Bearing capacity of seawater sea sand recycled aggregate concrete beams reinforced with glass fiber reinforced polymer bars

Abstract

In this study, seawater, sea sand and recycled coarse aggregate (RCA) are combined to prepare seawater sea sand recycled aggregate concrete (SSRAC) for use in beams. Nine beams are reinforced with glass fiber reinforced polymer (GFRP) bars, while 2 more beams are reinforced with steel bars for comparison. Unlike reinforced concrete (RC) beams that contain steel bars, SSRAC beams reinforced with GFRP bars (GFRP-SSRAC) are less stiff and ductile. For GFRP-SSRAC beams with a certain shell particle content in this study, the use of seawater and sea sand in concrete decreases the cracking load. The ultimate load is smaller overall for GFRP-SSRAC beams than RC beams with the same reinforcement ratio. The predictions of flexural capacities made using the ACI code are all lower than the test results. When the replacement ratio of RCA is 100%, the predictions for RAC/SSRAC beams using the Chinese code are lower than the measured values. Finally, the measured stress‒strain curves of SSRAC and GFRP bars are used to obtain the moment-curvature relationships according to reinforcement-based and concrete-based calculation methods. These calculations and results are discussed in this paper.

Keywords

seawater sea sand recycled aggregate concrete glass fiber reinforced polymer bar reinforced beams steel bar reinforced beams shell particles bearing capacity

Introduction

The production of concrete consumes large quantities of natural resources, particularly gravel and river sand, which leads to significant environmental concerns and resource shortages (Bendixen et al., 2019). Use of recycled aggregate concrete (RAC) technology is considered one of the inevitable requirements for the sustainable development of the construction industry. For decades, scholars have explored the material properties of RAC and mechanical behaviors of RAC structures (Xiao, 2018), which guided the application of RAC in engineering structures and successfully demonstrated the feasibility of its application in high-rise building structures (Wang et al., 2020).

Recycled coarse aggregates are suitable alternatives to natural gravels, and efforts have been made to find a feasible replacement for river sand and freshwater. In 2011, Teng et al. (2011) proposed the use of fiber reinforced polymer (FRP) to reinforce seawater sea sand concrete (FRP-SSC) structures, which inspired the direct use of sea sand that has not undergone desalination and untreated seawater in concrete. The production and application of seawater sea sand recycled aggregate concrete (SSRAC) are one of the effective solutions that can make good use of recycled aggregates and conserve natural resources (Xiao et al., 2017).

Many scholars have studied the material properties and structural behavior of FRP-reinforced SSRAC. Xiao et al. (2019) reported that the early compressive strength of SSRAC was from 13% to 52% greater than that of ordinary concrete, while the 28-, 90- and 180-day compressive strengths were less by between 5% and 29%. The 28-day modulus of elasticity of SSRAC was slightly less than that of ordinary concrete but significantly more than that of RAC. Similar to SSC, SSRAC also showed an enhancement in the early strength (Pan et al., 2021). This was mainly because chloride and sulfate ions in seawater and sea sand reacted with tricalcium aluminate (C₃A) and silicate hydration products, which formed more Friedel’s salts and calcium alumina. The products accelerated the hydration reaction and optimized the microstructure of mortar, thus contributing to improving the early compressive strength (Li et al., 2020; Qu et al., 2021). Test results showed that the bond strength between SSRAC and FRP bars increased with the compressive strength (Sun et al., 2021), and the presence of recycled aggregate reduced the bond strength, while seawater and sea sand had almost no effect on the bond strength (Xiao et al., 2019). Xiao et al. (2021) found that the peak stress and modulus of elasticity of SSRAC increased with the strain rate. The porosity increased significantly with increasing RCA content, while the addition of seawater and sea sand reduced the porosity of concrete. Zhang et al. (2022a) designed 12 sets of SSRAC specimens for accelerated carbonation tests. The carbonation depth of RAC decreased after the addition of seawater and sea sand. In addition, related studies were conducted on the fracture toughness of sea sand recycled concrete (Yang et al., 2021) and the dynamic bonding performance of sea sand recycled concrete with basalt fiber reinforced polymer (BFRP) bars at a high strain rate (Xiong et al., 2021).

Regarding the structural behavior of SSRAC reinforced with FRP, recent studies have focused on SSRAC columns (Huang et al., 2021; Li et al., 2021a, 2021b; Zhang et al., 2019, 2022b). For FRP-reinforced SSRAC beams, to the knowledge of the authors, a few investigations can be found in the literature. Younis et al. (2020) experimentally studied seawater mixed RAC beams reinforced with glass fiber reinforced polymer (GFRP) bars. To improve the stiffness of SSRAC beams reinforced with FRP bars, Zhou et al. (2021) studied the flexural performance of SSRAC beams reinforced with steel-FRP composite bars (SFCBs) and found two types of failure pattern of the beams. The beams showed significant post-yielding behavior compared with beams reinforced with pure FRP. Currently, many investigations have been conducted on SSC beams reinforced with FRP bars. Hua et al. (2020) tested the flexural behavior and crack development of SSC beams reinforced with steel bars, BFRP bars and GFRP bars and proposed a predictive model. Dong et al. (2022) studied the shear behavior of SSC beams reinforced with BFRP bars. Wang et al. (2022) found that the reinforcement and shear span ratios had a significant effect on the ultimate load of SSC beams reinforced with GFRP bars and changed the failure mechanism from the rupture of GFRP bars to shear failure and finally to concrete crushing. Han et al. (2021) experimentally investigated SFCB-reinforced SSC beams, and the results indicated that inferior bond behavior at the steel-FRP-concrete interface and the nonuniform strain distribution resulted in excessive deflection of the beams. Additionally, researchers have given much attention to the durability of SSC beams reinforced with FRP bars (Dong et al., 2017, 2018a, 2018b, 2020).

