Failure mechanisms and damage evolution of geopolymer concrete beams under flexural loading: Experimental investigation and finite element analysis

Abstract

This study investigates the failure behavior and damage mechanisms of geopolymer concrete (GPC) and ordinary Portland cement (OPC) reinforced concrete beams through a combined experimental and numerical approach. Flexural tests were conducted, and then displacement and crack development were monitored using high-precision total station measurements. Numerical analyses were performed using ABAQUS, and the consistency between experimental observations and numerical predictions was evaluated at yield and failure stages to characterize inelastic behavior and damage progression. The effects of key parameters, including tensile reinforcement ratio, geopolymer concrete formulations, and curing methods, on cracking behavior, stiffness degradation, and failure modes were investigated in detail. The results indicate that increasing the tensile reinforcement ratio enhances flexural stiffness and load-bearing capacity while reducing ductility at advanced damage stages. Compared to OPC beams, GPC beams exhibited narrower and more distributed crack patterns due to their distinct microstructural characteristics. Quantitatively, GPC beams exhibited approximately 15% greater deformation in the compression zone at failure, while tensile reinforcement strains were up to 23% higher at yield compared to OPC beams. In addition, the maximum crack width at failure in GPC beams was approximately 50% lower than that of OPC beams. These results indicate that, despite similar strength levels, GPC beams exhibit higher deformation capacity and more distributed damage behavior. The findings demonstrate that geopolymer concrete exhibits distinct failure characteristics compared to OPC and should be explicitly considered in structural design to improve damage control and failure prediction. Overall, the study highlights the potential of geopolymer concrete as a reliable and sustainable structural material.

Graphical Abstract

Keywords

geopolymer concrete failure mechanisms crack initiation and propagation damage evolution reinforced concrete beams experimental and numerical failure analysis

Highlights

• Failure mechanisms and damage evolution of geopolymer concrete beams under flexural loading were investigated using combined experimental and numerical approaches.

• Crack initiation and crack propagation were identified through experimental observations and crack measurements, while displacement responses were monitored using high-precision total station measurements.

• ABAQUS-based finite element simulations were conducted to evaluate inelastic behavior and failure progression.

• Geopolymer concrete beams exhibited more distributed cracking and delayed damage localization compared to OPC beams.

• Experimental–numerical consistency enabled identification of key damage mechanisms and implications for failure prevention.

Introduction

Geopolymer concrete (GPC) research has gained momentum as a sustainable alternative to traditional ordinary Portland cement concrete (OPC). By utilizing fly ash, a significant industrial by-product, GPC reduces the environmental impact of cement production and supports waste management efforts. The primary goal of GPC development is to produce eco-friendly materials with mechanical properties that meet or exceed those of OPC. This approach aligns with global efforts to lower carbon footprints and promote sustainable construction practices (Acar et al., 2020). The mechanical properties of GPC differ from those of OPC in several ways. While both materials can achieve similar compressive strengths, GPC typically exhibits a lower elastic modulus and higher tensile strength. These differences significantly affect the structural performance of GPC, including load-bearing capacity, deformation behavior, and cracking resistance. For instance, a lower elastic modulus allows for greater flexibility and deformation capacity, while the higher tensile strength enhances resistance to cracking under tensile stress. These unique characteristics necessitate a re-evaluation of design parameters for structures incorporating GPC (Çelik et al., 2022a; Özbayrak et al., 2023a).

The activation of fly ash in GPC relies on alkali solutions such as sodium hydroxide (SH) and sodium silicate (SS). The ratios of SH and SS, as well as their proportion to fly ash, critically influence the mechanical and dynamic properties of GPC (Kucukgoncu & Özbayrak, 2025, 2025eçen et al., 2023; Özbayrak, 2024). Optimizing these ratios can enhance compressive strength, elastic modulus, tensile strength, and fire resistance while improving microstructural stability and adherence strength between reinforcement and concrete at high temperatures (Aslanbay et al., 2024; Özbayrak et al., 2023b).

The experimental study of GPC faces challenges due to the time, cost, and labor involved in testing. Numerical simulation tools, particularly finite element analysis (FEA), provide a complementary approach by enabling the prediction of structural behaviors that are difficult to observe experimentally (Abdelwahed, 2020; Hassan et al., 2022; Korkut and Karalar, 2023; Venkatachalam et al., 2020; Çelik et al., 2022b). Numerous studies have confirmed the accuracy of FEA in simulating crack patterns, load-displacement relationships, and fracture mechanics for GPC structures. For example, FEA has been instrumental in studying crack initiation, propagation, and the influence of reinforcement on cracking behavior, showing strong agreement with experimental results (Abubakar, 2023; Chong et al., 2022; Darmawan et al., 2022; Zerfu and Ekaputri, 2022). The cracking behavior of GPC beams differs notably from that of OPC beams. While OPC beams typically exhibit wider cracks and sudden brittleness during failure, GPC beams demonstrate narrower crack widths, greater ductility, and enhanced bond strength with reinforcement. These differences are attributed to the higher fracture energy and improved microstructural properties of GPC. Experimental studies indicate that beam size and reinforcement ratio significantly affect cracking behavior (Aziz et al., 2022; Mortar et al., 2022; Wibowo et al., 2022). Numerical analyses further show that these parameters also influence the load-carrying capacity of reinforced concrete beams (Alex et al., 2022; Liu and Yan, 2022; Nofal et al., 2023).

Experimental and numerical studies on full-scale geopolymer beams in the literature have shown a significant correlation between load-displacement values and residual capacity estimates (Fathi et al., 2026; Özbayrak and Kucukgoncu, 2025). The shear behavior of geopolymer concrete beams is affected by the reinforcement ratio and shear span ratio, and the proposed numerical models have shown good agreement with the test results. In addition, the numerical models captured the failure modes and load-displacement behavior (Liu et al., 2025). On the other hand, in many studies on crack propagation, crack patterns, and fracture modes of GPC beams, FRP-based reinforcement has been used instead of steel reinforcement. When the crack width, number of cracks, and failure modes of CFRP geopolymer concrete beams under bending were examined, GPC beams exhibited smaller crack widths than OPC beams (Ahmed et al., 2020). In another study, the flexural performance of T-beams GPC reinforced with GFRP rods was experimentally investigated, and the failure mode was also affected, as the ultimate strain of GPC did not exhibit the same behavior as that of OPC (Hasan et al., 2023). In addition, the cracking patterns and failure modes of beams reinforced with GFRP rods under bending were experimentally investigated, and ductile fracture was observed. However, wide tensile cracks occurred in the concrete in the compression region. As the load increased, flexural cracks gradually formed in the constant moment region and then in the shear span (Junaid et al., 2019). Furthermore, the seismic model developed to study the seismic behavior of a prefabricated bridge made of FRP-reinforced geopolymer concrete has reliably captured the bridge’s damage and revealed the performance of OPC and GPC-reinforced bridges (Ngo et al., 2024).

Despite the increasing number of studies on geopolymer concrete, limited research has addressed the combined experimental–numerical evaluation of damage evolution and failure mechanisms at the structural element level. This study is based on full-scale bending tests, displacement measurements using a high-precision total station, and validated finite element modeling. The damage development and the crack propagation mechanisms of GPC beams were systematically investigated, and the results from GPC beams were compared with those of OPC beams at both the yield and failure stages. Furthermore, the agreement between experimental findings and numerical simulation results derived from ABAQUS was assessed to validate the interpretation of inelastic behavior and damage evolution. Moreover, this research aims to compare the fracture mechanisms and cracking characteristics of GPC and OPC beams using a thorough experimental-numerical methodology. The influence of critical variables, including reinforcement ratio, alkali activator ratio, and curing method parameters, on load-displacement response, deformation capacity, and crack characteristics was also investigated. The findings give quantitative insights into the failure mechanism of GPC beams and contribute to improving their applicability as sustainable alternatives to OPC in structural design.

