Finite Element Evaluation of RC Frames Strengthened with FRPs under Fire and Lateral Loads

Corresponding Author: Reza Salehi South Tehran Branch Islamic Azad University, Tehran, Iran Email: st_r.salehi@azad.ac.ir Abstract: Reinforced concrete is one of the most common structures in the world. These structures may be under extreme loading conditions such as earthquake or they may confront with other flooding, impact or even the fire load. In the term of fire load, RC structures are very sensitive and due to the brittle behavior, the fast collapsing happens. In this research, two experimental setups are validated: (1) RC frame and (2) RC column. The Reinforced Concrete (RC) frame is modeled using finite element ABAQUS software and validated with experimental program. The RC frame validation is subjected to lateral and vertical loads. On the other side, RC column is also modeled and validated using ABAQUS software. The RC column is subjected to fire load. The results of validations show that the simulation techniques are accurate to perform the further investigation. The RC frames are retrofitted by FRP sheets and reinforced using steel or FRP bars. The angle of FRP sheets is both convergent and divergent. The fire is applied at the inside surface of the frame by 200, 400, 600, 800 and 1000C and lateral displacement-control load is considered, concurrently. Forcedisplacement diagrams have been evaluated to check the load capacity, ductility, stiffness, seismic factor and crack propagations. The results show that using FRP has better performance at the lower fire temperature.


Introduction
The structures are encountered with natural problems such as earthquake, flooding and specially, extreme loading conditions. In fact, the structural elements may be affected by fire or impact loading or the simultaneous loads of earthquake and fire in disastrous manner. According to disastrous events during the last two decades like fire and explosion, the necessity of strengthening of structures plays a vital role. So, understanding the structural behavior and damage criteria of the existing structures can be useful to avoid collapsing and improve their capability (Fallahi et al., 2019;Maranan et al., 2016;Soleimani and Sayyar Roudsari, 2015;Soroushnia et al., 2011;Xiao et al., 2016). There are many studies for evaluating RC structures under extreme loading conditions like fire, air blast and so on. Kodur et al. (2003) performed an experimental study on five different concrete columns under fire loading condition. The investigated cases were Normal Strength Concrete (NSC) and High Strength Concrete (HSC) by using steel and polypropylene fibers. The results showed that the column with NSC material had better performance. Also, using polypropylene fibers could increase the ductility and load capacity. In this case, the load capacity of HSC columns was higher than columns with normal concrete. Anil and Altin (2007) had experimental investigation on infilled RC frames. The aim of their research was to find out the ductility behavior of RC frames under lateral cyclic loading. Nine one-story RC frames were tested in the laboratory under cyclic loading conditions. They casted one RC frame without infilled part called bar frame and eight other frames were infilled. The results showed that infilled frame had brittle behavior than bar frame. However, the initial stiffness and energy absorption of infilled frames is higher than bar frame. Also, the larger aspect ratio of infilled frame causes increasing lateral strength of infilled RC frame. Moreover, infilled RC frames have more stiffness and load capacity than simple frames. Al-Kamaki et al. (2015) studied on circular cross-section RC columns damages under temperature loading conditions. Twenty large size RC columns with 750204 millimeters in dimensions, were tested. Six of those columns were considered as control group and fourteen columns were heated fewer than 30% of maximum load. Also, eight of these columns were wrapped using Carbon Fiber Reinforced Polymer (CFRP). The results showed that using CFRP sheets can increase the durability of RC columns after 600, 800 and 1000C. Some of the researches indicated the effect of extreme loading conditions in normal RC members and investigated any deterioration and defects inside or on the surface of the concrete (Goldston et al., 2016;Pham and Hao, 2016;Sayyar Roudsari et al., 2019a;2019b;2019c;2020a;Soleimani and Sayyar Roudsari, 2019;Tang and Saadatmanesh, 2003). However, different studies also undertook to find out the effect of HSC and high-performance materials under fire condition. These studies were done by applying different fire temperatures in various elements (Baant et al., 1996;Hamoush et al., 2019;Khaliq and Kodur, 2011;Kodur and Sultan, 1998). Gyu-Yong et al. (2009) studied on the behavior of HSC under 700C to find out the effect of fire resistance of concrete. The results showed that the concrete strength reduced significantly after 400C. The reduction of module of elasticity also was evaluated under different temperature loading conditions (Castillo, 1987;Persson, 2004). Tan and Nguyen (2013) investigated RC columns under the combination of uniaxial eccentricity and temperature loading conditions. The authors used 29 and 55 MPa of compressive strength of concrete to test under elevated temperature. The RC column had a square cross-section of 300 and 3300 mm height. The results showed that applying simultaneous uniaxial eccentricity and temperature loads caused the faster failure of concrete. Roudsari and Abu-Lebdeh (2019) did analytical study on the effect of fire temperature loading (ASTM, 1990) time on reinforced concrete column behavior. His results show that by increasing the time of fire load, the stiffness is reduced. This paper focuses on RC frame under concurrent fire and lateral loading conditions. Two different validation of models are done: One as a frame without fire load and others as a sample with fire load. Different variables such as the type of material of bars like steel and Carbon Reinforced Polymer (CFRP) as well as the retrofitting pattern are used as the convergent or divergent angle. The pattern of wrapping is the state-of-the-art method is this research. Beside the fire and lateral load, the pressure load is applied on the beam, too. Different target temperatures are used including 200, 400, 600, 800 and 1000C. The models are 5 control samples, 15 retrofitted models with CFRP sheets and 11 reinforced models with CFRP bars. The FRP sheet's angles are 0, 45 and 90 degrees for beam and columns. In this research, ABAQUS software is used. The Concrete Damage Plasticity Model (CDPM) is used in order to define compressive strength, tensile strength and its damage parameters. The numerical results showed very good agreement with experimental output. This paper provides information as load capacity, ductility, stiffness regarding the effect of fire load and retrofitting method of these elements.

