Experimental, Numerical, and Theoretical Studies of Bond Behavior of Reinforced Fly Ash-Based Geopolymer Concrete

Abstract

This paper presents the results of an experiment study and suggests a theoretical formulation for the bond behavior of reinforced fly ash-based geopolymer concrete. Three grades (20 MPa, 30 MPa and 40 MPa) of a geopolymer concrete along with three reinforcement diameters (12, 16, and 20 mm) were selected for experimental work. The bond behavior of the reinforced geopolymer concrete is determined using pullout test, finite element analysis (FEA), and theoretical work. The test data indicated that the bond strength of reinforced fly ash-based geopolymer concrete increases about 1.97 to 2.56 times with the increase of compressive strength from 20.33 MPa to 41.12 MPa. For grade 30 MPa and 40 MPa specimens, the concrete cover to diameter ratio (c/d_b) increased up to 4.19 resulted in the increase of bond strength. Then, the bond strength decreases with the increase of the c/d_b ratio from 4.19 to 5.75, while grade 20 MPa specimens is vice versa. The bond-slip relations between the reinforcement and geopolymer concrete determined from FEA is in good agreement with experimental results. The coefficient of variation (CoV) is only 0.01. However, this behavior is quite different from the data calculated by the fib model.

1. Introduction

The emission of greenhouse gases from various sectors, including transport, energy supply, residential, businesses, industrial processes, agriculture, etc., has appeared as an extreme obstacle that significantly influences global climate change. The Portland cement (PC) manufacturing process is in charge of a large amount of carbon dioxide (CO₂) emission with up to 10% of CO₂ emission globally. Geopolymer material comprised alkaline solution and alumino-silicate sources to create a gel called N-A-S-H, which was reported to cut carbon footprint by 90% compared to the production of PC [1]. Depending upon local resources and availability, solid aluminosilicate precursors can be in natural forms such as zeolite, amphibole, shales, or industrial by-products such as fly ash, metakaolin, red mud, waste glass, etc. [2,3]. Alumina (Al₂O₃) as well as silica (SiO₂) are essential components of geopolymeric materials even in natural or by-products forms. These two factors play a significant role in the hardening of geopolymer materials. They produce the N-A-S-H gel which is in charge of properties of the final product. Based on Duxson et al. [4], the geopolymerization has various step such as dissolution, speciation equilibrium, gelation, reorganization, polymerization, and hardening. Aluminum (Al) and silicon (Si) are released during the dissolution step. The final Si-rich gel is formed by reaction between the Si in the solution and initial Al-rich gel. The main product of this process is the N-A-S-H gel [5]. Geopolymer materials have received much more attention in the construction field due to their high chemical resistance and good mechanical properties. Farhan [6] compared the compressive strength of Portland cement concrete (PCC) and fly ash-based geopolymer concrete (FAGC) cured at 80 °C for 24 h and showed that FAGC had higher tensile strength and early compressive strength compared to PCC. Mo [7] and Li [8] also stated that the elevating curing temperature would speed up the dissolution, polymerization, and reprecipitation process of the geopolymerization reaction. Additionally, it showed the ability to resist freeze-thaw and high temperature conditions compared to conventional concrete. Zhang [9] proved that geopolymer grout offers a heat resistance advantage, where its compressive strength is still maintained at 800 °C, while that of PC grout is lost entirely.

Incorporating steel reinforcing bars into geopolymer concrete for structural components such as columns, beams, and external walls has drawn tremendous attention from many scholars [10,11,12,13,14,15,16,17]. Their studies focused on the mechanical properties such as tensile and bond strength of reinforced FAGC. Reinforced FAGC with deformed steel bars were reported to attain higher splitting tensile strength than that of PCC [18]. One of the most crucial factors to identify the performance of reinforced concrete materials is bond property, which is considered as the stress transfer along the longitudinal direction of the reinforcing bars to the concrete matrix [19]. Similar to conventional reinforced concrete, reinforcing bar diameter and texture, splice length, concrete cover thickness, and strength of concrete play a significant role in the bond performance (such as failure modes and crack patterns of reinforced FAGC beams) [20]. In this regard, Cui et al. [13] investigated the bond strength of steel reinforcing bars, which included plain and ribbed ones with a nominal diameter of 16 mm, one embedded in FAGC using a beam-end pullout test, and ones worked with eight strain gauges. It was suggested that the bond strength between reinforcing bars and FAGC was up to 21% higher than that with conventional concrete, owing to the excellent adhesion and compact interface of the steel bars and geopolymer concrete matrix. This finding agreed with other studies carried out by [10,15], where the bond strength in FAGC with various diameters of steel bars ranging from 12–24 mm was higher by far. Besides, Albidah [21] had also confirmed that the bond strength of reinforcing bar embedded in geopolymer concrete is higher than the bond strength of rebar and conventional concrete. Recently, Cui [22] has been using beam end tests and statistical hypothesis tests to evaluate bond behavior of geopolymer concrete and compare with traditional Portland cement concrete. This research reported that the bond behavior of reinforced geopolymer concrete is significantly different with that of OPC. In summary, it has been shown that reinforced FAGC possesses favorable properties for its potential use as construction materials. The sufficient bonding between the rebar and concrete has a crucial effect on designing of reinforced concrete members. Thus, it is vital to have more knowledge about the bonding behavior in reinforced geopolymer concrete to apply it as a substitute material in conventional structural concrete. It is worthwhile to emphasize that while those studies provide a quick means to define the bonding performance, the preparation at the stage of casting must be noticed to ensure interfacial consistency and minimize the appearance of air void around the reinforcing bars.

