. This type of supports leads to higher axial forces because of the total horizontal restraint. It is expected that these beams inserted in a struc ture with more flexible supports will have lower axial forces compared to the ones obtained here. For the beam A3, the axial forces increase until the collapse of the beam. For the beams A1 and A2 the axial force increases until around 60 min and then starts to decrease. The decrease in the axial force happens due to the deterioration of the materials.
Table 2 – Location of the damage in the beam. Beam
Damage
Elements
Distance
A1 A2 A3
D0/D1 D2 D3
All 1 to 6 and 55 to 60 1 to 6 and 55 to 60
6m 0,6 m 0,6 m
4.5. Moments In Fig. 7 is represented the evolution of the mid-span moments in the beams. In the first minutes, there is a flexural restraint to the rotation created by the thermal gradient in the section of the beam. After that, there is a deterioration of the materials and the moments start to redistribute towards the mid-span of the beam. The moments in the mid-span of the beam start to increase and the moments in the supports decrease. The deterioration that leads to the redistribution of the mo ments happens first in the beam with damage D3, followed by the beam with damage D2 and followed by the beam with damage D0/D1. In Fig. 8 is represented the evolution of the moments in the supports of the beams. The evolution of the moments in the supports follows the same trend of the moments in the mid-span of the beam. In the first minutes, the moments increase due to the thermal gradient in the section of the beam and then due to the deterioration of the material the mo ments decrease.
Fig. 4. – Temperature evolution in the beams bottom reinforcing steel bars.
4.6. Mid-span displacement In Fig. 9 is represented the evolution of the displacements in the midspan of the beams. The higher vertical displacement observed is in the beam A1, -36,55 mm at 240 min. The highest displacement observed in beams A2 and A3 is at the time of collapse of the beams. The displace ment in beam A2 is 16,5 mm and the displacement in beam A3 is 10,49 mm.
Fig. 5. – Temperature evolution in the beams top reinforcing steel bars.
4.3. Time until conventional collapse
5. Post-earthquake fire analysis on RC columns under pure axial load
Table 3 represents the time until the collapse of the beams. The re sults show that the damage reduces the time until the collapse of the beam. For beam A1 there is not collapse until 240 min. The differences between the beams regarding the time until the collapse is not small. The difference between beam A2 and A3 is almost 60 min. The time until the collapse of beam A2 is more than double the time until the collapse of the beam A3.
5.1. Introduction The schematic of the column used in the numerical analysis is rep resented in Fig. 10. The column has one fixed support and a vertical
4.4. Axial force In Fig. 6 is represented the evolution of the axial forces in the beams. The evolution of the axial forces in the beams is similar until about 30 min. However, there is a slight difference, the beam with damage D3 Table 3 – Time until the collapse of the beam. Beam
Damage
Time (min)
A1 A2 A3
D0/D1 D2 D3
240,0 106,8 49,2
Fig. 6. Evolution of the axial force in the beams. 5
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Fig. 10. – Column with fixed support: (a) Column length and load applied; (b) Characterization of the finite element mesh.
Fig. 7. Evolution of the mid-span moments in the beams.
damage, fire frontiers and level of initial load are represented in (Fig. 12. In Fig. 10 b) the column is divided into 10 elements. Elements 1 and 2 are the elements where different types of damage will be considered. The other elements (3–10) will have always sections with damage D0/ D1, once it is assumed that the earthquake damage in typical columns and beams is concentrated in the extremities of RC elements. Later, when the damage of a column is mentioned is always the damage in elements 1 and 2 because the damage in elements 3 to 10 will always be damage D0/D1. 5.2. Thermal analysis In Figs. 13 and 14 it is represented the temperature evolution of the reinforcing steel bars. Fig. 13 represents the reinforcing steel bars in the corners of the sectionand Fig. 14 represents the reinforcing steel bars in the middle. As is possible to see in Fig. 12 each reinforcing steel bar is constituted by only one fiber. Each fiber has four different nodes and each node has different temperatures. The temperature considered to develop the graphs in Figs. 13 and 14 was the higher one of those four nodes. The difference between the temperatures in those four nodes is almost negligible and it was considered enough to analyze only the higher value. By analyzing the graphs in Figs. 13 and 14 is possible to see that the temperature in the corner reinforcing steel bars is higher when compared with the reinforcing steel bars in the middle, and this is true for all types of damage. The fire curve ISO 834 is represented in the graphs to serve as a comparison between the results. For the reinforcing steel bars in the corner, for section with damage D3, the evolution of the temperature is very similar to the fire curve ISO 834, especially about 90 min after the beginning of the fire curve. In each graph is also showed three different temperature lines that are associated with the reducing factors presented in the EN 1992-1-2 [32]. These values are helpful because allow the comparison between the effective yield strength in each steel bar for different types of damage. For damage D0/D1 it takes about 120 min for the steel bars to reach a temperature of 600 � C, it takes about 60 min for the section with damage D2 and about 20 min for the section with damage D3. For the steel bars in the middle it takes about 240 min for the steel bars in the section with damage D0/D1 to reach a temperature of 600 � C, it takes about 120 min for the section with
Fig. 8. – Evolution of the moments in the supports in the beams.
Fig. 9. – Evolution of displacement in the mid-span of the beam.
point load is applied. It is also represented the characterization of the finite element mesh used in SAFIR. The column was divided into 10 elements, each element with 15 cm. There were developed several nu merical analyses regarding the column. The main differences in the analysis are related to the damage, position of the fire frontiers and load applied. In Fig. 11 is represented the section of the column without damage, it also shows the location of the reinforcement (8Φ25). The different types of damage can be seen in Fig. 12. Although the fire frontiers can be different, the damage is applied in all the surfaces of the concrete section. All of the sections of columns developed, with different types of
Fig. 11. – Column section. 6
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Fig. 12. – Numerical models for damage D0/D1, D2 and D3 with four, three and one fire frontiers.
Fig. 14. – Temperature evolution in the columns’ middle reinforcing steel bars.
