Effect of Planting Rebars on the Shear Strength of Interface between Full Lightweight Ceramsite Concrete and Ordinary Concrete

Abstract

The use of full lightweight ceramsite concrete (FLWCC) for the repair of ordinary concrete (OC) structures has a good application prospect in the field of engineering structural strengthening. However, the interface here is less studied at present. For this purpose, 10 sets of FLWCC (new concrete)–OC (old concrete) specimens were produced for the shear test to test the bonding properties of the interface. The results showed that the damage form was changed from brittle damage to ductile damage after strengthening. It was proven that planting rebars in the interface could improve the shear performance. The interface shear strength increased with the number of rebars and it had a better effect after the number was more than 2. The strength was related to the rebar diameter and the maximum was obtained when the diameter was 8 mm. The most suitable spacing of the bars was 80 mm. The one-way analysis of variance (ANOVA) showed that the number of rebars had the greatest effect on shear strength followed by rebar diameter, while the effect of the spacing of the bars was less pronounced. Moreover, Fib’s (2010) specification of the interface shear strength formula could be used for the calculation of FLWCC–OC.

1. Introduction

Concrete materials are widely used in construction and transportation. However, in the course of daily use, concrete buildings can fail to reach their expected lifespan because they suffer from problems such as creeping and freeze-thaw cycles [1]. Strengthening is usually used in engineering to extend its life. Therefore, the choice of repair materials has an important influence on the strength of the reinforced concrete structure [1]. With the innovation of construction materials, lightweight [2,3], energy-saving and environmentally friendly materials have been widely used in building structures [4]. FLWCC, for example, has been extensively researched and commonly used in practical engineering and repair fields [5,6,7]. FLWCC is a kind of lightweight aggregate concrete with shale ceramic granules and shale ceramic sand instead of crushed stone and river sand. Shale ceramic granules are made from shale as raw material and industrial waste is added during the roasting process. This reflects its environmental advantages. Ceramic granules have a large number of pores inside, which gives them the advantage of being lightweight and having thermal insulation. Therefore, when FLWCC is used in construction projects, it not only reduces the dead weight of the structure and saves the use of cement and steel but also reduces the burden of indoor HVAC (heating, ventilation and air conditioning). Because of the water retention properties of ceramic granules, when FLWCC is used to strengthen OC, the water inside the ceramic granules can further promote the hydration reaction after the hardening of the interface between the new and old concrete, thus making the interface stronger. At present, there is a lot of research on the composition of raw materials [8,9,10], force characteristics [11,12,13] and durability properties [14,15,16]. The application of FLWCC in the field of repair and strengthening can give full play to its potential to replace the shortcomings of traditional concrete, which is in line with the environmental protection concept of “carbon neutrality”. And at the same time, it also brings a new direction for the topic of concrete structural strengthening.

The bonding interface is the weak part of the structure due to the discontinuity of aggregate particles in the transition region between the new and old concrete and the more complex load transfer [17]. The bonding strength of the interface is mainly influenced by the roughness of the interface, the Van der Waals force and the shrinkage and rebar difference between new and old concrete [18]. In recent years, scholars have conducted relevant studies mainly on roughness treatment [19], interface agent performance enhancement [20], high-tech repair material application [21] and rebar implantation [22]. Among them, the research direction of roughness, interface agent and high-tech repair materials is to improve the adhesion and friction of the bonding interface to improve the strength, which is to improve the bonding strength by mechanical occlusion force and its own strength and stiffness. Planting rebars in the interface can increase the ductility of the repaired structure relative to other methods, thus greatly improving the safety of the overall structure. Therefore, this method is widely used in strengthening works. In the process of rebar implantation, the influencing factors of bonding interface implantation are rebar diameter, rebar planting rates, spacing of bars, anchorage depth, properties and coating on rebars, etc. [23].

Even after controlling the influencing factors mentioned above, the effect of rebar implantation may show different results under different conditions. The five-zone three-layer model is a widely recognized microtheoretical basis for reinforced concrete [24]. Based on this microscopic model, many scholars have conducted research on the effect on bonding performance. The interfacial shear strength between the new and old concrete is the most important factor affecting the strengthening effect [25]. There are two dominant views on whether planting rebars strengthens the bonding ability: one is that scholars believe that rebars enhance the bonding effect. For example, Du [21] concluded from double-sided shear tests of OC strengthened with ultra-high performance RPC reinforcing mesh that the shear strength of the reinforced concrete was 1.37–3.11 times higher than before strengthening. Tian [26] carried out finite element simulations of the shear performance of bonding interfaces strengthened with rebars. They concluded that rebar implantation can inhibit the development of cracks. The rebar implantation makes the damage process of the new and old concrete structures ductile and it can increase the cracking load and damage load of the specimens to a certain extent. Yang [27] investigated the effects of different rebar planting rates, anchorage depths and different spacing of bars on the shear properties of the UHPC–stone interface. The results showed that the interfacial shear strength and ductility of the combined specimens increased step by step with the increase in the rebar planting rate when it was less than 0.269%.