The ions in seawater and sea sand react with the cement hydration products to generate swollen soft substances that can enhance the performance of old mortar and weak interfaces at the porous surface of RCAs and, to some extent, optimize the performance of RACs. In this investigation, GFRP-SSRAC beams were designed and tested to evaluate their bearing capacity in an effort to provide evidence for the design of SSRAC members and suggestions for the analysis of this kind of beam. This study is a stage of an ongoing project that focuses on the long-term performance of SSRAC members reinforced with FRP materials and reliability-based durability design in marine environments, particularly in coastal and offshore projects.

Experimental program

Material properties

Original seawater differs according to the area of the sea. Therefore, to eliminate the effects of original seawater on the properties of SSRAC, artificial simulated seawater (ASTM D1141-98, 2013) was used to prepare the SSRAC. The chemical composition of the simulated seawater was published previously (Xiao et al., 2021). The fine aggregates were the same as those used in a previous investigation of the authors (Xiao et al., 2021). Table 1 indicates that the content of Cl^- in sea sand is significantly higher than that in river sand and shell sand, while the content of SO₃ is almost the same. Table 2 presents the physical properties of the natural coarse aggregate (NCA) and RCA. The gradations of the sea sand and shell sand were also published previously (Xiao et al., 2021).

Table 1.

Physical properties of fine aggregates.

Fine aggregates	Apparent density (kg/m³)	Fineness modulus	SO₃ content (%)	Cl^- content (%)	Shell particle content (%)
River sand	2610	2.1	0.109	0.001	1.10
Sea sand	2660	2.7	0.123	0.057	2.31
Shell sand	2620	3.3	0.180	0.001	99.43

Table 2.

Physical properties of coarse aggregates.

Coarse aggregate	Bulk density (kg/m³)	Apparent density (kg/m³)	Crushing index (%)	Clay content (%)	Water content (%)	Water absorption (%)
NCA	1440	2660	5.1	0.80	0.40	1.03
RCA	1280	2590	11.0	0.71	3.87	6.60

Table 3 gives the tested results of GFRP bars, including two types with diameters of 8 and 14 mm. GFRP bars with a diameter of 14 mm were used for longitudinal bars, and 8 mm bars were used for stirrups. The measured stress‒strain curves of the GFRP bars are presented in Figure 1; the curves of the GFRP bars were straight lines. Figure 1 also presents the stress‒strain curves of steel bars with diameters of 6 and 14 mm, which indicate that the yield stresses of the reinforcements were 336 and 436 MPa, and the elastic moduli were 219 and 191 GPa, respectively.

Table 3.

Physical properties of GFRP bars.

Diameter (mm)	Tensile strength (MPa)	Modulus of elasticity (GPa)	Ultimate strain (%)
8	1281.4	56.2	2.28
14	978.6	52.9	1.85

Figure 1.

Stress‒strain curves of GFRP and steel bars.

Mix proportion

Six formulations of concrete with different proportions or ingredients were prepared as shown in Table 4. Additional freshwater or seawater was used in the preparation of concrete. With the tested water absorption and water content of RCA, the additional water was determined to be 30 kg/m³ for concrete with a 100% replacement ratio of RCA. Ordinary Portland cement with a grade of 42.5 defined in the Chinese code (JGJ55-2011, 2011) was used. Additionally, the superplasticizer was used with a content of 3.19 kg/m³. The symbols N, M and H represent the low, medium and high shell particle content (mass ratio of shell particles to fine aggregates) levels in concrete, respectively. RX represents that the replacement ratio of RCA is X as a percentage. As shown in Table 4, the sea sand was replaced by pure shell sand with a mass ratio of 1:4, and the shell particle contents of groups M and H were 2.31% and 21.73% by mass, respectively. Three cubes (150 mm × 150 mm × 150 mm) and prism specimens (100 mm × 100 mm × 300 mm) for each mix proportion were prepared in the fabrication of beams. Then, the specimens were exposed to outdoor atmospheric conditions until they were tested.

Table 4.

Mix proportions of concrete (kg/m³).

