Strengthening of reinforced concrete beams using fiber-reinforced cementitious matrix systems fabricated with custom-designed mortar and fabrics

Abstract

The performance of a new fiber-reinforced cementitious matrix (FRCM) system developed using custom-designed mortar and fabrics is investigated in this study. The behavior of this system is evaluated in terms of both the flexural and shear strengthening of reinforced concrete beams. Eight beams are designed to assess the effectiveness of the FRCM system in terms of flexural strengthening, and four specimens are designed to investigate their shear behavior. The parameters investigated for flexural strengthening are the number of layers, span/depth ratio, and the strengthening method. Unlike previous studies, custom fabrics with similar axial stiffness are used in all strengthening methods in this study. In the shear-strengthened specimens, the effects of the span/depth ratio and strengthening system type (fiber-reinforced polymer (FRP) or FRCM) are investigated. The proposed FRCM system exhibits desirable flexural and shear strengthening for enhancing the load capacity, provides sufficient bonding with the substrate, and prevents premature failure modes. Considering the similar axial stiffness of fabrics used in both FRCM and FRP systems and the higher load capacity of specimens strengthened by the former, cement-based mortar performs better than epoxy.

Graphical abstract

Keywords

fiber-reinforced cementitious matrix / flexural strengthening / shear strengthening / carbon fiber-reinforced polymer / shear span

1 Introduction

The rehabilitation and retrofitting of reinforced concrete (RC) structures have been investigated extensively owing to their practicality, as well as their necessity for repair owing to changes in the requirements of design codes, corrosion of steel bars, inappropriate maintenance, and aging. Fiber-reinforced polymer (FRP) composites are widely used for strengthening in the construction industry owing to their lightweightness, high tensile strength, resistance to corrosive agents, and easy utilization. However, the application of FRP composites presents a few disadvantages, such as susceptibility to fire, incompatibility with the concrete substrate, inability to be installed on wet surfaces, and difficulty in installation at low temperatures [1–4]. Fiber-reinforced cementitious matrix (FRCM) systems, which use an inorganic matrix as a binder, have been introduced as an alternative to overcome the aforementioned liabilities. Similar to FRP composites, FRCM systems are used increasingly to achieve external bonding to damaged RC elements by substituting epoxy resin with a cement-based mortar.

In recent years, the performance of FRCM-strengthened RC structures has been investigated in different areas. The application of FRCMs for the flexural [5–9] and shear strengthening [10–15] of RC beams has been extensively investigated; in this regard, satisfactory results have been reported for the confinement of columns [16,17], flexural strengthening of slabs [18], and strengthening of masonry structures [19,20]. The effectiveness of an E-glass fiber-reinforced cementitious matrix (GFRCM) for the confinement of concrete columns was investigated by testing eight concrete columns with internal steel reinforcement. The columns exhibited two types of cross-sectional geometries and two stirrup spacing values. The application of GFRCM jackets has shown to improve the axial strain and confined compressive strength and decreased the strength degradation of transverse steel bars in columns with different reinforcement ratios and cross-section geometries. Meanwhile, the fatigue performance of FRCM-strengthened RC beams has been investigated [21,22]. The behavior of corrosion-damaged RC beams strengthened in terms of both shear and flexure by FRCM composites has been analyzed [23,24]. The effects of environmental conditions, namely temperature and humidity, on the interfacial bond behavior and ultimate capacity of FRCM systems have been reported in the literature. de Domenico et al. [25] revealed that the peak load and displacement of specimens strengthened by a polyparaphenylene benzobisoxazole (PBO)–FRCM system were not affected by environmental conditions, including immersion in water at temperatures of 30 and 50 °C for 31 d. The conditioning factors, including immersion in water for different durations (from 4 to 74 d) at 23, 30, and 40 °C, can adversely affect the carbon fiber-reinforced polymer (CFRP) strengthening system, particularly as the exposure time increases. By contrast, the PBO–FRCM system is affected less by longer exposure to environmental conditions and is affected more significantly by short periods of exposure in terms of bond strength and failure loads [26]. The DIC method was successfully used to investigate the interfacial bond behavior between FRCM systems and concrete surfaces in notched concrete beams under different environmental conditions. DIC images were analyzed to elucidate the mechanical behavior of specimens, which revealed the interaction between the FRCM system and concrete surface [27]. Meanwhile, Awani et al. [28] conducted a comprehensive state-of-the-art review of FRCM systems.

Some parameters govern the efficiency of FRCM systems in strengthening RC structures, namely the fabric type, strengthening technique, number of FRCM layers, mortar type, concrete strength, tensile reinforcement ratio, and anchorage. The fabric type significantly affects the level of improvement in the load carrying capacity and failure mode of strengthened RC beams in flexure and shear [29–31]. A comparison was performed between carbon and PBO fabrics for flexural strengthening, and the result showed that a PBO–FRCM specimen failed due to debonding at the concrete–matrix interface, whereas a specimen strengthened with carbon fabric failed owing to the slippage of the fabric in the matrix. Furthermore, the gains in load-carrying capacity exhibited by the abovementioned specimens were 30% and 16%, indicating the better performance of the PBO–FRCM specimen compared with that of the carbon–FRCM specimen, which is attributable to the higher quality of bonding between the PBO fabric and matrix [32]. With regard to shear strengthening, Escrig et al. [33] revealed that PBO–FRCM was the most efficient fabric type for strengthening RC beams. Ebead and El-Sherif [6] compared the performances yielded by two techniques for the flexural strengthening of RC beams, namely, the externally bonded reinforcement (EBR) and near surface embedding (NSE) methods. Normalizing the results based on the amount of FRCM used in these methods revealed that the NSE method yielded better results than the EBR method. Results in the literature pertaining to the number of FRCM layers for flexural strengthening show that the relationship between the improvement level and number of layers is not necessarily proportional [34–38]. El-Maaddawy and El Refai [29] reported load-carrying capacity gains of 39% and 51% for two and four strengthening layers, respectively. As for the shear strengthening, Al-Salloum et al. [39] reported that strengthening using two layers resulted in a maximum strength gain of 37%, whereas that using four layers yielded strength gains of 46%–88%.

