Concrete Fracture Research Articles

A Weibull distribution-based method for the analysis of concrete fracture

Based on the design relation value of the variation dispersion coefficient β at the notch tip in concrete specimens at the peak load Pmax, a Weibull distribution method was employed to analyze the experimental data for different loading methods (3 PB, 4 PB, WS). The dispersion coefficient β, which complies with the Weibull distribution for notched specimens, leads to a Weibull distribution of the tensile strength ft and fracture toughness KIC. Furthermore, when the characteristic crack of concrete is αch∗=1.0dmax (or 1.5dmax), the coefficient of variation for the Weibull distribution is the smallest in most cases. By adopting the simple relation αch∗=1.0dmax (or 1.5dmax) and the fictitious crack growth, Δαf=βdmax, the fracture properties of concrete specimens withW/dmax = 4–50 under different loading conditions (3 PB, 4 PB, WS) were investigated. Because of the scatter in the peak load Pmax of the notched specimens and the variation in the fictitious crack growth Δαfici, a new statistical approach using the solution of the boundary effect model (BEM) was employed. The curves between the peak load Pmax and specimen height W were predicted. The critical values of the peak load Pmax and specimen height W were obtained, in which the notched specimen failure was controlled by the fracture toughness KIC.

Numerical Simulation on Dynamic Behavior of Slab–Column Connections Subjected to Blast Loads

Although many studies on the blast-resistant performance of structures have focused mainly on single members such as beams and columns, there is little research on the behavior of joints that are subjected to blast loads. In this study, the structural behavior of a slab–column connection subjected to blast load was investigated using a numerical analysis method. LS-DYNA was used as a finite element analysis program, and in order to improve the accuracy of numerical analysis, mesh size, material model, and simulation method of blast load were determined through preliminary analysis. The effect of different restraints of the joints, depending on the position of the columns in the slab, on the blast resistance performance was investigated. As a result, the highly confined slab-interior column connection showed better behavior than other edge and corner columns. The drop panel installed between the lower column and the slab was effective in improving the blast-resistance performance of the slab–column connection. For a more accurate evaluation of blast resistance performance, it was suggested that various evaluation factors such as ductility ratio, reinforcing stress, and concrete fracture area can be considered along with the support rotation, which is an important evaluation factor suggested by many standards.

Nonlinear Mechanical Effect of Free Water on the Dynamic Compressive Strength and Fracture of High-Strength Concrete.

It is well-known that the effect of interstitial fluid on the fracture pattern and strength of saturated high-strength concrete is determined by qualitatively different mechanisms at quasi-static and high strain rate loading. This paper shows that the intermediate range of strain rates (10−4 s−1 < < 100 s−1) is also characterized by the presence of a peculiar mechanism of interstitial water effect on the concrete fracture and compressive strength. Using computer simulations, we have shown that such a mechanism is the competition of two oppositely directed processes: deformation of the pore space, which leads to an increase in pore pressure; and pore fluid flow. The balance of these processes can be effectively characterized by the Darcy number, which generalizes the notion of strain rate to fluid-saturated material. We have found that the dependence of the compressive strength of high-strength concrete on the Darcy number is a decreasing sigmoid function. The parameters of this function are determined by both low-scale (capillary) and large-scale (microscopic) pore subsystems in a concrete matrix. The capillary pore network determines the phenomenon of strain-rate sensitivity of fluid-saturated concrete and logistic form of the dependence of compressive strength on strain rate. Microporosity controls the actual boundary of the quasi-static loading regime for fluid-saturated samples and determines localized fracture patterns. The results of the study are relevant to the design of special-purpose concretes, as well as the assessment of the limits of safe impacts on concrete structural elements.