Another view is that the presence of rebar breaks the continuity of the concrete near the bonding interface and affects the force transfer. Jiang [28] summarized from rebar pull-out tests that the average bonding strength of prefabricated connected members with notches is reduced by approximately 26%. The reduction in strength is explained by the discontinuity in the mechanical properties of the concrete around the rebars due to the presence of the bonding interface. Costa [29] evaluated the effect of normal stress and rebar planting rates on the shear resistance of the bonding interface of light aggregate concrete strengthened plain concrete. The tests illustrated that the bonding effect of the rebars comes into play only after the concrete near the bonding interface has cracked and bonding slip has occurred. The rebar planting rates do not contribute significantly to the maximum shear strength of the bonding interface. Goldyn [30] launched tests by strengthening plain concrete members with light aggregate concrete poured at different ages with bonding interfaces. Rebar implantation on the bonding interface causes a change in the damage mode of the member from brittle to ductile. The rebar planting rate was subjected to about 18%–23% of the stress at yield when the bonding interface was just cracked. This suggests that rebar can increase the post-peak residual stresses without significantly affecting the load-carrying capacity of the bonding interface.

The shear transfer mechanism of two layers of concrete in direct shear is complex, so it is necessary to evaluate the shear properties of the interface [31]. In response to the above research status, this paper investigated the shear performance of the bonding interface between FLWCC and OC. The rebar planting rate is varied by the number of rebars and diameter, so it is necessary to investigate which of the two ways enhances the interface shear best. Also, the spacing of the bars determines the rebar-concrete force transfer mode, so these three influencing factors are investigated in this experiment. The following work was performed using straight shear tests on the bonding interface. (1) The shear damage pattern and maximum shear strength under the influence of different factors were recorded and compared. (2) The most influential factors and factor levels were calculated and analyzed using one-way ANOVA combined with the analysis of the shear strength mechanism. (3) The predicted shear strength was predicted using the Fib (2010), the AASHTO (2010) and the ACI (2008) to derive the most appropriate expression for the specification expressing the present test situation. This paper expanded application areas for lightweight aggregate concrete. The properties of lightweight and thermal insulation give the ceramic granules a great research market with the potential to replace traditional concrete. This paper can provide macroscopic data reference for the study of the interface between old and new concrete and lay the foundation for the study of the microscopic interface of FLWCC–OC. Combined with the already available ceramsite concrete members’ stress characteristics, durability, etc., it fills part of the research field of ceramsite.

2. Experimental Materials and Specimen Production

2.1. Experimental Materials

(1)

Coarse aggregates

Ordinary crushed stone was used for OC in this study. The coarse aggregate of FLWCC used 900-grade crushed shale ceramsite pellets (as shown in Figure 1). Before concrete mixing, it was necessary to soak the ceramsite particles for 4 h and then dry for 12 h for prewetting treatment. The main physical properties of the coarse aggregates are shown in

Table 1. Physical property parameters of coarse and fine aggregates.

Type of Aggregate	Particle Size (mm)	Volume Density (kg/m3)	Apparent Density (kg/m3)	Compressive Strength of Concrete Cylinder (MPa)	Water Absorption in 1 h (%)	Mud Content	Fineness Modulus
Ordinary crushed stone	5~20	814	2688	6.8	2.42	/	/
Ceramsite pellets	5~20	896	1553	9.7	6.3	/	/
Ordinary river sand	/	890	2641	/	/	≤2	3.5
Ceramsite sand	/	1570	1479	/	/	≤2	2.7

.

(2)

Fine aggregate

The ceramsite granules were made of 800-grade shale ceramsite sand produced by Yichang Guangda Ceramsite Granule Products Limited company. Its relevant physical property parameters and the ordinary river sand are also shown in Table 1.

(3)

Cement

All of the cement’s physical property indexes meet the test specification requirements, as shown in

Table 2. Physical property parameters of cement.

