**1. Introduction**

Carbon-fiber-reinforced polymer (CFRP) has been widely used in the repair and strengthening of concrete structures, because of its favorable and prominent properties (e.g., high strength-to-weight ratio, excellent corrosion resistance, and durability) [1–3]. Recently, a new strengthening technique for concrete structures using CFRP grids and sprayed PCM has caught the attention and interest of the civil engineering realm [4–7]. CFRP grid is made from continuous impregnated high-strength carbon fiber roving alternating in both longitudinal and transverse directions to form a cross-laminated grid structure with a certain rigidity, as shown in Figure 1; it has unique mechanical characteristics compared to other CFRP composites (e.g., CFRP sheets, CFRP plates and strips); that is, the horizontal grids and vertical grids jointly resist the external loads applied on the CFRP grid. Some investigations have found that CFRP grid has a satisfactory strengthening effect in improving the mechanical performance of existing concrete structures, including beams, slabs, and columns in concrete member, as well as large-span structures such as bridges and tunnels [8–11]. In addition, CFRP grid can be applied to strengthen underwater

**Citation:** Dai, H.; Wang, B.; Zhang, J.; Zhang, J.; Uji, K. Study of the Interfacial Bond Behavior between CFRP Grid–PCM Reinforcing Layer and Concrete via a Simplified Mechanical Model. *Materials* **2021**, *14*, 7053. https://doi.org/10.3390/ ma14227053

Academic Editor: Krzysztof Schabowicz

Received: 11 October 2021 Accepted: 17 November 2021 Published: 20 November 2021

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structures, because of its good bond performance with existing concrete in low-temperature and moist environments [8,12]. Currently, FRP sheets and plates are mainly used as the strengthening materials in the FRP-strengthening technique. However, there are a few drawbacks for the FRP sheets/plates jacketing method, such as the insufficient bond strength between FRP sheets/plates and existing concrete in wet environments. For this new strengthening method, the drawbacks can be effectively avoided by riveting the CFRP grid to the concrete surface. Moreover, as a protective (thermal insulation) system for CFRP grid, PCM significantly improves the peeling resistance, fire resistance, and durability [5,6,13]. PCM, a new type of modified mortar, is formed by adding a certain content of organic polymer to the conventional cement mortar; it has some advantages over the conventional cement mortar, such as high tensile strength, low elastic modulus, favorable impermeability, and frost resistance, as well as excellent bond behavior with the existing concrete [5,6,14,15]. In this new strengthening method with CFRP grid and sprayed PCM, the CFRP grid is installed on the surface of existing concrete via a rivet anchor, and PCM is sprayed on the outside surface of the CFRP grid and concrete. By means of this construction technique, the CFRP grid–PCM reinforcing layer and the existing concrete structure would be given the integrity to resist external force [16–21], which could improve the bearing capacity, stiffness, and durability of existing concrete structures, as shown in Figure 2. Compared with the conventional strengthening method using steel or FRP plates for jacketing, this new strengthening method with CFRP grid and a PCM reinforcing layer has some technical advantages, including lesser thickness of the reinforcing layer (10–20 mm), more convenient construction, lower costs and environmental dependence, etc. [5,6].

**Figure 2.** Schematic diagram of strengthened concrete structures using CFRP grid and PCM.

In the past few years, some investigators have studied the effectiveness of CFRP grid in strengthening concrete structures, indicating that this strengthening method could significantly improve the mechanical behavior of concrete structures. Nevertheless, the tensile strength of CFRP grid has not been fully utilized, due to premature interface debonding of the reinforcing layer [5,6,13,22,23]. Therefore, it is clear that the reliable bond behavior between the CFRP grid, PCM, and concrete is the key to giving full play to the high tensile strength of CFRP grid, and improving the strengthening efficiency. Guo et al. [5,6] investigated the influence of parameters such as the number of grid points, grid interval, and type of PCM on the interface bond behavior, indicating that the interface peeling failure occurs when the tensile stress exceeds the ultimate bond strength between PCM and concrete. Ding et al. [17] conducted a pull-out experiment focusing on the effects of the embedded length of CFRP grid and horizontal grid on the bond behavior of the CFRP grid–concrete interface, and found the critical embedded length required to make full use of the tensile strength of the CFRP grid. Sugiyama et al. [24] tested the interfacial bond strength between the CFRP grid–PCM reinforcing layer and concrete, showing that the type of PCM has no effect on the bond strength. However, considering that the interface between the CFRP grid–PCM reinforcing layer and concrete consists of three materials, and the PCM–concrete interface is divided into a checkerboard pattern by CFRP grid, resulting in a complicated stress state of the interface, experiments alone are not enough to reveal the bond mechanisms between CFRP grid, PCM, and concrete in detail, and further investigations based on mechanical analysis and numerical simulation are needed—similar to the research of N.K. Banjara et al. [25]. Dung [26] studied the shear bond behavior of the interface between concrete substrate and repaired mortar by combining test and finite element analysis; however, the analysis did not consider the role of grid points, and the analysis content was not comprehensive enough.

