Investigating the shear behaviors of hollow core beams strengthened with ESS-HCC and shear steel rebars

Abstract

Insufficient shear load-carrying capacity of hollow slab bridges is caused by the web cracks and damage of hinged joints generated with the increasing traffic volumes, service life and degradation of material properties. The authors propose a novel composite strengthening method to improve the shear load-carrying capacity, a novel composite strengthening method is proposed by authors. It is defined as filling ESS-HCC (early-strength self-compacting shrinkage-compensating high-performance cementitious composite) and shear steel rebars. In this paper, nine hollow core beams (HCBs) were conducted and investigated. The main parameters were shear span-to-depth ratios and opening sizes. The failure mode and crack morphology, load-deflection behaviors and concrete strains were measured and analyzed. The experimental results showed that the HCB specimens strengthened with ESS-HCC and shear steel rebars exhibited excellent ductility. The shear load-carrying capacity showed a decreased tendency with the increase of the shear span-to-depth ratios. However, the opening sizes had little influence on the shear load-carrying capacity. According to ACI 318 (2019), EN 1168 (2005), GB 50010 (2010), and JTG 3362 (2018) standards, four modified models were proposed to evaluate the shear behaviors of the HCB specimens strengthened with ESS-HCC and shear steel rebars. Simultaneously, the influence of shear span-to-depth ratios on shear behaviors was considered. The theoretical results clearly showed reasonable accuracy with the experimental results. Combined with the ABAQUS finite element models, the optimum strengthened length was 0.2 times the length of the HCB specimens. The strength grade of the ESS-HCC should be one or two higher than that of the old concrete’s, which can obtain the most excellent shear stress.

Keywords

Hollow core beams ESS-HCC shear span-to-depth ratio opening sizes shear load-carrying capacity

Introduction

Hollow core beams (HCBs) are widely used in prefabricated buildings and bridges due to their excellent characteristics (Li et al., 2018; Liu et al., 2020; Thienpont et al., 2022). However, the web shear failure and damage to the hinged joints are common diseases due to the thinner web (Zhang et al., 2022). Many strengthening methods have been proposed by researchers. Some of them can effectively solve the shear cracking problem. For example, the core-filling method, enlarging sections, bonding carbon fibre-reinforced polymers (Duan et al., 2020) and sheets (Wu et al., 2017), external prestressing, and hybrid strengthening methods. The existing investigations showed that the core-filling method could significantly improve the shear behaviors of the HCBs (Du et al., 2023; Yang et al., 2021). The mechanical properties of the filler materials need to be studied to determine whether it they behave like unreinforced concrete or fully prestressed concrete (McDermott and Dymond, 2020). The results showed that the filler materials act as unreinforced concrete when it used to strengthen the damaged structures. Most investigations are mainly focused on the prestressed HCB specimens. The steel fiber-reinforced concrete, wire meshes, and concrete were used as filler materials to discuss (Lee et al., 2020). Because the compression strength of new concrete (28.3 MPa) was much lower than that of old concrete (60.5 MPa). The experimental results showed that the filler materials had little influence on the shear strength. In the core-filling method, researchers found that the number of filled cores shear reinforcement ratio, and strengthened length significantly influenced on the shear behaviors of the HCBs (Joo et al., 2020, 2021). The results showed that the shear strength of the prestressed HCB specimens with two middle filled cores was higher than that of four filled cores under the same conditions. The shear strength decreased with increased filled cores because interface slip occurred between prestressed HCB specimens and filled cores. Therefore, the influence of interface slip should be considered in the core-filling method. The higher shear reinforcement ratios had little influence on shear strength. It was suggested that the helix shear reinforcement rebars should be placed in the region where shear cracks occurred. Zhang et al. (2020) investigated the influence of the strengthened length on the prestressed concrete HCBs with a span of 20 m. Compared with the un-strengthened beam, the shear strain of the HCB specimens strengthened with the core-filling method in the shear-compression zone decreased by 40%. The strengthened length was two times of the height of the HCB specimen. Simultaneously, the load-carrying capacity of the substructure should be recalculated because of adding the self-weight of filled materials. Except for the strengthened length, the interface behaviors between new and old concrete have lagersignificantly affect on the shear behaviors. Araújo et al. (2020) found expansive additives can compensate for concrete shrinkage and improve interface properties between new and old concrete. The investigation provides a reference for the design of the filler material in this paper.

Moreover, little investigation is available to investigate the influence of the shear span-to-depth ratios and opening sizes on the shear behaviors of the HCB specimens strengthened with ESS-HCC (early-strength self-compacting shrinkage-compensating high-performance cementitious composite) and shear steel rebars. The expansive additive and copper-coated steel fibers were chosen to improve the shrinkage performance and cracking resistance of the ESS-HCC, respectively. Then, the modified and finite element models were used to evaluate and simulate the shear behaviors of the HCB specimens strengthened with ESS-HCC and shear steel rebars. The theoretical and simulation results showed good agreement with the experimental results. Finally, a parametric study was performed to evaluated the shear behaviors of strengthened HCB specimens. The optimum strengthened length, ESS-HCC strength grade, and parameters of shear steel rebars were given.

