Stress-crack Opening Relationship Research Articles

Effectiveness of the Concrete Equivalent Mortar Method for the Prediction of Fresh and Hardened Properties of Concrete

Modern concrete mix design is a complex process involving superplasticisers, fine powders, and fibres, requiring time and energy due to the high number of trial tests needed to achieve rheological properties in the fresh state. Concrete batching involves the extensive use of materials, time, and the testing of chemical admixtures, with various methodologies proposed. Therefore, in some instances, the required design properties (physical and mechanical) are not achieved, leading to the loss of resources. The concrete equivalent mortar (CEM) method was introduced to anticipate concrete behaviour at fresh and hardened states. Moreover, the CEM method saves time and costs by replacing coarse aggregates with an equivalent sand mass, resulting in an equivalent specific surface area at the mortar scale. This study aims to evaluate the performance of fibre in CEM and concrete and determine the relationships between the CEM and the concrete in fresh and hardened states. Steel and polypropylene fibres were used to design three series of mixtures (CEM and concrete): normal-strength concrete (NSC), high-strength concrete (HSC), high-strength concrete with fly ash (HSCFA), and equivalent normal-strength mortar (NSM), high-strength mortar (HSM), and high-strength mortar with fly ash (HSMFA). This study used three-point bending tests and digital image correlation to evaluate load and crack mouth opening displacement (CMOD) curves. An analytical mode I crack propagation model was developed using a tri-linear stress–crack opening relationship. Post-cracking parameters were optimised using inverse analysis and compared to actual MC2010 characteristic values. The concrete slump is approximately half of the CEM flow; its compressive strength ranges between 78% and 82% of CEM strength, while its flexural strength is 60% of CEM strength. The post-cracking behaviour showed a significant difference attributed to the presence of aggregates in concrete. The fracture energy of concrete is 28.6% of the CEM fracture energy, while the critical crack opening of the concrete is 60% of that of the CEM.

Analytical and numerical modeling of plain concrete’s post-cracking behavior using a trilinear softening curve

The aim of the present work is to investigate the softening behavior of a notched concrete beam under a three-point bending test analytically, experimentally, and numerically using XFEM in Abaqus. This study presented a trilinear stress-strain softening curve-based analytical model to describe the complete flexural behavior of plain concrete beams. The article also provides the mathematical equations necessary for calculating the force-crack opening displacement during all cracking phases until failure. An inverse analysis of the force-CMOD curves obtained experimentally has optimized the parameters required for the identification of the tensile stress-crack opening relationship. The ABAQUS environment was used for numerical modeling using the extended finite element method (XFEM), and a good agreement between the experimental and numerical results has been noticed.

A Simplified Inverse Analysis Procedure for the Stress-Crack Opening Relationship of Fiber-Reinforced Concrete

The direct tensile test (DTT) is the most recommended test to determine the tensile behavior of fiber-reinforced concrete (FRC). However, this test is challenging to perform. Several studies have investigated inverse analysis to determine this behavior through simplified tests, such as the bending test. This study deals with developing a new approach to perform an inverse analysis for the three-point bending test (3PBT) involving FRC. A new proposed methodology concerns carrying out the inverse analysis procedure by parts. Initially, the parameters that influence the initial part of the stress–crack opening curve are adjusted. Progressively, the other parameters are adjusted considering the increment of the curve section. This procedure provides an implemented algorithm with more efficiency. A new strategy that deals with the establishment of criteria for parameters is proposed. Its results are compared with experimental data from other literature, whose steel fiber-reinforced concrete (SFRC) tested characteristics present different attributes such as fibers, shape, and length. The proposed methodology obtained the stress–crack opening curves in direct tension with reasonable accuracy, indicating that this methodology can be helpful in the characterization of the post-cracking FRC behavior.

An inverse analysis method for multi-linear tensile stress-crack opening relationship of 3D/4D/5D steel fiber reinforced concrete

The tensile stress-crack opening (σ-w) relationship of steel fiber reinforced concrete (SFRC) is of much importance for calculating the resistance of structures at serviceability and ultimate limit state. In this paper, the analytical solutions for the flexural response of SFRC beams were firstly developed by considering the multi-linear σ-w relationship of SFRC. Then, the parameters of the multi-linear σ-w relationship were obtained by using an inverse analysis method based on the analytical solutions and the experimental results of ten groups of notched concrete beams with 3D, 4D and 5D steel fibers. Results showed that the σ-w relationship of SFRC are changed from strain softening to strain hardening with increasing fiber volume fraction and number of fiber end hooks. The concrete beams with 4D and 5D steel fibers possess the higher flexural properties than the concrete beams with 3D steel fibers. In addition, the proposed analytical solutions and inverse analysis method could be applied to notched and unnotched SFRC beams with 3D, 4D and 5D steel fiber.