Fig. 13. – Temperature evolution in the corner of the column reinforcing steel bars.
columns with four fire frontiers is lower than the time until the collapse in the columns with three fire frontiers. For the columns with only one fire frontier, there is no collapse of the column in less than 240 min for the loads and types of damage considered. The column dimensions used in the numerical analysis are higher than the dimensions provided by the EN 1992-1-2 to obtain a fire resistance of 240 min in a column exposed to 1 FF. The axis distance a of the main bars in the numerical analysis is lower than the value provided by the EN 1992-1-2, but the difference is not very high. This aspect gives credibility to the results in Table 4 regarding the time until collapse of the columns with 1 FF. The damage introduced in the columns is not sufficient to create times until collapse of the columns lower than 240 min [32]. In Figs. 15 and 16 it is repre sented the evolution of the times until the collapse of the columns with four and three fire frontiers, respectively, for different loads and types of damage. In Fig. 16 there is an interesting similarity in the results be tween columns with different loads and types of damage. For instance,
damage D2 and about 30 min for the section with damage D3. These examples allow a better understanding of the impact that the damage has on the effective yield strength of the steel bars. The difference in time between section with damage D0/D1 and D3 for the reinforcing steel bars to reach 600 � C is about 100 min for the reinforcing steel bars in the corner and 200 min for the reinforcing steel bars in the middle. These results show how much sooner the steel bars in the damaged sections reach less than half of their yield strength. 5.3. Time until conventional collapse The times until the collapse of the columns with four, three and one fire frontiers for different types of damage and loads are presented in Table 4. The analysis was considered until reaches 240 min or until the collapse of the structure. As expected, the time until the collapse in the 7
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collapse of the columns (times lower than 240 min) with damage D2 and D3 is possible to observe that the time until the collapse of the columns with damage D3 is always more than half of the time until the collapse of the columns with damage D2. Also, by comparing the results where there is collapse of the columns with damage D0/D1 and D2 the same conclusion is applicable to almost all the columns. The exceptions are the columns with relative axial force of 0,938 and the columns with relative axial force of 0,859 for three fire frontiers. In all the other col umns the time until the collapse of columns with damage D2 is more than half of the time until the collapse of the columns with damage D0/D1. In Figs. 15 and 16 the factor that remained constant was the number of fire frontiers. In Figs. 17–19 the factor that is constant is the load. This allows an analysis regarding the impact of the damage and fire frontiers on the columns. As said earlier, columns with one fire frontier do not collapse until 240 min. The Figures show that there is a big difference between the times until the collapse of columns with one fire frontier and the columns with three or four fire frontiers, especially for damage D3. This aspect is more evident in Fig. 19, for a load of 2750 kN (n ¼ 0,859), with damage D3, the column with one fire frontier do not collapses until 240 min and the columns with three or four fire frontiers collapse in less than 60 min.
Table 4 – Time until the collapse of the columns with 4, 3 and 1 fire frontiers. Load
ν
Damage
500 kN
0,16
750 kN
0,23
1000 kN
0,31
1250 kN
0,39
1500 kN
0,47
1750 kN
0,55
2000 kN
0,63
2250 kN
0,70
2500 kN
0,78
2750 kN
0,86
3000 kN
0,94
D0D1 D2 D3 D0D1 D2 D3 D0D1 D2 D3 D0D1 D2 D3 D0D1 D2 D3 D0D1 D2 D3 D0D1 D2 D3 D0D1 D2 D3 D0D1 D2 D3 D0D1 D2 D3 D0D1 D2 D3
4 FF
3 FF
1 FF
Time (min)
Time (min)
Time (min)
240,00 240,00 240,00 240,00 240,00 204,44 240,00 240,00 164,29 240,00 215,02 132,85 240,00 178,27 105,10 228,40 148,60 80,23 197,60 120,56 63,40 169,88 97,52 51,60 143,27 76,48 41,23 117,81 59,04 34,44 96,29 40,19 29,65
240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 217,69 240,00 240,00 179,02 240,00 223,19 140,65 240,00 180,23 108,10 240,00 143,94 78,77 216,94 109,77 60,69 181,19 82,65 46,77 147,65 60,44 38,27
240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00
6. Conclusions Regarding the numerical analysis of the beams, it was observed that the difference in time until the collapse between the beam with damage D0/D1 and D3 is more than 3 h. The beams considered have fixed sup ports that do not allow horizontal displacements in the beam. This sit uation leads to high axial forces created by the thermal elongation of the beam, which shows the impact that the temperature can have on the forces in the structure. Different types of damage in the beam can also change the evolution of the axial forces, bending moments and dis placements. As expected, the beams with damage D3 reach a higher displacement in the mid-span sooner than the beams with damage D2 and D0/D1. The final displacements in the mid-span of the beam do not follow the same trend because the damage has a huge impact on the time until the collapse of the beams. As to the numerical analysis of the columns, it was observed, once again, that the damage hugely influences the time until the collapse. For all the types of damage and relative axial force considered in the col umns with one fire frontier, it was observed that the columns do not collapse until 240 min. As for the columns with three and four fire frontiers the situation is very different. The time until conventional collapse decreases with the increase of the relative axial force, damage
the time until the collapse of the column with damage D0/D1 with a relative axial force of 0,859 is very similar to the column with damage D2 with a relative axial force of 0,625 and very similar with the column with damage D3 with a relative axial force of 0,469. Another example is between the column with damage D0/D1 with a relative axial force of 0, 938 and column with damage D2 with a relative axial force of 0,703 and the column with damage D3 with a relative axial force of 0,547. These examples follow the same trend in terms of variation of loads or relative axial force. There are also other similarities between other columns with damage D2 and D3. As for the columns with four fire frontiers, there are also similar results, but these are not as similar to the ones in the col umns with three fire frontiers. By comparing the results where there is
Fig. 15. – Time until the collapse of the columns with 4 fire frontiers. 8
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Fig. 16. – Time until the collapse of the columns with 3 fire frontiers.
and fire frontiers. The difference in time until the collapse between columns with damage D0/D1 and D3 can be more than 2 h, which shows the huge impact of the damage caused by the earthquake on the fire resistance of the column. There is a significative difference between time until the collapse of the columns with three and four fire frontiers, in some cases it can be higher than 1 h, which shows that considering three or four fire frontiers can lead to very different results. The lower fire resistance of the RC elements combined with higher response times of the rescue teams can lead to higher losses of lives and infrastructures. The reinforced concrete structures that suffer moderate/ severe earthquake damage will have lower post-earthquake fire resistance. Fig. 17. – Time until the collapse of the columns with a load of 1750 kN (n ¼ 0,547).
Declaration of competing interest The authors whose names are listed in the paper certify that they have no Conflicts of Interest or involvement in any organization or entity with any financial interest (such as honoraria; educational grants; participation in speakers’ bureaus; membership, employment, consul tancies, stock ownership, or other equity interest; and expert testimony or patent-licensing arrangements), or non-financial interest (such as personal or professional relationships, affiliations, knowledge or beliefs) in the subject matter or materials discussed in this manuscript. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.soildyn.2019.105900.
Fig. 18. – Time until the collapse of the columns with a load of 2250 kN (n ¼ 0,703).
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Fig. 19. – Time until the collapse of the columns with a load of 2750 kN (n ¼ 0,859).
