Study on Flexural Strength of Interface between Full Lightweight Ceramsite Concrete and Ordinary Concrete

Abstract

The efficacy of full lightweight ceramsite concrete as a restorative material has been widely acknowledged, given its light weight, strength, and durability. However, the extent of its performance in repairing existing or old concrete remains uncertain. This study examined the reparation of flexural performance with full lightweight ceramsite concrete, using 14 different combinations of old and new concrete test blocks. The primary focus of the study was on investigating the flexural bond strength of the interface between the old and the new concrete. This included understanding the effects of the interfacial roughness, interfacial agent type, and concrete curing age of the concrete on the flexural strength. The test results showed that increasing the interface roughness from 0 mm to 5 mm resulted a restoration of the flexural strength of the sample by approximately 59%. Additionally, the flexural strength of the specimens was restored by 62%–78% of their original strength with the application of different types of interfacial agent. To rank the impact of these factors on the flexural strength, a univariate analysis of variance was conducted. This allowed us to establish a mathematical formula for calculating the flexural capacity of old and new concrete interfaces, taking the three aforementioned factors into account.

1. Introduction

Numerous building structures annually encounter durability challenges due to adverse environmental conditions and external loads. For the safe operation of these structures, it is indispensable to repair and reinforce the whole or part of these structures. The patching and strengthening of concrete structures have thus emerged as crucial research topics in construction engineering [1,2]. Various bonding methods exist for concrete, most notably the sectional increase method [3] and the mechanical connection method [4]. The former, a widely adopted technique [5], is implemented by pouring new concrete onto existing concrete. However, this leads to the generation of new and old concrete interfaces, the most vulnerable parts of the repaired structure [6,7]. The mechanical properties of these interfaces critically influence the overall reliability of the structure, making their study an intriguing research subject.

In recent years, numerous experimental and theoretical studies have shed light on the factors affecting these interfaces’ mechanical properties. Factors such as old concrete intensity [8], water content [9], new concrete intensity [10], the interval between new and old concrete pouring [11], interface roughness [12], surface-preparation methods [13], the use of interface agents [14], and implanted steel bars [15] have all been identified as key determinants. In addition, the size of the bonding surface also has a certain impact on the bond strength. Some studies have found that the incorporation of fibers in concrete can reduce the size effect due to the bridging effect of fibers [16]. Advanced studies proposed that new and old concrete interfaces can be considered as concrete material 100 microns wide, with their mechanical strength determined by their microstructure [17,18]. Detailed microscopic studies further illuminated these findings.

Despite these insights, most studies have focused on the tensile and shear strengths of interfaces, while the knowledge on their flexural strength remains limited [19]. Given the inevitable cold joint defects in concrete structures due to on-site construction complexities, the cold joint (the interface between new and old concrete) significantly weakens the component’s flexural performance [20]. Meanwhile, under the action of bending load, the concrete bonding interface produces a complex stress state. This is expressed as partial tensile stress at the bonded surface, and the remainder is subjected to compressive stress. The areas with the greatest tensile stress may produce cracks [21]. Consequently, considering the interface’s flexural strength is essential [22]. Flexural testing is considered to be a more convenient and practical bonding test by some scholars [23]. On one hand, based on the results obtained by Madani [24] and Farzad [9], flexural strength is lower than tensile strength and shear strength. It requires a greater level of attention. On the other hand, the JC/T 2381-2016 [25] specification recommends describing the bonding strength of an interface based on its flexural strength, as it better represents the interface’s carrying capacity under bending and stretching. Hence, the study of the flexural strength of the interface offers immense research value.