Specimen	Free water	Additional water	Cement	Fine aggregates			Coarse aggregates
Specimen	Free water	Additional water	Cement	River sand	Sea sand	Shell sand	NCA	RCA
N-R0	150	0	319	829	0	0	1099	0
N-R100	150	30	319	829	0	0	0	1099
M-R0	150	0	319	0	829	0	1099	0
M-R100	150	30	319	0	829	0	0	1099
H-R0	150	0	319	0	663	166	1099	0
H-R100	150	30	319	0	663	166	0	1099

Design of SSRAC beams

Simply supported concrete beams, as shown in Figure 2, were designed in this investigation. The replacement ratio of RCA (0, 100%), reinforcement type (steel bar, GFRP bar), and stirrup ratio (0.67%, 1.12%) were chosen as the variables to be investigated, as shown in Table 5. The detailed reinforcement information is shown in Figure 2. For the GFRP-SSRAC beams, the top and bottom longitudinal bars were 14 mm with numbers of 2 and 3, and the stirrups were bars with diameter of 8 mm and spacing of 60 or 100 mm. From Figure 2(a), the thickness of the concrete cover was 15 mm, and the black rectangle represents the strain gauges as shown in Figure 2(b). Five concrete strain gauges were installed at equal intervals in the pure bending zone, and three concrete strain gauges, at a 45-degree angle, were installed on the shear-bending zones. The concrete beams were designed based on the existing design code for RFP bar reinforced concrete (RC) beams. In this experiment, the concrete is different, but the FRP is the same as specified in the code. The purpose is to investigate the feasibility of the design formulas in the existing code and give suggestions to the design of FRP-SSRAC beams.

Figure 2.

Dimension and GFRP bar distribution for reinforced SSRAC beams. (a) Dimension of beams and (b) Distribution of strain gauges of reinforcement.

Table 5.

Beam specimens and reinforcement ratio.

Specimen	Reinforcement ratio (%)	Stirrup ratio (%)
S-N-R0^a	1.13	0.38
S-N-R100^a	1.13	0.38
G-N-R0	1.13	1.12
G-N-R100	1.13	1.12
G-N-R100-L	1.13	0.67
G-M-R0	1.13	1.12
G-M-R100	1.13	1.12
G-M-R100-L	1.13	0.67
G-H-R0	1.13	1.12
G-H-R100	1.13	1.12
G-H-R100-L	1.13	0.67

^aIndicates the beams reinforced with steel bars.

Setup and loading

The apparatus consisted of an upper MTS head, load sensor, distribution beam and hinge support, as shown in Figure 2. The load sensor was used to measure the load during the test, and linear variable displacement transducers (LVDTs) were attached to the middle span of the beam and the supports. Reinforcement strain gauges were previously pasted on the surface of the GFRP bars. All the strain gauges were connected to a strain collector. The displacement-controlled loading method was applied at a rate of 0.2 mm/min during the test.

Before the test of the simply supported SSRAC beams, the reinforcement strain gauges, concrete strain gauges and LVDTs were checked to determine whether they worked normally in the preload step. As mentioned, the data collection frequency was set to 5 Hz during the test, and the cracks were marked on the surface of the beams until the end of loading. After the test, the failure patterns, load‒displacement curve, concrete strain, reinforcement strain, and information such as the position transformation of the neutral axis were obtained.

Compressive strength of cubes

Table 6 presents the mean value and standard deviation (SD) of the compressive strength. N-R0 had compressive strength of 25.02 MPa. For N-R100, the compressive strength decreased to 19.90 MPa. For M-R0 and M-R100, the compressive strengths were comparable: 23.11 and 23.09 MPa, respectively. The mean value and the SD of the compressive strength of H-R0 (17.42 MPa and 0.23 MPa) were all less than that of H-R100 (23.17 MPa and 2.90 MPa). When the replacement ratio of RCA was the same, the shell particle content had a negative effect on the mean value of compressive strength when the RCA was not involved (N-R0, M-R0 and H-R0). In contrast, for N-R100, M-R100 and H-R100, the compressive strength increased with the shell particle content for concrete with a 100% replacement ratio of RCA.

Table 6.

Compressive strength of the cube at 28 days (MPa).

Specimen	No.1	No.2	No.3	Mean	Standard deviation
N-R0	26.64	22.97	25.47	25.02	1.87
N-R100	19.76	19.06	20.89	19.90	0.92
M-R0	22.48	23.28	23.58	23.11	0.56
M-R100	22.82	22.61	23.83	23.09	0.65
H-R0	17.40	17.20	17.65	17.42	0.23
H-R100	20.99	26.46	22.05	23.17	2.90

Stress‒strain curves of SSRAC

The stress‒strain curves of the prisms are measured, and a total of three identical specimens were prepared for each group. The stresses of the three specimens at the same strain value were used to calculate the mean curves, as presented in Figure 3, and the values of peak stress are summarized in Table 7. N-R100 had the highest peak stress of 30.29 MPa, followed by M-R0 and N-R0. H-R0 and H-R100 had similar peak stresses, and M-R100 had the lowest peak stress of 18.48 MPa. The peak stresses of the prisms did not correspond to the strengths of the cubes, which may have been due to the development of strength over time. As the prisms and the beams were tested at the same time (over 180 days), while the cubes were tested after aging for 28 days, the test results of the prisms were used to analyze the behavior of the beams.

Figure 3.

Mean stress‒strain curves. (a) Unnormalized curves and (b) Normalized curves.

Table 7.

