Seismic performance evaluation of steel and GFRP reinforced concrete shear walls at high temperature

Abstract

Fire-induced structural damage to the seismic performance of reinforced concrete shear walls is critical in the event of a fire-earthquake scenario. However, only few researchers have studied the seismic performance of reinforced concrete shear walls at high temperatures. This study focuses on the seismic performance of fiber reinforced concrete shear walls at high temperatures by using finite element (FE) software, ABAQUS. The experimental test available in a literature on seismic behavior of shear walls exposed to fire and thermal properties of glass fiber reinforced polymer (GFRP) bars were used to validate the FE model and showed good agreement and thus used in the simulation.

The FE results showed that exposure of RC shear wall to fire reduced the strength of the wall. The strength of walls at the maximum applied drift of 3.2% with concrete cover thicknesses of 20 mm, 25 mm, and 30 mm was dropped by about 70%, 76%, and 85% of the reference shear wall, respectively. Similarly, the strength of RC walls was reduced by about 80%, 75%, and 68% of the reference shear wall for the duration of fire exposure of 30 min, 60 min, and 120 min, respectively. Additionally, the strength of walls due to one side, two sides, or all sides’ exposure to fire was decreased by about 68%, 56%, and 50% of the reference shear wall, respectively. It can generally be concluded that the fire exposure sides has largely affected the strength of the shear wall compared to the other parameters and GFRP bars were more sensitive to temperature than steel bars.

Introduction

According to global fire statistics, approximately one million people died in fires between 1993 and 2014 with structures accounting for roughly 40% of all fires [1]. Fire resistance is an important aspect of structural safety because rising temperatures in fire conditions reduce concrete’s load-carrying capacity [2]. Internal micro cracks or damages appear in concrete as a result of structural and chemical changes in the material caused by elevated temperatures [3]. Many researchers have studied the performance of different structural members such as beams, columns, and slabs at high temperatures, other than room temperature applied on the structures as per ISO-834 or ASTM E-119. However, there are only limited numbers of studies on seismic performance of reinforced concrete shear walls at high temperatures.

Different researchers carried out numerical and experimental tests on the residual strength and lateral load carrying capacity of reinforced concrete columns at high temperatures [1, 4,5,6], theoretical and experimental investigation on the structural performance of reinforced concrete (RC) walls subjected to fire [7,8,9,10], and RC slabs subjected to fire [7, 11]. Some researchers have also studied the behavior of GFRP reinforced structures exposed to fire [8,9,10]. The behavior of fire-damaged RC walls differs from that of other structural components such as beams and columns due to the fact that RC walls have large fire exposure surface and thus the damaged region caused by fire varies depending on the fire scenario [12].

Temperature change has a significant impact on material properties of concrete, steel or GFRP bars. Gui-rong et al. [13] experimentally investigated the seismic behavior of RC shear walls in terms of fire exposure, reinforcement ratio, and the presence of axial load under fire. The use of GFRP bars as primary reinforcement in concrete structures is becoming widely recognized. Many researchers have been looking into their seismic performance as a lateral resisting system in recent years. GFRP bars are still not recommended for seismic design because of the lack of experimental data [14]. One of the most critical issues for the acceptance of glass fiber-reinforced polymer GFRP reinforcing bars as reinforcement in concrete structures is their long-term behavior. The elasticity modulus of GFRP reinforcing bars is low by design, and it must not decrease significantly over time under load [15]. Nicoletta et al. [16] experimentally studied the GFRP-to-concrete bond and tensile strength of GFRP bars at elevated temperatures in slab.

Similarly, an experimental investigation was carried out by Gooranorimi et al. [17] and Hajiloo et al. [18] who looked at the residual strength of fire-exposed GFRP-RC slabs as well as the GFRP mechanical properties following furnace exposure. In the above reviewed literatures, it can be generalized that the performance of different structural elements such as columns, beams, slabs, and shear walls subjected to standard fire and lateral loads were studied. Although many studies have been conducted on reinforced concrete members subjected to fire, only a few studies on shear walls, particularly those with all-sided fire exposure, have been documented [19]. Additionally, there is insufficient data to understand the seismic behaviors of fire-damaged RC shear walls with different design parameters, such as type of reinforcing bar (i.e., steel bar and GFRP), thickness of clear concrete cover from the main bar, duration of fire exposure, and fire exposure sides.

Therefore, the main objective of this study is to predict the seismic behavior of steel and GFRP RC shear walls subjected to fire through load-displacement response, load at the applied drift ratio, and crack patterns. The lateral load performance of seventeen reinforced concrete shear walls at high temperatures were studied based on the parameters such as duration of fire exposure, fire exposure sides, thickness of clear concrete cover from main bar and using steel or GFRP bars as reinforcements.

Methods

Verification of experimental and FE model specimens

Experimental test on a shear wall [12] subjected to fire and cyclic loading was used to validate the FE model in ABAQUS. The shear wall under study was subjected to thermal loading in accordance with ISO-834 standard time-temperature curve and mechanical loading based on Eurocode-2-part1-2 [20]. The height and length of the reinforced concrete shear walls were 2400 mm and 960 mm, respectively. The wall thickness was 200 mm, and the reinforcements were as illustrated in Fig. 1. As clearly stated by Ryu et al. [12], the specimen was placed in a furnace, as shown in Fig. 2, only one face of the wall specimens was exposed to high temperatures for 2 h based on ISO-834. The geometry, steel material properties, mechanical loading, boundary conditions, and reinforcement details of the FE model were identical to that of experimental test. The advantage of the symmetrical nature of the geometry, loading, and boundary conditions was not taken since heat transfer is a matter of conductivity and depends on the size of the structure as well.