Full lightweight ceramsite concrete is a widely used artificial lightweight aggregate concrete, renowned for its light weight, high strength [26], superior fire resistance [27,28], strong seismic performance [29], and excellent durability [30]. It also presents substantial economic benefits. Previous studies suggested that under a constant water–cement ratio, the early autogenous shrinkage of ceramsite concrete decreases as the pre-wetting humidity of ceramsite increases, due to its water absorption and desorption capacity [31]. However, the addition of ceramsite with high water absorption or an excessive amount of ceramsite may have a negative impact on the mechanical properties of ceramsite concrete, such as the tensile strength, compressive strength, and elastic modulus [32,33]. Additionally, it is considered a promising new type of cover material, particularly for the repair and reinforcement of old concrete [11,12,14]. Despite these benefits, research on full lightweight ceramsite concrete interfaced with ordinary concrete, particularly in terms of its flexural strength, has remained largely unexplored. Based primarily on the flexural strength, the effect of repairing ordinary lightweight ceramsite concrete is unknown. The influence of various factors on the flexural strength of this type of interface remains unclear, and an applicable calculation formula is yet to be established. Therefore, a comprehensive exploration of the flexural strength of this type of interface is warranted.

This paper aims to systematically investigate the flexural strength of the interface between full lightweight ceramsite concrete and ordinary concrete. To achieve this goal, the first involved measuring the flexural strength of this interface via a bending test. Subsequently, the influence law and the degree of various factors, including interfacial roughness, the type of interfacial agent, and the concrete curing age, on this strength are revealed. Finally, a calculation model for the flexural strength of the interface is established. The intention of this research is to provide a scientific reference for a concrete-repair project that utilizes full lightweight ceramsite concrete as the repair material.

2. Bending-Strength Test of Bonding Surface

2.1. Concrete Raw Materials and Mix Ratio

Ordinary Portland cement, P.O.42.5, was adopted. Its density was 3.15 g/cm³ and its fineness was 6.5%. The mineral composition of cement clinker was C₃S, C₂S, C₃A, and C₃AF, and their contents were 45%, 25%, 12%, and 8%, respectively. The coarse aggregate used for preparing old concrete was ordinary crushed stone, and the coarse aggregate used for preparing new concrete was 900-grade crushed stone shale ceramsite. The ceramsite particles were pre-wetted and fully drained before use. Subsequently, a surface covering measure was used. River sand was used as fine aggregate in the preparation of old concrete. Among the fine aggregates used in construction of new concrete is ceramsite sand. The physical characteristics of aggregate are shown in

Table 1. Physical characteristics of aggregates.

Types of Aggregate	Particle Size (mm)	Apparent Density (kg/m3)
Crushed stone	5~20	1517
Shale ceramsite	5~20	1760
Ordinary river sand	0~5	2641
Ceramsite sand	0~5	1479

. Before the experiment, the fine aggregate was screened through a 4.75-mm square-hole sieve, and its relevant performance parameters met the specification requirements. High-performance polycarboxylate water reducers were used in the admixture. There were four types of interface agent: cement paste, silica-fume cement paste, polymer, and epoxy resin. The type of cement used in cement slurry was the same as that of concrete. In addition, the main component of silicon fume was SiO₂, and its content was 96.74%. Its unit weight was 1600–1700 kg/m³ and specific surface area was 20–28 g/m². The technical characteristics of polymer interface agent are shown in

Table 2. Technical characteristics of polymer-interface agents.

Type of Interface Agent	State	Color	Shear Bond Strength (MPa)	Tensile Bond Strength (MPa)	Solidification Time (d)
Polymer	Liquid	Milky white	1.5	1.0	1
Epoxy resin	Liquid	Milky white with a little yellow	1.6	0.8	2

. The mixing-water type was tap water.

The JGJ 55-2011 [34] and JGJ/T 12-2019 [35] provided specifications for the mix-ratio tests. Smooth preparation of C45 ordinary concrete and LC50 lightweight ceramsite concrete was achieved. The mix proportions are shown in

Table 3. Mix proportion of C45 ordinary concrete (kg/m³).

Gravel	Sand	Cement	Water	Water Reducing Agent
1050	565	605	230	0

and

Table 4. Mix proportion of LC50 full lightweight ceramsite concrete (kg/m³).

Ceramsite	Ceramsite Sand	Cement	Water	Water Reducing Agent
620	600	550	154	5.1

. Their compressive strength is shown in

Table 5. Compressive strength of C45 ordinary concrete and LC50 lightweight ceramsite concrete.