To achieve the objectives of this study, a systematic experimental–numerical workflow was followed. Initially, GPC and OPC beam specimens were designed, and material characterization tests were conducted. Subsequently, the full-scale four-point bending tests were performed, and displacement and crack development were monitored using high-precision total station measurements. The experimental data, including load–displacement responses and crack patterns, were then used to develop finite element models in ABAQUS. The numerical analyses incorporated CDP modeling, interaction definitions, and Dynamic Explicit procedures to simulate nonlinear behavior and damage evolution. Finally, experimental and numerical results were compared for model validation, followed by a detailed evaluation of failure mechanisms, damage evolution, and structural performance. The overall research methodology adopted in this study is illustrated in Figure 1. The workflow includes specimen design, material characterization, experimental testing, data acquisition, finite element modeling, damage analysis, and model validation, followed by a comprehensive evaluation of structural performance.

Figure 1.

Flowchart of the research methodology adopted in this study.

Methodology

Material properties

In this study, Class F fly ash, conforming to ASTM C618, was utilized to produce geopolymer concrete (ASTM C311, 2023; ASTM C618, 2022). The material had a density of 2.32 g/cm³. To qualify as Class F fly ash, the combined ratio of chemical components such as SiO₂, Al₂O₃, and Fe₂O₃ must exceed 70% of the total composition. The fly ash used met this requirement, with a combined SiO₂, Al₂O₃, and Fe₂O₃ content of 85%. As alkali activators, 14M sodium hydroxide (NaOH) and sodium silicate (Na₂SiO₃) solutions were employed. The coarse aggregate was crushed stone with a 2.6 g/cm³ density and a 7–14 mm particle size range. River sand with a density of 1.8 g/cm³ and a particle size range of 0.1–4 mm served as the fine aggregate. Both aggregates were used in a saturated surface-dry condition without adding water.

Two different types of geopolymer concrete (F1 and F2) were created, with the only difference being the ratio of sodium silicate to sodium hydroxide (SS/SH). Table 1 presents the mixed proportions of these formulations. Table 1 also provides information on OPC concrete mix proportions. As part of the TUBITAK-121M236 research project, a series of geopolymer and OPC concrete mixtures were developed and prepared for experimental investigations (Özbayrak et al., 2024a, 2025a). The SS/SH ratios were selected as 1.5 for F1 and 3.5 for F2, representing the typical range of SS/SH ratios (1.5–3.5) commonly reported in literature studies (Hardjito et al., 2004; Palomo et al., 1999; Rangan, 2008; Rattanasak and Chindaprasirt, 2009; Sathonsaowaphak et al., 2009; Swanepoel and Strydom, 2002). This range was chosen for a broader comparison with traditional reinforced concrete beams.

Table 1.

Components of geopolymer and OPC concrete (kg/m³) (Özbayrak et al., 2024a, 2025a).

Sample No	Sample name	FA	SS	SH	SS/SH	AA/FA	Fine aggregate	Coarse aggregate
1	F1	406	122	81	1.5	0.5	643	1194
2	F2	406	158	45	3.5	0.5	643	1194
FA: Fly Ash, SS: Sodium silicate Solution, SH: Sodium hydroxide Solution, AA: Sum of SS and SH
Sample No	Sample name	Cement	Water	-	-	Water/Cement ratio	Fine aggregate	Coarse aggregate
1	OPC	400	180	-	-	0.45	650	1050

To characterize the mechanical properties of the GPC and OPC mixtures, compression tests were conducted on cylindrical specimens (100 mm diameter × 200 mm height) using a compressometer. Six specimens were tested for each mixture type to derive compressive strength values and complete stress–strain relationships. In addition, the splitting tensile strength was evaluated via indirect tensile tests, with three specimens per mixture. Direct tensile tests were carried out to assess the mechanical properties of the reinforcement used in the beams. For each bar diameter, three steel samples were tested. Figure 2 presents the experimental setup and procedures for the concrete compression, splitting tensile, and reinforcement tensile tests conducted during the material characterization stage.

Figure 2.

Material testing of GPC, OPC, and Reinforcement samples: (a) Concrete compressive tests, (b) Concrete splitting tensile tests, (c) Reinforcement tensile tests (Özbayrak et al., 2024a, 2025a).

The compressive strength, splitting tensile strength, elastic modulus, and Poisson’s ratio for both GPC and OPC specimens, corresponding to the specific mix proportions, were determined through material testing. The experimentally obtained stress–strain curves for the GPC, OPC, and reinforcement specimens are presented in the numerical modeling section. These curves were adapted to fit the Concrete Damaged Plasticity (CDP) model. To characterize the damage behavior of the materials, the CDP model was calibrated using the mechanical properties of both GPC and OPC. B420 C reinforcing steel was used for numerical simulations, yield, and tensile strength values derived from tensile tests. The stress-strain curves of the reinforcing steel used in the FEM analysis are depicted in the numerical section.

Experimental method

In the numerical study, FEM analyses were conducted on 12 geopolymer concrete (GPC) reinforced concrete beams and three ordinary Portland cement (OPC) reinforced concrete beams, for which laboratory tests had previously been performed within the scope of the TUBITAK-121M236 research project (Özbayrak et al., 2024a). The primary variable parameters for the reinforced concrete beams were the SS/SH ratio, curing method, and tensile reinforcement ratio. GPC concrete mixtures were prepared with SS/SH ratios of 1.5 and 3.5 and an alkaline activator-to-fly ash (AA/FA) ratio of 0.5. The SS/SH and AA/FA ratios used in this study were selected based on preliminary material characterization tests and previous literature. These tests included compressive strength tests on cylindrical specimens, flexural performance of prism beams, and bond strength evaluations. The selected ratios were found to provide improved mechanical and bond performance and are consistent with previously validated mixture formulations reported in the literature (Aslanbay et al., 2024; Özbayrak et al., 2023a, 2023b, 2024a).

The beam samples were thermally cured at 90°C for 24 hours, either immediately after production or after 4 days of ambient storage. Three OPC beams were produced for comparison to evaluate the advantages and limitations of GPC concrete. Laboratory tests were conducted on all samples after 28 days. During the laboratory tests, displacements were measured using a total station, and deformations of the beams were monitored under various load stages, including the first crack, yielding, concrete crushing, and ultimate load conditions (Figure 3). Stress-strain curves and splitting tensile test results from cylindrical samples taken during beam production were utilized for numerical analysis. Finite element analyses were conducted to simulate bending tests, using a beam 150 × 300 × 3300 mm and a 3000 mm span between supports.

Figure 3.

Samples and setup of experimental and total station (Özbayrak et al., 2024a, 2025a).

Three tensile reinforcement ratios were used, representing minimum, balanced, and maximum reinforcement limits as specified in the design standards (ACI 318-14, 2014; TS-500, 2000). The concrete cover of the beams is 25 mm, and information on geometric details, solution ratio, curing method, and reinforcement layouts is given in Figure 4 and Table 2. The reinforcement ratios and curing start times were systematically varied across the samples, with tensile reinforcement details as follows: GB1 (2 Ø 12), GB2 (3 Ø 14), and GB3 (4 Ø 16). The SS/SH ratio was 1.5 (F1) or 3.5 (F2). C0 samples that are cured immediately after manufacturing (24 hours at 90°C), and C4 refers to samples that are kept under ambient conditions for 4 days after manufacturing and then heat cured (24 hours at 90°C). The properties of the geopolymer depend largely on the source material, the alkaline activator, the molarity of the activator, and the curing conditions (Benfratello et al., 2025). Curing conditions play an important role in determining the bending performance (Unver et al., 2026).

Figure 4.

GPC and OPC beam geometry and reinforcement details (Özbayrak et al., 2024a, 2025a).

Table 2.

GPC and OPC beam geometry, reinforcement, solution, and curing details (Özbayrak et al., 2024a, 2025a).