Materials and Methods
In order to use ABAQUS software, the validation of FEM with an experimental program is essential. In this study the experimental test performed by (Hemmati et al., 2016) is considered. In this research, two different concrete compressive strengths are used; at first a High-Performance Fiber Reinforced Cementitious Composite (HPFRCC) with 24 MPa used for beamcolumn joint-connection and 48 MPa as normal concrete for other section areas. The geometry and reinforcement details are shown in Fig. 1 and 2. Also, the loading conditions of experimental set up can be seen in the original article.
In this section, the concrete parameters are defined using the work performed by Sayyar Roudsari et al., 2018). They used MATLAB toolbox to compute different concrete parameters including compressive and tensile strain-stress and the corresponding damages. In research conducted by , he developed a model to employ the compressive strength and the failure strain of concrete. In this regard, the strain rate increment is computed based on division of failure strain to small number. Sayyar Roudsari et al. suggested the small number should be at least one-tenth of failure strain. In this step, the number of increments can be calculated. Then, the elastic and plastic strains are computed in both tensile and compressive. After computing the strains, the corresponding stresses are computed. In this step, the linear and nonlinear should be separated. Because, based on his novel theory, concrete damage plasticity model of ABAQUS should use the plastic side of stress-strain data. In order to adjust the boundary, 45% of compressive stress is considered. After modifying and generating the plastic stress-strain data, the damage parameters of tensile and compressive sides are also computed. These parameters can be used in ABAQUS software. The ABAQUS input data for 24 and 48 MPa is shown in Fig. 3  .
The material properties of steel bars as the yield stress, module of elasticity and ultimate strain are reported 400 MPa, 200 GPa and 14.5%, respectively (Obaidat et al., 2010). The CFRP sheets for retrofitting of the RC frame is one layer with 2 mm thickness. The ultimate tensile stress (ffu) of CFRP and elasticity modulus are 3500 MPa and 230 GPa, respectively and the width of sheet is 150 mm. The CFRP mechanical properties are demonstrated in the Table. 1. The mechanical properties of CFRP bars are 2900 MPa and 300 GPa (as ultimate stress and module of elasticity, respectively).
The fire criteria are considered by ASTM E119 standard (ASTM, 1990) to define the temperature-time amplitude (Fig. 4).

