#### Abstract

A newly coal gangue-based geopolymer concrete made from alkaline dry powder activator, coal gangue, and fly ash has been proposed by the authors. High-temperature behavior of the proposed geopolymer concrete beams with different cross sections reinforced with steel bars is investigated in the work here. High-temperature behavior by numerical simulation is validated by the existing experiment. High-temperature behavior is investigated by analysing the geopolymer concrete beams with different cross section dimensions. Temperature distribution and deformation of the beams from room temperature to fairly high temperature are studied. The isotherm contours of beams at different temperatures and the thermal stress contours of the beam at different time steps are obtained and analyzed. First, cracking load and ultimate load of the geopolymer beams with different concrete cover thicknesses are analyzed under different high temperature conditions. It is found that the temperature at the cross section centerline of coal gangue-based geopolymer concrete beam gradually decreases along the vertical direction. The cracking load and ultimate load of the geopolymer concrete beams at high temperature are affected by the thickness of concrete cover. With the increase of temperature, the mid-span deflection of the beam increases gradually. High temperature is a key factor for analysing the behaviors of coal gangue-based geopolymer concrete beams.

#### 1. Introduction

Geopolymer is a new environmentally friendly material with many advantages such as high strength, good corrosion resistance and durability, fast hardening, and early strength [1, 2]. Geopolymer is a kind of cementitious material that can replace cement, an environmental raw material for preparing concrete. Coal gangue is the largest solid waste discharged in China. Most coal gangue contains clay minerals, with similar chemical composition to clay, which can be used as raw materials for preparation of geopolymer and geopolymer concrete [3, 4].The authors have used coal gangue as the main raw material to prepare coal gangue-based geopolymer concrete, and its basic mechanical properties were studied [5–7]. It is found that coal gangue-based geopolymer concrete has good tensile and flexural strength and has wide application prospect in engineering.

Concrete beam is one of the important components in the structure, and its performance directly affects the performance and safety of the whole structure. Structural components such as concrete beams are often exposed to high-temperature environment due to functional requirements or emergencies (e.g., fire). Due to the complex stress state of the geopolymer concrete beams, its high-temperature performance is still a key issue to be studied further. As mentioned above, geopolymer concrete as a new environmental protection material, its high temperature performance has barely been studied, especially for geopolymer concrete structural components with complex force and stress states. As is known, flexural strength, shear strength, cracks, ductility, and other properties of the geopolymer concrete beams will be affected or changed under high temperature. However, study on high-temperature performance of geopolymer concrete components is so limited that it is hard to illustrate high-temperature behavior. Therefore, it is of great significance to study high-temperature performance of geopolymer concrete components to promote the wide application of the environmentally friendly material in practical engineering.

Although the research on the high-temperature performance of the geopolymer concrete components is still very limited, the research of geopolymer concrete components at room temperature has been reviewed to guide the thermal behavior study. Choi and Park [8] investigated the microstructures of fly-ash-based geopolymer composites exposed to high temperatures by surface fractal dimension analysis. It is found that the mechanical and microstructural properties of geopolymer composites changed after thermal exposure. Payakaniti et al. [9] studied changes in the compressive strength, microstructure, and magnetic properties of a high-calcium fly ash geopolymer subjected to elevated temperatures. Celik et al. [10] examined high-temperature behavior and some mechanical and microstructural characteristics of boron waste additive metakaolin-based geopolymer mortar composites reinforced with four various fiber types. Sumajouw et al. [11] studied the structural properties of fly ash-based geopolymer concrete beams. Flexural failure of six reinforced concrete beams with different reinforcement ratios (0.64%–2.69%) was tested. As expected, flexural capacity increases with the increase of tensile reinforcement ratio. In the Australian specification AS3600 [12], the test predicted ratios were between 0.98 and 1.28, most of which are conservative. Sumajouw and Rangan [13] reported 16 tensile strength ratios (0.64%–2.69%) and compressive strength (37 MPa–76 MPa) of 16 kinds of reinforced geopolymeric concrete beams. From the effect of tensile reinforcement ratio on flexural capacity and ductility, the properties of geopolymer concrete beams, including the effect of tensile reinforcement ratio on flexural capacity and ductility, are similar to those of traditional cement-based concrete beams. Lahoti et al. [14] investigated the effects of alkali cation type on high-temperature response of fly ash geopolymers aiming towards structural applications. Zhang et al. [15] presented results from high-temperature spalling tests on geopolymer concrete. The effect of moisture content, concrete strength, heating rate, and temperature level on the spalling behavior of geopolymer concrete was studied. Kumaravel and Thirugnanasambandam [16] employed ANSYS program for numerical analysis to predict the bending performance of unreinforced geopolymer concrete beams. Kumaravel et al. [17] obtained a good comparison between predicted and experimental load-rotation relationships. In addition, in the study of Nguyen et al. [18], although the predicted deviation values given by the finite element simulation of ABAQUS software were slightly different, there was still a good consistency between the experiment of reinforced geopolymer concrete beams and the load-deflection performance related to Si. Based on these studies, it was suggested that ANSYS and ABAQUS software could be useful tools to simulate the behavior of geopolymer concrete structural components. Some scholars have evaluated the bending performance of geopolymer concrete beams after corrosion. Wanchai [19] found that compared with the control beam containing traditional cement-based concrete, the fly ash-based geopolymer concrete beam showed a greater degradation in bending capacity under the accelerated corrosion of sodium chloride solution. When Kannapiran et al. [20] immersed reinforced concrete beams in sulfuric acid and hydrochloric acid and sulfuric acid solution for 180 days, the flexural capacity of decreased slightly (less than 8%), and the load-deflection barely changed.

