Shear Behavior of Geopolymer Concrete Slender Beams

Abstract

This study investigates the shear behavior of slender steel-reinforced geopolymer concrete (GPC) beams with the shear span to effective depth ratio ($a/d$) of 4.5 and 5.0. To investigate the effect of shear reinforcement, two ordinary Portland cement concrete (OPC) beams and two GPC beams without shear reinforcement, and two OPC beams and two GPC beams reinforced with shear stirrups were cast. All beams were 150 mm wide and 225 mm deep with lengths of 1770 mm ($a/d=4.5$) and 1950 mm ($a/d=5$). The beams were tested under a three-point bending test. The experimental results showed that OPC and GPC beams without and with shear reinforcements exhibited similar crack propagation and failure mechanism. The midspan deflections of GPC beams were greater than OPC beams. The normalized shear resistance of OPC and GPC beams with $a/d$ ratio 4.5 was greater than 4% and 30%, respectively, than beams with $a/d$ ratio 5. OPC beams showed a greater decrease in shear resistance with an increasing $a/d$ ratio compared to GPC beams. The shear resistances computed using empirical relationships available in various OPC design codes including AC1-318-14, AC1-318-19, fib-10 and JSCE-07 underestimated the experimental shear resistance of both OPC and GPC beams. In addition, the environmental assessment of OPC and GPC beams exhibited that GPC beams emit about 34% lower embodied CO₂ emissions than OPC beams.

1. Introduction

Concrete remains the second most popular material globally, only after water [1,2]. In the construction industry, cement has been extensively used as the primary binding material in concrete [3,4]. Cement production releases about 5–7% of the total global CO₂ emissions, which remains one of the main contributors of greenhouse gases (GHG) and rising temperature of the earth’s surface, and hence global warming [5,6]. Moreover, the manufacturing of cement is a highly energy-consuming process that uses nearly 4 GJ of energy to produce one ton of cement, and about 3.6 billion tons of cement are manufactured annually [7]. The annual cement production is steadily rising by about 9% [8]. Hence, it is necessary to find environmentally friendly alternatives to cement to reduce GHG emissions and reduce the negative impacts of cement production on climate change.

In 1979, Davidovits introduced geopolymers, which belong to a class of inorganic polymers, and are formed by the chemical reaction between alumino-silicate precursors sourced from natural minerals or industrial waste products and an alkaline activator solution [9]. In geopolymerization, three-dimensional polymeric ring structures of alumina silicate (Si-O-Al-O) chains are formed. These polymeric chains condensed to form polymeric structures, which provide strength to the geopolymers [10,11].

GPC has great potential to substitute OPC in construction, as GPC shows improved characteristics than OPC, such as enhanced flexural and bond strengths [12,13]. Hussin et al. [14] and Jiang et al. [15] also reported that GPC has a higher resistance to fire, chemicals and acid attacks. Hassan et al. [16] and Nawaz et al. [10] concluded that GPC attained the required mechanical characteristics to effectively substitute OPC in the construction industry.

Numerous research studies reported that GPC beams exhibited similar flexural behavior and strength as OPC beams with similar target compressive strengths [17,18]. It was found that initial flexure cracking load, size of the crack, load-displacement response, applied load and failure mechanisms of OPC and GPC beams were similar [19,20]. Mamdouh et al. [21] reported that slag-based ambient cured GPC beams exhibited 7.4% greater flexural strength and 17.5% reduced cracking moment than the OPC beams of similar compressive strengths. Zinkaah et al. [22] reviewed data from forty GPC beams and found that OPC and GPC beams exhibited similar flexure failures with similar crack width and crack propagation. GPC and OPC beams exhibited similar ductility. Tran et al. [23] concluded that fly ash (FA) and slag-based GPC has a lower modulus than OPC for similar strengths. Adak et al. [24] found that the flexural strength of nano-silica modified FA-based ambient cured GPC beams was greater than OPC beams. Kathirvel and Kaliyaperunal [25] noted that the flexural strength of slag-based ambient cured GPC beams was greater than OPC beams and both types of concrete beams exhibited similar failure modes. Kumaravel and Thirugnanasambandam [26] observed that FA-based heat cured (60 °C for 24 h) GPC beams exhibited 2.7% greater flexural strength than OPC beams. However, the deflection in GPC beams was 48.7% greater than that of OPC beams due to the lower stiffness of GPC.

Past studies mainly focused on the flexural strength of GPC beams while fewer research investigations evaluated the shear behavior of GPC beams. The beams are often classified into different groups based on the slenderness ratio. ASCE (2015) classifies beams based on the ($a/d$) ratio, i.e., very short, short, slender, and very slender beams having $a/d$ ratios ≤ 1 to 2.5, 2.5 to 6, and ≥6, respectively [27]. Numerous research investigations reported the shear behavior of short and slender GPC beams with $a/d$ ratios of less than 4. Wu et al. [28] concluded that FA with slag-based GPC beams under ambient and heat-cured conditions exhibited reduced shear strengths by 42.6–46.2% as the $a/d$ ratio was increased from 1.5 to 2.5. In addition, the observed crack patterns and failure modes in GPC beams were identical to OPC beams. Yacob et al. [29] investigated the shear behavior of five FA-based heat cured (65 °C for 28 h) GPC beams and a control OPC beam having $a/d$ ratios of 2 and 2.4. The shear resistance of OPC beam was 8% greater than that of the GPC beam for an $a/d$ ratio of 2. The addition of stirrups in beams shifted the failure pattern of tested specimens from shear-dominant to shear-flexure. Visintin et al. [30] found that the shear resistance of FA-based ambient cured GPC beams decreased by 29.5% and 60.9% as the $a/d$ ratios were increased from 2.5 to 3 and 2.5 to 3.5, respectively. The findings of the available experimental studies showed that the shear behavior of GPC beams was identical to OPC beams [31,32]. Yost et al. [33] and Chang et al. [34] found that both the cracking pattern and shear behavior of OPC and GPC beams were similar.

