Steel Fiber-reinforced Concrete Members Research Articles

Theoretical model of shear capacity of steel fiber reinforced concrete beams

One of the barriers to implementation of steel fiber reinforced concrete (SFRC) into structural applications is the lack of understanding of the shear behaviour of SFRC members. This paper proposes a theoretical model for the shear capacity of SFRC members with mild steel reinforcement based on the shear-carrying mechanisms and sectional analysis. The model is derived completely theoretically, based on concepts from the literature, and does not include new empirical aspects. The approach is then compared to 323 experiments from the literature of beams with slender, rectangular cross-sections failing in shear. It is found that the model is slightly conservative, and experimental research necessary to further develop the model is described. The presented theory aims to be a framework for a fully theoretical description of the shear capacity of SFRC members with longitudinal reinforcement and without shear reinforcement.

Structural behaviors of steel fiber-reinforced concrete-filled geotextile tube stub columns under axial compression

Geotextile materials are recently widely used for concrete casting formwork system; however, concrete is brittle whose inherent abrupt failure property needs to be improved. In this study, a novel composite stub column that consists of external geotextile tube and internal steel fiber reinforced concrete (SFRC) core is proposed. A total of 36 circular concrete stub columns are tested to analyze the effects of fiber volume fraction and cross-sectional diameter on structural behaviors of geotextile-tubed SFRC under axial compression. Based on the test results, geotextile-tubed SFRC stub columns showed superior properties in terms of strength characteristic, strain capacity, modulus of elasticity, ductility and toughness, while the effect of cross-sectional diameter on structural behaviors of the stub columns became less obvious with increasing fiber volume fraction. Furthermore, the experimental data of SFRC stub columns was collected to evaluate the effect of formwork systems. It is evident that the geotextile tube can effectively solve problems of poor mixing and consolidation of SFRC with a high fiber volume fraction to ensure the concrete properties. Finally, a non-linear calculation model was also developed to evaluate the compressive behaviors for geotextile-tubed SFRC. Therefore, use of geotextile is recommended to applied as formwork system of SFRC members, which can provide researchers with more insights into the construction technique of concrete structures.

A stereological approach to estimation of fibre distribution in concrete

Steel fibre reinforced concrete (SFRC) continues to gain popularity as a sustainable construction material with enhanced strength and durability properties. These mechanical properties are dependent on the distribution and orientation of steel fibres achieved during casting, the determination of which is challenging. Three-dimensional X-ray micro-CT scanning is currently the only technique that yields the true three-dimensional (3D) dispersion of fibres, but the technology is applicable only to small samples at laboratory settings. In this study, a mathematical framework is developed to utilize 2D probing, like X-ray projectional radiography, which is more practical for in situ nondestructive characterization of fibre dispersion in SFRC members. For the first time, fibres are treated as finite-sized inclusions, developing the appropriate mathematical formulations consistent with published research in the field of stereology and practically applying them to digitized X-ray projected images of SFRC and UHPFRC. Stereological principles were employed to establish the volume fraction of fibres (3D property) from their areal fraction in images. The method was developed and tested for both X-ray slices and projected images. Tests were performed on UHPFRC cores as well as SFRC dogbones with different nominal fibre dosages. It is shown that accurate estimation of fibre volume fraction and their spatial distribution can be robotically achieved from 2D imaging using the developed algorithms. The influence of parameters such as fibre geometry and thickness of structural members on the applicability of the stereological equations and accuracy of estimated results is investigated, with a comprehensive discussion of the stereology approach.

Experimental Study on Torsional Behavior of steel Fiber Reinforced Concrete Members under Pure Torsion

An experimental study was conducted on ten steel fiber reinforced concrete specimens with low longitudinal reinforcement ratio to investigate the torsional behavior under pure torsion. The crack patterns, cracking torque, ultimate torsional strength, and torsional ductility, were discussed. The major parameters were the ratio and type of adding steel fiber. The obtained results showed that the cracks width of end hooked steel fiber specimens were wider than the corrugated steel fibers specimens, the cracks width decrease with increase the steel fiber ratio, and the number of cracks of end hooked steel fiber specimens were less than the corrugated steel fibers specimens. In the specimens of mix steel fiber, the width and the number of cracks less and more than other specimens, respectively. The higher percentage of the steel fiber, gives greatest torsional resistance. However, with an increase in the percentage of steel fiber the workability decreases.

