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This study aimed to analytically develop tensile stress-crack width constitutive relationships for hybrid fibre reinforced concrete (HFRC). An inverse analysis was performed based on the fictitious crack hinge model to derive the stress-crack width relationship through careful calibrations of model parameters with the digital image correlation (DIC...
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... In the nonlinear cracked hinge model, the hinge width s is assumed to be equal to the half of the beam depth h above the notch, i.e. s = 0.5 h. The hinge will have moment resistance analogous to spring with nonlinear-rotational stiffness. The characteristics of the hinge in a specific area near the propagating fictitious crack are shown in Fig. 3. All the nonlinear stresses are assumed to act in this hinge area while the elements attached to boundaries of the hinge are expected to remain elastic (Fig. 3). These parts of the beam surrounding the hinge are modelled as rigid boundaries. However, the hinge is modelled as consisting of several horizontal layers through the depth of ...
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... will have moment resistance analogous to spring with nonlinear-rotational stiffness. The characteristics of the hinge in a specific area near the propagating fictitious crack are shown in Fig. 3. All the nonlinear stresses are assumed to act in this hinge area while the elements attached to boundaries of the hinge are expected to remain elastic (Fig. 3). These parts of the beam surrounding the hinge are modelled as rigid boundaries. However, the hinge is modelled as consisting of several horizontal layers through the depth of the beam, as shown in Fig. ...
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... Fig. 4, y and y o are the distances between any considered layer and the neutral layer (N-L) from the extreme compression layer, respectively. Based on the geometrical relationships from Fig. 3, a curvature for the neutral layer and a total strain value for any layer in the hinge can be calculated as ...
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... is the rotation at cracking, is the rotation at any loading stage, and s(h) is deformation at the tip of the notch (Fig. 3(a)). Therefore, at the first cracking point, the normalized rotation θ is equal to 1. The depth of the cracking was normalized with the hinge depth h. The total cracked depth of the hinge, α, is measured from the crack tip to the bottom-most layer of the hinge as: ...
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... illustrated in Fig. 3, when the rigid faces rotate by an angle of ϕ about the vertical axis, 2ϕ is the angle subtended by those two faces, which represents the rotation of the hinge. Also, 's' is the original width of all the layers of the hinge before any rotation. Ulfkjaer [17] suggested a hinge width value equal to half the depth of the hinge, i.e. s = ...
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... of the hinge before any rotation. Ulfkjaer [17] suggested a hinge width value equal to half the depth of the hinge, i.e. s = h/2. Here, h is the depth of the hinge above the notch depth a o . In this study, the initial assumption of the hinge width is as per Ulfkjaer [17] and need to be later confirmed with the help of the DIC measurements. Fig. 3(b) represents a simplified deformed hinge. Several previous works have assumed the width of the hinge to be equal to half the depth of the hinge in the inverse analysis. This research also focuses on the validation of these assumptions with the help of the experimentally observed DIC measurements from the fracture ...
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... that the beam under consideration is simply supported in the three-point bending test, the maximum moment on such a beam at the mid-span is given by: (27) where M is the bending moment, P is the applied vertical load at mid-span and L is the length of the beam between the supports. Both M and P depend upon the rotation θ of the beam as shown in Fig. 3. By using the normalized moment Eq. (7), the above load equation can be rewritten as: (28) The exact equations for the CTOD and CMOD to be used in the pre-peak zone have not been documented well in the previous works. These equations and their derivations are explained in detail in the following ...
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... The strain redistribution across the cracks in plain concrete is achieved through bridging actions in the form of aggregate interlock. In FRC, the fibre stretching and pull-out help with crack bridging in addition to the aggregate interlock [6]. An experimentally tested specimen showing the crack width behaviours for plain concrete and fibre-reinforced concrete is shown in Figure. ...
The assessment of surface cracks in concrete structures plays a pivotal role in determining structural integrity. However, current diagnostic technologies suffer from drawbacks such as being time-consuming, subjective, and reliant on inspectors' experience, resulting in low detection accuracy. This paper seeks to address these issues by proposing an automated, vision-based method for identifying the surface condition of concrete structures. The method integrates advanced pre-trained convolutional neural networks (CNNs), transfer learning, and decision-level image fusion. To develop and validate this approach, a total of 6,500 image patches from diverse concrete surfaces were generated. Each pre-trained CNN establishes a predictive model for the initial diagnosis of surface conditions through transfer learning. Given the potential for conflicting results among different CNNs due to architectural differences, a modified Deep Belief CNN algorithm is crafted, thereby enhancing crack detection accuracy. The effectiveness of the proposed method is confirmed through a comparison with other CNN models. Robustness is tested by subjecting the method to images with various types and intensities of noise, yielding satisfactory outcomes. In practical scenarios, the hybridised approach is applied to analyse field-captured images of concrete structures using an exhaustive search-based scanning window. Results showcase the method's capacity to accurately identify crack profiles, with minimal areas of incorrect predictions underscoring its potential for practical applications.