Hu and Wu, [35] reported that the shear resistance of OPC beams was reduced by 33.9% with an increase in the $a/d$ ratio from 1.9 to 3.1. Deng et al. [36] found that in OPC beams the shear resistance was increased by 6–28% by decreasing the $a/d$ ratio from 3 to 2.2. Moreover, shear resistance was enhanced with increasing aggregate size. Katkhuda and Shatarat, [37] reported that the shear resistance of OPC beams was reduced by 24% with increasing $a/d$ ratio from 2 to 3 and tested beams failed due to diagonal tension cracking. Slowik [38] concluded that the shear resistance of OPC beams decreased by 58.6% as the $a/d$ ratio was increased from 1.8 to 4.1. It is concluded from the review of the available studies that slenderness ($a/d$ ratio) of beams negatively influenced the shear resistance of OPC and GPC beams.

Meanwhile, previous studies adopted empirical equations intended for OPC beams available in various design codes to compute the shear resistance of GPC beams. Darmawan et al. [39] reported that ACI 318-14 [40] underestimated the shear resistance of FA-based ambient cured GPC beams having an $a/d$ ratio of 2.98 by 25%. Lee et al. [41] found that ACI 318-14 [40] underestimated the shear resistance of slag-based ambient cured GPC beams having $a/d$ ratio 3 by about 27%. Wu et al. [28] reported that ACI 318-19 [42], also underestimated the shear resistance of FA with slag-based GPC beams having $a/d$ ratios of 1.5, 2.5 and 4.0 by about 28%. Similarly, Maranan et al. [43] observed that JSCE-07 [44] underestimated the shear resistance of FA with slag-based ambient cured GFRP reinforced GPC beams having an $a/d$ ratio of 1.8 by 41.9%. Visintin et al. [30] found that fib-10 [45] yielded conservative results of the shear resistance of FA-based ambient cured GPC beams with the $a/d$ ratios of 2–3.5 by about 33%. It is concluded that the design equations intended for OPC beams underestimated the shear resistance of GPC beams having $a/d$ ratios between 1.5 and 4.0 by about 42%.

The review of the existing studies exhibited that the majority of existing studies investigated the smaller $a/d$ ratios. Limited studies investigated the shear behavior of FA-based GPC beams having $a/d$ ratios greater than 4. Hence, it is important to investigate the slender beams having an $a/d$ greater than 4 to fill the gap in the existing literature. This study investigates the shear behavior of slender GPC beams without and with shear stirrups. In addition, the failure mechanisms of GPC vs. OPC beams are also studied. It is important to investigate the shear capacity of GPC beams and also, to report the applicability of the design guidelines (ACI 318-14 [40], ACI 318-19 [42], JSCE-07 [44] and fib model code-10 [45]) for OPC beams to GPC beams. The findings of this study will help in understanding the shear behavior and failure mechanisms of GPC beams having $a/d$ ratios greater than 4.

2. Experimental Program

The experimental program comprised four OPC beams and four GPC beams. The width and depth of all eight beams were 150 mm and 225 mm, respectively. Two OPC and two GPC beams of length 1770 mm ($a/d$ ratio of 4.5), whereas the other two OPC and two GPC beams of length 1950 mm ($a/d$ ratio of 5) were cast. The shear span (a), which is measured between the center of the support and the loading point, was 810 mm for an $a/d$ ratio of 4.5, and 900 mm for an $a/d$ ratio of 5. The effective depth (d) of all the beams was kept at 180 mm. The clear concrete cover to the bottom reinforcement was 35.5 mm and 25.5 mm, respectively, for the beams without stirrups and with stirrups. The longitudinal reinforcement comprising two deformed steel bars of 19 mm diameter was provided in all eight beams. The longitudinal reinforcement ratio of all beams was 2.1%, and beams were transition reinforced to ensure that beams failed in shear. The longitudinal reinforcing bars at the ends were bent at 90^o to provide the required anchorage length. In two OPC and two GPC beams, no shear reinforcement was provided whereas in the other two OPC and two GPC beams, shear reinforcement comprising steel stirrups at the spacing of 90 mm ($d/2$) were provided. Three cylinders of 150 mm diameter and 300 mm depth corresponding to each beam were cast to determine the compressive strength (f_c′) of the concrete. The cross-sectional and longitudinal reinforcement details of the beams are presented in Figure 1.

The nomenclature of beams comprised three letters. The first letter denotes the type of concrete, e.g., OPCC (O) and GPC (G). The second letter denotes whether the beams were without steel stirrups (N) or with steel stirrups (S). The third letter denotes the $a/d$ ratio, i.e., 4.5 or 5.0. For example, ON-4.5 represents the OPC beam without stirrups having an $a/d$ ratio of 4.5. Similarly, GS-5 represents the shear-reinforced GPC beam having an $a/d$ ratio of 5 as tabulated in

Table 1. Test Matrix.

Beam ID	Width (mm)	Depth (mm)	Effective Depth, d (mm)	Length (mm)	$\mathit{a}/\mathit{d}$	Longitudinal Reinforcement	Stirrups Spacing
ON-4.5	150	225	180	1770	4.5	2–19 mm	-
OS-4.5							90 mm
ON-5				1950	5		-
OS-5							90 mm
GN-4.5				1770	4.5		-
GS-4.5							90 mm
GN-5				1950	5		-
GS-5							90 mm

.

2.1. Material Properties

2.1.1. Fly Ash

The FA was sourced from Sahiwal Coal Power Plant. The chemical analysis of FA was performed as per ASTM C114-19 [46] and is presented in

Table 2. Chemical Composition of FA.