Type of Cement	Code Number	Density (g/cm3)	Mineral Composition of Clinker				Fineness (%)
			C3S	C2S	C3A	C3AF	Margin of 80 μm Square Sieve
Ordinary silicate cement	P.O. 42.5	3.15	45	25	12	8	6.5

.

(4)

Water-reducing agent

The water-reducing agent was HsC polycarboxylate-type superplasticizers, as shown in

Table 3. Physical property parameters of water-reducing agent.

Appearance Color	PH Value	Specific Gravity	Solid Content (%)	Water Reducing Ratio (%)
Pale yellow	6~8	1.08 ± 0.02	40	25~35

.

(5)

Rebar

The tested rebar type was HRB400 and the rebar diameters were 6 mm, 8 mm and 10 mm. The basic physical properties tested according to GB/T28.1-2010 [32] are shown in

Table 4. Physical property parameters of rebar.

Category	Yield Strength (MPa)	Ultimate Strength (MPa)	Modulus of Elasticity (MPa)
HRB 400	435.5	671	$2.03\times {10}^5$

.

2.2. Mix Proportion

The old concrete was configured with strength grade C45. According to GB 50367-2013 [33], all new concrete should be one level higher than the strength grade of the original structural concrete. In order to meet the practical requirements of the project, new concrete with a strength class of LC50 was used. The proportions of OC and FLWCC are shown in

Table 5. Mixed proportion of FLWCC (Unit: kg/m³).

Cement	Coarse Aggregates	Fine Aggregate	Water-Reducing Agent	Water
605	1050	565	/	230
550	620	600	5.1	154

.

2.3. Physical and Mechanical Properties

Some of the necessary indicators were measured according to GB/T50081-2019 [34]. The test results are shown in

Table 6. Basic mechanical indices of concrete after 28 d maintenance.

Types of Concrete	Cube Compressive Strength (MPa)	Axial Compressive Strength (MPa)	Modulus of Elasticity (GPa)
LC50	53.66	46.53	3.067
C45	35.31	27.28	3.043

.

2.4. Specimen Design

The rebar connection of the interface is shown in Figure 2. The mode of arrangement was divided into the forms of 1, 2, 3 and 4 bars. The bonding performance under the action of number of rebars, rebar diameter (double rebars) and spacing of the bars (double rebars) were studied. The roughness of interface was processed using the manual chiseling method and the roughness was determined using the sand cone method. Three specimens were made in each group, which was for accuracy. The final results of the test should be taken as the average. Shear test groups are shown in

Table 7. Groups of shear tests.

Specimen Number	Number of Rebars	Rebar Planting Rate (%)	Spacing of Bars (mm)	Rebar Diameter (mm)	Anchorage Depth (mm)	Interface Roughness (mm)	Interface Agents	Number of Specimens
CZJ	/	/	/	/	/	/	/	3
SJ	/	/	/	/	/	2–3	cement paste	3
B1G1	1	0.223	C8	80	10 d	2–3	cement paste	3
B1G2	2	0.447	C8	80	10 d	2–3	cement paste	3
B1G3	3	0.670	C8	80	10 d	2–3	cement paste	3
B1G4	4	0.894	C8	80	10 d	2–3	cement paste	3
B2G1	2	0.251	C6	80	10 d	2–3	cement paste	3
B2G2	2	0.447	C8	80	10 d	2–3	cement paste	3
B2G3	2	0.698	C10	80	10 d	2–3	cement paste	3
B3G1	2	0.447	C8	60	10 d	2–3	cement paste	3
B3G2	2	0.447	C8	80	10 d	2–3	cement paste	3
B3G3	2	0.447	C8	100	10 d	2–3	cement paste	3

Note: The number of specimens was a shear test of each group of three specimens; “/” means that the group did not have this content. B1G1–B1G4 were the rebar planting rate groups. B2G1–B2G3 were the rebar diameter groups. B3G1–B3G3 were the spacing of bars groups. SJ was the cement net slurry treatment group. CZJ was the old concrete whole cast group. “d” was the diameter of the rebars.

.

2.5. Fabrication of Specimens

The poured interface of the old concrete was selected as the interface. After treatment with the manual chiseling method, rebars were then implanted on the interface. The method was scribing—drilling—clearing—filling with adhesives—implanting rebars—curing and maintenance. Before placing the new concrete, a cement paste was applied to the interface. The finished specimens are shown in Figure 3.

