Investigation of localised behaviour of strain-hardening cementitious composites for RC strengthening

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1 , 06, 8(6), aper Received 5/06/05; revised 06/03/06; accepted 07/03/06 ublished online ahead of print 9/03/06 Keywords: cracks & cracking/fracture & fracture mechanics/ modelling ICE ublishing: ll rights reserved Investigation of localised behaviour of strain-hardening cementitious composites for RC strengthening Yongxing Zhang ssociate rofessor, Key Laboratory of Concrete and re-stressed Concrete Structures of the Ministry of Education, Southeast University, Nanjing, China ssociate rofessor, School of Civil Engineering, Nanjing Forestry University, Nanjing, China ssistant rofessor, Hunan rovince Engineering Laboratory of ridge Structures, Changsha University of Science & Technology, Changsha, China (corresponding author: zhanguongxing8@aliyun.com) Shu ai Senior Engineer, Hunan rovincial Communications lanning Survey & Design Institute, Changsha, China Qingbin Zhang ssistant rofessor, Hunan rovince Engineering Laboratory of ridge Structures, Changsha University of Science & Technology, Changsha, China Strain-hardening cementitious composites (SHCCs) are an attractive construction material, due to their obvious advantage of large tensile strain capacity with pseudo strain-hardening, whereas this advantage is obviously reduced when SHCC is used. This study investigated, experimentally and numerically, the localised behaviour of SHCCs, with a focus on crack elongation performance and the ductility reduction of SHCC. The numerical investigation was implemented using a proposed scheme that considers the localised behaviour of SHCCs for strengthening RC structures with cracks. The effectiveness of the numerical scheme was confirmed through a comparison of experimental and numerical results. Notation a shear span length d effective depth G f fracture energy L elm element size l m measured length loading t SHCC layer thickness ε strain σ stress Introduction In comparison with conventional construction materials, (SHCCs) have obvious advantages for strengthening reinforced concrete (RC) structures, since they have the excellent material properties of a large tensile strain capacity with pseudo strain-hardening behaviour, as well as permeability and compatible thermal expansion (Kunieda and Rokugo, 006; Li and Leung, 99; Li and Wu, 99; Toshiyuki et al., 03). Several investigations on the behaviour of SHCCs for RC shear strengthening (Zhang et al., 05) and flexural strengthening (Horii et al., 998; Li et al., 000; Lim and Li, 997; Shin et al., 0; Xu et al., 0) have been carried out and have demonstrated much improved shear or flexural resistance compared with ordinary concrete and fibre reinforced concrete. However, the high tensile strain capacity of a SHCC is obviously reduced when it is adopted (Kamal et al., 008; Zhang et al., 05) since localised behaviour occurs in the SHCC strengthening layer (Kamal et al., 008; Zhang et al., 05). In view of previous works, Kamal et al. (008) developed a zero-span tensile test for evaluating the aforementioned localised behaviour of SHCC, the basic idea of which is based on the test method for thin-layer surface coating materials such as epoxy painting (JSCE, 00). However, the thickness of the SHCC layer in the zero-span tensile test is smaller than that of SHCC strengthening layers in practice, since the bond strength of the epoxy adhesive between the steel plate and the SHCC layer in the zero-span tensile test is usually insufficient with an increasing thickness of SHCC strengthening layer. The study reported here adopted a numerical scheme of the zero-span tensile model to investigate the localised behaviour of SHCCs for strengthening cracked RC structures, focusing on the crack elongation performance and the reduced tensile strain capacity of SHCCs. Of particular note is that the proposed numerical scheme of the zero-span tensile model can be implemented even with a significantly increased thickness of the SHCC strengthening layer. 44