Curing Age (d)	C45 Ordinary Concrete				LC50 Lightweight Ceramsite Concrete
	Sample 1	Sample 2	Sample 3	Average Value	Sample 1	Sample 2	Sample 3	Average Value
7	31.96	36.30	38.54	35.60	45.60	44.00	47.23	45.61
14	43.97	41.64	44.23	43.28	50.08	50.42	52.23	50.91
28	48.95	45.76	50.68	48.46	55.34	52.93	52.71	53.66

. After measurement and calculation, it was found that the density of full lightweight ceramsite concrete was 1741 kg/m³, and its slump and gas content were 70 mm and 5.65%, respectively. The density of C45 ordinary concrete was 2417 kg/m³, and its slump and gas contents were 75 mm and 6.71%, respectively.

2.2. Experimental Design of Flexural Strength

Using lightweight ceramsite concrete as a repair material, we studied the extent of the repair’s recovery of flexural performance. Simultaneously, the effects of interfacial roughness, interfacial agent, and curing age of existing concrete on the flexural strength of the repaired interface were discussed. It was possible to produce 14 groups of specimens (C-3, J-1, and L-90 are the same group of test blocks) in this experiment (see

Table 6. Grouping and interfacial flexural strength of bonding specimens between full lightweight ceramsite concrete and existing concrete.

Group Number	Interfacial Agent Type	Interfacial Roughness (mm)	Existing Concrete Age (d)	Age of New Concrete (d)	Flexural Strength (MPa)				Objective
					Sample 1	Sample 2	Sample 3	Average Value
Z-45	-	-	28	-	4.79	4.89	4.90	4.86	As a control group, it was used to evaluate the effect of the repair
Z-50			-	28	5.11	5.25	5.03	5.13
C-0	Cement paste	0	90 + 28	28	2.89	2.85	2.84	2.86	Exploring the effect of interfacial roughness on the flexural strength of the interface
C-1		1	90 + 28	28	3.17	3.10	3.15	3.14
C-3		3	90 + 28	28	3.33	3.28	3.14	3.25
C-5		5	90 + 28	28	3.20	3.11	3.26	3.19
J-0	-	3	90 + 28	28	3.06	2.98	3.02	3.02	Exploring the effect of interfacial agent types on the flexural strength of the interface
J-1	Cement paste	3	90 + 28	28	3.33	3.28	3.14	3.25
J-2	Silica-fume cement slurry	3	90 + 28	28	3.35	3.41	3.38	3.38
J-3	Polymer class	3	90 + 28	28	3.59	3.50	3.53	3.54
J-4	Epoxy resin	3	90 + 28	28	3.79	3.75	3.80	3.78
L-3	Cement paste	3	3 + 28	28	4.01	3.84	4.03	3.96	Exploring the influence of existing concrete’s curing age on interfacial flexural strength
L-7		3	7 + 28	28	3.87	3.96	3.84	3.89
L-14		3	14 + 28	28	3.72	3.52	3.74	3.66
L-28		3	28 + 28	28	3.43	3.26	3.45	3.38
L-90		3	90 + 28	28	3.33	3.28	3.14	3.25

Note: Z-45 and Z-50 represent integral test specimens with strength grades of C45 and LC50, respectively. C-0, C-1, C-3, and C-5 represent test specimens with interfacial roughness of 0, 1, 3, and 5 mm, respectively. J-0, J-1, J-2, J-3, and J-4 represent test specimens without interfacial agent and coated with cement paste, silcrete slurry, polymer class, and epoxy resin interfacial agent, respectively. L-3, L-7, L-14, L-28 and L-90 represent the bonding test specimens of existing ordinary concrete with ages of 3, 7, 14, 28, and 90 days, respectively.