Debonding of rubberised fibre-reinforced cement-based repairs under fatigue loading: experimental study and numerical modelling

ABSTRACT This study presents experimental and numerical studies of the initiation and propagation of interface debonding between the substrate and thin-bonded cement-based overlay under fatigue testing. The overlay material is mortar incorporating amorphous metallic fibres (30 kg/m) and/or rubber aggregates (30%), while the substrate is a plain mortar. Uniaxial tensile tests were carried out on overlay materials and substrate-overlay interface to obtain a residual normal stress-crack opening relationship (σ-w law) and residual normal stress and substrate-overlay interface debonding relation respectively. Three-point bending fatigue tests were carried out on the composite beam to analyse the structural behaviour of repaired beam. The propagation of debonding along the substrate-overlay interface was monitored by using the Digital 3D Image Correlation (DIC) technique. Three-point bending fatigue test was modelled by finite element method (FEM) using CAST3M, developed by French Atomic Energy Commission. Direct tension test results show reduction in tensile strength and improvement in strain capacity (1.5 times of control mortar) for rubberised mortars. For fibre-reinforced mortars, post-peak residual tensile strength is significantly enhanced. Rubberised fibre-reinforced mortars show positive synergetic effects both in the improvement of residual post-peak strength and strain capacity (3.5 times than control mortar). Results show that the rubberised fibre-reinforced thin-bonded cement-based overlay proved to be very effective in restraining crack opening, by transferring stresses through the crack, and enhancing the fatigue resistance of repair system, by limiting interface debonding propagation upto 50%. Experimental results of composite beams are in good agreement with modelling results.

Meso-Scale Formulation of a Cracked-Hinge Model for Hybrid Fiber-Reinforced Cement Composites

This study presents a non-linear cracked-hinge model for the post-cracking response of fiber-reinforced cementitious composites loaded in bending. The proposed displacement-based model follows a meso-mechanical approach, which makes it possible to consider explicitly the random distribution and orientation of the reinforcing fibers. Moreover, the model allows for considering two different fiber typologies whereas the cement matrix is modelled as a homogeneous material. The proposed mechanical model combines a fracture-based, stress-crack opening relationship for the cementitious matrix with generalized laws aimed to capture the crack-bridging effect played by the reinforcing fibers. These laws are derived by considering both the fiber-to-matrix bond mechanism and fiber anchoring action possibly due to hooked ends. The paper includes a numerical implementation of the proposed theory, which is validated against experimental results dealing with fiber-reinforced cement composites reinforced with different short fibers. The excellent theory vs. experiment matching demonstrates the high technical potential of the presented model, obtained at a reasonable computational cost.

Experimental and Numerical Modeling on Fatigue Damage in FRP and PM Confinement Tilt’s Fulcrum RC Segments under Humid and Constant Amplitude Loading

It is a stringent challenge to swiftly rehabilitate and strengthen the concrete segments on the metro tunnel that are under the humid environment and vibration fatigue by the locomotives. By means of fatigue experiments under the constant amplitude loading, the repair materials (fiber reinforced polymer (FRP) and polymer matrix (PM)) which can be moisture proof and resist the cyclic load are introduced. Hereafter, a fatigue model of tilt’s fulcrum reinforced concrete (RC) segments under constant amplitude loading are proposed by the calibration of S-N curves through these fatigue test. The fatigue model explains for the (a) scope of pre-damage, (b) mechanical properties of the repaired concrete segments, such as the specific rupture times of cycle and stress-crack opening relation, and (c) effective plastic strain behavior of the RC segments. The results show that the purely PM is an excellent candidate for repairing the fatigue loaded damaged RC segment. It (L-4-2) had an average mechanical behavior for cyclic load bearing compared with the remaining specimens. On the other hand, the numerical model predictions had an approximately 96.00% of agreement with the corresponding test results.