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... In the case of hybrid fiber combinations (HB Series), the hooked-ended steel fibers of length 30 mm and diameter of 0.6 mm are used [34]. Previously, authors investigated the shear and flexure behaviour of normal-strength fiber-reinforced concrete [35,36], self-consolidating fiber-reinforced concrete [37], and fracture behaviour of fiber-reinforced concrete [38] with hooked-ended fibers (aspect ratio 50). The results were found to be satisfactory in terms of ductility and strength development. ...
Ultra-High-Performance Fiber-Reinforced Concrete (UHPFRC) has excellent mechanical and durability properties compared to conventional concrete. It offers lightweight structures compared to reinforced concrete. In this study, the shear behaviour of post-tensioned UHPFRC girders is experimentally studied. The parameters considered in this study are (i) the level of prestressing, i.e., 0%, 35%, and 70% of ultimate tensile strength of strand (f pu), (ii) the volume fraction of fibers (V f), i.e., 1.0%, and 2.0%, and (iii) different types of steel fibers; straight fibers, hybrid fibers (straight and hooked ended). The principal tension and compression strain of beams along and across the cracks were measured throughout the loading and compared with localization strains from the direct tension test. Due to increase in prestress from 0% to 70% of f pu , the ultimate load-carrying capacity increased from 18% to 39% in girders with a 1% fiber volume fraction. Similarly, it increased from 24% to 50% for 2% fiber reinforced girders. This is due to increased active stress transfer across the concrete cross-section, which reduces the crack angle from 44 to 34 . Similarly, the shear cracking load increased, and the post-cracking reserve capacity reduced with an increase in fiber dosage. Digital image correlation analysis reveals that strain distribution across the crack is uniformly distributed at all loading stages.
... A significant number of studies are aimed at optimizing the parameters of fiber-reinforced concrete [8][9][10][11]. The shape, size and volume content of fibers affect the density, strength and workability of concrete. The paper [9] proposes a technique following which it is possible to obtain an optimized fiber-reinforced concrete with a dense structure, high fiber efficiency and excellent mechanical properties. ...
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... correlation (DIC) is a technique for measuring full-field strain and localised 315 displacements in the HCS specimen by correlating the speckled patterns on images captured at 316 different intervals during testing[44]. DIC analysis can predict the structural behaviour of 317 concrete successfully when used in conjunction with conventional measurements and after 318 proper calibration[31,45,46]. ...
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... Numerous studies have shown that the expansion and intersection of these cracks have an essential impact on the bearing capacity and durability of concrete structures and are the leading causes of engineering structures' ultimate failure (Wen et al., 2020;Zhang et al., 2013). Single crack growth processes in concrete under static and dynamic loadings have been systematically studied (Bhosale et al., 2020;Fan et al., 2020;Wu et al., 2011;Xu & Reinhardt, 1999a, 1999b. However, similar researches on cracks' expansion and interaction (including intersection) are still in its initial stage. ...
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In order to enhance the greenness in the strain-hardening composites and to reduce the high cost of typical polyvinyl alcohol fiber reinforced engineered cementitious composite (PVA-ECC), an affordable strain-hardening composite with green binder content has been proposed. For optimizing the strain-hardening behavior of cementitious composites, this paper investigates the effects of polypropylene fibers on the first cracking strength,
fracture properties, and micromechanical parameters of cementitious composites. For this purpose, digital image correlation (DIC) technique was utilized to monitor crack propagation. In addition, to have an in-depth understanding of fiber/matrix interaction, scanning electron microscope (SEM) analysis was used. To understand the effect of fibers on the strain hardening behavior of cementitious composites, ten mixes were
designed with the variables of fiber length and volume. To investigate the micromechanical parameters from fracture tests on notched beam specimens, a novel technique has been suggested. In this regard, mechanical and fracture tests were carried out, and the results have been discussed utilizing both fracture and micromechanical concepts. This study shows that the fiber length and volume have optimal values; therefore, using fibers without considering the optimal values has negative effects on the strain hardening behavior of cementitious composites.
... Foster et al. [38] estimated the shear capacities of SFRC beams by using the residual tensile strengths obtained from the inverse analysis. The tensile stress-strain response from the fracture test can be obtained from the multilinear tensile stress-strain response proposed by Bhosale et al. [7,39]. The interrelationship between the concrete matrix and fiber reinforcement components to shear capacity is shown in Figure 3. ...
... Foster et al. [38] estimated the shear capacities of SFRC beams by using the residual tensile strengths obtained from the inverse analysis. The tensile stress-strain response from the fracture test can be obtained from the multi-linear tensile stress-strain response proposed by Bhosale et al. [7,39]. The inter-relationship between the concrete matrix and fiber reinforcement components to shear capacity is shown in Figure 3. ...
... The FRC material was considered homo-geneous and isotropic. The average tensile strength of FRC can be obtained from RILEM recommendations, or the stress-crack opening relationship can be obtained from the inverse analysis [7,39,64,65], and the same was used for shear capacity calculations. The shear resistance offered by the fiber-reinforced prestressed concrete beams included the uncracked concrete contribution, shear reinforcement contribution, fiber contribution, aggregate interlock, the vertical component of prestressing force, and dowel action due to longitudinal rebars [32]. ...