At present, the main methods to study high-temperature performance of reinforced concrete structure are test measurement, practical chart method, and numerical simulation. Numerical simulation has become a promising method due to the high performance of the computers. Moreover, since the structural thermal analysis is governed by the nonlinear parabolic partial differential equations, it is an effective way to solve the equations numerically. Numerical simulation for studying the high-temperature performance of reinforced concrete structures can be divided into finite difference method and finite element method. It is easier to divide complex structures with various shapes using finite element methods. In the time domain, it can start from the initial value and calculate step by step with time to save computation time. Therefore, finite element method is popular in the high-temperature behavior analysis.

In the work here, the finite element method of numerical analysis is employed to study high-temperature behaviors of coal gangue-based geopolymer concrete beams. High-temperature behavior of the proposed geopolymer concrete beams with different cross sections reinforced with steel bars is investigated in the work here. High-temperature behavior by numerical simulation is validated by the existing experiment. High-temperature behavior is investigated by analysing the geopolymer concrete beams with different cross section dimensions.

#### 2. Preparation of Coal Gangue-Based Geopolymer Concrete

Preparation of coal gangue-based geopolymer concrete is illustrated as follows.(1)Preparation of required coal gangue and fly ash: the coal gangue in the experiment is spontaneous combustion coal gangue of Gaode Mine in Fuxin City, Liaoning Province; its chemical composition is shown in Table 1. This test uses Fuxin power plant grade I fly ash; chemical composition is shown in Table 2.(2)Standard sand is selected; technical indicators are shown in Table 3.(3)With commercially available sodium hydroxide and calcium carbonate reagents, the purity of sodium hydroxide was 99%.(4)Fine aggregate: local river sand (fineness modulus 2.4); coarse aggregate: crushed stone (after cleaning and screening, particle size is 5∼31.5 mm).

The process of making geopolymer concrete test blocks is as follows:(1)Firstly, the sodium hydroxide (SH) solution was mixed with calcium carbonate (CC) powder to form a solution consisting of calcium hydroxide (CH), sodium carbonate (SC), and pirssonite (P), which was dried in an oven at 80°C for 8 hours.(2)Then, the powder was crushed to fixed particle size, and the powder with particle size less than 0.03 mm in the activator powder was taken.(3)Then, the (spontaneously ignited) coal gangue block was crushed by a sledgehammer and then repeatedly crushed into small particles in a crusher. The powder with a particle size between 0.01 mm and 0.09 mm was screened.(4)During the production of the test block, sand and pebble were poured into the mixer and stirred for about 140 s. Then, coal gangue powder and fly ash were poured into the mixer and stirred for the 20 s. Finally, dry powder activator powder was added and stirred for the 120 s.

After mixing, the geopolymer concrete is poured into the mold, vibrated and compacted, and finally smoothed to make the geopolymer concrete test block, as shown in Figure 1. For the details and mechanical properties, the readers can refer to the authors’ previous published papers [5, 6].