No	Sample name	Beam size (mm)	Tensile reinforcement	Reinforcement ratio	SS/SH	Curing start
1	GB1F1C0	150 × 300 × 3300	2 Ø 12	0.005	1.5	Immediately
2	GB2F1C0	150 × 300 × 3300	3 Ø 14	0.010	1.5	Immediately
3	GB3F1C0	150 × 300 × 3300	4 Ø 16	0.018	1.5	Immediately
4	GB1F2C0	150 × 300 × 3300	2 Ø 12	0.005	3.5	Immediately
5	GB2F2C0	150 × 300 × 3300	3 Ø 14	0.010	3.5	Immediately
6	GB3F2C0	150 × 300 × 3300	4 Ø 16	0.018	3.5	Immediately
7	GB1F1C4	150 × 300 × 3300	2 Ø 12	0.005	1.5	+4 days
8	GB2F1C4	150 × 300 × 3300	3 Ø 14	0.010	1.5	+4 days
9	GB3F1C4	150 × 300 × 3300	4 Ø 16	0.018	1.5	+4 days
10	GB1F2C4	150 × 300 × 3300	2 Ø 12	0.005	3.5	+4 days
11	GB2F2C4	150 × 300 × 3300	3 Ø 14	0.010	3.5	+4 days
12	GB3F2C4	150 × 300 × 3300	4 Ø 16	0.018	3.5	+4 days
13	OPCB1	150 × 300 × 3300	2 Ø 12	0.005	-	-
14	OPCB2	150 × 300 × 3300	3 Ø 14	0.010	-	-
15	OPCB3	150 × 300 × 3300	4 Ø 16	0.018	-	-

Tensile reinforcement (GB1: 2 Ø 12, GB2: 3 Ø 14, GB3: 4 Ø 16), SS/SH ratio (F1: 1.5, F2: 3.5), Curing start (C0: Direct, C4: After 4 days).

The high-heat-capacity oven shown in Figure 5 was used to cure the GPC beam and cylinder samples. The study provides in-depth insights into the flexural behavior of GPC and OPC beams, accounting for variations in material composition, reinforcement, and curing conditions. In beam tests, the loading rate was 5 kN/min in load-controlled loading and 3 mm/min in displacement-controlled loading.

Figure 5.

Production and curing of GPC beams (Özbayrak et al., 2024a, 2025a).

Numerical method

The finite element simulations of GPC and OPC beams were performed using ABAQUS (ABAQUS v6.12, 2018), which is a widely adopted tool for modeling the nonlinear structural behavior of reinforced concrete elements (Demir et al., 2016; Khennane, 2013). Recent studies have demonstrated that finite element models developed in ABAQUS can accurately predict the flexural response and damage distribution of geopolymer concrete beams when validated against experimental results (Dong et al., 2026; George et al., 2023).

The analyses were carried out through the Dynamic Explicit procedure, and all modeling processes adhered to the SI unit system (Özbayrak et al., 2024a). The Dynamic Explicit procedure is an explicit time-integration scheme for highly nonlinear problems without iterative equilibrium calculations. It was adopted in this study for its robustness in modeling cracking, stiffness degradation, and damage evolution in reinforced concrete, while avoiding convergence difficulties associated with implicit analyses. To realistically represent the mechanical response of concrete under multi-axial loading, both elastic and inelastic properties were defined. The Concrete Damaged Plasticity (CDP) model was selected to simulate damage evolution and crack formation in concrete (Özbayrak et al., 2025b). This constitutive model incorporates isotropic elasticity subjected to degradation and models tensile and compressive plasticity in a coupled manner, enabling the accurate prediction of post-peak behavior (Cichocki et al., 2015; Lee and Fenves, 1998; Lubliner et al., 1989; Martin, 2010). The input parameters for the CDP model were determined from experimental results from compression and splitting tensile tests on cylindrical specimens prepared alongside the beam elements. Separate material definitions were created for geopolymer concrete mixes with two distinct SS/SH ratios (1.5 and 3.5), each subjected to different thermal curing conditions, namely, immediate demolding and delayed curing after 4 days.

Consequently, four GPC and one OPC material configurations were defined. A total of 12 GPC beam models and three OPC beam models, each with varying longitudinal reinforcement layouts, were analyzed numerically. Key parameters used in the CDP model are presented in Table 3. The dilation angle (φ = 30°), eccentricity (ε = 0.1), and the biaxial-to-uniaxial compressive strength ratio (

f_{b 0} / f_{c 0}

= 1.16) were adopted, with the latter two retained as default values (Ma et al., 2012; Ren et al., 2015). Additional parameters such as the K coefficient and viscosity parameter, were calibrated through sensitivity analyses. The CDP properties for GPC were established by drawing from recent literature and conducting a series of parametric evaluations (Abadel, 2023; Elchalakani et al., 2018; George et al., 2023; Raza et al., 2021; Yu et al., 2024; Zinkaah et al., 2022; Özbayrak et al., 2025a). Likewise, the OPC material parameters were determined through a similar approach based on literature guidance and numerical tuning (Birtel and Mark, 2006; Hany et al., 2016; Kamali, 2012; Lopez-Almansa et al., 2014). These values were verified and validated through multiple convergence studies and comparisons with reference sources (Grassl, 2004; Mercan et al., 2010). The summarized material input values for both concrete types are listed in Table 3.

Table 3.

CDP parameters for the ABAQUS material definition of GPC and OPC concrete (Özbayrak et al., 2024a, 2025a).

	Taken value	Description
GPC parameter
$φ$	30	Dilation angle (calibrated)
$ϵ$	0.1	Eccentricity (default)
$f_{b 0} / f_{c 0}$	1.16	The ratio of initial equibiaxial compressive yield stress to initial uniaxial compressive yield stress (default)
K	0.6667	$K_{c}$ , the ratio of the second stress invariant on the tensile meridian (default)
$υ$	0.0001	Viscosity parameter (calibrated)
OPC parameter
$φ$	50	Dilation angle (calibrated)
$ϵ$	0.1	Eccentricity (default)
$f_{b 0} / f_{c 0}$	1.16	The ratio of initial equibiaxial compressive yield stress to initial uniaxial compressive yield stress (default)
K	0.6667	$K_{c}$ , the ratio of the second stress invariant on the tensile meridian
$υ$	0.0005	Viscosity parameter (calibrated)

GPC and OPC material models

The stress–strain relationships obtained from uniaxial compression tests for each concrete type were incorporated into the constitutive material model. For all specimens, mechanical input parameters, including yield stress, ultimate compressive strength, and the corresponding strain values associated with these states, were defined in the finite element software. The elastic modulus for each mix was calculated from test data and assigned accordingly. The nonlinear behavior of concrete was represented using the Concrete Damaged Plasticity (CDP) model (Özbayrak et al., 2025c). The compressive stress–strain response of concrete was modeled according to established procedures, and the resulting constitutive behavior is presented in Figure 6 (Hibbitt et al., 2013). For compressive behavior modeling in ABAQUS, key parameters such as yield stress values and their corresponding inelastic strain components are required. These inelastic strains begin at the point of initial yielding and represent the deformation accumulated beyond the elastic range. The inelastic strain values were computed using equation (1) as proposed by Kamali (2012), while the corresponding stress values were obtained using equation (2). Although the software internally converts inelastic strain into plastic strain, this transformation was also explicitly computed using equation (3) for consistency.

Figure 6.

Compressive behavior of concrete in the post-cracking phase (Özbayrak et al., 2024a, 2025a).

Additionally, the damage parameter under compressive loading, denoted as d_c, was introduced through equation (4). This coefficient quantifies the degradation in elastic stiffness following the peak compressive strength and plays a critical role in accurately replicating the post-peak softening behavior of concrete within the CDP framework. Proper calibration of the d_c value is essential for simulating the material’s damage mechanics realistically, and its determination was guided by the empirical approach defined in the literature (Kamali, 2012). The parameter b_c, as defined in the governing equations, denotes the ratio of plastic strain to inelastic strain. Based on findings in current literature, this ratio typically ranges from 0.5 to 0.7 for concrete materials (Birtel and Mark, 2006; Grassl, 2004; Hany et al., 2016; Hibbitt et al., 2013; Krätzig and Pölling, 2004; Mercan et al., 2010). Under uniaxial tensile loading, the stress–strain (σ_t - ε_t) response of concrete remains linear-elastic up to the peak tensile stress (σ_t0 - f_ctk), as illustrated in Figure 6. The corresponding strain at peak stress, εt₀, is computed by dividing the peak stress by the initial elastic modulus (E₀).

