Shear strengthening of deficient RC deep beams using NSM FRP system: Experimental and numerical investigation

According to Table 1, beams were developed with a targeted compressive strength of 65 Mpa. Standard concrete cylinders, on the other hand, averaged a compressive strength of 68.5 Mpa after 28 days. Tables 2 and 3 list the typical characteristics of steel rebars and strengthening materials properties such as carbon fiber-reinforced polymer (CFRP) sheets, epoxy primer, and Sikadur 31 thixotropic epoxy resin mortar, respectively.

The experimental program described in this paper comprised results from three RC deep beam bending tests. The beams were supported on rigid steel rollers of 75 mm diameter and subjected to a static point load applied at the mid-span of the beam. Beams were rectangular in cross-section (100 mm width and 250 mm depth) with overall and effective span lengths of 1000 mm and 850 mm, respectively. All beams had a typical longitudinal reinforcement placed in two layers with 20 mm clear spacing, each comprising 2 φ 10 deformed steel bars. Horizontal web steel of 2 φ 6 was provided at the mid-height of the beam. One layer of compression steel 2 φ 6 was also placed mainly to hold the shear stirrups. Bottom steel was arranged in a U-shape to avoid anchorage issues as detailed in Figure 1. Clear concrete cover of 25 mm was adopted for all sides of the beam cross-section.

Fig. 1.

Shear reinforcement of the beams was considered the main variable of the test program. The first beam (DB-S-F) incorporated two-legged f6 mm plain steel shear stirrups distributed equally along the full span of the beam with center to center spacing of 100 mm. The second beam (DB-NS) is the same as SF0-F, but stirrups were distributed only in one half of the span, while the other half had no stirrups. It should be noted that beam SF0 was tested as a control as a part of a previous experimental program as detailed in Albidah et al. [18] and will be reported throughout this paper for the purpose of comparison with the other two specimens.

The third beam (DB-FRP) was the same as DB-NS but with FRP strengthening. For the half span of the beam with no shear reinforcements, near surface-mounted U-wraps of unidirectional CFRP strips. Two layers of the strips were provided in 25 mm wide grooves with a depth of 25 mm at a spacing of 100 mm. Following the epoxy setting of the CFRP U-wraps with the concrete, thixotropic epoxy resin mortar was used to fill and level the grooves. The centerline of the CFRP U-wraps fits the position of the missing shear reinforcements from the half span of the beam. A horizontal CFRP strip of 50 mm width was externally bonded at midheight of the beam. The horizontal strip extended from the beam end to the mid-span at both faces. In order to properly quantify the shear resistance of the repaired section of the beam, it was necessary to upgrade both the shear capacity of the other half of the span (which is half steel stirrups) and the beam flexural capacity. Therefore, the half span of the beam having shear reinforcements was retrofitted using one layer of externally bonded full U-wrap. Also, two layers of CFRP strips were externally bonded to the soffit of the beam along the whole span length of the beam. Details of the beams are presented in Figure 1.

The beams underwent testing using a three-point bending setup. A concentrated load was applied at the center of the beam, and this load was gradually increased until the beam failed. The loading process was controlled by displacements and maintained a rate of 0.5 mm/min. To measure the displacement of the beam, a linear variable displacement transformer (LVDT) was installed beneath the midpoint of the beam. Strain gauges were placed on steel stirrups, two layers of bottom steel, and CFRP (carbon fiber reinforced polymer) sheet and strips, as shown in Figure 2. All beams had strain gauges (SG-1, SG-2, SG-3, SG 4, SG-5, and SG-6) attached to common locations on the steel rebars, as depicted in Figure 2. However, in the case of the BD-FRP specimen, additional strain gauges were attached to the CFRP flexural sheet (SG-7) and the horizontal and vertical strips (SG-8 and SG-9).

Fig. 2.

Figures 7–9 display load-displacement relationship for various kinds of test specimens. Strains in longitudinal rebars, FRP strips, and/or shear stirrups are also shown in these diagrams to help interpret the observed behavior change. The shear stirrups and FRP strips referred to here have the same numbers displayed in Figure 2.

Fig. 7.

Fig. 9.

3.2.1.

DB-S-F specimen

The load steadily grew as the beam’s mid-span deflection continued, as seen in Figure 6, until it reached around 151 kN. Both the top and bottom longitudinal rebars were yielding at this stage, and the shear stirrups yielded 0.71 times the ultimate load (Pu), as illustrated in Figure 8. After this step, the beam continued to acquire strength, albeit with lower stiffness, until it achieved the peak load of 164.2 kN. The strain in the main longitudinal rebar was approximately 1.1% at this point. Following that, the beam exhibited protracted inelastic behavior with a stable strength reduction. While the peak reaction was primarily impacted by a substantial shear crack, the post-peak curve shows indications of significant flexural contribution.

Fig. 6.

Fig. 8.