Tensile characteristics of strain-hardening cement-based composites with different curing ages

This paper investigates tensile performances of strain-hardening cement-based composites (SHCC) with different curing ages varying from 3d to 28d. Cracking properties of SHCC specimens like the evolution of the number of cracks and the crack opening under direct tension was monitored simultaneously by using the digital images correlation (DIC) technique. Results show that the ultimate tensile strain in specimens cured for 7d is higher than that in specimens cured for 3d and 28d. The strain-hardening process involves three stages such as the initial, the intermediate, and the final stage, which are determined in terms of their cracking properties. Cracking properties of specimens cured for 3d and 7d display different rules from those of specimens cured for 28d at the intermediate strain-hardening stage, leading to different shape of stress-strain curve. Curing age influences fiber bridging stress-crack opening relation (σ(δ)) and interfacial mechanical behavior between PVA fiber and the matrix. σ(δ) gained by the DIC technique is similar to that observed in the tensile testing on notched specimens. The energy-based index of specimens cured for 7d has greater margin than that of specimens cured for 3d and 28d. The interfacial bond between fiber and matrix in specimens cured for 28d is larger than that in specimens cured for 3d and 7d.

Assessment of SFRC flat slab punching behaviour – part I: monotonic vertical loading

This paper presents a study of the behaviour and load capacity of steel-fibre-reinforced concrete (SFRC) flat slabs under monotonically increased concentrated vertical loads. The SFRC was used only in the local region of the slab–column connection, as the rest of the slab was cast using normal concrete without fibres. The six experimental test specimens had a thickness of 150 mm with different longitudinal reinforcement ratios, using a non-uniform distribution over the slab width. The concretes used were made with different Dramix 4D 65/60 BG steel fibre contents (0, 0·5, 0·75 and 1·0% volume content). The slab tests were complemented by flexural tests on notched beams. This made it possible to determine the tension behaviour of the different concretes used, through a linear post-cracking behaviour and inverse analysis. The inverse analysis made it possible to define the stress–crack opening relationship that characterises the tension behaviour of SFRC and to relate it to the observed behaviour and load capacity of the tested slabs. The tests results show that the tensile behaviour of the SFRC plays an important role in the behavioural and load capacity of the slabs and that it can be considered relevant to physically based models.

Influence of cohesive stresses on shear capacity of reinforced SFRC beams without stirrups: A discrete crack approach

An experimental investigation on the fracture behavior and the dilatant crack opening in the shear response of concrete with discrete steel fiber reinforcement is presented. Hooked-ended steel fibers are used at 0.5% and 0.75% volume fractions. From the experimental fracture response of steel fiber reinforced concrete beams, the cohesive stress-crack opening relationship is derived using the cracked hinge model. Load tests are conducted on laboratory-sized reinforced concrete beams without steel stirrups, designed to fail in shear. The crack growth and propagation in the shear behavior of concrete with and without fibers are evaluated from displacements measured using digital image correlation (DIC). The in-situ dilatant behavior of the shear crack is established from the slip and the crack opening displacements measured across the critical shear crack. A discrete crack-based formulation with internal contact forces on the crack faces and cohesive stress from fibers is developed for predicting the shear capacity of a reinforced concrete beam. The discrete crack-based model is derived using the physical observation on cracks in the reinforced concrete beams. The prediction of the model includes an increase in the contact forces with an increase in the fiber force at peak shear resistance with an increasing volume fraction of fibers. The additional contact forces mobilized across the crack by the fibers maintains the shear transfer across the crack and hence the load carrying capacity is sustained for a larger crack opening. The model derived from laboratory-sized specimens accurately predicts the scaling of the shear capacity with the size of the beam.

Fatigue behaviour of damaged RC beams strengthened with ultra high performance fibre reinforced concrete

This paper critically examines the performance of reinforced concrete (RC) beams retrofitted with a thin strip of ultra-high performance fibre-reinforced concrete (UHPFRC) under cyclic loading. RC beams were preloaded under static loading approximately to 70%, 80% and 90% of maximum load of control beams and then tested under fatigue loading with a stress ratio of 0.1 and frequency 2 Hz after retrofitting with a UHPFRC thin strip of 10 mm thickness. It has been found that the damaged RC beams can be successfully strengthened and rehabilitated by using a thin precast UHPFRC strip adhesively bonded to the prepared tensile surface of the damaged beams. No de-lamination of the strip was observed in any of the retrofitted beams. A finite element model was developed to predict the number of cycles to failure and load-deflection behavior of the retrofitted RC beams. The model accounts for the (i) degree of pre-damage, (ii) fracture behavior of concrete and UHPFRC through their respective specific fracture energy and stress-crack opening relation, and (iii) elasto-plastic behavior of the reinforcing steel. The model predictions are in very good agreement with the corresponding test results. It can be concluded that this UHPFRC is an excellent candidate for the repair and rehabilitation of damaged RC flexural elements.