The tensile behavior of concrete is shown in Figure 7 (Hibbitt et al., 2013), while different modeling approaches, including linear, bilinear, and exponential tension softening curves; are demonstrated in Figure 8 (Earij et al., 2017), where w represents the crack width. To simulate post-cracking tensile responses in ABAQUS, it is essential to define the softening behavior of concrete beyond the cracking threshold. According to the implemented constitutive model, the tensile stress values (σ_t) are calculated using equation (5), and the corresponding plastic strain values (ε_t^pl) are derived via equation (6) (Hibbitt et al., 2013). The d_t parameter quantifies tensile damage and is computed using equation (7), while the inelastic strain after cracking, denoted ε_t^ck, is calculated with equation (8) (Kamali, 2012; Lopez-Almansa et al., 2014). Literature suggests that the $b_{t}$ coefficient used in tensile damage modeling may range between 0.1 and 0.7 (Birtel and Mark, 2006; Kamali, 2012; Lopez-Almansa et al., 2014). In line with previous research and results from a series of sensitivity analyses, a calibrated value of 0.5 was selected for OPC beam modeling (Birtel and Mark, 2006; Hany et al., 2016; Kamali, 2012; Lopez-Almansa et al., 2014). Similarly, for geopolymer concrete elements, literature-based assessments and parametric evaluations supported selecting 0.7 as a representative value (Aslanbay et al., 2024; Elchalakani et al., 2018; George et al., 2023; Yu et al., 2024; Zinkaah et al., 2022; Özbayrak et al., 2025a).

ε_{c}^{i n} = ε_{c} - \frac{σ_{c}}{E_{0}}

(1)

σ_{c} = (1 - d_{c}) . E_{0} . (ε_{c} - ε_{c}^{p l})

(2)

ε_{c}^{p l} = ε_{c}^{i n} - \frac{d_{c}}{(1 - d_{c})} \frac{σ_{c}}{E_{0}}

(3)

d_{c} = 1 - \frac{σ_{c} / E_{0}}{σ_{c} / E_{0} + ε_{c}^{i n} (1 - b_{c})}

(4)

σ_{t} = (1 - d_{t}) . E_{0} . (ε_{t} - ε_{t}^{p l})

(5)

ε_{t}^{p l} = ε_{t}^{c k} - \frac{d_{t}}{(1 - d_{t})} \frac{σ_{t}}{E_{0}}

(6)

d_{t} = 1 - \frac{σ_{t 0} / E_{0}}{σ_{t 0} / E_{0} + ε_{t}^{c k} (1 - b_{t})}

(7)

ε_{t}^{c k} = ε_{t} - \frac{σ_{t 0}}{E_{0}}

(8)

Figure 7.

Tensile response curve of concrete (Özbayrak et al., 2024a, 2025a).

Figure 8.

Tensile behavior of concrete in the post-cracking stage (Özbayrak et al., 2024a, 2025a).

The mechanical properties of all material models were established based on compressive and tensile experimental data. Compressive stress–strain curves and corresponding damage diagrams were developed using the results of cylinder compression tests, while tensile response and damage profiles were obtained through splitting tensile tests. The compressive and tensile damage behavior of GPC mixtures, as derived from the experimental results and modeled through the aforementioned equations, is shown in Figures 9 and 10, respectively. The corresponding graphs for OPC specimens are presented in Figure 11. Moreover, the tensile stress–strain relationship for the steel reinforcement used in the experimental program was defined using the CDP model and implemented into the finite element simulation (Birtel and Mark, 2006; Earij et al., 2017; Grassl, 2004; Hany et al., 2016; Hibbitt et al., 2013; Krätzig and Pölling, 2004; Lopez-Almansa et al., 2014; Mercan et al., 2010; Pham et al., 2021). These curves, reflecting the plastic response of the reinforcement materials, are shown in Figure 12. An elastic modulus of 200000 MPa and a Poisson’s ratio of 0.3 were assigned to the reinforcement. The detailed material properties used for both GPC and OPC specimens are summarized in Table 4.

Figure 9.

Compressive and damage behavior curves of GPC samples obtained from the numerical model (Özbayrak et al., 2024a, 2025a).

Figure 10.

Tensile and damage behavior curves of GPC samples obtained from the numerical model (Özbayrak et al., 2024a, 2025a).

Figure 11.

Compressive and tensile damage behavior curves of OPC samples obtained from the numerical model (Özbayrak et al., 2024a, 2025a).

Figure 12.

Plastic strain curves of rebar with different diameters (Özbayrak et al., 2024a, 2025a).

Table 4.

Material mechanical properties of GPC and OPC concrete (Özbayrak et al., 2024a, 2025a).

Sample name	f _c (MPa)	f _t (MPa)	E _c (MPa)	υ, Poisson’s ratio
A1.5W0.5-C0	39.00	2.22	14067	0.20
A1.5W0.5-C4	41.21	3.17	19978	0.20
A3.5W0.5-C0	38.49	2.94	16714	0.20
A3.5W0.5-C4	43.09	3.40	23014	0.20
OPC	42.47	3.25	21022	0.18

Numerical modeling setup and simulation parameters

In the finite element model, the interaction between the reinforcement and the surrounding concrete was modeled using the embedded region technique, which allows the two materials to act as a fully bonded system. In this approach, the reinforcement elements (embedded) are kinematically constrained to the host concrete elements such that they share the same degrees of freedom, resulting in no relative slip or separation throughout the analysis. This assumption simplifies bond modeling and assumes perfect adherence between the two materials. In the present model, the embedded-region technique was adopted under the assumption of a perfect bond between reinforcement and concrete. This approach was considered appropriate because the numerical analyses were intended to capture the global flexural response and damage evolution of the beams, while previous bond-related studies on similar geopolymer concrete systems indicated adequate reinforcement–concrete interaction for structural-level modeling (Aslanbay et al., 2024; Demir et al., 2016; Khennane, 2013; Özbayrak et al., 2024a).

For the contact definition between the concrete specimen and the loading and support plates, a tie constraint was implemented. This ensures that the surfaces remain bonded throughout the analysis, preventing any sliding or detachment at the interfaces. The boundary conditions were defined by numerically coupling the degrees of freedom at the constrained surfaces, allowing them to displace together during the simulation. The applied loading configuration replicates a standard four-point bending test, with a 900 mm spacing between the two loading points. A prescribed displacement was assigned to the loading regions, and the loading amplitude was defined based on the duration and control settings of the explicit dynamic analysis. Structural responses, including deformation and load transfer, were monitored throughout the simulation. The load–displacement curves were generated by extracting reaction forces at the supports corresponding to the imposed displacements. The analysis was performed using the explicit dynamic solution method, which is particularly suitable for problems involving material degradation, cracking, and failure progression. Its ability to account for inertia and damping effects makes it appropriate for simulating post-cracking behavior and failure mechanisms observed in experimental conditions. During meshing, element types and mesh sizes were defined separately for concrete and reinforcement components.

For the concrete domain, C3D8R eight-node linear hexahedral elements with reduced integration were used to model nonlinear deformation in three dimensions accurately. Longitudinal and transverse reinforcements (including stirrups) were modeled using T3D2 elements, two-node truss elements designed to simulate bar-type behavior in 3D space. Mesh refinement was applied to the reinforcement and adjacent concrete regions to ensure accurate interaction representation. A parametric mesh sensitivity study was conducted to determine the optimal element size for concrete. Mesh sizes of 20, 25, 30, 40, and 50 mm (with an aspect ratio of 1:1:1) were evaluated. Based on the results, a mesh size of 25 mm was selected as the optimum for both concrete and reinforcement, offering a balance between computational efficiency and accuracy (Özbayrak et al., 2024a, 2025a). Loading and support plates were meshed with the same size to maintain geometric and bond consistency with the experimental specimens. The final finite element mesh and model configuration are illustrated in Figure 13, reflecting the structural layout, loading arrangement, and refined meshing strategy adopted in the numerical simulations.