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Soil Dynamics and Earthquake Engineering 128 (2020) 105900 [23] Franssen JM. SAFIR: a thermal/structural program modeling structures under fire. Eng J AISC. 2005;42(3):143–58. [24] Ervine A, Gillie M, Stratford TJ, Pankaj P. Thermal propagation through tensile cracks in reinforced concrete. J Mater Civ Eng 2012;24:516–22. 2012. [25] Franssen JM. Failure temperature of a system comprising a restrained column submitted to fire. Fire Saf J 2000;34:191–207. [26] Franssen JM, Gernay T. Modeling structures in fire with SAFIR®: theoretical background and capabilities. J Struct Fire Eng 2017. https://doi.org/10.1108/ JSFE-07-2016-0010. [27] Ronagh HR, Behnam B. Investigating the effect of prior damage on the postearthquake fire resistance of reinforced concrete portal frames. Int J Concr Struct Mater 2012;6(No.4):209–20. [28] FEMA356. Prestandard and commentary for the seismic rehabilitation of buildings: FEMA356. In: Rehabilitation requirements. Washington, DC, USA: Federal Emergency Management Agency (FEMA); 2000. [29] EN 1991-1-2. Eurocode 1: actions on structures – Part 1-2: general actions – actions on structures exposed to fire. Brussels, Belgium: European Committee for Standardization, English version; November 2002. [30] Mazza F, Alesina F. Fragility analysis of R.C seismically-isolated structures with residual mechanical properties after fire exposure. Soil Dyn Earthq Eng 2019;121: 383–98. [31] Gernay T, Franssen JM. A performance indicator for structures under natural fire. Eng Struct 2015;100:94–103. [32] EN 1992-1-2. Eurocode 2: design of concrete structures – Part 1-1: general rules – structural fire design. Brussels, Belgium: European Committee for Standardization, English version; December 2004. [33] Gernay T. Effect of transient creep strain model on the behavior of concrete columns subjected to heating and cooling. Fire Technol 2011;48(2):313–29. [34] Gernay T, Franssen J-M. A formulation of the Eurocode 2 concrete model at elevated temperature that includes an explicit term for transient creep. Fire Saf J 2012;51:1–9. [35] Franssen J-M, Kodur VKR, Mason J. Elements of theory for SAFIR 2002: a computer program for analysis of structures submitted to the fire. Belgium: University of Li�ege, Department ArGEnCO, Service Structural Engineering; 2002. [36] EN 1993-1-2. Eurocode 3: design of steel structures – Part 1-2: general rules – structural fire design. Brussels, Belgium: European Committee for Standardization, English version; April 2005.
[8] Shah AH, Sharma UK, Bhargava P. Outcomes of a major research on full scale testing of RC frames in post-earthquake fire. Constr Build Mater 2017;155: 1224–41. [9] Kamath P, et al. Full-scale fire test on an earthquake-damaged reinforced concrete frame. Fire Saf J 2015;73:1–19. [10] Shah AH, et al. Fire performance of earthquake-damaged reinforced-concrete structures. Mater Struct 2016;49:2971–89. [11] Shah AH, et al. Effect of ductile detailing on the performance of a reinforced concrete building frame subjected to earthquake and fire. J Perform Constr Facil 2016:04016035. [12] Behnam B, Ronagh HR, Lim PJ. Numerical evaluation of the post-earthquake fire resistance of CFRP-strengthened reinforced concrete joints based on experimental observations. Eur J Environ Civ Eng 2015;20(2):142–60. [13] Behnam B, Ronagh HR, August. Post-earthquake fire resistance of CFRP strengthened reinforced concrete structures. The Structural Design of Tall and Special Buildings; 2014. [14] Behnam B, Lim PJ, Ronagh HR. Plastic hinge relocation in reinforced concrete frames as a method of improving post-earthquake resistance. Structure 2015;2: 21–31. [15] Corte G, Landolfo R, Mazzolani FM. Post-earthquake fire resistance of moment resisting steel frames. Fire Saf J 2003;38:593–612. [16] Zografopoulou K, Pantousa D, Mistakidis E. Fire-After-Earthquake behavior of industrial facilities with fire protected steel structural system. In: 16th European conference on, earthquake thessaloniki engineering; 2018. [17] Arablouei A, Kodur V. Effect of fire insulation delamination on structural performance of steel structure during fire following an earthquake or an explosion. Fire Saf J 2016;84:40–9. [18] Song Q, Heidarpour A, Zhao X, Han L. Post-earthquake fire behavior of welded steel I-beam to hollow column connections: an experimental investigation. ThinWalled Struct 2016;98:143–53. [19] Pucinotti R, Bursi OS, Demonceau JF. Post-earthquake fire and seismic performance of welded steel-concrete composite beam-to-column joints. J Constr Steel Res 2011;67:1358–75. [20] Koseki Hiroshi, et al. Cause and countermeasure way of rubble fires occurred after 2011 Great earthquake of Japan. Procedia Eng 2012;45:617–27. [21] Murasawa N, et al. Great East Japan Earthquake disaster waste and the occurrence of fires. Procedia Eng 2014;84:472–84. [22] Franssen JM. User’s Manual for SAFIR 2011: a computer program for analysis of structures subjected to fire. Belgium: University of Li�ege, Department ArGEnCO, Service Structural Engineering; 2011.
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Contents lists available at ScienceDirect
Soil Dynamics and Earthquake Engineering journal homepage: http://www.elsevier.com/locate/soildyn
Evaluation of post-earthquake fire capacity of reinforced concrete elements Hugo Vitorino a, Hugo Rodrigues b, *, Carlos Couto c a
Escola Superior de Tecnologia e Gest~ ao, Instituto Polit�ecnico de Leiria, Leiria, Portugal RISCO, Escola Superior de Tecnologia e Gest~ ao, Instituto Polit�ecnico de Leiria, Departamento de Engenharia Civil, Leiria, Portugal c RISCO, Departamento de Engenharia Civil, Universidade de Aveiro, Portugal b
A R T I C L E I N F O
A B S T R A C T
Keywords: Fire after earthquake Fire safety assessment Fire resistance Reinforced concrete structure Earthquake damage Seismic assessment
Large earthquakes may cause a chain of events, and one of which can be fire after an earthquake. The effects of fire after earthquake on urban areas can be even worse than the effects of the earthquake itself. Buildings are not adequately designed for fire after an earthquake since most standards ignore that possibility. The aim of the work is to evaluate the consequences of the damage introduced due to the seismic events on the fire resistance of reinforced concrete elements. Several numerical analyses were performed to reinforce concrete elements using the program SAFIR, considering the thermal and mechanical analysis of the structure. The main variables in the analysis were the type of damage in the elements and the type of loads. The thermal analysis was performed using the standard fire curve ISO 834. The results show that the damage imposed by earthquake on reinforced concrete structures reduces the fire resistance, especially if the cover of the elements is removed and the rein forcement is exposed to fire.