Effect of recycled rubber aggregate size on fracture and other mechanical properties of structural concrete

Rubberised concrete (RC) is a green and environmentally friendly concrete type that can be used as a sustainable production material. However, investigations on the structural applications of RC are limited due to its increased cost and decrease in strength. In this study, economical mixture designs were formulated with low-level replacements of rubber aggregates from recycled end-of-life tyres, as a prospective approach. The size effect with coarse (15 mm tyre shreds) and fine (2–4 mm tyre crumbs) rubber aggregates on the fresh and mechanical properties of structural concrete, specifically its fracture properties, was investigated, incorporating preliminary testing and constitutive models. The damage evaluation and characteristics of Mode I fracture behaviour of RC were investigated using three-point bending tests on notched beams. Using digital image correlation which possibly can be used to replace the conventional tools, the crack patterns on the beams were detected and crack mouth opening displacements were measured. The rubber replacements led to crack bridging effects. Overall, the results indicate that addition of recycled tyre aggregates at low percentages results in improved ductility and higher energy absorption and thereby improving the toughness of concrete, with marginal impacts on its strength and other properties. Furthermore, the selected mathematical models for compression and fracture can be used to evaluate the performance of RC structural elements with different rubber replacement levels. The modified RC can be potentially applied to structural components for earthquake resistance, integral bridges, or impact resistant road barriers.

Design of concrete fracture property by average aggregate size

This study presents a design methodology for concrete fracture properties, linking the average aggregate size dav to the tensile strength ft and fracture toughness KIC for a given cement grade and water/cement (W/C) ratio. Two different concrete mixes with dav = 3.5 and 7 mm were tested and analyzed. Similar peak load Pmax values were obtained under three-point-bending conditions, but with different “ductility”. Variations of ft &KIC with dav were established by a simple design formula, which can be used to tailor bulk concrete fracture properties for specific purposes. A statistical method was introduced to estimate the effective dav if only the maximum aggregate size dmax was given. Comprehensive fracture data in literature were analyzed to demonstrate the estimation of dav from dmax. The purposely designed concrete mixes and data in literature show the significance of dav design even after the cement grade and W/C ratio are fixed.

Validation of the favorable quantity of fly ash in concrete and analysis of crack propagation and its length – Using the crack tip tracking (CTT) method – In the fracture toughness examinations under Mode II, through digital image correlation

This article focuses on the analysis of fracture processes in fly ash (FA) concrete considering the second model of cracking. The basic parameter of fracture mechanics in concrete elements according to Mode II fracture, i.e. KIIc, was determined. Two measuring devices were used in the studies. One of them was the Digital Image Correlation (DIC), which is now a popular and extensively used metrology technique. During the experiments, an attempt was made to validate the results of fracture toughness obtained in strength press tests. The main goal of the studies was to confirm the convergence and determine the discrepancy ranges, between the KIIc results obtained on the MTS 810 press and using the DIC technique. During the investigations a new concept was proposed in the analysis of concrete fracture processes under Mode II using the DIC method, i.e. evaluation the fracture toughness of the composite by the direct testing of the material with an initial defect – in the crack propagation area (Fig. 7b). In addition, it was attempted to determine the usefulness of the DIC system for the analysis of initial cracks development in concrete elements subjected to shear. For this purpose, basing on the images of major strains and displacements in the X direction, an in-depth assessment of the initial cracks growth was made. The article also presents an original, sophisticated solution for measuring the actual length of a propagating crack in the material with the use of the crack tip tracking (CTT) method. Principal strains ε11 were used to visualise the cracks, while their length was determined as the sum of the relative crack increments (generated at successive stages of the loading of the specimen) measured on the XY plane (rel XY).

Spatially random modulus and tensile strength: Contribution to variability of strain, damage, and fracture in concrete

This paper explores the computational modeling of nonlocal strain, damage, and fracture in concrete, considering the isolated contribution of two random, spatially variable properties related to the fracture process: Young’s modulus (E) and tensile strength (ft). Applying a continuum damage model, heterogeneous specimens of concrete with random and spatially varying E or ft were found to produce substantial differences when contrasted with traditional homogeneous (non-random) specimens. These differences include variable and uncertain strain and damage, wandering of the failure paths, and differing (sometimes lower) peak forces, i.e. increased probabilities of failure in the heterogeneous specimens. It is found that ft variability contributes more (from 1.7 to up to 4 times more, depending on the parameter) to the overall performance variability of the concrete than E variability, which has a comparatively lower contribution. Performance is evaluated using (1) force-displacement response, (2) individual, average, and standard deviation maps of non-local strain and damage, (3) fracture paths and strain and damage values along the fractures. The modeling methodology is illustrated for two specimen geometries: a square plate with a circular hole, and an L-shaped plate. The computational results correlate well with reported experimental data of fracture in concrete specimens.