Peak stresses of the prisms (MPa).

Specimen	No.1	No.2	No.3	Mean	COV (%)
N-R0	24.75	21.68	29.45	25.29	15.47
N-R100	31.63	27.90	31.34	30.29	6.85
M-R0	31.78	31.92	20.10	27.93	24.29
M-R100	19.95	16.62	18.86	18.48	9.19
H-R0	19.10	10.24^a	23.67	21.34	—
H-R100	22.67	18.16	21.23	20.69	11.14

^aThis peak stress was much lower than the designed strength, and it was not considered in the calculation of the mean value.

From Figure 3(a), the peak strain (strain at the peak stress) was approximately 0.002, particularly for N-R100 and M-R0. The peak strains of M-R100 and H-R100 were slightly greater than 0.002, while for N-R0 and H-R0, they were less than 0.002. Additionally, the elastic modulus of N-R100, M-R100 and H-R100 were relatively low because of the introduction of the RCAs. From the normalized stress‒strain curves in Figure 3(b), the descending branch was steeper when the replacement ratio of RCAs was 100%, such as the comparison of N-R100 and N-R0 and H-R100 and H-R0, which indicated that the former was more brittle than the latter. More details of the mechanisms were documented in previous studies (Xiao et al., 2018).

Analysis of test results

Failure patterns of beams

The failure patterns of the beams are shown in Figure 4. With the increase in applied load, vertical cracks first appeared at the bottom of the bending zone, and then cracks developed along the height of the beam. More cracks appeared with increasing load, and the deflection of the mid-span significantly increased. After reaching the yield load, for RC beams, as shown in Figure 4(a) and (b), the deflection of the mid-span significantly increased, while the applied load had a slight increase. The beams failed in concrete crushing in the compression zone, indicating that the beams underwent flexural failure. For concrete beams reinforced with GFRP bars, the crack development was similar to that of RC beams when the load was small. Because the GFRP bar had no yield plateau, the beams failed suddenly after reaching the ultimate load. Compared with the RC beams, the beams reinforced with GFRP bars failed in two different ways that depended on the stirrup ratio and concrete type. The G-M-R100-L and G-H-R100-L beams exhibited shear failures, as shown in Figure 4(d) and (f), and the other beams exhibited flexural failure.

Figure 4.

Failure patterns of beams. (a) S-N-R0, (b) S-N-R100, (c) G-M-R100, (d) G-M-R100-L, (e) G-H-R100, and (f) G-H-R100-L.

Strain analysis of concrete and reinforcing bars

For S-N-R0 and S-N-R100, as shown in Figure 5(a) and (b), the top compressive strain (Con-F1-T) increased with the load. Because of the elastic properties of the GFRP bars, when cracks developed in the shear zone, the compressive stress of the concrete in the bending zone decreased, and thus, the strain of G-M-R100-L and G-H-R100-L first increased and then decreased, as shown in Figure 5(c) and (d). Figure 6 presents the strain of concrete with the height of the cross section. When the load was small, the strain of concrete at different heights was a straight line, and with the increase in load, the strain was almost a straight line, indicating that the beam satisfied the assumption of planar sections. The bottom strain gauges failed due to the increase in concrete strain. For G-M-R100-L, because the failure pattern was shear failure, the tensile strain of the concrete was small compared that in other beams, and the strain showed almost no change with the increase in load, as presented in Figure 5(c) and Figure 6(c). When the load was less than 100 kN, the tensile strain was less than 200 με.

Figure 5.

Concrete strain at the middle span. (a) S-N-R0, (b) S-N-R100, (c) G-M-R100-L, and (d) G-H-R100-L.

Figure 6.

Distribution of concrete strain along the height of the cross section. (a) S-N-R0, (b) S-N-R100, (c) G-M-R100-L, and (d) G-H-R100-L.

Figure 7 shows the strain of the longitudinal bars. At the failure moment of the beams, the maximum tensile strain of the steel bar was approximately 3000 and 4100 με for S-N-R0 and S-N-R100, respectively. The maximum tensile strain of the GFRP bars was not available due to their large deformation. Thus, the strain gauges for the GFRP bar failed before the end of the test. The results indicated that the tensile strain was much greater for the GFRP bars than the steel bars.

Figure 7.

Strain of the longitudinal bars. (a) S-N-R0, (b) S-N-R100, (c) G-M-R100-L, and (d) G-H-R100-L.

Figure 8 shows the strain of the stirrups of some beams. Because some strain gauges broke before the end of the test, there were no strain data, such as the strain gauges in the left span of S-N-R100, as shown in Figure 8(b). For the distribution of the shear stress at the cross section, because the S2 and S3 strain gauges were closer to the neutral axis, they had relatively high strains. For RC beams, the maximum strains of the stirrups were 2200 and 3500 με for S-N-R0 and S-N-R100, respectively. Similar to the longitudinal bars in Figure 7, some strain gauges for the GFRP stirrups failed before the end of the test, and the measured maximum strain was over 10000 με, as shown in Figure 8(d).

Figure 8.

Strain of the stirrups. (a) S-N-R0, (b) S-N-R100, (c) G-N-R100, (d) G-N-R100-L, (e) G-M-R100-L, and (f) G-H-R100-L.

