Deep Embedment (DE) FRP Shear Strengthening of Concrete Bridge Slabs under Loads Close to Supports
Deep Embedment (DE) FRP Shear Strengthening of Concrete Bridge Slabs under Loads Close to Supports
Xia, Lipeng;Zheng, Yu
2018-05-04 00:00:00
applied sciences Article Deep Embedment (DE) FRP Shear Strengthening of Concrete Bridge Slabs under Loads Close to Supports ID Lipeng Xia and Yu Zheng * Department of Civil Engineering, Dongguan University of Technology, No. 1, University Road, Dongguan 523808, Guangdong, China; xialp@dgut.edu.cn * Correspondence: zhengy@dgut.edu.cn; Tel.: +86-158-9966-2977 Received: 10 April 2018; Accepted: 30 April 2018; Published: 4 May 2018 Abstract: Shear forces are the most common governing failure mechanism of reinforced concrete bridge deck slabs subjected to loads close to their supports. This paper reveals a comprehensive study of the behaviour of concrete slabs shear-strengthened with a deep embedment fibre reinforced polymer (FRP) technique. In the experimental investigation, a series of eight full scale concrete slabs were created and tested up to failure. Several structural variables were changed to assess the effectiveness of this shear strengthening technique. The behaviour of test slabs is discussed and the influence of this strategy was evaluated by comparing the test results. It was shown that brittle shear failures could be avoided by using this strengthening strategy. The ultimate capacity and deflection at the failure were both enhanced by using the deep embedment strengthening method. Additionally, a nonlinear finite element analysis (NLFEA) was proposed to develop further investigation. This NLFEA model gave excellent predictions for the structural behaviour of the test concrete slabs. Finally, a two-way theoretical model was proposed to predict the loading-carrying capacity of concrete slabs strengthened with deep embedment FRP bars. The ultimate strength predicted by this theoretical method showed good agreement with that from the test results. Keywords: deep embedment strengthening; FRP; concrete slabs; shear strengthening; ductility 1. Introduction Reinforced concrete slabs subjected to concentrated loads near linear supports are commonly found in practice, such as in bridge deck slabs [1]. The structural elements are characterized by high shear forces concentrated in the region between the concentrated loads and the linear support. Due to the increasing traffic loads and heavy truck loads close to supports, the existing bridge deck slabs could fail due to shear. Thus, more massive constructions or shear reinforcements are now required in bridge deck slabs [2]. This raises the question of whether there is a lack of safety for existing bridge deck slabs that were built mainly without shear reinforcement, or whether deck slabs under concentrated wheel loads exhibit reserves of shear capacity, which are neglected in current design codes [3]. Shear strengthening techniques based on the use of fibre reinforced polymer (FRP) materials have been proposed and developed in the past thirty years [4,5]. Externally bonded (EB) FRP is the most commonly used method for strengthening concrete structures using FRP material. To increase the shear behaviour of reinforced concrete structures, FRP sheets are generally applied on the side surface of concrete elements. Additionally, the near-surface-mounted (NSM) FRP rod method is another technique used to increase the shear resistance. In the NSM method, FRP rods are embedded grooves intentionally prepared on the concrete cover of the side faces of concrete structures. The efficiency of these strengthening schemes relies on the bond performance of concrete-adhesive-FRP interfaces. However, those two strengthening methods cannot be applied to increase the shear capacity of concrete deck slabs due to an inaccessible web of structures. Therefore, a new strengthening approach Appl. Sci. 2018, 8, 721; doi:10.3390/app8050721 www.mdpi.com/journal/applsci Appl. Sci. 2018, 8, x FOR PEER REVIEW 2 of 25 Appl. Sci. 2018, 8, 721 2 of 25 capacity of concrete deck slabs due to an inaccessible web of structures. Therefore, a new strengthening approach is adopted (see Figure 1): vertical holes are drilled into the deck slabs is adopted (see Figure 1): vertical holes are drilled into the deck slabs upwards from the soffit in the upwards from the soffit in the shear zones, high-viscosity epoxy resin is injected, and then FRP bars shear zones, high-viscosity epoxy resin is injected, and then FRP bars are embedded in place. This are embedded in place. This strengthening method is called deep embedment strengthening [6] or strengthening method is called deep embedment strengthening [6] or embedded through-section (ETS) embedded through-section (ETS) strengthening [7]. Previous research [8–10] revealed that this strengthening [7]. Previous research [8–10] revealed that this strengthening technique provided higher strengthening technique provided higher strengthening efficiency compared to the EB and NSM strengthening efficiency compared to the EB and NSM strengthening methods. In addition, the shear strengthening methods. In addition, the shear capacity of strengthened concrete beams can be enhanced capacity of strengthened concrete beams can be enhanced by this strengthening method [8–10]. by this strengthening method [8–10]. (a) (b) (c) (d) Figure 1. Deep embedment strengthening process: (a) Drill the hole; (b) Clean the hole; (c) Pour the Figure 1. Deep embedment strengthening process: (a) Drill the hole; (b) Clean the hole; (c) Pour the epoxy resin into the slab; (d) Embed fibre reinforced polymer (FRP) rod into slab. epoxy resin into the slab; (d) Embed fibre reinforced polymer (FRP) rod into slab. The aim of this paper is to study the structural behaviour of one-way reinforced concrete slabs The aim of this paper is to study the structural behaviour of one-way reinforced concrete slabs in bridge deck structures strengthened with deep embedment FRP bars, see Figure 2. A series of in bridge deck structures strengthened with deep embedment FRP bars, see Figure 2. A series of experimental tests were carried out to investigate some structural variables on the behaviours of experimental tests were carried out to investigate some structural variables on the behaviours of those slabs, which included deep embedment strengthening materials, spacing and diameter of deep those slabs, which included deep embedment strengthening materials, spacing and diameter of deep embedment strengthening FRP bars, and the drilling of holes. After comparing the results of different embedment strengthening FRP bars, and the drilling of holes. After comparing the results of different test specimens, the influence of the deep embedment strengthening scheme on ultimate strength and test specimens, the influence of the deep embedment strengthening scheme on ultimate strength and failure mode was discussed and presented. An understanding of the effect of deep embedment shear failure mode was discussed and presented. An understanding of the effect of deep embedment shear strengthening method on the behaviour of concrete deck slabs can be extended. In addition, a strengthening method on the behaviour of concrete deck slabs can be extended. In addition, a nonlinear nonlinear finite element analysis (NLFEA) model was developed simulate the behaviour of test slabs. finite element analysis (NLFEA) model was developed simulate the behaviour of test slabs. The results The results from this NLFEA model showed good convergence ability and gave good agreement with from this NLFEA model showed good convergence ability and gave good agreement with test results test results in the validation analysis. Finally, a tow-way design approach for the prediction of in the validation analysis. Finally, a tow-way design approach for the prediction of ultimate capacity ultimate capacity of concrete slabs strengthened with deep embedment FRP bars is proposed. The of concrete slabs strengthened with deep embedment FRP bars is proposed. The loading-carrying loading-carrying capacity predicted by this method showed good correlation with the test results. capacity predicted by this method showed good correlation with the test results. Appl. Sci. 2018, 8, 721 3 of 25 Appl. Sci. 2018, 8, x FOR PEER REVIEW 3 of 25 (a) (b) (c) (d) (e) Figure 2. Details of test specimens in elevation: (a) Specimen coded as S-Con; (b) Specimen coded as Figure 2. Details of test specimens in elevation: (a) Specimen coded as S-Con; (b) Specimen coded S-D-1; (c) Specimen coded as S-S-2-10, S-B-2-9, S-G-2-9, S-C-2-9; (d) Specimen coded as S-C-1-9; as S-D-1; (c) Specimen coded as S-S-2-10, S-B-2-9, S-G-2-9, S-C-2-9; (d) Specimen coded as S-C-1-9; and (e) Specimen coded as S-C-1-13. and (e) Specimen coded as S-C-1-13. 2. Background of Shear Behaviour of Concrete Bridge Deck Slabs 2. Background of Shear Behaviour of Concrete Bridge Deck Slabs The desired failure mode of bridge deck slabs is a ductile failure model, allowing large The desired failure mode of bridge deck slabs is a ductile failure model, allowing large deformations and significant redistribution of inner forces within the structures before collapse. deformations and significant redistribution of inner forces within the structures before collapse. Therefore, the typical concrete bridge deck slabs are designed for flexure and are checked according Therefore, the typical concrete bridge deck slabs are designed for flexure and are checked according to to the lower requirements for shear and punching of that area. Currently, due to an increase in traffic the lower requirements for shear and punching of that area. Currently, due to an increase in traffic loads, heavy design truck loads are used in the live load modes in current design codes. In addition, the position of those heavy truck loads is close to the support of the deck structures. Therefore, the Appl. Sci. 2018, 8, 721 4 of 25 loads, heavy design truck loads are used in the live load modes in current design codes. In addition, Appl. Sci. 2018, 8, x FOR PEER REVIEW 4 of 25 the position of those heavy truck loads is close to the support of the deck structures. Therefore, the governing failure mechanism of reinforced concrete deck slabs subjected to the concentrated load close governing failure mechanism of reinforced concrete deck slabs subjected to the concentrated load to the support is commonly shear, as it has been shown in experimental tests in the literature [11–14]. close to the support is commonly shear, as it has been shown in experimental tests in the literature The experimental test results by Rodirgues [11] and Lantsoght et al. [13] showed that the observed [11–14]. The experimental test results by Rodirgues [11] and Lantsoght et al.