Study on shear behavior of reinforced coral aggregate concrete beam

Abstract

Reinforced coral aggregate concrete beam and reinforced ordinary aggregate concrete beam with different concrete type, concrete strength, and steel type were designed in this study to investigate their shear behavior. The shear behavior of reinforced coral aggregate concrete beam was tested, the failure mode and deflection behavior were studied, and the calculating model for the ultimate shear capacity (V_cs) of reinforced coral aggregate concrete beam was proposed. Results showed that the failure mode of reinforced ordinary aggregate concrete beam and reinforced coral aggregate concrete beam were basically the same. As the concrete strength increases, the normal section cracking load (V_cr), inclined section V_cr, and V_cs of reinforced coral aggregate concrete beam increased gradually. Furthermore, V_cr and V_cs of reinforced coral aggregate concrete beam were as follows: 316 stainless steel > common steel > zinc-chromium coated steel > new organic coated steel. For the coral aggregate concrete structure in ocean engineering, in order to prolong its service life, the use of new organic coated steel was suggested. At the same time, the influence of high-strength coral aggregate concrete and stirrup corrosion was comprehensively considered and the calculation model for the V_cs of reinforced coral aggregate concrete beam was presented and was then verified.

Keywords

calculation model reinforced coral aggregate concrete beam shear behavior stirrup corrosion ultimate shear capacity

Introduction

For the ocean engineering construction background, the application of reinforced coral aggregate concrete (CAC) beam has important engineering benefits (Fathifazl et al., 2010; Lu et al., 2019; Ma et al., 2018). However, the corals which are natural porous structure and contain large amounts of Cl⁻ in CAC easily lead to the steel corrosion (Da et al., 2020; Wang et al., 2017). When the concrete cover is subject to Cl⁻, the steel corrosion will affect the structure properties. For steel, the sections and mechanical properties are reduced by the corrosion (Frangopol et al., 1997; Ma et al., 2016). For concrete (Chen et al., 2008; Zhang et al., 2008), concrete cover cracks are also formed due to steel corrosion, causing damage to the concrete. For reinforced concrete (Guzmán et al., 2011; Ou and Nguyen, 2016; Zhang et al., 2017), due to the influence of steel corrosion, the bond property between the concrete and steel is reduced. In addition, the shear failure of reinforced concrete beam is brittle failure, and its influence is more serious than flexural failure (Yang et al., 2016). Therefore, research on the shear behavior of reinforced CAC beam has important engineering significance for the ocean engineering.

Kakooei et al. (2012) studied on steel corrosion in CAC and found that the rate of steel corrosion in CAC was significantly higher than that in OAC with same mix proportion. Zhang (1995) studied on mechanical behavior of reinforced CAC beam/column; however, the common steel has been corroded in the test, and this corrosion did not introduce quantitative data analysis. Wang and Zhao (2012) studied on mechanical behavior of CAC and found that CAC was similar to lightweight aggregate concrete (LAC) in failure mode. Li et al. (2013) studied on elastic modulus and steel corrosion of CAC and found that proper amount of fly ash (FA) or slag (SG) added in CAC could improve its elastic modulus and anti-corrosion. Da et al. (2016b) studied on mechanical behavior of CAC, and the results showed that CAC was more brittle than OAC and LAC with same concrete strength. Da et al. (2016c) and Yu et al. (2017) investigated on the durability of concrete structure in the Xisha island, and the Cl⁻ diffusion and steel corrosion of CAC and OAC were analyzed. Therefore, based on current research status of CAC, this article studies the shear behavior of reinforced CAC beam.

To study the shear behavior of concrete beam, 12 reinforced CAC beams and 2 reinforced OAC beams with different of concrete type, concrete strength, and steel type were designed. The shear behavior of reinforced CAC beam was studied. Comprehensively considering the influence of steel corrosion and high strength CAC, the calculation model for V_cs of reinforced CAC beam was presented.