Along with the above-mentioned experimental studies, several researchers have also utilized numerical modelling methods to evaluate the bonding behavior of reinforced concrete [23,24,25]. In the studies by Lundgren [26] and Rolland [27], the finite element method (FEM) was applied to simulate the bonding between concrete and several types of reinforcement, including steel bars and fiber reinforced polymer bars. It was indicated that FEM had a great potential to evaluate the bond stress and splitting failures with good agreements to experimental test results. An implementation of the FEM was also used to assess the bonding behavior of FAGC with glass fiber reinforced polymer (GFRP) bars in the work of Tekle [28]. The surface-base cohesive behavior framework was employed to represent the bond between GFRP bars and concrete. The bond stress distribution along the length of GFRP bars obtained from the analysis showed a similar trend with the results from the pullout test. The numerical analysis was also employed to evaluate the bonding performance of metakaolin-based geopolymer concrete with ribbed steel rods [29], fiber reinforced geopolymer concrete [30,31], and steel-reinforced FAGC [32,33]. However, the investigation on the effects of reinforcement size and strength of concrete on the bonding behavior in reinforced geopolymer concrete has not yet been considered thus far.

Based on this background, this paper investigates the effects of geopolymer concrete compressive strength and reinforcing bar sizes on the bond performance of FAGC using both experimental and FEM. A pullout test was conducted to determine the bond stress and slip in reinforced FAGC comprising ribbed steel bars with diameters of 12, 16, and 20 mm and FAGC with various compressive strengths 20, 30, and 40 MPa. Numerical analysis by FEM was applied to simulate the bonding of the steel bars and FAGC. The bond-slip relation determined from simulation results was evaluated and compared with the experimental work. Up to now, there is no standard for geopolymer concrete. Thus, the proposed modelling in ABAQUS would be validated with experimental data. Eventually, the stress-slip curves of rebar in fly ash-based geopolymer concrete are also derived using non-linear regression for various experimental conditions. This proposed formulation and modelling could predict the bond-slip behavior of reinforced fly ash-based geopolymer concrete for practical purposes.

2. Materials and Experimental Methods

2.1. Materials, Mixture Proportions and Specimens’ Preparation

There are two main constituents for manufacturing geopolymer concrete: geopolymer binder and aggregate. In this study, geopolymer binder is a mixture of fly ash and alkaline liquid. Sodium silicate (Na₂SiO₃) along with sodium hydroxide (NaOH) are mixed in the ratio of 2.5 by mass to create an alkaline liquid. The modulus ratio (Ms) of the sodium silicates solution was 3.3 (where Ms = SiO₂/Na₂O, Na₂O = 8.37%, SiO₂ = 27.63%). The concentration of NaOH was 8M, where ‘M’ stands for the molarity of the concentration solution. Class F fly ash was obtained from a local coal power plant with a density of 2.5 g/cm³ and a particle size range of 5–10 μm, which is used as a solid binder for geopolymer preparation. The chemical compositions of the fly ash are presented in

Table 1. Chemical composition of fly ash.

Oxide	SiO2	Al2O3	Fe2O3	CaO	K2O & Na2O	MgO	SO3	LOI *
(%)	52	31.9	3.48	1.2	1.02	0.81	0.3	9.6

* LOI: loss on ignition.

. Both fine aggregates (FA) and coarse aggregate (CA) in a saturated surface dry condition were used in this experimental work. The ratio of coarse to fine aggregates was 70% and 30%. River sand with fineness modulus of 2.54 was used as fine aggregate, while a crushed stone was used as coarse aggregate with a mixture of three groups: 5–10 mm (45%), 10–20 mm (50%), and 20–25 mm (5%).