Components	Percentage	ASTM C618-19
SiO2	69.80	SiO2 + Al2O3 + Fe2O3 = 70% (Min)
Al2O3	11.34
Fe2O3	1.81
CaO	9.56	18% (Max)
MgO	2.20
SO3	1.30	5% (Max)
LOI	2	6% (Max)

. The sum of SiO_2, Al₂O_3, and Fe₂O₃ contents in FA was 82.95%, CaO content was 9.56%, SO₃ content was 1.30% and loss on ignition (LOI) was 2.0. The sum of SiO_2, Al₂O₃ and Fe₂O₃ was greater than 70%, SO₃ was less than 5%, CaO was less than 18%, and LOI was less than 6%. Based on ASTM C618-19 [47], the FA was classified as low-calcium Class F.

2.1.2. Aggregates

Locally available crush sourced from Margalla was used as coarse aggregates (CA). The sizes of CA ranged from 9.5 to 12 mm. The dry-rodded density of CA was 1542 kg/m³ and the loose bulk density of CA was 1427 kg/m³ as per ASTM C29-17 [48]. The specific gravity of CA was 2.71 as per ASTM C127-15 [49]. The aggregate impact value of CA was 17 as per BS 812-112 [50]. The aggregate crushing value of CA was 21 as per BS 812-110 [51].

Locally available sand sourced from Lawrencepur was used as fine aggregates. The fineness modulus (FM) of fine aggregate was 2.5 according to ASTM 33-18 [52]. The dry-rodded density of fine aggregates was 1778 kg/m³, and the loose bulk density of fine aggregates was 1626 kg/m³ as per ASTM C29-17 [48].

2.1.3. Alkaline Solution

The alkaline solution comprised sodium hydroxide (NaOH) and sodium silicate (Na₂SiO₃) solutions. The solid pellets of NaOH were added to water to produce the NaOH solution. In this study, 16 M NaOH solution was prepared by mixing 640 g of NaOH pellets in 1000 mL of solution [5]. The Na₂SiO₃ solution comprising 52% liquid and 48% solids was obtained from a local vendor. The SiO₂/Na₂O ratio was 3:1. In this study, the ratio of Na₂SiO₃ solution to NaOH solution was kept at 1.5 [5]. The alkaline solution was prepared 24 h prior to the casting of concrete to cool down the excessive heat during dissolving.

2.1.4. Steel Reinforcement

The nominal diameter of the longitudinal steel reinforcing bar was 19 mm, whereas the nominal diameter of the shear reinforcing bar was 10 mm. A tension test was performed on steel bars using 200 tons Shimadzu Universal Testing Machine (UTM) as per ASTM A615-20 [53]. The average yield and ultimate tensile strengths of 19 mm diameter bars were 450 MPa and 649 MPa, respectively. The average yield and ultimate tensile strengths of 10 mm diameter bars were 395 MPa and 526 MPa, respectively.

2.2. Mix Design

The target f_c′ of OPC was 21 MPa. The OPC mix comprised 380 kg of cement, 760 kg of fine aggregates, 1000 kg of CA and 209 kg of water per cubic meter. The water-to-cement ratio of the OPC mix was 0.54. The target f_c′ of GPC was also 21 MPa. The GPC mix comprised 420 kg of FA, 620 kg of fine aggregates, 1150 kg of CA, 210 kg of alkaline solution, 21 kg of additional water, and 4.2 kg of superplasticizer per cubic meter. The alkaline solution comprised 126 kg of sodium silicates and 84 kg of sodium hydroxide solution. The ratio of FA to aggregates was 0.237 and the ratio of FA to alkaline solution was 0.5.

The preparation of OPC was divided into two steps. In the first step, the dry mixing of cement and aggregates was conducted in a high-speed mixer for a minute. In the second step, water was added to the dry mix and mixed for additional two minutes to achieve a homogenous mix. The preparation of GPC was also conducted in two steps. In the first step, the FA and aggregates were dry-mixed for two minutes. In the second step, the alkaline solution, superplasticizer, and additional water were added to the dry mix and mixed for additional two minutes to achieve a homogenous mix. The freshly prepared GPC mix was stickier than OPC due to the presence of an alkaline solution. The 1% superplasticizer and 5% additional water were mixed in the GPC mix to obtain a workability of 75 mm. The GPC beams were ambient cured at room temperature using hessian rugs [3,30]. Similarly, OPC beams were ambient cured at room temperature by covering them with wet hessian bags.

2.3. Testing Setup

All beams were tested under a three-point bending test as simply supported beams using 1000 kN Shimadzu UTM as per ASTM C78-18 [54]. The testing was performed at a 0.5 mm/minute controlled displacement rate. The test setup is shown in Figure 2. The cylinders corresponding to each beam were tested under compression in a 3000 kN Denison compression testing machine as per ASTM C39-20 [55] on the same day.

3. Results and Discussions

The test results include failure modes, first inclined cracking load, peak flexural load ($P_u$), and maximum deflection at the mid-span of all the tested OPC and GPC beams.

3.1. Failure Mechanism of OPC and GPC Beams without Stirrups

The crack pattern and the failure mechanism of the tested OPC beams and GPC beams without shear reinforcement were similar. In Beams ON-4.5 and ON-5, and GN-4.5 and GN-5, the flexural cracks developed in the mid-span region at about 25–29% of $P_u$. The flexural cracks propagated vertically towards the point of application of load with increasing applied loads. The inclined cracks started to appear near the supports with increasing applied load. The first inclined crack both in OPC and GPC beams appeared around 65% of the $P_u$. The inclined cracks grew in width and length and propagated in the direction of the loading point with increasing load resulting in the shear failure of the beams. The failures in both OPC and GPC beams were brittle and a sudden drop in load was observed. The tested beams are shown in Figure 3, Figure 4, Figure 5 and Figure 6. Sinik and Arsalan, [56] and Lee et al. [41] reported similar cracking patterns and failure mechanisms of slender OPC and GPC beams. Deng et al. [36] reported that inclined cracking load in slender OPC beams was at about 62–79% of $P_u$.