[13] showed that the reinforced concrete bridge decks might be hybrid situations between shear and punching shear, and observed reinforced concrete bridge decks might be hybrid situations between shear and punching the shear or punching shear was the determinant failure mechanism. Therefore, a large shear problem shear, and the shear or punching shear was the determinant failure mechanism. Therefore, a large emerges for existing bridge deck slabs. Most of them do not contain any shear reinforcement in the shear problem emerges for existing bridge deck slabs. Most of them do not contain any shear area between the web of the bridge and the deck slab. Therefore, the requirement of structural safety reinforcement in the area between the web of the bridge and the deck slab. Therefore, the requirement often cannot be satisfied. of structural safety often cannot be satisfied. 3. Experimental Programme 3. Experimental Programme 3.1. Details of Test Slabs 3.1. Details of Test Slabs The experimental test specimens were created to investigate the behaviour of one-way slabs The experimental test specimens were created to investigate the behaviour of one-way slabs representative of the typical sections of full scale bridge deck slabs. According to previous tests of representative of the typical sections of full scale bridge deck slabs. According to previous tests of one-way shear behaviour of concrete deck slabs by the authors [15], the test slabs were 2400 mm one-way shear behaviour of concrete deck slabs by the authors [15], the test slabs were 2400 mm long long 400 mm width 200 mm depth, as illustrated in Figures 2 and 3. A summary of the × 400 mm width × 200 mm depth, as illustrated in Figures 2 and 3. A summary of the experimental experimental details is presented in Table 1 and Figure 2. It is shown that the experimental programme details is presented in Table 1 and Figure 2. It is shown that the experimental programme involves involves eight test slabs. As presented in Table 1, the name of the test specimen includes all of its eight test slabs. As presented in Table 1, the name of the test specimen includes all of its structural structural variables. For example, for the test specimen S-C-2-9, C is the strengthening material variables. For example, for the test specimen S-C-2-9, C is the strengthening material of CFRP (Carbon of CFRP (Carbon Fiber Reinforced Polymer), 2 is the strengthening configuration of two rows of Fiber Reinforced Polymer), 2 is the strengthening configuration of two rows of embedment bars (see embedment bars (see Figure 2c), and 9 is the diameter of embedment bars. Therefore, the variables to Figure 2c), and 9 is the diameter of embedment bars. Therefore, the variables to be investigated in be investigated in this test are as follows: this test are as follows: Influence of strengthening materials, including steel, BFRP (Basalt Fiber Reinforced Polymer), Influence of strengthening materials, including steel, BFRP (Basalt Fiber Reinforced Polymer), GFRP (Glass Fiber Reinforced Polymer), and CFRP (test specimens labelled as S-S-2-10, S-B-2-9, GFRP (Glass Fiber Reinforced Polymer), and CFRP (test specimens labelled as S-S-2-10, S-B-2-9, S-G-2-9, and S-C-2-9); S-G-2-9, and S-C-2-9); Influence of quantity of strengthening embedment bars (test specimens labelled as S-C-2-9 and Influence of quantity of strengthening embedment bars (test specimens labelled as S-C-2-9 and S-C-1-9). The strengthening configuration is shown in Figure 2c,d; S-C-1-9). The strengthening configuration is shown in Figure 2c,d; Influence of diameter of embedment bars (test specimens labelled as S-C-2-9 and S-C-1-13). Influence of diameter of embedment bars (test specimens labelled as S-C-2-9 and S-C-1-13). 125m m 150m m 125m m 400m m Figure 3. Details of test specimens in cross section. Figure 3. Details of test specimens in cross section. 200m m Appl. Sci. 2018, 8, 721 5 of 25 Table 1. Experimental variables. Embedment Diameter of Maximum Reinforcement Embedment Failure Load Model fcu (MPa) * Strengthening Embedment Failure Mode ** Deflection at Percentage (%) Bar Type (kN) Configuration Bar/Hole (mm) Failure (mm) S-Con 1.1 24.5 N/A N/A N/A 130 SF 8.67 S-D-1 1.1 27 N/A N/A -/16 134 SF 8.34 S-S-2-10 1.1 24.5 Steel 2 2 10/16 142 BF 22.54 S-B-2-9 1.1 25.1 BFRP 2 2 9/16 144 BF 17.61 S-G-2-9 1.1 25.6 GFRP 2 2 9/16 140 BF 19.36 S-C-2-9 1.1 25.3 CFRP 2 2 9/16 142 BF 17.4 S-C-1-9 1.1 25.4 CFRP 2 1 9/16 142 BF + SF 18.7 S-C-1-13 1.1 25.8 CFRP 2 1 13/20 148 BF 20.58 * Compressive strength based on cube tests; ** SF = shear failure; BF = bending failure. Appl. Sci. 2018, 8, 721 6 of 25 Appl. Sci. 2018, 8, x FOR PEER REVIEW 6 of 25 Appl. Sci. 2018, 8, x FOR PEER REVIEW 6 of 25 In addition, the control specimen, not strengthened with embedded bars, is labelled as S-Con. In addition, the control specimen, not strengthened with embedded bars, is labelled as S-Con. In addition, the control specimen, not strengthened with embedded bars, is labelled as S-Con. An unstrengthened test slab with drilling holes coded as S-D-1 is adopted to investigate the structural An unstrengthened test slab with drilling holes coded as S-D-1 is adopted to investigate the structural An unstrengthened test slab with drilling holes coded as S-D-1 is adopted to investigate the structural damage degree from the drilling-hole process. The test slabs were constructed by using normal-weight damage degree from the drilling-hole process. The test slabs were constructed by using normal- damage degree from the drilling-hole process. The test slabs were constructed by using normal- ready mixed concrete. The concrete average compressive strength (fcu) of the test slabs was evaluated weight ready mixed concrete. The concrete average compressive strength (fcu) of the test slabs was weight ready mixed concrete. The concrete average compressive strength (fcu) of the test slabs was at 28 days by carrying out direct compression tests on cube specimens of 100 mm 100 mm 100 mm. evaluated at 28 days by carrying out direct compression tests on cube specimens of 100 mm × 100 evaluated at 28 days by carrying out direct compression tests on cube specimens of 100 mm × 100 We obtained fcu values between 24.1 MPa to 26.1 MPa at 28 days. For the internal reinforcement of the mm × 100 mm. We obtained fcu values between 24.1 MPa to 26.1 MPa at 28 days. For the internal mm × 100 mm. We obtained fcu values between 24.1 MPa to 26.1 MPa at 28 days. For the internal slab strips, high bond steel bars of 16 and 18 mm diameter were used. The configuration of internal reinforcement of the slab strips, high bond steel bars of 16 and 18 mm diameter were used. The reinforcement of the slab strips, high bond steel bars of 16 and 18 mm diameter were used. The reinforcement in the test slabs is shown in Figures 4 and 5. The yielding stress and tensile strength configuration of internal reinforcement in the test slabs is shown in Figures 4 and 5. The yielding configuration of internal reinforcement in the test slabs is shown in Figures 4 and 5. The yielding were obtained by means of uniaxial tensile tests. We obtained an average of 438 MPa and 458 MPa, stress and tensile strength were obtained by means of uniaxial tensile tests. We obtained an average stress and tensile strength were obtained by means of uniaxial tensile tests. We obtained an average respectively. The test method for the embedded steel bars was the same as the internal reinforcement. of 438 MPa and 458 MPa, respectively. The test method for the embedded steel bars was the same as of 438 MPa and 458 MPa, respectively. The test method for the embedded steel bars was the same as The test method for the embedment FRP bars was carried out according to the requirement of ACI the internal reinforcement. The test method for the embedment FRP bars was carried out according the internal reinforcement. The test method for the embedment FRP bars was carried out according 440-R06 [16] with the loading rate of 0.2 N/s. The test results of embedment strengthening bars are to the requirement of ACI 440-R06 [16] with the loading rate of 0.2 N/s. The test results of embedment to the requirement of ACI 440-R06 [16] with the loading rate of 0.2 N/s. The test results of embedment shown in Table 2. To bond the ETS steel bars to the concrete substrate, an FY-Z epoxy based adhesive strengthening bars are shown in Table 2. To bond the ETS steel bars to the concrete substrate, an FY- strengthening bars are shown in Table 2. To bond the ETS steel bars to the concrete substrate, an FY- was used. The tensile behaviour and elastic modulus of this adhesive were obtained by carrying out Z epoxy based adhesive was used. The tensile behaviour and elastic modulus of this adhesive were Z epoxy based adhesive was used. The tensile behaviour and elastic modulus of this adhesive were direct tensile tests. As shown in Table 2, the tensile strength and elastic modulus of the FY-Z epoxy are obtained by carrying out direct tensile tests. As shown in Table 2, the tensile strength and elastic obtained by carrying out direct tensile tests. As shown in Table 2, the tensile strength and elastic 40.5 MPa and 1.2 GPa, respectively. modulus of the FY-Z epoxy are 40.5 MPa and 1.2 GPa, respectively. modulus of the FY-Z epoxy are 40.5 MPa and 1.2 GPa, respectively. Figure 4. Reinforcement layout in frame work before casting. Figure 4. Reinforcement layout in frame work before casting. Figure 4. Reinforcement layout in frame work before casting. 3Φ16 3Φ16 Φ16@200 Φ16@200 3Φ18 3Φ18 Figure 5. Details of reinforcement configuration. Figure 5. Details of reinforcement configuration. Figure 5. Details of reinforcement configuration. Appl. Sci. 2018, 8, 721 7 of 25 Table 2. Mechanical property of embedment bars and adhesives. Appl. Sci. 2018, 8, x FOR PEER REVIEW 7 of 25 Deep Embedment Diameter Tensile Strength Elastic Modulus Ultimate Table 2. Mechanical property of embedment bars and adhesives. Bar/Epoxy (mm) (MPa) (GPa) Strain Deep Embedment Diameter Tensile Strength Elastic Modulus Ultimate Steel 10 504 200 0.0025 Bar/Ep CFRP oxy (mm) 9 (MP 1581 a) (GP 156a) 0.0101 Strain BFRP 9 1011 83 0.0122 Steel 10 504 200 0.0025 GFRP 9 835 480 0.0174 CFRP 9 1581 156 0.0101 FY-Z epoxy N/A 40.5 1.2 0.0017 BFRP 9 1011 83 0.0122 GFRP 9 835 480 0.0174 3.2. Strengthening Technique FY-Z epoxy N/A 40.5 1.2 0.0017 To simplify the drilling process and avoid intersecting the longitudinal bars, the deep embedment 3.2. Strengthening Technique strengthening process was executed with a special drilling machine invented by the authors, as shown To simplify the drilling process and avoid intersecting the longitudinal bars, the deep in Figure 6, which can be used in vertical and inclined embedment strengthening, as shown in embedment strengthening process was executed with a special drilling machine invented by the Figure 6a,b. The strengthening steps are: (1) Holes = 1.5 times of the diameter of embedded bars are authors, as shown in Figure 6, which can be used in vertical and inclined embedment strengthening, drilled through the depth of concrete slabs. During the drilling process, the concrete dust is aspired as shown in Figure 6a,b. The strengthening steps are: (1) Holes = 1.5 times of the diameter of using a vacuum system (see Figure 1a); (2) The holes are cleaned using a helicoid-shaped steel brush embedded bars are drilled through the depth of concrete slabs. During the drilling process, the capable of removing the particles from the walls of the hole, the particles are then eliminated by the concrete dust is aspired using a vacuum system (see Figure 1a); (2) The holes are cleaned using a