). The dimension of each flexural specimen was 100 mm × 100 mm × 400 mm. First, the old concrete specimen (100 mm × 100 mm × 200 mm) was adopted from C45 ordinary concrete. In addition, the old concrete specimens were cured for 3 days, 7 days, 14 days, 28 days, and 90 days after demolding. In addition, their surfaces needed to be chiseled manually. Referring to the experimental design in the relevant research [14,36,37,38], the interface roughness was treated as 0 mm, 1 mm, 3 mm, and 5 mm, respectively. Subsequently, different interfacial agents were applied to the old concrete surface. Finally, one end of the 100 mm × 100 mm × 400 mm mold was placed. The LC50 full lightweight ceramsite concrete was poured into these molds for bonding to the C45 ordinary concrete specimen, as shown in Figure 1. After 28 days of standard curing (temperature 20 ± 2 °C, relative humidity above 95%), the new and old concrete specimens were successfully acquired.

The bonding effect of new and old concrete was influenced by multiple factors. One of the most important signs of successful bonding was the excellent treatment of the bonding surface of new and old concrete. Therefore, the influence of roughness on the flexural performance of the interface between old and new concrete needs to be investigated. Using a sand-cone method, the roughness of the interface was measured, and the old concrete-base surface was treated manually with chisels. The roughness values of chiseling treatment were 0 mm, 1 mm, 3 mm, and 5 mm, respectively. The roughness of the bonding surface was calculated using Equation (1).

$$h=\frac{V}{S}$$

(1)

In the equation, h is the average depth of sand filling (mm), S is the surface area of the joint surface (mm²), and V is the volume of sand filling (mm³).

This experiment used a microcomputer-controlled electro-hydraulic servo universal testing machine to load. A four-point bending test was conducted to explore the influence of various factors on the flexural strength of prisms (100 mm × 100 mm × 400 mm). The loading speed of the testing machine was controlled at 0.05 MPa/s~0.08 MPa/s, and the specific loading mode is illustrated in Figure 2. The flexural strength of the interface between old and new concrete was calculated by using Equation (2).

$$f_f=\frac{Fl}{b{h}^2}$$

(2)

In the equation, $f_f$ is the flexural strength of the concrete (MPa), F is the failure load of the specimen (N), l is the span between supports (mm), h is the cross-sectional height of the specimen (mm), and b is the cross-sectional width of the specimen (mm).

3. Results and Discussion

3.1. Test Phenomena and Strength

3.1.1. Experimental Phenomena of the Interface-Roughness Factor

According to Figure 3, the damage conditions of the interface at different roughness levels were different. Almost no sound was heard when the specimen with the interfacial roughness of 0 mm reached its ultimate load. Suddenly, the specimen broke at the point at which the new and old concrete interfaced. It can be observed from Figure 3a that the failure surface of the new and old concrete presented a smooth and complete state, and there was no aggregate attached to the fracture surface. When the specimen with the interfacial roughness of 1 mm reached the ultimate load, it made a slight cracking sound. Figure 3b shows the old concrete’s fracture surface in black and white. The black part is mainly composed of ceramsite sand and shale ceramsite. This phenomenon showed that the interface between the new and old concrete had a bonding effect. The specimen with an interfacial roughness of 3 mm produced the sound of fine breakage during the loading process. It also produced the sound of clicking when the bearing capacity reached its limit. The specimen broke along the bonding surface of the new and old concrete. As shown in Figure 3c, more full lightweight ceramsite concrete was bonded on the failure surface of the old concrete. This shows that the new concrete and the old concrete combined very well. The failure state of the specimens with an interface roughness of 5 mm is displayed in Figure 3d. It can be seen that large areas of aggregate were exposed at the interface between old and new concrete.

3.1.2. Experimental Phenomena of Interfacial Agent Factors

The damage to the interface under different interface agents is indicated in Figure 4. The specimen without the interfacial agent did not produce a cracking sound accompanied by a uniform load increase. In contrast, the specimen coated with the interfacial agent generated a fine breaking sound. It was found that the specimen coated with the cement paste had more cement slurry on the fracture surface, as shown in Figure 4a,b. Figure 4c shows that the fracture surface had obvious black silcrete slurry. In addition, a distinct white gummy substance was observed on the failure surface, as depicted in Figure 4d,e. Simultaneously, some broken gravel could be seen on the broken torus in Figure 4e.