In beams, shear is either resisted by arch action or beam action. Arch action is dominant in short and very short beams, whereas beam action is dominant in slender beams. The tested beams were slender so shear resistance was provided by beam action. After the formation of inclined cracks, the shear resistance in beams without stirrups is primarily governed by aggregate interlock and the dowel action of steel reinforcement.

3.2. Failure Mechanism OPC and GPC Beams with Shear Reinforcement

The OPC and GPC beams reinforced with shear stirrups failed in flexure. Flexural cracks developed in the midspan region of the OPC (OS-4.5, OS-5) and GPC (GS-4.5, GS-5) beams at about 13–16% of $P_u$. Meanwhile, the first inclined crack appeared at about 38–46% of $P_u$, which was significantly lower than that of the beam without stirrups. It was observed that the maximum loads of the shear-reinforced beams were significantly higher than those of beams without stirrups. Therefore, the ratio of the first inclined load to the maximum load of shear-reinforced beams was lower in shear-reinforced beams than in beams without stirrups. The propagation of flexural cracks occurred vertically towards the compression side of the beam and deflection at midspan increased with the applied load, and failure occurred due to flexure. In shear-reinforced beams, it is anticipated that after the development of the first inclined crack the redistribution of stresses occurred, and stirrups were activated in resisting the applied load and hence increasing the shear resistance of beams leading to flexure failure occurred. The failure modes of tested shear-reinforced beams are shown in Figure 7, Figure 8, Figure 9 and Figure 10. The similar failure mode and cracking pattern of shear-reinforced OPC and GPC beams was reported by Wu et al. [28]. The flexural cracking load in shear-reinforced OPC and GPC beams was about 13–16%. Wu et al. [28] observed that the flexural load of beams that failed in flexure was about 8–18% of peak flexural load.

3.3. Inclined Cracking Load

In concrete beams, cracking occurs once the concrete tensile strength exceeds principal tensile stresses. Flexure cracking occurs in a region of maximum moment on the tension side and transverse to the longitudinal axis of beams. Meanwhile, near supports, large shear forces due to diagonal tension stresses are generated at about 45° to the axis of beams resulting in the development of inclined cracks. The load at the first inclined crack ($P_{cr}$) of beams ON-4.5, ON-5, OS-4.5 and OS-5 was 58 kN, 37 kN, 57 kN and 52 kN, respectively. Beam ON-5 exhibited 36% smaller P_cr than Beam ON-4.5, and Beam OS-5 exhibited 9% lower $P_{cr}$ than that of Beam OS-5. Beams GN-4.5, GN-5, GS-4.5 and GS-5 exhibited $P_{cr}$ at 63 kN, 47 kN, 53 kN and 46 kN, respectively. The $P_{cr}$ of Beam GN-5 was 25% smaller than that of Beam GN-4.5, whereas Beam GS-5 exhibited 13% smaller $P_{cr}$ than that of Beam GS-4.5. It was noted in both OPC and GPC beams that $P_{cr}$ decreased with increasing $a/d$ ratios from 4.5 to 5. Visintin et al. [30] reported that $P_{cr}$ is inversely proportional to the shear span of concrete beams. Deng et al. [36] also noted that $P_{cr}$ of OPC beams increased by 6–23% with a decreasing $a/d$ ratio from 3 to 2.2.

In shear-reinforced concrete beams, shear resistance is contributed by the concrete and the stirrups. The stirrups resist a minor segment of the shear force during the initial loading stage. Consequently, the presence of the stirrups exhibited no effect on the load initiation and location of shear cracks. The redistribution of shear stresses occurs as inclined cracks appeared in beams with a major segment of shear resisted by the concrete and the remaining is resisted by the stirrups.

3.4. Applied Loads ($P_u$) and Midspan Deflections of OPC and GPC Beams

The load-deflection curves of all beams are presented in Figure 11 and Figure 12. For OPC beams, increasing the $a/d$ ratio from 4.5 to 5 resulted in reduced $P_u$ and increased mid-span deflection at the maximum load. The $P_u$ of Beam ON-5 was 24% smaller than that of Beam ON-4.5, while the $P_u$ resisted by Beam OS-5 was 5% lower than that of Beam OS-4.5.

For shear-reinforced beams, $P_u$ decreased with increasing $a/d$ ratios from 4.5 to 5. The $P_u$ of Beam GS-5 was 9% smaller than that of Beam GS-4.5 because load carrying capacity was reduced with increasing span. However, the $P_u$ of Beam GN-4.5 which failed in shear, was 9% lower than that of Beam GN-5. The decrease in $P_u$ of Beam GN-4.5 was higher due to the higher compressive strength of Beam GN-5 than that of Beam GN-4.5, as shear resistance is mainly dependent on fc’.

The midspan deflection at $P_u$ of Beam GN-4.5 was 3% greater than that of Beam ON-4.5. Similarly, the midspan deflection at $P_u$ exhibited by Beam GS-4.5 was 16% larger than that of Beam OS-4.5. The midspan deflection at $P_u$ of Beam GN-5 was 2% lower than that of Beam ON-5. The midspan deflection at $P_u$ of Beam GS-5 was 36% larger than Beam OS-5. In general, the midspan deflections at $P_u$ of GPC beams were 18% greater than OPC beams due to the lower stiffness of GPC beams than OPC beams with similar fc’. Alex et al. [57] reported that GPC beams exhibited 9% greater midspan deflection than OPC beams. Zinkaah et al. [22] also reported that midspan deflections of GPC beams were greater than OPC beams.

The nominal moment capacity ($M_n$) of shear reinforced beams expected to fail in flexure was computed using Equation (1). The estimated $M_n$ and $P_u$ of OPC and GPC beams are presented in

Table 3. Estimated and experimental flexural Loads of shear reinforced specimens.