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#### 3. Finite Element Analysis Theories of High-Temperature Behavior

##### 3.1. Fundamental Assumptions

The following assumptions are made to study high-temperature performance of coal gangue-based geopolymer concrete beams:(1)The decisive factor of the temperature field of beam components is the heat exchange with the surrounding environment and has nothing to do with the stress and strain of the material. Once structural concrete cracks, heat invades, affecting the temperature distribution nearby, and is no longer equivalent along the axis.(2)There is no slippage between steel and concrete. The good bond between steel and concrete is the basis of their work together. Before the cracking of concrete components, the deformations of the two are equal without relative slip. After cracking, the deformation of the two near the crack is different, and there must be relative slip. At room temperature, the bond-slip between steel and concrete has reliable reference or formula, but there is no unified formula or reference in this aspect at high temperature.(3)It is considered here that the heat conduction of geopolymer concrete is isotropic and uniform in all directions. Coal gangue-based geopolymer concrete is a kind of composite material. In a local small range, the heat conduction of concrete is different, but in a large area, this heat conduction is isotropic and uniform.(4)There is no heat source in the coal gangue-based geopolymer concrete beam. The above studies have found that the polymerization of coal gangue-based geopolymer concrete will produce hydration heat, and after the component is heated, the chemical reactions of various heat release will occur in its constituent materials. This study ignores this heat.(5)The boundary without thermal load is treated as completely adiabatic.(6)The crack depth and width of coal gangue-based geopolymer concrete beam are proportional to the heating time.

##### 3.2. Equations of Heat Conduction

The temperature field analysis of coal gangue-based geopolymer concrete beam can be regarded as the heat conduction problem of solid; that is, the differential equation of heat conduction can be established and solved.

The finite element format of transient heat conduction equation is written aswhere is the node temperature array, is the derivative array of time, is the specific heat matrix, is the heat conduction matrix, and is the temperature load matrix.

##### 3.3. Initial Conditions and Boundary Conditions

Assuming that the temperature of the whole structure is uniform and equals to the ambient temperature , the initial condition is written as

Boundary conditions are related to many factors such as the environment of the structure and the heat transfer conditions of the surrounding medium, which can be generally divided into four categories.(1)The temperature on the structural boundary is a function of time , such as(2)The heat flux (*n* is normal) on the structural boundary is a function of time .(3)Given the temperature of fluid medium in contact with the structure, the heat flow through the boundary can be expressed as where is the heat transfer coefficient between the structural boundary and the surrounding fluid medium. It is defined as the unit time, unit temperature difference through the unit area of heat; unit is .(4)The structure is in contact with other solid materials and the heat transfer conditions on the boundary are known.

In the work here, the third boundary condition is taken after the initial high temperature. With the continuous high temperature, the first boundary can be taken.

##### 3.4. Nonlinear Theories of Geopolymer Concrete

Before the cracking of geopolymer cementitious materials in geopolymer concrete, the polymer slurry can be regarded as linear elastic isotropic material. Once the effective principal stress combination reaches the tension state of the structure to fracture, the concrete beam will show cracks perpendicular to the principal stress direction, and its direction is fixed. At this stage, the constitutive relations of each homogeneity are replaced by the constitutive relations of orthogonal anisotropy at the beginning. The evolution of damage is achieved by reducing the elastic modulus in the crack direction.where is the Young modulus of undamaged geopolymer concrete and is the destroy variable, which reflects the decrease of .where is the strain of peak stress under uniaxial tension and is a parameter that controls the slope of the exponential strain softening curve and can be determined from the fracture energy. Since a fixed anisotropic viscous-cracking model is used to reflect the ability of shear stress to occur in the crack, a shear retention factor is adopted, which is inversely proportional to the crack stress , it is given by

Since the magnitude and direction of stress and strain in the evolution process of temperature field may change with the change of temperature field, the stiffness recovery caused by crack closure is also considered in the analysis.

To describe the fracture failure process in a local N-S coordinate system, follow the following loading method.where is a historically dependent damage parameter used to remember the highest values, defined as

The loading mode in formula (8) depends on Kuhn–Tucker loading-loading conditionwhere is the ratio. In the whole loading process, value increases monotonically.

For nonlinear mechanical analysis, Newton–Raphson iteration method is combined with finite element method based on minimum potential energy principle. In order to calculate the energy stored in heated concrete, the elastic strain energy of two-dimensional analysis can be calculated as follows:where is the effective stress, is the elastic strain, is the surface area of each element, and is the number of elements.

For different temperatures, the temperature-related concrete model proposed by Shoukry et al. is employed to calculate the parameters of the concrete model.where , and are compressive strength, tensile strength and elastic modulus of concrete, and temperature, respectively. The data of coal gangue-based geopolymer at are determined by the experimental values of coal gangue-based geopolymer concrete cured at room temperature for 28 days.

#### 4. High-Temperature Analysis of Coal Gangue-Based Geopolymer Concrete Beam

##### 4.1. Validation

The proposed numerical method was validated by the thermal finite element analysis of the concrete beam in [21]. The numerical simulation is performed on ANSYS; the position of seven measuring points and all parameters are consistent with the settings in [21]. The meshing of the finite element model and the position of each measuring point is shown in Figure 2.