Experimental programme

Material properties

The HCB specimens were made of ready-mix concrete with a concrete grade of C50. During the process of casting HCB specimens, three cubic samples (150 mm × 150 mm × 150 mm) were reserved to measure the 28-days compressive strength of the concrete. The average values were found to be 57.35 MPa. The detail of the ESS-HCC matrix can be referred to the previous study (Du et al., 2022, 2023). The average compression strength of the ESS-HCC was determined to be 61.99 MPa. Two 14 mm diameter and two 28 mm diameter steel reinforcements were arranged in the tensile zone. Three ribbed bars with a diameter of 10 mm were placed in the compression zone. The diameter and spacing of stirrups were 8 mm, 100 mm, and 200 mm, respectively. The mechanical properties of steel are given in Table 1.

Table 1.

Mechanical Properties of Steel.

Diameter (mm)	Yield strength (MPa)	Tensile strength (MPa)	Elongation (%)	$R_{m}^{0} / R_{e l}^{0}$	$R_{e l}^{0} / R_{e l}$
8	540	645	12.1	1.19	1.35
10	470	565	13.3	1.20	1.18
14	410	560	14.7	1.37	1.07
28	455	620	15.8	1.36	1.14

Note: R⁰_m represents the measured tensile strength, R⁰_el represents the lower yield strength, R_el represents the eigenvalue of yield strength.

Details of the specimens

Nine HCB specimens were conducted in this study. The section details of the HCB specimens are shown in Figure 1. The cross-section and length of the HCB specimen were similar with to the previous research study (Du et al., 2023). The width, height, and length of the HCB specimens were 400 mm, 350 mm, and 8000 mm, respectively. The ratio of the void to cross-section was 35%. The concrete protective cover of all HCB specimens was 30 mm. Figure 1(a) shows the spacing of stirrups is 100 mm at 800 mm from the end of HCB specimens, and the other positions are 200 mm. The cross-sections of un-strengthened and strengthened HCB beams are shown in Figure 1(b)∼(c). The strengthened length was 1600 mm. The shear steel rebars’ diameter, spacing, and length were 8 mm, 200 mm, and 216 mm, respectively. They were used to improve the mechanical properties of the HCB specimens. Figure 2 shows the design of opening sizes. Two small opening sizes are 100 mm × 100 mm and 200 mm × 100 mm, respectively, as shown in Figure 2(a). The distances between small openings and edges of the HCB specimens were 300 mm and 1200 mm, respectively. The Whole opening size is 1600 mm × 100 mm, as shown in Figure 2(b). Details of all HCB specimens are shown in Table 2. Each beam is named using an HCB-C/S-i format. The letter C and S indicate shear behaviors and control specimens, respectively. The letter i represents the number of the HCB specimens. The opening sizes were preserved in the HCB specimen. The HCB-C/S-1 specimens are mainly used to investigate the variation in the spacing of stirrups. Figure 3 shows the detail of the spacing of the stirrups. The loading point was designed on the interface of variation in the spacing of stirrups (i.e., the end of stirrups with a spacing of 100 mm and the beginning of stirrups with a spacing of 200 mm). The HCB-C/S-2 and HCB-C/S-3 specimens are mainly used to investigate the influence of shear span-to-depth ratios (a₁/d) on the shear behaviors. d is the distance from extreme compression fiber to the centroid of longitudinal tension reinforcement. The HCB-C/S-4 specimens are mainly investigate used to investigate the interfacial behaviors between un-strengthened and strengthened zones. The HCB-C/S-2 and HCB-C/S-5 specimens are used primarily to investigate the influence of opening sizes on the shear behaviors. In Table 2, a₁ is the distance from the loading point to the edge of support (JTG 3362, 2018). λ₁ is the shear span-to-depth ratio (Aldemir et al., 2022).

Figure 1.

Section details of the HCB specimens (Unit: mm): (a) Elevation view, (b) Cross-section of un-strengthened beam, (c) Cross-section of strengthened beam.

Figure 2.

Design of opening sizes (Unit: mm): (a) 100 mm × 100 mm and 200 mm × 100 mm, (b) 1600 mm × 100 mm.

Table 2.

Details of Test Specimens.

Specimens	a₁ (mm)	λ ₁	Strengthening method	Experimental details
HCB-C-1	425	1.39	None	Variation in spacing of stirrups
HCB-C-2	725	2.38		1< λ < 3
HCB-C-3	1125	3.69		λ > 3
HCB-C-4	1325	4.34		Interface between unstrengthened and strengthened zones
HCB-S-1	425	1.39	Core-filling method	Variation in spacing of stirrups
HCB-S-2	725	2.38x		1< λ < 3
HCB-S-3	1125	3.69		λ > 3
HCB-S-4	1325	4.34		Interface between unstrengthened and strengthened zones
HCB-S-5	725	2.38		Opening sizes (100 mm × 1600 mm)

Figure 3.