Geopolymer concrete specimens were manufactured by mixing fly ash, alkaline liquid, coarse aggregate, fine aggregate, and superplasticizer. Firstly, the alkaline liquid was initially prepared by mixing a NaOH and Na₂SiO₃ solution according to suggestions from a study by Davidovits [34] to promote better polymerization. Fly ash and the alkaline liquid was mixed for five minutes. Then, both CA and FA were added to the slurry and mixed for five minutes. Finally, the superplasticizer was poured into the mixture and mixed for three minutes. Fresh geopolymer concrete was cast and compacted into the cylindrical mold (150 × 300 mm) and cured in an oven at 60 °C for 4, 8, and 12 h. For specimens used for the pullout test, the reinforcing bars embedded in the geopolymer concrete were carefully wrapped by PVC tube to manage the bonded length, which is 100 mm. Later, the fresh geopolymer concrete was poured into prepared molds and cured in an oven with the same conditions. In this research, specimens were mixed and cast with three mixture proportions and cured at three different conditions as shown in

Table 2. Mixture proportions of this research.

Name	CA	FA	Fly Ash	Na2SiO3 Solution	NaOH Solution	AL/GS	Superplasticizer	Description of Mixtures
	(kg)	(kg)	(kg)	(kg)	(kg)		(kg)
GP1								Cured at 60 °C, 4 h
GP2	1294	554	476	120	48	0.35	7	Cured at 60 °C, 8 h
GP3								Cured at 60 °C, 12 h

.

2.2. Test Method

Figure 1 shows the testing program used to investigate the bond behavior of reinforced geopolymer concrete, including the compressive strength test and pullout test. Three 150 × 300 mm specimens from each mixture group were prepared for the compression test. The compressive strength test applies a compressive axial load to the 150 × 300 mm cylinder specimens at rates ranging from 0.15 to 0.35 MPa/s, until failure occurs according to ASTM C39 [35].

Several tests have been used to obtain the bond strength of reinforcing bar embedded in concrete. There are three kinds of specimens including beam-end specimens, beam with lap splices, and pullout specimens. In this research, the pullout testing was chosen to assess the bond strength of various rebars. A traditional pullout testing is given in Figure 2 and the loading rate is chosen at 1 mm/min. The samples of pullout testing are straightforwardly built and tested. This method has also been used to evaluate the bonds in concrete for many years. The results of the pullout test can be utilized to determine the bond strength of rebars in case the premature splitting of the surrounding specimens is innocent. Besides, when the relative bond resistance is allowed, this test is chosen as the most useful method for comparing the bond-slip curves of numerous types of rebars. Thus, the pullout test must be an acceptable method to determine the influence of many variables on bond behavior (for example, comparing the bond-slip relation of the different concrete mix proportions, sizes of rebar, and other factors with supplementary geopolymer concrete).

The bond stress is calculated by assuming that the bond stress is uniformly distributed along the embed length of the bar:

$${\tau }_{\max }=\frac{P_{\max }}{\pi ·d_b·l_b}$$

(1)

where τ_max is the maximum bond stress, P_max is the corresponding applied force at failure, d_b is the bar diameter, and l_d is the bar embedded length.

In this research, the bond behavior of reinforced geopolymer concrete was evaluated by considering the effect of compressive strength (f’_c) of geopolymer concrete, the concrete cover to bar diameter ratio (c/d_b) on the bond strength and bond-slip relation. Three diameters of reinforcing bars, as shown in

Table 3. Details of rebar.

Rebar	Rib Height (mm)	Rib Spacing (mm)
d12	0.78	7.8
d16	1.04	10.4
d20	1.3	13

, were used. The details of specimens are given in

Table 4. Details of geopolymer concrete specimens.

Name of Specimen	db	c	c/db	ld
	(mm)	(mm)		(mm)
GP1 R1	12	69	5.75	100
GP1 R2	16	67	4.19	100
GP1 R3	20	65	3.25	100
GP2 R1	12	69	5.75	100
GP2 R2	16	67	4.19	100
GP2 R3	20	65	3.25	100
GP3 R1	12	69	5.75	100
GP3 R2	16	67	4.19	100
GP3 R3	20	65	3.25	100

and Figure 2. In this Table, the samples are named GPxRy, which GP stands for geopolymer concrete; x (1,2,3) is the number of mix proportion; R stands for reinforcing bar; and y (1,2,3) refers the diameter of reinforcing bar 12 mm, 16 mm, and 20 mm, respectively.