The temperature loading function is written as

The temperature loading function was fitted according to the experimental furnace temperature curve. The thermal variation of each measuring point calculated is compared with the experiment, as shown in Figure 3.

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It can be seen from Figure 3 that the temperature variation of each measuring point is basically consistent with that from the experiment, which validates the numerical simulation in the work here. The reason why the numerical results are different from those from the experiments would be that the uniform model is adopted in the numerical simulation, resulting in symmetry temperature gradient curve. In addition, the mesoscopic characteristics of the concrete such as nonuniformity and random distribution of large aggregates in the concrete are not considered in the uniform model, which can be reflected in the experiment results (i.e., nonuniform distribution in temperature gradient curve). Therefore, to obtain more accurate numerical results, mesoscopic characteristics of the concrete should be considered.

##### 4.2. High-Temperature Behavior of Coal Gangue-Based Geopolymer Concrete Beam

After validation, the nonlinear finite element analysis of the high-temperature behavior of coal gangue-based geopolymer concrete simply supported beam is carried out, and it is performed by APDL in ANSYS.

It is common for ordinary concrete beam that, with the increase of time and the touching area of component in high temperature, the temperature field distribution of component section will be changed. Accordingly, in order to accurately investigate the high-temperature behavior of coal gangue-based geopolymer concrete beam, two types of simply supported geopolymer concrete beam with different cross section sizes are selected for analysis. The detailed data of the beam are shown in Table 4.

The characteristics of these four different cross-sectional beams at room temperature (20°C), 200°C, 400°C, 600°C, and 800°C were analyzed. The geometrical size and reinforcement distribution of coal gangue-based geopolymer beam are shown in Figure 4.

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###### 4.2.1. Properties of Reinforcement Materials

The reinforcement in the geopolymer concrete beam is in the uniaxial stress state, and its mechanical model is simplified into a linear ideal elastic-plastic model. Both the reinforcement and the support plate adopt the classical bilinear kinematic hardening model, Mises yield criterion, and kinematic hardening criterion, and the stress-strain relationship of the material is described by two straight lines. The material parameters of steel bars at different temperatures [22] are shown in Table 5.

###### 4.2.2. Properties of Coal Gangue-Based Geopolymer Concrete Materials

Concrete is an elastoplastic material, so it is necessary to consider its nonlinearity and define the failure criterion of concrete by definition. It is assumed that tensile and compressive failure of concrete are two main failure mechanisms; like other constitutive models, the basic elements are yield criterion, flow rate, and hardening rule to consider the change of strength under tension and compression conditions.

In this paper, two-stage model [23] is employed as the stress-strain curve of geopolymer concert,where is peak strain, is peak stress, and *a* and *b* are the functions of the service life, respectively.

###### 4.2.3. High-Temperature Behavior of Coal Gangue-Based Geopolymer Concrete Beam

The finite element models with two different cross-sections are established in ANSYS. The mesh of concrete and reinforcement with different cross-sections are shown in Figures 5 and 6, respectively. Figures 7 and 8 show the isotherm contour of beams at different temperatures (600°C and 800°C).

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It can be seen from the contours that the transverse layers of the simply supported beam of geopolymer concrete experience thermal expansion due to the high temperature. If the macroscopic phenomenon is elongational expansion, the layers will have different degrees of elongation due to the existence of temperature gradient. The expansion of the lower end is the largest, and the upper end is the smallest. Therefore, it can be inferred that the two ends of the simply supported beam will bend upward and reach its maximum at a certain temperature, accompanied by changes in physical and mechanical properties. Meanwhile, it is found that among the three tensioned steel bars at the bottom, the temperature of the tensioned steel bars near the two sides of the concrete increases faster, and the middle-tensioned steel bars slower. The thickness of protective layer at the bottom and subside of the concrete beam at high temperature affects the temperature rise of internal reinforcement, so it is of great significance to select a reasonable thickness of concrete protective layer. Figure 9 shows the temperature distribution at the cross section centerline of the two beams.

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It can be seen from Figure 9 that the temperature at the cross section centerline gradually decreases along the *y*-direction, and there is a critical position on the cross section centerline. The slope of the curve below this position changes slightly, and the slope of the curve above this position changes greatly. Taking the beam with 200 mm × 400 mm section as an example, the positions of the points are 0.28 m, 0.24 m, 0.2 m, and 0.18 m, respectively, so it can be seen that the critical position moves downward with the increase of the three-side temperature.