Load deflection curves

Figure 9 presents the load-deflection curves of the beams. For steel bar reinforced beams, the load capacity of S-N-R100 was lower than that of S-N-R0. When the NCA was replaced with RCA, the elastic modulus of the RAC showed an obvious decreasing trend (Xiao et al., 2018), which caused less stiffness for S-N-R100 than S-N-R0. Due to the greater elastic modulus and plastic properties of steel bars, the RC beams were significantly stiffer and more ductile compared with concrete beams reinforced with GFRP bars.

Figure 9.

Load-deflection curves of beams.

Characteristic loads and deflection

The characteristic loads, deflections and failure patterns are presented in Table 8. S-N-R0 had the highest cracking load of 41.91 kN, followed by S-N-R100. The cracking loads of the beams reinforced with GFRP bars were within the interval from 21.22 kN to 28.35 kN, indicating that these values were much lower than those of the RC beams. G-N-R100-L, G-M-R100-L and G-H-R100-L had the greatest cracking loads, i.e., 28.35, 24.46 and 25.59 kN among the G-N, G-M and G-H groups, respectively. This may have been due to the smaller stirrup ratio in the bending zone, which made positive contributions to the bond properties between the GFRP bars and concrete. From the viewpoint of shell particle content, there was no obvious difference in the cracking loads of G-M and G-H.

Table 8.

Characteristic loads and failure patterns of beams.

Specimen	Cracking load (kN)	Ultimate load (kN)	Mid-span deflection at ultimate load (mm)	Failure pattern
S-N-R0	41.91	248.91	36.45	Concrete crushed
S-N-R100	37.11	210.78	11.91	Concrete crushed
G-N-R0	25.17	167.64	25.27	Concrete crushed
G-N-R100	26.87	203.99	33.89	Concrete crushed
G-N-R100-L	28.35	182.91	33.01	Concrete crushed
G-M-R0	22.52	137.32	22.01	Concrete crushed
G-M-R100	22.35	190.85	33.86	Concrete crushed
G-M-R100-L	24.46	146.74	23.46	Shear failure
G-H-R0	22.60	159.49	27.65	Concrete crushed
G-H-R100	21.22	226.83	39.66	Concrete crushed
G-H-R100-L	25.59	170.81	25.94	Shear failure

Similar to the cracking loads, S-N-R0 had the highest ultimate load of 248.91 kN, followed by G-H-R100 and S-N-R100. In this investigation, most of the beams failed through concrete crushing, and the GFRP bars were not broken, indicating that the GFRP bars still had the potential capacity to carry loads. Because of the earlier failure of concrete, the ultimate load of concrete beams reinforced with GFRP bars was less than that of the RC beams except for the G-H-R100 beam. As shown in Figure 10(a), the beams made with SSRAC and reinforced with a 1.12% stirrup ratio had the greatest ultimate loads. G-N-R100, G-M-R100 and G-H-R100 had the greatest ultimate loads among the G-N, G-M and G-H groups, followed by G-N-R100-L, G-M-R100-L and G-H-R100-L. Figure 10(a) also indicates that the shell particle content influenced the ultimate load. The group of G-N beams had the largest values, while the G-M beams had the smallest values. This may have been due to the combined effects of the RCAs and shell particles. The previous investigation showed that the larger content of shell particles, i.e., group G-H in this study, contributed to the decrease in pore ratio and thus led to compressive strength that was greater than that of the concrete made with medium shell particle content (Xiao et al., 2021), i.e., group G-M in this investigation. Additionally, the introduction of RCA increased the pore ratios and detracted from the properties of concrete (Xiao et al., 2021). Therefore, the ultimate load of group G-H was larger than that of group G-M but smaller than that of group G-N.

Figure 10.

Ultimate load and the corresponding deflection. (a) Ultimate load and (b) Deflection at ultimate load.

The mid-span deflection at the ultimate load of S-N-R0 was 36.45 mm, as shown in Table 8, which was the largest value among the beams. Figure 10(b) presents the mid-span deflection at the ultimate load for GFRP bar RC beams. The mid-span deflections were strongly related to the ultimate load for GFRP bar RC beams. G-N-R100, G-M-R100 and G-H-R100 had the largest mid-span deflections among the G-N, G-M and G-H groups. S-N-R100 has the smallest mid-span deflection at ultimate load, which may have been due to the earlier crushing of the RAC in the compressive zone, and thus made no contribution to the increase in the arm of the force of the cross section.

Prediction of bearing capacity

Current models

Models have been proposed to predict the bearing capacity of GFRP-SSC beams. In this investigation, the models in the ACI (ACI440.1R-15, 2015) and the Chinese code (GB 50608-2020, 2020) are summarized.