Experimental and analytical studies on steel-reinforced concrete composite members with bonded prestressed CFRP tendon under eccentric tension

This paper reported the very earliest experimental and analytical studies on the bonded Prestressed CFRP tendon enhanced Steel Reinforced Concrete (PSRC) members under eccentric tensile loads. Eight PSRC members were tested under monotonic eccentric tensile loading, and three Steel Reinforced Concrete (SRC) members were simultaneously tested for comparison. The load–deflection relationship, the strain distributions as well as the crack propagation and fracture of concrete were investigated experimentally and analytically. The results demonstrated an improvement in the eccentric tensile capacity of PSRC members upon increasing both the steel and reinforcement ratios, or by reducing the prestress eccentricity. The results also suggested that an enhancement in the level of prestressing increased can decrease the crack propagation and lateral deflection. Moreover, the validity of the plane-section assumption was confirmed. An analytical model was proposed for predicting the elastic bending capacity of the PSRC members based on the experimental results. The study provided an in-depth understanding of the structural behaviour of PSRC members with bonded prestressed CFRP tendon under the eccentric tension underpinned by the elaborate experimental design and practical analytical model.

Scale‐dependent maximum reinforcement percentage in reinforced concrete beams

AbstractThe Cohesive/Overlapping Crack Model is able to describe the transition between cracking and crushing failures occurring in reinforced concrete beams by increasing beam depth and/or steel percentage. Within this Nonlinear Fracture Mechanics model, the tensile and compressive ultimate behaviors of the concrete matrix are modeled through two different process zones that advance independently one of another. Moreover, this model is able to investigate local mechanical instabilities occurring in the structural behavior of reinforced concrete structures: tensile snap‐back and snap‐through, which are due to concrete cracking or steel fracture, and the compressive snap‐back occurring at the end of the plastic plateau, which is generated by the unstable growth of the crushing zone. In this context, the application of the Cohesive/Overlapping Crack Model highlights that the ductility, which is represented by the plastic rotation capacity of a reinforced concrete element subjected to bending, decreases as reinforcement percentage and/or beam depth increase. Thus, a scale‐dependent maximum reinforcement percentage beyond which concrete crushing occurs prior to steel yielding is demonstrated to exist. In particular, the maximum steel percentage results to be inversely proportional to h0.25, h being the beam depth. In this way, a rational and quantitative definition of over‐reinforcement is provided as a steel percentage depending on the beam depth.

Thermo-chemo-hygro-mechanical simulation of the restrained shrinkage ring test for cement-based materials under distinct drying conditions

A thermo-chemo-hygro-mechanical (TCHM) simulation approach for modelling the concrete behaviour during restrained shrinkage ring tests under two distinct drying conditions, namely, top and bottom as well as circumferential drying, is presented herein. The models were calibrated using data from an extensive round robin testing programme, which involved measurements on the time dependent properties of a specific concrete mix. Experiments and simulations accounted for the evolution of cement hydration, moisture diffusion, mechanical and viscoelastic properties and concrete fracture. The modelling approach was validated using results from an unrestrained shrinkage prism test and a restrained shrinkage ring test under top and bottom drying, and insights are obtained for the behaviour of restrained concrete rings under the two distinct drying conditions. It was observed that drying develops faster in rings under top and bottom drying compared to those under circumferential drying and so develops microcracking which is initiated at the steel–concrete interface. Conversely for circumferential drying, microcracking firstly occurs at the outer circumference due to the self-restraining effects arising from moisture gradients and is eventually induced in the steel–concrete interface. The top and bottom drying condition may be adopted for shorter testing duration; however, it does not encapsulate the self-restraining effects well.