Flexural behavior of RC beams retrofitted with ultra-high strength concrete

The performance of popular techniques of rehabilitation and strengthening of concrete elements using externally bonded steel plates and fiber-reinforced plastic (FRP) laminates has been extensively investigated and several de-lamination failures have been reported primarily due to the mismatch of their tensile strength and stiffness with that of the concrete structure. To overcome some of these drawbacks, this paper critically examines the performance of Reinforced Concrete (RC) beams retrofitted with a thin ultra-high strength concrete (UHSC) strip. All the reinforced concrete beams were retrofitted with UHSC strips of single thickness after they had been subjected to several levels of damage. It is found that the damaged reinforced concrete beams can be successfully strengthened and rehabilitated by using a thin precast UHSC strip adhesively bonded to the prepared tensile surface of damaged beams. A finite element model was developed to predict the failure load and load–deflection behavior of the retrofitted RC beams. The model accounts for the (i) degree of pre-damage, (ii) fracture behavior of concrete and UHSC through their respective specific fracture energy and stress-crack opening relation, and (iii) elasto-plastic behavior of the reinforcing steel. The model predictions are in good agreement with the test results. It is concluded that UHSC is an excellent prospective candidate for the repair and rehabilitation of damaged RC flexural elements.

Sectional analysis for design of ultra-high performance fiber reinforced concrete beams with passive reinforcement

Sectional flexural analysis, as performed in normal strength concrete design, requires uniaxial constitutive models. For ultra-high performance fiber reinforced concrete (UHPFRC), the constitutive model tensile backbone varies with section heights for different flexural members, due to the size-dependent stress-crack opening relation used to derive it. In this paper, several simplified size-independent constitutive models were investigated. For unreinforced sections with heights between 51 mm and 1067 mm, the elastic-perfectly-plastic tension model leads to conservative ultimate moment prediction (or results within 5%) when compared to that obtained by the size-dependent model. For reinforced sections, the difference between the two models is affected by the reinforcing condition and is even smaller than the unreinforced cases. By assuming an elastic-perfectly-plastic tension model, the flexural strength of rectangular or T section UHPFRC beams was estimated analytically. The flexural strengths are greatly influenced by the reinforcement ratio and yielding strength of the longitudinal reinforcement. Including shear strength predictive equations from past research, the load capacity and failure mode for rectangular and T beams are presented in a design chart. The impact of several factors on UHPFRC beam flexural responses were investigated, such as different compressive strength, curing conditions, and anisotropic fiber orientation distributions. The load-deflection relationships generated from beam flexural analysis were compared to experimental results for both unreinforced and reinforced beams, with or without fiber alignment. Factors affecting the first crack strength in tension (i.e., fiber orientation distribution) had greater impact on the flexural strength of UHPFRC beams than the effect of using a size-dependent model.

Mechanical and fracture properties of a self-compacting version of CARDIFRC Mix II

CARDIFRC is the trade name of two main groups of ultra-high performance fibre-reinforced concrete mixes – Mixes I and II – differing primarily in the maximum size of quartz sand used (0.6 mm in Mix I, and 2 mm in Mix II). In this paper, the conversion of CARDIFRC Mix II to a self-compacting and industrially competitive ultra-high performance fibre-reinforced concrete (UHPFRC) is described. A full mechanical and fracture characterisation (i.e. size-independent fracture energy and the corresponding bi-linear stress-crack opening relationship) of this UHPFRC is provided.

Cohesive cracked-hinge model for simulation of fracture in one-way slabs on grade

Numerical analysis of slab on grade structures subjected to mechanical loads is a complex matter often requiring computationally expensive models. In order to develop a simplified and general concept for non-linear analysis of slab on grade structures, this paper presents a cohesive cracked-hinge model aimed at the analysis of the bending fracture of the cemented material. The model is based on the fracture mechanics concepts of the fictitious crack model with a linear stress–crack opening relationship. Moreover, the paper presents a two-parameter spring foundation model applied to realistically capture the continuity in the supporting medium. The functionality of the proposed model is compared to numerical analysis with application of the more conventional cohesive zone model. The results obtained show that the methodology is a attractive and powerful one well-suited for practical use and further development.

General cracked-hinge model for simulation of low-cycle damage in cemented beams on soil

The need for mechanistic constitutive models to evaluate the complex interaction between concrete crack propagation, geometry and soil foundation in concrete- and composite pavement systems has been recognized. Several models developed are either too complex or designed to solve relatively simple problems, e.g. limited to one type of load configuration or test set-up. In order to develop a general and mechanistic modeling framework for non-linear analysis of low-cycle damage in cemented materials, this paper presents a cracked-hinge model aimed at the analysis of the bending fracture of the cemented material. The model is based on the fracture mechanics concepts of the fictitious crack model. The proposed hinge is described in a general and consistent format, allowing for any type of stress-crack opening relationship and unloading- reloading formulation. The functionality of the proposed hinge model is compared to numerical- and experimental results. The proposed hinge shows good performance and seems promising for the description of low-cycle fracture behavior in cemented materials.