2 Localised behaviour of SHCCs for RC strengthening Characteristics of RC members Figure shows RC members with shear and flexural strengthening using SHCC. The RC members were 00 mm long with cross-sections of 00 mm 00 mm for shear strengthening (Figure ) and 00 mm 50 mm for flexural strengthening (Figure ); the thickness of the SHCC layer was 0 mm in both specimens. rior to applying the SHCC layers, the side surfaces of both RC members (i.e. the interface between the RC member and the SHCC strengthening layer) were washed using a retarder in order to obtain a rough surface. In both RC members, two 0 mm diameter deformed bars were arranged as longitudinal reinforcement, the Young s modulus and yield strength of which were 00 Ga and 345 Ma, respectively. Moreover, deformed bars of 6 mm diameter were arranged as stirrups in the shear span of the RC member with flexural strengthening; Young s modulus and the yield strength of these bars were 00 Ga and 95 Ma, respectively. No web reinforcement was used for the RC member with shear strengthening. s shown in Figure, the specimens with SHCCs for RC shear strengthening and flexural strengthening were loaded under setups of three-point bending and four-point bending, respectively. The load and displacements (labelled as and in Figure ) were respectively measured using displacement transducers and load cells. ehaviour of the materials used Figure shows the uniaxial tensile stress strain curves and ultimate crack pattern of the SHCC used for RC flexural strengthening. The strain is defined as elongation rate over a measurement length of 00 mm. s shown in Figure, all the specimens showed significant strain-hardening behaviour until ultimate tensile strength ( and represent different ultimate tensile strengths for two specimens): multiple fine cracks occurred and propagated after the initial tensile strength (point ) and all the specimens finally failed due to localisation of some multiple fine cracks thereafter. The compressive strength and Young s modulus of the SHCC used for RC flexural strengthening were 7 Ma and 5 Ga, respectively, and the corresponding values for the concrete were 7 Ma and 3 5 Ga. Load-carrying capacity Figure 3 shows the load displacement curves obtained from the experiment. The load-carrying capacity of the shearstrengthened RC member (Figure 3) was significantly higher than that of the original RC member. This is due to contributions of not only the contact effect but also the fibre bridging effect for shear stress transfer behaviour on the localised crack surface of the SHCC layer. On the other hand, the t 00 t D0 d = a = t = 0, 0 D6 D t t = 0, 0 00 Figure. Geometry of RC member with SHCC strengthening: shear strengthening; flexural strengthening (units in mm) 45

3 Uniaxial tensile test Stress: Ma mm Strain Figure. Stress strain curves and crack pattern of SHCC obtained from uniaxial tensile test Load: kn Strengthened RC RC load displacement curve of the RC member with flexural strengthening (Figure 3) indicates that the SHCC layer carried the load with ductile behaviour due to occurrence of multiple fine cracks in the SHCC layer and then the loadcarrying capacity of the strengthened RC member gradually dropped due to localisation of some multiple fine cracks. This is verified by the cracking pattern of the specimen shown in Figure 4, in which points to 3 refer to the positions labelled in Figure 3. Load: kn Displacement: mm Strengthened RC RC Displacement: mm Figure 3. Experimental load displacement curves: shear strengthening; flexural strengthening 3 Crack patterns s shown in Figure 4, the multiple fine cracks in the diagonal direction of the SHCC layer for RC shear strengthening are obviously decreased compared with those of SHCC in uniaxial tensile behaviour, and the ductility of the SHCC strengthening layer is thus reduced accordingly. On the other hand, the multiple fine cracks in the SHCC layer for RC flexural strengthening (Figure 4) are distributed adjacent to the existing localised crack in the RC substrate member, and the SHCC strengthening layer gradually failed due to localisation of some multiple fine cracks thereafter. Therefore, the multi-cracking behaviour of SHCC for RC flexural strengthening is also decreased compared with the uniaxial tensile behaviour of SHCC, and the ductility of the SHCC strengthening layer is thus reduced accordingly. Numerical scheme for modelling localised behaviour of SHCC In order to model the localised behaviour of SHCCs for RC strengthening, a numerical scheme was adopted that includes & & the tri-linear curve model taking into account the fracture energy for modelling the uniaxial tensile property of SHCCs the zero-span tensile model for modelling the crack propagating performance of SHCC layers for strengthening RC substrate members with cracks. 46