The thermal stress contours of beams are analyzed at different times, as shown in Figures 10 and 11, respectively.

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It can be seen from Figures 10 and 11 that with the increase of time, the temperature of coal gangue-based geopolymer concrete beam gradually increases from outside to inside, and the bottom temperature of the beam rises fastest, and the temperature on both sides of the beam rises slowly. Among the three stress steels at the bottom, the temperature of the stress steel near the two sides of the concrete is relatively high. It is inferred that reasonable concrete protective layer thickness is of great significance to the high-temperature performance of the geopolymer concrete beam.

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Figure 12 shows the mid-span deflection with different section dimensions at different high temperatures.

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The following conclusions can be drawn from the analysis in Figure 12,(1)The variation law of the coal gangue-based geopolymer concrete beams of different cross section sizes with temperature variation is basically the same. With the increase of temperature, the mid-span deflection of the beam increases gradually. The mid-span deflection of the beam at room temperature is the smallest, and the mid-span deflection of the beam at 800°C is the largest, indicating that high temperature has a negative impact on the deformation of the geopolymer concrete beam.(2)The mid-span deflection of beams of different cross sections is different for high temperature. It can be found that the larger the cross section is, the smaller the mid-span deflection is. The deformation of beam at high temperature can be effectively reduced with the increase of the cross section dimension.

The cracking load and ultimate load of beams with different section sizes with different concrete cover thickness are shown in Tables 6 and 7, respectively.

The following can be concluded from Tables 6 and 7.(1)The cracking load and ultimate load are affected by the thickness of concrete cover.(2)For high temperature, with the increase of the cross section dimension, the cracking load and ultimate load increase as well, indicating that bearing capacity of the beam can be improved by increasing the cross section dimension.(3)The cracking load and ultimate load of the geopolymer concrete beams are affected by the temperature. With the increase of temperature, the cracking load of the beam decreases, indicating that the bearing capacity decreases due to the high temperature. At room temperature, with the increase of concrete cover thickness, the cracking load of beams with different cross section sizes increases slightly. However, with the increase of temperature (>200°C), the cracking load of 35 mm protective layer is larger than that of beams with 25 mm and 40 mm protective layer, indicating that 35 mm is the optimal thickness of protective layer. With the increase of the section dimension, the cracking load increases with the increase of the protective layer thickness. Therefore, with the increase of the beam section dimension, the bearing capacity of the beams at high temperature can be improved by increasing the protective layer thickness.(4)At room temperature, with the increase of concrete cover thickness, the ultimate load of beams with different section dimension increases slightly. However, when the temperature is higher than 200°C, the ultimate load with 35 mm protective layer of 150 mm × 200 mm section is higher than that of beams with 25 mm and 40 mm protective layer, indicating that 35 mm is the optimal protective layer thickness of this section size.

#### 5. Conclusions

High-temperature behaviors of coal gangue-based geopolymer concrete beams have been studied. The main conclusions are as follows:(1)With the increase of temperature, the cracking load of the beam decreases, indicating that the bearing capacity decreases due to the high temperature. With the increase of the cross section dimension, the cracking load and ultimate load increase as well. Bearing capacity of the beams at high temperature can be improved by increasing the protective layer thickness and the cross section dimension.(2)With the increase of temperature, the mid-span deflection of the beam increases gradually. The mid-span deflection of the beam at 800°C is the largest. The larger the cross section is, the smaller the mid-span deflection. The deformation of beam at high temperature can be effectively reduced with the increase of the cross section dimension.(3)In the future work, mesoscopic characteristics of the concrete will be taken into account to establish a nonuniform model to obtain more accurate results for high-temperature performance of coal gangue-based geopolymer concrete.

#### Data Availability

The data used to support the findings of this study are included within the article.

#### Conflicts of Interest

The authors declare that they have no conflicts of interest regarding the publication of this paper.

#### Acknowledgments

This study was supported by the National Natural Science Foundation (no. 52178468), Guangxi key Laboratory Fund of Embedded Technology and Intelligent System, Guangxi Key Laboratory of Geomechanics and Geotechnical Engineering (GUIKENENG19-Y-21-2), Guangxi Key Laboratory of New Energy and Building Energy Saving Foundation (Gui Keneng 19-J-21-14), Joint Cultivation Program of National Natural Science Foundations of Guangxi (2019GXNSFAA245037), Guangxi Youth Innovative Talents Research Project (Guike AD19245012), and Scientific and Technology Startup Foundation of Guilin University of Technology (GUTQGJJ2019041 and GUTQDJJ2019042).