Commercial FRCM materials were primarily used in previous studies to strengthen RC beams. In the present study, we designed and fabricated a new cement-based mortar to be used as a binder in an FRCM system and utilized a custom-designed carbon mesh as the fabric. The performance of the custom-developed FRCM system was investigated both in flexural and shear strengthening. Twelve RC beams were manufactured, among which eight and four beams were used to investigate the effectiveness of the system in terms of flexural and shear strengthening, respectively. For the specimens strengthened in flexure, the effects of the shear-span-to-beam depth ratio, number of strengthening layers, and strengthening technique on the performance of the strengthening system were investigated. The effect of the span/depth ratio on the performance of FRP-strengthened RC beams has been investigated extensively [40–43], whereas the effect of the span/depth ratio on the behavior of FRCM systems is rarely investigated. The strengthening techniques used in this study were EBR, NSE, and the installation of custom-designed carbon bars in grooves. In most previous studies, the effectiveness of different strengthening methods was compared using different amounts of fabric for each strengthening method. By contrast, custom fabrics with similar axial stiffness were used in this study in both the EBR and NSE methods, which allowed an accurate comparison between these methods. The NSE method yielded marginally better results because of the better bond strength between the substrate and mortar. In the shear strengthening of the specimens, the effects of the span/depth ratio and strengthening system type (FRP and FRCM) were examined. Changing the span/depth ratio of the specimens significantly affected the load-carrying capacity of the FRCM-strengthened RC beams. One of the main objectives of this study was to compare the bonding quality yielded by the epoxy and mortar used in the FRP and FRCM systems. Using carbon fabrics with similar axial stiffness in both the FRCM and FRP systems allows the effect of fabrics used in these systems to be disregarded and the performance of the adhesives (epoxy and mortar) to be compared solely. The results suggest the better performance of mortar compared with that of epoxy in terms of the shear strengthening of RC beams.

2 Experimental program

2.1 Material properties

The beam specimens were cast using the same batch of concrete and featured a cylindrical compressive strength of 35 MPa (based on the average of five test specimens) with a standard deviation of 0.85 MPa. Each cubic meter of the concrete used contained 950 kg of sand, 820 kg of gravel, and 380 kg of cement. Because one of the objectives of the present study was to compare the experimental and analytical results, the exact values of the tensile strength and elasticity modulus of the reinforcing bars must be obtained. Hence, the nominal tensile strength test was performed on tensile and compressive steel bars. The tensile bars used featured diameters of 18 and 20 mm; their elasticity moduli were 204 GPa (standard deviation = 3.3 GPa) and 201 GPa (standard deviation = 4.55 GPa), respectively, whereas their yield strengths were 473 (standard deviation = 9 MPa) and 460 MPa (standard deviation = 11.09 MPa), respectively. Meanwhile, the elasticity modulus and yield strength of compressive bars with a diameter of 10 mm were 190 GPa (standard deviation = 6.65 GPa) and 462 MPa (standard deviation = 13.47 MPa), respectively. Each of the values reported for the tensile properties of the steel bars was the average value of three samples. The ultimate strain of non-spliced and spliced steel bars can be estimated using machine learning-based models such as that proposed by Dabiri et al. [44], who applied random forest and decision tree techniques as an alternative to performing experimental tests. The CFRP sheets (QUANTOM Wrap 300C) used for fabricating the FRCM strengthening system were of the unidirectional type. The fibers of the CFRP sheets had a tensile strength of 4950 MPa, elasticity modulus of 240 GPa, and rupture strain of 1.5%. Fig.1 shows the custom-designed CFRP mesh used in the FRCM system. As shown in this figure, the warps of the mesh used in the EBR method have a center-to-center distance of 10 mm. With regard to flexural strengthening, because of the smaller width of the strengthening layer in the NSE method compared with that in the EBR method (16 mm vs. 20 mm) and to provide the same axial stiffness for both methods, a mesh fabricated with warps in closer proximity was used in the NSE method. As shown in Fig.2, carbon strings were fabricated by weaving multiple CFRP warps together such that custom carbon bars can be shaped to be placed in the grooves. For a valid comparison between the strengthening methods, the cumulative axial stiffness of the three tailored carbon bars was ensured to be the same as that of the two layers of FRCM mesh used in the NSE and EBR methods. A non-commercial custom-developed cement-based mortar was used as the matrix in the FRCM system to achieve maximum bonding quality among the mortar, concrete surface, and fabrics. Each cubic meter of mortar contained 610 kg of cement, 315 kg of silica fume, 144 kg of ground-granulated blast-furnace slag, 34 kg of water, 620 kg of stone powder, and 16.5 kg of polypropylene fibers. Tests performed on five cubic specimens showed that the mortar had a compressive strength of 50 MPa with a standard deviation of 2.16 MPa, which satisfied the ASTM C109 standard [45], whereas tests performed another five specimens revealed that the tensile strength of mortar was 4.8 MPa with a standard deviation of 0.09 MPa, which satisfied the ASTM C307 standard [46].

2.2 Specifications of RC beams

Twelve RC beams with a width of 200 mm, depth of 300 mm, and length of 2200 mm were constructed. Among them, eight beams were designed to investigate the flexural performance of the custom-developed FRCM strengthening system, and the remaining four beams were designed to evaluate the shear behavior of the system. In the case of flexural strengthening, the main parameters investigated were the number of strengthening layers, strengthening method, and span/depth ratio. To examine the effect of the number of layers, beams strengthened with one, two, and three layers were constructed. Three different strengthening techniques were adopted to strengthen the specimens, including EBR (which is the most typical external strengthening technique), NSE, and the installation of tailored bars in grooves. Furthermore, the contribution of the span/depth ratio to the performance of the strengthening system was assessed by varying the ratio to 3.25, 2.75, and 2.25. In the case of shear strengthening, the effects of the span/depth ratio (1.5 and 2.5) and strengthening system type (FRP and FRCM) were investigated. The FRCM system comprised a carbon mesh and cement-based mortar, whereas the FRP system comprised carbon sheets and an epoxy. Because a custom-designed mesh was used in the FRCM layers, the axial stiffness of both the FRP and FRCM systems was the same. Consequently, these systems were compared primarily based on the adhesive performance and system response, instead of the fabrics used in the systems.