Fig. 1

Reinforcement details of the shear wall [12]. a Elevation (all dimensions are mm). b Cross section (all dimensions are mm)

Fig. 2

Thermal loading test set up [12]

The shear wall was loaded axially with a constant axial load of 10% of the axial strength of concrete and laterally by the lateral loading protocol as shown in Fig. 3. In this paper the cyclic loading protocol (Fig. 4) was changed to monotonic loading by applying the maximum drift ratio of 3.2% (maximum displacement of 77 mm) applied at the center of the actuator load to the negative X-direction as shown in Fig. 5. Figure 6 illustrates the monotonic loading protocol used in the model. The lateral load was applied in terms of displacement-controlled step, where the displacement is determined from the drift ratio (%) based on Eq. (2.1).

$$Drift\ ratio\ \left(\%\right)=\frac{\Delta }{L}{\ast}_{100}$$

(2.1)

Fig. 3

Mechanical loading of test set up [12]

Fig. 4

Mechanical loading protocol used in test [12]

Fig. 5

Mechanical loading and boundary conditions used in the model

Fig. 6

Monotonic loading protocol used in the model

Where Δand L are the applied displacement at the center of top beam through RP1 and length of the shear wall respectively.

Meshing and interactions used in the model

The elements used and their mesh size plays a significant role in a numerical simulation. In finite element modeling, a finer mesh typically results in a more accurate solution. As shown in Fig. 7, a 50-mm mesh size was used for all elements in the model. The thermal elements used were DC3D8 (an 8-node linear heat transfer brick) for concrete and DC1D2 (a 2-node heat transfer link) for reinforcements and the structural elements used in the stress analysis were C3D8R (an 8-node linear brick) for concrete and T3D2 (a 2-node linear 3D-truss) for steel respectively [21]. There were 1484 T3D2 and 4408 C3D8R (see Fig. 8) leading to a total of 5892 elements and 7398 nodes in the developed model with a mesh size of 50 mm. An eight-node hexahedral (brick) element has higher capabilities of converging due to its increased node count, resulting in a more accurate analysis [22]. To manage the accuracy and computing resource, a mesh convergence study was performed in this study. In order to perform mesh size sensitivity of the finite element model, the specimen with 50 mm, 55 mm and 60 mm element mesh sizes were examined in terms of lateral load-displacement responses. Figure 9 compares the simulation results of the specimen SW-C1 using 50 mm, 55 mm and 60 mm element mesh sizes against the test results presented in experimental study by Ryu et al. (2020). After conducting the mesh sensitivity analysis, it was found that mesh size 50 mm leads more reliable results in comparison to the other two and a good agreement with the test result; therefore, 50 mm mesh size was used for all elements.

Fig. 7

Meshing used in the model

Fig. 8

Three-dimensional eight-node linear hexahedral (brick) element with reduced integration (C3D8R)

Fig. 9

Different mesh sizes analysis

As indicated in Fig. 10 a two-node linear three-dimensional truss elements (T3D2) having three degrees of freedom in each node were used to model steel reinforcements. Two types of interactions were utilized in the finite element modeling of this study. The first interaction was the embedded bond between the concrete and the steel reinforcement. Interface modeling in reinforced concrete elements is vital and particularly in modeling reinforced structures [23]. The interaction between concrete and reinforcement after cracking, such as bond slip was incorporated only in a simplified way using the tension stiffening in the concrete model [24, 25]. The second interaction was defined in the form of a surface-based tie constraint in which a constraint was formed between a master and a slave surface.

Fig. 10

Two-node linear three-dimensional truss element (T3D2)

Materials

Thermal and mechanical properties of concrete

The first thermal property of concrete at elevated temperature is thermal conductivity (λ_c). The thermal conductivity of concrete gradually decreases as the temperature rises. Equation (2.2) shows relationship of thermal conductivity and temperature [20]. Figure 11 shows the upper limit of thermal conductivity of normal weight concrete as a function of temperature used in the study based on Eurocode-2-part1-2.

$${\lambda}_c=2-0.2451\left(\frac{\theta }{100}\right)+0.0107{\left(\frac{\theta }{100}\right)}^2\ \left(W/ mK\right)\kern0.5em \frac{\textrm{for}\ {20}^{{}^{\circ}}\textrm{C}\le \theta }{\le 1{200}^{{}^{\circ}}\textrm{C}}$$

(2.2)

Fig. 11

Thermal conductivity of concrete [20]

Where θ is the concrete temperature and λ_c is thermal conductivity

The second thermal property of normal weight concrete at elevated temperature is specific heat. Equations (2.2)–(2.5) show relationship of specific heat, c_p(θ), of dry concrete (u = 0%) and temperature [20]. Figure 12 shows the specific heat of normal weight dry siliceous and calcareous aggregates concrete as a function of temperature used in the study based on Eurocode-2-part1-2.

$${\displaystyle \begin{array}{cc}{C}_p\left(\theta \right)=900\ \left(J/ kg\ K\right)& \textrm{for}\end{array}}\ 2{0}^{{}^{\circ}}\textrm{C}\le \theta \le 100{0}^{{}^{\circ}}\textrm{C}$$

(2.2)

$${\displaystyle \begin{array}{cc}\begin{array}{cc}{C}_p\left(\theta \right)=900+\left(\theta -100\right)\ \left(J/ kg\ K\right)& \textrm{for}\end{array}\ 10{0}^{{}^{\circ}}\textrm{C}<\theta \le 20{0}^{{}^{\circ}}\textrm{C}&\ \end{array}}$$

(2.3)

$${\displaystyle \begin{array}{cc}{C}_p\left(\theta \right)=1000+\frac{\left(\theta -200\right)}{2}\left(J/ kg\ K\right)& \textrm{for}\ 20{0}^{{}^{\circ}}\textrm{C}<\theta \le 40{0}^{{}^{\circ}}\textrm{C}\end{array}}$$

(2.4)

$${\displaystyle \begin{array}{cc}{C}_p\left(\theta \right)=1100\ \left(J/ kg\ K\right)& \textrm{for}\ 40{0}^{{}^{\circ}}\textrm{C}<\theta \le 120{0}^{{}^{\circ}}\textrm{C}\end{array}}$$