4 Enlargement oint oint oint 3 Figure 4. Experimental crack patterns: shear strengthening; flexural strengthening Tri-linear curve model taking into account fracture energy The tri-linear curve model taking into account fracture energy is proposed for modelling the uniaxial tensile property of SHCCs The concept of the model is illustrated in Figure 5 and the fracture energy obtained from the uniaxial tensile stress strain curve is shown in Figure 5. In Figure 5, point is defined as the point where an initial crack appears and point indicates ultimate tensile strength in uniaxial tensile behaviour. The strain at point C, ε C, is represented by Equation, by accounting for the fracture energy in a localised element : ε C ¼ ε þ G f σ L elm where ε is the strain at point, σ is the stress at point, L elm is the element size (mm) and G f is the fracture energy in uniaxial tensile behaviour, equal to the area of the stress displacement relationship after peak (N/mm). Figure 6 illustrates the numerically simulated uniaxial tensile behaviour of SHCCs using the tri-linear curve model taking into account fracture energy as the uniaxial tensile property of SHCCs with mesh sizes of 0 mm and 0 mm, the parameters of which are summarised in Table. Figure 6 clearly shows that the numerical results agree very closely with the experimental uniaxial tensile stress strain curve. Furthermore, the numerical results are also independent of element size, confirming that the tri-linear curve model taking into account fracture energy can model the uniaxial tensile behaviour of SHCCs and avoid the problem of result dependence on mesh size (ažant, 00). 47

5 σ (ε,σ ) 0 mm 0 (ε,σ ) Small element size 0 mm 5 Stress: Ma bstracted tri-linear curve Test Strain C(ε C,σ C ) G f = 0 N/mm l m = 00 mm G f = fracture energy G f l f = measured length l m Zero-span tensile model Figure 7 shows the concept of the adopted zero-span tensile model, in which a pair of steel plates is adopted to form an artificial crack, representing a localised crack in the RC substrate members. The thickness of the SHCC layer in the numerical scheme is the same as that used for RC member strengthening and perfect bond is assumed between the steel plate and the SHCC layer with the same nodes in the interface. In the numerical model, the SHCC layer is meshed with a small element size (e.g. mm), less than the crack spacing in the experiment (larger than 3 mm). The numerical scheme can reflect the cracking behaviour of SHCC used, by directly applying the uniaxial tensile behaviour of SHCC as a material property, since a mesh of small element size ( mm) is used. Moreover, the longitudinal length of the localised strain in the SHCC layer should be smaller than that of the numerical zero-span tensile model, the longitudinal length of which was chosen as 5 mm for simulating the aforementioned experiment on SHCC for RC shear and flexural strengthening. ε Figure 5. Tri-linear curve model taking into account fracture energy: concept of the tri-linear curve model; fracture energy Stress: Ma Test 0 mm mesh 0 mm mesh Strain Figure 6. Numerical simulated uniaxial tensile behaviour of SHCC: mesh size; numerical result L elm :mm σ :Ma ε σ :Ma ε σ C :Ma ε C Table. Tri-linear curve model obtained from uniaxial tensile behaviour for mesh sizes of 0 mm and 0 mm Some boundary conditions are applied in the model. ll the nodes of the left-hand end are fixed in the longitudinal direction, those of the top surface are fixed in the vertical direction and horizontal loads are applied to all the nodes at the right-hand end in the longitudinal direction, controlled by displacement increment. Modelling the localised behaviour of SHCC for RC strengthening Numerical simulation The localised behaviour of SHCC was simulated using the adopted zero-span tensile model. In the numerical simulation, the thickness of the SHCC layer was 48