Experiment

Raw materials

Table 1 is the basic parameters of coral aggregate. Other materials included the following: P·II52.5 ordinary Portland cement, FA, SG, calcium nitrate inhibitor, and water reducer, and the chemical composition of cement, FA, and SG is also shown in Table 2. According to ASTM D1141-2003, the mix proportion of seawater is NaCl: KCl: CaCl₂: MgCl₂·6H₂O: Na₂SO₄ = 24.5: 0.7: 1.2: 11.1: 4.1. The steel included (a) common steel, (b) new organic coated steel, (c) zinc-chromium coated steel, (d) 2205 duplex stainless steel, and (e) 316 stainless steel, and the chemical composition of steel is given in Table 3.

Table 1.

Basic parameters of coral aggregate.

Basic parameter	Coral	Coral sand
Bulk density (kg/m³)	1000	1115
Apparent density (kg/m³)	2300	2500
Chloride content (%)	0.074	0.112
Mud content (%)	–	0.5
Fineness modulus	–	2.9

Table 2.

Chemical composition of cement, fly ash, and slag (%).

Material	SiO₂	Al₂O₃	CaO	MgO	SO₃	Fe₂O₃	IL	K₂O
Cement	21.53	4.60	64.09	0.96	2.09	3.37	1.84	0.62
Fly ash	54.88	26.89	4.77	1.31	1.16	6.49	3.10	–
Slag	33.48	12.21	36.35	10.59	0.66	1.40	0.36	0.56

Table 3.

Chemical composition of steel (%).

Steel	C	Si	Mn	P	S	Cr	Ni	Mo	N
A	0.20	0.56	1.42	0.021	0.039	–	–	–	–
D	0.03	0.48	0.83	0.026	0.004	21.6	4.71	2.68	0.162
E	0.029	0.60	0.80	0.013	0.073	17.14	12.58	2.28	–

Component preparation

The size of reinforced concrete beam is 150 mm × 200 mm × 1500 mm. The mix proportion and basic parameter of reinforced concrete beam are shown in Table 4 and Table 5, respectively. Among them, the shear span ratio (λ) was 1.23 and the thickness of concrete cover was 30 mm; f_cu, f_c, and f_t were concrete cube compressive strength, axial compressive strength, and axial tensile strength, respectively; and f_y and f_yv were longitudinal steel yield strength and stirrup yield strength, respectively. In order to cause shear failure of beam, the beam bottom was configured with 2Φ16 rebar steels, the hanger steel with 2Φ10 rebar steels, stirrups with Φ6 plain round steels, and the stirrup spacing was 100 mm. The dimensions and steel details of reinforced concrete beam are shown in Figure 1.

Table 4.

Mix proportion of coral aggregate concrete (kg/m³).

Concrete strength	Cement	Slag	Fly ash	Coral	Coral sand	Water	Water-reducer	Inhibitor	W/B
C25	275	150	75	582	873	250	–	15.0	0.50
C50	429	83	38	680	1020	200	3.3	16.5	0.36
C60	780	150	70	300	700	264	6.0	30.0	0.26

The mix proportion of C35 OAC and C25 CAC was the same.

Table 5.

Basic parameter of reinforced concrete beam.

No.	Concrete type	Concrete strength	f_cu (MPa)	f_c (MPa)	f_t (MPa)	Steel type	f_y (MPa)	f_yv (MPa)
BJ1-1	OAC	C35	51.9	43.8	5.0	B	457	440
BJ1-2	OAC	C35	51.3	43.4	5.0	B	457	440
BJ2-1	CAC	C25	42.7	37.1	4.3	B	457	440
BJ2-2		C25	42.4	36.9	4.3	B	457	440
BJ3-1		C50	66.7	54.6	6.2	B	457	440
BJ3-2		C50	66.6	54.5	6.2	B	457	440
BJ4-1		C60	75.9	61.3	6.9	B	457	440
BJ4-2			76.4	61.6	7.0	B	457	440
BJ5-1			76.2	61.4	6.9	A	457	440
BJ5-2			76.2	61.4	6.9	A	457	440
BJ6-1			75.4	60.9	6.9	C	457	440
BJ7-1			76.3	61.5	6.9	D	591	588
BJ8-1			75.8	61.2	6.9	E	811	805
BJ8-2			76.2	61.5	6.9	E	811	805

OAC: ordinary aggregate concrete; CAC: coral aggregate concrete.

