Model For Steel Fiber Reinforced Concrete Research Articles

Dynamic constitutive modeling of steel fiber reinforced concrete considering damage evolution under high strain rate

This study conducted quasi-static compression and splitting tensile tests on steel fiber reinforced concrete (SFRC), as well as dynamic compression tests using the split Hopkinson pressure bar (SHPB). The mechanical properties of SFRC with varying fiber contents and under different loading strain rates were examined separately. Experimental results indicate that the addition of steel fibers effectively enhances the properties of concrete. The dynamic mechanical performance of SFRC specimens (compressive strength, peak toughness, ultimate toughness, and energy absorption capacity) demonstrated a clear strain enhancement effect. The dynamic stress-strain curves of SFRC reveal the material's good viscoelastic properties. Then, a viscoelastic constitutive model for SFRC considering damage under high strain was proposed, with parameter fitting based on SHPB test results. The constitutive model was applied to the numerical simulation by the user-defined material (UMAT) in ABAQUS. The dynamic stress-strain curves and damage patterns obtained by numerical simulation are basically consistent with the test results. This further demonstrates that the proposed constitutive model effectively describes the dynamic characteristics of SFRC.

Research and mechanism analysis on dynamic compressive behavior of steel fiber reinforced concrete

This paper describes an investigation of the influence of steel fiber on the dynamic compressive behavior of steel fiber reinforced concrete (SFRC) at different strain rates, and reveals the mechanism of its change from the macro and meso levels. Meanwhile, a suitable dynamic constitutive model for SFRC is proposed. Four kinds of steel fiber contents (0 %, 1 %, 2 %, 3 %) and four kinds of high strain rates (40 s−1–220 s−1) were considered in the Split Hopkinson pressure bar (SHPB) test. Based on the designed tests, the failure pattern, the stress–strain curve, and the mechanical characteristic parameters of the SFRC under different loading conditions were obtained. The effects of steel fiber content and strain rate on the dynamic mechanical properties of concretes were analyzed. It is indicated that there are great differences in the failure pattern of the SFRC under different loading conditions. On the one hand, with the increase in the strain rate, the specimen is broken more completely. On the other hand, the reinforcing effect of steel fibers is obvious and as the steel fiber content increases, the crushing degree of the sample decreases significantly. The dynamic compressive strength of the SFRC is most sensitive to the strain rate and reaches its maximum value when the fiber content is 1 %. However, the variation of the peak strain showed no obvious regularity. The reinforcement mechanism of steel fibers was analyzed via the CT scanning technology. The results show that the main factors affecting the mechanical properties of SFRC are fiber content and porosity, but the fiber distribution is almost unaffected. The SFRC dynamic constitutive model was proposed by improving the HJC dynamic constitutive model. In the proposed model, the influence of steel fiber on strength was introduced and the influence term of strain rate was adjusted. The proposed model was verified by applying it to the numerical simulation of the dynamic compression performance of SFRCs and it shows good applicability. The presented research provides a theoretical basis for calculation and analysis of SFRC structures under extreme dynamic loads.

Analysis and prediction of the compressive and splitting tensile performances for the novel multiple hooked‐end steel fiber reinforced concrete

AbstractIn recent years, the application of the novel multiple hooked‐end steel fiber has gradually become a hot spot in the engineering due to its several excellent properties. In this study, the splitting tensile and compressive properties of the SFRC with 3D single hooked‐end and 4D/5D multiple hooked‐end steel fibers were studied. The variables of the experimental investigation included the concrete matrix strength, steel fiber content, and aspect ratio. The results showed that the compressive strength of steel fiber reinforced concrete (SFRC) increased first and then decreased with the increasing steel fiber content. The concrete matrix, aspect ratio, and end hook number of steel fiber had the significant effect on the optimal steel fiber content. In addition, increasing the content of steel fiber was the most effective way to improve the splitting tensile strength of SFRC, and the splitting tensile strength increased with the increase of the aspect ratio and end hook number of steel fiber. Finally, the splitting tensile strength prediction model of SFRC with novel multiple hooked‐end steel fiber was proposed by introducing the steel fiber number in the SFRC section, and the accuracy of the model was verified by comparison with experimental data.