For the specimens strengthened in flexure and shear, two steel bars with a diameter of 18 mm and three bars with a diameter of 20 mm were used as internal tensile reinforcement, respectively. In all the specimens, two steel bars with a diameter of 10 mm were used as compression reinforcement. The geometry and internal reinforcement arrangement of the specimens strengthened in flexure and shear are shown in Fig.3 and Fig.4, respectively. As shown in Fig.4, which presents the stirrup spacings in the specimens with two different span/depth ratios, in the case of shear strengthening, one region of the specimens was shear deficient, which was then strengthened using FRCM strips. The properties of all the specimens are listed in Tab.1. The beams strengthened in flexure were named in the “Fa-E/N/B-b” format, where a denotes the shear-span/depth ratio; “E”, “N”, and “B” refer to the EBR method, NSE method, and utilization of tailored carbon bars, respectively; and “b” indicates the number of FRCM layers. The beams strengthened in shear were named in the “Sa-FRCM/FRP-D20” format, where a denotes the span/depth ratio; FRCM/FRP refers to the use of FRCM or FRP for strengthening; and the number after “D” is the diameter of the tensile bars. The control specimens (with the control label) were not strengthened.

2.3 Strengthening procedure

The EBR method was used for the flexural and shear strengthening of five and three specimens, respectively. In this method, the tensile surface of the beam was roughened with a hand grinding machine to remove a weak layer of concrete, which rendered the aggregates visible. Subsequently, the surface was cleaned with water and air jets to ensure that no dust or loose particles remained on the surface. Prior to the strengthening procedure, the beam surface was saturated for 30 min. The first layer of mortar with a thickness of 4 mm was applied to the surface (Fig.5(a)). After a first layer was deposited on the entire surface, the FRCM mesh was gently pressed into the mortar. Subsequently, a second layer of mortar was applied to sandwich the mesh between the two mortar layers (Fig.5(b)). Finally, the strengthening layer was smoothed using a trowel. The same procedure was repeated on beams with two and three strengthening layers. For the shear strengthening of the specimens, a U-warp scheme was adopted, where strips with a width of 50 mm were used, and the beam edges were rounded to a radius of 20 mm.

For the NSE method, a layer of concrete with a thickness of approximately 8 mm was removed from the beam. Subsequently, the surface was cleaned with water and air jets to achieve an appropriate surface for strengthening (Fig.6(a)). The first mortar layer, which featured a thickness of 4 mm, was applied to the section wherein the cover was removed. Subsequently, the mortar was impregnated with an FRCM mesh (Fig.6(b)) and a second layer of mortar was deposited onto the mesh. In the third strengthening method, customized FRCM strings were used to shape carbon bars using the same carbon fabrics as in the other two methods. As shown in Fig.7(a), to install the customized carbon bars, three grooves (1800 mm (length) × 8 mm (width) × 10 mm (depth)) were carved into the beam using a hand grinding machine. The bars were placed in the grooves (Fig.7(b)), and the grooves were filled with the same mortar used in the other strengthening methods. Finally, the surface of the beam was troweled to obtain a smooth surface. The FRCM mesh used for strengthening in the EBR and NSE methods measured 1800 mm long and 0.167 mm thick. The tailored bars featured a length of 1800 mm as well. For the EBR and NSE methods, the widths of the mesh were set to 190 and 160 mm, respectively. In previous studies, the performances of different FRCM strengthening methods were compared by normalizing their results to accommodate the differences in the properties of the FRCM mesh used in different methods. For a more accurate comparison, in this study, custom-designed meshes with the same axial stiffness were used for all three strengthening methods. The axial stiffness (E_fA_f) of the strengthening layer depends on both the modulus of elasticity and total area of the fibers, which were fixed in all three strengthening methods.

2.4 Test setup and instrumentation

As shown in Fig.8 and Fig.9, the beams strengthened in flexure and shear were subjected to four-point and three-point flexural tests, respectively. For the former, three different shear spans of 812.5, 687.5, and 562.5 mm were used to achieve span/depth ratios of 3.25, 2.75, and 2.25, respectively. The load was applied using a hydraulic jack with a capacity of 600 kN in a displacement-controlled manner at a rate of 0.02 mm/s. The mid-span deflection was measured using two linear variable differential transformers (LVDTs) mounted below the beam, and the applied load was recorded using a load cell connected to a data acquisition system. The beams were observed meticulously throughout the loading process to monitor and record their cracking patterns and failure modes. To investigate the performance of the strengthening systems after the peak load more effectively, the authors recorded the results of the test long after the peak load was reached, and the test was terminated only when stability was achieved. However, in specimens that exhibited brittle failure, the test was terminated when the LVDTs were detached from the specimens. In the shear-strengthened specimens, two shear spans were used, i.e., 375 and 625 mm. Two LVDTs were placed below the specimens: one beneath the loading point and one at the mid-span.

3 Test results

The results of flexural and shear strengthening of the beams obtained using the custom-developed FRCM system are reported separately in the following two subsections.

3.1 Flexural strengthening

All the test results, including the load-carrying capacity, mid-span deflection corresponding to the ultimate load, area under the load–deflection curve, cracking load, and failure modes, are summarized in Tab.2. The results are discussed in the following sections based on the number of layers, shear span/depth ratio, and strengthening method.