A proper infill sampling strategy for improving the speed performance of a Surrogate-Assisted Evolutionary Algorithm

In the present paper, an improved Surrogate-Assisted Evolutionary Algorithm is proposed. It combines the Differential Evolution algorithm with a quadratic surrogate approximation and a proper infill sampling strategy to choose appropriate sample points. The selection of the new candidate points is arranged to enhance both the local accuracy and the global optimum search. A comparison between performances of different evolutionary algorithms is carried out by searching the global minimum of two benchmark functions, by solving a dynamic identification problem of a three floor frame and by calibrating the non-linear stress-crack opening relation for Fibre-Reinforced Concrete specimens starting from experimental data.

A simplified five-point inverse analysis method to determine the tensile properties of UHPFRC from unnotched four-point bending tests

Abstract Characterisation of the tensile behaviour of UHPFRC remains a challenge for researchers, and an agreement on the standard test set-up and advisability of notch is yet to be reached. Bending tests are easier to conduct if compared to direct tensile tests, but require a sophisticated post-process to obtain the uniaxial tensile behaviour of specimens. Unlike notched tests, unnotched tests allow the determination of strain-hardening behaviour, which characterises UHPFRC tensile behaviour. However, post-cracking behaviour is more difficult to analyse. This work focuses on the development of a new simplified inverse analysis method applied to unnotched four-point bending tests which improves current simplified methods, but maintains the accuracy of more complex ones. For this purpose, an analytical model based on a quadrilinear assumption of tensile behaviour in tension was assumed. A statistical analysis of theoretical flexural strength vs. displacement on mid-span analytical curves was conducted to link the assumed tensile behaviour to the analytical flexural behaviour that derived from it. After this process, a simplified method to obtain not only the stress–strain behaviour prior to crack localisation, but also the stress–crack opening relationship after that point is proposed. The new method is based on the determination of only five key points in experimental bending strength vs. displacement at mid-span curves and in the application of a back-of-the-envelope calculation. The analytical basis on which the method is based, justification of key point selection, and the process followed to achieve the simplified formulation, which allows dispensing with the use of a computer, are presented. An application example on a UHPFRC unnotched four-point bending test specimen, and its comparison with a point-by-point inverse analysis, are included.

Structural performance of final lining according to the rock load shape

The purpose of this study is to analyze the structural performance of the lining according to the magnitude as well as shape of rock load. Four cases of rock load shape were applied on the final lining (concrete lining) to perform structural analysis using beam spring model. This study includes two contents; firstly, the stability of the lining was analyzed using capacity diagrams. Secondly, the serviceability of the lining was analyzed using the cracked hinge model. While assessing the stability of the lining, FS = 2.45 was used according to LRFD specifications. The stress-crack opening relationship, represented by g(w) function, was used to assess the serviceability of the lining. The critical parameters used in this study are the K0 condition, load direction and application of the wedge load. Based on the results obtained after analysis, it was concluded that the K0 condition could change the thrust force-bending moment relationship which affects the stability and serviceability of the lining. Rock load in vertical direction affected the lining more than that in horizontal direction. Lastly, the development of wedge load proved to be more adverse than the application of larger uniform rock load on the lining.

The influence of fibre orientation on the post-cracking tensile behaviour of steel fibre reinforced self-compacting concrete

Adding fibres to concrete provides several advantages, especially in terms of controlling the crack opening width and propagation after the cracking onset. However, distribution and orientation of the fibres toward the active crack plane are significantly important in order to maximize its benefits. Therefore, in this study, the effect of the fibre distribution and orientation on the post-cracking tensile behaviour of the steel fibre reinforced self-compacting concrete (SFRSCC) specimens is investigated. For this purpose, several cores were extracted from distinct locations of a panel and were subjected to indirect (splitting) and direct tensile tests. The local stress-crack opening relationship (?-w) was obtained by modelling the splitting tensile test under the finite element framework and by performing an Inverse Analysis (IA) procedure. Afterwards the ?-w law obtained from IA is then compared with the one ascertained directly from the uniaxial tensile tests. Finally, the fibre distribution/orientation parameters were determined adopting an image analysis technique.