Finite Element Modeling and Validations
To validate by ABAQUS software, we selected two experimental. These validations include a frame without fire loading and a sample under fire loading. The first validation considers the RC frame without fire load. The modeling of RC frame is based on (Hemmati et al., 2016) using ABAQUS software. The C3D8R (8-node element using reduced integration) is used for modeling of the frame, S4R and Truss element (T3D2) are employed for CFRP sheets and modeling of bars and stirrups. The Embedded Region Coupling has been utilized to create bonding conditions between bars and concrete elements. The interaction between CFRP sheets and concrete surface is subjected to Tie interaction. The interaction modeling is shown in Fig. 5a. The Non-Linear General Static analysis is used for modeling of RC frame. This RC frame is without fire load. The boundary conditions are divided into two different loading categories. The first load is pressure loading (at the center-top of the beam). The lateral load is applied using displacement-control by defining the Displacement/Rotation category. U1, U2 are fixed and U3 is released. This issue is taken into account by defining a Set of Nodes using ABAQUS tools. The bottom surface of slab is pinned (U1, U2 and U3 = 0). The lateral constant load and pressure are considered 65.5 mm and 1 MPa, respectively. Figure 5b shows the boundary conditions of RC frame.
After analysing the RC frame, the shear forcedisplacement diagram is carried out. This validation is shown in Fig. 6. According to Fig. 6, the FEM modeling has a very good accuracy with experimental tests. By comparing the maximum load capacity, it can be declared that the maximum load capacity in laboratory is 65.31 kN while this parameter is 65.25 kN in ABAQUS (the difference is just about 0.01%).   The second validation is based on (Zhang et al., 2017). He did experimental study on the RC column under fire and earthquake loading conditions. The column geometry was 350×350 mm with 8 longitudinal bars with 20 mm diameters and transvers bar with 10 mm diameter. The lateral load was applied by displacement control up to 600 mm as cyclic load and the fire temperature was considered based on ISO-834 standard fire curve. The maximum furnace temperature of this experimental study reached 900C. Figure 7 shows the modeling of the RC column by ABAQUS. The results of experimental test and finite element modeling are shown in Fig. 8. The load-displacement diagram indicates very good agreement of fire modeling by ABAQUS (about 2% differences). In other word, the finite element output is about 214 kN while the experimental result is 210 kN.

Parametrical Study
In this section, a parametrical study under temperature analysis is developed. The RC frame is used for analysing under 200, 400, 600, 800 and 1000C. The frames are divided into three different groups. The first group is RC frames using only steel rebars under temperature analysis. The second group regards the same frames retrofitted by CFRP sheets. The third group is considered by reinforcing the frames with CFRP bars. For modeling of frames using CFRP bars, the reinforcing is done by; firstly, the longitudinal bars of the beam are just CFRP bars and steel bars are used for members (column, slab). Secondly, all longitudinal bars in both beam and column are reinforced by CFRP bars. Figure 9 shows the geometry shape and details of retrofitting by CFRP wrapping. As it can be seen in Fig. 9, the layout angle of CFRP is different in the beam and columns. The method of retrofitting is shown as model 1, model 2 and model 3. These models have specific configurations which are shown in Fig. 9. It should be noted that the layout direction is divergent. In other word, looking to  Fig. 9 and for example the model 1, the left and right columns have divergent layout direction. Moreover, in models 2 and 3, the same concept is considered. In the Table 2 the description of wrapping and reinforcing models by CFRP is shown. It should be noted that the model's name with steel bars under temperature analysis is called M200 (200C), M400 (400C), M600 (600C), M800 (800C) and M1000 (1000C).  In order to apply the fire load in these models, the same features of first validation model (RC frame) are considered and some other fire load criteria are applied as the Temperature-Dependent Data is provided. The initial fire temperature is zero and the maximum target one depends upon the fire temperature, for instance at 200C, it should be 200. Also, the Specific Heat is considered 5700 for bars, 6000 for CFRP sheets and 1000 for concrete using Constant Volume criteria. The range of conductivity for FRP bars and layout are 0.003-0.0057 and 0.035-0.006, respectively. The conductivity for steel bars is 0.04-0.0518 and the specific heat is 5255. The conductivity parameters for concrete is 0.0005-0.00114. The Hashin Damage parameters are used to define the tensile and compressive behavior of FRP layout (the longitudinal tensile strength is 1278 MPa and its elasticity modulus is 46000 MPa). In terms of fire analysis, the Coupled Temp-Displacement (Transient) Analysis is used to apply for simultaneous fire and lateral displacement. It should be noted that, the time of fire depends on the amount of temperature. Figure  10 shows the time-amplitude of temperature analysis.
Also, the Max Allowable Temperature Change Per Increment is applied 10C. In the interaction module, the Surface Film Condition as the Film Coefficient and Sink Temperature are considered 0.01 and 25, respectively. The lateral and pressure loading are considered as the same as validation model. In the loading module also, the Predefined Field is created to make environment temperature of Concrete Frame by applying 25C. The fire load is utilized by choosing Other/Temperature from Boundary Condition, applying at the inside surface of frame. Each temperature has its own amplitude using Fig. 10. Also, the Heat Flux is applied "10"for all elements (Sayyar Roudsari et al., 2020b). Time (second) Amplitude (Temperature) Figure 11a demonstrates the temperature, pressure and lateral displacement loading conditions of RC frame. Eventually, in the term of meshing criteria, the mesh study is used to verify the mesh seed size. Also, the Mesh Type is Coupled-Temperature-Displacement (Fig. 11b).