Figure 1.

Dimensions and steel details of reinforced concrete beam (mm).

Test method

According to GB/T 50152-2012, the four-point loading method was adopted in the test. The devices are shown in Figure 2. During the loading process, a load sensor of 50 t was used to measure the load changes. DH3818-2 strain indicator collects readings from steel, concrete, and displacement sensor. The development and width of cracks are measured by SW-LW-201 crack detector. In addition, YWC-50 displacement sensors were installed on the supports, loading points, and midspan of beam, respectively, to obtain the overall deformation of beam.

Figure 2.

Schematic of loading devices (mm).

To measure the steel stress during loading, the four strain gauges were attached to stirrups in the shear zone. At the same time, the six strain gauges were attached to the midspan of longitudinal steels and the loading points. In order to measure the deformation of beam, the five strain gauges were arranged in the pure bending section of beam. To explore the concrete strain development, the two strain gauges were attached to the tensile and compression zones. Meanwhile, to analyze the distribution of principal stress in the shear bending section, the strain rosette was attached to the midpoint between loading point and support (Figure 1).

Results and discussion

Failure mode

Figure 3 shows the failure mode of reinforced concrete beam. As shown in Figure 3, the shear failure occurred in both reinforced OAC/CAC beam, and the failure mode was basically the same. However, for the same mix proportion (Figure 3(a)–(b)), there were more cracks in the reinforced CAC beam than in the reinforced OAC beam. The main reason is that the coral aggregates are naturally porous structural materials (Da et al., 2016b), which has the characteristic of “absorb and return water.” In the process of cement hardening, the water released was used to hydration of cement. This “micro-pump” effect reduced W/B around the coral aggregates, thus improving the bonding strength between coral aggregates and cement. At the same time, the rough surface of coral aggregates makes its surface area larger and improves the interfacial strength. Therefore, this characteristic of coral aggregates can effectively inhibit the development of inclined cracks.

Figure 3.

Failure mode of reinforced concrete beam: (a) BJ1-2, (b) BJ2-2, (c) BJ3-2, (d) BJ4-1, (e) BJ6-1, and (f) BJ8-2.

Furthermore, the test found that the shear strength of coral aggregates was very low, and when the shear cracking of reinforced CAC beam occurs, the coral aggregate on the cracks was cut off, failing to maintain its completion. Consequently, after the inclined sections were sheared to crack, the bonding force between the aggregates will be significantly reduced and stirrups will share more shear strength, which illustrated the low shear strength of CAC.

Bearing capacity

Table 6 shows test results of reinforced concrete beam. Among them, f_max is the maximum midspan deflection and w_max is the maximum crack width. As shown in Table 6, for reinforced CAC beam with the same steel type, as the concrete strength increases, the normal section cracking load (V_cr), inclined section V_cr, and ultimate shear capacity (V_cs) of reinforced CAC beam increased gradually. The main reason is that the higher CAC strength, the higher f_t; thus, V_cr and V_cs increased.

Table 6.

Test results of reinforced concrete beam.

No.	Concrete type	Concrete strength	Normal section V_cr (kN)	Inclined sectionV_cr (kN)	V_cs (kN)	f_max (mm)	Bend crack,w_max (mm)	Inclined crack,w_max (mm)
BJ1-1	OAC	C35	13	70	140	3.17	0.24	–
BJ1-2	OAC	C35	11	75	168	3.59	0.24	1.86
BJ2-1	CAC	C25	11	65	184	3.34	0.30	1.8
BJ2-2		C25	10	70	214	2.95	0.35	1.2
BJ3-1		C50	17	85	220	4.11	0.24	1.7
BJ3-2		C50	16	85	233	2.65	0.20	1.45
BJ4-1		C60	15	100	278	3.42	0.26	1.5
BJ4-2			20	95	329	3.35	0.44	–
BJ5-1			16	100	311	3.81	–	–
BJ5-2			18	95	333	3.80	0.22	–
BJ6-1			20	90	326	3.25	0.28	1.54
BJ7-1			35	95	204	2.82	0.38	1.34
BJ8-1			35	105	354	3.90	0.24	0.78
BJ8-2			40	100	368	3.51	0.22	1.68

OAC: ordinary aggregate concrete; CAC: coral aggregate concrete.