(2.5)

Fig. 12

Specific heat for siliceous concrete [20]

The third thermal property of normal weight concrete at elevated temperature is density. The variation of density with temperature, ρ(θ), is influenced by water loss and is defined as follows in Eqs. (2.6)–(2.9) [20]. Figure 13 shows the density of normal weight concrete as a function of temperature used in the study based on Eurocode-2-part1-2. The density of concrete at ambient temperature used in the study ρ(20 ° C) is 2330 kg/m³. Figure 14 shows the coefficient of thermal expansion of concrete at elevated temperatures.

$${\displaystyle \begin{array}{cc}\rho \left(\theta \right)=\rho \left(2{0}^{{}^{\circ}}C\right)& \textrm{for}\ 2{0}^{{}^{\circ}}\textrm{C}\le \theta \le 11{5}^{{}^{\circ}}\textrm{C}\end{array}}$$

(2.6)

$${\displaystyle \begin{array}{cc}\rho \left(\theta \right)=\rho \left(2{0}^{{}^{\circ}}C\right)\left(1-0.02\left(\frac{\theta -115}{85}\right)\right)& \textrm{for}\ 11{5}^{{}^{\circ}}\textrm{C}<\theta \le 20{0}^{{}^{\circ}}\textrm{C}\end{array}}$$

(2.7)

$${\displaystyle \begin{array}{cc}\rho \left(\theta \right)=\rho \left(2{0}^{{}^{\circ}}C\right)\left(0.98-0.03\left(\frac{\theta -200}{200}\right)\right)& \textrm{for}\ 20{0}^{{}^{\circ}}\textrm{C}<\theta \le 40{0}^{{}^{\circ}}\textrm{C}\end{array}}$$

(2.8)

$${\displaystyle \begin{array}{cc}\rho \left(\theta \right)=\rho \left(2{0}^{{}^{\circ}}C\right)\left(0.95-0.07\left(\frac{\theta -400}{800}\right)\right)& \textrm{for}\ 40{0}^{{}^{\circ}}\textrm{C}<\theta \le 120{0}^{{}^{\circ}}\textrm{C}\end{array}}$$

(2.9)

Fig. 13

Density of concrete at elevated temperatures [20]

Fig. 14

Coefficient of thermal expansion of concrete at elevated temperatures [20]

The mechanical properties of concrete at elevated temperatures are compressive strength, tensile strength, modulus of elasticity, and poison’s ratio. The mean cylindrical compressive and tensile strengths of concrete at ambient temperature were 60.8 MPa and 3.5 MPa, respectively [12] for validation. For parametric study, the characteristic cylindrical compressive strength of concrete was 30 MPa for reference wall (control specimen). Based on Eurocode-2-part1-2, the compressive and tensile strength of concrete at temperature, θ, were determined by multiplying the factors given for the respective temperature and characteristic compressive or tensile strength [20]. As depicted in Eurocode-2-part-1-2, the strength and deformation properties of uniaxially stressed concrete at elevated temperatures shall be obtained from the stress-strain relationships shown in Eq. (2.10). For ε_{c1, θ} ≤ ε ≤ ε_{cu1, θ}any linear or non-linear descending branch can be adopted as stated in Eurocode-2-part-1-2. Where σ(θ) is stress at temperatureθ, εis any strain within the range, f_{c, θ}is compressive strength of concrete at temperature θ, ε_{c1, θ} is the strain at f_{c, θ} and ε_{cu1, θ} is the peak strain at temperature, θ. In this study, a non-linear descending branch at elevated temperatures was adopted for numerical purpose as shown in Fig. 15. Figure 16 shows the relationship of stress- strain of concrete in tension at elevated temperature used in this study. Figure 17 shows the relationship of compressive strength of concrete and temperature. The tensile strength of concrete at elevated temperatures is depicted in Fig. 18. The Poisson’s ratio of concrete used in the model was 0.15 and Young’s modulus of concrete at elevated temperature was determined by using Eq. (2.15). Figure 19 shows modulus of elasticity of concrete at elevated temperature.

$${\displaystyle \begin{array}{cc}\sigma \left(\theta \right)=\frac{3\varepsilon {f}_{c,\theta }}{\varepsilon_{c1,\theta\ \left(2+{\left(\frac{\varepsilon }{\varepsilon_{c1,\theta }}\right)}^3\right)}}& \textrm{for}^{\varepsilon \le {\varepsilon}_{c1,\theta }}\end{array}}$$

(2.10)

$$fck,t\left(\theta \right)= kc.t{\left(\theta \right)}^{\ast } fck,t$$

(2.11)

$$\textrm{Where},{\kern0.75em }^{fck,t=0.3321\sqrt{F_{ck}}}\kern0.5em \left(\textrm{MPa}\right)$$

(2.12)

$${\displaystyle \begin{array}{cc} kc,t\left(\theta \right)=1& \textrm{for}\ 20{}^{\circ}\textrm{C}\le \theta\ \end{array}}\le 10{0}^{{}^{\circ}}\textrm{C}$$

(2.13)

$${\displaystyle \begin{array}{cc} kc,t\left(\theta \right)=1-\frac{\theta -100}{500}& \textrm{for}\ 100{}^{\circ}\textrm{C}\le \theta \le 60{0}^{{}^{\circ}}\textrm{C}\end{array}}$$

(2.14)

$$Ec\left(\theta \right)=4700\sqrt{fc,\theta }$$

(2.15)

Fig. 15

Stress-strain relationships of concrete under uniaxial compression at elevated temperatures

Fig. 16

Stress-strain relationship of concrete in tension at elevated temperatures [20, 26]

Fig. 17

Compressive strength of concrete at elevated temperatures [20]

Fig. 18

Tensile strength of concrete at elevated temperatures [20]