Specimen ID	fc’ (MPa)	Mn (kN-m)	Estimated Load (kN)	Applied Load ${\mathit{P}}_{\mathit{u}}$ (kN)	Estimated/Exp.	Average Estimated/Exp.
OS-4.5	25	35.76	88.30	125	0.71	0.68
OS-5	28	34.87	77.49	119	0.65
GS-4.5	23	36.86	91.01	133	0.68	0.68
GS-5	27	36.52	81.15	120.5	0.67

. The estimated $P_u$ of Beam OS-4.5 and Beam OS-5 were 71% and 65%, respectively, of the experimental $P_u$. Similarly, the estimated $P_u$ of Beam GS-4.5 and Beam GS-5 were 68% and 67%, respectively, of the experimental $P_u$. The average estimated experimental ratios of $P_u$ of OPC and GPC beams were 0.68. It was noted that both OPC and GPC beams behaved similarly in flexure.

$$M_n=A_S{f}_y\left(d-\frac{a}{2}\right)$$

(1)

where, $A_S$ is area of steel, $f_y$ is yield stress of steel, d is the effective depth of the beam and a is concrete compression zone depth.

3.5. Shear Resistance of OPC and GPC Beams

The $V_c$ of beams without stirrups was taken as half of the experimental $P_u$ and it was only contributed by concrete while the dowel action was not explicitly considered. The shear resistance is normalized as $V_c/\sqrt{fc’}bd$ to incorporate the variation in concrete strength. The $V_c$ and normalized shear resistance of OPC and GPC beams are summarized in

Table 4. Experimental results of without stirrups beams.

Beam ID	fc′ (MPa)	Inclined Cracking Load, Pcr (kN)	Applied Peak Load (kN)	Exp. Shear Resistance, Vc (kN)	$\frac{\mathit{V}\mathit{c}}{\sqrt{{\mathit{f}}_{\mathit{c}}’}\mathit{b}\mathit{d}}$	Failure Mode
ON-4.5	22	58	76	38	0.30	Shear-dominant
GN-4.5	25	63	71.6	35.8	0.27
ON-5	22	37	57.5	28.8	0.23
GN-5	31	47	79	39.5	0.26

.

The normalized shear resistance of both OPC and GPC beams reduced with increasing an $a/d$ ratio from 4.5 to 5. The normalized shear resistance of Beam ON-4.5 was 30% greater than that of Beam ON-5. Similarly, Simik and Arsalan [56] found that the shear resistance of OPC beams decreased by 53% with increasing $a/d$ ratios from 2.5 to 6. Meanwhile, the normalized shear resistance of Beam GN-4.5 was 4% greater than Beam GN-5. In general, OPC beams exhibited a higher reduction in shear resistance with increasing $a/d$ ratio compared to GPC beams. Visintin et al. [30] noted that $V_c$ of GPC beams decreased by 8.7% with an increasing $a/d$ ratio from 2.5 to 3. The effect of $a/d$ ratio on $V_c$ of GPC beams is more significant at lower $a/d$ ratios compared to higher $a/d$ ratios. The normalized shear resistance of OPC and GPC beams is presented in Figure 13. The normalized shear resistance of Beam ON-4.5 was 12% greater than that of Beam GN-4.5. However, the normalized shear resistance of Beam GN-5 was 13% greater than Beam ON-5. Mourougane et al. [58] found that GPC beams exhibited greater shear resistance than OPC beams by about 14%. However, Yacob et al. [29] observed an 8% increase in the shear resistance of the OPC beam compared to the GPC beam. Similarly, Wu et al. [28] reported that the shear resistance of the OPC beam was 6% greater than the GPC beam.

3.6. Empirical Equations of Shear Resistance ($V_c)$ of Beams

The empirical equations to determine the $V_c$ of OPC beams in various design codes including ACI 318-14 [40], ACI 318-19 [42], JSCE-07 [44], and fib-10 [45] are used to compute the $V_c$ of the tested beams.

3.6.1. ACI 318-14 [40]

ACI 318-14 [40] provides Equation (2) to compute $V_c$ of OPC beams.

$$V_c=\left(0.16\lambda \sqrt{fc’}+17{\rho }_w \frac{V_u.d}{M_u}\right)b$$

(2)

$V_u$ is the factored shear, $M_u$ is the factored bending moment, ρ_w is the ratio of flexural reinforcement, and λ is taken as 1 for normal weight concrete. The term ($\frac{V_u.d}{Mu}$) is equivalent to the reciprocal of $a/d$ ratio. Hence, Equation (2) considers the impact of $a/d$ ratio on the $V_c$.

3.6.2. ACI 318-19 [42]

ACI 318-19 [42] suggests Equations (3) and (4) to compute $V_c$ of OPC beams. ACI 318-19 [42] ignores the influence of $a/d$ ratio on $V_c$ of beams. Equation (3) is used when shear reinforcement is greater than the minimum requirement, and Equation (4) is used when shear reinforcement is less than the minimum requirement of shear reinforcement.

$$V_c=\left(0.66\lambda {(\rho w)}^{\frac{1}{3}}\sqrt{fc’}+\frac{N}{6A_g}\right)bd$$

(3)

$$V_c=\left(0.66\lambda \lambda { }_s{({\rho }_w)}^{\frac{1}{3}}\sqrt{fc’}+\frac{N_u}{6A_g}\right)bd$$

(4)

$$\lambda { }_s=\sqrt{\frac{2}{1+0.004d}}\le 1.0$$

(5)

where A_g is the area of the beam, λ_s is the size effect modification factor calculated from Equation (5), $N_u$ is the factored axial load and $\frac{N_u}{6A_g}$ shall not be greater than 0.05 f_c$’$, and ${\rho }_w$ is longitudinal reinforcement ratio.