In this study, pull-out tests of four plate-type specimens with CFRP grid–PCM reinforcing layer and concrete were conducted to ascertain the maximum tensile loads and failure modes corresponding to different CFRP grid types and grid intervals. Based on the experimental results, the preliminary investigation of the bond mechanism between concrete and the CFRP grid–PCM reinforcing layer was carried out via strain analysis of the CFRP grid. Compared with the existing research, interfacial bond strength between the CFRP grid–PCM reinforcing layer and concrete was quantified via strain analysis. In addition, a simplified analysis model was proposed based on mechanical analysis. Compared with the existing models, the proposed model is more convenient to apply. Finally, in order to verify the accuracy of this proposed model, a two-dimensional finite element (FEM) analysis was conducted, putting forward a new method for the follow-up study of concrete strengthened by CFRP grid–PCM.

#### **2. Experimental Program**

#### *2.1. Details of Specimens*

Four plate-type specimens composed of concrete, CFRP grid, and PCM were fabricated. The investigation variables included the type of CFRP grid (CR6 and CR8) and the grid interval (50 mm and 100 mm). Table 1 summarizes the details of all specimens. Figure 3 shows the specimens' geometry and the arrangement of the strain gauges. The production process of the specimens can be summarized as three stages: When the curing time of concrete in a moist environment reached 21 days, the concrete surface was treated via vacuum blast. After 28 days, the CFRP grid was installed on the concrete surface by coating with epoxy primer and spraying PCM with a thickness of 40 mm. Finally, pull-out tests were carried out after the age of concrete reached 46 days. Tables 2 and 3 show the mix proportions of the concrete and PCM, respectively. The material properties of the concrete and PCM are summarized in Table 4. The material properties of the CFRP grid are shown in Table 5.


**Table 1.** Types of the specimens.

**Figure 3.** Dimensions of the specimens and arrangement of strain gauges on the CFRP grid. (**a**) C6D50; (**b**) C6D100; (**c**) C8D50; (**d**) C8D100 (units: mm).

**Table 2.** Mixture proportions of concrete.


\* Gmax: maximum size of coarse aggregate; \* SL: slump of concrete; \* W: water; \* C: cement; \* S: fine aggregate; \* G: coarse aggregate.

**Table 3.** Mixture *Proportions* of PCM.


**Table 4.** Mechanical properties of concrete and PCM.


**Table 5.** Mechanical properties of CFRP grid.


#### *2.2. Load Program*

Pull-out tests were conducted based on JSCE-E 539-2007 [27] and ACI 440.1R-06 [28]. The monotonic tensile load with a loading rate of 200 N/mm2/s was subjected to a vertical CFRP grid extended from the bond interface. To prevent eccentricity loads during the loading process, four iron blocks and steel plates were used to fix the position of the specimens. The strain gauges were installed on the surface of the CFRP grid to measure the strain values of the CFRP grid. The test schematic is shown in Figure 4.