Peridynamics modelling of dynamic tensile failure in concrete

Concrete as a brittle material suffers from tensile failures such as fracture and spalling under tension. These tensile failures are believed to be associated with the initiation, propagation, and coalescence of cracks. The purpose of this study is to present a numerical investigation on the dynamic tensile failures in concrete. For this purpose, the non-ordinary state-based peridynamics (NOSB-PD) theory is employed as an analysis tool to avoid the difficulties encountered in the finite element method in dealing with discontinuities such as cracks. Furthermore, to obtain the realistic stress field in the concrete and so as to update the nonlinear relationship between the force states and the displacement vectors required in the NOSB-PD theory, a well-developed rate-dependent plastic-damage model for concrete is incorporated. This model is modified from the Kong-Fang concrete model which has been verified to be suitable for the modeling of dynamic tensile failures in concrete within the classical continuum mechanics. Several numerical examples including dynamic fracture tests and spall tests are presented to demonstrate the performance of the current model. The results reveal that the dynamic fracture and spalling in concrete can be well captured and are observed to be greatly influenced by the loading rates. The predicted crack patterns of the concrete under different loading rates are found to be comparable to the corresponding experimental results.

Axial compressive behavior of stainless steel tube confined concrete column piers

The steel tube confined concrete (STCC) column piers of marine structures have been proposed in recent years. The main advantages of STCC piers include the convenient construction process and improved core concrete strength. This research presents an experimental investigation on stainless steel tube confined concrete (SSTCC) column piers subjected to axial loading. Thirty two specimens were prepared and tested. Test variables included section shape, steel tube thickness, and concrete strength. Failure modes, axial ultimate compressive strength, strain characteristics, rigidity, confinement effect, and ductility were comprehensively investigated. Test results demonstrated that the main failure modes for circular and square specimens were concrete shear failure and steel tube fracture caused by concrete deformation, respectively. The axial compressive ultimate strength was affected by the tube thickness and concrete strength. The ultimate strength increased with the increase in the confinement factor, and the increasing ratio of the circular specimens was five times to that of square specimens. The differences in axial ultimate compressive strength of SSTCC column piers, carbon steel tube confined concrete column piers, and concrete filled steel tube column piers were also analyzed. Increasing tube thickness could increase the ductility and rigidity of the specimens. Moreover, axial ultimate compressive strengths were calculated and discussed based on different calculation models.

Linear-elastic stress field of notched concrete beam: An application of finite element in theory of critical distances

Fatigue failures occur in all structures including brittle and ductile structures. However, the study on fatigue in ductile material like metal and steel has tremendously developed compared to brittle material such as concrete. Fortunately, the Theory of Critical Distance (TCD) is witnessed successfully assess fatigue fracture in concrete. In obtaining one of the outputs using TCD which is critical distance, fatigue limit of concrete that is obtained through laboratory testing and stress field generated using computational analysis engineering software (CAE) are required. In this article, the concern will be on producing the valid and reliable stress field data since inaccurate input into the CAE will result unreliable output that is exposed to errors. In order to guarantee the result is accurate, validation works were conducted in preprocess and post-process phase while analysing finite model using ABAQUS. As the outputs comply accordingly based on the validation works, the critical distance is confidence to be consumed for the subsequent research related to TCD.

Dynamic response of cylindrical water storage tanks made byECC compared to normal concrete

In this paper, the dynamic behaviour and seismic damages of concrete cylindrical water storage tanks are investigated. Furthermore, by modeling the reservoirs, using normal concrete and engineered cementitious composite (ECC), the effects of ECC on reducing the seismic damages of reservoirs are investigated. For this purpose, ANSYS software is used to perform the nonlinear dynamic analysis of the tanks and different parameters including the hoop force and bending moment of the wall and cracking or crushing of the concrete were examined. According to the results, the relationships and criteria provided in the ACI standard for design of tanks are recommended to be revised in certain parts. Unlike the normal concrete tanks, in those made of ECC, concrete fracture is not observed and the crack width remains very small at a level that is not problematic. Finally, the use of ECC in cylindrical water storage tanks is suggested as a strategy for reducing the seismic vulnerability of this type of hydraulic structures.

Mechanical Properties and Durability of Rubberized and Glass Powder Modified Rubberized Concrete for Whitetopping Structures.