3.1.3. Experimental Phenomena of Age Factors in Existing Concrete

Figure 5 illustrates the failure conditions of specimens with different ages of concrete. The bonds tested differed significantly between the curing times of 3 days, 7 days, 14 days, and 28 days, 90 days. The fracture surfaces of the specimens were black and white, as shown in Figure 5a–c. In addition, a large area of aggregate was exposed at the interface when specimens aged 3 days were broken. This phenomenon showed that the interface between the new and the old concrete had a certain flexural performance at this time. The failure conditions of the specimens at 28 days and 90 days were essentially the same. Simultaneously, some aggregate was exposed at the interface, as shown in Figure 5d,e.

3.1.4. Test Results

The flexural strength was used as an index to analyze the effects of the interfacial roughness, the interfacial agent, and the age of the existing concrete on the flexural performance. The specimens in Table 6 were grouped and their flexural strengths are shown.

3.2. The Effect of Repair

By calculating the data in Table 6, the flexural strength of the LC50 full lightweight ceramsite concrete was found to be equivalent to that of the C50 ordinary concrete. Its strength grade was one level higher than that of the original structure. Therefore, LC50 lightweight concrete can be used as a repair material for C50 ordinary concrete, according to GB 50367-2013 [39]. The interface between the old and the new concrete was the most vulnerable part of the structure, so the flexural strength at the interface could represent the flexural strength of the repaired structure. The group Z-45 was undamaged old concrete, with an average bending strength of 4.86 MPa. The groups of C-0~C-5 and J-0~J-4 were specimens repaired by interfacial-roughness and interface agents, respectively. Their flexural strengths ranged from 2.86 MPa to 3.96 MPa. It was seen from simple calculations that with the enhancement of the roughness, the flexural strength of the interface increased to varying degrees. It was possible to restore the flexural strength of the specimen to 59% of the undamaged specimen. The new and old concrete interfaces were coated with different interfacial agents. The flexural strength of the specimen was restored to 62%~78% of the undamaged strength.

3.3. Influencing Factors and Rules of Flexural Strength

3.3.1. Effect of Interfacial Roughness on Flexural Strength

It can be seen in Figure 6 that with the increase in the interfacial roughness, the flexural strength of the new and old concrete increased first and then decreased. The flexural strength of the interface reached its maximum when the interfacial roughness reached 3 mm. Moreover, a positive quadratic functional relationship between the two was observed through data fitting. The fitting relation is shown in Equation (3), and the R² is 0.93. It can be observed that, in Equation (3), when the roughness (average depth of the rough surface) is about 3 mm, the flexural strength reaches 3.31 MPa. Clearly, the interfacial roughness played an important role in the flexural strength of the interface. The reason for this phenomenon was that appropriate interfacial roughness can provide sufficient mechanical biting force to improve the flexural performance of the interface [40]. However, if the interfacial roughness is overtreated, microcracks occur in the near surface layer. In this way, the integrity of ab existing concrete structure is damaged and the interfacial bond strength decreases [41]. As a result, in relevant repair works, the roughness of the interface between new and old concrete should be controlled reasonably.

$$f_f=-0.05h^2+0.3h+2.86$$

(3)

where $f_f$ represents the flexural strength of the interface (MPa) and h represents the interfacial roughness (mm).

3.3.2. Effect of Interfacial Agents on Flexural Strength

An investigation of the flexural strengths of specimens without and with various interfacial agents is presented in Figure 7. It can be observed that brushing the interfacial agent at the interface can effectively improve its flexural strength. The reason for this is that brushing the interfacial agent can improve the microstructure of the interfacial area, including the compactness, morphology, and distribution characteristics of hydration products [42]. Microlevel mechanical occlusion increases flexural strength at the interface by improving mechanical occlusion. In addition, the flexural strength of the interface was significantly improved after it was coated with an epoxy-resin interfacial agent. The use of the specimen restored its flexural strength to 77% of its pre-damage value. The influence sequence of the interfacial agents was polymer-class interfacial agent, silica-fume interfacial agent, and cement-paste interfacial agent. This is because polymer-based organic interfacial agents form films and cover aggregates and cement particles with their surface chemistry. Polymers, which form the film, prevent micro-cracks from developing and enhance their adhesion to concrete [5]. This showed that brushing the interfacial agent was an effective way to enhance the interface flexural strength.