3. Simulation Analysis

3.1. General Description of Numerical Model

This section used numerical models developed by the ABAQUS/CAE tool to simulate the bond strength and pull-out behavior of reinforcement steel bars in a fly ash-based geopolymer concrete. In the following section, details of the numerical model are presented.

The simulation models were developed based on a 3D modelling tool in ABAQUS, where deformable, eight-node with reduced integration hexahedral elements (C3D8R) were selected. The model consisted of two components: the concrete block and the steel bar as depicted in Figure 3. Due to the symmetry of the specimen, only a quarter of the specimen was modelled. The concrete block was modelled with the exact dimension of the specimen, while the hole and the steel bar were modelled with the same diameter as the steel bar. This led to a contact condition between the surfaces of the steel bar and concrete block at the prescribed area where they were in contact with each other.

As described in the experimental program shown in Figure 2, the top surfaces of the concrete block were imposed to the restraining devices. Hence, these surfaces were assigned the clamped boundary condition with no translation of degrees of freedom. A prescribed displacement was imposed to the steel bar to simulate the pull-out force as a displacement-control algorithm was adopted. Static analyses with material and geometrical nonlinearities were performed. After taking the convergence investigation, the concrete block was meshed with ten elements in the radius direction, while the number of elements modelling the steel bar was 12 in the radius direction. In the height direction, the model was fine meshed at the part where steel bar and concrete block were in contact, and the mesh size at this location is 2 mm in the height direction. The mesh of a simulation model is illustrated in Figure 4.

3.2. Constitutive Models of Concrete and Steel

The concrete damaged plasticity (CDP) model in ABAQUS was chosen to model the concrete material thanks to its simple modelling and stable numeric calculation. In the CDP model, concrete’s uniaxial tension and compression responses were fundamental components. The compressive behavior of concrete was defined based on the formula proposed by Popovics [36] as follows

$$\frac{\sigma }{f_c^{\prime }}=\frac{\epsilon }{{\epsilon }_c^{\prime }}\frac{n}{n-1+{\left(\epsilon /{\epsilon }_c^{\prime }\right)}^n}$$

(2)

where f’_c is the compressive strength of concrete and ε’_c is the corresponding compressive strain, n is the power index and can be expressed as an approximate function of the compressive strength of normal-weight concrete as:

$$n=0.4\times {10}^{-3}{f}_c^{\prime }+1.0$$

(3)

and compressive strain of concrete at peak compressive stress is given by:

$${\epsilon }_c^{\prime }=2.7\times {10}^{-4}\sqrt[4]{f_c^{\prime }}$$

(4)

The tensile behavior of concrete is characterized by the uniaxial tensile stress f_t and fracture energy per unit area as follows:

$$f_t=0.3{\left(f_c^{\prime }-8\right)}^{2/3}$$

(5)

$$G_F=0.073{\left(f_c^{\prime }\right)}^{0.18}\left(N/mm\right)$$

(6)

where Equation (5) are retrieved from Eurocode 2 [37] and Equation (6) is defined in fib 2010 [38]. The elastic modulus of concrete E_c is taken as the empirical equation suggested in ACI 318 [39], and the Poisson’s ratio of concrete is 0.2.

$$E_c=4700\sqrt{f_c^{\prime }}$$

(7)

Other parameters of the CDP model are taken as follows as suggested by Luna Molina et al. [40] and Pereira et al. [41].

-

Dilation angle ψ = 40°.

-

Flow potential eccentricity e = 0.1.

-

Ratio of initial equiaxial compressive yield stress to initial compressive yield stress $f_{b0}/f_{c0}=1.16$.

-

Ratio of second stress invariant on the tensile meridian K = 0.667.

-

Viscosity parameter μ = 0.001.

It was noted herein that the current problem does not consider the reloading stage, and only the bond strength is of interest. Hence, the damage parameters are not involved in the model.

The elastic-perfect plastic model with isotropic hardening was adopted to model the steel bar, the elastic modulus of the steel bar was taken as E_s = 200,000 MPa, and the corresponding Poisson’s ratio is 0.3.

3.3. Interaction between Steel and Concrete

This study modelled the interaction between the steel bar and concrete block using the contact modelling option with cohesive behavior provided in ABAQUS. In this modelling technique, a bond-slip law calibrated from the experimental results was used to represent the interaction between the steel bar and concrete block. In reality, the interaction between the steel bar and concrete block was induced by the locking phenomenon between the ribs of steel bar with surrounding concrete and bond strength. In this research, the proposed modelling approach allowed us to carry out the simulations in a simple manner wherein these two effects were accounted for in a cohesive model. Hence, there was no need to model the ribs of steel bars, which could complicate the simulation model.