helicoid-shaped steel brush capable of removing the particles from the walls of the hole, the particles vacuum system (see Figure 1b); the cleaning procedure is repeated until the dust is totally removed; are then eliminated by the vacuum system (see Figure 1b); the cleaning procedure is repeated until (3) The epoxy resin is prepared according to the recommendations of the supplier, and is slowly poured the dust is totally removed; (3) The epoxy resin is prepared according to the recommendations of the into the holes (see Figure 1c); (4) The deep embedment bars are cut in the desired length, cleaned supplier, and is slowly poured into the holes (see Figure 1c); (4) The deep embedment bars are cut in with acetone, and are slowly introduced into the holes, removing the excess resin (see Figure 1d). the desired length, cleaned with acetone, and are slowly introduced into the holes, removing the To guarantee a proper curing of the adhesive, the specimens are tested at least two weeks after the excess resin (see Figure 1d). To guarantee a proper curing of the adhesive, the specimens are tested deep embedment application. at least two weeks after the deep embedment application. (a) (b) Electronic drilling Steel clamp Concrete component (c) Figure 6. Details of invented drilling equipment: (a) Vertical drilling; (b) Inclined drilling; (c) Drilling equipment. Appl. Sci. 2018, 8, x FOR PEER REVIEW 8 of 25 Figure 6. Details of invented drilling equipment: (a) Vertical drilling; (b) Inclined drilling; (c) Drilling equipment. Appl. Sci. 2018, 8, 721 8 of 25 Appl. Sci. 2018, 8, x FOR PEER REVIEW 8 of 25 3.3. Test Set-Up and Monitoring System Figure 6. Details of invented drilling equipment: (a) Vertical drilling; (b) Inclined drilling; (c) Drilling 3.3. Test Set-Up and Monitoring System equipment. As shown in Figure 7, the slab strips are tested in three-point load flexure. The load was applied As shown in Figure 7, the slab strips are tested in three-point load flexure. The load was applied at a distance of three times the effective depth of test slabs (see Figure 2), which was chosen to allow 3.3. Test Set-Up and Monitoring System at a distance of three times the effective depth of test slabs (see Figure 2), which was chosen to allow the shear capacity to be larger than the flexural capacity in the unstrengthened test slabs. To meet the the shear capacity to be larger than the flexural capacity in the unstrengthened test slabs. To meet the As shown in Figure 7, the slab strips are tested in three-point load flexure. The load was applied objective and the scope of the study, a very comprehensive and carefully engineered measuring objective and the scope of the study, a very comprehensive and carefully engineered measuring scheme at a distance of three times the effective depth of test slabs (see Figure 2), which was chosen to allow scheme was adopted for the study (Figures 7 and 8). The vertical displacement of the test specimens was adopted for the study (Figures 7 and 8). The vertical displacement of the test specimens was the shear capacity to be larger than the flexural capacity in the unstrengthened test slabs. To meet the was measured using six linear variable-displacement transducers as shown in Figure 7. The exact measured using six linear variable-displacement transducers as shown in Figure 7. The exact positions objective and the scope of the study, a very comprehensive and carefully engineered measuring positions of those displacement transducers are shown in Figure 8a. As shown in Figure 8b, the scheme was adopted for the study (Figures 7 and 8). The vertical displacement of the test specimens of those displacement transducers are shown in Figure 8a. As shown in Figure 8b, the vibrating wire vibrating wire strain gauges were located at the midspan, the one-fourth span, and the ends of the was measured using six linear variable-displacement transducers as shown in Figure 7. The exact strain gauges were located at the midspan, the one-fourth span, and the ends of the concrete slabs. concrete slabs. The electrical resistant strain (ERS) gauges were glued to the transverse steel positions of those displacement transducers are shown in Figure 8a. As shown in Figure 8b, the The electrical resistant strain (ERS) gauges were glued to the transverse steel reinforcing bars and reinforcing bars and embedded steel/FRP bars to monitor strain values at different loading stages, vibrating wire strain gauges were located at the midspan, the one-fourth span, and the ends of the embedded steel/FRP bars to monitor strain values at different loading stages, such as yielding in steel such as yielding in steel and maximum strain in FRP. The positions of those ERS gauges are shown concrete slabs. The electrical resistant strain (ERS) gauges were glued to the transverse steel and maximum strain in FRP. The positions of those ERS gauges are shown in Figure 8c. Readings of all in Figure 8c. Readings of all the displacement transducers and strain gauges were recorded at each reinforcing bars and embedded steel/FRP bars to monitor strain values at different loading stages, the displacement transducers and strain gauges were recorded at each load increment. load increment. such as yielding in steel and maximum strain in FRP. The positions of those ERS gauges are shown in Figure 8c. Readings of all the displacement transducers and strain gauges were recorded at each load increment. Figure 7. Loading configuration in the test. Figure 7. Loading configuration in the test. Figure 7. Loading configuration in the test. 150m m 150m m 150m m 150m m 50m m 50m m 50m m 50m m T5 T4 T3 T2 T1 T6 T5 T4 T3 T2 T1 T6 26 265m 5mmm 51 510m 0mmm 2727 5m5m m m 415m 415m m m 2400m m 2400m m (a) (a) 1550m m 550m m 1550m m 550m m 500m m 275m m 275m m 500m m 275m m 275m m 150m m 2100m m 150m m 150m m 2100m m 150m m 2400m m 2400m m (b) (b) Figure 8. Cont. 200m m 200m m 200m m 200m m 200m m 200m m 20m m 20m m 20m m 20m m 40m m 40m m 112 90 70 70 96 90 70 70 96 1 2 120 108 120 108 98 86 75 55 80 60 40 30 98 86 96 82 65 35 40 80 75 60 55 45 65 40 30 65 35 Appl. Sci. 2018, 8, 721 9 of 25 Appl. Sci. 2018, 8, x FOR PEER REVIEW 9 of 25 2340m m 585m m 585m m 585m m 585m m Appl. Sci. 2018, 8, x FOR PEER REVIEW 9 of 25 R4- R3 R2 R1 2340m m 585m m 585m m 585m m 585m m 150m m 2100m m 150m m 2400m m R4- R3 (c) R2 R1 Figure 8. 150m m Measurement set-up in this test: (210 a) Di 0m splace m ment transducers (T1-T6: displacem 150m ment Figure 8. Measurement set-up in this test: (a) Displacement transducers (T1-T6: displacement 2400m m transducers); (b) Strain gauges for concrete slabs; (c) Strain gauges for embedded bars and steel transducers); (b) Strain gauges for concrete slabs; (c) Strain gauges for embedded bars and steel (c) reinforcement (R1-R6: electrical resistant strain (ERS)). reinforcement (R1-R6: electrical resistant strain (ERS)). Figure 8. Measurement set-up in this test: (a) Displacement transducers (T1-T6: displacement 3.4. Test Procedure transducers); (b) Strain gauges for concrete slabs; (c) Strain gauges for embedded bars and steel 3.4. Test Procedure reinforcement (R1-R6: electrical resistant strain (ERS)). In each test, to ensure that the deflections were not influenced by the settling (e.g., softboard), In each test, to ensure that the deflections were not influenced by the settling (e.g., softboard), two preliminary test loads (20–25 kN) were held for two minutes and the recovery measured. The 3.4. Test Procedure two preliminary test loads (20–25 kN) were held for two minutes and the recovery measured. test model was then loaded in 20 kN increments until cracking occurred on the bottom surface. After The test model was then loaded in 20 kN increments until cracking occurred on the bottom surface. In each test, to ensure that the deflections were not influenced by the settling (e.g., softboard), cracking on the bottom surface of the slab appeared, the load increment was decreased to 5–10 kN Aftertcracking wo prelim on inary the tbottom est loadsurface s (20–25 k ofN the ) were he slab appear ld for two mi ed, the nutes a load incr nd the recovery mea ement was decreased sured. The to 5–10 kN until failure. At each load increment, the surface was examined and the crack propagation recorded. test model was then loaded in 20 kN increments until cracking occurred on the bottom surface. After until failure. At each load increment, the surface was examined and the crack propagation recorded. After testing, the models were carefully removed and photographed to reveal the distribution of cracking on the bottom surface of the slab appeared, the load increment was decreased to 5–10 kN After testing, the models were carefully removed and photographed to reveal the distribution of cracks cracks on the two lateral sides of the slabs. until failure. At each load increment, the surface was examined and the crack propagation recorded. on the two lateral sides of the slabs. After testing, the models were carefully removed and photographed to reveal the distribution of 4. Discussion of Test Results cracks on the two lateral sides of the slabs. 4. Discussion of Test Results 4.1. Failure Mode and Ultimate Loads 4. Discussion of Test Results 4.1. Failure Mode and Ultimate Loads Figure 9a,b shows the propagation of crack patterns through the depth of the unstrengthened Figur 4.1. Fai el9 ua,b re M shows ode andthe Ultipr ma opagation te Loads of crack patterns through the depth of the unstrengthened test test slabs. For those two test specimens, it can be found that the first flexural cracks started to appear slabs. For those two test specimens, it can be found that the first flexural cracks started to appear in in the moment zone at an applied load of 25 kN. Those flexural cracks propagated upwards as the Figure 9a,b shows the propagation of crack patterns through the depth of the unstrengthened the moment zone at an applied load of 25 kN. Those flexural cracks propagated upwards as the load load was increased. Flexural cracks then formed over wider areas until a load of 100 kN, when test slabs. For those two test specimens, it can be found that the first flexural cracks started to appear was dia incr gona eased. l shea Flexural r cracks ap cracks peared then in tformed he shearover zonewider . The un arstrengthe eas untiln aed test load of specimens both 100 kN, whenfailed diagonal in in the moment zone at an applied load of 25 kN. Those flexural cracks propagated upwards as the shear brit load w cracks tle she aa appear s inc r at aroun reased. F ed in d the 13 lex 0 ural c shear kN. Th rzone. ac e lo ks th ad The en formed ing p unstr roced engthened o ure ver had wider ar ttest o beeas until a lo specimens terminated, both a ad s sof 100 failed hown in F kN, in bri iwhen gttle ure 1 shear 0. Those two concrete sl diagonal shear cracks a b ap s p were eared sepa in tra he te sh d to two co ear zone. Th mponents through thi e unstrengthened test sspecimens both diagonal shear failed crack in , see at around 130 kN. The loading procedure had to be terminated, as shown in Figure 10. Those two brittle shear at around 130 kN. The loading procedure had to be terminated, as shown in Figure 10. Figure 10a. In addition, the crack