3.3.3. Effect of Curing Age on Flexural Strength of Existing Concrete

Figure 8 illustrates the effect of the differences in curing age of the existing concrete on the flexural strength of the interface between the new and the old concrete. It was found that the flexural strength of the existing concrete decreased rapidly when the curing age was less than 28 days. As the curing age continued to increase, the flexural strength decreased slowly with the growth of the curing age until it became stable. Due to the water membrane, the active ions in new concrete penetrate into the pores of existing concrete during the repair process. The existing concrete’s pores are filled with reaction products when they react with cement. Eventually, a permeable layer is formed. However, with the increase in curing age, the existing concrete’s porosity decreases gradually. Consequently, the permeable layer becomes thinner, reducing the adhesion between the new and the old concrete [43]. When the curing period exceeds 28 days, the concrete’s strength stabilizes. It is rare for new concrete or old concrete to lose flexural strength with the aging process [44].

A positive negative exponential relationship was found between the two forms of concrete after fitting the data. The equation for this relationship is shown in Equation (4) and R² is 0.97. Therefore, the earlier the existing concrete was repaired in the project, the better the effect. The concrete’s age was over 28 days, and the age of the repaired interface had little effect on its flexural strength.

$$f_f=0.93{exp}^{(-T/18.11)}+3.22$$

(4)

where $f_f$ is the flexural strength of the interface (MPa), and T represents the curing age of the existing concrete (d).

4. Analysis of Results

4.1. Degrees of Influence of Various Influencing Factors on New and Old Concrete

It can be concluded, based on the research presented above, that the flexural strength of the interfaces between the new and the old concrete was influenced by factors like the roughness, the type of interfacial agent, and the curing age. However, in actual repair projects, it might not be possible to consider these factors together for some reason. It may therefore be more helpful to guide related repair work if these factors can be quantified, as they affect the bending strength of the interface.

The difficulties above can be resolved very effectively through univariate variance analysis, based on previous findings [6,14,45]. With this method, F-values can be calculated for the interface between old and new concrete based on the impact of various factors on flexural strength. In

Table 7. Calculation formulas and results for each parameter.

Calculation Parameters	Calculation Formula	Interfacial Roughness	Interfacial Agent	Difference in Curing Age between New and Old Concrete
Within-group sum of squares	$SSE={\sum }_{j=1}^m\left[{\sum }_{i=1}^{n_j}{\left(x_{ij}-\stackrel{-}{x_j}\right)}^2\right]$	0.0348	0.03	0.1028
Sum of squares of deviations between groups	$SSA={\sum }_{j=1}^m{n}_j{\left(\stackrel{-}{x_j}-\stackrel{-}{x}\right)}^2$	0.6519	1.0029	1.3617
Within-group mean square deviation	$MSE=\frac{SSE}{n-m}$	0.0044	0.003	0.0103
Mean-square deviation between groups	$MSA=\frac{SSA}{m-1}$	0.2173	0.2507	0.3404
F value	$F=\frac{MSA}{MSE}$	49.37	83.56	33.05
$F_{0.025}\left(m-1,n-m\right)$	According to the F-distribution table	14.54	8.84	8.84
$F_{0.05}\left(m-1,n-m\right)$		8.85	5.96	5.96
$F_{0.1}\left(m-1,n-m\right)$		5.25	3.92	3.92
Level of influence	If F > F0.025, this factor has an extremely significant impact on the flexural strength. If F0.025 > F > F0.05, then this factor has a significant impact on the flexural strength. If F0.05 > F > F0.1, then this factor has almost no effect on the flexural strength. If F < F0.1, then this effect has no effect on the flexural strength.	Extremely significant impact	Extremely significant impact	Extremely significant impact

, we present the calculation program and the results of the analysis of variance for the three influencing factors.