Besides, for reinforced CAC beam with the same concrete strength, the rule of normal section V_cr and V_cs of reinforced CAC beam were as follows: 316 stainless steel > common steel > zinc-chromium-coated steel > new organic coated steel > 2205 duplex stainless steel. The main reason is as follows: (a) the stirrup shared part of the shear stress before cracks occurred, and the yield strength of common steel was lower than that of 316 stainless steel, so the stirrup shear strength of 316 stainless steel was the highest, and its normal section V_cr was the largest. (b) The V_cs of reinforced concrete beam was composed of the stirrup and the concrete. For the same concrete strength of reinforced CAC beam, as the stirrup strength increases, the stirrup shear capacity (V_s) increased gradually, indicating that the V_cs of 316 stainless steel CAC beam was the largest. (c) In the tests, the 2205 duplex stainless steel was plain round steel, which reduced the bonding strength between the steel and concrete, leading to a big slip between the steel and CAC. As a result, the normal section V_cr and V_cs were greatly reduced while the deflection increased.

Midspan deflection

Figure 4 shows bending moment–midspan deflection curves of reinforced concrete beam. As shown in Figure 4, (a) curves were divided into two stages, namely, the stage before concrete cracking and the stage from concrete cracking to failure. After the normal section was cracked, the curves showed its obvious linear feature. Upon reaching to V_cs, the components suddenly lost the bearing capacity, indicating obvious brittle failure. (b) For the same steel ratio, V_cs of reinforced CAC beam (BJ2-2) was higher than that of reinforced OAC beam (BJ1-1). Thus, the shear strength of C25-reinforced CAC beam was better than that of C35-reinforced OAC beam. Besides, the midspan deflection of BJ2-2 was larger than the BJ1-1, this is due to lots of Cl⁻ in CAC, which accelerated the steel corrosion (Da et al., 2016a), reduced the stiffness, and increased the midspan deflection. (c) As the concrete strength increases, the V_cs increased, the main reason is that V_cs was composed of concrete shear capacity (V_c) and V_s. When V_s was constant, with the increase in V_c, the V_cs increased.

Figure 4.

Bending moment–midspan deflection curves of reinforced concrete beam: (a) concrete type and strength and (b) steel type.

As is shown in Figure 4(b), the stiffness of BJ4-2 and BJ6-1 was higher than that of BJ5-2, indicating that the common steel (BJ5-2) had serious corrosion in reinforced CAC beam with a large amount of Cl⁻, which reduces the beam stiffness (Bhargava et al., 2006). However, the new organic coated (BJ4-2) and zinc-chromium coated (BJ6-1) had excellent anti-corrosion behavior to inhibit steel corrosion (Figures 8–9).

Stirrup strain

Figure 5 shows load-stirrup strain curves of reinforced CAC beam. As shown in Figure 5, as the load increases, the stirrup strain increased gradually. In the initial stage of loading, the strain of stirrups was very small. But due to the emergence of inclined section cracks, the strain of stirrups increased rapidly. Based on the mechanical test results, the strain of stirrup yield (ε) is as follows: common steel ε=f_y/E_s= 440×10⁶/(2.1 × 10⁵) = 2095 με, 2205 duplex stainless steel ε = 588 × 10⁶/(2.1 × 10⁵) = 2800 με, and 316 stainless steel ε = 805 × 10⁶ / (2.1×10⁵)= 3833 με.

Figure 5.

Load–stirrup strain curves of reinforced CAC beam.