To fully describe the bond strength-slippage response, the interaction condition was modelled by adopting the normal surface-based cohesive behavior model and the normal contact behavior and damage option. The concrete and steel surfaces were assigned to master and slave surfaces, respectively, as illustrated in Figure 5. The hard contact condition was selected to ensure that there was no penetration between the two surfaces. At the same time, the damage parameters were defined to represent the softening stage in the stress-slip diagram, wherein a reduction in bond strength was observed.

In ABAQUS, the bond-slip relation could be modelled using a two-stage traction-separation law as described in Figure 6. In the first stage, the traction stresses evolved linearly with the increase of separations and reached the ultimate values $\left(t_n^0,t_s^0,t_t^0\right)$.

After that, bond strength damage commenced and was characterized by damage parameters to represent descending trends until the tractions became null. The first stage could be considered an elastic response and was described by an elastic constitutive matrix relating tractions stresses and separations. The uncoupled elastic constitutive matrix was chosen and represented as follows

$$t=\left\{\begin{array}{c}{t}_n\\ t_s\\ t_t\end{array}\right\}=\left[\begin{array}{ccc}{K}_{nn}& 0& 0\\ 0& K_{ss}& 0\\ 0& 0& K_{tt}\end{array}\right]\left\{\begin{array}{l}{\delta }_n\hfill \\ {\delta }_s\hfill \\ {\delta }_t\hfill \end{array}\right\}=\mathbf{K}\mathsf{\delta }$$

(8)

where t is the nominal traction stress vector, its components t_n, t_s, and t_t represent the normal and the two shear tractions corresponding to the displacements related to the normal (δ_n) and transversal directions (δ_s, δ_t), respectively, in the separation vector δ. K_nn, K_ss and K_tt are the stiffness coefficients in stiffness matrix K. The values of these coefficients could be obtained by the following approximation formulations [42,43].

$$K_{ss}=K_{tt}=\frac{{\tau }_{\max }}{s_1}$$

(9)

$$K_{nn}=100\frac{{\tau }_{\max }}{s_1}$$

(10)

where τ_max is the maximum shear stress and s₁ is the displacement when τ_max is reached. These values are calibrated with respect to reinforcing bar diameter d and concrete compressive strength f’_c based on regression analysis of experimental results. The calibrated formulas used to predict the maximum shear stress and corresponding slip are given as follows:

$${\tau }_{\max }=1.1132{\left(\frac{c}{d_b}\right)}^{1/5}\sqrt{f_c^{\prime }}+1.8868(\mathrm{MPa})$$

(11)

$$s_1=-0.0074f_c^{\prime }\sqrt{\frac{d_b}{c}}+1.2825(\mathrm{mm})$$

(12)

where f’_c is in MPa and d_b is in mm. The damage initiation, which marked the beginning of the cohesive response’s degradation, was defined using a maximum nominal stress criterion. Then, the damage evolution was defined to describe the degradation rate of cohesive stiffness after the corresponding initiation criterion was met.

$${\delta }_m^{\max }=1.2819f_c^{\prime }\frac{c}{d_b}+45.1599(\mathrm{mm})$$

(13)

$$\alpha =0.5878f_c^{\prime }\frac{c}{d_b}+2.5432$$

(14)

4. Results and Discussions

4.1. Effect of Compressive Strength on Bond Strength

In this section, the effect of concrete compressive strength on the bond behavior of GPC is investigated. Three types of geopolymer concrete were conducted with three diameters reinforcing bar d12, d16, and d20. The specimens were cured at 60 °C for 4, 8, and 12 h. The correlation between compressive strength and bond strength is illustrated in Figure 7.

According to Figure 7, the bond strength of geopolymer concrete increases with the increase of compressive strength. For specimens using d12, the bond strength increases about 2.16 times when the compressive strength increases from 20 MPa to 41 MPa. For a group of d16 and d20, the increase is about 2.56 and 1.97, respectively. In this study, the difference in compressive strength of the geopolymer concrete comes from the curing conditions. For all three groups of geopolymer concrete, only one mixture was chosen for making specimens. However, the curing condition was selected as 60 °C for 4, 8 and 12 h. Based on the previous research [44], more product of geopolymerization process is produced with a longer curing time. Thus, the structure of geopolymer concrete is denser and results in higher compressive strength. This trend is similar to the results of a previous study [45].