Detail of spacing of the stirrups (HCB-C/S-1 specimens).

Instrumentation and testing procedure

The strengthening process was similar to the author’s previous research (Du et al., 2023). Each HCB specimen was tested using a single-point loading manner. The roller and pin supports were selected to simulate a simply supported beam. The variation in vertical loading was monitored throughout the test process using a load cell connected to a 1000 kN hydraulic jack. Figure 4 demonstrates the test setup of the HCB specimen. Each HCB specimen was tested twice to achieve more data. The average value was used to analyze the shear behaviors. The span length between the roller and pin supports was 6300 mm. The distance of the pin and roller supports from both ends of the specimen were 200 mm and 1500 mm, respectively. The distance between the roller support and the end of the HCB specimen exceeded the distance from the applied point load to the pin support (McDermott and Dymond, 2020). This ensured the first test results had a little influence on the opposite end when the HCB specimens were rotated and tested. Before concrete cracking, the loading rate was 0.2 mm/min. A concentrated load was applied on the top of specimens with a loading rate of 0.3 mm/min after concrete cracking. Liner variable differential transducers (LVDTs) were arranged to measure vertical displacements (Alnuaimi and Bhatt, 2006) and slip. Strain gauges and rosettes are used to measure the concrete strains at mid-span and web sections, respectively, as shown in Figure 5. The crack propagation paths were recorded with the increasing load, and a crack observer measured the maximum crack width.

Figure 4.

Test setup. (a) Shear test setup, (b) Test specimen.

Figure 5.

Measurement arrangement.

Experimental results and discussion

Failure mode and crack morphology

Figure 6 exhibits the failure modes of all HCB specimens. No obvious interface slip phenomena were observed between ESS-HCC and concrete. Failure modes of all HCB specimens were changed from web-shear to bending shear failure with the increasing of shear span-to-depth ratios. The brittle failure occurred on the control specimens and shear cracks generated on the web (shear span-to-depth ratio is small). While the flexural shear cracks generated on the strengthened specimens and showed more excellent ductility. The applied loads corresponding to the first oblique crack increased with the increasing of shear span-to-depth ratios. The ratios of cracking load and ultimate load varied from 0.32 to 0.46. The transverse cracks were observed on the section of 50 mm distance from the bottom of all HCB specimens. The ratios of applied load corresponding to the transverse cracks and ultimate load varied from 0.40 to 0.63.

Figure 6.

Failure models of all HCB specimens: (a) HCB-S-1, (b) HCB-S-1, (c) HCB-C-2, (d) HCB-S-2, (e) HCB-C-3, (f) HCB-S-3, (g) HCB-C-4, (h) HCB-S-4, (i) HCB-C-5 (1), (j) HCB-S-5 (2).

Load-deflection behaviors

Figure 7 shows the load-deflection behaviors of all HCB specimens. The shear load-carrying capacity exhibited a decreasing tendency with the increase in shear span-to-depth ratios. The web shear strength near the supports was sharply improved. The cracking load of the HCB-C/S specimens was about 6.7% to 13.5% of the corresponding ultimate loads. While the yielding loads were about 75.26% to 96.34 % of the ultimate loads. The ESS-HCC can improve the cracking and yielding loads. Compared with the control specimens, the cracking and yielding loads of strengthened specimens showed a decreasing tendency with the increasing of the shear span-to-depth ratios. The initial stiffness (Di et al., 2020; Du et al., 2021, 2023) of the HCB-S-1 specimen increased by 64.51% compared with the HCB-C-1 specimen. With the increasing of the shear span-to-depth ratios, the initial stiffness showed a decreasing tendency. Compared with the HCB-S-2 specimen, the initial stiffness of the HCB-S-5 specimen decreased by 6.86%. The whole opening size had a negligible influence on the shear load-carrying capacity. Therefore, the top concrete was partially not fully removed when the actual bridges were strengthened with the core-filling method. The opening sizes should meet the requirements of ESS-HCC injection.

Figure 7.

Load-deflection curves of all HCB specimens.

Table 3 shows the experimental results of all HCB specimens. In Table 3, F_c, F_y, and F_u are the cracking loads corresponding to the first crack generated on the HCB specimens, yielding load and ultimate load, respectively. CD, YD, and UD are the cracking deflection, yielding deflection, and ultimate deflection corresponding to F_c, F_y, and F_u, respectively. Compared with the HCB-S-1 specimen, the shear load-carrying capacity of the HCB-S-2 and HCB-S-4 specimens decreased by 54.16% and 31.33%, respectively. The results showed that the variation in spacing of the stirrups significantly influenced the on the shear load-carrying capacity. Therefore, the additional shear steel rebars should be added in the HCB specimens where the spacing of stirrups was relatively large. The shear load-carrying capacity of the HCB-S-4 specimen was lower than that of other specimens. Because a stiffness plummet occurred on the interface between un-strengthened and strengthened zones. It also indicated that the appropriate stiffness of the filler material should be considered. Simultaneously, the shear behavior of the interface between ESS-HCC and concrete needs other ways to strengthen. Compared with the shear load-carrying capacity of the HCB-S-2 specimen, the HCB-S-5 specimen only improved by 0.55%. The shear behaviors of the HCB specimens with small opening sizes were more excellent than those of whole opening sizes.