2.6. Test Device and Loading Method

Four-point loading of distribution beams was used as the test loading method. And the main instruments of the test were a microcomputer-controlled electro-hydraulic servo universal testing machine, a loading sensing cell, etc.

The conceptual and field diagrams of the test setup are shown in Figure 4. It can be seen that the relationship between the distance d₂ between the far loading point and the bonding interface and the distance d₁ between the near loading point and the interface was $d_1=\frac{2}{5}{d}_2$. The compact four-point shear loading was $p_1=\frac{5}{2}{p}_2$ and the load at the interface could be calculated as $P_3=\frac{3}{7}F$. That is to say, the shear force at the bonding interface was 3/7 times of the load loaded by the testing machine.

3. Experimental Results

3.1. Destruction Form

The damage pattern of 12 groups of specimens in a direct shear test is shown in Figure 5, Figure 6, Figure 7 and Figure 8. When the shear force of the interface without rebars group (SJ) reached its limit, the specimens cracked along the interface instantly. There was no obvious crack from a macroscopic point of view before fracture of the interface and its damage form was brittle damage. The damage pattern of the interface showed that the damage interface was in the same direction as the shear force action. The damage interface on the old concrete side was similar to the interface morphology after the old concrete was chiseled at the beginning. This fully proved that the interface was the weak part of shear damage resistance.

The damage of the bonding interface group (B1G1–B1G4, B2G1–B2G3, B3G1–B3G3) is shown in Figure 6, Figure 7 and Figure 8. The whole damage process could be divided into four stages: At the beginning of loading, the specimens had no obvious changes. With the increase in load, small cracks appeared at the edge of interface. Upon continued loading, the cracks gradually penetrated, with their width widened, and a small amount of sheared aggregate was dislodged from the surface. When the ultimate load was finally reached, the rebars were not pulled out or cut off and the concrete was not partially pulled out.

Observation of the damage pattern showed that the damage pattern of the interface group was that cracks extended from the interface to the concrete on both sides caused by the shearing force. The destruction process of the specimens with different variables was approximately the same. The main cracks were the oblique cracks distributed between the shear supports, and some specimens also had a small number of micro cracks. This phenomenon was due to the axial pulling force of the rebars after cracks appeared in the specimens, which caused tensile stresses in the concrete around the rebars, therefore causing micro cracks.

What could also be seen was that aggregate shedding from the outer surface was a little more common in the groups with low rebar planting rates, such as B1G1, B1G2 and B2G1. It was clear to see that this phenomenon diminished as the rates were increased. This was due to the fact that the rebar bond to the concrete in the group with lower rebar planting rates had a smaller area of influence.

3.2. Shear Strength Analysis

The results of the shear strength tests at the interface are shown in

Table 8. Results of shear test.

Group Number	Shear Load/kN	$\mathbf{Shear} \mathbf{Strength} \mathit{\tau }$/MPa	Average Shear Strength/kN	$\frac{\mathit{\tau }}{{\mathit{\tau }}_{\mathbf{S}\mathbf{J}}}$	Strength Gain Rate/%
CZJ	252.35	11.22	11.22
	256.90	11.42		/	/
	247.80	11.01
SJ	139.80	6.21	6.29
	143.25	6.37		1	0
	141.53	6.29
B1G1	142.30	6.32	6.32
	143.60	6.38		1.005	0.5
	141.00	6.27
B1G2	188.30	8.37	8.46
	179.35	7.97		1.345	34.5
	203.60	9.05
B1G3	181.30	8.06	9.02
	201.45	8.95		1.434	43.4
	225.90	10.04
B1G4	196.65	8.74	9.47
	218.75	9.72		1.505	50.5
	223.65	9.94
B2G1	142.23	6.32	6.32
	141.01	6.27		1.005	0.5
	143.45	6.38
B2G2	188.30	8.37	8.46
	179.35	7.97		1.345	34.5
	203.60	9.05
B2G3	147.40	6.55	7.46
	168.50	7.49		1.185	18.5
	187.40	8.33
B3G1	155.50	6.91	7.56
	165.35	7.35		1.202	20..2
	189.30	8.41
B3G2	188.30	8.37	8.46
	179.35	7.97		1.345	34.5
	203.60	9.05
B3G3	154.65	6.87	7.44
	177.75	7.90		1.184	18.4
	170.10	7.56

Note: τ_SJ was the shear strength of SJ group, $\frac{\tau }{{\tau }_{\mathrm{S}\mathrm{J}}}$ was the ratio of shear strength of each group to SJ group.