3.1.1 Number of strengthening layers

The first flexural crack in specimen F2.75-Control, i.e., the unstrengthened specimen, occurred at a load of 30 kN. Meanwhile, in specimens F2.75-E-1L, F2.75-E-2L, and F2.75-E-3L, which were strengthened with one, two, and three layers, respectively, the first crack occurred at loads of 60, 60, and 70 kN, respectively, in the constant-moment region. The analytical cracking loads of these specimens were 36, 39, 42, and 45 kN, respectively. Fig.10 shows the cracking patterns of these beams. Two operators constantly monitored the surface of the beam during the loading process, and noticeable changes were recorded from the beginning of the test until the test was terminated. Cracks that appeared during loading and their progression were highlighted using a marker, and the corresponding load of each crack was recorded next to it.

Fig.11 shows the load vs. deflection response of these specimens. The load–deflection curves of the strengthened specimens featured three distinct regions. In the first region, in which the specimens had not reached a deflection of 2 mm, elastic linear behavior was observed until the formation of the first flexural crack (limited to a load of 70 kN). In this elastic region of the curve, no significant difference was indicated between the control and strengthened specimens. The behavior indicated in the second region was similar to that in the first region and continued to the point where the tensile bars yielded. In this region (after a deflection of 2 mm), the strengthened specimens benefited from a higher stiffness compared with the control specimen. In this region, the mid-span deflections of all the specimens were limited to 10 mm, and their corresponding loads were between 165 and 220 kN. Finally, the third region represented the hardening process, which continued until the redution of the load. For specimens F2.75-E-2L and F2.75-E-3L, this region was accompanied by an increase in the load-carrying capacity of the specimen by approximately 25 kN. In the third region (after a deflection of 10 mm), the specimens strengthened with two and three layers indicated relatively higher stiffness.

The results show that the specimens with more strengthening layers exhibited higher stiffness in the post-yielding region. The ultimate load-carrying capacities of specimens F2.75-Control, F2.75-E-1L, F2.75-E-2L, and F2.75-E-3L were 183, 198, 224, and 243 kN, respectively. Implementing one, two, and three FRCM layers improved the load-carrying capacity by 8%, 22%, and 33%, respectively, compared with the control specimen. This indicates that the efficiency of the FRCM strengthening system depends on the number of layers and that the system is more effective when more layers are implemented. The level of improvement yielded by one strengthening layer was insignificant; meaningful improvement was achieved when at least two strengthening layers were implemented. The relatively proportional increase in the load capacity owing to an increase in the number of layers was consistent with the results of several previous studies; however, in some other studies, a disproportionate trend was observed. Ebead et al. [8] reported load-carrying capacity gains of 14.4%, 28.9%, and 46.8% by implementing one, two, and three strengthening layers, respectively, in specimens reinforced with steel bars measuring 16 mm in diameter; and gains of 23.1%, 28.9%, and 77.5% by implementing one, two, and three layers, respectively, in specimens with steel bars measuring 12 mm in diameter. Ombres [1] reported gains of 16%, 33%, and 40% by strengthening via one, two, and three layers, respectively, although a proportional trend was observed for only cases involving one and two layers. Some parameters affected the effectiveness contributed by the number of layers, such as the mortar strength, internal reinforcement ratio, and fabric type. However, in most previous studies, the effectiveness of using one layer was insignificant, which is consistent with the findings of the present study. This is attributable to the low stiffness and integrity of strengthening with one layer, as the bottom side of the fabric is only shielded by one mortar layer. In this case, the rupture of one warp results in the progressive rupture of all fabrics within the mortar. By contrast, strengthening systems comprising two and three layers showed higher stiffness and better integrity. However, when the number of layers increased, the probability of premature debonding failure increased. The mid-span deflections of specimens F2.75-Control, F2.75-E-1L, F2.75-E-2L, and F2.75-E-3L were 33, 31.4, 17.7, and 15.3 mm, respectively. The control beam exhibited a more ductile behavior, and strengthening with one, two, and three layers reduced the deflection by 5%, 46%, and 54%, respectively, compared with the control beam. Different results pertaining to the effect of the number of layers on the level of improvement provided by a strengthening system have been reported in previous studies.

A detailed observation of the control specimen during the loading process revealed that a microcrack first appeared in the center of the beam when the load reached 30 kN. As the load increased, more flexural cracks appeared and propagated toward the upper side of the beam. At a load of 120 kN, the first shear–flexural crack occurred near the support, followed by tensile bar yielding at 160 kN. The control beam reached its final stage when the concrete on the compressive side of the beam was crushed. The cracking pattern of this specimen was similar to that of an under-reinforced RC beam, characterized by the emergence of large flexural cracks in the mid-span region as a result of steel bar yielding. The behavior and failure mode of the strengthened beams were governed by the number of FRCM layers. Specimens F2.75-E-1L (Fig.10(b)) and F2.75-E-2L (Fig.10(c)), which were strengthened with one and two FRCM layers, respectively, failed because of FRCM fabric rupture. This occurred after numerous flexural macrocracks were formed on the entire beam. The first few cracks initiated in the central section of the beam; however, more cracks began to appear outside this region as the load increased. As presented in Fig.12, a large vertical crack at the bottom center of the beam that subsequently separated into two horizontal cracks above the tensile bars caused the fabric rupture, which featured widths of 3.7 and 4.3 mm, immediately prior to the rupture in specimens F2.75-E-1L and F2.75-E-2L.

In specimen F2.75-E-3L, a diagonal crack that extended 45° from the longitudinal axis of the beam appeared at the end point of the FRCM layer when a load of 130 kN was imposed. When the load increased to 220 kN, the crack was separated into two: one continuing in the direction of the main crack and one propagating in the horizontal direction. As shown in Fig.13, the latter initiated below the tensile bars and stopped propagating in the constant-moment region. Finally, the concrete cover was detached from the endpoint of the FRCM layer at a load of 243 kN. The specimen failed via concrete cover separation, and a large longitudinal crack emerged due to the merging of numerous microcracks below the tensile bars along the axis of the beam. The failure mode of the control specimen was concrete crushing, whereas the specimens strengthened with one and two layers failed via FRCM fabric rupture, and the specimen with three layers failed by the detachment of the FRCM layer accompanied by concrete shielding from the tensile side of the beam. This indicates that the number of strengthening layers significantly affects the failure mode of the beam, which is consistent with the result of previous studies.