1. Introduction There is historical evidence that confirms the possible occurrence of fire after an earthquake event in the built urban environment. The consequences lead to an increase in the losses of lives and property. There are three main combined aspects that under normal circumstances allow a response to fires in buildings, both active and passive fire pro tection systems and manual fire-fighting by a fire brigade. It is necessary to have the availability of water supplies due to the difficulty of extin guishing the fire without water. The water distribution systems are susceptible to earthquake damage and failures are likely. The earth quakes can cause structural and non-structural damage which leads to failure of the passive protection systems, possibly creating openings that increase the ventilation in the compartments. These openings allow the movement of smoke and hot gases to different areas of the building. The active protection systems, such as detection, alarm and suppression systems, can also be damaged after an earthquake, leading to defective functioning, which can cause unnoticed ignitions resulting in larger fires that are more difficult to extinguish. It is possible that after a major earthquake the fire teams are faced with several problems that prevent them from rapidly proceeding the rescues and the put out of fires. Those problems can be related to reporting delays, impassable access routes,
traffic jams, loss of operational vehicles and loss of equipment. The firemen’s presence will be delayed due to the possible appearance of multiple simultaneous ignitions and insufficient resources for fire fighting [1,2]. After an earthquake, and given the higher number of occurrences, the rescue teams will be very solicited, and the response times will consequently be higher. This situation together with the eventual reduction of the fire resistance of the damaged reinforced concrete elements can lead to the loss of lives and structures. Thus, a better understanding of the fire behavior following an earthquake, particularly in major structures, is important so that it is possible to implement some prescriptive measures that can ensure better perfor mance of structures in those circumstances. 2. Post-earthquake fire – brief overview 2.1. Earthquake damages in buildings Earthquakes can cause different types of structural and nonstructural damage in buildings. In common reinforced concrete (RC) infilled buildings, the masonry walls normally are not considered as structural elements [3]. The masonry bricks usually have brittle behavior and can modify the structural response of the building by
* Corresponding author. Civil Engineering Department School of Technology and Management, Polytechnic Institute of Leiria, Campus 2 - Morro do Lena - Alto do Vieiro, Apartado, 4163-2411-901, Leiria, Portugal. E-mail addresses: [email protected] (H. Vitorino), [email protected] (H. Rodrigues), [email protected] (C. Couto). https://doi.org/10.1016/j.soildyn.2019.105900 Received 23 May 2019; Received in revised form 7 October 2019; Accepted 10 October 2019 Available online 18 October 2019 0267-7261/© 2019 Elsevier Ltd. All rights reserved.
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instance, the likelihood of several simultaneous ignitions, detection delays, reporting delays and water supplies reduced or exhausted. The widespread effects of earthquakes can generate several simultaneous ignitions. The post-earthquake fires have the opportunity to grow and spread and are more difficult to extinguish when compared to fires that happen at any other time. The difficulty to extinguish the fire arises from the insufficient fire service resources after an earthquake. Damage in detectors or distracted observers can lead to detection delays but the time of discovery of post-earthquake fire is usually not different from the time of discovery of any other fire. The failure of communications sys tems and the overload from high usage levels lead to reporting delays [1, 7]. The main ignition sources of post-earthquake fire are electrical or gas-related. Other sources can also be, open flames, hot surfaces, exothermic chemical reactions from spilled chemicals and fires inten tionally lit [1,2]. The earthquake shaking can stress the electrical wiring which leads to short-circuits that can cause ignitions. The earthquake shaking can also cause damage to gas appliances and gas supply lines which can be ignited by electrical sources or flames present in the ap pliances. Certain electrical appliances (e.g. cookers, gas-fueled water heaters, and solid-fueled burners) that are not properly restrained can topple and their residual heat may initiate fires if brought in contact with combustible materials. The restoration of electrical and gas sup plies to damaged appliances and wiring can also cause fires. If some preventive practices and installation procedures are performed it is possible to reduce the fire risk after a major earthquake. The main ac tions to reduce the post-earthquake fire sources are the education of the population to minimize the risk of fire and the adequate design of the gas networks including an automatic valve that reduces the gas quantities in case of damage in the network. These automatic valves are placed in the pipe after the gas meter; with these, after an earthquake, the amount of gas inside the house is reduced. The electric power networks usually have a security device that shuts off the network for several seconds after the beginning of a big earthquake [1]. The effects of fire after an earthquake on the RC buildings are not very well known. In the past years, there were developed several numerical and experimental studies regarding the post-earthquake fire to be able to better understand the phenomenon. Some experimental studies developed in frames showed that using a standard fire curve may not be very accurate since different elements can have different temperature profiles [8–11]. In the same studies, the cracks that appeared in the different elements of the analyzed structure indicate that the detailing of reinforcement has consequences on the global behavior of the structure when exposed to fire. In the majority of the structural members, the temperatures in the RC frame with nonductile detailing were much higher than those with ductile detailing [10,11]. It was observed that the brick infill walls provide insulation to the RC structural elements and slow the trans mission of heat to these elements. This shows the beneficial effect that the masonry walls have on the columns and beams integrated into the masonry walls, and this beneficial effect should be considered while designing the columns and beams [8]. The position of the openings in the compartments and the resulting movement of fire plume and hot gases have also an influence in terms of the evolution of temperatures in the structural sections. This situation may or may not lead to an overlap between the locations of the damage caused by the earthquake and the damage caused by the fire [9]. Some numerical and experimental studies were also developed regarding the fire resistance of CFRP-strengthened reinforced concrete elements [12,13]. The results show that the fire resistance of the specimens subjected to life safety (LS) and collapse prevention (CP) damage levels are about 32 and 15 min and for the CFRP-strengthened specimen is about 43 and 23 min, respectively. This solution represents a 25% increase at LS level and 35% increase at the CP level [12]. Also, regarding the use of CFRP, using this solution to relo cate plastic hinges of the beams away from the columns improve the post-earthquake fire resistance of the frames [14]. Beyond the research of post-earthquake fire on RC buildings, there are also works developed regarding the post-earthquake fire on steel structures. In some works,