ACI model (ACI440.1R-15, 2015)

The balanced reinforcement ratio $ρ_{f b}$ in the ACI code was determined as follows:

ρ_{f b} = 0.85 β_{1} \frac{f_{c}^{'}}{f_{f u}} \frac{E_{f} ε_{c u}}{E_{f} ε_{c u} + f_{f u}}

(1)

f_{f u} = C_{E} f_{f u}^{*}

(2)

where

β_{1}

is a factor.

f_{c}^{'}

is the specified strength of concrete in compression,

f_{f u}

is the design strength of FRP in tension,

f_{f u}^{*}

is the guaranteed tensile strength of FRP bar,

C_{E}

is the environmental reduction factor,

ε_{c u}

is the ultimate strain of the concrete, and

E_{f}

is the elastic modulus of FRP.

When $ρ_{f}$ is not lower than $ρ_{f b}$ , the moment capacity of beams can be determined by equation (3):

M_{n} = ρ_{f} f_{f} (1 - 0.59 \frac{ρ_{f} f_{f}}{f_{c}^{'}}) b d^{2}

(3)

f_{f} = [\frac{{(E_{f} ε_{c u})}^{2}}{4} + \frac{0.85 β_{1} f_{c}^{'}}{ρ_{f}} E_{f} ε_{c u} - 0.5 E_{f} ε_{c u}] \leq f_{f u}

(4)

where

f_{f}

is the tensile stress of FRP bars, b is the width of rectangular cross section, and d is the distance from the centroid of the tension reinforcement to the extreme compression fiber.

When $ρ_{f}$ is lower than $ρ_{f b}$ , the moment capacity is calculated by equation (5):

M_{n} = A_{f} f_{f u} (d - \frac{β_{1} c}{2})

(5)

where c is the distance from the neutral axis to the extreme compression fiber.

The shear capacity of concrete reinforced with FRP bars is determined by equation (6):

V_{n} = V_{c} + V_{f}

(6)

V_{c} = \frac{2}{5} \sqrt{f_{c}^{'}} b k d

(7)

V_{f} = \frac{A_{f v} f_{f v} d}{s}

(8)

k = \sqrt{2 ρ_{f} n_{f} + {(ρ_{f} n_{f})}^{2}} - ρ_{f} n_{f}

(9)

f_{f v} = 0.004 E_{f} \leq f_{f b}

(10)

f_{f b} = (0.05 \cdot \frac{r_{b}}{d_{b}} + 0.3) f_{f u} \leq f_{f u}

(11)

where

V_{c}

is the nominal shear resistance provided by concrete,

V_{f}

is the shear resistance provided by FRP stirrups,

A_{f v}

is the area of FRP stirrups,

f_{f v}

is the design value of tensile strength for shear, s is the stirrup spacing,

n_{f}

is the ratio of elastic modulus of FRP bars to concrete,

f_{f b}

is the strength of the bent portion of FRP bar,

r_{b}

is the internal radius of the bend in FRP reinforcement, and

d_{b}

is the diameter of FRP bar.

Chinese code model (GB 50608-2020, 2020)

In the Chinese code, $ρ_{f b}$ is determined as follows:

ρ_{f b} = \frac{α_{1} f_{c}}{f_{f d}} \cdot ξ_{f b}

(12)

ξ_{f b} = \frac{β_{1 c} ε_{c u}}{ε_{c u} + f_{f d} / E_{f}}

(13)

where

α_{1}

is a constant equal to 1.0,

f_{c}

is the compressive strength of concrete,

f_{f d}

is the design value of the tensile strength of GFRP bars, and

ξ_{f b}

is the relative height of the compressive zone, which is determined by equation (13),

β_{1 c}

is a constant and equals 0.8.

The effective stress of the FRP $f_{f e}$ is related to $ρ_{f}$ and can be calculated by equation (14) as follows:

f_{f e} = {\begin{cases} f_{f d} (ρ_{f} < 1.5 ρ_{f b}) \\ {(ρ_{f} / ρ_{f b})}^{- 0.55} f_{f d} (ρ_{f} \geq 1.5 ρ_{f b}) \end{cases}

(14)

Then, the moment capacity of beams is derived as follows:

M \leq A_{f} f_{f e} (h_{0 f} - \frac{x}{2})

(15)

x = {\begin{cases} [\frac{0.14}{1 + 400 (f_{f e} / E_{f})} + \frac{ρ_{f} f_{f e}}{f_{c}}] h_{0 f} (ρ_{f} < 1.5 ρ_{f b}) \\ \frac{ρ_{f} f_{f e}}{α_{1} f_{c}} h_{0 f} (ρ_{f} \geq 1.5 ρ_{f b}) \end{cases}

(16)

where

A_{f}

is the area of FRP bars,

h_{0 f}

has the same meaning as d in the ACI code, and x is the height of the equivalent rectangular stress block.

The shear capacity model of concrete beams reinforced with GFRP bars in the Chinese code is the same as the ACI model except for the shear resistance provided by concrete, which is determined as follows:

V_{c c} = 0.86 f_{t} b c

(17)

c = k \cdot h_{0 f}

(18)

where

f_{t}

is the tensile strength of concrete, and k has the same meaning as that in equation (9).

Comparison between the measured results and predictions

Based on equation (1), the $ρ_{f b}$ was approximately 0.482%, which was less than the $ρ_{f}$ in this investigation (1.13%). Therefore, equation (3) was used to calculate the moment capacity when the ACI model was applied. For the Chinese code, $ρ_{f b}$ was approximately 0.790% with the consideration of equation (12), and then $f_{f e}$ was taken as $f_{f d}$ in equation (14).