3.1.2 Shear span/depth ratio

The effect of the shear span/depth ratio on the behavior of RC beams strengthened by FRP composites has been investigated in previous studies [43]. However, the effect of this parameter on FRCM systems is yet to be investigated. In this study, the effect of the span/depth ratio on the performance of FRCM strengthening was evaluated by comparing the results of specimens F3.25-E-2L, F2.75-E-2L, and F2.25-E-2L, which were set with span/depth ratios of 3.25, 2.75, and 2.25, respectively. All specimens comprised two FRCM layers and were strengthened using the EBR method. As presented in Fig.14, the first flexural cracks in specimens F3.25-E-2L, F2.75-E-2L, and F2.25-E-2L appeared at 45, 60, and 85 kN (whereas the analytical cracking loads were 36, 42, and 51 kN, respectively), respectively, and the specimens failed at 181, 224, and 288 kN, respectively. By changing the span/depth ratio from 3.25 to 2.25, the occurrence of the first flexural crack was delayed significantly, and the load-carrying capacity increased by 59%. This shows the significant effect of this parameter on the behavior of FRCM-strengthened beams at both the early and final stages of load support. However, as in Fig.14 and Fig.15, the failure mode of all these specimens was FRCM fabric rupture, indicating that the investigated range of span/depth ratio (2.25 to 3.25) did not significantly affect the failure mode. Only a slight difference was observed between their failure modes, i.e., the rupture of the fabrics in specimen F3.25-E-2L was accompanied by the delamination of the FRCM layer from the soffit in the mid-span region. The cracking patterns depicted in Fig.12–Fig.15 highlight the importance of the interaction between the bending moment and shear resistance. This interaction can be accurately explained using two models, namely variable strut inclination and compression chord capacity models [47,48], which consider the variation in shear stresses along the depth of the beam at imminent failure caused by interaction with bending.

The moment vs. deflection response of the specimens is shown in Fig.16. The maximum flexural moments of specimens F3.25-E-2L and F2.75-E-2L were 73 and 77 kN∙mm, respectively, and their mid-span deflections were 19 and 17.7 mm, respectively. This shows that changing the span/depth ratio from 3.25 to 2.75 increases the maximum flexural moment by 6% while reducing the mid-span deflection by 7%. The maximum flexural moment and mid-span deflection of specimen F2.25-E-2L were 81 kN∙mm and 18.8 mm, respectively. This indicates that changing the span/depth ratio from 3.25 to 2.25 increases the maximum flexural moment by 11% while the mid-span deflection remains unchanged.

3.1.3 Strengthening method

The performances of the three methods used for flexural strengthening of RC beams, i.e., EBR, NSE, and the installation of tailored carbon bars in grooves, were assessed by comparing the results of specimens F2.75-E-2L, F2.75-N-2L, and F2.75-B. The first flexural cracks in specimens F2.75-E-2L, F2.75-N-2L, and F2.75-B appeared at loads of 60, 75, and 55 kN, respectively, whereas the analytical cracking loads were 42, 41, and 41 kN, respectively. As shown in Fig.13 and Fig.17(a), the failure modes of specimens F2.75-E-2L and F2.75-N-2L were FRCM mesh ruptures, indicating that both methods were effective in utilizing the full capacity of the strengthening material. The failure mode of specimen F2.75-B was concrete crushing with large flexural cracks in the constant-moment region due to steel yielding (Fig.17(b)), which represents the typical failure mode exhibited in under-reinforced RC beams. The only difference between the failure mode of this specimen and that of the control specimen was that the cracks of the former were wider.

Fig.18 presents the load–deflection curves of specimens F2.75-Control, F2.75-E-2L, F2.75-N-2L, and F2.75-B, whose load-carrying capacities were 183, 224, 230, and 190 kN, respectively. Strengthening via the EBR and NSE methods resulted in improvements in the load-carrying capacity by approximately 22% and 26%, respectively. The specimens strengthened by tailored bars exhibited similar load-carrying capacities and failure modes as the control specimen. Furthermore, their load–deflection response and the slope of their curves were identical. However, the strengthening system was not fully utilized because of the premature slippage of the tailored bars within the strengthening mortar. This is attributable to the size of the grooves created on the tensile side of the beam, the shape of the tailored bars, and the quality of bonding between the mortar and bars. This phenomenon should be investigated further by performing experiments using more specimens to achieve a firm conclusion. The mid-span deflections of specimens F2.75-Control, F2.75-E-2L, F2.75-N-2L, and F2.75-B were 32.9, 17.7, 15.5, and 30.8 mm, respectively, which implies that the EBR and NSE methods reduced the mid-span deflection by 46% and 53%, respectively, compared with the control specimen.

A review of Refs. [7,11] shows that the most typical failure modes in FRCM-strengthened RC beams are debonding at the fiber–matrix interface and debonding at the substrate-strengthening layer interface, which are both associated with the inability of mortar to provide adequate bonding between the substrate and fabrics. By contrast, in this study, the failure modes of the externally strengthened specimens were FRP rupture and concrete cover separation, both of which are not associated with the mortar used in the FRCM system. This indicates that the mortar used as the matrix provided sufficient bonding and prevented premature failure modes. Notably, several preliminary tests were conducted on the custom mortar used in this study prior to strengthening the RC beams to ensure that using the proposed strengthening system can yield desirable results. However, to characterize the interfacial bond performance between the concrete surface and the proposed FRCM system more effectively, single- or double-lap shear tests should be conducted in future studies.