Table 3.

Experimental Results of all HCB Specimen.

Specimens	λ ₁	F_c (kN)	CD (mm)	F_y (kN)	YD (mm)	F_u (kN)	UD (mm)
HCB-C-1	1.39	41.00	2.73	237.64	20.01	303.79	25.84
HCB-C-2	2.38	22.00	3.00	–	–	327.97	39.02
HCB-C-3	3.69	23.00	3.52	186.13	33.19	220.25	40.24
HCB-C-4	4.34	15.20	2.53	139.53	32.56	185.40	44.85
HCB-S-1	1.39	43.25	2.99	447.15	21.50	480.70	40.13
HCB-S-2	2.38	44.50	4.99	308.10	29.70	330.10	59.24
HCB-S-3	3.69	25.65	2.5p8	205.20	35.45	220.35	62.97
HCB-S-4	4.34	15.05	2.82	188.25	40.75	195.40	62.10
HCB-S-5	2.38	33.05	5.30	310.15	32.65	331.90	57.32

An approximate negative correction exists between shear-to-span ratios and shear load-carrying capacity. The relationship can be expressed as an exponential function. The ductility coefficient was defined as the ratio of deflection measured at 80% of the maximum shear load and that at the initial shear cracking (Jin et al., 2021; Lee et al., 2020). The ductility coefficients showed a decrease tendency with the increase in shear span-to-depth ratios. Combined with the Figure 7, the HCB-S-1 and HCB-S-2 specimens exhibit an excellent initial stiffness and ductility coefficients. Compared with the HCB-S-2 specimen, the ductility coefficient of the HCB-S-5 specimen decreased by 24.56%. Therefore, the complete removal of the top concrete was not recommended in this composite strengthening method.

Concrete strains

The strain rosettes were designed to measure the concrete strains in the shear-compression zone. The variation of the shear span-to-depth ratios determined the number of strain rosettes. The strain gauge of 45° direction (ε₄₅) was perpendicular to the connection between the applied load point and the nearest support. ε₄₅ was used to examine the abdominal shear oblique crack. The other two directions (ε₀ and ε₉₀) were perpendicular to each other. The principal strains and inclination angle of the principle tensile strain of concrete were calculated as follows (Di et al., 2020; Du et al., 2024):

ε_{\max / \min} = 0.5 [(ε_{0} + ε_{90}) \pm \sqrt{2 [{(ε_{0} - ε_{45})}^{2} + {(ε_{45} - ε_{90})}^{2}]}]

α_{0} = 0.5 \arctan [(2 ε_{45} - ε_{0} - ε_{90}) / (ε_{0} - ε_{90})]

where ε_max and ε_min are the principal tensile and compression strain, respectively, α₀ is the inclination of the principle tensile strain, ε_i (i = 0, 45, 90) is the concrete strain of three directions in strain rosettes.

Figure 8 illustrates the principle strain of concrete in the HCB-C/S-1 specimen. In this Figure, the notation of No. i (i = 1, 2) indicates the number of strain rosettes in the HCB-C/S-1 specimens. T and C indicate the principal tensile strain and compression strain, respectively. Figure 8(a) demonstrates that the values of the principal tensile and compression strain are basically identical. Simultaneously, the direction of them was perpendicular to each other before the concrete cracked. However, the stress redistribution occurred after concrete cracking. Figure 8(b) presents the inclination angle of the principal tensile strain, which varies from 25° to 40°. These calculated values were consistent with the experimental phenomenon. For the simply supported beam, the bending moment of the No. 2 strain rosette was close to the applied load point. The angle of the principal tensile strain of the No. 2 strain rosette was relatively larger than that of the No. 1 strain rosette.

Figure 8.

Principle strain of concrete in the HCB-C/S-1 specimen: (a) Load versus Principal strain of the HCB-C/S-1 specimen, (b) Load versus Inclination angle of principle tensile strain of the HCB-C/S-1 specimen.

Theoretical evaluation of the shear load-carrying capacity of the HCB specimens

The equations for calculating the shear load carrying capacity of the HCB beams strengthened with ESS-HCC and shear steel rebars were scarce. In the ACI Committee (2019), EN 1168 (2005), GB 50010 (2010), and JTG 3362 (2018) standards, only the EN 1168 standard provided the calculation equations. Simultaneously, the relative investigations showed that the total shear capacity of the HCB beams strengthened the core-filling method, including the summation of the shear contributions from the HCB member (V_c), core-filling concrete (V_core) and stirrups (V_sv) (Joo et al., 2021). The corresponding equations for calculating the shear load-carrying capacity of reinforced concrete structures according to the above four standards are summarized in Table 4.