Results and Discussion
In this section, the results of RC frames are discussed. The RC frame is evaluated under 200, 400, 600, 800 and 1000C. Then, the RC frame is reinforced by CFRP bars under the same loading temperature conditions and eventually, the RC frames are strengthened using CFRP sheet. The load-displacement diagrams are evaluated in this section by considering the load capacity, ductility, energy absorption and stiffness.
The load-displacement diagram shows in Fig. 12 is regarding the RC frame models without and with fire loading condition. It should also be noted that these samples are modeled using only steel bars. The model's name indicates the fire loading; as an illustration, M-200 means 200C applied as fire temperature and so on. +2.215e+00 -7.461e-01 -3707e+00 -6.668e+00 -9.629e+00 -1.   As it is clear in Fig. 12, by increasing the fire temperature, the load capacity is reduced, so that it has significant reduction in load capacity for models of M-800 and M-1000. By looking at the model M-1000, the maximum displacement is about 47 mm due to high temperature. In other word, in higher temperature not only the load capacity is reduced but also it causes remarkable deduction in displacement. In Fig. 13 the Von Misses and temperature stress distribution of M-200 and M-1000 is shown. In Fig. 13a, the plastic hinge is occurred at the bottom sides of columns. This figure also shows that the buckling of longitudinal bars. On the other hand, in Fig. 13b, the stress distribution of the beam's reinforcements is over the yield and buckling happened. The stress and temperature distribution in Fig. 13b also show that the most area of beam and columns show as plastic characteristic due to high fire temperature which causes un-stability of RC frame. Furthermore, Table 3 shows the von misses stress of models under selected fire loading. Table 3 depicts the behavior of F-CbTotal models under fire temperature loading conditions. These strengthened models are strong enough so that the RC frame is stable even for 1000C.
In Fig. 14, the load displacement diagrams of retrofitted models by CFRP sheets is shown. The information for the name of models is shown in the Table. 1. In these figures, FC-C45B90 has the higher load capacity than others. Granted these models have been analyzed under different fire temperature, but according to the maximum load capacity, they have much more load capacity than models with only steel bars. More importantly, the load capacity of retrofitted models is enhanced when the temperature increases. According to Fig. 14d, the first slope of load displacement diagram is positive compared with models without retrofitting (Fig.  12). This means that by retrofitting, the buckling of RC frame is solved due to enhancement of the load capacity. Figure 15 shows the result of model reinforced with CFRP bars at only the beam (F-CB-Beam) and both beam-columns (F-CB-Total). In Fig. 15a, using CFRP bars do not affect the elastic zone under 200C of fire. On the other hand, by contrasting the Fig. 15b-e, in higher temperatures using CFRP bars at the beam section has better performance. It has to be mentioned that, by comparing the load capacity results for F-CB-Beam in the Fig. 15b-e, one finds out that the elastic and plastic zones have much better capability of load and CFRP bars prevent buckling during the fire temperature procedures. Also, the models reinforced by CFRP bars in both beam and columns (F-CB-total) loaded under 200C has higher load capacity (about 65% enhancement compared to model with steel bars under 200C). In the Fig. 15e, the load capacity of model with CFRP bars in the beam and columns (F-CB-total) under 1000C is 44.3 kN so that it increased about 550 percent compared with model reinforced by steel bars under 1000C. In addition to the mentioned models, one model has been evaluated under the extreme fire temperature loading condition (1000C). In this model, the CFRP bars have been used only and only for the tension part of the beam which is called (F-CB-Beam-Bot). The result of this model is shown in the Fig. 16 demonstrating that using CFRP bars at the tensile area of the RC beam can significantly improve the load capacity, stiffness and avoid the buckling issue of the beam.