pattern of the test slabs with drilling holes (test specimen coded as concrete slabs were separated to two components through this diagonal shear crack, see Figure 10a. Those two concrete slabs were separated to two components through this diagonal shear crack, see S-D-1) was similar as that in the control model (S-Con). The ultimate capacities of those two models In addition, the crack pattern of the test slabs with drilling holes (test specimen coded as S-D-1) was Figure 10a. In addition, the crack pattern of the test slabs with drilling holes (test specimen coded as are also close, as shown in Table 1. This indicates that the drilling procedure does not cause significant similar as that in the control model (S-Con). The ultimate capacities of those two models are also close, S-D-1) was similar as that in the control model (S-Con). The ultimate capacities of those two models structural damage for the concrete slabs. as shown in Table 1. This indicates that the drilling procedure does not cause significant structural are also close, as shown in Table 1. This indicates that the drilling procedure does not cause significant damage for the concrete slabs. structural damage for the concrete slabs. (a) S-Con (a) S-Con (b) S-D-1 (b) S-D-1 (c) S-S-2-10 (c) S-S-2-10 Figure 9. Cont. 132 90 200m m 200m m 100m m 100m m 50m m 50m m 50m m 50m m 108 35 3 70 70 55 55 98 98 50 50 92 124 114 70 92 55 60 65 55 30 45 92 45 92 Appl. Sci. 2018, 8, x FOR PEER REVIEW 10 of 25 Appl. Sci. 2018, 8, 721 10 of 25 Appl. Sci. 2018, 8, x FOR PEER REVIEW 10 of 25 75 70 65 45 106 45 65 45 35 40 (d) S-B-2-9 (d) S-B-2-9 98 75 116 85 55 98 40 35 35 116 85 55 104 35 35 (e) S-G-2-9 (e) S-G-2-9 (f) S-C-2-9 (f) S-C-2-9 85 85 85 85 35 90 90 (g) S-C-1-9 (g) S-C-1-9 85 104 90 90 65 65 40 85 40 35 40 (h) S-C-1-13 (h) S-C-1-13 Figure 9. Crack patterns in test slabs. Figure 9. Crack patterns in test slabs. Figure 9. Crack patterns in test slabs. (a) (b) (a) (b) (c) (d) Figure 10. Comparisons of failure modes in the strengthened test slabs and unstrengthened test slabs. (a) S-Con; (b) S-C-2-9; (c) S-C-1-9; (d) S-C-1-13. (c) (d) The crack patterns of all the strengthened test slabs are shown in Figure 9c–h. Similar to the Figure 10. Comparisons of failure modes in the strengthened test slabs and unstrengthened test slabs. Figure 10. Comparisons of failure modes in the strengthened test slabs and unstrengthened test slabs. unstrengthened slabs, multiple flexural cracks formed in the moment zone up to the appearance of (a) S-Con; (b) S-C-2-9; (c) S-C-1-9; (d) S-C-1-13. (a) S-Con; (b) S-C-2-9; (c) S-C-1-9; (d) S-C-1-13. shear cracks (the applied load reached 100 kN). As the applied load increased, the inclined shear crack appeared in the shear zone, particularly in the area between two embedment strengthening The crack patterns of all the strengthened test slabs are shown in Figure 9c–h. Similar to the bars, as shown in Figure 9c–f. Interestingly, these shear cracks are prevented from opening further The crack patterns of all the strengthened test slabs are shown in Figure 9c–h. Similar to the unstrengthened slabs, multiple flexural cracks formed in the moment zone up to the appearance of unstrengthened slabs, multiple flexural cracks formed in the moment zone up to the appearance of shear cracks (the applied load reached 100 kN). As the applied load increased, the inclined shear shear cracks (the applied load reached 100 kN). As the applied load increased, the inclined shear crack appeared in the shear zone, particularly in the area between two embedment strengthening crack appeared in the shear zone, particularly in the area between two embedment strengthening bars, bars, as shown in Figure 9c–f. Interestingly, these shear cracks are prevented from opening further 90 90 130 130 122 122 92 92 65 85 65 85 70 70 85 94 122 Appl. Sci. 2018, 8, 721 11 of 25 Appl. Sci. 2018, 8, x FOR PEER REVIEW 11 of 25 as shown in Figure 9c–f. Interestingly, these shear cracks are prevented from opening further by the deep embedment strengthening bars. In addition, no shear cracks formed in the test slabs strengthened by the deep embedment strengthening bars. In addition, no shear cracks formed in the test slabs with large embedment bars (test specimen S-C-1-13). This indicates that the embedment strengthening strengthened with large embedment bars (test specimen S-C-1-13). This indicates that the embedment bars crossed by the cracks are successful in preventing shear failure. Thus, the strengthened specimens strengthening bars crossed by the cracks are successful in preventing shear failure. Thus, the are strengthened forced to a ductile specimens ar flexural e forc failur ed to e, as a ductile flex shown in ur Figur al fa es ilur 10 e, as and sh 11 own . When in Fithe gures 10 applied and 1 load 1. When reached the applied load reached the ultimate strength, the failure mode of all the test slabs with deep the ultimate strength, the failure mode of all the test slabs with deep embedment bars was concrete embedment bars was concrete crush at the loading positions. In all the tests, no debonding failure of crush at the loading positions. In all the tests, no debonding failure of embedment strengthening embedment strengthening bars occurred. Due to this high bond-slip behaviour, the embedment bars occurred. Due to this high bond-slip behaviour, the embedment strengthening materials do not strengthening materials do not influence the crack pattern and failure mode significantly. influence the crack pattern and failure mode significantly. S-Con S-D-1 S-S-2-10 S-B-2-9 S-G-2-9 S-C-2-9 S-C-1-9 S-C-1-13 0 5 10 15 20 25 Vertical displacement(mm) Figure 11. Comparisons of load vs. vertical deflection at loading point in test slabs. Figure 11. Comparisons of load vs. vertical deflection at loading point in test slabs. The ultimate loads of all the test slabs are shown in Table 1. The application of deep embedment The ultimate loads of all the test slabs are shown in Table 1. The application of deep embedment strengthening methods results in larger ultimate capacity of test slabs. The loading carrying capacity strengthening methods results in larger ultimate capacity of test slabs. The loading carrying capacity was enhanced by more than 10% by this strengthening method. As discussed in the section on crack was enhanced by more than 10% by this strengthening method. As discussed in the section on crack pattern and failure mode (see Figures 9 and 10), the test slabs with deep embedment strengthening pattern and failure mode (see Figures 9 and 10), the test slabs with deep embedment strengthening methods failed in flexure tests. Because this strengthening method has no effect on flexural behaviour methods failed in flexure tests. Because this strengthening method has no effect on flexural behaviour and flexural capacity of the unstrengthened test slab is larger than the shear capacity, increasing the and flexural capacity of the unstrengthened test slab is larger than the shear capacity, increasing the degree of the ultimate capacity (around 10%) is not as significant as that obtained in the test results degree of the ultimate capacity (around 10%) is not as significant as that obtained in the test results of of the embedment strengthened concrete beams (around 30–40%) [8,10]. Additionally, the variation the embedment strengthened concrete beams (around 30–40%) [8,10]. Additionally, the variation of of strengthening materials and strengthening ratios did not have a significant effect on ultimate strengthening materials and strengthening ratios did not have a significant effect on ultimate capacity capacity of the strengthened test slabs. of the strengthened test slabs. 4.2. Load vs. Deflection Responses 4.2. Load vs. Deflection Responses Figure 11 shows the curves representing the load versus the maximum vertical deflection (T3 as Figure 11 shows the curves representing the load versus the maximum vertical deflection (T3 as shown in Figure 8a) at the loading position for all the test slabs. For the unstrengthened test slabs, the shown in Figure 8a) at the loading position for all the test slabs. For the unstrengthened test slabs, bilinear behaviour of the load-deflection curves is characteristic of a shear failure. The first part of the bilinear behaviour of the load-deflection curves is characteristic of a shear failure. The first part this curve is up to flexural crack load (around 25 kN), while the second part represents the crack slab of this curve is up to flexural crack load (around 25 kN), while the second part represents the crack with reduction stiffness. When the applied load reached the shear capacity, the applied load was slab with reduction stiffness. When the applied load reached the shear capacity, the applied load was terminated suddenly. This corresponds to the observation of the test process (see Figure 10). Before terminated the applied l suddenly oad reac . hed the shea This corresponds r capacity of the co to the observation ncrete slof abs, the beha the test prv ocess iour of (see the l Figur oad-defl e 10e ).cti Befor on e the response applied of t load he stren reached gthened test the shear slabs capacity was sof imilar the to concr thaete t of the slabs, unstrengthened the behaviourtest sla of thebload-deflection s, see Figure 11. As the load increased, the application of the deep embedment shear strengthening method response of the strengthened test slabs was similar to that of the unstrengthened test slabs, see Figure 11. resulted in higher ductile structural response compared to the unstrengthened test slabs. Figure 11 As the load increased, the application of the deep embedment shear strengthening method resulted in Applied load (kN) Appl. Sci. 2018, 8, 721 12 of 25 higher ductile structural response compared to the unstrengthened test slabs. Figure 11 reveals that the strengthened specimens showed a greater overall stiffness compared with the S-Con and S-D-1 slabs. Using this strengthening scheme, the test specimens strengthened with deep embedment bars, which reached their flexural capacity (see Figure 11), failed in a ductile manner. Therefore, the slabs with deep embedment strengthening methods exhibited a higher deflection at the loading point and maximum load at failure compared to unstrengthened test slabs (see Figure 11). Generally, the ductility of reinforced concrete flexural components can be considered as the ability to sustain inelastic deformation without degeneration of loading-carrying capacity before structural failure. Based on this theoretical assumption, deformation or energy absorption can be defined as structural ductility. For steel reinforced concrete flexural components, ductility can be expressed as the ratio of ultimate deformation to deformation at yield. Therefore, the ductility of all the test slabs can be evaluated by means of a deformation factor (DF) [17]. This factor is defined as a ratio of the energy absorption at failure (area under load-deflection curve up to ultimate load) to that at service load (at the serviceability deflection limit of span/800 [18]). The results of DF values for all the test slabs are listed in Table 3. It was found that the embedment strengthening method improved the ductility of the strengthened test slabs significantly as reported in the test results of deep embedment strengthening concrete beams [6,7]. As shown in Table 3, it can be seen that using this strengthening scheme resulted in increasing the DF values by around 200%. This suggests that the ductility of concrete slabs subjected to loads close to the support is enhanced significantly by deep embedment strengthening methods. As expected, the concrete slabs strengthened with deep embedment steel bars attained the largest DF of 28.67, due to having the highest strengthening stiffness. As shown in Table 1, the decrease in stiffness of strengthening materials results in slightly smaller DF values of strengthened concrete slabs. Table 3. Deformability factors of all the test slabs. Diameter of Increase in DF Model RP * (%) fcu (MPa) EBT ** ESC *** Embedment DF Compared to Bar/Hole (mm) S-Con Beam (%) S-Con 1.1 24.5 N/A N/A N/A 7.7 N/A S-D-1 1.1 27 N/A N/A -/16 6.54 15% S-S-2-10 1.1 24.5 Steel 2 2 10/16 28.67 272% S-B-2-9 25.1 BFRP 2 2 9/16 23.03 199% 1.1 S-G-2-9 1.1 25.6 GFRP 2 2 9/16 23.05 199% S-C-2-9 1.1 25.3 CFRP 2 2 9/16 25.01 225% S-C-1-9 1.1 25.4 CFRP 2 1 9/16 20.79 170% S-C-1-13 1.1 25.8 CFRP 2 1 13/20 25.44 230% * RP = Reinforcement percentage; ** EBT = Embedment bar type; *** ESC = Embedment strengthening configuration; DF = Deformation factor. 