When load reached to V_cs, the stirrups of both beam did not yield. The main reason is that the stirrup spacing was too small. Moreover, by comparing the load-stirrup strain curves of BJ3-2, BJ4-2, and BJ5-2, it is found that the strain of stirrup increased rapidly at 75, 85, and 90 kN when the inclined cracks of beam occurred, indicating that with the increase in concrete strength, the load of stirrup strain began to mutate is larger. The concretes shared part of shear strength, and the required external load increased when the stirrups began to work.

Crack width

Figure 6 is the load–maximum crack width (w_mas) curves of reinforced CAC beam. As shown in Figure 6, as the load increases, the w_mas increased gradually. In the initial loading stage, bending cracks in normal sections occur near beam midspan with slow expansion. However, as the load increases, inclined cracks are formed from the support to the concentrated force point, which eventually widen and lead to the beam failure. As shown in Figure 6(a), the rule of the bearing capacity of reinforced CAC beam with the same w_mas was as follows: BJ2-1 > BJ3-1 > BJ4-2. The result indicates that the development of w_mas was related to the concrete strength. The main reason is that the V_cs was composed of V_c and V_s; when V_s was constant, with the increase in V_c, the V_cs increased and resulted in smaller w_mas. As shown in Figure 6(b), for the reinforced CAC beam with the same w_mas (0.1 mm), the load of BJ4-2, BJ5-1, BJ6-1, BJ7-1, and BJ8-1 reached to 34.7%, 54.9%, 23.3%, 30.0%, and 42.5%, respectively, in terms of V_cs. It was obvious that the w_mas development was related to the steel type. The loads of BJ4-2 and BJ6-1 were small, mainly due to greater slip between the CAC and the coated steel that destroyed the bonding strength.

Figure 6.

Load-maximum crack width curves of reinforced CAC beam: (a) concrete strength and (b) steel type.

Calculation model

Based on the different codes, the calculation models for the V_cs of reinforced CAC beam was as follows

GB 50010 - 2010 : V_{cs} = \frac{1.75}{λ + 1} f_{t} b h_{0} + f_{yv} \frac{A_{sv}}{s} h_{0}

(1)

JGJ 12 - 2006 : V_{cs} = \frac{0.175}{λ + 1.5} f_{c} b h_{0} + 1.25 f_{yv} \frac{A_{sv}}{s} h_{0}

(2)

where V_cs is the ultimate shear capacity (kN) and λ is the shear span ratio. For the GB 50010-2010, when λ < 1.5, λ = 1.5 and when λ > 3, λ = 3; for the JGJ 12-2006, when λ < 1.4, λ = 1.4 and when λ > 3, λ = 3; f_t, f_c are the concrete axial tensile and compressive strength (MPa), respectively; b is the rectangular section width (mm); h₀ is the section effective depth (mm); f_yv is the stirrup yield strength (MPa); A_sv is the stirrup sectional area in the same section (mm²); and s is the stirrup spacing (mm).

Using equations (1) and (2), the V_cs of reinforced CAC beam was shown in Figure 7 and Table 7. The mean values of $V_{cs}^{t} / V_{cs}^{c}$ were 1.664 and 1.918, the standard deviations were 0.257 and 0.312, and the variation coefficients were 0.155 and 0.163, respectively. As shown in Figure 7 and Table 7, there is a large error between $V_{cs}^{c} and V_{cs}^{t}$ . The reasons are as follows: (a) The strength of LAC was low, whereas the CAC strength was high. (b) The coral natural porous structure and lots of Cl⁻ in CAC easily lead to the steel corrosion. Consequently, the strength and section area of stirrup were reduced, which seriously affected the shear capacity of reinforced CAC beam (Zhang et al., 2014b; Zhao et al., 2013). However, steel corrosion was not taken into account in equations (1) and (2). Above all, consider the influence of high-strength CAC, stirrup corrosion on V_c and V_s, and a calculation model suitable for the V_cs of reinforced CAC beam.

Table 7.

$V_{cs}^{c}$ and $V_{cs}^{t}$ of reinforced CAC beam.