Table 4.

Code Equations for Calculating the Shear Strength of Reinforced Concrete Structures.

Standards	V_core (kN)	V_c (kN)	V_s (kN)
ACI 318	–	$V_{c} = 0.17 λ \sqrt{f_{c}^{'}} b_{w} d$	$V_{s} = \frac{A_{t} f_{y t} d}{s}$
BS EN 1168	$V_{c o r e} = \frac{2 n b_{c} d_{1} f_{c t d}}{3}$	$V_{c} = [0.18 k {(100 ρ_{l} f_{c k})}^{1 / 3}] b_{w} d$	$V_{s} = \frac{A_{t} f_{y t} (0.9 d)}{s} \cot θ$ $1.0 \leq \cot θ < 2.5$
GB 50010	–	$V_{c} = α_{c v} f_{t} b h_{0}$	$V_{s} = \frac{f_{y t} A_{t} h_{0}}{s}$
JTG 3362	–	$V_{c s} = 0.45 \times 10^{- 3} α_{1} α_{2} α_{3} b h_{0} \sqrt{(2 + 0.6 P) \sqrt{f_{c u, k}} (ρ_{s v} f_{s v})}$

Note: versus is the shear contributions from tensile reinforcement.

It can be concluded that the shear load-carrying capacity of the ACI 318 standard (V_ACI318) and EN 1168 standard (V_EN1168) did not influence on the shear span-to-depth ratios. The shear load-carrying capacity of the GB 50010 standard (V_GB50010) and JTG 3362 standard (V_JTG3362) showed a decreasing tendency with the increase in shear span-to-depth ratios. However, the experimental results showed that the shear span-to-depth ratios had a significantly influenced the shear load-carrying capacity. Therefore, the modified formulas are obtained considering the influence of shear span-to-depth ratios, as shown in equations (1) to (4).

V_{A C I 318} = [m + n \exp (λ_{1} / k)] (0.17 λ \sqrt{f_{c}^{'}} b_{w} d + 0.17 \sqrt{f_{c}} b_{c} d_{1}) + \frac{A_{t} f_{y t} d}{s}

(1)

V_{E N 1168} = [m + n \exp (λ_{1} / k)] [0.18 k {(100 ρ_{l} f_{c k})}^{1 / 3} b_{w} d + κ \frac{2 n}{3} b_{c} d f_{c t d}] + \frac{A_{v} (0.9 d) f_{y t}}{s} \cot θ

(2)

V_{G B 50010} = [m + n \exp (λ_{1} / k)] (f_{t} b h_{0} + f_{e t} b_{1} h_{1}) + f_{y v} \frac{A_{v}}{s} h_{0}

(3)

V_{J T G 3362} = 0.45 \times 10^{- 3} \times α_{1} α_{3} [a + b \exp (λ_{1} / c)] \sqrt{(2 + 0.6 P) ρ_{s v} f_{s v}} (ψ_{c s} b_{w} h_{0} f_{c u, k}^{1 / 4} + b_{j} h_{j} f_{s u, k}^{1 / 4})

(4)

where, m, n, and k are the constant, respectively. A_t is the area of stirrups within spacing s (mm²), b_w and b_c are the web width of the HCB specimen and filled core, respectively (mm), d is the distance from extreme compression fiber to centroid of longitudinal tension reinforcement (mm), d₁ is the effective depth of the ESS-HCC (mm), f_c^’ and f_c are the specified compressive strength of concrete and actual compressive strength of the ESS-HCC, respectively (MPa), f_yt, f_ctd^, and f_ck are the specified yield strength for nonprestressed reinforcement, tensile strength of the ESS-HCC and compressive strength of concrete, respectively (MPa), s is the spacing of stirrups (mm), λ is the modification factor to reflect the reduced mechanical properties of lightweight concrete relative to normal weight concrete of the same compressive strength, α_cv is the coefficient related to shear span-to-depth ratio, f_et and f_t are the tensile strength of the ESS-HCC and main concrete (MPa), respectively, b₁ and b are the width of the ESS-HCC and HCB specimen (mm), respectively, h₀ and h are the height of the ESS-HCC and HCB specimen (mm), respectively.

The main experimental results are summarized in Table 5. V_i represents the experimental and calculation values according to the test and four standards, i is exp, ACI 318, EN 1168, GB 50010, and JTG 3362 standards, respectively. The average experimental and calculation values ratios were 0.95, 0.97, and 1.00, respectively. The standard deviation and coefficient of variance were 0.07 and 0.06, respectively. The relative errors of the HCB-S-4 specimen were 0.88 according to the ACI 318 and JTG 33362 standards. That’s because the stiffness mutation occurred at the interface of un-strengthened and strengthened zones. The high accuracy also indicated that the equations (1) to (4) can explain the shear behaviors of the HCB specimens strengthened with ESS-HCC and shear steel rebars.