Diverse angle-length-width model for 3D/4D/5D steel fiber reinforced concrete under tension

The most important characteristic of steel fiber reinforced concrete (SFRC) is its excellent post-cracking behavior. An analytical diverse angle-length-width model (DAM) was proposed to calculate the tensile stress-crack width (σ-w) constitutive behavior of SFRC members subjected to tension and to evaluate its post-cracking behavior. In the proposed model, the tensile stress in SFRC members with end-hooked steel fibers was generated from the straight fiber part, the end-hooked fiber part, and the concrete part. The effects of straight and end-hooked parts were separately considered, and three cases for different crack width ranges were analyzed for each part. The model was derived by considering all of the possible fiber inclination angles, fiber embedded lengths, and crack widths. It was found that SFRC members with new types of 4D and 5D steel fibers possessed a higher tensile stress than those with 3D steel fibers, and the tensile stress intensity increased with the increasing fiber volume fraction. Finally, the accuracy of the model was verified by comparing the values by DAM with the experimental results based on the sectional analysis.

Simplified prediction of the time dependent deflection of SFRC flexural members

It is well known that the inclusion of steel fibres into a concrete matrix has the potential to improve both the serviceability and strength characteristics of reinforced concrete. As a result of decades of academic interest into the material, design provisions for flexural strength, shear strength and short-term serviceability have been incorporated into international codes of practice. However, available design guidelines typically contain little or no guidance for engineers to confidently predict the long-term behaviour of structures manufactured with steel fibre reinforced concrete (SFRC). This limits the full utilization of the material in design practice. This paper presents a simplified model, suitable for design, that can reliably predict the effects of creep and shrinkage in SFRC members containing conventional reinforcement which are subjected to a sustained in-service flexural load. Predictions of the proposed model are compared to available data in the literature and are shown to correlate well.

Design of SFRC members aided by a multiscale model: Part II – Predicting the behavior of RC-SFRC beams

In the preceding Part I of this study, an experimental program and numerical analyses using a multiscale model are performed to obtain the post-cracking parameters of steel fiber reinforced concrete (SFRC) through the simulation of three-point bending tests (3-PBT) according to EN 14651. In the present Part II, both numerical and experimental parameters obtained from the 3-PBT are used on the design of beams with combined reinforcement of steel fibers and rebars (RC-SFRC beams) according to fib Model Code 2010 in order to study their influence on the amount of bending and shear reinforcements required. In addition, the RC-SFRC beams designed are numerically simulated using the mesoscale model and the results are compared to the designed ones in terms of crack width, mean crack spacing, deflection and ultimate and service loads. The results demonstrated that computational simulations with an appropriated approach to represent the composite may be an important tool to contribute on the design of SFRC structural members.

Design of SFRC members aided by a multiscale model: Part I – Predicting the post-cracking parameters

The use of steel fiber reinforced concrete (SFRC) is directly related to its post-cracking behavior in tension. The flexural three-point-bending test (3-PBT) according to EN 14651 is among the most recommended tests to evaluate the post-cracking parameters for application of SFRC as structural material. However, due to the intrinsic variability of the mechanical properties of this composite, its characterization using exclusively experimental tests would be very expensive and time-consuming. The present Part I of this two-part study aims to investigate the applicability of a recently proposed numerical model to obtain the post-cracking parameters of SFRC. A series of 3-PBT was experimentally performed for three different fiber contents: 15kg/m3, 30kg/m3 and 45kg/m3. These tests are simulated to study the main factors that may influence the numerical responses such as: mesh refinement; constitutive integration scheme; fiber distributions; fibers/concrete interface parameters and mesoscale vs. multiscale analysis. The results show that this strategy is able to predict the post-cracking parameters and can be applied as an aid tool, extrapolating the experimental results for better understanding the material responses. The influence of experimental and numerical post-cracking parameters on the design of beams according to fib Model Code 2010 is discussed in the accompanying Part II.