. In summary, the shear strength was improved overall after 2 to 3 mm of manual chiseling method as well as rebar planting. The gain in shear strength rose from 0.48% to 50.52%. This indicated that the rebar planting played a good role in improving the shear resistance of the new and old concrete interface. A reasonable number of rebars, rebar diameter and spacing of the bars could significantly improve the shear strength so that the bonding performance could be enhanced.

• Number of rebars

Figure 9 illustrates the influence pattern of the number of rebars on the shear strength. In conjunction with Table 8, the increase in shear strength was 0.5%, 34.5%, 43.4% and 50.5% when the number w increased from 0 to 4 (SJ, B1G1–B1G4). This indicated that the method of growing the rebar planting rate by increasing the number of rebars was effective in improving the shear strength of the interface. This finding was also in agreement with Yang [27]. This was because when the number of rebars increased, the tensile force generated by the rebars at the interface also increased. This led to an improvement in friction and pinning action at the interface.

Individually, B1G1 only increased by 0.5% compared to SJ, while B2G2 had a large increase of 34.5%. This implied that the degree of improvement in shear strength was not significant with a low rebar planting rate. When analyzed in conjunction with Yang’s [27] study, this was because at a low rebar planting rate, the shear strength was mainly supported by the concrete and the rebars were unable to give full play to its ductile role. When the rate was high, the role of rebars in the middle and late stages of loading was more significant, thus the interface was strengthened by the rebars and the ductility was more obvious.

2.

Rebar diameter

As can be seen from Figure 10, the shear strength increased and then decreased with the growth of the rebar diameter. The shear strength reached its maximum at a diameter of 8 mm (B2G2), which was 34.5% higher than that of the SJ group. When the diameter was 10 mm (B2G3), the shear strength tended to decrease to 7.46 MPa, which was still larger than that of 6.32 MPa for 6 mm (B2G1). It could be seen that too large a rebar diameter did not improve the shear strength well. On the one hand, the increase in the diameter reduced the bonding performance with the concrete. On the other hand, it reduced the area of the concrete that was effectively loaded [35]. The selection of the appropriate rebar diameter in the actual project could better improve the interface bearing capacity.

Combining B1G3 and B2G3, although the rebar planting rates were almost the same, the former had more than twice the rate of gain in shear strength than the latter. Figure 9 illustrates that the shear strength was positively correlated with the number of rebars within a certain range, while Figure 10 does not have this pattern. If the shear strength was to be increased by increasing the rebar planting rate, the number of rebars had a better gain than the rebar diameter. What was being suggested was that increasing the number of rebars in a strengthening project would be better than using larger diameters. Similarly, in practice, uniform sizes of smaller diameter rebar are also better constructed than different sizes of larger diameter.

3.

Spacing of bars

Figure 11 depicts that the shear strength increased and then decreased with a rising spacing of the bars. This suggested that unsuitable spacing weakened the shear resistance of the rebars. The interface shear strength of the B3G2 group reached a maximum of 8.46 MPa. The shear strength of B3G1 was greater than B3G3. The reason for this phenomenon was the anchor group effect [36]. The internationally accepted method for calculating concrete post anchorage was the CCD method (concrete capacity design). It is shown in Figure 12, where h_ef is the anchorage depth. At a spacing of 60 mm (B3G1), the bearing areas of the two bars overlapped too much. As a result, the bars could not make good use of the concrete taper to transfer the load. When the spacing was 100 mm (B3G3), although the two bars could make better use of the concrete taper than with a spacing of 60 mm (B3G1), the edge distance of the rebar anchorage of 25 mm was too small for the cross-section of 150 mm × 150 mm. Hence, the cracks near the maximum stress of the bars developed toward the outer edge of the specimens, eventually leading to concrete splitting damage. Therefore, the spacing of 80 mm (B3G2) was the most appropriate in this test to achieve a balance in terms of edge distance and spacing compared to the other two groups. This conclusion was similar to that of Abbas [37]. The group anchor effect had to be taken into account in the actual project so that the connection between the rebar and concrete could be utilized as much as possible.

3.3. One-Way ANOVA

The variation in the maximum shear strength reflected the effect of three influencing factors on the bonding performance. However, the strength of the influence of these factors was difficult to visualize. Therefore, in this section, one-way ANOVA was used to determine the strength and to further analyze which level of shear strength was greatest for a given factor.