6 Localised crack 8 6 Numerical scheme Uniaxial tension Multipte fine cracks Stress: Ma 4 Localised crack Substrate member Displacement: mm 5 0 SHCC Multiple fine cracks Figure 8. Stress displacement curve obtained from numerical scheme L elm :mm σ :Ma ε σ :Ma ε σ C :Ma ε C mm Table. Tri-linear curve model obtained from uniaxial tensile behaviour (L elm = mm) 3 mm steel plate t mm SHCC layer Figure 7. Concept of the zero-span tensile model: originality for zero-span tensile model; sketch for zero-span tensile p model 0 mm, corresponding to the experimental conditions. The parameters of points, and C with a mm mesh in the trilinear curve model taking into account fracture energy are summarised in Table ; these were also based on the abstracted tri-linear curve with minimum ultimate tensile strength as shown in Figure 5. Numerical results Figure 8 shows the numerical tensile stress displacement curve obtained from simulations using the zero-span tensile model compared with the curve in uniaxial tensile behaviour. The figure clearly shows that the tensile strength and crack elongation performance of SHCC obtained from the zerospan tensile model are less than those of SHCC in uniaxial tension. Figure 9 shows the longitudinal strain distribution from the numerical scheme at point (peak stress) and point marked in Figure 8. It can be seen that the longitudinal strain distribution spread from the artificial crack through the depth of the cross-section and the localised area of longitudinal strain was 3 mm, without varying after the peak stress. This means that multiple fine cracks propagated from the artificial crack due to a stress concentration in a constant area after the peak stress. This behaviour is similar to the multiple fine cracking behaviour of the SHCC layer observed in the experiment. Therefore, the tensile strength obtained by the zero-span tensile model is smaller than that in uniaxial tensile behaviour in which strain is distributed uniformly in the crosssection. Conclusions The localised behaviour of (SHCCs) for reinforced concrete (RC) strengthening was experimentally and numerically investigated. The following conclusions can be drawn from the work presented in this paper. The crack elongation performance of SHCCs for RC strengthening is decreased compared with that of SHCCs in uniaxial tensile behaviour, and the ductility of SHCCs is thus reduced accordingly. The numerical scheme adopted is effective for evaluating the localised behaviour of SHCCs, 49

7 mm mm Figure 9. Longitudinal strain distribution obtained from numerical scheme: point ; point focusing on crack opening performance and the reduced ductility of SHCC layers. cknowledgements The authors acknowledge support from the National Natural Science Foundation of China (54084, 55789), the Natural Science Foundation of Jiangsu rovince (K04069), the China ostdoctoral Science Foundation, the Open Fund of Hunan rovince Engineering Laboratory of ridge Structures (Changsha University of Science & Technology) and the Open Fund of the Key Laboratory of Concrete and re-stressed Concrete Structures of the Ministry of Education (Southeast University). REFERENCES ažant Z (00) Concrete fracture models: testing and practice. Journal of Engineering Fracture Mechanics 69(): Horii H, Matsuoka S, Kabele et al. (998) On the prediction method for the structural performance of repaired/ retrofitted structures, fracture mechanics of concrete structures. roceedings of the 3rd Conference on Fracture Mechanics for Concrete and Concrete Structures, Gifu, Japan (Mihashi H and Rokugo K (eds)). I-FraMCoS, reckenridge, CO, US, pp JSCE (Japan Society of Civil Engineers) (00) Test method for opening performance of concrete surface coating materials over concrete crack (JSCE-K ). Standard Specification for Concrete Structures: Test Methods and Specification. JSCE, Tokyo, Japan, pp Kamal, Kunieda M, Ueda N and Nakamura H (008) Evaluation of crack elongation performance of a repair material with strain hardening behavior. Cement & Concrete Composites 30(0): Kunieda M and Rokugo K (006) Recent progress of HFRCC in Japan-required performance and applications. Journal of dvanced Concrete Technology 4(3): Li VC and Leung CKY (99) Theory of steady state and multiple cracking of short random fiber composites. Journal of Engineering Mechanics SCE 88(): Li VC and Wu HC (99) Conditions for pseudo strain hardening in fiber reinforced brittle matrix composites. pplied Mechanics Review 45(8): Li VC, Horii H, Kabele, Kanda T and Lim YM (000) Repair and retrofit with engineered cementitious composites. Engineering Fracture Mechanics 65(3): Lim YM and Li VC (997) Durable repair of aged infrastructures using trapping mechanism of engineered cementitious composites. Cement & Concrete Composites 9(4): Shin SK, Kim K and Lim YM (0) Strengthening effects of DFRCC layers applied to RC flexural members. Cement & Concrete Composites 33(): Toshiyuki K, Kabele, Fukuyama H et al. (03) Strain hardening cement composites: structural design and performance. In RILEM State-of-the-rt Reports (Rokugo K and Kanda T (eds)). Springer, London, UK, vol. 6, pp

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