Investigation of mechanical characteristics and specimen size effect of steel fibers reinforced concrete

Steel fiber reinforced concrete (SFRC) is a new construction material with good tensile strength, fracture toughness, and ductility. Although many aspects of SFRC have been investigated extensively, the size effects on structural strength of SFRC members remain largely preoccupant. This study investigates the size effect on flexural strength of SFRC beams under three-point bending tests. For this purpose, four mixtures were made: a concrete without fibers as control concrete, and concretes reinforced with 0.5, 1, and 1.5% of steel fibers (SFs) of total concrete volume. The experimental test results indicate that the addition of fibers, even small quantities reduces concrete workability that needs more superplasticizer added. Flexural and compressive strength are improved and crack opening is limited as the fiber content increases. SFs are more efficient in flexural strength and make SFRC more sensitive to the size effect. New relationships are presented which fit the data quite well and give an accurate correlation with the experimental results according to the size effect and the quantity of fibers present in concrete mix.

Effective flexural rigidities for RC beams and columns with steel fiber

Influences of different variables that affect the effective flexural rigidity of reinforced concrete (RC) members are not considered in the most seismic codes. Furthermore, in the last decades, the application of steel fibers in concrete matrix designs has been increased, requiring development of an accurate analytical procedure to calculate the effective flexural rigidity of steel fiber reinforced concrete (SFRC) members. In this paper, first, a nonlinear analytical procedure is proposed to calculate the SFRC members\' effective flexural rigidity. The proposed model\'s accuracy is confirmed by comparing the results obtained from nonlinear analysis with those recorded from the experimental testing. Then a parametric study is conducted to investigate the effects of different parameters such as varying axial load and steel fiber are then investigated through moment-curvature analysis of various SFRC (normal-strength concrete) sections. The obtained results show that increasing the steel fiber volume percentage increases the effective flexural rigidity. Also it\'s been indicated that the varying axial load affects the effective flexural rigidity. Lastly, proper equations are developed to estimate the effective flexural rigidity of SFRC members.

Estimation of Minimum Torsional Reinforcement of Reinforced Concrete and Steel Fiber-Reinforced Concrete Members

The current code specifies a minimum torsional reinforcement ratio to prevent possible brittle failure after torsional cracking in concrete members. However, since there are many researches, in which even the concrete members with the minimum torsional reinforcement fail to secure sufficient reserved strength after torsional cracking, continuous research needs to be carried out. Accordingly, in the authors’ previous research, a minimum torsional reinforcement ratio was proposed based on the reserved strength concept and was extended to the steel fiber-reinforced concrete members in order to suggest the minimum fiber factor as the minimum torsional reinforcement ratio. In the present study, a pure torsion test was carried out on reinforced concrete and steel fiber-reinforced concrete members after a brief introduction on the above, and the proposed model was verified based on the test results. The test results of six torsional specimens were compared with those of the proposed model, and it was found that the proposed model provides a reasonable evaluation on the torsional failure mode of the specimen according to the reserved strength ratio.

Two-Dimensional Numerical Model of the Fracture Process in Steel Fibre Reinforced Concrete with the Continuum Strong Discontinuity Approach and Functional Data Analysis

Abstract This paper presents the formulation of a two-dimensional numeri-cal model able to describe the fracture process in structural mem-bers of steel fibre reinforced concrete (SFRC) from the volume ratio of the fibres and the mechanical properties of the compo-nents: a concrete matrix and a set of steel fibres with a random orientation. The relationship between the stress and the strain fields of the composite material is obtained using the mixture theory with a compatibility strain of its component materials. The concrete matrix is represented with a scalar damage constitutive model with a softening strain and a different strength in tension and compression. The mechanical strain of an insulated fibre and the slip between the fibre and the matrix are simultaneously de-scribed with a one-dimensional plasticity constitutive model. The cracking of the composite material indicates a jump in the dis-placement field and non-bounded values of the strain field, which are represented by the Continuum Strong Discontinuity Ap-proach. The model has been implemented in the framework of the nonlinear analysis with the Finite Element Method, using con-stant strain triangular elements. Moreover, the fibres distribution and orientation change randomly in each finite element and each simulation or observation. The structural responses of the simula-tions are treated as curves and analysed by tools from the Func-tional Data Analysis. Confidence intervals for the structural re-sponse are built using bootstrap methodology. Finally, experi-mental tests of SFRC members subjected to tension and bending are simulated. The structural response and the cracking patterns obtained from the numerical simulation are satisfactory.