Fig. 19

Elasticity of concrete at elevated temperature [20]

where Fc, θ is as defined above (MPa)

Thermal and mechanical properties of steel reinforcement

The first thermal property of steel at elevated temperature is thermal conductivity (λ_s). Equations (2.16) and (2.17) show relationship of thermal conductivity and temperature [20]. Figure 20 shows the thermal conductivity of reinforcing steel as a function of temperature used in the study based on Eurocode-2-part1-2.

$${\displaystyle \begin{array}{cc}{\lambda}_s=54-3.33\ast 1{0}^{-2}\ast {\theta}_s\left(W/ mK\right)& \textrm{for}\ 20{}^{\circ}\textrm{C}{\le}^{\theta_s}\le 80{0}^{{}^{\circ}}\textrm{C}\end{array}}$$

(2.16)

$${\displaystyle \begin{array}{cc}{\lambda}_s=27.3\left(W/ mK\right)& \textrm{for}\ 800{}^{\circ}\textrm{C}{<}^{\theta_s}\le 120{0}^{{}^{\circ}}\textrm{C}\end{array}}$$

(2.17)

Fig. 20

Thermal conductivity of steel [20]

where θ_s the steel temperature [°C] and λs is thermal conductivity of reinforcing steel in W/mK. The second thermal property of reinforcing steel at elevated temperature is specific heat. Equations (2.18)–(2.21) show relationship of specific heat, C_s(θ), reinforcing steel, and temperature [20]. Figure 21 shows the specific heat of reinforcing steel as a function of temperature used in the study based on Eurocode-2-part1-2.

$${\displaystyle \begin{array}{cc}{C}_s\left(\theta \right)=425+7.73\ast {10}^{-1}{\theta}_s-1.69\ast {10}^{-3}{\theta}_s^2+2.2\ast {10}^{-6}{\theta}_s^3& 20{}^{\circ}\textrm{C}{\le}^{\theta_s}\end{array}}<600{}^{\circ}\textrm{C}$$

(2.18)

$${\displaystyle \begin{array}{cc}{C}_s\left(\theta \right)=666+\frac{13002}{738-{\theta}_s}\left(J/ kg\ K\right)& 60{0}^{{}^{\circ}}\end{array}}\textrm{C}{\le}^{\theta_s}73{5}^{{}^{\circ}}\textrm{C}$$

(2.19)

$${\displaystyle \begin{array}{cc}{C}_s\left(\theta \right)=545+\frac{17820}{\theta_s-731}\left(J/ kg\ K\right)\ & 735{}^{\circ}\textrm{C}\ {<}^{\theta_s}<90{0}^{{}^{\circ}}\textrm{C}\end{array}}$$

(2.20)

$${\displaystyle \begin{array}{cc}{C}_s\left(\theta \right)=650\ \left(J/ kg\ K\right)& 900{}^{\circ}\textrm{C}{\le}^{\theta_s}<120{0}^{{}^{\circ}}\textrm{C}\end{array}}$$

(2.21)

Fig. 21

Specific heat of steel [20]

Where C_s(θ) is specific heat of steel in J/kg K and θ_s is the steel temperature [°C]. The third thermal property of reinforcing steel at elevated temperature is density. The variation of density with temperature, ρ(θ), for steel reinforcement is not defined in Eurocode-2-part1-2. The density of reinforcing steel at ambient temperature used in the study ρ(20 ° C) is 7850 kg/m³. The last thermal property of reinforcing steel at elevated temperature is thermal strain and coefficient of thermal expansion Fig. 22 depicts the coefficient of thermal expansion of steel at elevated temperatures. The thermal strain, ℇ_s (ϴ) of steel may be determined from the following equations with reference to the length at 20 °C.

$${\displaystyle \begin{array}{cc}{\varepsilon}_s\left(\theta \right)=-2.416x1{0}^{-4}+1.26x1{0}^{-5}{\theta}_s+0.4x1{0}^{-8}{\theta}_s^2& \textrm{for}\ 20{}^{\circ}\textrm{C}\ {<}^{\theta_s}\le 75{0}^{{}^{\circ}}\textrm{C}\end{array}}$$

(2.22)

$${\displaystyle \begin{array}{cc}{\varepsilon}_s\left(\theta \right)=11x1{0}^{-3}& \textrm{for}\ 750{}^{\circ}\textrm{C}\ {<}^{\theta_s}\le 86{0}^{{}^{\circ}}\textrm{C}\end{array}}$$

(2.23)

$${\displaystyle \begin{array}{cc}{\varepsilon}_s\left(\theta \right)=-6.2x1{0}^{-3}+2x1{0}^{-5}{\theta}_s& \textrm{for}\ 860{}^{\circ}\textrm{C}\ {<}^{\theta_s}\le 120{0}^{{}^{\circ}}\textrm{C}\end{array}}$$

(2.24)

Fig. 22

Coefficient of thermal expansion of steel [20]

Coefficient of thermal expansion of steel was obtained from thermal strains. The stress strain relationship of reinforcing steel at elevated temperature was modeled based on EN 1992-1-2 [20] as shown in Eqs. (2.25)–(2.34). The equation of stress at temperature θ, σ(θ), is given for different strain ranges in EN 1992-1-2. The strength and deformation properties of reinforcing steel at elevated temperatures shall be obtained from the following equations. Figure 23 shows the stress strain relationship of reinforcing steel at elevated temperatures used in this paper based on EN 1992-1-2

$${\displaystyle \begin{array}{cc}\sigma \left(\theta \right)=\varepsilon {E}_{s,\theta }& \textrm{for}^{\varepsilon \le {\varepsilon}_{sp,\theta }}\ \end{array}}$$

(2.25)

$${\textrm{where}}^{E_{s,\theta =\frac{f_{sp,\theta }}{\varepsilon_{sp,\theta }}}}$$