3.6.3. JSCE-07 [44]

JSCE-07 proposes Equation (6) to compute $V_c$ of OPC beams. JSCE-07 [44] also considers the influence of $a/d$ ratio and is inversely related to the $V_c$ of OPC beams.

$$V_c={\mathsf{\beta }}_d.{\mathsf{\beta }}_n .{\mathsf{\beta }}_p.{\mathsf{\beta }}_a.f_{dd} .{\mathrm{b}}_d.d/{\mathsf{\gamma }}_b$$

(6)

where ${\mathsf{\beta }}_d$ is related to the influence of the depth of members on the $V_c$, ${\mathsf{\beta }}_n$ is related to the impact of axial force on $V_c$, ${\mathsf{\beta }}_p$ is related to the effect of longitudinal reinforcement on $V_c$, ${\mathsf{\beta }}_a$ is related to the effect of $a/d$ ratio on $V_c$, $f_{dd}$ is related to the effect of concrete compressive strength, ${\mathsf{\gamma }}_b$ is the member factor taken 1.3.

$${\mathsf{\beta }}_d=\sqrt[4]{1000/d}$$

(7)

$${\mathsf{\beta }}_n=1+2M_o/M_{ud} (\mathrm{f}\mathrm{o}\mathrm{r} \mathrm{N}{\prime }_{\mathrm{d}}\ge 0)$$

(8)

$${\mathsf{\beta }}_n=1+4M_o/M_{ud} (\mathrm{f}\mathrm{o}\mathrm{r} \mathrm{N}{\prime }_{\mathrm{d}}<0)$$

(9)

$${\mathsf{\beta }}_p=\frac{1+\sqrt{100\mathsf{\rho }\mathrm{w}}}{2}$$

(10)

$${\mathsf{\beta }}_a=\frac{5}{1+{\left(\frac{a}{d}\right)}^2}$$

(11)

$$f_{dd}=0.19\sqrt{f_{c’\mathrm{d}}}$$

(12)

3.6.4. Fib Model Code-10 [45]

The fib model code-10 [45] introduces Equation (13) to compute the $V_c$ of OPC beams without stirrups. This approach also ignores the effect of slenderness on $V_c$ of beams.

$$V_c=\left[k_v\frac{\sqrt{f_{ck}}}{{\mathsf{\gamma }}_c}\right]z{b}_w$$

(13)

where f_ck is the concrete compressive strength, γ_c is the partial safety factor which is taken 1, z is the effective depth, and k_v is the aggregate interlock factor, computed by Equation (14)

$$k_v=\frac{180}{1000+1.25z}$$

(14)

3.7. Comparison of Experimental and Empirical Shear Resistance of Beams

The shear resistance of tested OPC and GPC beams is computed using $V_c$ equations in ACI 318-14 [40], ACI 318-19 [42], JSCE-07 [44], and fib-10 [45] and are presented in

Table 5. Experimental & empirical shear resistance of GPC & OPC.

Experimental and Estimated Shear Resistance						Estimated/Experimental
Beam	Vc (kN)	ACI 318-14 (kN)	ACI 318-19 (kN)	JSCE-07 (kN)	fib-10 (kN)	ACI 318-14	ACI 318-19	JSCE-07	fib-10
ON-4.5	38.00	22.41	23.07	8.0	18.61	0.59	0.61	0.21	0.49
ON-5	28.75	22.19	23.07	6.54	18.61	0.77	0.80	0.23	0.65
GN-4.5	35.95	23.75	24.60	8.53	20.23	0.66	0.68	0.24	0.55
GN-5	39.50	25.98	27.39	7.77	22.09	0.66	0.69	0.20	0.56
					Mean	0.67	0.70	0.22	0.56

and Figure 14. Moreover, the ratios of estimated to experimental shear resistance are presented in Figure 15.

3.7.1. OPC Beams

All the considered design guides underestimated the $V_c$ of the tested OPC beams at $a/d$ ratios of 4.5 and 5. ACI 318-14 [40] underestimated the shear resistance of Beam ON-4.5 and Beam ON-5 by 41% and 23%, respectively. ACI 318-19 [42] underestimated the $V_c$ of Beam ON-4.5 and Beam ON-5 by 39% and 20%, respectively. JSCE-07 [44] underestimated $V_c$ of Beam ON-4.5 and Beam ON-5 by 79% and 77%, respectively. fib-10 [45] underestimated the shear resistance of Beam ON-4.5 and Beam ON-5 by 49% and 65%, respectively.

The shear resistance computed using ACI 318-19 [42] matched best with experimental $V_c$ of OPC beams. In the available literature, the studies reported that $V_c$ computed using ACI 318-19 [42] was closer to the experimental shear resistance of OPC beams having $a/d$ ratios between 2.4 and 8.1 [59,60].

The estimated $V_c$ and ratios of estimated to experimental $V_c$ of OPC beams reported in the literature are calculated and presented in

Table 6. Comparison of experimental and estimated shear resistance of OPC beams of previous literature studies.

Study	Beam	$\mathit{a}/\mathit{d}$	Vc exp (kN)	ACI 318-14 (kN)	ACI 318-19 (kN)	JSCE-07 (kN)	fib-10 (kN)	ACI-14	ACI-19	JSCE-07	fib-10
Deng et al. [36]	B2.2-10-1	2.2	101.5	81.01	68.62	82.28	56.03	0.80	0.68	0.81	0.55
	B3-10-1	3	79	78.66	68.62	48.05	56.03	1.00	0.87	0.61	0.71
	B2.2-20-1	2.2	101.5	82.37	69.92	83.84	57.09	0.81	0.69	0.83	0.56
	B3-20-1	3	81.5	80.03	69.92	48.96	57.09	0.98	0.86	0.60	0.70
	B2.2-30-1	2.2	108	81.28	68.88	82.60	56.25	0.75	0.64	0.76	0.52
	B3-30-1	3	92.4	78.94	68.88	48.24	56.25	0.85	0.75	0.52	0.61
	B2.2-40-1	2.2	123.2	84.51	71.94	86.27	58.75	0.69	0.58	0.70	0.48
	B3-40-1	3	99	82.16	71.94	50.38	58.75	0.83	0.73	0.51	0.59
Sinik and Arsalan [56]	C2.5R	2.5	84.93	27.87	25.65	24.92	22.39	0.33	0.30	0.29	0.26
	C3.5R	3.5	74.49	27.08	25.65	13.63	22.39	0.36	0.34	0.18	0.30
	C4.5R	4.5	66.19	24.82	23.78	7.88	20.76	0.38	0.36	0.12	0.31
	C6R	6	55.58	25.75	25.11	4.78	21.92	0.46	0.45	0.09	0.39