No.	λ	h₀ (mm)	Ω (%)	$V_{cs}^{t}$ (kN)	Equation (1)		Equation (2)		Equation (7)
No.	λ	h₀ (mm)	Ω (%)	$V_{cs}^{t}$ (kN)	$V_{cs}^{c}$ (kN)	$V_{cs}^{t} / V_{cs}^{c}$	$V_{cs}^{c}$ (kN)	$V_{cs}^{t} / V_{cs}^{c}$	$V_{cs}^{c}$ (kN)	$V_{cs}^{t} / V_{cs}^{c}$
BJ2-1	1.23	162	0.60	184	122	1.508	108	1.701	166	1.112
BJ2-2	1.23	162	0.60	214	122	1.760	108	1.985	165	1.298
BJ3-1	1.23	162	0.29	220	158	1.391	135	1.626	221	0.997
BJ3-2	1.23	162	0.29	233	158	1.475	135	1.723	220	1.057
BJ4-1	1.23	162	0.19	278	172	1.617	146	1.908	242	1.150
BJ4-2	1.23	162	0.19	329	173	1.905	146	2.250	243	1.355
BJ5-1	1.23	162	0.80	354	172	1.805	146	2.425	241	1.466
BJ5-2	1.23	162	0.80	368	172	1.932	146	2.521	241	1.524
BJ6-1	1.23	162	0.18	350	171	1.963	145	2.412	240	1.455
BJ7-1	1.23	162	0.05	204	186	1.096	163	1.251	260	0.786
BJ8-1	1.23	162	0.04	254	205	1.725	187	1.356	283	0.897
BJ8-2	1.23	162	0.04	306	206	1.787	188	1.629	284	1.077

CAC: coral aggregate concrete.

Figure 7.

Comparison of $V_{cs}^{c}$ and $V_{cs}^{t}$ of reinforced CAC beam.

V_s coefficient correction

Figure 8 shows the steel corrosion status in C60-reinforced CAC beam. Figure 9 shows electrochemical test results of steel in CAC by linear polarization resistance (LPR) method and electrochemical impedance spectroscopy (EIS) method. Among them, the concrete cover thickness is 15 mm and the steel diameter is 10 mm, R_p is the polarization resistance (kΩ cm²), and R_ct is the charge transfer resistance (kΩ cm²); the larger of R_p and R_ct, the stronger anti-corrosion of steel bars in CAC. As shown in Figures 8 and 9, in addition to the stainless steels were not corroded, coated steels and common steel were corroded. Besides, in the ocean environment, the anti-corrosion of steel in CAC was as follows: 2205 duplex stainless steel > 316 stainless steel > new organic coated steel > zinc-chromium-coated steel > common steel. According to GB 50082-2009, mass loss rate (ω) of steel is given in Table 7. The research of Mohamed et al. (2014) shows that steel corrosion mainly influences the reduction of steel strength and section area. Consequently, in terms of stirrup corrosion, the calculation model for the V_cs of reinforced CAC beam is as follows

V_{cs} = \frac{0.175}{λ + 1.5} f_{c} b h_{0} + 1.25 α f_{yv} \frac{A_{sv}}{s} h_{0}

(3)

α = α_{1} \cdot α_{2} = {\begin{matrix} (1 - ω_{s}) (1 - 1.608 ω_{s}) & 0 < ω_{s} \leq 5 % \\ (1 - ω_{s}) (0.962 - 0.848 ω_{s}) & ω_{s} > 5 % \end{matrix}

(4)

where α is the stirrup corrosion reduction coefficient, ω_s is the mean section loss rate (%), and α₁, α₂ are the stirrup section and strength reduction coefficient; other parameters are equal in meaning with those in equation (2).