Figure 13.

Numerical model representation: (a) Boundary conditions and loading configuration, (b) Meshing discretization accuracy (Özbayrak et al., 2025a).

Mesh sensitivity

During the meshing phase, suitable element types were assigned to each material component based on their mechanical behavior and geometric representation. All structural components were defined in three dimensions. The beam geometry was discretized using C3D8R elements, eight-node linear hexahedral (brick) elements with a single integration point and reduced order, and three translational degrees of freedom per node. These solid elements provided sufficient accuracy for modeling the nonlinear behavior of concrete under flexural loading. The same element type (C3D8R) was also employed for the loading and support plates; however, a relatively coarse mesh was adopted for these components to reduce computational cost without compromising the accuracy of the load transfer simulation. The longitudinal and transverse reinforcement bars were modeled using T3D2 elements, which are two-node, three-dimensional truss elements with one translational degree of freedom at each node, ideal for capturing the axial behavior of embedded steel components. To evaluate the influence of mesh density on numerical results, a mesh-convergence study was conducted. Three mesh configurations classified as fine, medium, and coarse were developed for both concrete and reinforcement domains. The mesh sizes corresponding to each configuration are detailed in Table 5. Throughout the simulations, different mesh densities were tested for both the concrete matrix and reinforcing steel. The impact of mesh refinement on the structural response was evaluated by comparing load–displacement curves, as illustrated in Figure 14, which shows the load–displacement curves obtained from the analyses of the selected representative geopolymer concrete (GPC) specimen at different mesh sizes.

Table 5.

The mesh sizes used for the representative GPC specimen (Özbayrak et al., 2025a).

Sample name	Rebar mesh size (mm)	Concrete mesh size (mm)
GB1F2C4-0	25 × 25	25 × 25
GB1F2C4-1	20 × 20	20 × 20
GB1F2C4-2	30 × 30	30 × 30
GB1F2C4-3	40 × 40	40 × 40
GB1F2C4-4	50 × 50	50 × 50

Figure 14.

Load–displacement curves of the representative GPC specimen at different mesh sizes (Özbayrak et al., 2025a).

The comparison of numerical and experimental load–displacement responses revealed that finer mesh configurations tend to yield lower predicted load capacities. Among the mesh sizes evaluated, a 25 mm discretization provided the closest alignment with the experimental behavior, particularly for the GB1F2C4 specimen. This mesh size demonstrated optimal accuracy in replicating the structural response observed in physical testing. Based on the mesh sensitivity analysis, a mesh dimension of 25 × 25 mm was selected as the most effective resolution for both the concrete matrix and the reinforcement elements of the specimen (Özbayrak et al., 2025a). This mesh density offered a balanced trade-off between computational cost and fidelity of the results. The same mesh configuration was subsequently employed for all other GPC and OPC beam specimens, as it consistently produced simulation results in strong agreement with the corresponding experimental data. Accordingly, the 25 mm mesh size was adopted as the standard discretization approach throughout the numerical modeling process.

Results and discussion

The results discussed in this section are derived from the GPC and OPC beam models developed and analyzed within the scope of the present study. This section presents both the experimental and numerical findings, including load–displacement behavior, deformation characteristics, and crack patterns. In addition, a detailed discussion is provided to interpret the damage evolution and to compare the structural performance of GPC and OPC beams.

Comparison of the results for GPC and OPC beams

During the experiments, displacement readings were obtained using a total station placed at six points along the reinforced concrete beams. These readings enabled precise determination of displacement geometries at key stages, including the appearance of the first crack, the yield point, the crushing of the compression zone, and the final state. Additionally, damage patterns in the tensile and compression zones were monitored and systematically compared to the numerical model results. The analysis evaluated the similarities and differences in the behavior and crack development of OPC and GPC beams under loading, both experimentally and numerically. Using the finite element method (FEM) analyses, deformations in steel and concrete that were difficult to assess during laboratory experiments were investigated in more detail. This allowed for a strong comparison of how OPC and GPC-reinforced concrete beams behave and the types of damage they exhibit, despite having similar compressive strength. The load–displacement behavior, together with the compression and tensile damage responses for the GB1 beam and the corresponding OPC series, is illustrated in Figures 15 –19, enabling a detailed comparison between experimental results and FEM predictions.

Figure 15.

Comparison of GB1F1C0 experimental and finite element analysis results.

Figure 16.

Comparison of GB1F1C4 experimental and finite element analysis results.

Figure 17.

Comparison of GB1F2C0 experimental and finite element analysis results.

Figure 18.

Comparison of GB1F2C4 experimental and finite element analysis results.

Figure 19.

Comparison of OPCB1 experimental and finite element analysis results.

Figures 15 –19 display side-by-side comparisons of experimental and finite element analysis (FEA) results for GB1 beam specimens. Each figure includes crack patterns from physical tests, damage distribution maps from FEA (for tensile and compressive damage), and corresponding load-displacement curves. The progression of damage and crack development is shown at key loading stages: first crack, yield, failure, and ultimate points. Reinforced concrete GPC beams, analyzed with three different tensile reinforcement ratios, were compared internally based on their SS/SH ratio and curing method, with fundamental differences revealed. The DAMAGET menu was utilized in ABAQUS to evaluate tensile damage and crack development, while the DAMAGEC menu was employed for compression damage (ABAQUS v6.12, 2018; Nguyen et al., 2018, 2020; Pham et al., 2021). In GB1 beams with 2Ø12 tensile reinforcement, key behavioral findings were obtained by identifying where the tensile reinforcement yielded and where the concrete in the compression zone was crushed. Initially, experimental results and FEM analysis outcomes were compared separately for GPC and OPC concretes. For comparison, the results for all GPC-reinforced concrete beams were averaged, regardless of SS/SH ratio and curing methods. A detailed evaluation of GPC beams concerning their SS/SH ratio and the impact of the curing method is presented at the end of the chapter. Furthermore, comparisons between the experimental and FEM analysis results of GPC and OPC concretes were conducted. This allowed for a comprehensive investigation of the behavior of GPC and OPC concrete individually and in relation to each other through experimental and numerical analyses. Table 6 presents a comparison of the load–displacement responses of the GB1 and OPC beams obtained from experimental tests and FEM analyses at the yield and failure states.

Table 6.

% differences in reinforced concrete beams with longitudinal tensile reinforcement 2Ø12 (GB1).

% Differences	FEM & experimental				GPC avg. & OPC
GB1 beams	GPC avg.		OPC		FEM		Experimental
GB1 beams	Load	Disp.	Load	Disp.	Load	Disp.	Load	Disp.
Yield point	1%	−5%	−4%	−24%	−3%	−20%	1%	−6%
Failure point	−5%	−1%	16%	−3%	18%	−17%	−4%	−15%