Mesoscopic Modeling Approach and Application for Steel Fiber Reinforced Concrete under Dynamic Loading: A Review

Steel fiber reinforced concrete (SFRC) has drawn extensive attention in recent years for its superior mechanical response to dynamic and impact loadings. Based on the existing test results, the high-strength steel fibers embedded in a concrete matrix usually play a strong bridging effect to enhance the bonding force between fiber and the matrix, and directly contribute to the improvement of the post-cracking behavior and residual strength of SFRC. To gain a better understanding of the action behavior of steel fibers in matrix and further capture the failure mechanism of SFRC under dynamic loads, the mesoscopic modeling approach that assumes SFRC to be composed of different mesoscale phases (i.e., steel fibers, coarse aggregates, mortar matrix, and interfacial transition zone (ITZ)) has been widely employed to simulate the dynamic responses of SFRC material and structural members. This paper presents a comprehensive review of the state-of-the-art mesoscopic models and simulations for SFRC under dynamic loading. Generation approaches for the SFRC mesoscale model in the simulation works, including steel fiber, coarse aggregate, and the ITZ between them, are reviewed and compared systematically. The material models for different phases and the interaction relationship between fiber and concrete matrix are summarized comprehensively. Additionally, some example applications for SFRC under dynamic loads (i.e., compression, tension, and contact blast) simulated using the general mesoscale models are given. Finally, some critical analysis on the current shortcomings of the mesoscale modeling of SFRC is highlighted, which is of great significance for the future investigation and development of SFRC.

Condition Detection and Maintenance of Steel-Fiber-Reinforced Concrete Based on Markov Random Matrix

The condition detection and maintenance of steel-fiber-reinforced concrete (SFRC) involves a combination of qualitative and quantitative assessment methods, while the ineffectiveness of the Markov chain can analyze the fluctuation law of gray fitting accuracy indexes and use this to correct the detection results of the residual gray model, having outstanding advantages. On the basis of summarizing and analyzing previous works of literature, this study expounded the research status and significance of the condition detection and maintenance of SFRC, elaborated the development background, current status, and future challenges of the Markov random matrix, introduced the methods and principles of feature extraction network and loss function, proposed the detection process analysis of SFRC based on Markov random matrix, constructed a detection model of SFRC, analyzed the maintenance monitoring method of SFRC based on Markov random matrix, discussed the maintenance effect evaluation of SFRC, and finally carried out a simulation experiment and its result analysis. The results show that the most important feature of Markov random matrices is the absence of aftereffects, which means that the condition evolution of SFRC can be regarded as a multiple Markov chain. When carrying out the dynamic condition maintenance of SFRC, the maintenance object should be first determined, then the condition detection of the object should be carried out to obtain information characteristics and to assess its condition, and then the condition should be compared with the condition set to determine its position in the set to make fault prediction based on the Markov chain constructed from the set of conditions. Under other excepted standards and maintenance conditions with the increase of steel fiber content, the flexural strength of concrete decreased first and then increased, but the difference of maintenance conditions had obvious influence on the flexural strength of concrete. The results of this paper provide a reference for further research on the condition detection and maintenance of SFRC based on the Markov random matrix.