4.3. Strain Response Figure 12 presents the curves of the load versus the maximum compressive strain of concrete slabs for the test specimens. It was observed that the curves have the same tendency for all the test specimens before the applied load reached the around 130 kN. This loading corresponds to the shear failure load of the unstrengthened test slab. Due to shear failure of the concrete slabs, the maximum compressive strain of concrete in the unstrengthened slab did not reach the crush strain (0.003) at the ultimate load. As the applied load increased, the compressive strain of all the strengthened test slabs increased more than the crush strain of concrete (0.003). It is noted that the failure mode of strengthened concrete slabs is flexural failure with concrete crush, which can be found in the observation of the test results (see Figure 10). Appl. Sci. 2018, 8, x FOR PEER REVIEW 13 of 25 Appl. Sci. 2018, 8, 721 13 of 25 Appl. Sci. 2018, 8, x FOR PEER REVIEW 13 of 25 S-Con S-Con 100 S-S-2-10 S-S-2-10 S-B-2-9 S-B-2-9 S-G-2-9 S-G-2-9 S-C-2-9 S-C-2-9 S-C-1-9 S-C-1-9 S-C-1-13 0 S-C-1-13 -5000 -4000 -3000 -2000 -1000 0 -5000 -4000 -300 MicroStrain ( 0 -200 με)0 -1000 0 MicroStrain (με) Figure 12. Applied load vs. maximum compressive strain of concrete slabs. Figure 12. Applied load vs. maximum compressive strain of concrete slabs. Figure 12. Applied load vs. maximum compressive strain of concrete slabs. Figures 13 and 14 illustrate the relationship of applied load and maximum tensile strain in Figures 13 and 14 illustrate the relationship of applied load and maximum tensile strain in longitudin Figures al 1 steel re 3 and 1 inforc 4 illu ement and e strate the rel mbedment streng ationship of applied thening load bars. It can be and maxim seen in F um tensi ig le st ure 13 th rain in at longitudinal steel reinforcement and embedment strengthening bars. It can be seen in Figure 13 that all the curves of load versus maximum tensile strain in steel reinforcement have a similar tendency longitudinal steel reinforcement and embedment strengthening bars. It can be seen in Figure 13 that all the curves of load versus maximum tensile strain in steel reinforcement have a similar tendency for al for a l thll t e curves he test of loa specimens. T d versus max his mean imum s th t ae t using nsile st the de rain in steel re ep embedment strengthening method d inforcement have a similar tendenc oes not y all the test specimens. This means that using the deep embedment strengthening method does not have a strong effect on the contribution of steel reinforcement to the ultimate capacity of the concrete for all the test specimens. This means that using the deep embedment strengthening method does not have a strong effect on the contribution of steel reinforcement to the ultimate capacity of the concrete have slabs. a Exam strong effect on the ination of the ccontribu urves in ti Fig on uof re 1 steel 4 rev rei eals that none o nforcement to the ul f the deep timaembed te capam cient strengthening ty of the concrete slabs. Examination of the curves in Figure 14 reveals that none of the deep embedment strengthening bars contributed to the loading carrying capacity before they reached the shear cracking load (around slabs. Examination of the curves in Figure 14 reveals that none of the deep embedment strengthening bars contributed to the loading carrying capacity before they reached the shear cracking load (around ba 100 kN). A rs contributed to the l ll the strain values reported oading carrying ca in this pacity be paper fore they are the m reach aximum me ed the sheaasur r crack ed v ing alues. A load (around fter the 100 kN). All the strain values reported in this paper are the maximum measured values. After the applied load increased beyond 100 kN, the strain in the deep embedment bars started to increase to 100 kN). All the strain values reported in this paper are the maximum measured values. After the applied load increased beyond 100 kN, the strain in the deep embedment bars started to increase to a a large value (see Figure 14), the level at which the concrete slabs failed. It can be summarised that applied load increased beyond 100 kN, the strain in the deep embedment bars started to increase to large value (see Figure 14), the level at which the concrete slabs failed. It can be summarised that the the deep embedment strengthening material started to contribute to shear resistance after the a large value (see Figure 14), the level at which the concrete slabs failed. It can be summarised that deep embedment strengthening material started to contribute to shear resistance after the formation formation of the concrete struts in the shear behaviour. After the embedment bars started to the deep embedment strengthening material started to contribute to shear resistance after the of the concrete struts in the shear behaviour. After the embedment bars started to contribute to the contribute to the shear capacity, the strain in all the test slabs was increased with a constant slope. formation of the concrete struts in the shear behaviour. After the embedment bars started to shear capacity, the strain in all the test slabs was increased with a constant slope. Additionally, the Additionally, the maximum strain value of steel embedment bars at failure is smaller than those in contribute to the shear capacity, the strain in all the test slabs was increased with a constant slope. maximum strain value of steel embedment bars at failure is smaller than those in embedment FRP embedment FRP bars, which could be due to the larger stiffness in steel bars compared to the FRP Additionally, the maximum strain value of steel embedment bars at failure is smaller than those in bars, which could be due to the larger stiffness in steel bars compared to the FRP materials. materials. embedment FRP bars, which could be due to the larger stiffness in steel bars compared to the FRP materials. S-Con S-S-2-10 S-Con S-B-2-9 S-S-2-10 S-G-2-9 S-B-2-9 S-C-2-9 S-G-2-9 S-C-1-9 S-C-2-9 S-C-1-13 S-C-1-9 S-C-1-13 0 1000 2000 3000 4000 5000 6000 MicroStrain (με) 0 1000 2000 3000 4000 5000 6000 MicroStrain (με) Figure 13. Applied load vs. maximum tensile strain in longitudinal reinforcement. Figure 13. Applied load vs. maximum tensile strain in longitudinal reinforcement. Figure 13. Applied load vs. maximum tensile strain in longitudinal reinforcement. Load (kN) Load (kN) Load (kN) Load (kN) Appl. Sci. 2018, 8, 721 14 of 25 Appl. Sci. 2018, 8, x FOR PEER REVIEW 14 of 25 Appl. Sci. 2018, 8, x FOR PEER REVIEW 14 of 25 S-S-2-10 S-S-2-10 S-B-2-9 S-B-2-9 S-G-2-9 S-G-2-9 S-C-2-9 S-C-2-9 S-C-1-9 S-C-1-9 S-C-1-13 S-C-1-13 -50 450 950 1450 1950 2450 2950 -50 450 950 1450 1950 2450 2950 MicroStrain (με) MicroStrain (με) Figure 14. Applied load vs. maximum tensile strain in deep embedment strengthening bars. Figure 14. Applied load vs. maximum tensile strain in deep embedment strengthening bars. Figure 14. Applied load vs. maximum tensile strain in deep embedment strengthening bars. 5. Finite Element Analysis 5. 5. F Finite inite E Element lement An Analysis alysis 5.1. Proposed NLFEA Model 5.1. Proposed NLFEA Model 5.1. Proposed NLFEA Model The proposed NLFEA model is a two-dimensional finite element (FE) model that was The proposed NLFEA model is a two-dimensional finite element (FE) model that was The proposed NLFEA model is a two-dimensional finite element (FE) model that was implemented in ABAQUS [19], as shown in Figure 15. This NLFEA model is on the basis of the implemented in ABAQUS [19], as shown in Figure 15. This NLFEA model is on the basis of the implemented in ABAQUS [19], as shown in Figure 15. This NLFEA model is on the basis of the smeared cracked approach so that the crack paths do no need to predefined, and it employs the crack smeared cracked approach so that the crack paths do no need to predefined, and it employs the crack smeared cracked approach so that the crack paths do no need to predefined, and it employs the crack band model to overcome the mesh sensitivity problem associated with the smeared crack model. An band model to overcome the mesh sensitivity problem associated with the smeared crack model. band model to overcome the mesh sensitivity problem associated with the smeared crack model. An appropriate bond-slip model published in the literature [20,21] is adopted to simulate the bond-slip An appropriate bond-slip model published in the literature [20,21] is adopted to simulate the bond-slip appropriate bond-slip model published in the literature [20,21] is adopted to simulate the bond-slip interaction between the concrete and deep embedment FRP bars. Further details of the NLFEA model interaction between the concrete and deep embedment FRP bars. Further details of the NLFEA model interaction between the concrete and deep embedment FRP bars. Further details of the NLFEA model are presented in the following section. are presented in the following section. are presented in the following section. Figure 15. Proposed numerical model for concrete slabs. Figure 15. Proposed numerical model for concrete slabs. Figure 15. Proposed numerical model for concrete slabs. 