4.2. Effect of Concrete Cover to Diameter (c/d_b) of Reinforcing Bar on Bond Strength

Figure 8 shows the influence of concrete cover to diameter ratio (c/d_b) of reinforcement bar on the bond behavior of geopolymer concrete. The test data show two different trends when the c/d_b ratio is also raised from 3.25 to 5.75. Firstly, for GP2 and GP3, the bond strength increases with the increase of c/d_b ratio from 3.25 to 4.19. Then, the bond strength decreases with the rise of c/d_b ratio from 4.19 to 5.75. Secondly, for GP1, the trend is opposite to the other groups. The bond strength decreases when the c/d_b ratio increases from 3.25 to 4.19. Later, the bond strength slightly increases according to the increase of c/d_b ratio. The behavior of GP2 and GP3 is consistent with the previous research [46]. In contrast, GP1 show the opposite behavior. It can be concluded that for specimens with the grade 20 MPa of compressive strength, the concrete cover to diameter ratio has an insignificant effect on the bond strength (with only a slight change observed).

4.3. Comparison Experimental Test with the Previous Study

In the previous work, Orangun et al. [47] proposed the formula to predict the bond strength:

$${\tau }_u=0.083045\sqrt{f_c^{\prime }}\left[1.2+3\left(\frac{c}{d_b}\right)+50\left(\frac{d_b}{l_d}\right)\right]$$

(15)

where c is the minimum concrete cover (mm), $f_c^{\prime }$ is the cylinder compressive strength of concrete (MPa), d_b is the bar diameter (mm), and l_d is the development length (mm)

Kim and Park [48] proposed an equation for predicting bond stress of geopolymer concrete:

$${\tau }_u=\sqrt{f_c^{\prime }}\left[2.07+0.2\left(\frac{c_{\min }}{d_b}\right)+4.15\left(\frac{d_b}{l_d}\right)\right]$$

(16)

where c_min is smaller of the minimum concrete cover of 1/2 of the clear spacing between bars (mm)

The experimental and predicted data of bond strength using the two above equations are presented in

Table 5. Comparison between experimental results and previous researches.

Specimen	db	c	c/db	ld	τ (Experiment)	τ (Orangun [47])	τ (Kim and Park [48])
	(mm)	(mm)		(mm)	(MPa)	(MPa)	(MPa)
GP1 R1	12	69	5.75	100	6.80	9.08	16.63
GP1 R2	16	67	4.19	100	6.01	8.08	15.97
GP1 R3	20	65	3.25	100	6.38	7.78	15.88
GP2 R1	12	69	5.75	100	11.54	11.31	20.70
GP2 R2	16	67	4.19	100	11.86	10.06	19.89
GP2 R3	20	65	3.25	100	10.14	9.69	19.77
GP3 R1	12	69	5.75	100	14.38	13.00	23.81
GP3 R2	16	67	4.19	100	15.40	11.57	22.87
GP3 R3	20	65	3.25	100	12.61	11.14	22.73

and Figure 9.

From Table 5 and Figure 9, it is evident that the calculated values from the previously proposed formulation show significant differences. In the case of expression developed by [47], the tendency revealed that the bond strength of specimens decreased when the bar diameter is higher. The remarkable dissimilarity in bond behavior might be generated by the different types of samples and rebars. This study employed the cylinder geopolymer concrete specimens while [47] operated with the beam specimens. On the other side, the equation’s results by [45] showed a similar trend with [47]. That is, the bond strength of geopolymer concrete reduces when the bar diameter increases. Moreover, the experimental results have an unlike performance with [48]. The current bond strength of the group of GP2 and GP3 increases with the increased diameter of reinforcement from 12 mm to 16 mm, and the bond strength decrease with the increased diameter of rebars from 16 mm to 20 mm. While the calculated values from [48] decrease in accordance with the increase of rebars from 12 to 20 mm. In the case of GP1, the bond strength shows a similar trend with [48]. In the first stage, they decrease in accordance with the increase of the diameter of rebars from 12 mm to 20 mm.

However, the bond strength slightly increases when that which was calculated from [48] keeps decreasing. The reason may come from the components of geopolymer concrete and curing conditions. This study used only fly ash on the geopolymer binder, while [48] used the combination of fly ash and slag as a geopolymer binder. Besides, the curing conditions used for this study was 60 °C for 4, 8 and 12 h, while the previous research was 70 °C and 24 h. With the different components of geopolymer concrete and curing conditions, the hardening of the geopolymer occurs in different ways. As a result, the microstructure of specimens shows different behavior. Even the specimens have similar compressive strength values. There is a need for studies to focus more on the effect of components of geopolymer binder and curing condition on the bond strength of reinforced geopolymer concrete in the future.