changing the structural stiffness, attracting forces to structural elements not designed to resist such forces. This situation can be avoided with more ductile masonry walls. There is also the structural damage in the RC elements like beams, columns, walls, slabs and even foundations. To assure proper structural behavior under an earthquake action it is important to have structural elements with proper strength, stiffness, and ductility but it is also important that the beam-column joints are well connected and with proper ductile behavior. The poor detailing of the reinforcing steel is a common deficit in the existing structures, especially on old reinforced concrete structures, designed without seismic concerns. There are several cases reported related to the poor detail, namely related to the confinement reinforcement not correctly placed at the beam-column joints, deficiency of transverse reinforce ment in the columns with wide spacing of the ties and poor confinement of the concrete core. The short lap splices and incorrect end hook angle are also examples of poor detailing of the reinforcing steel. The use of smooth reinforcing bar that creates a weaker bond between concrete and steel can also be observed in some cases [4]. There are other cases that lead to a poor behavior of the structures to the seismic action, such as, poor concrete quality, damage related with strong beam-weak column, soft stories at the first-floor level, and defects in the workmanship [5,6]. 2.2. Fire action Fire is a combustion characterized by the appearance, conservation and propagation of flame, heat release, gas emission, and smoke production. During the natural development of a fire, from the beginning until the extinction, there are several important stages, namely: ignition, growth, flashover, burning, and decay [8]. The fire evolution from the ignition until the flashover depends on several factors, some related to the fuel and oxidizer, others related to the local characteristics of the place where the fire develops. The main factors are: (i) type and quantity of available fuel, (ii) quantity of oxidizer (oxygen) available, that de pends on the compartment ventilation conditions and the dimensions of the openings, (iii) compartment geometry, (iv) type of pavements, walls and coatings, and (v) atmospheric conditions (temperature, wind di rection, etc). After the ignition, the fire starts to develop according to the fuel available in the place, releasing heat that leads to the temperature increase. In this phase, the fire can conclude due to the lack of fuel material (fire controlled by the fuel), or by oxidizer deficit (fire controlled by ventilation). If there is sufficient fuel and oxidizer and no outside intervention, the temperature in the compartment continuous to increase. This situation leads to the ignition of materials that until that moment had not initiated the combustion process yet. The flashover establishes the transition to the burning phase. The burning phase takes place when all the fuel in the compartment is involved in the fire. The temperature inside a compartment where a fire is developing is not uniform, near the ceiling the temperature is higher when compared with the flooring and lower places of the walls. The hot gases produced during the fire go to the higher part of the compartment and the flames elongate towards the ceiling [1]. Not all the fires have a complete development, due to direct intervention (firefighters’ action or auto matic extinguishing systems, for example), or due to the compartment characteristics (lack of oxidizer, for example), the fire can be extin guished before reaching the burning phase [8]. 2.3. Post-earthquake fire The urban fires will normally follow several stages, ignition, growth, detection, report, response, suppression activities and extinguishment (due to the suppression activities or due to the exhaustion of the fuel). The development of post-earthquake fires will be similar to fires that occur at any other time. The main difference is related to the response of rescue teams, that will probably be disrupted during and after a major earthquake. The disruption can happen due to several factors, for 2
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the focus is the analysis of the behavior of steel frames to post-earthquake fire [15]. There are studies where the aim is to analyze the impact that the earthquake has on the passive fire protection of the steel structures. Some materials that are used as passive fire protection have a brittle behavior and suffer damage due to the seismic action, leading to a lower fire resistance of the steel structures [16,17]. There is also research regarding the behavior of the joints and connections of the steel frames. The results show that severe damage to the connections lead to reduced fire resistance capacities [18,19].
structure is calculated, based on the geometry, support conditions, loads and the strength of the materials. The increase in temperature changes the strength of the materials and leads to thermal elongation. The reduction of the strength and stiffness combined with the thermal elongation leads to an increase in the displacements until the collapse of the structure. The mechanical behavior is directly influenced by the loss of strength, stiffness and thermal elongation which is the result of the temperature increase. In SAFIR, the numerical analysis will stop at the time specified by the user (240 min), or if it finds numerical problems at the material level, or when it cannot converge to a state of equilibrium [25,26]. The first procedure performed was the creation of different sections for the beam and column, with different types of damage and number of fire frontiers. A thermal analysis was developed in the sections to determine the influence of the damage and fire frontiers in the tem perature of the reinforcing steel bars. Subsequently, the different sec tions were incorporate in the RC elements to be able to develop a structural analysis of the beams and columns. The materials properties used in the analysis of the beam and column are the same. The damage in the sections was simulated by reducing the thickness of the cover. The damage D0/D1 corresponds to an intact section or a section with minor cracks, the damage D2 corresponds to the slight damage with some concrete spalling, traduced in the removal of the exterior fibers in the numerical model and damage D3 corresponds major damage level, corresponding to the large concrete spalling, traduced in the removal of the entire cover, leaving the reinforcement steel exposed in the nu merical model. In the beam cross-section, the damage was considered in the bottom and sides and in the columns the damage is considered in all the column cross-section sides. It was considered that the damages represented in the R.C elements (D0/D1, D2 and D3) correspond to the structural performance levels presented in FEMA356. In the Immediate Occupancy (IO) level is observed minor damage in the structural ele ments, which in the following analysis corresponds to damage D0/D1. In the Life Safety (LS) level is observed extensive damage to beams and spalling of cover and shear cracking for ductile columns, which in the following analysis corresponds to damage D2. Regarding the collapse prevention (CP) level, it is observed extensive spalling in columns and beams, which corresponds to damage D3 in the following analysis [27, 28]. The fire curve used was ISO 834 [29]. For the section of the beams, the fire frontiers were considered on the bottom and sides. For the section of the columns, it was considered three different dispositions of fire frontiers, with one, three and four fire frontiers. The standard fire curve ISO 834 represents the time-temperature evolution during an actual fire, from flashover to the full development of the fire. Fires in buildings have a heating phase followed by a cooling phase, which is not represented in the standard fire curve ISO 834. The mechanical prop erties of R.C structures after the fire can be lower or higher than during the fire. Usually, the load-bearing capacity of a structure continues to decrease in the cooling phase, reaching the lowest load-bearing capacity followed by a partial or complete recovery when the structure is back to ambient temperature. This situation brings a threat that is not consid ered when the standard fire curve ISO 834 is used, the possibility of structural failure a period of time after the maximum temperature in the compartment [30,31]. This situation is important and deserves more study to be able to better understand the materials and structures behavior under decreasing temperatures. However, this aspect was not considered in the following numerical analysis, and the collapse of the R. C structural elements coincide with the highest temperature. In Table 1 are represented all the material properties for the RC el ements used in the numerical analysis. The concrete compression strength and the reinforcing steel yield strength evolution with tem perature will be according to EN 1992-1-2 [32]. There are several con crete parameters introduced in the model, the aggregate type (siliceous or calcareous), Poisson’s ratio, compressive strength and tensile strength. It is also necessary to indicate in the model if the transient creep is treated implicitly or explicitly. The implicit formulation