(2.26)

$${\displaystyle \begin{array}{cc}\sigma \left(\theta \right)={f}_{sp,\theta }-c+\left(\frac{b}{a}\right){\left({a}^2{\left({\varepsilon}_{sy,\theta }-\varepsilon \right)}^2\right)}^{0.5}& \textrm{for}^{\varepsilon_{sp,\theta}\le \varepsilon \le {\varepsilon}_{sy,\theta }}\end{array}}$$

(2.27)

$${\textrm{Where}}^{a^2=\left({\varepsilon}_{sy,\theta }-{\varepsilon}_{sp,\theta}\right)\left({\varepsilon}_{sy,\theta }-{\varepsilon}_{sp,\theta }+\frac{C}{\varepsilon_{s,\theta }}\right)}$$

(2.28)

$${b}^2=c\left({\varepsilon}_{sy,\theta }-{\varepsilon}_{sp,\theta}\right){E}_{s,\theta }+{c}^2$$

(2.29)

$$c=\frac{{\left({f}_{sy,\theta }-{f}_{sy,\theta}\right)}^2}{\left({\varepsilon}_{sy,\theta }-{\varepsilon}_{sp,\theta}\right){E}_{s,\theta }-2\left({f}_{sy,\theta }-{f}_{sy,\theta}\right)}$$

(2.30)

$${\displaystyle \begin{array}{cc}\upsigma \left(\uptheta \right)={\textrm{f}}_{\textrm{sy},\uptheta}& {\textrm{for}}^{\upvarepsilon_{\textrm{sy},\uptheta}\le \upvarepsilon \le {\upvarepsilon}_{\textrm{st},\uptheta}}\end{array}}$$

(2.31)

$${\displaystyle \begin{array}{cc}\upsigma \left(\uptheta \right)={\textrm{f}}_{\textrm{sy},\uptheta}\left(1-\left(\frac{\upvarepsilon -{\upvarepsilon}_{\textrm{st},\uptheta}}{\upvarepsilon_{\textrm{su},\uptheta}-{\upvarepsilon}_{\textrm{st},\uptheta}}\right)\right)& {\textrm{for}}^{\upvarepsilon_{\textrm{st},\uptheta}\le \upvarepsilon \le {\upvarepsilon}_{\textrm{su},\uptheta}}\end{array}}$$

(2.32)

$${\displaystyle \begin{array}{cc}\upsigma \left(\uptheta \right)=0& {\textrm{for}}^{\upvarepsilon ={\upvarepsilon}_{\textrm{su},\uptheta}}\end{array}}$$

(2.33)

$${\displaystyle \begin{array}{c}{\upvarepsilon}_{\textrm{sp},\uptheta}=\frac{{\textrm{f}}_{\textrm{sp},\uptheta}}{{\textrm{E}}_{\textrm{s},\uptheta}}\\ {}{\upvarepsilon}_{\textrm{sy},\uptheta}=0.02,{\upvarepsilon}_{\textrm{st},\uptheta}=0.15\ {\textrm{and}}^{\upvarepsilon_{\textrm{su},\uptheta}=0.20}\end{array}}$$

(2.34)

Fig. 23

Stress-strain of steel at elevated temperature [20]

The mechanical properties of the longitudinal reinforcement and stirrups in numerical modeling were exactly the same as the material properties used in the test [12] and Poisson’s ratio of 0.3.

The characteristic yield strength and modulus of elasticity of reinforcing steel at ambient temperature was given in Table 1. Modulus of elasticity of reinforcing steel decreases at elevated temperatures as shown in Fig. 24. Similarly, the yield strength of reinforcing steel decreases at elevated temperature as depicted in Fig. 25.

Table 1 Mechanical properties of steel at ambient temperatures

Fig. 24

Elasticity of reinforcing steel at elevated temperature [20]

Fig. 25

Yield strength of reinforcing steel at elevated temperature [20]

Thermal and mechanical properties of GFRP reinforcement

The thermal and mechanical properties of GFRP bar at elevated temperature are not specified in codes. Therefore, it is opted to extract them from journal articles and validate them too. The properties of GFRP bars at elevated temperatures used in this paper were extracted from [27]. The density and modulus of elasticity of GFRP bars at room temperature were taken as 1600 kg/m³ and 41 GPa respectively [28]. The extracted properties are not blindly used (used after validating them) for parametric study. There are limited test data on thermal conductivity and specific heat of GFRP. This is attributed to lack of research and specific instrumentation required to handle the complex nature of chemical reactions taking place in GFRP at high temperatures. Figure 26 shows the thermal conductivity of GFRP bars as a function of temperature used in the study [27]. Figure 27 shows the specific heat of GFRP bars as a function of temperature used in the study based on [27]. The variation of density with temperature, ρ(θ), for GFRP bar was not defined in [27]. The coefficient of thermal expansion of the GFRP bar at room temperature is 6.58 × 10⁻⁶ [1/K] [28]. Glass fiber reinforced polymer (GFRP) composite bars have been used as reinforcement in concrete constructions where steel reinforcement is expected to corrode over the last two decades thanks to technological advancements [17]. The modulus of elasticity and tensile strength of GFRP bars at elevated temperatures were shown in Figs. 28 and 29 respectively.

Fig. 26

Thermal conductivity of GFRP bar [27]

Fig. 27

Specific heat of GFRP bar [27]

Fig. 28

Elasticity of GFRP bar at elevated temperature [27]

Fig. 29

Tensile strength of GFRP bar at elevated temperature [27]

Parameters of the study

One of the parameter of this study was effect of increasing or decreasing clear thickness of concrete cover. Demir et al. [1] tested reinforced concrete columns under a constant axial load and reversed cyclic lateral displacements after being exposed to an ISO-834 standard fire. The test results revealed that fire exposure reduced the structure’s lateral load-carrying capacity, and the thickness of the concrete cover had only a minor impact on the columns' seismic behavior at high temperatures, according to the test results. Similarly, Cai et al. [29] used the ABAQUS finite-element analysis (FEA) software to investigate the performance of RC beams at high temperatures. The results revealed that the cover thickness, time of fire exposure, longitudinal reinforcement ratio, and shear span to effective depth ratio all had a significant impact on the flexural capacity of RC beams after fire exposure.