4.4. Comparison Experimental Test with the Analytical Model and Numerical Parametric Study

4.4.1. Comparison Experimental Test with the Analytical Model

In this section, the bond stress-slip curves obtained from experimental results are presented and compared with the numerical results in Figure 10. In addition, the experimental results and numerical results for maximum bond stress τ_max and corresponding slip u₁ are shown in

Table 6. Comparison between test results and FEM results.

Db	f’c	s1 Exp	s1 FEM	τmax Exp	τmax FEM	(s1 Exp)/(s1 FEM)	(τmax Exp)/(τmax FEM)
(mm)	MPa)	(mm)	(mm)	(MPa)	(MPa)
12	20.33	1.28	1.93	6.8	6.82	0.67	1
16	20.33	1.17	2.28	8.65	8.68	0.51	1
20	20.33	1.13	1.4	8.63	8.82	0.81	0.98
12	31.45	1.12	1.58	8.01	8.09	0.71	0.99
16	31.45	1.09	2.28	11.86	11.69	0.48	1.01
20	31.45	1.05	1.23	12.32	12.37	0.86	1
12	41.12	1.32	1.93	10.64	10.34	0.69	1.03
16	41.12	1.29	1.66	12.67	12.79	0.78	0.99
20	41.12	1.05	1.23	12.61	12.54	0.86	1.01
					mean	0.71	1
					CoV	0.2	0.01

. It is apparent that bond stress-slip curves achieved from the numerical results are well correlating with experimental results, especially for the hardening stage of the bond stress-slip curves. The results in Table 6 show that the FEM models can provide exact results for the maximum bond stress. While the numerical results of the corresponding slips are slightly larger than the experimental values. Therefore, the proposed numerical approach can be effectively used to model steel reinforcement bond-stress slip relations with the fly ash-based geopolymer concrete.

As observed in Figure 10 and Table 6, the experimental results show that the bond-stress increases with the increase of concrete compressive strength. In addition, the bond stress for d12 reinforcing bars is smaller than those of d16 and d20 bars, which are close to each other. The experimental results of u₁ range between 1.0 and 1.3 mm. This is in good agreement with the suggested value in fib model code 2010 [38]. The mean value of τ_maxExp/τ_maxFEM is 1.00. The coefficient of variation (CoV) is only 0.01. This means that an excellent agreement between the proposed FEM model and experimental results is archived. For the simulation results of bond-slip at maximum bond stress, the mean values of s_1Exp/s_1FEM are 0.71, and the corresponding coefficient of variation is 0.2. These results indicate that the numerical results of the corresponding slips are slightly larger than the experimental values. This slightly small error could be attributed to the simplified modelling technique employed in this study. However, it can be seen that the results for the slips at maximum bond stress are relatively small, and the numerical results could be acceptable. In Figure 10, the full range of bond stress-slip curve proposed in [34] for common concrete is also depicted. The details of the bond stress-slip curve of the fib model are given as follows

$$\begin{array}{lll}{\tau }_b={\tau }_{b\max }{\left(s/s_1\right)}^{0.4}\hfill & \mathrm{for}\hfill & 0\le s\le s_1\hfill \\ {\tau }_b={\tau }_{b\max }\hfill & \mathrm{for}\hfill & s_1\le s\le s_2\hfill \\ {\tau }_b={\tau }_{b\max }-\left({\tau }_{b\max }-{\tau }_{bf}\right)\left(s-s_2\right)/\left(s_3-s_2\right)\hfill & \mathrm{for}\hfill & s_2\le s\le s_3\hfill \\ {\tau }_b={\tau }_{bf}\hfill & \mathrm{for}\hfill & s_3<s\hfill \end{array}$$

(17)

where s is the relative displacement, ${\tau }_{b\max }=2.5\sqrt{f_c^{\prime }}$ (MPa), s₁ = 1 mm, s₂ = 2 mm, s₃ is the clear distance between ribs which can be taken as 0.6d_b, and ${\tau }_{bf}=0.4{\tau }_{\max }$. As shown in Figure 10, the fib model overestimates the bond stress between reinforcing bars and fly ash-based geopolymer concrete, while its predicted values for slips are acceptable. To adopt the bond stress-slip model of fib code [38], a modified model is proposed in this study to represent the bond stress-slip of steel reinforcing bars and fly ash-based geopolymer concrete as follows

$$\begin{array}{lll}{\tau }_b={\overline{\tau }}_{b\max }{\left(s/{\overline{s}}_1\right)}^{0.4}\hfill & \mathrm{for}\hfill & 0\le s\le {\overline{s}}_1\hfill \\ {\tau }_b={\overline{\tau }}_{b\max }\hfill & \mathrm{for}\hfill & {\overline{s}}_1\le s\le {\overline{s}}_2\hfill \\ {\tau }_b={\overline{\tau }}_{b\max }-\left({\overline{\tau }}_{b\max }-{\overline{\tau }}_{bf}\right)\left(s-{\overline{s}}_2\right)/\left({\overline{s}}_3-{\overline{s}}_2\right)\hfill & \mathrm{for}\hfill & {\overline{s}}_2\le s\le {\overline{s}}_3\hfill \\ {\tau }_b={\overline{\tau }}_{bf}\hfill & \mathrm{for}\hfill & {\overline{s}}_3<s\hfill \end{array}$$