. Deng et al. [36] reported that ACI 318-14 [40], ACI 318-19 [42], JSCE-07 [44], and fib-10 [45] underestimated the $V_c$ of seven OPC beams at $a/d$ ratios 2.2 and 3, by 2–25%, 13–42%, 17–49% and 29–52%, respectively. ACI 318-14 [40], ACI 318-19 [42], JSCE-07 [44], and fib-10 [45] underestimated the shear resistance of four OPC beams of $a/d$ ratios of 2.5, 3.5, 4.5, and 6 by 54–67%, 55–70%, 71–91% and 61–74%, respectively.

3.7.2. GPC Beams

The $V_c$ of tested GPC beams were underestimated by the empirical equations available in ACI 318-14 [40], ACI 318-19 [42], JSCE-07 [44], and fib-10 [45]. ACI 318-14 [40], computed the shear resistance of Beam GN-4.5 and Beam GN-5 as 66% of experimental $V_c$. ACI 318-19 [42] computed the shear resistance of Beam GN-4.5 and Beam GN-5 as 32% and 31% smaller, respectively, than the experimental $V_c$. JSCE-07 [44] computed the shear resistance of Beam GN-4.5 and Beam GN-5 as 76% and 80%, respectively, of the experimental $V_c$. fib-10 [45] computed the shear resistance of Beam GN-4.5 and Beam GN-as 45% and 44% smaller, respectively, than experimental $V_c$.

The results of JSCE-07 [44] were more conservative compared to other design codes. The empirical results computed using ACI 318-19 [42] and ACI 318-14 [40] were closer to the $V_c$ of GPC beams. Nikbakht et al. [61] reported similar findings that ACI (2019) based results were closer to experimental results.

The estimated shear resistance of GPC beams reported in previous experimental investigations is computed and presented in

Table 7. Comparison of experimental and estimated shear resistance of GPC beams of previous literature studies.

Study	Beam	$\mathit{a}/\mathit{d}$	Vc exp (kN)	ACI 318-14 (kN)	ACI 318-19 (kN)	JSCE-07 (kN)	fib-10 (kN)	ACI 318-14	ACI 318-19	JSCE-07	fib-10
Wu et al. [28]	G1-N1.8-I	2.5	89.4	65.99	63.04	55.15	44.87	0.74	0.71	0.62	0.50
	G2-N1.8-I	2.5	114.9	93.15	92.90	81.27	66.12	0.81	0.81	0.71	0.58
	G1-H1.8-I	2.5	94.5	67.61	64.82	56.71	46.13	0.72	0.69	0.60	0.49
	G2-H1.8-I	2.5	150.2	105.53	106.52	93.18	75.81	0.70	0.71	0.62	0.50
	G3-H1.8-I	2.5	185.2	108.02	109.26	95.58	77.76	0.58	0.59	0.52	0.42
	G1-N2.7-I	2.5	79.6	75.91	79.05	68.31	49.27	0.95	0.99	0.86	0.62
	G2-N2.7-I	2.5	122.7	96.76	105.23	90.93	65.59	0.79	0.86	0.74	0.53
	G3-N2.7-I	2.5	120.3	98.83	107.83	93.18	67.21	0.82	0.90	0.77	0.56
	G2-N1.8-D	1.5	230.8	75.78	67.46	131.65	48.01	0.33	0.29	0.57	0.21
	G1-N1.8-D	1.5	256.4	103.41	97.83	190.92	69.63	0.40	0.38	0.74	0.27
	G2-N2.7-S	4	82.2	72.43	80.78	29.77	50.35	0.88	0.98	0.36	0.61
	G2-N2.7-S	4	122.2	90.39	103.33	38.08	64.41	0.74	0.85	0.31	0.53
Yacob et al. [29]	GN6-2	2	209	60.13	54.48	75.72	44.61	0.29	0.26	0.36	0.21
Lee et al. [41]	S19-0	3	111.2	77.24	73.47	50.92	58.41	0.69	0.66	0.46	0.53
	S22-0	3	102.2	79.28	81.09	55.58	58.41	0.78	0.79	0.54	0.57
	S25-0	3	86.7	81.73	88.66	60.44	58.41	0.94	1.02	0.70	0.67
Visintin et al. [30]	B1-T1	2	79	30.91	25.37	36.13	23.57	0.39	0.32	0.46	0.30
	B2-T1	2.5	72	32.12	27.13	26.64	25.19	0.45	0.38	0.37	0.35
	B3-T1	2.5	82.4	30.31	28.89	28.02	24.82	0.37	0.35	0.34	0.30
	B4-T1	2.5	51.8	35.72	27.32	27.29	27.00	0.69	0.53	0.53	0.52
	B2-T2	3	65.8	31.67	27.13	19.31	25.19	0.48	0.41	0.29	0.38
	B4-T2	3	40	43.63	34.25	24.80	33.84	1.09	0.86	0.62	0.85
	B1-T2	3.5	31.1	29.44	25.37	13.63	23.57	0.95	0.82	0.44	0.76
	B3-T2	3.5	51.2	29.53	28.89	15.33	24.82	0.58	0.56	0.30	0.48