**Figure 4.** Diagram of specimen loading.

#### **3. Experimental Results and Discussion**

*3.1. Failure Patterns and Maximum Loads*

Figure 5 shows the failure patterns of all specimens. The loading position is at the bottom of the sketch. It can be observed that the vertical tensile grids in all specimens were pulled out, and PCM developed surface cracks to varying degrees, while the interface between the PCM and the concrete remained intact throughout the whole loading process. This could attributable to the fact that epoxy primer was used on the surface between the CFRP grid–PCM reinforcing layer and the concrete, resulting in the improvement of interface bond action. For the specimens C6D50 and C6D100, no cracks appeared on the surface of the PCM, and the specimens failed due to the vertical tensile grids being pulled out. For the specimens C8D50 and C8D100, the vertical tensile grids were pulled out, and cracks appeared on the PCM. It can be seen that the degree of damage to the CFRP grids for specimens C6D50 and C6D100 was more severe than that for specimens C8D50 and C8D100. This might be attributable to the fact that the ultimate tensile action (24.5 kN) of the CR6-type CFRP grid used in specimens C6D50 and C6D100 was lower than that (36.96 kN) of the CR8-type CFRP grid used in specimens C8D50 and C8D100. Table 6 shows the maximum loads and failure patterns of all specimens. The tensile strength utilization ratio of CFRP was defined as the ratio of the maximum tensile load of the specimens to the test ultimate tensile action of the CFRP grids [29]. The tested ultimate tensile loads of the CR8 and CR6 CFRP grids were 45.07 kN and 28.6 kN, respectively. It can be seen that the tensile strength utilization ratio of the CFRP grid in specimen C6D50 was 84% higher than that in specimen C6D100, and the tensile strength utilization ratio of the CFRP grid in specimen C8D50 was 23% higher than that in specimen C8D100, indicating that the tensile strength utilization ratios of the CFRP grid with small grid intervals were higher than those with large grid intervals. This might be attributable to the fact that the smaller grid interval has more grid points to resist the tensile load, resulting in the higher tensile strength utilization ratio of the CFRP grid for specimens with smaller grid intervals compared to the specimens with larger grid intervals. In addition, it can be seen that the maximum load of specimen C8D50 with the CR8@50-type CFRP grid was 133% higher than that of specimen C6D50 with the CR6@50-type CFRP grid, and the maximum load of specimen C8D100 with the CR8@100-type CFRP grid was 247% higher than that of specimen C6D100 with the CR6@100-type CFRP grid, indicating that the specimen with the larger cross-sectional area of the CFRP grid could obtain a higher tensile capacity under the precondition of reliable interface bonding. Meanwhile, comparing specimens C6D100 and C8D50 showed that the simultaneous use of a CFRP grid with a larger cross-sectional area and smaller grid interval can significantly improve the interfacial bearing capacity between the CFRP grid–PCM reinforcing layer and the concrete.


**Table 6.** Summary of test results.

**Figure 5.** Failure patterns of the specimens: (**a**) failure pattern of PCM for specimen C6D50; (**b**) failure pattern of CFRP grid for specimen C6D50; (**c**) failure pattern of PCM for specimen C6D100; (**d**) failure pattern of CFRP grid for specimen C6D100; (**e**) failure pattern of PCM for specimen C8D50; (**f**) failure pattern of CFRP grid for specimen C8D50; (**g**) failure pattern of PCM for specimen C8D100; (**h**) failure pattern of CFRP grid for specimen C8D100.

#### *3.2. Strain Distribution of CFRP Grids*

According to the analysis above, the stress transfer mechanism between the CFRP grid–PCM reinforcing layer and the concrete is rather complicated. So as to preliminarily investigate the mode of tensile stress transfer between the three materials, the specimens C8D50 and C8D100 were taken as examples to analyze the strain distribution of the vertical tensile CFRP grid, as shown in Figure 6. It can be observed that the strain on the vertical tensile grid gradually decreased from the loaded edge to the free edge at the lower load level. However, the strain distribution patterns changed at the higher load level. For the specimen C8D50, as shown in Figure 6a, the strain of grid point GP3 sharply increased and exceeded the strain of grid point GP2 after the tensile load reached approximately 10 kN. This might be attributable to the fact that the restraining action for grid point GP3 from PCM gradually decreased with the increase in the tensile load due to the fracture of PCM (see Figure 5e), resulting in a change in the tensile stress transfer mode of the CFRP grid. For the specimen C8D100, as shown in Figure 6b, when the tensile load exceeded approximately 15 kN, the strain of grid point GP2 increased sharply, while the strain of grid point GP1 increased slightly, indicating that under the higher load, the PCM near the loaded edge fractured severely, and lost its restraining action on the grid points; after this, the tensile load was transferred to other grid points, where the PCM was relatively intact or only slightly fractured. In addition, comparing the strain distributions of two specimens, it can be found that the strain difference between the vertical grid near the loaded edge and the vertical grid far away from the loaded edge for specimen C8D50 was smaller than that for specimen C8D100, indicating that the strain distribution of the vertical grid in specimen C8D50 was more uniform than that in specimen C8D100. This might be explained by the fact that the grid interval of the CFRP grid in specimen C8D50 was smaller than that in specimen C8D100, resulting in more grid points in specimen C8D50 to share the tensile load compared to specimen C8D100.

