Bond Behavior Between Steel Fiber Reinforced Polymer (SRP) and Concrete

The concrete was produced from normal-weight dolomitic limestone coarse aggregate with a maximum size of 16 mm, natural river sand, and commercial Portland Type I/II cement. The concrete mixture had a design compressive strength of 30 MPa to represent concrete used in existing civil structures in need of strengthening. The mixture proportions by weight ratio were (cement: sand: aggregate) = (1:00: 3.33: 2.51), and the water-cement ratio was 0.59. The concrete compressive and splitting tensile strengths were obtained experimentally using 101.6 mm diameter × 203.2 mm long cylinders in accordance with ASTM C39/C39M (ASTM C39/C39M-17b 2017) and ASTM C496/C496M (ASTM C496, C496M 2017), respectively. The compressive and splitting tensile strengths, each determined as the average of three tests, were 25.79 MPa (CoV = 0.08) and 2.47 MPa (CoV = 0.07), respectively.

The polymeric matrix used in the SRP composite was a thixotropic epoxy (Kerakoll 2020). The tensile strength, shear strength, flexural elastic modulus, and secant Young’s modulus under compression, according to the manufacturer (Kerakoll 2020), were \(>\) 14 MPa, \(>\) 20 MPa, \(>\) 2.5 GPa, and \(>\) 5.3 GPa, respectively.

The SRP composite fibers were made of unidirectional high strength steel cords, see Fig. 1. Each cord had a cross sectional area (\(A_{cord}\)) of 0.538 mm² and consisted of five wires. Three straight wires formed the core of the cord, and two wires were twisted around them in a helical manner, see Fig. 1. The wires were galvanized with a zinc coating and were laid on a fiberglass mesh backing to facilitate installation. According to the manufacturer (Kerakoll 2020), the fiber sheet had a tensile strength of > 3000 MPa, and an elastic modulus of > 190 GPa.

Different fiber sheet densities, defined in terms of net fiber weight per unit fiber sheet area (in g/m²), were achieved by different cord spacings. Two fiber sheet densities were tested in this study, referred to herein as medium density (MD) and low density (LD) fibers, see Fig. 1a. Most tests in this study were conducted using the MD fibers because the direct shear test specimens with MD fibers achieved the desired failure mode (composite debonding), whereas the specimens with LD fibers failed due to fiber rupture, as discussed in Sect. 4. The properties of the fiber sheets provided by the manufacturer are listed in Table 1. It should be noted that the properties given in Table 1 generally apply to composites of relatively wide width, with a large number of cords.

Three MD bare fiber tensile coupons with 15 steel cords were tested in uniaxial tension, see Table 2. Figure 1b shows the tensile test of a MD bare fiber sheet. An extensometer was used to measure the axial strain in the fibers. The applied load-axial strain relationship of specimen BF_2 is plotted in Fig. 2. As the load approached the maximum load, one fiber chord ruptured followed by sudden rupture of the remaining fiber chords, see Fig. 3b and c. The maximum applied load was 23.88 kN. Considering the actual cross sectional area of the fibers in the tensile coupon, 15 ×  0.538 mm² = 8.07 mm², a maximum stress of 2959 MPa was obtained from the maximum load, which is similar to the value provided by the manufacturer. Based on the actual cross sectional area, the elastic modulus was determined from the secant slope at 5 kN, and values are reported in Table 2. The average elastic modulus for the MD bare fiber sheet was 190.8 GPa (CoV = 0.05). This value is slightly larger (approximately 5%) than the values reported in (Ascione et al. 2017), where the cross sectional area of the fiber sheet was computed by multiplying the equivalent thickness of the fibers by the width of the assumed equivalent strip instead of using the area corresponding to the actual number of cords.

Four 50 mm wide × 4 mm thick SRP tensile coupons consisting of MD fiber sheets with 15 steel cords embedded in the polymeric matrix were fabricated and tested in tension, see Fig. 1a and b. Digital image correlation (DIC) (GOM 2020; Zhu et al. 2014) was employed on one of the four coupons to determine the axial strain along the fiber direction on the surface of the SRP plate. The images were taken by a Sonyα6000 camera remotely controlled by a computer. With the control unit, the camera was triggered at a selected frequency. The images were evaluated using a commercial software package (GOM 2020).