Discussion of Parametrical Study
In this section, different results based on parametrical studies have been investigated. In this study the ductility, stiffness, load capacity and seismic factor (R) have been presented. The ductility factor is computed by dividing the maximum displacement (∆ult) on the displacement corresponding to yield force (∆y). Equation 1 explains the ductility formulation:  Eventually, the seismic factor (R) is defined by multiplication of strength reduction factor (Ru) by strength enhancement factor (Rs), Equation 3: In the Equation (3), the strength reduction factor (Ru) is regarding the maximum load if the structure's behavior remains in elastic zone; ((Vel) over the yield load Sayyar Roudsari et al.). Equation (4): In the Fig. 17, the load capacity of models including control (FEM-NON: Without fire temperature load), steel bars, CFRP bars and sheets under different temperature loading is shown. In these figures, the maximum load capacity under all temperature loading conditions belongs to model of FC-C45B90. Also, using CFRP sheets have more load capability than CFRP and steel bars. Moreover, the effect of RC frame by steel bars and CFRP bars just at the tensile area of the beam are almost the same for 200 and 400C. This issue is different for higher fire temperature. As a matter of fact, even using CFRP bars at the tensile part of concrete have good effect on the load capacity. The reason of better performance of models retrofitted by CFRP sheets is on the wake of the mechanical properties of CFRP wraps. Since it can protect the concrete surface during the fire load until rapture of the CFRP sheets. By increasing the lateral load and fire temperature, the cracks start to be propagated in the concrete which leads to complete failure. Generally, in terms of load capacity, the maximum load capacity reduction is for models under 1000C.
In the Fig. 18, the stiffness of all models is shown. In the Fig. 18a, the stiffness of retrofitted models is almost in the same level (about 26.67 which are under 200C) but by increasing the temperature, the stiffness of retrofitted models has been changed. In fact, in higher fire temperature load, FC-C0B90 model has better performance among retrofitted models. On the other hand, the stiffness of CFRP bars for model of F-CB-Total is higher than F-CB-Beam in all fire temperatures. The model of F-CB-Total has the best performance in the maximum fire temperature loading conditions such as 800 and 1000C by having 33 and 22 GPa, respectively. In addition, the performance of models with steel bars under different loading conditions are divides into two parts. As a matter of fact, it does have a boundary as 600C. So that under 600C the stiffness is increased but after 600C degree shows a reduction trend. The reason of this issue goes back to the RC frame. In other word, RC frame tolerates both fire temperature and lateral loadings until 600C. After that, the steel bars start to be failed due to 800 and 1000C and this issue causes buckling of the beam. Figure 19 depicts the ductility of models. In these figures, the steel bars models have appropriate performance for 200, 400 and 600°C, but after that is has a reduction trend. Moreover, for the ductility of retrofitted models, FC-C0B90 has always more value than FC-C45B45 and FC-C45B90. The steel bars models have more ductility under 600°C especially for 400 and 600°C. This phenomenon occurs on the grounds of the better ductility of steel bars than CFRP bars. In fact, CFRP bars have brittle behavior and during the fire temperature (from 200 to 600°C and after the boundary temperature 600°C), the models using steel bars start to be buckled. Therefore, the CFRP bars models have better performance in 800 and 1000°C loading conditions.   Figure 20 shows the seismic factor of R. The R factor FC-C0B90 is higher for models under 200, 400 and 600°C and it has reduction trend for 800 and 1000°C. Also, using CFRP bars at the beam has the lowest value of R among all models, event thought models with steel bars have increasing trend from 200 to 1000°C.

Conclusion
On the basis of the presented modeling and analyzing and evaluated results, the followings are concluded:


The maximum load capacity for 200, 400, 600 and 800°C is belonged to FC-C45B90 model, Fig. 17  The CFRP sheets and bars have much better performance than steel bars for avoiding the buckling and collapsing of RC frame. In effect, they can provide enough strength for system to delay the failure of RC frame