Table 5.

Verification Results of Proposed Equations.

Specimens	λ ₁	Vexp (kN)	VACI318 (kN)	Vexp/V_ACI318	VEN1168 (kN)	V_exp/V_EN1168	VGB50010 (kN)	V_exp/V_GB50010	VJTG3362 (kN)	V_exp/V_JTG3362
HCB-S-1	1.39	480.70	464.48	1.03	477.09	1.01	472.44	1.02	480.35	1.00
HCB-S-2	2.38	330.10	363.56	0.91	347.02	0.95	345.32	0.96	330.70	1.00
HCB-S-3	3.69	220.35	222.99	0.99	205.55	1.07	207.06	1.06	221.07	1.00
HCB-S-4	4.34	195.40	222.99	0.88	205.55	0.95	207.06	0.94	221.07	0.88
Average				0.95		1.00		1.00		0.97
Standard Deviation				0.07		0.06		0.06		0.06
Coefficient of variance				0.07		0.06		0.06		0.06

Numerical analysis

Finite element model

Due to the limited number of tests, the ABAQUS software was selected to simulate the shear behaviors of the HCB specimens (Ellobody 2016; Wang et al., 2022). The stress-strain relationship of concrete and steel reinforcements was similar to the previous study (Du et al., 2023). Concrete and steel rebars were modeled by 8-node linear brick elements (C3D8R) and truss elements (T3D2), respectively. The slip between ESS-HCC and concrete was ignored. The concrete damage plasticity model was used to simulate the nonlinear behavior of concrete. The ratio of initial biaxial compressive yield stress to initial uniaxial compressive yield stress (f_b0/f_c0) was 1.16. The ratio of the second stress invariant on the tensile meridian to that on the compressive meridian (K_c) was 0.6667. The eccentricity (∈) and dilation angle (ѱ) were 0.1 and 30°, respectively. The maximum principle tensile stress was 0.33 $\sqrt{f_{c}^{'}}$ (Wahyuni et al., 2012). According to the test results, the maximum principle tensile stress was 2.5 MPa. The elastic stress-strain behavior of steel rebars was adopted (Du et al., 2023). The relationship of stress and strain was linear before the steel rebars yielding. While the stress remained stable when the strain was more than 0.01. The boundary conditions of the simplified beam were roller (left end) and pinned supports (right end). The control and strengthened specimens are shown in Figure 9.

Figure 9.

Finite element models of the HCB specimens: (a) Un-strengthened specimen (b) Strengthened specimen.

Result of simulation

Shear span-to-depth ratio

Figure 10 shows the comparison of load-deflection curves from experimental and finite element analysis. The force loading method was selected to simulate the shear behaviors of the HCB specimens. The shear behaviors of the HCB specimens showed a decreasing tendency with the increasing of shear span-to-depth ratios. The initial stiffness of finite element modes was higher than that of experimental results. That’s because the defects of concrete and steel rebars were not considered. It can be seen that the simulation results of strengthened HCB specimens showed a good agreement with experimental data. Simultaneously, the high accuracy and feasibility of the simulation with the finite element method were verified. These finite element models of strengthened HCB specimens can be used to investigate the strengthened parameters. Table 6 gives the comparison of results of the experimental and finite element results. It can be concluded that the relative error of shear load-carrying capacity of the un-strengthened and strengthened HCB specimens was within 10%. The predicted finite element model’s stiffness was a little higher than that of the experimental result. The reason was that the slip between concrete and steel needed to be considered.

Figure 10.

Comparison of load-deflection curves from experimental and finite element analysis: (a) Un-strengthened specimen (b) Strengthened specimen.

Table 6.

Comparison of Experimental and Finite Element Results.

Specimens	a₁ (mm)	λ ₁	U_e (mm)	U_s (mm)	(U_s–U_e)/U_e (%)	F_e (kN)	F_s (kN)	(F_s–F_e)/F_e (%)
HCB-C-1	425	1.39	26	52	100.00	303.8	291.16	−4.16
HCB-C-2	725	2.38	35	43	22.86	286.3	270.65	−5.47
HCB-C-3	1125	3.69	37	53	43.24	202.3	184.19	−8.95
HCB-C-4	1325	4.34	45	50	43.24	183.6	171.53	−6.57
HCB-S-1	425	1.39	40	44	−9.09	474.6	483.00	−1.74
HCB-S-2	725	2.38	40	43	7.50	326.8	317.00	−3.00
HCB-S-3	1125	3.69	52	55	5.77	219.1	220.00	0.41
HCB-S-4	1325	4.34	68	70	2.94	196.4	191.00	−2.75
HCB-S-5	725	2.38	45	49	8.89	331.7	321.00	−3.23

The shear stress of the HCB-C/S-2 specimens was investigated to study the strengthening effectiveness. Figure 11 illustrates the shear stress of the HCB specimen before and after strengthening. In Figure 11, the gray area represents shear stress, which is more than 2.50 MPa (Collins and Mitchell, 1991; Wahyuni et al., 2012). It can also represent the tendency to generate and develop shear cracks. The ultimate load of the HCB-C-2 specimen was 270.65 kN. Compared with the HCB-C-2 specimen, the gray area on the web of the HCB-S-2 specimen was dramatically reduced. It can be concluded that the ESS-HCC can improve the shear stress of the web.