The concrete damaged plasticity (CDP) model, widely employed in FE investigations (e.g., [31–33]), was utilized to predict the behavior of concrete and Sikadur resin mortar materials. The CDP model includes isotropic damaged elasticity and compressive and tensile plasticity to effectively represent the plastic responses [1]. Hognestad [34] developed a compressive concrete model for nonlinear FE investigations. Moreover, Stoner [35] modified the curve to account for the influence of concrete confinement by introducing stirrups and the ultimate concrete strain. This study used this model to represent the stress-strain behavior of concrete under compression. When modeling tension behavior in concrete, it is noted that before reaching fracture stress, the behavior is linear and elastic, showing a steady stress increase. Following this, a gradual decrease in the stress-strain curve is noted, representing a decrease in concrete strength. The current study employed the model developed by Wang and Hsu [36] for modeling the stressstrain curve of concrete under tension. The failures in tension and compression were represented using the DAMAGET and DAMAGEC options, which were specified during the modeling phase [30]. Table 6 presents the material parameters employed in the concrete and Sikadur mortar materials within the context of the CDP. Titoum et al. [37] developed idealized stress-strain curves to model the behavior of steel reinforcement in the FE investigations, shown in Figure 9. The FRP material (i.e., CFRP) was modeled as having linear behavior, as demonstrated in other research [38, 39]. The composite laminate mode was utilized to simulate the CFRP sheets available in the ABAQUS software [30]. Table 5 presents the FRP material parameters employed in the FE investigation.

Figure 10(a) depicts the utilization of the eightnode element (C3D8R) to simulate the concrete and Sikadur mortar components. The longitudinal reinforcing bars and stirrups were depicted using a two-node and linear truss element, denoted as T3D2, as illustrated in Figure 10(a). The simulation of CFRP sheets was conducted with a shell element known as S4R, which is a three-dimensional structure consisting of four nodes. The modeling of the supports was conducted by applying a boundary condition at the reference points (RP) that attach to the lower supporting cylinders, as depicted in Figure 10(b). Displacement control was employed to gradually apply the load, utilizing the two RPs assigned to the top cylinder, as depicted in Figure 10(b). The perfect bond and interface element approaches were employed by the researchers to simulate the interfaces of the NSM [12–17]. The experimental testing did not reveal significant separation or debonding at the interfaces between the concrete, Sikadur mortar, and NSM components. Hence, the assumption of a successful bond was made in the FE modeling [40–44]. According to the findings of Banjara and Ramanjaneyulu [45], it was demonstrated that the utilization of the perfect bond yielded more accurate FE outcomes in comparison to the interface element, as evidenced by the experimental result comparison. In this study, the embedded function was employed to simulate the interactions between the concrete and steel reinforcement, as well as between the Sikadur mortar and CFRP components. The strong bond between epoxy and concrete is a consequence of the adhesive qualities of epoxy. The failure of either the concrete elements or the epoxy directly influences the total failure of the system. The mesh convergence analysis was carried out on the DB-S-F specimen using three different meshing types. The geometry, element types, and material properties remain consistent across the modeling process of the three meshing types. The results of the three meshing types are illustrated in Table 7. A comparison of the three meshing types was made to choose the appropriate mesh size. In comparison to the experimental findings, the use of mesh type 3 produced higher convergence and more accurate outcomes, as shown in Table 7. The use of a finer mesh than mesh type 3 necessitated increased allocation of resources and computer running times without achieving any convergence improvement. Finally, a mesh size of 7 mm was chosen due to its ability to produce satisfactory outcomes when compared to the experimental data, as depicted in Figure 10(c).

Fig. 10.

In this section, a numerical validation of the experimental findings is presented. Table 7 provides a summary of the obtained results, whereas Figure 11 illustrates the failure modes, and Figure 12 presents the load-deflection curves. The FE models have exhibited the capacity to predict with accuracy the failure patterns observed in experimental tests of RC deep beams exposed to flexural loads using different strengthening techniques. A comparison between the failure modes of experimental and FE outcomes for all specimens is illustrated in Figure 11. The observed deformation patterns and stress graphs in the FE models exhibit similarities to the experimental findings. Figure 12 illustrates a comparison of the loaddeflection curves obtained from the FE models and the experimental findings. The agreement level between the experimental and FE outcomes is considered acceptable. The FE model accurately represents the maximum loads recorded by the experimental specimens, as shown in Table 8. The variation seen between the FE models and experimental results is within a satisfactory range. According to the results shown in Table 6, it is evident that the highest deviation between the FE and experimental outcomes reached approximately 6%. The simulated FE models exhibited variations from the experimental specimens in certain instances. The observed variances in the FE curves and failure mechanisms can be attributed to the flawless performance exhibited by the FE specimens throughout the modeling procedures. The FE simulation utilized in this investigation was unable to totally adequately account for the initial concrete weaknesses, such as nonuniformity, deterioration, and early cracking. In summary, the simulation outcomes have presented substantial confirmation for the dependability of the FE models, thereby demonstrating their appropriateness for producing further predictions.

Fig. 11.

Fig. 12.

The integration of experimental tests and Finite Element modeling (FEM) yields a thorough comprehension of the load-displacement characteristics of deep beams. The FE model of the DB-S-F specimen showed very satisfactory results compared to the results of the experimental test, where both curves were almost the same up to the highest resistance, then the FE curve showed values slightly higher than the experimental curve.

The same trend was noticed in the FE model of the DB-NS specimen. For the FE model of the DB-FRP specimen, the FE curve showed values lower than the experimental curve. It is worth mentioning that the FE modeling curves did not illustrate any small breaks that were observed in the experimental curves. The observed variances in the FE curves can be attributed to the flawless performance (such as nonuniformity, deterioration, and early cracking) exhibited by the FE specimens throughout the modeling procedures.