In the ocean environment, pitting corrosion of steel is easy to occur. Therefore, the minimum section of steel is the easiest to break. That is to say, the position of maximum section loss rate (ω_sm) is the easiest to break. Therefore, ω_sm used to calculate the α is more accurate. Wang and Zhong (2005) studied ω_sm and mean section loss rate (ω_s) of reinforced concrete, and the research showed that the ω_sm and ω_s form a linear relationship

ω_{sm} = 1.301 ω_{s}

(5)

In addition, the research shows that (Yuan et al., 2001; Zhang et al., 2014a) ω and ω_s are roughly equal. Therefore, based on rationality and practicality, α is expressed as follows

α = {\begin{matrix} (1 - 1.301 ω) (1 - 1.608 ω) & 0 < ω_{s} \leq 5 % \\ (1 - 1.301 ω) (0.962 - 0.848 ω) & ω_{s} > 5 % \end{matrix}

(6)

Figure 8.

Steel corrosion status in C60 reinforced CAC beam (test time: 90 days).

Figure 9.

Electrochemical test results of steel in CAC: (a) LPR method and (b) EIS method (test time: 90 days).

V_c coefficient correction

According to equation (3), V_c could be replaced by (V_cs−1.25αf_yvh₀A_sv/s). Figure 10 shows the relationship between V_c/(f_cbh₀) and λ with different reinforced CAC beam. As shown in Figure 10, the $V_{c}^{t}$ of four reinforced CAC beams are smaller than the $V_{c}^{c}$ by equation (3). Therefore, the 0.175/(λ + 1.5) was high, and it was not safe to design the V_c of reinforced CAC beam according to JGJ 12-2006.

Figure 10.

Relationship between V_c/(f_cbh₀) and λ of reinforced CAC beam.

While calculating the V_cs of reinforced OAC beam, the rule for coefficient of V_c was as follows: at the range of the shear compression failure (λ = 1–3), the coefficient indicated the “lower enveloping curve” of all test points. For V_cs of reinforced CAC beam in this test λ = 1.23 and in the study by Zhang (1995), λ = 0.84–2.60. As shown in Figure 10, when λ ≤ 1.3, the coefficient of V_c can be 0.104. When λ ≥ 2.8, the coefficient of V_c can be 0.022. Therefore, the coefficient of V_c could be obtained as follows: 0.1/(2.4(λ − 0.9)), namely, 0.042/(λ − 0.9).

Therefore, comprehensively consider the influence of high-strength CAC and stirrup corrosion, and the calculation model for the V_cs of reinforced CAC beam was as follows

V_{cs} = V_{c} + V_{s} = \frac{0.042}{λ - 0.9} f_{c} b h_{0} + 1.25 α f_{yv} \frac{A_{sv}}{s} h_{0}

(7)

where V_c and V_s are shear capacity of concrete and stirrup (kN), and other parameters are equal to those in equations (2) and (6).

Using equation (7), the V_cs of reinforced CAC beam was shown in Figure 7 and Table 7. The mean value of $V_{cs}^{t} / V_{cs}^{c}$ was 1.197, and the standard deviation and variation coefficients were 0.183 and 0.153, respectively. Compared with the results according to GB 50010-2010, JGJ 12-2006, and Zhang (1995), the mean value was approximated to 1, the standard deviation decreased by 28.9%, 41.3%, and 31.5%, respectively, and the variation coefficient decreased by 1.2%, 6.0%, and 3.4%, respectively. Therefore, equation (7) is the optimal model.

Calculation model verification

The V_cs of 11 reinforced CAC beams in Zhang (1995) was calculated according to equation (7). The basic parameter and calculation results of reinforced CAC beam were shown in Figure 11 and Table 8, and the literature (Zhang, 1995) model of $V_{cs}^{c}$ and $V_{cs}^{t}$ was exactly in agreement with the results of equation (7). In literature (Zhang, 1995) model, the mean value of $V_{cs}^{t} / V_{cs}^{c}$ was 1.072 and the standard deviation and variation coefficient were 0.442 and 0.412, respectively. In equation (7), the mean value of $V_{cs}^{t} / V_{cs}^{c}$ was 1.052 and the standard deviation and variation coefficient were 0.223 and 0.212, respectively. By comparison of the standard deviations and variation coefficients of $V_{cs}^{t} / V_{cs}^{c}$ , the discreteness of shear capacity model proposed in this study was less than the calculation model in literature (Zhang, 1995). Therefore, equation (7) is more reasonable.