2.4. Review of historical data Throughout history is possible to find several examples of postearthquake fires, for instance, the Hokkaido Nansei-Oki earthquake, Northern Japan in 1993. In this earthquake 246 people were dead or missing, 190 houses and buildings were consumed by fire over an 11-h period [17]. The town of Aonae was destroyed by conflagration following earthquake and tsunami. Building-to-building fire spread was accelerated by externally stored propane and kerosene tanks used for cooking and heating. Another example is the 1994 earthquake in Northridge, San Fernando Valley in Southern California. This earth quake had 58 fatalities (none from fire) and 1500 serious injuries. There were 30–50 significant fires initially following the earthquake, and after less than 8 h the total number of fires was about 110. The principal cause was gas leaks from natural gas pipelines and appliances. The restoration of gas and power after a few days caused a significant number of fires [1, 2]. There is also a different perspective for the post-earthquake fire when the fire does not start immediately after the earthquake. The Great East Japan Earthquake, which occurred on 11 March 2011 was one of the largest earthquakes in recent Japanese history and resulted in the gen eration of large amounts of disaster waste. It was necessary the creation of outdoor storage areas to deposit disaster waste. In these areas, in the Tohoku region, more than 40 fires occurred. One probable cause of the fire is thought to have been the heat generated by fermentation of mi croorganisms. The microorganisms can thrive easily in those conditions, and the heat created can lead to spontaneous ignition. The materials deposited in the outdoor storage areas have a huge influence on this process, it is expected that the presence of wood will most likely lead to more ignitions than the presence of concrete, for instance. A study performed in this topic revealed that the heat generated during fermentation of wood chips and rotten tatami was most likely the trigger of the spontaneous ignition. This situation only serves as an example that the post-earthquake fires can appear from different causes and maybe in places where not initially expected [20,21]. 3. Research methodology The numerical analysis was developed with SAFIR, a computer program for the analysis of structures under ambient temperature and elevated temperature conditions. The program is based on the Finite Element Method (FEM) and can be used to study the behavior of one, two and three-dimensional structures. SAFIR can perform thermal and mechanical analysis. They are performed separately and subsequently. The temperature distribution will deeply influence the mechanical response, but the opposite is not currently handled by the software. There is no influence of the cracking of the concrete determined in the analysis of the thermal conductivity that is used in the thermal analysis [22,23]. Some studies showed that there is no significant increase or decrease in the thermal propagation through concrete with tensile cracking where the cracks are up to the order of 101 mm at the heated surface. This situation shows that performing sequentially thermal then me chanical analysis of heated structures is a valid approach [24]. The gas temperatures produced by the fire are entered as input data in the SAFIR. With these, SAFIR will calculate the evolution of the temperatures in the structure. After that, the mechanical behavior of the 3
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Table 1 – Concrete and reinforcing steel properties used in the numerical analysis. Concrete properties Concrete model Specific mass of concrete Water content Coefficient of convection on heated surfaces Coefficient of convection on unheated surfaces Emissivity Compression strength Tensile strength Poisson’s ratio Reinforcing Steel properties Steel model Modulus of elasticity Yield strength Poisson’s ratio Coefficient of convection on heated surfaces Coefficient of convection on unheated surfaces Emissivity Reinforcing Steel diameter
rho w hh hc
ε
fc fct v
Es fy v hh hc
ε Φs
Siliceous aggregate [32] 2300 kg/m3 46 kg/m3 25 W/m2K 4 W/m2K 0,7 30 MPa Zero 0,2
Hot rolled, class B [32,36] 210 GPa 500 MPa 0,3 25 W/m2K 4 W/m2K 0,7 25 mm
Fig. 2. – Beam section.
different types of damage can be seen in Fig. 3. The damage D0/D1 corresponds to an intact section or a section with small cracks, the damage D2 corresponds to the removal of the exterior fibers and damage D3 corresponds to the removal of the entire cover, leaving the rein forcement visible. The fibers on the top side were not removed. This assumption is consistent with the expected earthquake damage. There is also no fire frontier on the top side of the beam, it was considered that the fire develops below the beam (see Fig. 3). There were developed three different beams in SAFIR to better un derstand the fire after earthquake phenomenon. Table 2 shows the description and the location of the damage in each beam. In beam A1 all the 60 elements have the section with damage D0/D1, and in beams A2 and A3 the damage is in the 6 elements closer to the fixed supports, simulating the earthquake damage the expected beam areas. All the elements not mentioned in Table 2 have a section with damage D0/D1.
corresponds to the model in the Eurocode. The explicit formulation is a refinement of the Eurocode that is calibrated to yield the same response as the Eurocode model but is also able to consider the non-reversibility of transient creep strain when the stress and/or temperature is decreasing [33,34]. The beam element was used in the FEM simulation. The position of the beam element is defined with three nodes, two end nodes and a node that defines the position of the local y-axis of the beam. A fiber model is used to define the geometry of the cross-section. It is possible to create composite sections by defining different materials in different fibers. There are some assumptions considered in the beam element: the cross-section remains plane under bending moments, the plasticization is only considered in the longitudinal direction of the member and the non-uniform torsion is considered [35].
4.2. Thermal analysis In Figs. 4 and 5 are presented the evolution of the temperature in the beam reinforcing steel bars. The evolution of the temperature in the steel bars is compared with the fire curve ISO 834. For the section with damage D0/D1 and D2, the bottom steel bars present a higher temper ature. For the section with damage D3, with the steel bars directly exposed to the fire, the temperature of the bottom and top steel bars is the same. In the section with damage D3, the temperature of the steel bars is similar to the temperature of the fire curve ISO 834. In Figs. 4 and 5 are also represented three temperature lines (500, 600 and 700 � C) that can be associated with the effective yield strength (k) of the rein forcing steel bars [32]. These temperature lines allow a comparison between the sections with different damage. For example, in Fig. 4, the reinforcement steel bar reaches a temperature of 700 � C in 180 min for the section with damage D0/D1, 90 min for the section with damage D2 and about 15 min for the section with damage D3. This comparison shows the huge impact of the damage on the evolution of the temper atures in the sections.
4. Post-earthquake fire analysis on RC beams 4.1. Introduction The schematic of the beam used in the numerical analysis is repre sented in Fig. 1. The beam has fixed supports and a continuous load of 45 kN/m is applied. It is also represented the characterization of the finite element mesh used in SAFIR. The beam with 6 m was divided into 60 elements, each element with 10 cm. In Fig. 2 is represented the section of the beam without damage and the location of the reinforcement (4Φ25). There were considered three different beam sections, each one with different simulated damage. The
Fig. 1. – Beam with fixed supports: (a) Beam length and load applied; (b) Characterization of the finite element mesh.