The number of rebars (Factor A), rebar diameter (Factor B) and spacing of the bars (Factor C) were selected for significance analysis. The four levels of Factor A: A₁, A₂, A₃, and A₄ meaning the number of rebars 1 (B1G1), 2 (B1G2), 3 (B1G3) and 4 (B1G4), respectively. As above, the three levels of Factor B: B₁, B₂, B₃ meaning the diameter of rebar 6 mm (B2G1), 8 mm (B2G2) and 10 mm (B2G3). The three levels of Factor C: C₁, C₂, C₃ meaning the spacing of bars 60 mm (B3G1), 80 mm (B3G2) and 100 mm (B3G3). The formula and results are shown in

Table 9. One-way analysis of variance table.

Source of Variance	Calculated Formula	Value
		Number of Rebars (Factor A)	Rebar Diameter (Factor B)	Spacing of Bars (Factor C)
Correction $C$	$\frac{T_{..}^2}{rl}$	830.17	494.77	550.53
Total sum of square $S_T$	$\sum \sum x_{ij}^2-C$	20.81	9.07	4.21
Sum of effect squares $S_A$	$\frac{1}{l}\sum T_i^2-C$	17.42	6.88	1.88
Error sum of squares $S_e$	$S_T-S_A$	3.39	2.19	2.34
Total degree of freedom ${df}_T$	$rl-1$	11	8	8
Effect square and degree of freedom ${df}_A$	$r-1$	3	2	2
Error square and degree of freedom ${df}_e$	${df}_T-{df}_A$	8	6	6
Mean squared sum of effects ${\overline{S}}_A$	$\frac{S_A}{{df}_A}$	5.81	3.44	0.94
Mean square sum of errors ${\overline{S}}_e$	$\frac{S_e}{{df}_A}$	0.42	0.36	0.39
Statistic $F$	$\frac{{\overline{S}}_A}{{\overline{S}}_e}$	13.72 **	9.43 *	2.41
$F_{0.01}\left({df}_A,{df}_e\right)$	Checklist	7.59	10.90	10.90
$F_{0.05}\left({df}_A,{df}_e\right)$	Checklist	4.07	5.14	5.14

Note: “**” means that the effect of this level on the test results was highly significant; “*” means that this level had a significant effect on the results of the test.

.

In a further F-test, if F < F_0.05, it means that this level had a nonsignificant effect on the results of the test. If F_0.05 < F < F_0.01, it means that this level had a significant effect on the results of the test (indicated by “*” in the following tables). If F > F_0.01, it means that the effect of this level on the test results was highly significant (indicated by “**” in the following tables).

The F-test can only test that the variation in the results stems mainly from the variation between levels. It cannot detect whether the difference between the level means is significant. To address this issue, multiple comparisons were further used to determine the significance of the difference between two horizontal means. As shown in

Table 10. Multiple comparison table of average shear strength under number of rebars.

Group Number	Number of Rebars	Level	$\mathbf{Average} {\overline{\mathit{x}}}_{\mathit{i}}$	$|{\overline{\mathit{x}}}_{\mathit{i}}$ − 9.47|	$|{\overline{\mathit{x}}}_{\mathit{i}}$ − 9.02|	$|{\overline{\mathit{x}}}_{\mathit{i}}$ − 8.46|
B1G1	1	A1	6.32	3.14 *	2.69 *	2.14 **
B1G2	2	A2	8.46	1.00	0.55
B1G3	3	A3	9.02	0.45
B1G4	4	A4	9.47

Note: The minimum significant differences at the significant level of 0.05 and 0.01, respectively, were ${LSD}_{0.05}=t_{0.025}({df}_e)S_{{\overline{x}}_i-{\overline{x}}_j}$ = 1.225, ${LSD}_{0.005}=t_{0.005}({df}_e)S_{{\overline{x}}_i-{\overline{x}}_j}$ = 1.7822. “**” means that the effect of this level on the test results was highly significant; “*” means that this level had a significant effect on the results of the test.

and

Table 11. Multiple comparison table of average shear strength under rebar diameter.