5.2. Modelling of Concrete Material 5.2. Modelling of Concrete Material 5.2. Modelling of Concrete Material In this numerical study, a material model named Concrete Damage Plasticity Model [22,23] was In this numerical study, a material model named Concrete Damage Plasticity Model [22,23] was In this numerical study, a material model named Concrete Damage Plasticity Model [22,23] was adopted based on the previous testing of concrete deck slabs [24]. This model assumes non-associated adopted based on the previous testing of concrete deck slabs [24]. This model assumes non-associated adopted based on the previous testing of concrete deck slabs [24]. This model assumes non-associated potential plastic-flow where the flow potential is defined by the Drucker-Prager hyperbolic function potential plastic-flow where the flow potential is defined by the Drucker-Prager hyperbolic function potential plastic-flow where the flow potential is defined by the Drucker-Prager hyperbolic function and the yield function. The equation by Thorenfeldt et al. [25] combined with the Hognestad’s [26] and the yield function. The equation by Thorenfeldt et al. [25] combined with the Hognestad’s [26] and the yield function. The equation by Thorenfeldt et al. [25] combined with the Hognestad’s [26] assumption on the elastic modulus of concrete were used to model compressive stress vs. strain assumption on the elastic modulus of concrete were used to model compressive stress vs. strain assumption on the elastic modulus of concrete were used to model compressive stress vs. strain relationship of concrete material. This model was given by Equations (1) to (5). relationship of concrete material. This model was given by Equations (1) to (5). relationship of concrete material. This model was given by Equations (1) to (5). f f # n n c c c c f n c= c (1) (1) nk nk f 0 # 0 (1) nk cf c n n 1+ 1(#( /# /0) ) ' ' c c ' f c c n 1 ( / c ) ' ' ' c c c f 0 n # 0 = f (2) 0 ' f c ' n E n 1 c c ' (2) c ' ' (2) c ' E n1 E n1 c f 0 n = 0.8 + (3) Load (kN) Load (kN) Appl. Sci. 2018, 8, 721 15 of 25 When #/# 0 is less than 1, k equals 1. When #/# 0 exceeds 1, k is a number larger than 1. c c f 0 k = 0.67 + (4) E = 4723 f (5) c c The tensile response of reinforced concrete is modelled using a non-linear tension stiffening model. Tension stiffening is influenced by the reinforcement ratio, crack spacing, and quality of the bond between the concrete and reinforcement. Before the occurrence of cracks, the tension behaviour of concrete was assumed to be linear. After this stage, the stress and strain relationship of concrete under uniaxial tension was expressed as below [27–29]: " # s w t w t t (c ) t 3 ( c ) 2 2 cr = 1 + c e (1 + c )e (6) f w w t cr cr w = 5.14 (7) cr where w is crack open displacement; w is cracking opening displacement at the complete release t cr of stress or fracture energy; s is tensile stress normal to crack direction; ft is concrete uniaxial tensile strength; G is fracture energy required to create a stress-free crack over a unit area; and c = 3.0 and F 1 c = 6.93 = constants determined from tensile tests of concrete. In this study, G could be estimated 2 F from the equation of CEB-FIB [30] as below: 0.7 2 c G = (0.0469d 0.5d + 26)( ) (8) F a Additionally, the damage parameters are defined for compressive failure and tension failure in this material model. The evolution of the compressive damage component d is linked to the corresponding pl in 1 plastic strain # which is determined proportional to the inelastic strain # = # s E using constant c c c c c pl in bc with the expression of # = b # . c c s E d = 1 (9) pl # (1/b 1) + s E c c c c In Equation (9), b is equal to 0.7 according to the reported experimental test results [31]. Similar pl to the Equation (9), the tensile damage d depends on # and experimentally determined parameter b = 0.1 [32]. Therefore, the unloading is assumed to return almost back to the origin and to leave only a small residual strain (see Equation (10)). s E d = 1 (10) pl # (1/b 1) + s E t t pl in in where # = b # and # = # s E . t t t t t t t 5.3. Modelling of Steel and FRP Bars The deep embedment FRP bars and steel reinforcement were represented using truss elements. Those elements are only deformable in the axial direction, whilst bending and shear deformations are not allowed. In the proposed FE model, the material models for steel and FRP are assumed to be elastic-perfectly plastic and linear-elastic-brittle, respectively. Von Mises yield criterion with associated plastic flow and isotropic hardening are used for those two materials. Appl. Sci. 2018, 8, 721 16 of 25 5.4. Modelling of FRP Bar–to-Concrete Interface Appl. Sci. 2018, 8, x FOR PEER REVIEW 16 of 25 For modelling the interaction between the deep embedment FRP bars and the surrounding 5.4. Modelling of FRP Bar–to-Concrete Interface concrete, the interface element coded as COH2D4 in ABAQUS is used. For the direction parallel For modelling the interaction between the deep embedment FRP bars and the surrounding to the FRP-concrete interface, the properties of the interfacial elements are defined by using the concrete, the bond-slip model interface by Mofidi elem et ent coded al. [20]. The as COH ascending 2D4 in branch ABAQ isUS is this model used. Fo is ar the parabolic direction p bond str aress-slip allel to the FRP-concrete interface, the properties of the interfacial elements are defined by using the bond- relationship, up to the bond strength (t ), and given by slip model by Mofidi et al. [20]. The ascending branch is this model is a parabolic bond stress-slip t = t (s/s ) (11) relationship, up to the bond strength ( ), and given m by m (⁄) = (11) The descending branch is described by the following linear relationship: The descending branch is described by the following linear relationship: t = t [1 p(s/s 1)] (12) m m (⁄) = 1− −1 (12) where t is the bond stress at a specific slip s, s is the slip value at t , a is a curve-fitting parameter, m m where is the bond stress at a specific slip , is the slip value at , is a curve-fitting and p is a parameter controlling the descending part of the bond-slip relationship [20]. A series of parameter, and p is a parameter controlling the descending part of the bond-slip relationship [20]. A direct pull-out tests were conducted to determine those variables, see Figure 16. On the basis of the series of direct pull-out tests were conducted to determine those variables, see Figure 16. On the basis similar experimental test results, those coefficients were determined as shown in Table 4. of the similar experimental test results, those coefficients were determined as shown in Table 4. (a) 4 BFRP CFRP GFRP 0 0.1 0.2 0.3 0.4 0.5 0.6 Slip(mm) (b) Figure 16. Bond-slip test for deep embedment FRP bars and concrete: (a) Test specimen; (b) Test Figure 16. Bond-slip test for deep embedment FRP bars and concrete: (a) Test specimen; (b) Test results. results. Table 4. The coefficients for bond-slip constitutive model. Table 4. The coefficients for bond-slip constitutive model. Type of FRP t (MPa) s (mm) a p m m Type of FRP τm (MPa) sm (mm) α p BFRP 7 BFRP .42 7.42 0.1 0.133 0.0850.085 0.09350.0935 GFRP 7.75 0.13 0.098 0.05 GFRP 7.75 0.13 0.098 0.05 CFRP 7.69 0.11 0.087 0.068 CFRP 7.69 0.11 0.087 0.068 5.5. Solution Strategy Due to the brittle behaviour of shear failure, numerical instability and convergence problems could occur in the traditional static analysis-implicit analysis [24]. In this study, a dynamic approach Bond stress(kN) Appl. Sci. 2018, 8, 721 17 of 25 5.5. Solution Strategy Appl. Sci. 2018, 8, x FOR PEER REVIEW 17 of 25 Due to the brittle behaviour of shear failure, numerical instability and convergence problems could occur in the traditional static analysis-implicit analysis [24]. In this study, a dynamic approach in explicit analysis was employed for the numerical solution of the FE model [33]. In this method, the in explicit analysis was employed for the numerical solution of the FE model [33]. In this method, quasi-static analysis is developed with small load increments. However, this analysis procedure does the quasi-static analysis is developed with small load increments. However, this analysis procedure not terminate after structural failure. Therefore, a failure criterion based on balances of forces is does not terminate after structural failure. Therefore, a failure criterion based on balances of forces adopted in this numerical analysis. As shown in Figure 17, the reaction load is nearly equal to the is adopted in this numerical analysis. As shown in Figure 17, the reaction load is nearly equal to the applied load before the failure. The balance of those two loads was broken as soon as the occurrence applied load before the failure. The balance of those two loads was broken as soon as the occurrence of of punching failure. A detailed description of the quasi-static solution strategy is given in Zheng et punching failure. A detailed description of the quasi-static solution strategy is given in Zheng et al. [33]. al. [33]. Applied load Reaction 00.5 11.5 22.5 33.5 Loading time (s) Figure 17. Applied load and reaction load vs. loading time in nonlinear finite element analysis Figure 17. Applied load and reaction load vs. loading time in nonlinear finite element analysis (NLFEA) (NLFEA) (Model S-C-2-9, Test failure load = 138 kN, NLFEA failure load = 144 kN). (Model S-C-2-9, Test failure load = 138 kN, NLFEA failure load = 144 kN). 5.6. FE Model Validation 5.6. FE Model Validation Based on the numerical model and failure criterion presented above, NLFEA of the deep Based on the numerical model and failure criterion presented above, NLFEA of the deep embedment FRP strengthened concrete slabs was conducted. The accuracy of NLFEA model was embedment FRP strengthened concrete slabs was conducted. The accuracy of NLFEA model evaluated by comparing the test results with the numerical predictions. Those comparisons included was evaluated by comparing the test results with the numerical predictions. Those comparisons loading-carrying capacity, load-deflection response, crack patterns, and strain values in deep included loading-carrying capacity, load-deflection response, crack patterns, and strain values in embedment FRP bars and steel reinforcement. The experimental and NLFEA predicted loading- deep embedment FRP bars and steel reinforcement. The experimental and NLFEA predicted carrying capacities are given in Table 5. The overall mean predicted/experimental ultimate strengths loading-carrying capacities are given in Table 5. The overall mean predicted/experimental ultimate ratio is 1.01. The standard deviation and coefficient of variation of this validation study are both 0.03. Figure 18 demonstrates that there is a very good match between experimental and NLFEA-predicted strengths ratio is 1.01. The standard deviation and coefficient of variation of this validation study load-vertical deflection response from initial loading up to structural failure. It was found that the are both 0.03. Figure 18 demonstrates that there is a very good match between experimental and trend of the load-deflection responses in the test and numerical results were similar, particularly in NLFEA-predicted load-vertical deflection response from initial loading up to structural failure. It was the ductile behaviour in the deep embedment FRP strengthened concrete slabs. However, it was found that the trend of the load-deflection responses in the test and numerical results were similar, found that the prediction from the NLFEA simulation was stiffer than that in the test results. This particularly in the ductile behaviour in the deep embedment FRP strengthened concrete slabs. However, over-stiff phenomenon is also found in the comparison of load vs. maximum strain in steel it was found that the prediction from the NLFEA simulation was stiffer