Fig. 3. – Different sections of the beam according to the type of damage. The fire frontiers are also represented. 4
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reaches higher axial forces sooner than the beam with damage D2 and the beam with damage D2 reaches higher axial forces sooner than the beam with damage D0/D1. One possible explanation for this is related to the thermal elongation of the steel bars. The effect of the temperature happens earlier in the beam with damage D3 because the steel bars are exposed. For the other beams, the idea is the same, the steel bars in the beam A1 are more protected than the steel bars in the beam A2 and that leads to the later thermal elongation of the steel bars. Since the beams have fixed supports there is no horizontal displacement in the beam. This type of supports leads to higher axial forces because of the total horizontal restraint. It is expected that these beams inserted in a struc ture with more flexible supports will have lower axial forces compared to the ones obtained here. For the beam A3, the axial forces increase until the collapse of the beam. For the beams A1 and A2 the axial force increases until around 60 min and then starts to decrease. The decrease in the axial force happens due to the deterioration of the materials.
Table 2 – Location of the damage in the beam. Beam
Damage
Elements
Distance
A1 A2 A3
D0/D1 D2 D3
All 1 to 6 and 55 to 60 1 to 6 and 55 to 60
6m 0,6 m 0,6 m
4.5. Moments In Fig. 7 is represented the evolution of the mid-span moments in the beams. In the first minutes, there is a flexural restraint to the rotation created by the thermal gradient in the section of the beam. After that, there is a deterioration of the materials and the moments start to redistribute towards the mid-span of the beam. The moments in the mid-span of the beam start to increase and the moments in the supports decrease. The deterioration that leads to the redistribution of the mo ments happens first in the beam with damage D3, followed by the beam with damage D2 and followed by the beam with damage D0/D1. In Fig. 8 is represented the evolution of the moments in the supports of the beams. The evolution of the moments in the supports follows the same trend of the moments in the mid-span of the beam. In the first minutes, the moments increase due to the thermal gradient in the section of the beam and then due to the deterioration of the material the mo ments decrease.
Fig. 4. – Temperature evolution in the beams bottom reinforcing steel bars.
4.6. Mid-span displacement In Fig. 9 is represented the evolution of the displacements in the midspan of the beams. The higher vertical displacement observed is in the beam A1, -36,55 mm at 240 min. The highest displacement observed in beams A2 and A3 is at the time of collapse of the beams. The displace ment in beam A2 is 16,5 mm and the displacement in beam A3 is 10,49 mm.
Fig. 5. – Temperature evolution in the beams top reinforcing steel bars.
4.3. Time until conventional collapse
5. Post-earthquake fire analysis on RC columns under pure axial load
Table 3 represents the time until the collapse of the beams. The re sults show that the damage reduces the time until the collapse of the beam. For beam A1 there is not collapse until 240 min. The differences between the beams regarding the time until the collapse is not small. The difference between beam A2 and A3 is almost 60 min. The time until the collapse of beam A2 is more than double the time until the collapse of the beam A3.
5.1. Introduction The schematic of the column used in the numerical analysis is rep resented in Fig. 10. The column has one fixed support and a vertical
4.4. Axial force In Fig. 6 is represented the evolution of the axial forces in the beams. The evolution of the axial forces in the beams is similar until about 30 min. However, there is a slight difference, the beam with damage D3 Table 3 – Time until the collapse of the beam. Beam
Damage
Time (min)
A1 A2 A3
D0/D1 D2 D3
240,0 106,8 49,2
Fig. 6. Evolution of the axial force in the beams. 5
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Fig. 10. – Column with fixed support: (a) Column length and load applied; (b) Characterization of the finite element mesh.
Fig. 7. Evolution of the mid-span moments in the beams.
damage, fire frontiers and level of initial load are represented in (Fig. 12. In Fig. 10 b) the column is divided into 10 elements. Elements 1 and 2 are the elements where different types of damage will be considered. The other elements (3–10) will have always sections with damage D0/ D1, once it is assumed that the earthquake damage in typical columns and beams is concentrated in the extremities of RC elements. Later, when the damage of a column is mentioned is always the damage in elements 1 and 2 because the damage in elements 3 to 10 will always be damage D0/D1. 5.2. Thermal analysis In Figs. 13 and 14 it is represented the temperature evolution of the reinforcing steel bars. Fig. 13 represents the reinforcing steel bars in the corners of the sectionand Fig. 14 represents the reinforcing steel bars in the middle. As is possible to see in Fig. 12 each reinforcing steel bar is constituted by only one fiber. Each fiber has four different nodes and each node has different temperatures. The temperature considered to develop the graphs in Figs. 13 and 14 was the higher one of those four nodes. The difference between the temperatures in those four nodes is almost negligible and it was considered enough to analyze only the higher value. By analyzing the graphs in Figs. 13 and 14 is possible to see that the temperature in the corner reinforcing steel bars is higher when compared with the reinforcing steel bars in the middle, and this is true for all types of damage. The fire curve ISO 834 is represented in the graphs to serve as a comparison between the results. For the reinforcing steel bars in the corner, for section with damage D3, the evolution of the temperature is very similar to the fire curve ISO 834, especially about 90 min after the beginning of the fire curve. In each graph is also showed three different temperature lines that are associated with the reducing factors presented in the EN 1992-1-2 [32]. These values are helpful because allow the comparison between the effective yield strength in each steel bar for different types of damage. For damage D0/D1 it takes about 120 min for the steel bars to reach a temperature of 600 � C, it takes about 60 min for the section with damage D2 and about 20 min for the section with damage D3. For the steel bars in the middle it takes about 240 min for the steel bars in the section with damage D0/D1 to reach a temperature of 600 � C, it takes about 120 min for the section with
Fig. 8. – Evolution of the moments in the supports in the beams.
Fig. 9. – Evolution of displacement in the mid-span of the beam.
point load is applied. It is also represented the characterization of the finite element mesh used in SAFIR. The column was divided into 10 elements, each element with 15 cm. There were developed several nu merical analyses regarding the column. The main differences in the analysis are related to the damage, position of the fire frontiers and load applied. In Fig. 11 is represented the section of the column without damage, it also shows the location of the reinforcement (8Φ25). The different types of damage can be seen in Fig. 12. Although the fire frontiers can be different, the damage is applied in all the surfaces of the concrete section. All of the sections of columns developed, with different types of
Fig. 11. – Column section. 6
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Fig. 12. – Numerical models for damage D0/D1, D2 and D3 with four, three and one fire frontiers.
Fig. 14. – Temperature evolution in the columns’ middle reinforcing steel bars.