Table 7 clearly shows that the F values for the interfacial roughness, type of interfacial agent, and curing age of the new and old concrete were 49.37, 83.56, and 33.05, respectively. The data showed that the interfacial agent had the greatest impact on the flexural strength of the new and old concrete, followed by the interfacial roughness, and the existing concrete’s curing age had the smallest impact. Therefore, it is recommended to use interfacial agents when repairing concrete in practical engineering projects.

4.2. Formula for Flexural Bearing Capacity of New and Old Concrete

Based on the analysis above, only a single factor was considered to influence the flexural strength of old and new concrete. In the actual repair work, the flexural strength of the interface between the new and the old concrete was often influenced by multiple factors. The comprehensive effects of the interfacial roughness, interfacial agents, and differences in curing ages were not considered in this experiment. In the process of repairing existing concrete, the flexural strength of new concrete can be determined through flexural tests. However, it is difficult to determine the flexural strength of old and new concrete interfaces, which requires the theory to be extended. The idea of establishing the equation while taking multiple factors into account is similar to those of Ding [46] and Huang [14]. Therefore, based on the flexural strength of the new concrete and considering three influencing factors, a formula for calculating the flexural strength of the interface between the new and the old concrete was derived.

$$f_f=K{\alpha }_1{\alpha }_2{\alpha }_3{f}_c$$

(5)

In the equation, $f_f$ is the flexural strength of the interface between the full lightweight ceramsite concrete and the ordinary concrete (MPa), K is the correction factor, ${\alpha }_1$ is the influence coefficient of the interfacial roughness, ${\alpha }_2$ is the influence coefficient of the interfacial agent, ${\alpha }_3$ is the influence coefficient of the difference in curing age between the new and the old concrete, and $f_c$ is the compressive strength (MPa) of full lightweight ceramsite concrete.

4.2.1. Influence Coefficient of Interface Roughness ${\alpha }_1$

The 28-day-cured full lightweight ceramsite concrete had a compressive strength of 53.66 MPa, according to Table 5. It is possible to calculate the flexural strength of the interface between new and old concrete cured for 28 days with different interfacial-roughness values by using Equation (6).

$${\alpha }_1=\frac{-0.05h^2+0.3h+2.86}{53.66}=-0.00093h^2+0.00559h+0.0533$$

(6)

where ${\alpha }_1$ is the influence coefficient of interfacial roughness, and h is the interfacial roughness (mm).

4.2.2. Influence Coefficient of Interface Agent ${\alpha }_2$

The values of the different interfacial agents in Table 6 were calculated by combining the data from groups J-0 to J-4. In the absence of interfacial agents, ${\alpha }_2$ was taken as 0.0563. The ${\alpha }_2$ was 0.0606, 0.0630, 0.0660, and 0.0704 when cement paste, silica fume, polymers, and epoxy resin were used as the interfacial agents.

4.2.3. Influence Coefficient of Difference in Curing Age between New and Old Concrete ${\alpha }_3$

The same determination process for ${\mathsf{\alpha }}_1$, ${\mathsf{\alpha }}_3$ was obtained by a simple calculation, as shown in Equation (7).

$${\alpha }_3=\frac{0.93{exp}^{(-T/18.11)}+3.22}{53.66}=0.0173{exp}^{(-T/18.11)}+0.0600$$

(7)

where ${\alpha }_3$ is the influence coefficient of the difference in curing age between new and old concrete, and T is the difference in curing age (d) between new and old concrete.