Group Number	Rebar Diameter	Level	$\mathbf{Average} {\overline{\mathit{x}}}_{\mathit{i}}$	$|{\overline{\mathit{x}}}_{\mathit{i}}$ − 6.32|	$|{\overline{\mathit{x}}}_{\mathit{i}}$ − 7.46|
B2G1	C8	B2	8.46	2.14 **	1.00
B2G2	C10	B3	7.46	1.14
B2G3	C6	B1	6.32

Note: The minimum significant differences at the significant level of 0.05 and 0.01, respectively, were ${LSD}_{0.05}=t_{0.025}({df}_e)S_{{\overline{x}}_i-{\overline{x}}_j}$ = 1.207, ${LSD}_{0.005}=t_{0.005}({df}_e)S_{{\overline{x}}_i-{\overline{x}}_j}$ = 1.828. “**” means that the effect of this level on the test results was highly significant.

, Factor C was not subjected to multiple comparisons because its effect was not significant.

Table 9 demonstrates the formula and results of the calculations. The quantitative results of the completed analysis were used to accurately rank the strong and weak effects of the three factors and ten levels. These data tested the conclusions of the previous section.

4.

Number of rebars

It is described in Table 9 that the F value of Factor A was 13.72, which was higher than F_0.01 and F_0.05. This indicated that the effect of the number of rebars on the improvement in the shear strength was highly significant. As can be seen from Table 10, among the four levels of Factor A, $\left|{\overline{x}}_1-9.47\right|$= 6.44 and $|{\overline{x}}_1-9.02|$ = 2.69. So A₁ was significantly higher than A₂, A₃, and A₄, and more compared to the untreated (SJ). In addition, the enhancement effect of the number of rebars 4 (B1G4) was significantly higher than others.

5.

Rebar diameter

The F value of Factor B was 9.43, which was less than F_0.01 and greater than F_0.05, indicating that the rebar diameter had a significant effect on the enhancement of the shear strength. Of the three levels of Factor B, $|{\overline{x}}_1-6.32|$ = 2.14, $|{\overline{x}}_1-8.46|$ = 1.00, so B₂ was significant over B₃ and the others were not.

6.

Spacing of the bars

The F value of Factor C was 2.41, which was less than F_0.01 and F_0.05, suggesting that the spacing of the bars had no significant effect on the improvement in the shear strength. In general, when using the rebar implantation method to strengthen the OC, the spacing of the bars should satisfy the specifications and combine the actual conditions.

7.

Summary

Combined with the above analysis, the interface shear performance was most influenced by the number of rebars. As two ways to increase the rebar planting rate, the former was a bit more significant. This was because a growth in the number of rebars not only quickly improved the planting rate, but also made the arrangement more stable. In a multiple rebar arrangement, the rebars were able to affect a larger area of concrete, resulting in a more uniform force. Smaller diameters but a greater number could be used while keeping the rebar planting rates constant.

The weakest influence was the spacing of the bars. The effects of the anchor groups on the rebar–concrete transfer mode should be considered during the structural design.

4. Shearing Mechanism and Comparison of Results

4.1. Analysis of the Shear Resistance Mechanism

Currently, the shear theories of shear resistance are based on the shear-friction theory proposed by Birkeland [38], and on this basis, Randle [39] established the formula for shear resistance. The currently accepted shear bearing capacity of the interface consists of three components: the force of cohesion V_u(coh), the friction V_u(f) and the pin force V_u(da) [40].

$$v_{\mathrm{u}}=\frac{V_{\mathrm{u}\left(\mathrm{c}\mathrm{o}\mathrm{h}\right)}+V_{\mathrm{u}\left(\mathrm{f}\right)}+V_{\mathrm{u}\left(\mathrm{d}\mathrm{a}\right)}}{A_{\mathrm{c}\mathrm{v}}} (A_{\mathrm{cv}} \mathrm{is} \mathrm{the} \mathrm{interface} \mathrm{area})$$

The shear force transfer mechanism [21] is shown in Figure 13. When the interface undergoes relative slip u due to shear, the rebars are also driven and thus generate tension F_t and create an angle α with the rough interface. At this point, the component F_tcosα of the tensile force in the direction parallel to the interface is the pin force V_u(da). Its component F_tsinα in the direction perpendicular to the interface is the pressurizing effect [39]. The concrete is produced under pressure because of the extrusion of the tensile rebar. The friction V_u(f) generates on the rough bonding interface, which is μF_tsinα, its magnitude depends on the roughness and pressure magnitude. Moreover, it decreases slightly with an increasing slip. In addition to the shear resistance, the interface itself has an adhesive cohesion V_u(coh), consisting of Van der Waals forces, chemical action, interface tension and mechanical occlusion [41]. The above constituted the shear resistance of the interface.