The experimental and FEM analysis results for GPC beams with 2Ø12 tensile reinforcement were found to be compatible. However, a notable observation is that while the load values of OPC beams matched those of GPC at the yield point, geopolymer beams exhibited less deflection than traditional reinforced concrete beams at both the yield and failure points. This indicates that OPC beams outperform GPC beams in terms of energy dissipation at a minimum reinforcement ratio. During crack monitoring and analysis, the maximum crack width in all beams was measured as 0.5 mm at the yield point and 5 mm at the failure point. These results suggest that the maximum crack widths of GPC and OPC-reinforced concrete beams at both the yield and failure points in the plastic phase are equivalent. Overall, the crack development and patterns in GPC beams were similar to those of OPC beams, consistent with findings in the literature (Chaudhari et al., 2017; Ranjbar et al., 2016; Sumajouw and Rangan, 2006; Tran et al., 2019; Yost et al., 2013). However, cracks in GPC beams propagated more frequently and were thinner, whereas OPC beams exhibited fewer, wider cracks. FEM analysis also revealed that the compressive and tensile damage at the failure point differed between OPC and GPC beams due to the higher number of wide cracks observed in OPC beams. Another contributing factor to these differences is the higher splitting tensile strength of GPC compared to OPC, as determined in prior cylindrical tests (Özbayrak et al., 2023a). Additionally, the elastic modulus of GPC under compression was lower than that of OPC in these studies (Ganesan et al., 2014; Nguyen et al., 2016; Noushini et al., 2016; Olivia and Nikraz, 2012; Pan et al., 2011). The low tensile reinforcement ratio highlights the influence of concrete tensile strength on deflection. Consequently, OPC-reinforced concrete beams exhibited more significant deflection and severe damage in the compression zone. In contrast, the higher tensile strength of GPC reduced deflection in these beams. However, the low elastic modulus of GPC, combined with a flexural strength comparable to OPC, increased the deformation demand required for damage to occur in the compression zone. As a result, no visible damage was observed in the compression zone of GPC beams that deflected less in FEM analyses. Conversely, the damage distribution in OPC beams was more pronounced at the failure point. Load-displacement graphs, compression and tensile damage behavior graphs for GB2 and the related OPCB2 series are shown in Figures 20 –24.

Figure 20.

Comparison of GB2F1C0 experimental and finite element analysis results.

Figure 21.

Comparison of GB2F1C4 experimental and finite element analysis results.

Figure 22.

Comparison of GB2F2C0 experimental and finite element analysis results.

Figure 23.

Comparison of GB2F2C4 experimental and finite element analysis results.

Figure 24.

Comparison of OPCB2 experimental and finite element analysis results.

The load level at which the first crack appeared increased by an average of 50% in GB2 beams compared to GB1 beams, as observed in the experimental results. A similar trend was also noted between GPC and OPC beams. As the tensile reinforcement ratio increased, the deflection at the onset of the first crack decreased in both GPC and OPC beams. In GB2 beams with 3Ø14 tensile reinforcement, the flexural load and deflection increased when the tensile reinforcement yielded. However, the deflection capacity decreased significantly at the failure point compared to GB1 beams. Although the load-bearing capacity increases with higher tensile reinforcement ratios, the post-yield deformation capacity tends to become more limited, indicating a relative reduction in deformation-based ductility. Table 7 presents a comparison of the load–displacement responses of the GB2 and OPC beams obtained from experimental tests and FEM analyses at the yield and ultimate states.

Table 7.

% differences in reinforced concrete beams with longitudinal tensile reinforcement 3Ø14 (GB2).

% Dfferences	FEM & experimental				GPC avg. & OPC
GB2 beams	GPC avg.		OPC		FEM		Experimental
GB2 beams	Load	Disp.	Load	Disp.	Load	Disp.	Load	Disp.
Yield point	0%	−11%	0%	−10%	5%	3%	4%	1%
Failure point	−6%	5%	2%	−10%	7%	14%	0%	32%

As shown in Table 7, experimental and FEM analysis results for GPC beams with 3Ø14 tensile reinforcement were found to be compatible. While no difference in load was observed at the yield point, experimental displacement results for GPC and OPC concrete were approximately 10% lower than the numerical results. The yield-point results for GPC and OPC beams are consistent; however, at failure, GPC beams exhibited greater deflection than OPC beams, as evidenced by both experimental and numerical data. Increasing the tensile reinforcement and approaching the balanced reinforcement ratio has a decisive effect on beam deflection. GPC beams, characterized by a lower modulus of elasticity, were crushed later and exhibited more significant deflection while consuming more energy during the crushing phase in the compression zone, attributed to their high deformation capacity (Özbayrak et al., 2024b). The difference in elastic modulus makes the tensile reinforcement ratio particularly significant, leading to fundamental behavioral differences between GPC and OPC. Numerical analyses also reveal differences in failure patterns and the extent of tensile and compressive damage. Crack monitoring and analysis showed that all beams’ maximum crack width at the yield point was 0.1 mm, increasing to 3 mm at the failure point. Experimental results indicate that GPC and OPC beams differ significantly regarding crack propagation and width at the yield and ultimate points. Numerically, OPC beams sustain more damage than GPC beams in failure and ultimate damage distributions. This difference can be attributed to the broader tensile cracks in OPC beams compared to GPC beams, which exhibit both wide and narrow cracks. Load-displacement graphs, compression and tensile-damage behavior graphs for GB3 and the related OPCB3 series are shown in Figures 25-29.

Figure 25.

Comparison of GB3F1C0 experimental and finite element analysis results.

Figure 26.

Comparison of GB3F1C4 experimental and finite element analysis results.

Figure 27.

Comparison of GB3F2C0 experimental and finite element analysis results.

Figure 28.

Comparison of GB3F2C4 experimental and finite element analysis results.

Figure 29.

Comparison of OPCB3 experimental and finite element analysis results.

The study demonstrates that increasing tensile reinforcement enhances the load level at which the first crack occurs in GB3 beams compared to GB1 and GB2. However, the initial crack point deflection decreases in both GPC and OPC beams. In GB3 beams with 4Ø16 tensile reinforcement, the maximum flexural load and deflection increased when the reinforcement yielded, yet the deflection capacity at failure declined significantly compared to GB1 and GB2. This indicates that while the beam’s load-bearing capacity improves, its ductility diminishes. Experimental bending capacity at the yield point in GB3 beams consistently exceeded numerical predictions. Analytical calculations based on tensile reinforcement ratios generally align with experimental data. However, discrepancies in GB3 beam results, despite using consistent material models, could stem from deviations in loading rates, connection conditions, and other experimental variables from the idealized theoretical assumptions. Table 8 presents a comparison of the load–displacement responses of the GB3 and OPC beams obtained from experimental tests and FEM analyses at the yield and failure states.

Table 8.

% differences in reinforced concrete beams with longitudinal tensile reinforcement 4Ø16 (GB3).

% Differences	FEM & experimental				GPC avg. & OPC
% Differences	GPC avg.		OPC		FEM		Experimental
GB3 beams	Load	Disp.	Load	Disp.	Load	Disp.	Load	Disp.
Yield point	12%	−6%	16%	22%	2%	13%	−1%	−13%
Failure point	6%	1%	7%	12%	3%	−5%	2%	−14%

As shown in Table 8, the numerical results for GPC beams with 4Ø16 tensile reinforcement are in good agreement with the experimental data. However, the numerical load and displacement values for OPC beams were more significant at the yield point. This discrepancy was reduced by approximately half at the failure point. When GPC and OPC are compared, the load values are experimentally and numerically consistent, but significant differences are observed in deflection behavior. Despite these variations, they do not hinder the distinction between GPC and OPC using numerical analysis. GPC and OPC beams showed compatibility in terms of failure and ultimate tensile damage, though OPC exhibited more significant compressive damage, consistent with prior experimental findings. This difference diminishes as the tensile reinforcement ratio increases. At the yield point, the maximum crack width in all beams was 0.25 mm, while at the failure point, it reached 1.5 mm for GPC beams and 3.5 mm for OPC beams. These measurements, obtained during crack monitoring and analysis, indicate that while the crack pattern and propagation are similar, there are notable variations in crack widths. Although GPC and OPC beams are comparable in strength, minor differences in behavior were identified. Due to the lower elastic modulus of GPC, deformations at peak and ultimate loads increased, while the initial stiffness decreased compared to OPC. The changes in the load-displacement behavior of beam samples, classified parametrically by SS/SH ratio and curing method, are analyzed in Table 9.

Table 9.

% differences between the OPC and the numerical and experimental load-displacement results for GPC formulations.

% Differences	OPC & GPC avg.				FEM & Exp.
	FEM		Experimental		GPC
	Load	Disp.	Load	Disp.	Load	Disp.
F1C0	−3%	2%	2%	0%	−7%	−2%
F1C4	2%	8%	4%	7%	−4%	−2%
F2C0	−3%	6%	−5%	3%	1%	−1%
F2C4	−5%	−6%	−3%	−8%	−3%	−1%

SS/SH ratio (F1: 1.5, F2: 3.5), Curing start (C0: Direct, C4: After 4 days).