4.2.4. Determination of the Formula for Calculating the Flexural Strength of the Interface between New and Old Concrete

Firstly, Equations (6) and (7) were substituted into Equation (5) to obtain Equation (8). Based on this analysis, the K value was 266.959 and the R² was 0.99. A final calculation was performed using Equation (9) to determine the flexural strength at the interface between the new and the old concrete.

$$f_f=K(-0.00093h^2+0.00559h+0.0533{)\alpha }_2(0.0173{exp}^{(-T/18.11)}+0.0600{)f}_c$$

(8)

$$f_f=266.959(-0.00093h^2+0.00559h+0.0533{)\alpha }_2(0.0173{exp}^{(-T/18.11)}+0.0600{)f}_c$$

(9)

where $f_f$ is the flexural strength of the interface between the full lightweight ceramsite concrete and the ordinary concrete (MPa), h is the interfacial roughness (mm), and T is the difference in curing age between the new and the old concrete (d). When the interfacial agent is not used, the influence coefficient of the interfacial agent is taken as 0.0563. When using interfacial agents such as cement paste, silica-fume cement paste, polymer interfacial agent, and epoxy-resin interfacial agent, the influence coefficients of the interfacial agents are 0.0606, 0.0630, 0.0660, and 0.0704, respectively. The $f_c$ is the compressive strength (MPa) of the full lightweight ceramsite concrete.

4.3. Calibration of Formulas

In order to calibrate the formula for calculating the flexural capacity of old and new concrete, as shown in

Table 8. Calibration data for new and old concrete flexural capacity equations.

Group Number	Compressive Strength of Lightweight Aggregate Concrete (MPa)	Interfacial Roughness (mm)	Interfacial Agent	Curing Age (d)	Measured Value (MPa)	Calibration Value (MPa)
a	43.27	2	cement paste	28	1.03	2.71
b	53.70	1.5			1.07	2.96
c	53.70	2			1.52	3.36
d	63.50	2			2.01	3.97

, we collected four sets of data on the flexural properties of old and new concrete and substituted them into Equation (9). Finally, the calibrated data were compared with the original data. The data were taken from [47]. As shown in Figure 9, the change trends of the test results and calibration results were consistent. This indicated that the calibration results were accurate. However, there was a certain gap between the two flexural strength values. This may have been due to factors such as different aggregate particle sizes [48], different mix proportions [49] and different curing conditions for lightweight aggregate concrete [50]. In view of the results presented, the formula can be used in similar case studies.

5. Conclusions

The following conclusions can be drawn from the above results and discussion.

(1)

The repair of C45 ordinary concrete with LC50 lightweight ceramsite concrete can make the flexural strength of the repaired structure reach about 75% of that of an existing concrete structure. Moreover, the composite structure can fulfil relevant specifications after repair.

(2)

As the interfacial roughness increased, the flexural strengths of the new and old concrete increased to varying degrees. When the roughness was 3 mm, the flexural strength reached its maximum value. However, if the treatment level of the interfacial roughness continued increase, this might have led to microcracks at the interface. This would have destroyed the integrity of the existing concrete and eventually led to a decrease in the flexural strength at the interface. Therefore, when the roughness of the new and old concrete interface was processed, the interfacial roughness should be reasonably controlled.

(3)

By comparing the repair effects of different interfacial agents on the flexural strength of the interface between the new and the old concrete, it was found that the coating interfacial agent effectively improved the flexural performance of the new-and-old-concrete interface. In particular, the epoxy-resin interfacial agent had the greatest effect on the flexural strength of the interface, restoring the flexural strength of the specimen to 77% before damage occurred.

(4)

The existing concrete’s curing age and its interface’s flexural strength exhibited a negative exponential relationship. When the curing age was less than 28 days, the flexural strength of the interface decreased rapidly. After 28 days of curing, the flexural strength decreased slowly with the increase in the age until it tended to become stable.

(5)

Through the single-variable analysis of variance, it was found that the order of influence of three factors on the flexural strength of the interface was interfacial agent > interfacial roughness > existing concrete’s curing age. Therefore, in the actual repair project, the use of interfacial agents to repair the interface should be given priority.

(6)

The flexural strength of the interface between full lightweight ceramsite concrete and ordinary concrete was calculated using a formula. Three influencing factors were also taken into account in the formula. This study aimed to provide a scientific reference for the reinforcement of concrete projects with full lightweight ceramsite concrete.