. Wu et al. [28] tested GPC beams of $a/d$ ratios 1.5, 2.5 and 4. ACI 318-14 [40], ACI 318-19 [42], JSCE-07 [44], and fib-10 [45] underestimated $V_c$ by 5–42%, 1–41%, 14–48% and 38–58%, respectively. Yacob et al. [29] reported GPC beam with $a/d$ ratio 2. ACI 318-14 [40], ACI 318-19 [42], JSCE-07 [44], and fib-10 [45] underestimated the $V_c$ by 71%, 74%, 64% and 79%, respectively. Lee et al. [41] investigated GPC beams having $a/d$ ratio 3. ACI 318-14 [40], ACI 318-19 [42], JSCE-07 [44], and fib-10 [45] underestimated the $V_c$ by 6–31%, 21–34%, 30–46% and 43–47%, respectively. Visintin et al. [30] investigated eight GPC beams of $a/d$ ratios 2, 2.5, 3 and 3.5. ACI 318-14 [40], ACI 318-19 [42], JSCE-07 [44], and fib-10 [45] underestimated the $V_c$ by 5–61%, 14–68%, 38–71% and 15–70%, respectively. It is concluded that ACI 318-14 [40], ACI 318-19 [42], JSCE-07 [44], and fib-10 [45] underestimated the $V_c$ of GPC specimens.

3.8. Proposed Equation for $V_c$ of GPC Beams

Based on the available data from existing studies and test data of this research study, an equation is proposed for the determination of $V_c$ of GPC beams. In ACI 318-14 [40] equation, the coefficient of 0.16 is modified to 0.20 (Equation (15)).

$$V_c=\left(0.20\lambda \sqrt{fc’}+17{\rho }_w \frac{V_u.d}{M_u}\right)b$$

(15)

The applicability of Equation (15) is evaluated using available data of GPC beams, presented in Table 7. The $V_c$ of GPC beams was computed with a mean value of 0.82 and standard deviations of 0.26 as presented in Figure 16.

4. Environmental Assessment

The environmental assessment of OPC beams and GPC beams with varying $a/d$ ratios (4.5 and 5) was carried out based on embodied carbon dioxide (e-CO₂) emissions. Based on previous studies, the considered e-CO₂ emissions of OPC, FA, coarse aggregates, fine aggregates, sodium hydroxide, sodium silicate and water are 0.8300 kg/kg, 0.0090 kg/kg, 0.0459 kg/kg, 0.0139 kg/kg, 0.9355 kg/kg, 0.7873 kg/kg and 0.0003 kg/kg, respectively [62]. The computed e-CO₂ of OPC beams (ON-4.5, OS-4.5) and GPC beams (GN-4.5, GS-4.5) were 22.22 kg and 14.699 kg, respectively. The computed e-CO₂ of OPC beams (ON-5.0, OS-5.0) and GPC beams (GN-5.0, GS-5.0) were 24.488 kg and 16.190 kg, respectively. The e-CO₂ emissions of GPC beams were 65.7% of OPC beams. Hence, the use of GPC as a substitute for OPC can reduce the e-CO₂ emissions by one-third of the total e-CO₂ emissions while maintaining comparable structural performances.

5. Conclusions

Four OPC beams and four GPC beams having $a/d$ ratios of 4.5 and 5 were cast and tested under a three-point bending test. All beams were 150 mm wide and 225 mm deep with lengths of 1770 mm ($a/d=4.5$) and 1950 mm ($a/d=5$). The experimental shear resistance is compared to the estimated shear resistance computed using the available OPC design code equations in ACI 318-14 [40], ACI 318-19 [42], JSCE-07 [44], and fib-10 [45]. The following conclusions are drawn based on the experimental research works carried out in this research study.

i.

The crack propagation and failure mechanisms of GPC beams without stirrups and with stirrups (shear reinforcement) were similar to corresponding OPC beams. The loads corresponding to the first inclined crack of the OPC beams and GPC beams were similar which, shows that GPC beams behaved similarly to the OPC beams.

ii.

The normalized shear resistance of OPC and GPC beams with $a/d$ ratio 4.5 was greater than 4% and 30%, respectively, than beams with $a/d$ ratio 5. The $P_u$ of shear-reinforced OPC and GPC beams decreased by about 5% and 9%, respectively, with an increase in the $a/d$ ratio from 4.5 to 5. GPC beams exhibited about 18% higher midspan deflection at $P_u$ than OPC beams.

iii.

The shear resistance of GN-4.5 was underestimated by ACI 318-14 [40], ACI 318-19 [42], JSCE-07 [44], and fib-10 [45] by 34%, 32%, 76% and 45%, respectively. The shear resistance of GN-5 was underestimated by ACI 318-14 [40], ACI 318-19 [42], JSCE-07 [44], and fib-10 [45] by 34%, 31%, 80% and 44%, respectively. The results exhibited that ACI 318-19 [42] and ACI 318-14 [40] exhibited a good match with the experimental shear resistance. The JSCE [44] exhibited conservative results.

iv.

All the design code equations computed the shear resistance for both OPC and GPC beams on the conservative side. The $P_u$ of shear-reinforced beams which failed in flexure, were also underestimated by the available equations. Therefore, these equations are safely applicable for GPC specimens for design purposes. Furthermore, experimental testing on large-scale beams is needed to validate the applicability of the available equations.

v.

Equation (15) after modifying ACI 318-14 [40] Equation has been proposed. The proposed equation computed shear resistances closer to experimental shear resistances.

6. Future Developments and Applications

FA-based GPC is a major advancement in the construction industry as GPC is environmentally friendly concrete with significantly reduced embodied CO₂ emissions. The findings of this research study exhibited that the shear behavior of slender GPC beams is identical to OPC beams. Further, the design code equations intended for OPC are applicable to GPC. This makes GPC a promising alternative to OPC.