than that in the test results. reinforcement, see Figure 19. This could be due to the major drawback of smeared crack and perfect This over-stiff phenomenon is also found in the comparison of load vs. maximum strain in steel bonding assumptions used in this study [34]. Interestingly, the proposed NLFEA model accurately reinforcement, see Figure 19. This could be due to the major drawback of smeared crack and perfect predicted the load-strain in deep embedment FRP bars based on the bond-slip model discussed bonding assumptions used in this study [34]. Interestingly, the proposed NLFEA model accurately above, as shown in Figure 20. The FE cracking patterns at ultimate loads are illustrated in Figure 21. predicted the load-strain in deep embedment FRP bars based on the bond-slip model discussed By comparing to the cracking pattern in the test (see Figures 9 and 10), the proposed numerical model above, as shown in Figure 20. The FE cracking patterns at ultimate loads are illustrated in Figure 21. gives accurate prediction in crack propagations and failure modes of deep embedment FRP By comparing to the cracking pattern in the test (see Figures 9 and 10), the proposed numerical strengthened concrete slabs. Based on the validation analysis results, it can be summarised that the model gives accurate prediction in crack propagations and failure modes of deep embedment FRP proposed NLFEA model and solution strategy are suitable for the objective of this structural analysis. strengthened concrete slabs. Based on the validation analysis results, it can be summarised that the Therefore, this NLFEA model can be adopted to develop further studies of the structural performance proposed NLFEA model and solution strategy are suitable for the objective of this structural analysis. of this strengthened concrete structure in the future. Therefore, this NLFEA model can be adopted to develop further studies of the structural performance of this strengthened concrete structure in the future. Load (kN) Appl. Sci. 2018, 8, 721 18 of 25 Appl. Sci. 2018, 8, x FOR PEER REVIEW 18 of 25 Table 5. Experimental and NLFEA prediction loading-carrying capacity. Table 5. Experimental and NLFEA prediction loading-carrying capacity. Test Specimen Pt-Test * (kN) Pp-NLFEA ** (kN) Pp/Pt-NlFEA Test Specimen Pt-Test * (kN) Pp-NLFEA ** (kN) Pp/Pt-NlFEA S-Con 130 133.06 1.02 S-ConS-S-2-10 14 1302 14 133.064.28 1.021.02 S-S-2-10 142 144.28 1.02 S-B-2-9 144 141.84 0.98 S-B-2-9 144 141.84 0.98 S-G-2-9 138 140.71 1.02 S-G-2-9 138 140.71 1.02 S-C-2-9 138 144.78 1.05 S-C-2-9 138 144.78 1.05 S-C-1-9 142 142.93 1.00 S-C-1-9 142 142.93 1.00 S-C-1-13 148 143.92 0.97 S-C-1-13 148 143.92 0.97 Average = 1.01 Average = 1.01 Standard deviation = 0.03 Standard deviation = 0.03 Coefficient of variation = 0.03 Coefficient of variation = 0.03 * Pt = Ultimate capaciyt in test; ** Pp-NLFEA= Predicted ultimate capacity in the NlFEA method. * Pt = Ultimate capaciyt in test; ** Pp-NLFEA= Predicted ultimate capacity in the NlFEA method. Test NLFEA 02468 10 Vertical deflection (mm) (a) Test NLFEA 0 5 10 15 20 Vertical deflection (mm) (b) Figure 18. Cont. Load (kN) Load (kN) Appl. Sci. 2018, 8, 721 19 of 25 Appl. Sci. 2018, 8, x FOR PEER REVIEW 19 of 25 Appl. Sci. 2018, 8, x FOR PEER REVIEW 19 of 25 1416 0 0 Test Test NLFEA NLFEA 0 5 10 15 20 25 0 5 10 15 20 25 Vertical deflection (mm) Vertical deflection (mm) (c) (c) Figure 18. Comparison of load-vertical deflection responses: (a) Test model coded as S-Con; Figure 18. Comparison of load-vertical deflection responses: (a) Test model coded as S-Con; (b) Test Figure 18. Comparison of load-vertical deflection responses: (a) Test model coded as S-Con; (b) Test model coded as S-C-2-9; (c) Test model coded as S-C-1-9. model coded as S-C-2-9; (c) Test model coded as S-C-1-9. (b) Test model coded as S-C-2-9; (c) Test model coded as S-C-1-9. Test Test NLFEA NLFEA 0 500 1000 1500 2000 2500 3000 3500 0 500 1000 1500 2000 2500 3000 3500 MicroStrain(με) MicroStrain(με) (a) (a) Test Test NLFEA NLFEA 0 0 500 1000 1500 2000 2500 3000 3500 0 500 1000 1500 2000 2500 3000 3500 MicroStrain(με) MicroStrain(με) (b) (b) Figure 19. Cont. Load (kN) Load (kN) Load (kN) Load (kN) Load (kN) Load (kN) Appl. Sci. 2018, 8, 721 20 of 25 Appl. Sci. 2018, 8, x FOR PEER REVIEW 20 of 25 Appl. Sci. 2018, 8, x FOR PEER REVIEW 20 of 25 Test Test NLFEA NLFEA 20 20 0 1000 2000 3000 4000 5000 0 1000 2000 3000 4000 5000 MicroStrain(με) MicroStrain(με) (c) (c) Figure 19. Comparison of load vs. strain in longitudinal reinforcement: (a) Test model coded as S- Figure 19. Comparison of load vs. strain in longitudinal reinforcement: (a) Test model coded as S- Figure 19. Comparison of load vs. strain in longitudinal reinforcement: (a) Test model coded as S-Con; Con; (b) Test model coded as S-C-2-9; (c) Test model coded as S-C-2-1. (Con; b) Test (b) Test model m coded odel code as S-C-2-9; d as S-C-2-9 (c) Test ; (cmodel ) Test mode coded l code as S-C-2-1. d as S-C-2-1. Test Test NLFEA NLFEA -50 450 950 1450 1950 2450 -50 450 MicroStrain( 950 1με 45)0 1950 2450 MicroStrain(με) (a) (a) 16 14 00 Test NLFEA Test NLFEA 0 100 200 300 400 500 600 700 MiroStrain (με) 0 100 200 300 (b) 400 500 600 700 MiroStrain (με) Figure 20. Comparison of load vs. strain in deep embedment strengthening bars: (a) Test model coded (b) as S-C-2-9; (b) Test model coded as S-C-1-9. Figure 20. Comparison of load vs. strain in deep embedment strengthening bars: (a) Test model coded Figure 20. Comparison of load vs. strain in deep embedment strengthening bars: (a) Test model coded as S-C-2-9; (b) Test model coded as S-C-1-9. as S-C-2-9; (b) Test model coded as S-C-1-9. Load (kN) Load (kN) Load (kN) Load (kN) Load (kN) Load (kN) Appl. Sci. 2018, 8, 721 21 of 25 Appl. Sci. 2018, 8, x FOR PEER REVIEW 21 of 25 (a) Crack patterns at 90% of ultimate load of S-Con. (b) Crack patterns at ultimate load of S-Con. (c) Crack patterns at ultimate load of S-C-2-9. (d) Crack patterns at ultimate load of S-C-1-9. (e) Crack patterns at ultimate load of S-C-1-13. Figure 21. Finite element (FE) crack patterns of test slabs. Figure 21. Finite element (FE) crack patterns of test slabs. 6. Loading-Carrying Capacity Prediction Method 6. Loading-Carrying Capacity Prediction Method In this study, a design model is proposed to predict the loading-carrying capacity of concrete In this study, a design model is proposed to predict the loading-carrying capacity of concrete slabs slabs shear strengthened with deep embedment FRP bars. It was found in the test that the failure shear strengthened with deep embedment FRP bars. It was found in the test that the failure mode of mode of concrete slabs could be varied from brittle shear failure to ductile flexural failure by using concrete slabs could be varied from brittle shear failure to ductile flexural failure by using the deep the deep embedment strengthening method. As a result, a two-way prediction approach, including embedment strengthening method. As a result, a two-way prediction approach, including bending bending and shear ultimate strengths, is adopted in this paper as shown below: and shear ultimate strengths, is adopted in this paper as shown below: Flexural Capacity: Flexural Capacity: The flexural capacity of concrete slabs is predicted by using the equations in a bridge structure The flexural capacity of concrete slabs is predicted by using the equations in a bridge structure design code named BS5400 [35], which is given by: design code named BS5400 [35], which is given by: = 1−0.59 / (13) M = r f bd 1 0.59r f / f (13) b y y cu = (14) ( − 0) P = M (14) b b (l a)a In Equation (13), is the steel reinforcement percentage, b and d are width and effective depth of concrete slabs respectively, and are yield strength of steel bars and concrete strength, Appl. Sci. 2018, 8, 721 22 of 25 In Equation (13), r is the steel reinforcement percentage, b and d are width and effective depth of concrete slabs respectively, f and f are yield strength of steel bars and concrete strength, respectively. y cu In order to relate the bending moment (M ) to the applied load (P ), relevant elastic analysis is adopted b b as shown in Equation (14). Shear Capacity: The shear capacity of concrete slabs shear strengthened with deep embedment FRP bars is considered as the combination of the contribution of concrete and deep embedment FRP bars. In this study, the contribution of concrete to shear capacity is predicted by the design method in BS 5400 [35], due to the consideration of the influence of longitudinal steel reinforcement in this theoretical model, which is given by Equation (15) [35]. 1/4 1/3 400 f 1/3 cu P = 0.79(100r) bd (15) cs d 25 A theoretical model proposed by Mofidi et al. [20] is adopted to predict the shear capacity contributed by the application of deep embedment FRP shear strengthening method, as shown in Equation (16). A E # D (sin q + cos q) f r p f r p f r p f r p P = k k (16) FRPs s f r p where A is deep embedment FRP bar cross-sectional area, d is effective shear depth (the greater f r p f r p of 0.72 h and 0.9 d), q is inclination angle of FRP bars (90 degrees for this test), s is spacing between f r p FRP bars. # is effective strain in FRP bars, which can be calculated as below: f r p 8 t s m m # = 0.004 (17) f r p D E 1 + a f r p f r p In Equation (16), D is diameter of FRP bars used in deep embedment strengthening, E f r p f r p is elastic modulus of FRP bars. t , s , and are coefficients in the BPE (Eligehausen, Popov, and m m Bertero Model) modified bond-slip model [36] using in this theoretical model. The values of those coefficients are shown in Table 4 based on the bonding test results. In addition, k is a decreasing coefficient (0 k 1) that represents the effect of FRP bars having an anchorage length shorter than the minimum anchorage length needed (L as shown in Equations (19) and (20)). The effective eff anchorage length coefficient (k ) can be determined using the following equations: e f f > 1 L e f f < 2 d d k = f r p f r p (18) > e f f E D 2 f r p f r p sm 1+a 2 tm 2 (1 a) f (s )D m 1 + a f r p L (s ) = (19) e f f 4t 1 a 8E t s f r p m m f (s ) = (20) D 1 + a f r p Additionally, k accounts for the effect of the internal stirrup on the effective strain of strengthening FRP bars. Due to no stirrup used in this test, k can be set to 1 [20]. Therefore, the shear capacity of the concrete slabs shear strengthened with deep embedment FRP bars can be determined as: P = P + P (21) s cs FRPs Appl. Sci. 2018, 8, 721 23 of 25 Based on the calculation procedure discussed above, the loading-carrying capacity of the test slabs in this study can be expressed as below: I f P < P ! P = P s p b b (22) I f P > P ! P = P s p s Table 6 presents the comparison of the loading-carrying capacities from the test results and the theoretical models discussed above. It can be noted that the adopted theoretical method yielded accurate and reliable predictions with an average Pp/Pt of 0.96 and a corresponding COV (Coefficient of variation) of 3%. Additionally, using the deep embedment strengthening scheme results in increasing shear strength of the concrete slabs, which is enhanced to be equal to or more than the flexural strength of those slabs in this theoretical prediction (see Table 6). This indicates that the failure mode is varied from brittle shear failure to ductile flexural failure, which corresponds to the test results. Table 6. Experimental and theoretical prediction loading-carrying capacity. Test Specimen Pt (kN) Pcs (kN) P (kN) Ps (kN) Pb (kN) Pp * (kN) Pp */Pt FPRs S-Con 130 120.4 — 120.4 137.41 120.4 0.93 S-B-2-9 144 120.4 15.87 136.27 137.41 136.27 0.95 S-G-2-9 138 120.4 14.65 135.05 137.41 135.05 0.98 S-C-2-9 138 120.4 35.4 155.8 137.41 137.41 1.00 S-C-1-9 142 120.4 38.62 159.02 137.41 137.41 0.97 S-C-1-13 148 120.4 62.94 183.34 137.41 137.41 0.93 Average = 0.96 Standard deviation = 0.03 Coefficient of variation = 0.03 * Pp = Predicted ultimate capacity in the proposed method. 