Average results for GPC formulation results, regardless of tensile reinforcement ratio, were compared with OPC results experimentally and numerically. Additionally, the percentage differences between numerical and experimental GPC results were calculated to evaluate the effects of curing methods and alkaline activator ratios in detail. According to Table 9, the SS/SH ratio and curing method did not significantly affect the load-displacement relationship when comparing the experimental and numerical results of OPC and GPC. Among GPC formulations, the maximum (F2C4) and minimum (F1C4) results showed differences of 7–8% in load and 15–16% in displacement. Increasing the SS/SH ratio from 1.5 (F1) to 3.5 (F2) increased the bending capacity and energy consumption of thermally cured beams kept at ambient temperature for 4 days. The alignment of numerical results with experimental findings allows further exploration of unmeasured test data through numerical simulations. Strain values in the compression zone and in the tensile reinforcement were investigated numerically to better understand GPC behavior under yielding and failure conditions. Except for the F2C4 samples, OPC beams exhibited greater deflection than GPC. OPC experimental results were 1% lower in load and 4% lower in deflection than numerical results, indicating substantial agreement. However, GPC’s lower elastic modulus increased its deformation demand to achieve a similar load-bearing capacity. These findings were validated numerically, with strain values at yield and failure points calculated using ABAQUS. Examples from the F1C0 and OPC series are shown in Figures 30-35.

Figure 30.

Strain values of the GB1F1C0 beam at the yield and failure point.

Figure 31.

Strain values of the OPCB1 beam at the yield and failure point.

Figure 32.

Strain values of the GB2F1C0 beam at the yield and failure point.

Figure 33.

Strain values of the OPCB2 beam at the yield and failure point.

Figure 34.

Strain values of the GB3F1C0 beam at the yield and failure point.

Figure 35.

Strain values of the OPCB3 beam at the yield and failure point.

Each figure includes finite element analysis results highlighting the strain distribution in both the concrete body and internal rebar, enabling assessment of the damage development and plastic deformation under flexural loading conditions. Table 10 presents the deformation characteristics of GPC and OPC beams at the yield and failure points. In particular, it summarizes the concrete deformation values in the compression zone, allowing a direct comparison between the two beam types at critical loading stages.

Table 10.

Compression zone concrete deformation values of GPC and OPC beams at yield and failure points.

CONCRETE
GB1 avg.		GB2 avg.		GB3 avg.		GPC avg.
Yield point	Failure point	Yield point	Failure point	Yield point	Failure point	Yield point	Failure point
0.00112	0.00381	0.00157	0.00424	0.00212	0.00428	0.00160	0.00411
OPCB1		OPCB2		OPCB3		OPC avg.
Yield point	Failure point	Yield point	Failure point	Yield point	Failure point	Yield point	Failure point
0.00117	0.00311	0.00155	0.00378	0.00227	0.00385	0.00166	0.00358

Deformation in the compression zone

As shown in Table 10, GPC beams exhibited an average yield strain 4% lower than OPC beams. However, at the failure point, GPC beams deformed approximately 15% more than OPC beams, with average strain values of 0.0040 for GPC and 0.0035 for OPC. This trend, observed regardless of the tensile reinforcement ratio, indicates that GPC undergoes higher deformation at the yield and failure points in the compression zone. Moreover, increasing the tensile reinforcement ratio further elevated deformation rates at these critical stages. Experimental results and numerical analyses were consistent with these observations. The tensile reinforcement strain values for GPC and OPC beams at the yield and failure points are summarized in Table 11, enabling a comparative evaluation of reinforcement response under critical loading conditions.

Table 11.

Tensile reinforcement strain values of GPC and OPC beams at yield and failure points.

REBAR
GB1 avg.		GB2 avg.		GB3 avg.		GPC avg.
Yield point	Failure point	Yield point	Failure point	Yield point	Failure point	Yield point	Failure point
0.02445	0.03909	0.01417	0.03133	0.00617	0.01106	0.01493	0.02716
OPCB1		OPCB2		OPCB3		OPC avg.
Yield point	Failure point	Yield point	Failure point	Yield point	Failure point	Yield point	Failure point
0.02022	0.03308	0.01173	0.02761	0.00449	0.00838	0.01215	0.02302

Deformation in tensile reinforcement

As presented in Table 11, the strain values of GPC tensile reinforcement were 23% higher on average at the yield point compared to OPC, exceeding the steel yield strain limit of 0.002 for B420 C steel. At the failure point, GPC reinforcement deformed 18% more than OPC. These differences are attributed to GPC’s lower elastic modulus, which requires greater deformation in concrete and reinforcement to achieve similar strength. Increasing the tensile reinforcement ratio reduced the reinforcement deformation rate for both GPC and OPC beams. Average failure strains were 0.027 for GPC and 0.023 for OPC, confirming that numerical results aligned with experimental findings.

Influence of SS/SH ratio and curing methods

A comparative evaluation of compression zone concrete deformation between GPC and OPC beams at the yield and failure points, considering SS/SH ratio and curing method, is presented in Table 12.

Table 12.

Comparison of compression zone concrete of GPC and OPC beams for deformation at yield and failure points.

Concrete	Deformation		Change according to OPC
Concrete	Yield point	Failure point	Yield point	Failure point
F1C0	0.00152	0.00402	0.92	1.12
F1C4	0.00154	0.00436	0.93	1.22
F2C0	0.00168	0.00404	1.01	1.13
F2C4	0.00167	0.00401	1.00	1.12
OPC	0.00166	0.00358	1.00	1.00

SS/SH ratio (F1: 1.5, F2: 3.5), Curing start (C0: Direct, C4: After 4 days).

Concerning concrete deformation (Table 12), the maximum difference among GPC formulations at the yield and failure points was 10% and 9%, respectively. As the SS/SH ratio increased, the deformation value at the yield point increased, while it decreased at the failure point. When evaluated by the curing method, the deformation value increased slightly at both the yield and failure points with the C4 curing method. The curing method was the primary factor contributing to concrete deformation. Table 13 presents a comparison of tensile reinforcement deformation between GPC and OPC beams at the yield and failure points, accounting for SS/SH ratio and curing method.

Table 13.

Comparison of the tensile reinforcement of GPC beams and OPC beams for deformation at the yield and failure points.

Rebar	Deformation		Change according to OPC
Rebar	Yield point	Failure point	Yield point	Failure point
F1C0	0.01466	0.02708	1.21	1.18
F1C4	0.01696	0.02743	1.40	1.19
F2C0	0.01434	0.02768	1.18	1.20
F2C4	0.01375	0.02644	1.13	1.15
OPC	0.01215	0.02302	1.00	1.00

SS/SH ratio (F1: 1.5, F2: 3.5), Curing start (C0: Direct, C4: After 4 days).

For tensile reinforcement (Table 13), the maximum differences were 23% at the yield point and 5% at the failure point, with yield point differences attributed to SS/SH ratio variations. Besides, the SS/SH ratio increases, and the deformation at the reinforcement yield point decreases. When comparing curing methods, for samples with an F1 mix ratio, reinforcement deformation increases at both the yield and failure points with the C4 curing method, whereas for samples with an F2 mix ratio, a decrease is observed with the C4 curing method. Therefore, the SS/SH ratio was the primary factor contributing to reinforcement deformation. The curing method also played a role. Thermally cured beams with a higher SS/SH ratio (F2C4) displayed enhanced deformation behavior, reflecting increased bending capacity and energy absorption. While GPC and OPC beams exhibit comparable strength and bearing capacity, their deformation behavior differs due to the lower elastic modulus of GPC. This increases deformation demands, particularly in GPC’s compression zone and tensile reinforcement. These differences align with previous research findings (Özbayrak et al., 2024b). Evaluating GPC using current reinforced concrete design specifications may be inadequate, as elastic modulus variations affect critical parameters such as stress block properties, balanced reinforcement ratios, and dynamic responses. Therefore, design calculations should incorporate these deformation-related differences, particularly inelastic behavior.