A meso-mechanical model for post-cracking tensile constitutive behavior of steel fiber reinforced concrete

Steel fiber reinforced concrete (SFRC) with hooked-end steel fiber is extensively used in practical structures due to the excellent post-cracking tensile behavior. And the post-cracking tensile stress of SFRC is directly affected by the pullout behavior of the single fiber and the number of fibers that crossed the crack plane. This study presents a theoretical model to estimate the pullout response of the single hooked-end steel fiber, which considers the plastic deformation of the end-hook, residual friction, spalling of the matrix, and snubbing effect. A simplified model is also presented based on the theoretical model for design purposes. The validity of the theoretical and simplified model is evaluated by the comparisons of the predicted and experimental results. Furthermore, a meso-mechanical tensile constitutive model of SFRC is developed to estimate the post-cracking tensile behavior of SFRC with the contribution of the matrix and the steel fibers are taken into account. Then, a bilinear tensile stress-crack width relationship is put forward considering the effect of the fibers. The contribution of the fibers is related to the fiber inclining angle, the fiber embedded length, the pullout force of the single fiber, and the number of fibers that crossed the crack plane. Finally, it can be found that the proposed model can accurately estimate the post-cracking tensile behavior of SFRC by comparing the estimated results with test data.

Numerical simulations of blast responses for SFRC slabs using an orthotropic model

This paper proposes a material model of steel fiber reinforced concrete (SFRC) subjected to dynamic loadings on the basis of an orthotropic concrete model. The effects of strain rate and fiber reinforcement are taken into account in the material model of SFRC from the uniaxial stress-strain relation to the triaxial strength envelope. The compressive and tensile strains as failure criteria are developed by reflecting the dynamic material properties, respectively. In particular, the post-cracking response according to steel fiber addition is investigated to improve the accuracy of the blast analysis for SFRC structures, and the proposed model is implemented as a user defined material model in LS-DYNA. The numerical results are compared with the experimental data in terms of damage pattern and average diameter of the damaged area for RC and SFRC slabs under explosions. The plastic based concrete models of K&C and CSCM are additionally compared to predict the behavior of SFRC structures. Furthermore, parametric studies are conducted with the proposed model to investigate the effects of reinforcement spacing and steel fiber on improving the structural resistance of SFRC slabs.

A strain rate dependent nonlinear elastic orthotropic model for SFRC structures

A strain rate dependent orthotropic model for steel fiber reinforced concrete (SFRC) structures subjected to impact or blast loads is proposed in this paper. Based on the previously introduced orthotropic model for plain concrete, an improved strain rate dependent material model for SFRC is developed to account for the effect derived from the addition of steel fibers in the concrete matrix and to cope with the multiaxial strain rate dependent behavior of SFRC. In addition to verification of the constructed multiaxial strength envelope of SFRC through correlations with experimental data, improved failure strains in the uniaxial stress-strain relation are also introduced to minimize the mesh size dependency in the numerical results. Finally, the proposed orthotropic model is incorporated into LS-DYNA as a user defined material model. Numerical analyses were performed for experiments of RC and SFRC slabs under projectile impact and blast loading, and the obtained results show that the addition of the steel fibers provides a considerable improvement in the structural resistance and the proposed model effectively simulates the structural responses of SFRC structures while minimizing the mesh size dependency in the numerical results.

Three-dimensional meso-scale modelling of failure of steel fiber reinforced concrete at room and elevated temperatures

Steel fiber reinforced concrete (SFRC) is composed of coarse aggregate particles, mortar matrix, fibers, pores and microcracks from the viewpoint of meso-scale. To reflect the mesoscopic characteristics more realistically, a three-dimensional meso-scale model for SFRC was established. In the model, the fibers were explicitly modelled while the concrete matrix was regarded as a tri-phase composite consisting of aggregate, mortar matrix and the interface transition zones (ITZs) between them. Based on the idea of classical random aggregate model for plain concrete, a programme was designed to randomly distribute aggregate particles and steel fibers. The meso-scale numerical model was verified by the good agreement between simulation results and the available test results. The dynamic failure behavior of SFRC at room and elevated temperatures was investigated by utilizing the simulation method. The simulation results indicate that for fiber content no larger than 2% volume, the influence of steel fiber on thermal conduction of SFRC can be ignored. Compared with that of plain concrete, strain rate effect on compressive strength of SFRC is weaker and it would be further decreased under high temperatures. The improvement of SFRC performance induced by steel fiber increases for higher fiber volume fraction whilst decreases with respect to strain rates, regardless of temperature. When the fiber amount is identical, the dynamic compressive strength of SFRC decreases slightly in the case of larger fiber diameter or smaller fiber length.