Fig. 13. – Temperature evolution in the corner of the column reinforcing steel bars.
columns with four fire frontiers is lower than the time until the collapse in the columns with three fire frontiers. For the columns with only one fire frontier, there is no collapse of the column in less than 240 min for the loads and types of damage considered. The column dimensions used in the numerical analysis are higher than the dimensions provided by the EN 1992-1-2 to obtain a fire resistance of 240 min in a column exposed to 1 FF. The axis distance a of the main bars in the numerical analysis is lower than the value provided by the EN 1992-1-2, but the difference is not very high. This aspect gives credibility to the results in Table 4 regarding the time until collapse of the columns with 1 FF. The damage introduced in the columns is not sufficient to create times until collapse of the columns lower than 240 min [32]. In Figs. 15 and 16 it is repre sented the evolution of the times until the collapse of the columns with four and three fire frontiers, respectively, for different loads and types of damage. In Fig. 16 there is an interesting similarity in the results be tween columns with different loads and types of damage. For instance,
damage D2 and about 30 min for the section with damage D3. These examples allow a better understanding of the impact that the damage has on the effective yield strength of the steel bars. The difference in time between section with damage D0/D1 and D3 for the reinforcing steel bars to reach 600 � C is about 100 min for the reinforcing steel bars in the corner and 200 min for the reinforcing steel bars in the middle. These results show how much sooner the steel bars in the damaged sections reach less than half of their yield strength. 5.3. Time until conventional collapse The times until the collapse of the columns with four, three and one fire frontiers for different types of damage and loads are presented in Table 4. The analysis was considered until reaches 240 min or until the collapse of the structure. As expected, the time until the collapse in the 7
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collapse of the columns (times lower than 240 min) with damage D2 and D3 is possible to observe that the time until the collapse of the columns with damage D3 is always more than half of the time until the collapse of the columns with damage D2. Also, by comparing the results where there is collapse of the columns with damage D0/D1 and D2 the same conclusion is applicable to almost all the columns. The exceptions are the columns with relative axial force of 0,938 and the columns with relative axial force of 0,859 for three fire frontiers. In all the other col umns the time until the collapse of columns with damage D2 is more than half of the time until the collapse of the columns with damage D0/D1. In Figs. 15 and 16 the factor that remained constant was the number of fire frontiers. In Figs. 17–19 the factor that is constant is the load. This allows an analysis regarding the impact of the damage and fire frontiers on the columns. As said earlier, columns with one fire frontier do not collapse until 240 min. The Figures show that there is a big difference between the times until the collapse of columns with one fire frontier and the columns with three or four fire frontiers, especially for damage D3. This aspect is more evident in Fig. 19, for a load of 2750 kN (n ¼ 0,859), with damage D3, the column with one fire frontier do not collapses until 240 min and the columns with three or four fire frontiers collapse in less than 60 min.
Table 4 – Time until the collapse of the columns with 4, 3 and 1 fire frontiers. Load
ν
Damage
500 kN
0,16
750 kN
0,23
1000 kN
0,31
1250 kN
0,39
1500 kN
0,47
1750 kN
0,55
2000 kN
0,63
2250 kN
0,70
2500 kN
0,78
2750 kN
0,86
3000 kN
0,94
D0D1 D2 D3 D0D1 D2 D3 D0D1 D2 D3 D0D1 D2 D3 D0D1 D2 D3 D0D1 D2 D3 D0D1 D2 D3 D0D1 D2 D3 D0D1 D2 D3 D0D1 D2 D3 D0D1 D2 D3
4 FF
3 FF
1 FF
Time (min)
Time (min)
Time (min)
240,00 240,00 240,00 240,00 240,00 204,44 240,00 240,00 164,29 240,00 215,02 132,85 240,00 178,27 105,10 228,40 148,60 80,23 197,60 120,56 63,40 169,88 97,52 51,60 143,27 76,48 41,23 117,81 59,04 34,44 96,29 40,19 29,65
240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 217,69 240,00 240,00 179,02 240,00 223,19 140,65 240,00 180,23 108,10 240,00 143,94 78,77 216,94 109,77 60,69 181,19 82,65 46,77 147,65 60,44 38,27
240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00 240,00
6. Conclusions Regarding the numerical analysis of the beams, it was observed that the difference in time until the collapse between the beam with damage D0/D1 and D3 is more than 3 h. The beams considered have fixed sup ports that do not allow horizontal displacements in the beam. This sit uation leads to high axial forces created by the thermal elongation of the beam, which shows the impact that the temperature can have on the forces in the structure. Different types of damage in the beam can also change the evolution of the axial forces, bending moments and dis placements. As expected, the beams with damage D3 reach a higher displacement in the mid-span sooner than the beams with damage D2 and D0/D1. The final displacements in the mid-span of the beam do not follow the same trend because the damage has a huge impact on the time until the collapse of the beams. As to the numerical analysis of the columns, it was observed, once again, that the damage hugely influences the time until the collapse. For all the types of damage and relative axial force considered in the col umns with one fire frontier, it was observed that the columns do not collapse until 240 min. As for the columns with three and four fire frontiers the situation is very different. The time until conventional collapse decreases with the increase of the relative axial force, damage
the time until the collapse of the column with damage D0/D1 with a relative axial force of 0,859 is very similar to the column with damage D2 with a relative axial force of 0,625 and very similar with the column with damage D3 with a relative axial force of 0,469. Another example is between the column with damage D0/D1 with a relative axial force of 0, 938 and column with damage D2 with a relative axial force of 0,703 and the column with damage D3 with a relative axial force of 0,547. These examples follow the same trend in terms of variation of loads or relative axial force. There are also other similarities between other columns with damage D2 and D3. As for the columns with four fire frontiers, there are also similar results, but these are not as similar to the ones in the col umns with three fire frontiers. By comparing the results where there is
Fig. 15. – Time until the collapse of the columns with 4 fire frontiers. 8
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Fig. 16. – Time until the collapse of the columns with 3 fire frontiers.
and fire frontiers. The difference in time until the collapse between columns with damage D0/D1 and D3 can be more than 2 h, which shows the huge impact of the damage caused by the earthquake on the fire resistance of the column. There is a significative difference between time until the collapse of the columns with three and four fire frontiers, in some cases it can be higher than 1 h, which shows that considering three or four fire frontiers can lead to very different results. The lower fire resistance of the RC elements combined with higher response times of the rescue teams can lead to higher losses of lives and infrastructures. The reinforced concrete structures that suffer moderate/ severe earthquake damage will have lower post-earthquake fire resistance. Fig. 17. – Time until the collapse of the columns with a load of 1750 kN (n ¼ 0,547).
Declaration of competing interest The authors whose names are listed in the paper certify that they have no Conflicts of Interest or involvement in any organization or entity with any financial interest (such as honoraria; educational grants; participation in speakers’ bureaus; membership, employment, consul tancies, stock ownership, or other equity interest; and expert testimony or patent-licensing arrangements), or non-financial interest (such as personal or professional relationships, affiliations, knowledge or beliefs) in the subject matter or materials discussed in this manuscript. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.soildyn.2019.105900.
Fig. 18. – Time until the collapse of the columns with a load of 2250 kN (n ¼ 0,703).
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Fig. 19. – Time until the collapse of the columns with a load of 2750 kN (n ¼ 0,859).
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