Evaluation of the results for GPC and OPC beams

The comparative evaluation of GPC and OPC beams based on tensile reinforcement ratios, GPC formulations, and curing methods reveals significant differences in strength, behavior, and deflection. Key results and interpretations are summarized below.

Tensile reinforcement ratio effects

(1) Yield Point: Increasing the tensile reinforcement ratio enhances the beam’s flexural stiffness and load-bearing capacity, increasing deflection values for both OPC and GPC beams.

(2) Failure Point: While flexural stiffness and load-bearing capacity continue to improve with increased tensile reinforcement, deflection decreases for both beam types.

(3) Crack Behavior: GPC beams show reduced crack widths with increasing tensile reinforcement ratios. At failure, maximum crack widths are 5 mm in GB1, 3 mm in GB2, and 1.5 mm in GB3 beams. Compared to OPC, GPC beams with maximum tensile reinforcement have a smaller maximum crack width (1.5 mm vs 3.5 mm). Additionally, GPC beams develop fewer, narrower cracks than OPC beams, thereby improving crack propagation control.

Load-displacement behavior

GPC and OPC beams exhibit similar load values at yield and failure points across all tensile reinforcement ratios. However, deflection behavior varies with reinforcement ratios.

(1) Minimum and Maximum Ratios: OPC beams exhibit higher deflection values, leading to brittle fractures.

(2) Balanced Ratio: GPC beams show greater deflection, indicating superior energy absorption and ductility compared to OPC.

Influence of SS/SH ratio and curing methods

(1) According to Table 9, load-displacement differences between OPC and GPC beams remain within ±8%, demonstrating consistency between experimental and numerical results for failure analysis.

(2) The SS/SH ratio and curing methods have a slight effect on deformation in both the concrete compression zone and the tensile reinforcement, as indicated by the numerical results from the failure analysis.

Deformation analysis

The concrete and reinforcement deformation behaviors were investigated in detail by using numerical data derived from ABAQUS software for failure analysis.

(1) Compression Zone Concrete: Deformations at yield and failure points increase with higher tensile reinforcement ratios in GPC and OPC. GPC beams exhibit an average ultimate deformation of 0.0041 at the failure point, compared to 0.0035 for OPC. This highlights the need to revise GPC crushing deformation limits in design calculations.

(2) Tensile Reinforcement: GPC reinforcement exhibits deformation values approximately 20% higher than those of OPC at both yield and failure points. This is attributed to GPC’s lower elastic modulus, which requires greater deformation to achieve similar strength. The deformation disparity between GPC and OPC is more pronounced in tensile reinforcement than in compression concrete, as the tensile reinforcement governs flexural stiffness and bearing capacity.

(3) Formulation Effects: While the curing method is more effective in influencing deformations in concrete at yield and failure points, the SS/SH ratio is a more influential variable in influencing deformations in reinforcement at yield and fracture points. However, the effect of both these variables on deformations in concrete and reinforcement is quite limited when considered individually. The higher deformation in concrete and reinforcement at the failure point in the F1C4 formulation than in the F2C4 formulation. This indicates that higher SS/SH ratios, when delayed thermal curing is applied (after 4 days), reduce deformation at the failure point.

Key behavioral differences

GPC beams exhibit higher deformation in both compression and tensile zones than OPC beams under similar loads, primarily due to GPC’s lower elastic modulus. Despite comparable strength, the deformation characteristics of GPC necessitate modifications to traditional reinforced concrete design parameters, such as stress block properties, balanced reinforcement ratios, and deformation limits. These findings underscore the need to adapt current reinforced concrete design specifications to account for the unique deformation and behavioral characteristics of GPC beams. By integrating these differences into design calculations, engineers can better harness GPC’s benefits in terms of ductility, energy absorption, and crack control, particularly for structures that require sustainable, high-performance materials.

Conclusion and recommendations

Conclusion

In this study, numerical models of 12 geopolymer concrete (GPC) and three ordinary Portland cement (OPC) reinforced concrete beams were developed and evaluated under varying parameters, including the SS/SH ratio, curing method, and tensile reinforcement ratio. Experimental flexural tests were conducted, and displacement responses were monitored using high-precision total station measurements. The experimental observations were compared with ABAQUS-based numerical analyses, with particular emphasis on load–displacement behavior at yield and failure stages to characterize inelastic deformation and damage progression. The close agreement between experimental results and numerical predictions confirms the reliability of the adopted failure analysis methodology.

Although GPC and OPC beams exhibited comparable ultimate strengths, significant differences were observed in their deformation demand and failure characteristics. GPC beams required higher deformation to reach similar strength levels due to their lower elastic modulus, leading to distinct inelastic response and damage development. Differences in crack initiation, propagation patterns, and crack widths were identified between the two material systems. The enhanced gel-based microstructure of geopolymer concrete improved the bond between reinforcement and concrete, resulting in more effective stress redistribution, increased formation of fine capillary cracks, and suppression of localized wide cracks that typically precede brittle failure.

The results further indicate that while the curing method alone did not directly govern the failure behavior, its combined interaction with the SS/SH ratio influenced the deformation capacity of concrete and reinforcement, as well as damage evolution. These interactions affected crack growth rates and stiffness degradation, highlighting the importance of mixture design parameters in controlling failure mechanisms.

From an engineering failure analysis perspective, the findings demonstrate that conventional reinforced concrete design assumptions may not fully capture the damage and failure characteristics of geopolymer concrete elements. In particular, the higher deformation demand and altered cracking mechanisms observed in GPC beams should be explicitly considered in design and assessment procedures to enhance damage control and prevent premature failure. Overall, geopolymer concrete has strong potential as an alternative structural material, offering comparable load-bearing capacity to OPC while providing improved crack distribution and stress transfer characteristics that are beneficial for failure mitigation and structural safety.

Recommendations

Based on the findings of this study, GPC beams can be considered as an effective alternative structural member to OPC beams when designed with appropriate reinforcement ratios and mix proportions. The results indicate that GPC exhibits higher deformation capacity and more distributed cracking behavior, which may contribute to improved damage tolerance. The enhanced microstructural characteristics and gel formation of geopolymer concrete also promote better interaction between reinforcement and concrete, reducing stress concentrations and limiting the formation of wide cracks. However, the present study is limited to monotonic loading conditions. For future research, it is recommended to investigate the behavior of GPC beams under cyclic and repeated loading, particularly to evaluate stiffness degradation, energy dissipation capacity, and hysteretic response. Such studies might provide further insight into the seismic performance and long-term structural reliability of GPC members. Additionally, future work might consider different reinforcement configurations, varying mix proportions, and extended durability assessments to enhance the applicability of GPC in structural design.

Footnotes

Acknowledgments

We would like to thank the Proofreading & Editing Office of the Dean for Research at Erciyes University for copyediting and proofreading service for this manuscript.

ORCID iDs

Ahmet Özbayrak

Hurmet Kucukgoncu

Yuksel Gul Aslanbay

Huseyin Hilmi Aslanbay

Author contributions

Ahmet Özbayrak: Methodology, Investigation, Conceptualization, Writing – review & editing, Supervision, Data curation, Project administration, Resources, Funding acquisition. Hurmet Kucukgoncu: Methodology, Investigation, Visualization, Conceptualization, Formal analysis, Data curation, Writing – original draft. Yuksel Gul Aslanbay: Visualization, Conceptualization, Data curation, Validation, Writing – review & editing. Huseyin Hilmi Aslanbay: Visualization, Investigation, Conceptualization, Formal analysis, Writing – original draft, Validation, Software. Fatih Altun: Visualization, Conceptualization, Validation, Writing – review & editing.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was supported by TÜBİTAK (The Scientific and Technological Research Council of Türkiye) under Grant Number 121M236.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.*

Appendix

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