7. Conclusions This paper presents the results of an experimental investigation involving eight tests on concrete slabs strengthened with deep embedment FRP bars subjected to loads close to the supports. A NLFEA model was proposed to simulate the structural behaviour of the test slabs. The accuracy of the proposed numerical model was validated by using the experimental results in this study. Additionally, a design method for prediction of loading-carrying capacity, including flexural and shear capacity, was adopted. The ultimate capacity predicted by this method showed good agreement with the test results. The main findings of this research are shown as follows: 1. Due to the loading location close to the support, shear failure occurred in the unstrengthened test slabs. The failure mode is brittle and sudden. The deep embedment shear strengthening technique can be used to avoid the occurrence of shear failure of concrete slabs subjected to load close to supports. It was found that the failure mode of concrete slabs varied from brittle shear failure to ductile flexural failure. This was attributed to the broken continuity of shear cracking development by the deep embedment strengthening method. 2. It was found that the material type of embedment strengthening materials does not influence the behaviour of strengthened test slabs. Interestingly, increasing the diameter of embedded FRP bars results in larger ultimate capacity and higher ductility. 3. Due to the small flexural stiffness of test slabs, the ultimate capacity was enhanced by around 10% by using the deep embedment strengthening method. However, the ductility of the test slabs was improved significantly. The maximum vertical deflection of concrete slabs at failure was increased by more than 100%, and the ductility was increased by more than 200%. 4. A NLFEA model for the concrete slabs shear strengthened with deep embedment FRP bars was developed and validated using the test results in this study. This NLFEA model shows a good capability of simulating the structural behaviour of the test slabs accurately, including the Appl. Sci. 2018, 8, 721 24 of 25 ultimate capacity, strain response, and cracking patterns. This numerical model can be used by engineers and researchers for the structural analysis and assessment of the structural performance of concrete slabs strengthened with deep embedment FRP bars. 5. By using the model by Modifi et al. [20] to predict the shear resistance contributed by deep embedment FRP bars, a two-way design approach was proposed in this study, in which flexural and shear capacity were predicted separately. With the comparison of the test results, it was found that this theoretical model can predict the loading-carrying capacity and failure mode of the strengthened concrete slabs accurately. Author Contributions: Lipeng Xia and Yu Zheng conceived and designed the experiments; Lipeng Xia performed the experiments; Lipeng Xia and Yu Zheng analyzed the data; Lipeng Xia and Yu Zheng wrote the paper. Acknowledgments: The authors wish to express their sincere appreciation of the Guangdong Science and Technology Planning (No. 2016A010103045), the Innovation Research Project by Department of Education of Guangdong Province (No. 2015KTSCX141), the National Science Natural Science Foundation of China (No. 51678149), and Division of Transportation Guangdong Province (No. 2013-02-029) in supporting this research. Conflicts of Interest: The authors declare that there are no conflicts of interest regarding the publication of this paper. References 1. Francisco, N.; Miguel, F.R.; Aurelio, M. Shear strength of RC slabs under concentrated loads near clamped linear support. Eng. Struct. 2014, 76, 10–23. 2. Rombach, G.A.; Latte, S. Shear resistance of bridge decks without shear reinforcement. In Tailor Made Concrete Structures; Walraven, J.C., Stoelhorst, D., Eds.; Taylor & Francis Group: London, UK, 2008. 3. Rombach, G.; Kohl, M. Shear design of RC bridge Deck slabs according to Eurocode 2. J. Bridg. Eng. 2013, 18, 1261–1269. [CrossRef] 4. Teng, J.G.; Chen, J.F.; Smith, S.T.; Lam, L. Behaviour and strength of FRP-strengthened RC structures: A state-of-the-art review. Proc. ICE—Struct. Build. 2003, 156, 51–62. [CrossRef] 5. Lorenzis, D.L.; Teng, J.G. Near-surface mounted FRP reinforcement: An emerging technique for strengthening structures. Compos. Part B Eng. 2007, 38, 119–143. [CrossRef] 6. Valerio, P.; Ibell, T.J.; Darby, A.P. Deep embedment of FRP for concrete shear strengthening. Proc. Inst. Civ. Eng. Struct. Build. 2009, 162, 311–321. [CrossRef] 7. Chaallal, O.; Mofidi, A.; Benmokrane, B.; Neale, K. Embedded through-section FRP rod method for shear strengthening of RC beams: Rerformance and comparison with existing techniques. J. Compos. Constr. ASCE 2011, 15, 374–383. [CrossRef] 8. Valerio, P.; Ibell, T.; Darby, A. Shear assessment and strengthening of contiguous-beam concrete bridges using FRP bars. In Proceedings of the 7th International Symposium on Fiber Reinforced Polymer Reinforcement for Concrete Structures (FRPRCS-7), Kansas City, MO, USA, 6–9 November 2005; pp. 825–848. 9. Jemaa, Y.; Jones, C.; Dirar, S. Deep embedment strengthening of full-scale shear deficient reinforced concrete beams. In Proceedings of the 12th International Symposium on Fiber Reinforced Polymers for Reinforced Concrete Structures (FRPRCS-12), Nanjing, China, 14–16 December 2015. 10. Barros, J.A.O.; Dalfré, G.M.; Trombini, E.; Aprile, A. Exploring the possibilities of a new technique for the shear strengthening of RC elements. In Proceedings of the International Conference of Challenges Civil Construction (CCC2008), Porto, Portugal, 16–18 April 2008. 11. Rodrigues, V.R. Shear Strength of Reinforced Concrete Bridge Deck Slabs. Ph.D. Thesis, Ecole Polytechnique 0 0 F ed erale de Lausanne, Lausanne, Switzerland, 2007. 12. McComb, C.; Tehrani, F.M. Enhancement of shear transfer in composite deck with mechanical fasteners. Eng. Struct. 2014, 76, 10–23. [CrossRef] 13. Lantsoght, E.; Veen, C.V.; Walraven, J. Shear tests of reinforced concrete slabs with concentrated load near to supports. In Proceedings of the 8th fib-PhD Symposium, Kongens Lyngby, Denmark, 20–23 June 2010; pp. 81–86. Appl. Sci. 2018, 8, 721 25 of 25 14. Breveglieri, M.; Aprile, A.; Barros, J.A.O. Embedded Through-Section shear strengthening technique using steel and CFRP bars in RC beams of different percentage of existing stirrups. Compos. Struct. 2015, 126, 101–113. [CrossRef] 15. Zheng, Y.; Li, C.H.; Yang, J.B.; Sun, C. Influence of arching action on shear behaviour of laterally restrained concrete slabs reinforced with GFRP bars. Compos. Struct. 2015, 132, 20–34. [CrossRef] 16. American Concrete Institute (ACI). Guide for the Design and Construction of Concrete Reinforced with FRP Bars; ACI 440.1R-06; ACI: Farmington Hills, MI, USA, 2006. 17. Mohamed, S.I.; Ibrahim, M.M.; Sherif, M.E. Influence of fibers on flexural behavior and ductility of concrete beams reinforced with GFRP rebars. Eng. Struct. 2011, 33, 1754–1763. 18. American Association of State Highway and Transportation Officials (AASHTO). Standard Specifications for Design of Highway Bridges; American Association of State Highway and Transportation Officials: Washington, DC, USA, 2000. 19. HKS (Hibbitt, Karlsson & Sorensen, Inc.). ABAQUS Theory Documentation Version 6.10; HKS: Providence, RI, USA, 2010. 20. Mofidi, A.; Chaallal, O.; Benmokrane, B.; Neale, K. Experimental tests and design model for RC beams strengthened in shear using the embedded through-section FRP Method. J. Compos. Constr. ASCE 2012, 16, 540–550. [CrossRef] 21. Michael, Q.; Samir, D.; Yaser, J. Finite element parametric study of reinforced concrete beams shear-strengthened with embedded FRP bars. Compos. Struct. 2016, 149, 93–105. 22. Lubliner, J.; Oliver, J.S.; Oñate, O.E. A plastic-damage model for concrete. Int. J. Solids Struct. 1989, 25, 299–329. [CrossRef] 23. Lee, J.; Fenves, G.L. Plastic-damage model for cyclic loading of concrete structures. J. Eng. Mech. 1988, 124, 892–900. [CrossRef] 24. Zheng, Y.; Robinson, D.; Taylor, S.; Cleland, D. Finite element investigation of structural behaviours of deck slabs in composite bridges. Eng. Struct. 2009, 31, 1762–1776. [CrossRef] 25. Thorenfeldt, E.; Tomaszemicz, A.; Jensen, J.J. Mechanical properties of high-strength concrete application in design. In Proceedings of the Symposium Utilization of High Strength Concrete, Tapir Trondheim, Norway; 1978; pp. 149–159. 26. Mattock, A.H.; Kriz, L.B.; Hognestad, E. Rectangular concrete stress distribution in ultimate strength design. Proc. ACI 1961, 57, 875–928. 27. Hordijk, D.A. Local Approach to Fatigue of Concrete. Ph.D. Thesis, Delft University of Technology, Delft, The Netherlands, 1991. 28. Jendele, L.; Cervenka, J. Finite element modelling of reinforcement with bond. Comput. Struct. 2006, 84, 1780–1791. [CrossRef] 29. Chen, G.M.; Teng, J.G.; Chen, J.F. Finite-Element modeling of intermediate crack debonding in FRP-plated RC beams. J. Compos. Constr. ASCE 2011, 15, 339–353. [CrossRef] 30. CEB-FIP. CEB-FIP Model Code 90; Thomas Telford: London, UK, 1993. 31. Sinha, B.P.; Gerstle, K.H.; Tulin, L.G. Stress-strain relations for concrete under cyclic loading. J. ACI 1964, 61, 195–211. 32. Reineck, K.H. Hintergründe zur Querkraftbemessung in DIN 1045-1 für Bauteile aus Konstruktionsbeton mit Querkraftbewehrung. Bauingenieur 2001, 76, 168–179. 33. Zheng, Y.; Robinson, D.; Taylor, S.E.; Cleland, D. Non-linear finite-element analysis of punching capacities of steel–concrete bridge deck slabs. Proc. Inst. Civ. Eng. Struct. Build. 2012, 165, 255–269. [CrossRef] 34. Ricardo, E.A.; Martha, L.F.; Bitttenourt, T.N. Combination of smeared and discrete approaches with the use of interface elements. In Proceedings of the European Congress on Computational Methods in Applied Sciences and Engineering, Barcelona, Spain, 11–14 September 2000. 35. BSI. BS 5400: Part 4: British Standard for the Design of Steel, Concrete and Composite Bridges; BSI: London, UK, 1990. 36. Cosenza, E.; Manfredi, G.; Realfonzo, R. Behaviour and modeling of bond of FRP rebars to concrete. J. Compos. Constr. ASCE 1997, 1, 40–51. [CrossRef] © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png
Applied Sciences
Multidisciplinary Digital Publishing Institute
http://www.deepdyve.com/lp/multidisciplinary-digital-publishing-institute/deep-embedment-de-frp-shear-strengthening-of-concrete-bridge-slabs-JkPkcT0T5x