The other parameter of this study was the effect of reinforcing the shear wall completely with GFRP (glass fiber reinforced polymer) or reinforcing steel. Technologies developed over the last two decades have introduced the use of glass fiber reinforced polymer (GFRP) composite bars as reinforcement in concrete structures when corrosion of the steel reinforcement is likely to occur [17]. As it can be seen from [27], FRP loses nearly 50% of its strength in the temperature range of 250–350 °C, which is much more rapid as compared to loss in strength of steel bars. Therefore, a concrete cover of 30 mm with duration of fire exposure of 60 min was used for better performance of GFRP bars and for comparing performance of steel or GFRP reinforced shear wall at high temperatures.

For concrete structures reinforced with fiber-reinforced polymer (FRP) bars, large temperature variations cause problems. The reason for this is the large difference in transverse thermal expansion coefficients between these bars and hardened concrete. This pressure difference causes radial pressure at the FRP bar/concrete interface, which can result in concrete splitting cracks [7]. The effect of high temperatures on the behavior of FRP bars was also investigated by using steady state and transient temperature protocols with a temperature range of 25 °C–360 °C. A small number of specimens were also studied to see how embedment length affected the results. The findings for temperatures below 80 °C apply to higher service temperatures as well, and higher temperatures have a significant impact on fire performance [30].

Moreover increasing or decreasing fire exposure sides and duration of fire were also parameters of this study. Demir et al. [1] tested reinforced concrete columns under a constant axial load and reversed cyclic lateral displacements after exposure to an ISO-834 standard fire for 30, 60, and 90 min, respectively and fire exposure reduced the structure’s lateral load carrying capacity, according to the results of the tests. Chinthapalli and Agarwal [4] tested the behavior of RC columns at high temperatures and found that the axial load–carrying capacity of RC columns at elevated temperatures decreases as the duration of fire exposure increases. Similarly, Cai et al. [29] used the FEA software to investigate the performance of RC beams at high temperatures. The results showed that the time of fire exposure, ratio of longitudinal reinforcement had a significant impact on the flexural capacity of RC beams after fire exposure. The parameters of this study are summarized in Table 2 below.

Table 2 Summary of parameters of the study

Where

RF-SW	Reference shear wall (control specimen)
SW-C1-3	Shear wall with cover of 20 mm, 25 mm, and 30 mm respectively
SW-D1-3	Shear wall with duration of 30 min, 60 min, and 120 min respectively
SW-S1-3	Shear wall with one-sided, two-sided, and all-sided fire exposures respectively
SW-GF	Shear wall with GFRP bars as reinforcement
SW-GF-S1-3,SW-STEEL-S1-3	GFRP and steel reinforced concrete shear wall heated on one, two, and all sides respectively
L	Length of wall
tw	Thickness of wall
tc	Thickness of cover from main bar

Results and discussion

Validation of FE model

Thermal and mechanical analysis results

Experimental test on a shear wall subjected to fire was validated and it gave good results which confirms with that of experimental test result. The temperature distribution across the cross section of the shear wall subjected to fire for 2 h in one side is shown in Fig. 30 below. The temperature range is 229 °C–1024 °C. Figure 31 depicts temperature distributions at different locations from heated surface draws a comparison between the averages predicted and measured temperature in the cross section of RC shear wall for the entire fire exposure. It is clear from this figure that there is a good agreement between the measured and predicted temperatures throughout the fire test. The maximum average deviation between the predicted and measured results was 3%. Material properties and geometric dimensions of shear wall [12] which was tested experimentally under lateral loading with maximum lateral drift ratio of 3.2% at the top of shear wall was validated and gave good result. The temperature range on the surface of reinforcement for the shear wall heated for 2 h based on ISO-834 standard time-temperature curve is 258 °C–833 °C (Fig. 32 below). The thermal properties of GFRP bars at elevated temperatures presented in [27] were validated and gave good results which agree to experimental results. Figure 33 shows the comparison of the temperature distributions on the surface of GFRP bar in [31] and that of FE model. The deviation of the results was 3% so that the thermal properties presented in [31] were used for thermomechanical analysis of GFRP reinforced shear wall. Figure 34a shows a comparison of force versus deflection at ambient temperature and the force versus deflection at the top of shear wall between the experimental and simulation results during the course of mechanical analysis and thermomechanical analysis respectively. It can be seen from Fig. 34a that there is a good agreement between the measured and simulated envelope curves. The maximum average deviation between the predicted and measured results was within 5%. Figure 34b, c depicts cyclic response (in terms of crack) of steel RC shear wall subjected to fire for 2 h and mechanical loading in test by Ryu et al. (2020) and monotonic response (in terms of crack) of steel RC shear wall subjected to fire for 2 h and mechanical loading using FEM. As it can be seen from the figures the responses are in good agreement.

Fig. 30

Temperature distribution across the cross section of the shear wall

Fig. 31

Temperature distributions at different locations from heated surface

Fig. 32

Temperature distributions on the reinforcements

Fig. 33

Temperature distribution on GFRP. a Load-displacement curve. b Crack distribution at 2% drift in test. c Crack distribution at 2% drift in FEM

Fig. 34

Comparison of load-displacement curve (a) and crack distributions at drift of 2% in test and FEM (b and c)

Parametric study

A parametric study was carried out using the developed FE control model (reference shear wall) to investigate the influence of thickness of concrete cover, the effect of duration of fire, effect of different fire exposure sides and the effect of using steel bars or GFRP bars as reinforcement. The seismic responses of shear walls at high temperatures due to lateral loads such as temperature distributions, strength and drift capacity, envelope curves, and damages are discussed herein.