The applied load-axial strain response of specimen SRP_4_D is plotted together with the DIC results of axial strain at different load levels in Fig. 2. Figure 2 shows that the stress–strain behavior is nonlinear. It can be seen that at the beginning of loading, the applied load increased linearly, and no cracks were observed on the SRP surface according to the DIC results. At a load level of approximately 12 kN, the first crack, marked by larger axial strain on the surface of the specimen shown in the DIC results, occurred within the SRP matrix along the transversal direction (perpendicular to the fibers), resulting in a reduction of the slope of the applied load-axial strain curve. With further increase in load, more cracks were observed on the surface of the SRP, and the existing cracks became wider. At the peak load, the average spacing of cracks was around 10 mm, see the multiple large axial strain bands in the DIC results.

Similar to the bare fiber test in Sect. 2.3, the secant slope at 5 kN was taken as the elastic modulus of the SRP plate, \(E_{f,SRP}\), see Table 2. It should be noted that \(E_{f,SRP}\) was determined with respect to the equivalent thickness of the fibers (\(t_{f}\), see Table 1) for comparison with values reported in previous studies (Carloni et al. 2017; Santandrea 2018) and for use in calculations later in this paper. The average \(E_{f,SRP}\) for the SRP tensile coupons with MD fibers was 257.2 GPa (CoV = 0.08). This value is similar to the values determined by similar tension tests of SRP plates with the same fibers but different sheet densities and polymer matrix reported in (Carloni et al. 2017; Santandrea 2018).

The failure mode of each specimen is reported in Table 3. Regarding specimens with MD fibers, most specimens failed due to debonding of the composite, which occurred within the concrete adjacent to the matrix-concrete interface. A thin layer of concrete was still attached to the SRP strip after debonding failure (Fig. 5). The failure was brittle and catastrophic. Two specimens, MD_120_8 and MD_210_7_D, failed due to fiber rupture, with a maximum load of 22.70 kN and 24.12 kN, respectively. The maximum loads achieved by these specimens were the highest of all specimens and were approximately equal to the tensile strength of the fibers and SRP plate, see Table 2. All specimens with LD fibers failed due to fiber rupture, see Table 3.

From the beginning of loading to the failure of specimens, no obvious cracks were observed on the surface of the concrete substrate, nor were any cracking sounds noted. However, one salient difference between SRP- and FRP-concrete joints is that the SRP strips exhibited multiple cracks along the transversal direction, similar to the response of the SRP tensile coupons discussed in Sect. 2.4. As an example, Fig. 6 shows the load response of specimen MD_210_8_D and the axial strain along fiber direction measured by DIC. At Point A, initial cracking occurred at the loaded end of the specimen. After the applied load reached a peak value, see Point C in Fig. 6a, there was a dramatic load drop. The load drop was caused by the first wave of local debonding of a portion of the SRP strip near the loaded end, see the comparison between Points C and D in Fig. 6b. Then, with the increase of global slip, the transversal cracks became wider until the load reached another local peak, Point F, see Fig. 6a. After Point F, there was another dramatic load drop, which was caused by the formation of another transversal crack, and the second wave of interfacial debonding, see the comparison between Points F, G, H, and I in Fig. 6b. Then the load increased to Point K and axial strain was recorded at the free end of the bonded area. The load increased again until the failure of the specimen, Point M, see Fig. 6a. At Point M, several large transversal cracks were detected by DIC along most of the bonded length, see Fig. 6b. The transversal cracks were slightly unsymmetrical, which is likely the result of non-uniform bonding conditions due to local variations in the concrete surface (e.g., presence of aggregate) since the load-history responses of the two LVDTs used to measure and control the loaded end slip were consistent with one another. The DIC results clearly show the initiation and widening of the transversal cracks caused by longitudinal interfacial cracking, which was visibly observed on the side of the specimen. The longitudinal interfacial crack formed at the loaded end and propagated towards the free end with the increasing global slip.