**Figure 6.** Strain distribution patterns of the vertical grid. (**a**) C8D50; (**b**) C8D100.

#### **4. Interface Bond Mechanism**

#### *4.1. General*

The tensile stress transfer process between the CFRP grid–PCM reinforcing layer and the concrete can be divided into two stages, as shown in Figure 7. In the first stage, the tensile load applied to the vertical CFRP grid was transferred to the PCM via the anchorage action of the CFRP grid in the PCM, as shown in Figure 7b. In the second stage, the tensile stress borne by the PCM was transferred to the concrete via the interface bond between the CFRP grid–PCM reinforcing layer and the concrete, as shown in Figure 7a. Based on the experimental results mentioned above, it can be seen that the epoxy primer as an interfacial binder could effectively improve the bond behavior between the CFRP grid–PCM reinforcing layer and the concrete. Similarly, the failure modes of the specimens mainly depended on the CFRP grid and the PCM. So as to make full use of the high tensile strength of the CFRP grid, a credible anchorage of the CFRP grid in the PCM must be ensured. Previous investigators have noted that the anchorage action of the CFRP grid in PCM is mainly provided by two parts: the resistant action of the horizontal grid, and the bond action of the vertical grid [30]. In addition, it is clear that the tensile stress transfer mode between the CFRP grid and the PCM changes with the generation of cracks on the surface of the PCM. Consequently, the specimen C8D100 was taken as an example to reveal the stress behavior of the CFRP grid in PCM in further detail, based on the strain analysis of the CFRP grid.

#### *4.2. Load–Strain Difference Curves*

As discussed previously, the interface bond between CFRP grid–PCM reinforcing layer and concrete can be significantly improved by using the epoxy primer, and the tensile bearing capacity of the specimen is determined by the anchorage action of the CFRP grid in the PCM. So as to further clarify the anchorage action of the CFRP grid in the PCM, the resistant action of the horizontal grid and bond action of the vertical grid were characterized based on the strain difference on both sides of the grid points for the vertical grid, and the strain difference between the bottom and top ends within the grid interval, as shown in Figure 8. The strain values can be measured by strain gauges arranged on the CFRP grid. It was found that, under the lower load, with the increase in the tensile load, the strain difference of grid points near the loaded edge sharply increased, while the strain difference of the grid points far away from the loaded edge increased slightly. This indicates that the tensile stress was transferred from the loaded edge to the free edge by the resistant action of the horizontal grid at the grid points. However, under the higher load, the tensile stress transfer mode changed. As shown in Figure 8a, the strain difference

ε (2CH)–ε (6CH) of grid point GP1 gradually decreased after the tensile load exceeded 8.45 kN, while the strain differences of the remaining grid points continued to increase with the increase in the tensile load. Past a load of 13.18 kN, the strain difference of grid point GP1 was lower than the strain difference ε (8CH)–ε (12CH) of grid point GP2. This phenomenon might be attributable to the fact that the PCM at grid point GP1 fractured, which reduced the resistant action of grid point GP1, resulting in the transfer of tensile stress from grid point GP1 to grid points GP2 and GP3. Accordingly, the resistant action of grid points GP2 and GP3 gradually increased. In addition, it can be found that the strain difference of grid point GP1 began to increase after the tensile load reached 21.47 kN. This might be caused by the pulling out of the vertical grid (2CH) near the loaded edge. As shown in Figure 8b, under the lower load, with the increase in the tensile load, the increase in strain difference within the grid interval near the loaded edge was more significant than that far away from the loaded edge—especially the strain difference ε (12CH)–ε (14CH) far away from the loaded edge, which began to increase until the tensile load reached ~4.83 kN. This indicates that the tensile stress was transferred from the loaded edge to the free edge by the bond action between the vertical grid and the PCM. However, under the higher load (i.e., 13.59 kN), with the increase in the tensile load, the strain difference ε (6CH)–ε (8CH) near the loaded edge gradually decreased, while the strain difference ε (12CH)–ε (14CH) far away from the loaded edge continued to increase. When the tensile load exceeded 17.95 kN, the strain difference ε (12CH)–ε (14CH) was larger than the strain difference ε (6CH)–ε (8CH). This might be attributable to the fact that the fracture of the PCM near the loaded edge reduced the bond action of the vertical grid, resulting in the transfer of tensile stress via the bond action of the vertical grid far away from the loaded edge.

**Figure 7.** Schematic diagram of the stress transfer process for the specimen: (**a**) interface bond stress between the CFRP grid–PCM reinforcing layer and the concrete; (**b**) anchorage action of the CFRP grid in the PCM. *τ*cp: bond stress between the reinforcing layer and the concrete; *f* b: bond action between the vertical grid and the PCM; *f*r: resistant action of the horizontal grid.

**Figure 8.** Load–strain difference curves of the grid points: (**a**) strain difference of the grid points; (**b**) strain difference in grid intervals.