This study investigates the effectiveness of hybrid fibers (steel and macro-synthetic) on the shear behavior of prestressed concrete beams. The hybrid fiber combination was selected to avoid workability issues at high volume dosages and ensure effective crack arresting over the crack opening range. Fracture studies included testing notched concrete prisms to identify the role of hybrid fibers in the crack bridging mechanism. Seven hybrid fiber reinforced prestressed concrete (HFRPC) beams were tested at a low shear span (a) to depth (d) ratio of 2.4. The effects of hybrid fibers on load–deflection behavior and strain in the strand are reported. Similarly, the crack opening, crack slip and crack angle variation regarding applied shear were investigated using the digital image correlation (DIC) technique. Test results of HFRPC beams showed considerable improvements in peak load and the post-peak response with a higher hybrid fiber dosage. The crack opening and crack slip measurement across the major shear crack revealed continuous dilatant behavior. The kinematic response of critical shear crack reflects the sustained dilation response up to the ultimate load, which depends on the critical shear crack angle of the tested beams. As the fiber dosage increases, the shear crack slip and width are reduced, indicating the roles of hybrid fibers in improving ductility and the change in failure mode from brittle shear tension to relatively ductile shear tension.
... The multi-linear tensile stress-strain behaviour of specimens with different fibre volume fractions was obtained from the inverse analysis. More information on inverse analysis can be found elsewhere [42]. ...
... Similarly, the stress-strain response of fibre reinforced concrete under compression is modelled using Yu-Chen et al. [47] model. The tension-stress strain behaviour is obtained from the inverse analysis developed by Bhosale et al. [42]. The stress-inelastic strain in both compression and tension for FRCs with different fibre dosages are shown in Fig. 11. ...
... The fracture energy (G f ) is calculated as per JCI-S-001-2003 [49]. The tensile strength from the inverse analysis [42] is used as tensile behaviour as input for concrete. The multi-linear stress-strain response obtained from inverse analysis (Fig. 11) is used as input for inelastic strain and damage (d t ) parameters. ...
Shear behaviour of macro synthetic fibre reinforced beams are investigated. Macro Synthetic fibre volume fraction of 0.0%, 0.5%, 1.0% and 1.5% are considered. A three-dimensional nonlinear finite element (FE) analysis is carried out. Low fibre dosage of 0.5% did not produce an improvement in shear resistance. Post-cracking behaviour, ductility, and shear strength improved at high fibre dosages. a b s t r a c t Experimental and numerical studies on shear behaviour of macro synthetic fibre reinforced prestressed concrete (MSFRPC) beams are presented. MSFRPC beams are tested at a shear span to depth ratio (a/d) of 2.4 to understand the role of macro synthetic polyolefin fibres on the shear resistance and failure modes. The fibre volume fraction of 0.0%, 0.5%, 1.0% and 1.5% are considered as study parameters. A three-dimensional nonlinear finite element (FE) analysis is carried out to understand the influence of fibres on shear behaviour using the concrete damage plasticity model. Tensile constitutive relations of FRC is derived using inverse analysis from fracture test results and used as input in the FE model. A stage-wise analysis is conducted to include the effects of prestressing and applied external shear loads. The results from FE analysis showed a good agreement with experimental results for different fibre dosages. The effect of level of prestressing and varying compressive strength is studied through calibrated FE models. Due to the addition of macro synthetic fibres, no significant improvement in compressive strength is observed. Low fibre volume addition of 0.5% did not produce an appreciable improvement in shear behaviour. However, test and FE results of beams with higher volume fractions of 1.0% and 1.5% significantly improved the post-cracking behaviour, ductility, and ultimate shear resistance of MSFRPC beams.
... Reddy and Subramaniam (2017), using the inverse analysis and cracked hinge model, introduced an analytical formulation for macro-synthetic fiber reinforced concrete, in which the multi-linear cohesive stress-crack opening relationship was found from the flexural notched beam response. Bhosale et al. (2020) developed a softening function for hybrid fiber reinforced concrete (HFRC). They performed an inverse analysis based on the fictitious crack hinge model to derive the softening law by carefully calibrating model Table 1 Softening models for concrete Hillerborg et al. (1976) Linear softening curve ( , ′ ) Petersson (1981) Bilinear softening curve ( , ′ ) ...
Softening function is the primary input for modeling the fracture of concrete when the cohesive crack approach is used. In this paper, based on the laboratory data on notched beams, an inverse algorithm is proposed that can accurately find the softening curve of the concrete. This algorithm uses non-linear finite element analysis and the damage-plasticity model. It is based on the kinematics of the beam at the late stages of loading. The softening curve, obtained from the corresponding algorithm, has been compared to other softening curves in the literature. It was observed that in determining the behavior of concrete, the usage of the presented curve made accurate results in predicting the peak loads and the load-deflection curves of the beams with different concrete mixtures. In fact, the proposed algorithm leads to softening curves that can be used for modeling the tensile cracking of concrete precisely. Moreover, the advantage of this algorithm is the low number of iterations for converging to an appropriate answer.