After failure of the specimens, in general, a relatively large piece of concrete detached from the substrate near the composite loaded end, while a smaller piece of concrete sometimes detached near the free end of the SRP strip (Fig. 5). The thickness of the concrete layer attached to the debonded SRP strip elsewhere varied approximately between 1 and 8 mm. The surface of the failure zone of the concrete prism was uneven, with the aggregate being clearly visible (Fig. 5).

The load responses of the single-lap shear tests are plotted in Figs. 7, 8, and 9 for all specimens, maintaining the distinction between different bonded lengths, fiber sheet densities, and presence/absence of the matrix in the unbonded region. Figure 7a and b show that, for specimens with a relatively short bonded length (L = 30 and 60 mm), the load increased almost linearly until failure. There was a consistent initial slope among different specimens. It is interesting to see the formation of a concrete bulb of thickness of 4–10 mm at the composite loaded end, see Fig. 5a and b. For specimens with a bonded length equal to or larger than 90 mm, Fig. 7c–h show that the initial linear response was followed by a non-linear branch until a larger load was achieved, which sometimes corresponded to the peak (maximum) load of the specimen. The drop in load that followed marks the onset of the interfacial crack propagation (Carloni et al. 2017), as explained in Sect. 4.1. For specimens with L > 120 mm, as the interfacial crack propagated, the load remained approximately constant with fluctuations until the failure of the specimen.

Figure 8 shows the load responses of the specimens with LD fibers and a bonded length L = 240 mm. It can be seen that the load response was initially linear with a slight softening behavior until around 12 kN where fiber rupture occurred, which provides a lower shear capacity of the SRP-concrete joints compared with specimens with MD fibers with the same bonded length.

Figure 9 shows the load responses of the specimens with MD fibers, bonded length L = 240 mm, and bare fibers in the unbonded region. Comparing the results with those in Fig. 7h, it can be seen that the load response is almost the same as the response of similar specimens with matrix along the unbonded region. This indicates that the presence of the matrix in the unbonded region did not significantly influence the results.

Values of the peak load, \(P_{max}\), and the global slip at failure (referred to as the ultimate global slip), \({g}_{ult}\), are listed in Table 3. It should be noted that only specimens with the failure mode of debonding are considered when computing average values in Table 3. Figure 10 plots the relationship between \(P_{max}\) and L for all specimens with MD fibers that failed due to debonding, with the exception of those with bare fibers in the unbonded region. The results in Fig. 10 show that \(P_{max}\) increases as L increases from 30 mm to 120 mm, and then \(P_{max}\) remains nearly constant for larger values of L. These results are used in Sect. 5 to determine the bond-slip relationship for the SRP-concrete interface.

Figure 11 plots the relationship between \({g}_{ult}\) and L for specimens with MD fibers that failed due to debonding, with the exception of those with bare fibers in the unbonded region. The results in Fig. 11 show that \({g}_{ult}\) increases with L, however, a large scatter was observed, especially for specimens with long bonded length.

Chen and Teng proposed a semi-empirical equation to predict \(P_{max}\) and \(L_{e}\) based on a modification of an existing fracture mechanics model with suitable simplifications (Chen and Teng 2001). The equation is given as:where, \(\beta_{w} = \sqrt {\frac{{2 - b_{f} /b_{c} }}{{1 + b_{f} /b_{c} }}}\), and \(\beta_{l} = \left\{ {\begin{array}{ll} {1, \quad\quad\quad\quad\quad if\quad L \ge L_{e} } \\ {\rm sin}\left( {\frac{\pi L}{{2L_{e} }}} \right),\quad if\quad L < L_{e} \\ \end{array} } \right.\). The effective bond length \(L_{e}\) is given as:

Lu et al. proposed the following equation based on a meso-scale finite element analysis (Lu et al. 2005):where \(G_{f} = 0.308\beta_{w}^{2} \sqrt {f_{t} }\), \(\beta_{w} = \sqrt {\frac{{2.25 - b_{f} /b_{c} }}{{1.25 + b_{f} /b_{c} }}}\), \(\beta _{l} = \left\{ {\begin{array}{ll} {1,~\,\,\,\,\quad \quad \quad\quad \quad if\quad~L \ge L_{e} } \\ {\frac{L}{{L_{e} }}\left( {2 - \frac{L}{{L_{e} }}} \right),~\quad if\quad~L < L_{e} } \\ \end{array} } \right.\)and \(f_{t}\) is the tensile strength of concrete. \(L_{e}\) is given as:

Units of MPa and mm shall be used in Eqs. (13)–(16).