Flexural analysis of steel fibre-reinforced concrete members

A numerical approach for the evaluation of the flexural response of Steel Fibrous Concrete (SFC) cross-sections with arbitrary geometry, with or without conventional steel longitudinal reinforcing bars is proposed. Resisting bending moment versus curvature curves are calculated using verified non-linear constitutive stress-strain relationships for the SFC under compression and tension which include post-peak and post-cracking softening parts. A new compressive stress-strain model for SFC is employed that has been derived from test data of 125 stress-strain curves and 257 strength values providing the overall compressive behaviour of various SFC mixtures. The proposed sectional analysis is verified using existing experimental data of 42 SFC beams, and it predicts the flexural capacity and the curvature ductility of SFC members reasonably well. The developed approach also provides rational and more accurate compressive and tensile stress-strain curves along with bending moment versus curvature curves with regards to the predictions of relevant existing models.

A Model for the Prediction of the Tensile Strength of Fiber-Reinforced Concrete Members, Before and After Cracking

The tensile behavior of concrete or mortar plays an important role for delaying the formation and propagation of cracks, and also for upgrading the bearing capacity of existing concrete and masonry constructions. Although the presence of steel fibers is known to improve, often considerably, the tensile capacity of concrete members, methods for the quantification of this improvement are still limited. For this reason, a model has been developed for the prediction of the tensile strength of steel fiber-reinforced concrete members, as crack opening occurs. Given the geometry and the physical characteristics of reinforced concrete member and fibers, the model predicts: (1) the number of fibers crossing a crack’s surface; (2) the distribution of these fibers in terms of (i) the angle a fiber forms with the crack surface (fiber inclination) and (ii) the embedded length of the fiber at both sides of the surface; (3) resistance to crack opening provided by each fiber, in relation to its position and inclination. On the results of the results obtained, the influence of the number of fibers on the reduction of crack widening in concrete or mortar is remarkable and can be estimated with satisfactory precision. In upgrading existing concrete and masonry constructions, this tensile behavior is found to play important role.

Modelling the tension stiffening effect in SFR-RC

The understanding of the performance and cracking behaviour of steel fibre reinforced concrete (SFRC) has developed greatly in recent times. Many of these studies, however, are limited to SFRC without conventional reinforcement. This paper reports on the tensile behaviour of SFRC members co-reinforced with conventional reinforcing bars (SFR-RC). A physical description of the behaviour of the specimens is presented and an analytical model is derived. The model adopts the load-sharing concept between the tensile stresses resisted by the steel fibres and the steel reinforcing bar as well as the bond between the concrete and reinforcing bar to the tension stiffening effect of these members. The model is founded upon a previously reported tension chord model and allows for explicit identification of the three components to the tension stiffening effect. An experimental programme is reported here and the model is shown to correlate well with the experimental data and test data reported elsewhere.

Fiber efficiency in SFRC members subjected to uniaxial tension

This paper investigated the tensile behavior of steel fiber-reinforced concrete (SFRC) through an experimental program in which 64 specimens with end-hooked steel fibers were tested under uniaxial tension. The test variables were the concrete compressive strength, fiber volumetric ratio, and fiber aspect ratio (length to diameter). The test results showed that more ductile behavior could generally be achieved with a higher fiber volumetric ratio and a higher fiber aspect ratio; however, the tensile stress attained by the steel fibers did not increase when additional steel fibers were added because the fiber efficiency on the tensile behavior decreased. By comparing the test results and the predictions of the Diverse Embedment Model (DEM), a rational SFRC tension model, a coefficient to reflect the fiber efficiency was derived. The tensile behavior of SFRC members can be more accurately predicted with the proposed fiber efficiency factor, particularly for members with a high fiber volumetric ratio.