Table 8.

$V_{cs}^{t} and V_{cs}^{c}$ of reinforced CAC beam based on equation (7) and Zhang (1995) model.

No.	Λ	b (mm)	h₀ (mm)	f_c (MPa)	f_yv (MPa)	s (mm)	$V_{cs}^{t}$ (kN)	Zhang (1995)		Equation (7)
No.	Λ	b (mm)	h₀ (mm)	f_c (MPa)	f_yv (MPa)	s (mm)	$V_{cs}^{t}$ (kN)	$V_{cs}^{c}$ (kN)	$V_{cs}^{t} / V_{cs}^{c}$	$V_{cs}^{c}$ (kN)	$V_{cs}^{t} / V_{cs}^{c}$
BV1-2	1.40	121	179	32.9	260	200	98.4	61.4	1.603	79.2	0.805
BV1-3	1.97	120	178	30.5	260	200	48.0	61.6	0.779	44.8	0.933
BV1-4	2.53	121	178	30.9	260	200	35.6	44.1	0.807	36.4	1.021
BV1-5	3.07	123	179	30.9	260	200	30.0	34.1	0.880	32.5	1.083
BV2-1	1.12	122	179	32.6	260	120	134.0	–	–	168.1	1.254
BV2-2	1.67	124	180	32	260	120	99.5	68.1	1.461	71.3	0.717
BV2-3	2.22	124	180	32	260	120	65.0	56.6	1.149	55.1	0.848
BV3-1	1.12	118	178	26.8	260	200	87.0	45.4	1.916	126.7	1.456
BV3-2	1.69	122	178	26.4	260	200	47.0	75.0	0.627	49.7	1.057
BV3-3	2.23	122	179	26.4	260	200	34.2	43.3	0.790	37.5	1.097
BV3-4	2.79	122	179	26.4	260	200	24.7	35.0	0.706	32.1	1.301

CAC: coral aggregate concrete.

Figure 11.

Comparison of $V_{cs}^{t} and V_{cs}^{c}$ of reinforced CAC beam based on equation (7) and Zhang (1995) model.

Conclusion

The failure mode of reinforced OAC beam and reinforced CAC beam was basically the same. In addition, due to the coral naturally porous structure, which has the characteristic of “absorb and return water,” this characteristic can effectively inhibit the development of inclined section cracks.

As the concrete strength increases, the normal section V_cr and inclined section V_cr and V_cs of reinforced CAC beam increased gradually. Furthermore, V_cr and V_cs of reinforced CAC beam were as follows: 316 stainless steel > common steel > zinc-chromium coated steel > new organic coated steel.

For the CAC structure in ocean engineering, in order to prolong its service life, the use of new organic coated steel was suggested.

Comprehensively considering the influence of high-strength CAC and stirrup corrosion, the calculation model for the V_cs of reinforced CAC beam was presented and was then verified.

Footnotes

Appendix 1 Acknowledgements

The authors gratefully acknowledge the financial supports from the National Natural Science Foundation of China under Grant Nos 11832013, 51678304, and 51878350; the Natural Science Foundation of Jiangsu Province under Grant No. BK20180433; the Guangxi Science Fund for Distinguished Young Scholars under Grant No. 2019GXNSFFA245004; and the Systematic Project of Guangxi Key Laboratory of Disaster Prevention and Structural Safety under Grant No. 2019ZDK006.

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) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Bo Da

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Study on shear behavior of reinforced coral aggregate concrete beam

Abstract

Keywords

Introduction

Experiment

Raw materials

Component preparation

Test method

Results and discussion

Failure mode

Bearing capacity

Midspan deflection

Stirrup strain

Crack width

Calculation model

Vs coefficient correction

Vc coefficient correction

Calculation model verification

Conclusion

Footnotes

Appendix 1

Acknowledgements

Declaration of Conflicting Interests

Funding

ORCID iD

References

V_s coefficient correction

V_c coefficient correction