(18)

where ${\overline{\tau }}_{b\max }$ is defined by Equation (11) ${\overline{s}}_1$ is calculated in Equation (12), ${\overline{s}}_2={\overline{s}}_1+1mm$, ${\overline{s}}_3$ is defined similarly to $s_3$, and ${\tau }_{bf}=0.2{\overline{\tau }}_{\max }$.

4.4.2. Numerical Parametric Study

To study the influence of different variables on the bond strength and corresponding slip of reinforced geopolymer concrete, two following variables was evaluated: (1) compressive strength of geopolymer concrete (f’_c); and (2) concrete cover (c). To investigate the effect of varying the compressive strength of geopolymer concrete on bond strength and corresponding slip of specimens, compressive strengths of 20 MPa, 25 MPa, 30 MPa, 35 MPa, 40 MPa, 45 MPa, 50 MPa and 60 MPa were chosen. In the case of concrete cover, the concrete cover would be considered in the range of 30 mm to 80 mm. The results of the parametric study are illustrated in Figure 11 and Figure 12.

As shown in Figure 11, parametric investigations indicate that the bond strength increase considerably with the rise of concrete compressive strength, while a reverse trend is observed in case of the values of bond slips at maximum bond stress. For the influence of concrete cover, the results shown in Figure 12 points out that the thickness cover slightly influence the bond strength. These results are consistent with those observed in the experiments.

4.5. Failure Mode

There are three failure patterns of specimens in the pull-out test, such as rebar pull-out failure, splitting of concrete, and yielding of the steel bar. In this study, the embedded length was chosen 100 mm for all specimens. The failure occurs in cracking the concrete cover and propagating along with the length of the bar as shown in Figure 13. According to a previous study [49], the specimens without confining reinforcement failed due to brittle development. Also, the test variables such as bar diameter and cover thickness did not affect the failure.

5. Conclusions

This paper investigates the bond behavior of reinforced fly ash-based geopolymer concrete using experimental work, simulation analysis, and theoretical work. To evaluate the bond behavior, experiments were conducted using 150 × 300 mm cylindrical specimens with and without rebar cured in an oven at 60 °C for 4, 8 and 12 h. Numerical analysis was then performed to compare and verify the bond behavior based on bond stress slip relationships The crucial points of this research are the following:

• The bond strength of reinforced fly ash-based geopolymer concrete increases about 1.97 to 2.56 times with the increase of compressive strength from 20.33 MPa to 41.12 MPa. By comparison, with the different components of the geopolymer binder, the microstructure of specimens shows other behavior. Even the samples have similar compressive strength values. The bond strength shows a significant difference. There is a need for studies to focus more on the effect of components of geopolymer binder and curing condition on bond strength of reinforced geopolymer concrete in the future.
• For the geopolymer concrete with the curing time of 8 and 12 h, the bond strength of reinforced geopolymer concrete rises when the c/d_b ratio varies from 3.25 to 4.19. Then, the bond strength decreases with the increase of c/d_b ratio from 4.19 to 5.75 whereas the bond strength of geopolymer concrete with a shorter curing time, 4 h, has the opposite tendency.
• The bond behavior of the reinforced fly ash-based geopolymer concrete is well correlating with simulation analytical using ABAQUS/CAE tool. However, this behavior is quite dissimilar with the data computed from the fib model.
• The bond-slip relationship of reinforced geopolymer concrete could be predicted using the proposed expression. This proposed formulation can be used to predict the bond slip behavior of reinforced fly ash-based geopolymer concrete for practical purposes.
• The numerical parametric study is performed with two variables, namely the compressive strength of geopolymer concrete and the concrete cover. The bond strength increases considerably with the rise of concrete compressive strength, while a reverse trend is observed in case of the values of bond slips at maximum bond stress. For the influence of the concrete cover, the results revealed that the thickness cover slightly influence the bond strength. These results are consistent with those observed in the experiments.

In the future work, the authors are working on investigating the bond behavior of reinforced geopolymer concrete under the corrosion conditions. The performance of ribbed steel bar would be evaluated by using proposed modelling in this study and experiment.