Analysis of Steel Fiber-Reinforced Concrete Elements Subjected to Shear

In this paper, a rational analysis procedure is presented for modeling the shear behavior of steel fiber-reinforced concrete (SFRC) elements. In the development of the analysis procedure, the Disturbed Stress Field Model (DSFM), based on the Modified Compression Field Theory (MCFT), is modified by implementing constitutive models for SFRC, which are derived from the Diverse Embedment Model (DEM). For the contribution of steel fibers, a local stiffness matrix for fibers has been developed separately from those for concrete matrix and conventional reinforcement. The composite element stiffness matrix for an SFRC element with conventional reinforcement is then derived by superposing the three local stiffness matrixes. In the element stiffness matrix, the effect of shear slip at a crack is also taken into account by considering the resistance due to steel fibers against shear stress on crack surface. Through comparisons with the test results of SFRC panels previously reported in the literature, it is shown that the actual shear behavior of SFRC panels are accurately predicted by the proposed analysis procedure, not only for the shear strength but also for the shear strain at the failure. Through implementation into finite element analysis programs, the analysis procedure devel oped in this paper can be useful in the modeling of SFRC members and structures also containing conventional reinforcement.

Flexural modelling of steel-fibre-reinforced concrete member with conventional tensile rebars

This paper presents an analytical model for the determination of the ultimate flexural capacity of steel-fibre-reinforced concrete (SFRC) rectangular sections using the principles of strain compatibility and the force equilibrium. The proposed model considers an elastic–perfectly plastic model for the compression, and an elastic constant post-peak response of the SFRC in tension. Unlike other flexural models in the literature, the proposed model considers the random distribution and orientation of steel fibres at the cracked section in the analysis, and it is simple enough to find applications in routine practice. The model was verified using existing experimental results, and it predicts the flexural capacity of SFRC beams reasonably well. A parametric study using the proposed model was conducted to assess the effect of fibre parameters, conventional reinforcing bars and the strength of the concrete on the ultimate flexural capacity of a SFRC beam section. Normalised design charts are presented to simplify the analysis procedure, and these can be used for selection of the fibre and the quantity of conventional reinforcing steel during the flexural design of SFRC members.

Torsional responses of steel fiber-reinforced concrete members

This study introduces two analytical approaches to estimate the torsional behavior of steel fiber reinforced concrete (SFRC) members. The first approach utilized the tensile constitutive relationship of SFRC in tension derived from SFRC panel test results, and the second approach adopted the direct tension force transfer model, which were applied to the smeared-truss model. In addition, three torsional members including two SFRC specimens with large amounts of transverse reinforcement were tested, and twenty-three SFRC torsional specimens were collected from literature to verify the proposed models. From this study, it appears that the proposed approaches provide enhanced analysis accuracy in estimating the torsional capacities of SFRC members, and closely capture their overall torsional responses compared to other models examined in this study.

Compressive Behavior of Fiber-Reinforced Concrete with End-Hooked Steel Fibers.

In this paper, the compressive behavior of fiber-reinforced concrete with end-hooked steel fibers has been investigated through a uniaxial compression test in which the variables were concrete compressive strength, fiber volumetric ratio, and fiber aspect ratio (length to diameter). In order to minimize the effect of specimen size on fiber distribution, 48 cylinder specimens 150 mm in diameter and 300 mm in height were prepared and then subjected to uniaxial compression. From the test results, it was shown that steel fiber-reinforced concrete (SFRC) specimens exhibited ductile behavior after reaching their compressive strength. It was also shown that the strain at the compressive strength generally increased along with an increase in the fiber volumetric ratio and fiber aspect ratio, while the elastic modulus decreased. With consideration for the effect of steel fibers, a model for the stress–strain relationship of SFRC under compression is proposed here. Simple formulae to predict the strain at the compressive strength and the elastic modulus of SFRC were developed as well. The proposed model and formulae will be useful for realistic predictions of the structural behavior of SFRC members or structures.