Figure 11.

Shear stress of the HCB specimen ( $λ_{1}$ = 2.38): (a) Before strengthening, (b) After strengthening.

Opening sizes

In this strengthening method, the opening sizes of filling ESS-HCC had a influence on the shear behaviors. Figure 12 shows the comparison of load-deflection curves of the HCB-S-2 and HCB-S-5 specimens between simulation results and tests data. It can be seen that the opening sizes had little influence on shear load-carrying capacity. Compared with the HCB-S-5 specimen, the shear load-carrying capacity and shear stress of the HCB-S-2 specimen decreased by 0.54% and 57.98%, respectively. Combined with the experimental phenomenon, the interface properties of the HCB-S-5 specimen were lower than that of the HCB-S-2 specimen. Therefore, the opening sizes only need to meet the requirements of filling ESS-HCC considering the environmental impact and low-carbon benefit.

Figure 12.

Comparison of the load-defection curves of the HCB-S-2 and HCB-S-5 specimens.

Analysis of factors affecting shear behaviors

In this part, the strengthened length, ESS-HCC strength grade, and parameters of shear reinforcement as main parameters were investigated, respectively.

Strengthened length

For this strengthening method, the strengthened length significantly influenced the HCB specimens’ behaviors. The optimum strengthened length ensures that additional self-weight meets the requirements and can dramatically improve shear behaviors. In this part, the load-deflection curves were investigated with different strengthened lengths.

Figure 13 shows the influence of strengthened length on load-deflection curves of the HCB specimens with different shear span-to-depth ratios. When the shear span-to-depth ratio was 1.39, the shear load-carrying capacities were 421.65 kN, 451.08 kN, and 467.76 kN corresponding to the strengthened lengths were 700 mm, 1200 mm, and 1600 mm, respectively. The maximum increment of shear load-carrying capacities is 10.94% between two adjacent strengthened lengths, as shown in Figure 13(a). When the shear span-to-depth ratio is 2.38, the maximum increment is 16.78%, as shown in Figure 13(b). When the shear span-to-depth ratios are 3.69 and 4.34 (Figure 13(c) and (d), the maximum increments are 4.30% and 3.18%, respectively. It can be concluded that the strengthened length had little influence on the shear load-carrying capacity when the shear span-to-depth ratio was more than 3. The shear load-carrying capacity increased tendency with the increasing strengthened length when the shear span-to-depth ratio was more than one and less than 3. The shear load-carrying capacity basically maintaining stability when the strengthened length was more than optimum strengthened length.

Figure 13.

Influence of strengthened length on load-deflection curves of the HCB specimens with different shear span-to-depth ratios: (a) $λ_{1}$ = 1.39, (b) $λ_{1}$ = 2.38, (c) $λ_{1}$ = 3.69, (d) $λ_{1}$ = 4.34.

Figure 14 shows a quadratic function’s the relationship between load and strengthened length. The load increased first and then decreased with the increasing strengthened length. Therefore, there existed an optimum strengthened length to make the shear load reach its maximum value. According to the fitting formula, the optimum strengthened length of the HCB-S-2 specimen was 1532.45 mm. The optimum strengthened length was about 4.38 times of the height of the HCB specimens.

Figure 14.

Relationship between load and strengthened length.

To further investigate the influence of strengthened length on the shear behaviors of the HCB specimens, the shear stress distribution of the HCB-S-2 specimen was selected for further study. Figure 15 shows shear stress distribution of the HCB-S-2 specimen with different strengthened lengths. In Figure 15, the gray area represents the shear stress is more than 2.5 MPa. In this part, the deflection loading method was selected to investigate the shear behaviors of the HCB specimens strengthened with ESS-HCC and shear steel rebars. The ultimate deflection was 40 mm. It can be obtained that the strengthened length had a significant influence on the shear stress. With the increasing strengthened length, the gray area showed first decreased and then increased tendency. The gray area reached the minimum value when the strengthened length was 1600 mm. Therefore, the optimum strengthened length of the HCB-S-2 specimen was 1600 mm.

Figure 15.

Shear stress distribution of the HCB-S-2 specimen with different strengthened lengths: (a) 600 mm, (b) 1000 mm, (c) 1200 mm, (d) 1600 mm, (e) 2000 mm.