3.1.4 Comparison between experimental and analytical results

The experimental and analytical results of the specimens strengthened in flexure were compared. The load-carrying capacity of RC beams strengthened with FRCM layers can be predicted based on ACI 318-14 [49] and ACI-549.4R-13 [50]. The first step is to acquire the effective strain of the FRCM materials using Eq. (1).

(1){\epsilon }_{\mathrm{f}\mathrm{e}}={\epsilon }_{\mathrm{f}\mathrm{u}}⩽0.012,

where {\epsilon }_{\mathrm{f}\mathrm{u}} is the ultimate tensile strain of FRCM materials obtained via the tensile test. The effective tension in the FRCM can be calculated using Eq. (2).

(2)f_{\mathrm{f}\mathrm{e}}=E_{\mathrm{f}}{\epsilon }_{\mathrm{f}\mathrm{e}},{\epsilon }_{\mathrm{f}\mathrm{e}}⩽{\epsilon }_{\mathrm{f}\mathrm{d}}.

The strains of the compressive concrete and steel bars are correlated as shown in Eq. (3).

(3)\frac{{\epsilon }_{\mathrm{f}\mathrm{e}}}{d_{\mathrm{f}}-c_{\mathrm{u}}}=\frac{{\epsilon }_{\mathrm{t}}}{d-c_{\mathrm{u}}}=\frac{{\epsilon }_{\mathrm{s}}^{\prime }}{c_{\mathrm{u}}-d^{\prime }}=\frac{{\epsilon }_{\mathrm{c}}}{c_{\mathrm{u}}},

where d is the distance from the extreme compression fiber to the center of the tensile bars; d_f is the effective depth of the FRCM layer; c_u is the neutral axis depth; and {\epsilon }_{\mathrm{t}} and {\epsilon }_{\mathrm{s}}^{\prime } are the net strains in the tensile and compressive bars, respectively.

Because concrete does not reach its ultimate strain under compression, a Whitney rectangular block cannot be used. The nonlinear stress–strain relationship of concrete can be transformed into a rectangular block using {\alpha }_1 and {\beta }_1. The width and height of the equal rectangular blocks are denoted as {\alpha }_1{f}_{\mathrm{c}}^{\prime } and {\beta }_{1}c, respectively. The parameters {\alpha }_1 and {\beta }_1 are calculated using Eqs. (4) and (5), respectively.

(4){\beta }_1=\frac{4{\epsilon }_{\mathrm{c}}^{\prime }-{\epsilon }_{\mathrm{c}}}{6{\epsilon }_{\mathrm{c}}^{\prime }-2{\epsilon }_{\mathrm{c}}},

(5){\alpha }_1=\frac{3{\epsilon }_{\mathrm{c}}^{\prime }{\epsilon }_{\mathrm{c}}-{\epsilon }_{\mathrm{c}}^2}{3{\beta }_1{{\epsilon }_{\mathrm{c}}^{\prime }}^2}.

In Eqs. (4) and (5), {\epsilon }_{\mathrm{c}}^{\prime }=1.7f_{\mathrm{c}}^{\prime }/\phantom{1.7f_{\mathrm{c}}^{\prime }{E}_{\mathrm{c}}}{E}_{\mathrm{c}}, where {\epsilon }_{\mathrm{c}} is the maximum compressive strain of the concrete. Using the equal stress block and equilibrium of forces in the section, the neutral axis depth can be obtained using Eq. (6). The nominal flexural strength of the beam can be calculated using Eq. (7).

(6)c=\frac{A_{\mathrm{s}}{f}_{\mathrm{s}}+A_{\mathrm{f}}{f}_{\mathrm{f}\mathrm{e}}-A_{\mathrm{s}}^{\prime }{f_{\mathrm{s}}}^{\mathrm{\prime }}}{{\alpha }_1{f}_{\mathrm{c}}^{\prime }{\beta }_{1}b},

(7)M_{\mathrm{n}}=A_{\mathrm{s}}{f}_{\mathrm{s}}(d-\frac{{\beta }_{1}c}{2})+A_{\mathrm{s}}^{\prime }{f}_{\mathrm{s}}^{\prime }(d-d^{\prime })+{\psi }_{\mathrm{f}}{A}_{\mathrm{f}}{f}_{\mathrm{f}\mathrm{e}}(d_{\mathrm{f}}-\frac{{\beta }_{1}c}{2}).

Finally, the load-carrying capacity can be predicted using Eq. (8), where P_{\mathrm{u}}^{\mathrm{t}\mathrm{h}} and L_1 are the theoretical ultimate load-carrying capacity and shear span obtained from the four-point bending test, respectively.

(8)P_{\mathrm{u}}^{\mathrm{t}\mathrm{h}}=\frac{2(M_{\mathrm{s}}+M_{\mathrm{f}})}{L_1}.

To predict the debonding strain, the equations proposed by Mandor and El Refai [51] were adopted. They investigated the flexural capacity of FRCM-strengthened flexural members, focusing primarily on estimating the debonding strain in FRCM systems. Their results indicated the debonding strain was primarily governed by the axial stiffness of the FRCM composites, the concrete compressive strength, and the tensile strength of concrete. They proposed three models to estimate the debonding strain in FRCM strengthening systems.