Neubauer and Rostasy proposed the following equation (Neubauer and Rostasy 1997):where \(\beta_{w} = \sqrt {1.125\frac{{2 - b_{f} /b_{c} }}{{1 + b_{f} /400}}}\), and \(L_{e}\) is given by:

Maeda et al. proposed the following equation (1997):where \(\tau_{u} = 110.2 \times 10^{ - 6} E_{f} t_{f}\), and \(L_{e}\) is given by:

Units of MPa and mm shall be used in Eqs. (19) and (20).

The models described above have been calibrated based on experimental data. It should be noted the model by Maeda et al. (1997) is the only model considered herein that does not consider the effect of the concrete strength.

In order to examine the validity of the equations described in Sect. 6.1 for SRP-concrete joints, a database of test results was collected from the literature (Ascione et al. 2017; Santandrea 2018). The database included the results of the present study as well as others that met the following criteria: (1) the specimen was tested in single-lap shear; (2) the specimen failed due to interfacial debonding; and (3) the elastic modulus of the SRP strip \(E_{f,SRP}\) with the corresponding sheet density has been reported in the literature. In addition, specimens with a loading rate that was dramatically different from the rate utilized in this study (0.00084 mm/s) and in (Santandrea 2018) were excluded. The database included 170 test results and is presented in Additional file 1. Test specimens included SRP strips with three different sheet densities, and the SRP composite was provided by the same manufacturer. Values of \(E_{f,SRP}\) were reported in Sect. 2.4 or in (Santandrea 2018). The compressive strength of concrete ranged from 12.8 to 39.7 MPa. For the specimens reported in 0, the tensile strength of concrete was not reported; therefore the expression \(f_{t}{^{ \prime}} = 0.3f_{c}{^{\prime}}^{2/3}\) from Eurocode 2 (Bamforth et al. 2008) was used to determine the concrete tensile strength of strength classes ≤ C50/60.

Figure 13 plots the predicted versus experimental value of \(P_{max}\) determined by Eqs. (13), (15), (17), and (19). The average ratio of \(P_{max}\) predicted by Eq. (13) to the corresponding experimental value is 0.95 with a CoV of 0.28. The average ratio of \(P_{max}\) predicted by Eq. (15) to the corresponding experimental value is 0.97 with a CoV of 0.29. The average ratio of \(P_{max}\) predicted by Eq. (17) to the corresponding experimental value is 1.16 with a CoV of 0.29. The average ratio of \(P_{max}\) predicted by Eq. (19) to the corresponding experimental value is 1.11 with a CoV of 0.32. Thus, all equations are in reasonable agreement with the experimental results, but Eqs. (13) and (15) tend to underestimate the experimental value of \(P_{max}\), whereas Eqs. (17) and (19) tend to overestimate the experimental value of \(P_{max}\). The variation is mainly caused by the large scatter of the test data of (Ascione et al. 2017), which can be attributed, in part, to the fact that different surface treatments were evaluated in that study, which resulted in different strengths of the concrete adjacent to the bond adhesive. In addition, it should be noted that the elastic modulus \(E_{f,SRP}\) considered in this evaluation corresponds to the initial response of the SRP plate tensile stress–strain behavior, as discussed in Sect. 2.4. Although the stress–strain response becomes non-linear at relatively high axial strain levels, (see Fig. 2), this simplification was justified by results in (Carloni et al. 2017) that show that the axial strain in the SRP strip along the bonded length reduces rapidly with increasing distance from the loaded end. However, future work should investigate the effect of the non-linear response of the SRP plate, which may help to improve the overall accuracy of the analyses and predicted results.

For the specimens with MD fibers that exhibited the failure mode of debonding in this study, the effective bond length \(L_{e}\) predicted by Eqs. (14), (16), (18), and (20) is 93 mm, 113 mm, 94 mm, and 51 mm, respectively. All four equations underestimated the effective bond length compared with the results given by Eq. (12) of 118 mm. Of the four equations, Eq. (16) has the best accuracy (within 4%).