Temperature distribution

The temperature distribution across the concrete section and on the surface of reinforcing bar was different for different parameters. Figure 35 depicts the temperature distribution across the cross section of shear wall. The maximum temperature recorded across the cross section of the shear wall was 1024 °C which was independent of increasing or decreasing of concrete cover as far as the total thickness of RC shear wall is constant. As shown in Fig. 36a–c, the maximum temperatures recorded on the surface of reinforcing bars for the clear concrete cover of 20 mm, 25 mm, and 30 mm were 833 °C, 730 °C, and 630 °C respectively. From these results, it was observed that as the concrete cover increased from 20 mm to 25 mm the maximum temperature on the surface of the reinforcement was reduced to 87.74%. Similarly, the maximum temperature on the surface of reinforcement was reduced to 75.72% as the clear thickness of concrete cover was increased from 20 mm to 30 mm.

Fig. 35

Temperature distributions across the cross section of shear wall

Fig. 36

Temperature distributions on the surface of reinforcements for different concrete cover. a 20mm cover. b 25 mm cover. c 30 mm cover

As duration of fire increases the maximum temperature across the cross section of the reinforced concrete shear wall increases. As shown in the Fig. 37a–c below the maximum temperatures recorded across the cross section of the wall for the duration of fire for 30 min, 60 min, and 120 min were 740 °C, 890 °C, and 1024 °C respectively. As depicted in the Fig. 38a–c below the maximum temperatures recorded on the surface of reinforcements for the duration of fire for 30 min, 60 min, and 120 min were 520 °C, 668 °C, and 833 °C respectively. As fire exposure sides increases the maximum temperature across the cross section of the reinforced concrete shear wall increases. As shown in the Fig. 39a, b below the maximum temperatures recorded across the cross section of the wall exposed to fire in two sides and all sides were 1026 °C and 1040 °C respectively. Refer Fig. 37c for the maximum temperatures recorded across the cross section of the shear wall with one-sided fire. Refer Fig. 38c for the maximum temperatures recorded on the surface of reinforcements with one-sided fire.

Fig. 37

Temperature distributions across the cross section of wall for different fire durations. a 30 min. b 60 min. c 120 min

Fig. 38

Temperature distributions on the surface of reinforcements for different fire durations. a 30 min. b 60 min. c 120 min

Fig. 39

Temperature distributions across the cross section of wall for different fire exposure sides. a Two-sides (concrete). b All-sides (concrete). c Two-sides (reinforcement). d All-sides (reinforcement)

The temperature distribution on the surface of steel bars and GFRP bars for different fire exposure sides of reinforced concrete shear wall were studied for the same thickness of concrete cover. As shown in the Fig. 40 below the maximum temperatures recorded on the surface of reinforcements (i.e., steel bars and GFRP bars) for fire exposure in one side, two sides and all sides for concrete cover of 20 mm and 30 min duration of fire exposure were around 503 °C and 489 °C for GFRP and steel bars respectively. From these results, it can be concluded that GFRP bars were more sensitive to temperature than steel bars.

Fig. 40

Temperature distributions on the surface of steel and GFRP bars. a GFRP reinforcement 30 min, one side. b steel reinforcement 30 min, one side

Strength and drift capacity

Regardless of the thermal boundary conditions, fire exposure generally reduces the lateral strength and stiffness of the shear wall. The rate of reduction was different for different parameters. The lateral strength of RC walls at high temperatures and at the maximum applied drift with concrete cover thicknesses of 20 mm, 25 mm, and 30 mm was dropped to roughly 70%, 76%, and 85% of the reference shear wall (control specimen), respectively. A maximum drift ratio of 3.2% was applied to all specimens in terms of displacement. The no-fire shear wall (control specimen) reached the ultimate load at drift of 1.86%. whereas, the fire exposed reinforced concrete shear walls with clear concrete covers of 20 mm, 25 mm, and 30 mm reached the maximum load at applied drift (i.e., the shear wall was not investigated to failure) at the drift ratios of 3.09%, 3.14%, and 3.16% respectively.

The lateral strength of fire exposed RC walls at the maximum applied drift (i.e., 3.2%) with duration of fire exposure of 30 min, 60 min, and 120 min was dropped to roughly 80.4%, 75.35%, and 67.77% of the reference shear wall respectively. These results showed that as duration of fire exposure of shear wall increases the strength of shear wall decreases. The fire exposed reinforced concrete shear walls with duration of fire exposure of 30 min, 60 min, and 120 min reached the maximum load at applied drift at the drift ratios of 2.46%, 2.7%, and 3.1% respectively. The lateral strength of fire exposed RC walls at the maximum applied drift due to one side, two sides, and all sides’ exposure to fire was dropped to roughly 67.77%, 56.08%, and 49.56% of the reference shear wall respectively. These results showed that as fire exposure sides increases the strength of shear wall decreases. The fire exposed reinforced concrete shear walls with one side, two sides, and all sides’ exposure to fire reached the maximum load at applied drift at the drift ratios of 2.82%, 2.85%, and 2.9% respectively. The lateral strength of fire exposed GFRP reinforced shear walls is generally less than the lateral strength of fire exposed steel bars reinforced concrete shear walls.

Envelope curves

Envelope curves of fire exposed reinforced concrete shear walls for different parameters were discussed herein. Figure 41 shows force versus lateral deflection at the top of the shear wall for different concrete cover thicknesses. Maximum load due to the applied drift ratio and displacements at F_max were summarized in Table 3 below. Figure 42 shows force versus lateral deflection at the top of the shear wall for different durations of fire exposure. Maximum load due to the applied drift ratio and displacements at F_max were summarized in Table 3 below. Figure 43 shows force versus lateral deflection at the top of shear wall for different fire exposure sides. Maximum load due to the applied drift and displacements at F_max are summarized in Table 3 below. As it was mentioned in above envelope curves of fire exposed steel bars or GFRP bars reinforced concrete shear walls of concrete cover 30 mm with 60 min duration of fire in two sides and all sides were compared and the results were plotted in the Figs. 44 and Fig. 45 below respectively. The results showed that steel bars reinforced concrete shear walls performed better than GFRP bars reinforced concrete shear walls after exposure to fire regardless of duration of fire and exposure sides.