{\epsilon }_{\mathrm{d}\mathrm{e}\mathrm{b}}=0.79\frac{{f_{\mathrm{c}\mathrm{t}}}^{1.191}{f_{\mathrm{c}\mathrm{m}}}^{0.056}{\mathrm{e}}^{0.032f_{\mathrm{c}}}}{{(E_{\mathrm{f}}{A}_{\mathrm{f}})}^{0.091}},(\mathrm{M}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}1)

{\epsilon }_{\mathrm{d}\mathrm{e}\mathrm{b}}=0.77\frac{{f_{\mathrm{c}\mathrm{t}}}^{1.232}{\mathrm{e}}^{0.035f_{\mathrm{c}}}}{{(E_{\mathrm{f}}{A}_{\mathrm{f}})}^{0.083}},(\mathrm{M}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}2)

{\epsilon }_{\mathrm{d}\mathrm{e}\mathrm{b}}=0.95\frac{{f_{\mathrm{c}\mathrm{m}}}^{0.28}{\mathrm{e}}^{0.056f_{\mathrm{c}}}}{{(E_{\mathrm{f}}{A}_{\mathrm{f}})}^{0.153}}.(\mathrm{M}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}3)

The equation for Model 1 considers the debonding strain as a function of the concrete and FRCM mortar properties, as well as the axial stiffness of the FRCM layers. However, a study conducted by Wakjira et al. [52] showed that omitting the compressive strength of FRCM mortar did not significantly affect the results. Additionally, they reported that the results obtained based on Models 1 and 2 agreed well with the experimental results, whereas the debonding strain yielded by Model 3 was unsatisfactory. The ratio of the predicted-to-experimental load-carrying capacity is listed in Tab.3. In all three models, the values obtained using the prediction formulas were lower than the experimental values. With regard to Model 1, the ratios of the analytical-to-experimental load-carrying capacity for specimens F2.75-E-1L, F2.75-E-2L, and F2.75-E-3L were 0.87, 0.83, and 0.81, respectively, indicating that increasing the number of strengthening layers resulted in more conservative results. Meanwhile, the ratios for specimens F3.25-E-2L, F2.75-E-2L, and F2.25-E-3L were 0.87, 0.83, and 0.78, respectively, indicating that the results become more conservative at lower span/depth ratios. The lower predicted-to-experimental ratio for specimen F2.75-N-2L strengthened using the NSE method compared with that of specimen F2.75-E-2L strengthened by the EBR method (0.83 vs. 0.8) was due to the higher experimental load-carrying capacity of specimen F2.75-N-2L. The ratios of the predicted-to-experimental results for specimens F3.25-E-2L, F2.75-E-2L, and F2.25-E-2L based on Model 1 were 0.87, 0.83, and 0.78, respectively. A similar trend was observed in the other models. Additionally, the predicted load-carrying capacity under a span/depth ratio of 3.25 was similar to the experimental results, and as the span/depth ratio decreased, the predicted values deviated further from the experimental results.

3.2 Shear strengthening

The test results of the specimens strengthened in shear, including the load-carrying capacity, mid-span deflection corresponding to the ultimate load, and failure modes, are listed in Tab.4. The load–deflection curves of the specimens are shown in Fig.19.

For a span/depth ratio of 1.5, specimens S1.5-FRCM-D20 and S1.5-FRP-D20, which were strengthened by the FRCM and FRP systems, respectively, failed at loads of 270 and 248 kN, respectively, which demonstrates the superior performance of the FRCM system. Considering the equal axial stiffness of the FRCM and FRP fabrics used in this study, the higher load-carrying capacity of the FRCM-strengthened specimen is attributable to the higher bond quality provided by the cement-based mortar compared with that provided by the epoxy resin and the sandwiching mechanism used in the FRCM system. The vertical deflection of the FRCM-strengthened specimen was slightly lower than that of the FRP-strengthened specimen. At the span/depth ratio of 2.5, the load-carrying capacity of specimen S2.5-FRCM-D20 strengthened by FRCM composites was 21% higher than that of its unstrengthened counterpart (S2.5-Control-D20). The deflections of both specimens were similar. A comparison between specimens S1.5-FRCM-D20 and S2.5-Control-D20 shows that changing the span/depth ratio from 2.5 to 1.5 increased the load-carrying capacity by 27%. This highlights the effect of the span/depth ratio on the shear capacity of RC beams.

All the specimens failed in a brittle manner, which suggests shear failure, except for specimen S2.5-FRCM-D20, which indicated a more ductile failure. As shown in Fig.20, specimen S1.5-FRCM-D20 failed because the FRCM fabric ruptured. The failure was initiated by the formation of shear cracks in the strengthened area. Upon increasing the load, the width of the main diagonal crack increased, thus resulting in fiber rupture at the bottom of the strip near the support (Fig.21(a)). Specimen S1.5-FRP-D20 failed by the debonding of both CFRP strips from the surface of the beam (Fig.21(b)), which is the typical failure mode of RC beams strengthened by FRP strips using a U-wrap scheme. The strip near the support was completely detached from the surface because of the diagonal crack near the bottom of the beam, whereas the strip near the loading point detached partially from the upper side because the diagonal crack propagated only to that area. A comparison of the failure modes of the FRCM and FRP-strengthened specimens (fabric rupture vs. debonding) shows that in the former, the full capacity of the strengthening materials was utilized, whereas the latter experienced premature failure. This suggests that cement-based mortar exhibits better behavior than epoxy. In S2.5-FRCM-D20, flexural cracks first appeared below the loading point, followed by the development of shear cracks throughout the strengthening area, which resulted in fiber slippage in the strip below the loading point. The specimen finally failed due to concrete crushing as the flexural cracks propagated over the entire depth of the beam. Specimen S2.5-Control-D20, which was an unstrengthened specimen, failed via the formation of a single diagonal crack. A crack appeared in the vicinity of the support and extended along the shear span until it reached the loading point, which resulted in diagonal tension failure.

A comparison was also made between the experimental and analytical results for shear-strengthened specimens. As proposed by most existing design codes, the shear capacity of RC beams strengthened by the FRCM system is calculated using Eq. (9).

(9)V=V_{\mathrm{c}}+V_{\mathrm{s}}+V_{\mathrm{f}}.

The terms V_c and V_s, which refer to the contributions of the concrete and stirrup to shear resistance, respectively, can be calculated using simple equations presented in ACI 318-14. Meanwhile, V_f can be calculated using Eq. (10) specified in Canadian Highway Bridge Design Code (CAN/CSA-S6-06) [53].