From Table 9, for the ACI code, the predicted flexural capacities were all less than the test results. The relative errors ranged from −18.69% for G-M-R0 to −63.55% for G-H-R100. The G-H group had the largest relative errors compared with the same specimens in the G-N and G-M groups. For the Chinese code, the absolute values of the relative errors were overall less than those of the ACI code. Unlike the ACI code, the G-M group had the largest relative errors compared with the same specimens in the G-N and G-H groups for the Chinese code.

Table 9.

Predictions of bearing capacity.

Beams	Test results $M_{u}$ (kN·m)	ACI code model $M_{A C I}$ (kN·m)	Chinese code model $M_{C C}$ (kN·m)	$\frac{M_{A C I} - M_{u}}{M_{u}}$ (%)	$\frac{M_{C C} - M_{u}}{M_{u}}$ (%)
G-N-R0	56.58	34.12	57.27	−39.69	1.23
G-N-R100	68.85	40.86	58.58	−40.64	−14.91
G-N-R100-L	61.73	40.86	58.58	−33.80	−5.12
G-M-R0	46.35	37.68	58.02	−18.69	25.19
G-M-R100	64.41	24.92	44.89	−61.31	−30.31
G-M-R100-L	(73.37)	(56.25)	(76.20)	(-23.33)	(3.85)
G-H-R0	53.83	28.78	55.81	−46.53	3.68
G-H-R100	76.56	27.91	55.51	−63.55	−27.49
G-H-R100-L	(85.41)	(56.86)	(77.17)	(-33.42)	(-9.64)

The values in brackets for G-M-R100-L and G-H-R100-L beams are the shear capacity in kN and the relative errors in percentage.

As the failure pattern of G-M-R100-L and G-H-R100-L was shear failure with concrete crushing, Table 9 provides the measured and predicted shear capacities. For G-M-R100-L, the tested value was 73.37 kN, and the predicted values were 56.25 and 76.20 kN for the ACI code and the Chinese code, with relative errors of −23.33% and 3.85%, respectively. For G-H-R100-L, the tested value was 85.41 kN, and the predicted values from the ACI code and Chinese code were all less than those from the test. Comparing the relative errors of the predictions showed that the shear capacity obtained from the Chinese code was much closer to the test values. Considering that the contribution of shear capacity from the GFRP bars was the same for both code models, the difference in predictions was due to the contribution of concrete, as shown in equations (7) and (17). Additionally, the measured value for G-H-R100-L was larger than that of G-M-R100-L because the compressive strength of H-R100 was higher than that of M-R100, as presented in Table 7. The reason was that the porosity of H-R100 was less than that of M-R100, consequently leading to a greater strength, as reported in a previous investigation (Xiao et al., 2021).

Calculation and discussion of the moment-curvature relationships

In this investigation, the bearing capacity of GFRP-SSRAC beams was calculated by the ACI code and the Chinese code, while the moment-curvature relationships cannot be directly obtained from the codes. As mentioned in Chapter 2.6, the stress‒strain curves of the prisms corresponded to the FRP bar reinforced SSC beams in this investigation. Therefore, these stress‒strain curves can be used for the calculation of the moment-curvature relationships of beams.

With the planar section assumption, the strain of GFRP bars at a different level of load and the strain of concrete along with the height of the middle span can be obtained with the measured strain data. Then, the stress can be calculated based on the stress‒strain model of the concrete and GFRP bars. Here, the stress‒strain model of the GFRP bars was a straight line, as presented in Figure 1. For SSC, particularly for SSRAC, no stress‒strain models were proposed in the literature. Therefore, based on the previous investigation of the stress‒strain models of RAC (Xiao et al., 2018), this paper modified the RAC model with the tested stress‒strain curves to describe the uniaxial compressive behavior of SSRAC. Then, the distribution of compressive stress was finally determined, as shown in Figure 11.

Figure 11.

Strain, stress and resultant force of the cross section.

With the measured strain, the curvature ( $ϕ$ ) of the cross section can be obtained. In Figure 11, the stress distribution can be assumed as continuous thin layers in which the stress has the same value. The resultant force of concrete (F_c) was obtained by adding the force of each layer, as shown in equation (19). Then, based on equation (20), the position of the resultant force ( $y_{c}$ ) was calculated, and thus, the moment of the cross section was obtained:

F_{c} = \int_{0}^{x} σ_{c} (ε_{c}) \cdot b \cdot d y

(19)

y_{c} = \frac{\int_{0}^{x} σ_{c} (ε_{c}) \cdot b \cdot y \cdot d y}{F_{c}} = \frac{\int_{0}^{x} σ_{c} (ε_{c}) \cdot y \cdot d y}{\int_{0}^{x} σ_{c} (ε_{c}) \cdot d y}

(20)

M_{f} = F_{f} \cdot z

(21)

M_{c} = F_{c} \cdot z

(22)