Constitutive modeling of steel fiber-reinforced concrete

Experimental studies within the previous years showed that the behavior of concrete is improved by adding steel fibers. Due to bridging effect, steel fibers in a concrete matrix prevent crack propagation under static loads. This phenomenon increases the load-bearing capacity of steel fiber-reinforced concrete, specifically after the peak load. In contrast to similar studies, in this study the effect of fibers on steel fiber-reinforced concrete is directly described based on uniaxial compressive and tensile stress–strain curves. For this purpose, the effect of fiber on the stress variations is extracted from the difference between steel fiber-reinforced concrete and its corresponding concrete matrix uniaxial stress–strain curves. These differential stress curves were extracted from 103 experimental specimens, collected from the literature. Then, some equations were developed for them with appropriate accuracy, using genetic programming technique. These equations were only based on primary specifications of fibers and concrete matrix. In the next stage, an elastoplastic damage constitutive model initially developed for plain concrete was modified, using the developed steel fiber-reinforced concrete modeling equations. The proposed model was implemented in a finite element analysis software and successfully simulated the steel fiber-reinforced concrete behavior subjected to uniaxial and flexural experiments.

Behavioral Simulation Model for SFRC and Application to Flexural Fatigue in Tension

A fatigue behavioral simulation for steel fiber reinforced concrete (SFRC) subjected to high cycle repetition of loads is presented. The fatigue constitutive models for normal strength concrete developed in the past decades are extended to those for SFRC with regard to tension, compression and shear transfer along dispersed cracking. The hysteretic path-dependency of SFRC is extensively focused on as well as post-cracking tension softening, because it greatly affects the stress-strain amplitudes of SFRC inside structures. The interaction of multi-directional cracks is taken into account based upon the fixed crack approach for enabling the damage evolution under the principal stress rotation. The rate effect on the stress and strain relation is also formulated to take into account the nonlinearity related to both loading rates and numbers of cycles. These proposed models for SFRC are experimentally verified in view of S-N diagrams of flexural tension for practical use.

Tensile cracking constitutive model of Steel Fiber Reinforced Concrete (SFRC)

This paper deals with the tensile cracking constitutive relationship of Steel Fiber Reinforced Concrete (SFRC) considering the effects of steel fiber content and fiber length. To investigate the effect of fiber content and length, notched 3-point bending tests were executed, where the fiber content was varied from 0.87% to 2.61%. From the bending tests, it was found that the flexural tensile strength of SFRC linearly increases with increasing fiber content and the rule of mixture can be applied to SFRC. Additionally, an inverse analysis was performed to determine the tensile cracking constitutive model of SFRC and a tri-linear tensile softening model is also suggested. The suggested model successfully represents the increase of the stress-constant bridging zone and the decrease of the stress-resisting zone with increasing fiber content. The proposed constitutive models including both long and short fibers for various fiber contents are simple and can be effectively applied to the numerical analysis of SFRC, which can consider steel fiber effects.

Three-dimensional modelling of steel fiber reinforced concrete material under intense dynamic loading

This paper presents a new three-dimensional numerical model to study the dynamic response and failure mode of steel fiber reinforced concrete (SFRC) material under impact and blast loading. In the 3D numerical model, SFRC is assumed to be composed of two components, that is, the homogeneous concrete matrix with lower strength and the steel fibers with higher strength. The straight round steel fibers are assumed to be dispersed with random locations and orientations in the matrix and a 3D grid algorithm is introduced to generate the finite element analysis model. The interaction between fibers and matrix is modeled by the bonding and sliding contact algorithm. The mechanical behavior of SFRC material is simulated and a good agreement with the test data is observed. The verified numerical model is then employed to perform a series simulation of split Hopkinson pressure bar (SHPB) and split Hopkinson tensile bar (SHTB) in order to study the dynamic increase factor (DIF) of SFRC material with different fiber volume percentage (Vf) under high strain rate loading. And the influence of Vf on the dynamic properties of SFRC is analyzed. Further numerical studies of the SFRC specimens under contact detonation are carried out and compared with the test data. The result shows that the developed numerical model for SFRC could precisely predict the failure mode.