(10)V_{\mathrm{f}}=\frac{A_{\mathrm{f}}{E}_{\mathrm{f}}{\epsilon }_{\mathrm{f}\mathrm{e}}{d}_{\mathrm{f}}(\cot \theta +\cot \alpha )\sin \alpha }{s_{\mathrm{f}}}.

In the equation above, A_{\mathrm{f}} is the effective cross-sectional area of the fabric reinforcement, {\epsilon }_{\mathrm{f}\mathrm{e}} is the effective strain of the fabric, E_{\mathrm{f}} is the tensile modulus of the fibers, s_{\mathrm{f}} is the distance between the strips, and d_{\mathrm{f}} is the effective depth of the strengthening layer. Angles \theta and \alpha are the average angle of the diagonal cracks and the orientation of the strips relative to the longitudinal axis, respectively. The ratios of the predicted-to-experimental results are listed in Tab.4. For specimens with a span/depth ratio of 1.5, the predicted results were highly conservative, whereas for specimens with span/depth ratio of 2.5, the predictions were more accurate.

The results yielded the FRCM system composed of custom fabrics and mortar show that the proposed FRCM strengthening system performed well in terms of flexural and shear strengthening. In particular, it improved the load-carrying capacity, provided sufficient bonding with the concrete surface, and prevented premature failure modes. The FRCM system can be regarded an effective strengthening system based on its own performance relative to that of the FRP system. Because the mortar used in the FRCM system is composed of local materials and the cost of its production is much lower than that of the epoxy used in FRP systems, the total cost of using the proposed FRCM system is almost one-half that of the FRP system, which can significantly decrease the repair costs of the structural elements in certain cases. Meanwhile, applying FRP composites to repair historical and masonry structures can result in some issues because using epoxy prevents the flow of water in the strengthened elements, which results in water accumulation in the element. Furthermore, for operations under hot weather or in locations with high humidity levels, the FRCM system is the only viable option. The FRCM system can mitigate some environmental issues encountered when using epoxy materials. To apply the proposed FRCM system, the EBR method is preferred because of the ease in surface preparation and the similar performance yielded compared with using the NSE method for flexural strengthening. The evaluated gains in the load-carrying capacity of the specimens strengthened in flexure and the desirable failure mode of the specimens strengthened in shear shows the superiority of the proposed system.

Several parameters can significantly affect the results reported herein and can be further investigated in future studies. Changing the spacing between the warps of the custom mesh used in the FRCM system can alter the interlock mechanism between the mesh and mortar, thus result in a change in the behavior of the strengthening system and the bonding quality between the mortar and fabrics. By modifying this parameter, fabric slippage in the mortar can be prevented. The mortar type, fabric type (carbon, PBO, or glass), and anchorage system can affect the failure mode and level of improvement of the load-carrying capacity provided by the strengthening system. With respect to shear strengthening, changing the wrapping scheme (continuous/intermittent) or the spacing between the strips can alter the adhesion surface and thus the bonding performance of the FRCM system. Similarly, the temperature and humidity affect the bonding quality between the surface and FRCM composites. The performances of FRCM and FRP systems can be differentiated more comprehensively based on different temperatures and humidity levels. Furthermore, the different efficiency levels of the FRCM system in a range of span/depth ratios wider than those investigated in this study can result in different results because changing the span/depth ratio directly affects the cracking pattern, interaction between the flexural moment and shear resistance, and load-bearing mechanism of RC beams.

4 Conclusions

In this study, the performance of FRCM systems fabricated using custom-designed cement-based mortar and fabrics was investigated. The performance of this system was analyzed in terms of both the flexural and shear strengthening of RC beams. The effects of the number of layers, shear span/beam depth ratio, strengthening system (FRCM/FRP), and strengthening method were investigated. The specimens were strengthened using three methods: EBR, NSE, and installation of custom-designed carbon bars in grooves. Based on the results, the following conclusions were inferred.

1) Flexural strengthening with one, two, and three FRCM layers increased the load-carrying capacity by 8%, 22%, and 33%, respectively, and reduced the deflection by 5%, 46%, and 54%, respectively, compared with the control specimen. This indicates that the gain in load-carrying capacity was insignificant when using one layer and that the strengthening system should be composed of at least two layers to achieve meaningful improvement.

2) The specimens strengthened in flexure by one and two layers failed via FRCM fabric rupture, whereas in the specimen with three layers, concrete cover separation was observed.

3) Flexural strengthening via the EBR and NSE methods, which involved the use of fabrics with the same axial stiffness, improved the load-carrying capacity by 22% and 26%, respectively, compared with the control specimen. This is attributable to the higher bond strength between the substrate and mortar afforded by the NSE method. Installing custom-designed carbon bars in grooves with the same axial stiffness as the fabrics used in the EBR and NSE methods was not as effective as using other methods because of the slippage of carbon bars in the grooves and the inability to fully utilize the capacity of FRCM materials.

4) Changing the span/depth ratio of the specimens strengthened in flexure from 3.25 to 2.75 increased the maximum flexural moment by 6%, whereas changing the span/depth ratio from 3.25 to 2.25 increased the maximum flexural moment by 11%. This shows that the span/depth ratio does not significantly affect the load-carrying capacity of the FRCM-strengthened specimens in flexure.

5) In the case of flexural strengthening, a comparison between the experimental and predicted results revealed that by increasing the number of strengthening layers, the theoretical methods yielded more conservative results. Moreover, the predicted results were more accurate when higher span/depth ratios were used.

6) Changing the span/depth ratio of the specimens strengthened in shear from 2.5 to 1.5 increased the load-carrying capacity by 27%, which demonstrates the considerable effect of the span/depth ratio on the shear capacity of FRCM-strengthened RC beams.

7) The specimen strengthened in shear using the FRCM system had a higher load-carrying capacity than that strengthened by the FRP system. Because fabrics with similar axial stiffness were used in both systems, one can conclude that the cement-based mortar performed better than the epoxy.

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