Figure 12 provides a comparison of the measured and calculated moment-curvature relationships. As some strain gauges failed before the applied load reached the ultimate load, the calculated maximum moments were not the ultimate tested moment. The moment obtained from the product of the force of the GFRP bar times the distance (from the position of the resultant Fc to the centroid of GFRP bars) was defined as $M_{f}$ , i.e., the reinforcement-based moment (Equation (21)), and the product of the resultant Fc times the distance was defined as $M_{c}$ , i.e., the concrete-based moment (Equation (22)). From Figure 12(a), for G-M-R100, the calculated moments were initially less and then greater than the measured values. $M_{f}$ was much greater than $M_{c}$ when the curvature exceeded 0.03 m⁻¹. In contrast, $M_{f}$ was less than $M_{c}$ and the test result when the curvature was less than 0.04 m⁻¹ for G-M-R100-L. Similar results were found for G-H-R100, and the turning curvature was approximately 0.03 m⁻¹. According to Figure 12(d), $M_{f}$ and $M_{c}$ were much closer to the test results than were other beam specimens.

Figure 12.

Moment-curvature relationships of the GFRP-SSRAC beams. (a) G-M-R100, (b) G-M-R100-L, (c) G-H-R100, and (d) G-H-R100-L.

$M_{f}$ was almost a straight line when the curvature was less than 0.03 m⁻¹ for the beam specimens, and this may have been mainly because of the linear elastic properties of the GFRP bars. Because of the nonlinear stress‒strain properties of SSRAC applied in the calculation, $M_{c}$ was a curve from the beginning to the calculated maximum curvature. Additionally, $M_{c}$ was overall higher than the test result for the above beam specimens, and $M_{f}$ and $M_{c}$ were not equal. The reasons may have been as follows: (a) the measured strain of concrete and GFRP bars was applied to determine the curvature and the strain distribution of concrete based on the planar section assumption. However, according to Figure 6, the strain was not a straight line along the height of the cross section, which may have been due to the precision of the measurement. As the stress and resultant force were obtained from the measured strain, the calculated moments were different from the test results. (b) The stress‒strain behavior of SSRAC in the beam was different from that under uniaxial compression. The stress condition in beams was much more complicated, and therefore, the calculation based on the latter condition caused relative errors. (c) The stress of the GFRP bars was assumed to have a uniform distribution, and the stress was the same for each longitudinal GFRP bar. Meanwhile, the bond slip between the concrete and GFRP bars was not considered in the calculation, which may have had a significant effect on the strain distribution of the GFRP bars. The above assumptions may have been different from the actual behavior of the test beams.

Conclusions

Seawater sea sand recycled aggregate concrete (SSRAC) beams reinforced with GFRP bars (GFRP-SSRAC) were tested to study their bearing capacity. The failure patterns, strain development, load-deflection curves, cracking and ultimate loads were obtained. The following main conclusions can be drawn.

1) Crack development was similar in SSRAC and RC beams reinforced with GFRP bars. The beams failed suddenly after reaching the ultimate load because the GFRP bars had no yield plateau. The failure pattern of RC beams was concrete crushing, while the beams reinforced with GFRP bars underwent two different patterns of failure, concrete crushing and shear failure with concrete crushing.

2) Stiffness and ductility were significantly greater for concrete and RAC beams reinforced with steel bars than those reinforced with GFRP bars for the same reinforcement ratio. For SSRAC with a certain shell particle content, when the stirrup ratio was the same, the content of shell particles had no obvious effects on cracking loads, but the introduction of seawater and sea sand caused the cracking loads to decrease.

3) The ultimate loads of the beams reinforced with GFRP bars were less overall than those of the RC beams. Higher content of shell particles contributed to greater compressive strength of SSRAC, but the introduction of RCA usually had a negative effect on the properties of concrete. All the flexural capacities predicted by the ACI code were less than the test results. When the replacement ratio of RCA was 100%, the predictions of the flexural capacities of RAC/SSRAC beams by the Chinese code were less than the measured values. For shear capacity, the predictions obtained by the Chinese code were closer to the experimental values and greater than those obtained by the ACI code.

4) The moment-curvature relationships differed depending on the calculation method. For $M_{f}$ , the curve was almost a straight line, while $M_{c}$ was a curve with increasing curvature. This indicated that future studies should consider some of the assumptions made in this investigation, such as the stress distribution of FRP bars in beams, stress‒strain behavior of SSRAC, and bond-slip behavior between SSRAC and GFRP bars.

5) Additional related investigations are needed on multiple scales, such as explaining failure patterns in terms of microstructure properties, performing simulations to clarify the cooperative mechanism of GFRP bars and SSRAC, conducting a parametric analysis of bearing capacity, and exploring the long-term performance of SSRAC beams reinforced with FRP bars.

Footnotes

Declaration of conflicting interests

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

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors wish to acknowledge the financial support from the National Natural Science Foundation of China (NSFC, No. 52008304, 52078358), the China Postdoctoral Science Foundation (2019M661620), the Startup Foundation of Scientific Research by Fuzhou University (No. GXRC21060), Fuzhou University Testing Fund of precious apparatus (No. 2022T023), and Science and Technology Innovation Research.

ORCID iD

Jianzhuang Xiao

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