A New Technique for Constitutive Modeling of SFRC

The application of steel fiber reinforced concrete (SFRC) is continuously increasing; however its potentials are limited due to the lack of universally accepted and reliable design guidelines. The main reason for that is a complex issue of quantifying the tensile stresses, called as residual stresses (σfr), which a cracked section is able to carry due to concrete interaction with fibers. This paper deals with a determination of the stress-crack opening (σfr-w) relation of tensile SFRC. The inverse technique was proposed for determination of σfr employing the experimental data from three-point bending tests on notched beams. Attained residual stress-crack opening relations were compared with the post-cracking behavior, defined using RILEM technique. It was observed, that the inverse technique, proposed by the authors, is an accurate method for determination of the residual stresses of SFRC in tension.

Torsional behavior model of steel-fiber-reinforced concrete members modifying fixed-angle softened-truss model

Steel-fiber-reinforced concrete (SFRC) is an efficient cement-based composite material that can compensate for the drawbacks of the material properties of conventional concrete and has better structural performances than conventional concrete. It can improve torsional behavior as well as flexural and shear behavior. However, analysis of the torsional behavior of SFRC members is quite complicated because force equilibrium and strain compatibility in a three-dimensional space should be satisfied. Accordingly, many studies proposed empirical evaluation equations for the torsional strength of SFRC members based on experimental results. Therefore, this study derived a constitutive model of SFRC in tension, which greatly influences the torsional behavior of SFRC, based on the test results of SFRC shear panels under biaxial stress, and this tensile behavior model was introduced to a fixed-angle softened-truss model. A theoretical evaluation model based on the modified fixed-angle model for torsional behavior of SFRC was developed, and the performance of the analytical model was also evaluated compared to test results obtained from literature.

Diverse Embedment Model for Steel Fiber-Reinforced Concrete in Tension: Model Verification

Results obtained from the Diverse Embedment Model (DEM) for analysis of steel fiber-reinforced concrete, described in an accompanying paper, are compared with experimental results produced by several independent researchers. Variation of the fiber orientation factor, which accounts for the effects of finite member dimensions on fiber orientation and embedment, is also theoretically investigated and compared with experimental data. Verification studies show that the proposed model provides accurate predictions of the tensile stress and crack width relationship of uniaxial tension specimens containing straight or end-hooked steel fibers. In addition, the proposed model provides accurate calculations of the distribution of tensile stress provided by fibers. The proposed model is also shown to be useful in modeling aspects of the tensile behavior, such as crack spacing and tension stiffening, of fiber-reinforced concrete (FRC) members reinforced with ordinary steel reinforcing bars.

Diverse Embedment Model for Steel Fiber-Reinforced Concrete in Tension: Model Development

In this paper an analysis model is presented for calculating the response of steel fiber-reinforced concrete (SFRC) members subjected to tension. To predict the tensile stress of fibers across a crack, the pullout behavior of a single fiber with both sides embedded in cracked concrete is analytically investigated, considering both frictional bond behavior and mechanical anchorage effects. Thus, the proposed Diverse Embedment Model (DEM) can be applied to end-hooked and straight fibers. The model is derived with consideration given to all possible fiber orientations and embedment lengths and as influenced by the member’s finite dimensions. The details of the experimental verification for the proposed analysis model, including the proposed fiber orientation factors, are presented and discussed in an accompanying paper.