ESS-HCC strength grades

Relative investigations showed that the types of filling materials had little influence on the shear behavior of the HCB specimens (Lee et al., 2020). However, the ESS-HCC strength grades should be higher than that of old concrete according to the GB 50367-2013 and JTG/T J22-2008 standards. Therefore, the influence of the ESS-HCC strength grades on shear behaviors in this strengthening method was further to investigated. The deflection loading manner was adopted and the maximum deflection was 40 mm. Figure 16 shows the influence of the ESS-HCC strength grades on the shear behaviors of strengthened HCB specimens. The results showed that it had little influence on shear load-carrying capacity. Compared with the shear load-carrying capacity of the HCB specimens filled with ESS-HCC (Grade C50), the C70 ESS-HCC only increased by 2.56%. However, it had a significant influence on the shear stress. The shear stress of C60 ESS-HCC was higher than that of other strength grades. Compared with the shear stress of C50 ESS-HCC, the ESS-HCC with grades C30, C65, and C70 increased by 0.37%, 0.93%, and 6.69%, respectively. While the shear stresses of C55 ESS-HCC and C60 ESS-HCC decreased by 59.80% and 65.03%, respectively. Therefore, the ESS-HCC strength grades should be one or two higher than those of old concrete.

Figure 16.

Influence of the ESS-HCC strength grades: (a) C30, (b) C50, (c) C55, (d) C60, (e) C65, (f) C70.

Parameters of shear steel rebars

Additional shear steel rebars were added in this strengthening method to improve the interface bonding property between ESS-HCC and concrete. The influence of the additional shear steel rebars (spacing and shape) on shear behaviors needs to be further investigated. The simulation results showed that the spacing of shear steel rebars had little influence on the shear load-carrying capacity. However, the reasonable spacing can save costs and improve the interface bonding behaviors between ESS-HCC and concrete. Figure 17 shows the spacing of shear steel rebars. In Figure 17, the red dashed and black solid lines in the vertical direction represent shear steel rebars and stirrups, respectively. The spacing of additional shear steel rebars was 100 mm, 150 mm, and 200 mm, respectively. The optimum spacing should be designed according to the original stirrups spacing. Take the HCB-S-5 specimen as an example, the influence of transverse rebars on minimum tensile stress is shown in Figure 18. The ultimate deflections of the HCB specimens strengthened with ESS-HCC and shear steel rebars with and without transverse rebars were 40 mm. The transverse rebars had little influence on the shear load-carrying capacity. Compared with the HCB-S-5 specimen filled with ESS-HCC and shear steel rebars with transverse rebars, the minimum stress of the shear steel rebars without transverse rebars decreased by 58.97%. Therefore, it was suggested that the transverse rebars should meet the construction requirements and stability.

Figure 17.

Spacing of shear steel rebars (Unit: mm).

Figure 18.

Influence of transverse rebars on minimum tensile stress: (a) With transverse rebars, (b) Without transverse rebars.

Conclusions

The shear behaviors of four un-strengthened and five HCB specimens strengthened with ESS-HCC and shear steel rebars were conducted and investigated. The shear span-to-depth ratios and opening sizes were chosen as two main parameters to discuss and analyze. According to experimental, theoretical and simulation results, the shear load-carrying capacity and parameters of the strengthened HCB specimens were investigated. The main conclusions can be drawn:

(1) Failure modes of the HCB specimens strengthened with ESS-HCC and shear steel rebars were changed from web-shear to bending shear failure with the increasing of shear span-to-depth ratios. The opening sizes had a negligible influence on the failure modes. The shear cracks generated on the web of un-strengthened specimens. While the flexural shear cracks generated on the strengthened specimens and showed more excellent ductility.

(2) The shear behaviors showed a decreasing tendency with the increasing of shear span-to-depth ratios. While the opening sizes had a little influence on the shear load-carrying capacity. The maximum initial stiffness of the strengthened specimens increased by about 60%. While the cracking load of the strengthened HCB specimens increased by 50% in the shear-compression zone.

(3) Analytical models of the HCB specimens strengthened with the ESS-HCC and shear steel rebars were estimated by four standards. The modified shear load-carrying capacity of the strengthened HCB specimens was proposed considering the influence of shear span-to-depth ratios. The relative errors of the calculation and experimental results were within 10%.

(4) Combined with the finite element models, the shear behaviors of the strengthened HCB specimens were investigated. The optimum strengthened length was 1600 mm in this test. The ESS-HCC strength grades should be one or two higher than those of old concrete. The reasonable additional shear steel rebars should be designed in the spacing of the original stirrups.

Footnotes

Author contributions

Wen-Ping Du: Investigation, Data Curation, Writing-Origin draft preparation. Guan-Jun Zhang: Methodology, Investigation. Cai-Qian Yang: Conceptualization, Supervision, Project administration, Writing-review & editing. Zhi-Hong Pan: Writing-review & editing. Hans De Backer: Writing-review & editing. Kai Ming: Methodology, Investigation. Yong Pan: Resources and Project Administration.

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: This work was supported by the National Natural Science Foundation of China (Grant No. 52078122).

ORCID iDs

Wenping Du

Caiqian Yang

Data availability statement

All data, models, and code generated or used during the study appear in the submitted article.

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