Fig. 41

Load-displacement curves for different cover

Table 3 Summary of fire exposed RC shear wall responses due to different cover

Fig. 42

Load-displacement curve for different durations of fire exposure

Fig. 43

Load-displacement curves for different fire exposure sides

Fig. 44

Load-displacement curve of two faces heated RC shear wall of cover 30 mm

Fig. 45

Load-displacement curve of all faces heated RC shear wall of cover 30 mm

Crack distribution (damages)

The damages recorded on the fire exposed RC shear walls subjected to combined action of axial and monotonic lateral loads were different for different drift ratios. In this study, three drift ratios (i.e., 1%, 2%, and 3%) were used to study crack patterns of the shear wall for each parameter. Figure 46a–i shows crack distributions on the shear wall for concrete cover thicknesses of 20 mm, 25 mm, and 30 mm respectively for different drift ratios. Crack distributions on the shear wall for the parameter duration of fire exposure were different for different duration and different drift ratios. Figure 47a–f shows crack distributions on the shear wall for duration of fire exposure of 30 min and 60 min respectively and refer Fig. 46a–c for crack distribution on the shear wall for the duration of 120 min for different drift ratios. It was observed that the distribution of cracks on the shear wall for different fire exposure sides of shear wall and for different drift ratios were different. Figure 48a–f shows crack distributions on the shear wall for fire exposure sides in two-sides and all-sides respectively and refer Fig. 46d–f for crack distribution on the shear wall exposed to fire in one side for different drift ratios. The performance of GFRP-reinforced concrete shear wall is less than steel bar reinforced concrete shear wall because of the susceptibility of GFRP bars to degradation at elevated temperatures as shown in Fig. 49. When increasing the temperature, the breaking of molecular bonds started and the ductility of the material increased, leading to a decrease of mechanical strengths and stiffness of the material. Mechanical properties, such as tensile strengths and flexural elastic modulus of GFRP bars decreased when the temperature increased. That is why GFRP bars reinforced concrete shear wall performed less than steel bars reinforced concrete shear walls under fire and mechanical loading. Figure 49 shows the distribution of cracks on the shear wall for different type of reinforcements (steel or GFRP). Figure 49a–c shows crack distributions on the fire exposed GFRP bars reinforced concrete shear wall exposed to fire in two sides. Figure 49d–f shows crack distributions on the fire exposed steel bars reinforced concrete shear wall exposed to fire in two sides.

Fig. 46

Distribution of crack for different thickness of concrete cover. a 20 mm at 1% drift. b 20 mm at 2% drift. c 20 mm at 3% drift. d 25 mm at 1% drift. e 25 mm at 2% drift. f 25 mm at 3% drift. g 30 mm at 1% drift. h 30 mm at 2% drift. i 30 mm at 3% drift

Fig. 47

Distribution of crack for different durations of fire exposure. a 30 min at 1% drift. b 30 min at 2% drift. c 30 min at 3% drift. d 60 min at 1% drift. e 60 min at 2% drift. f 60 min at 3% drift

Fig. 48

distribution of crack for different fire exposure sides. a Two-sides at 1% drift. b Two-sides at 2% drift. c Two-sides at 3% drift. d All-sides at 1% drift. e all-sides at 2% drift. f All-sides at 3% drift

Fig. 49

distribution of crack for steel or GFRP reinforced shear wall. a Steel 60 min, all sides (1% drift). b Steel 60 min, all sides (2% drift). c Steel 60 min, all sides (3% drift). d GFRP 60 min, all sides (1% drift). e GFRP 60 min, all sides (2% drift). f GFRP 60 min, all sides (3% drift)

Conclusions

The seismic responses of reinforced concrete shear walls subjected to fire were studied using FE simulations using ABAQUS for thermal and mechanical analysis. Then, a parametric study was carried out to investigate the effect of concrete cover, duration of fire, and fire exposure sides and comparison was made between steel and GFRP bars being used as reinforcement on the seismic performance of fire exposed shear walls. The following conclusions were drawn based on the simulation results of this study.

• Fire decreases both the strength and stiffness of a wall, with the magnitude of decrease in strength and stiffness greatest in walls subjected to fire in all sides.

• The duration of fire and fire exposure sides are the most important parameters that influence the fire exposed lateral load performance of reinforced concrete shear walls. This is because walls with all-sided fire exposure will lose more structural capacity than those with only one-sided or two-sided fire exposure. Similarly, walls exposed to fire for durations of 2 h will lose more structural capacity than those exposed to fire for 30 min and 60 min durations. On average, the lateral strength of fire exposed RC shear walls considered in this study is roughly reduced to 57.8%, 74.51%, and 77% due to effects of fire exposure sides, durations of fire exposure, and thickness of concretes’ cover, respectively.

• As the concrete cover thickness increases, the temperature in the reinforcements decreases leading to loss of lateral strength of fire exposed RC walls considered in this study exposed to fire for 2 h by 30%, 24%, and 15% for concrete cover thicknesses of 20 mm, 25 mm, and 30 mm respectively.

• The fire exposed seismic performance of steel bars reinforced concrete shear wall is better than that of GFRP reinforced concrete shear walls due to sensitivity of GFRP bars to temperature.

• As fire exposure sides or faces increases, the fire exposed RC walls of cover thickness of 20 mm exposed to fire for 2 h lose its strength by 32.23%, 43.92%, and 50.4% for exposure to fire in one side, in two sides and in all sides respectively.