4.2. Analysis of the Application of Existing Shear Strength Calculation Formulae

Most of the existing well-established shear formulas are mostly based on the above theory, refined and extended in terms of quantification of roughness, correction of friction coefficient and different types of concrete [40].

Table 12. Typical formula for calculating the shear strength of the bonding interface of new and old concrete.

Specification	Calculation Formula	Annotation
Fib Model Code for Concrete Structures (2010) [42]	${\tau }_{\mathrm{u}}={\tau }_{\mathrm{a}}+\mu (\rho k_1{f}_y+{\sigma }_{\mathrm{n}})+k_2\rho \sqrt{f_{\mathrm{y}}{f}_{\mathrm{c}}}$)	τa, c—Interface cohesion μ—Interface friction coefficient ρ—Bonding rate of interface σn—Normal stress caused by interface shear k1—Bending coefficient k2—Interaction coefficient between steel bar and concrete under dowel action fy—Tensile strength of rebar fc—Axial compression strength of concrete Asv, Avf—Total cross-sectional area of interfacial shear rebar Acv—Interfacial area Pc—Positive interface pressure caused by external force
AASHTO LRFD Bridge Design Specifications (2010) [43]	$V_{\mathrm{u}}={cA}_{\mathrm{c}\mathrm{v}}+\mu (A_{\mathrm{s}\mathrm{v}}{f}_{\mathrm{y}}+P_{\mathrm{c}})$
ACI 318-08 (2008) [44]	$V_{\mathrm{u}}=\mu A_{\mathrm{v}\mathrm{f}}{f}_{\mathrm{y}}$

has shown some representative formulas for calculating the shear strength of the interface of new and old concrete at present.

Figure 14 expresses the ratio of theoretical value to test value. It can be seen that The Fib (2010) takes into account the coupling between friction and pin force. The shear strength value is considered to be equal to the algebraic sum of the force of cohesive, friction and pin force. It is worth mentioning that these three do not reach the maximum value at the same time during the shear resistance. The expression in the form of multiplication by a subfactor in front can better predict the shear strength in this test. For the FLWCC, the calculated value of Fib (2010) was conservative and the maximum error was controlled at about 25%, which was a better fit. The theoretical value of the AASHTO (2010) was lower and would be used to predict this test with some error. The reason was that although it used friction and pin force to resist external loads at the same time, the values of the bonding force and friction coefficient are taken roughly. The smallest theoretical value of the ACI (2008) was due to the fact that only the pinning action of the rebar is considered, ignoring the contribution of the concrete itself.

It can be seen that all three specifications take the total cross-sectional area of Acv as a major variable, which also corresponds to the results of the factor analysis in Section 3 of this paper. In other words, the shear strength is linearly related to the rebar planting rate and the rebar diameter. Definitely, there are Chinese specifications that codify the spacing of bars as an independent variable in the formula. Such as JTG/T J22-2008 [45]. But its calculated value differed greatly from the test value. The reason, as analyzed above, was that the effects of anchor groups affect mainly the way in which the forces are transferred between the rebar and the concrete. Thus the effect of this factor was difficult to quantify in different situations with different members, loading methods and different usage scenarios.

5. Conclusions

Based on the above results and discussions, the following conclusions can be drawn:

• The form of shear damage at the unstrengthened FLWCC–OC interface was brittle damage. But the damage form becomes ductile after rebar implantation. This showed that rebar implantation could increase the ductility of the interface of FLWCC–OC.
• The rebar planting rate had a significant effect on the interfacial shear strength. The strength reached a maximum of 9.47 MPa when the rate was 0.894%. Rebar was not effective at low rates. The interfacial shear strength was positively correlated with the number of rebars, which increased and then decreased with the increase in rebar diameter. The number of rebars enhanced the shear strength better than the rebar diameter for the same planting rate.
• The shear strength was related to the spacing of the bars. In this test, the strength was maximum when the spacing was 80 mm. Too much or too little spacing affected the way the rebars transmitted force and thus the bonding action of the rebars.
• The one-way ANOVA was used to analyze the effects of the number of rebars, rebar diameter and spacing of the bars on the interfacial shear strength. The results showed that the most obvious effect of the number of rebars was followed by rebar diameter, and the effect of the spacing of the bars was less significant.
• The calculated strength of the Fib (2010) formula agreed well with the measured values in this text. It was recommended to refer to the Fib (2010) to calculate the interfacial shear strength of the rebar implantation when strengthening OC with FLWCC.