This paper analyzes concrete fine aggregate (sand) modification by scrap tire rubber particles-fine crumb rubber (FCR) and coarse crumb rubber (CCR) of fraction 0/1 mm. Such rubberized concrete to get better bonding properties were modified by car-boxylated styrene butadiene rubber (SBR) latex and to gain the strength were modified by glass waste. The following tests—slump test, fresh concrete density, fresh concrete air content, compressive strength, flexural strength, fracture energy, freezing-thawing, porosity parameter, and scanning electron microscope—were conducted for rubberized concretes. From experiments, we can see that fresh concrete properties decreased when crumb rubber content has increased. Mostly it is related to crumb rubber (CR) lower specific gravity nature and higher fineness compared with changed fine aggregate-sand. In this research, we obtained a slight loss of compressive strength when CR was used in concrete However, these rubberized concretes with a small amount of rubber provided sufficient compressive strength results (greater than 50 MPa). Due to the pozzolanic reaction, we see that compressive strength results after 56 days in glass powder modified samples increased by 11–13% than 28 days com-pressive strengths, while at the same period control samples increased its compressive strength about 2.5%. Experiments have shown that the flexural strength of rubberized concrete with small amounts of CR increased by 3.4–15.8% compared to control mix, due the fact that rubber is an elastic material and it will absorb high energy and perform positive bending toughness. The test results indicated that CR can intercept the tensile stress in concrete and make the deformation more plastic. Fracturing of such conglomerate concrete is not brittle, there is no abrupt post-peak load drop and gradually continues after the maximum load is exceeded. Such concrete requires much higher fracture energy. It was obtained that FCR particles (lower than A300) will entrap more micropores content than coarse rubbers because due to their high specific area. Freezing-thawing results have confirmed that Kf values can be conveniently used to predict freeze-thaw resistance and durability of concrete. The test has shown that modification of concrete with 10 kg fine rubber waste will lead to similar mechanical and durability properties of concrete as was obtained in control concrete with 2 kg of prefabricated air bubbles.

Static and fatigue responses of retrofitted RC beams with GGBS based UHPC strips

The strengthening techniques are primarily studied and well documented for the monotonic responses of RC structures. Perhaps, the knowledge concerned about fatigue or cyclic responses of RC structures is limited in the literature. Hence, the static and fatigue responses of retrofitted RC beams with GGBS based ultra-high performance concrete strips (5, 10 and 15 mm thick) have been investigated in this study. The results illustrated that even a thin UHPC strip (5 mm) can significantly increase the static and fatigue performance of RC members. A finite element model has been developed to predict the numerical response of retrofitted RC beams subjected to static and fatigue loads. Numerical studies incorporated with crucial parameters such as concrete damage model, failure criteria, stress-crack relation and fracture properties are performed. The predicated numerical model correlates with the corresponding experiments with a little deviation of less than 12%. These deviations could be mainly attributed to the porosity of concrete, rebar slip, and experimental errors in testing the massive specimen under fatigue loading.

Deformation Properties of Nano-Silica Modified Concrete Mixtures under Uniaxial Compression Loading

The enhancement that nano-silica (NS) constitutes in the microstructure of concrete would affect its deformation behavior. In this work, the pre-peak and post-peak stress–strain diagram characteristics of concrete mixtures with NS (1.5% of cement by wt.) under uniaxial compression were investigated. The results were compared with the mixtures containing micro-silica (MS) (7.3% of cement by wt.). Aggregate characteristics in the range of 16 to 22 mm, as another variable, were also changed by utilizing river gravel (RG II) or crushed sandstone (CS II). Compared to reference concrete, the addition of NS did not improve the compressive strength and modulus of elasticity significantly. However, the addition of only 1.5% NS significantly affected the stress–strain diagram characteristics, such as discontinuity and critical stress limits before the peak load. Relative to the mixtures containing MS, the effect of NS on the pre-peak region was more significant. For example, when the mixtures containing RG II as coarse aggregate are considered, with respect to reference mixture, the increase in normalized discontinuity stress limits at 28 days was found as 52% and 26%, respectively, for the mixtures containing NS and MS. However, in the same order, the increase in 28-day compressive strength was just 8.1% and 5.2%. Post-peak behavior of the mixtures also indicated that the fracture of concrete is more brittle when MS or NS is used. Among these, the effect of NS on the post-peak region was found to be more dominant.

Experimental Study and Extended Finite Element Simulation of Fracture of Self-Compacting Rubberized Concrete

Self-compacting rubberized concrete (SCRC) is a high-performance concrete that can achieve compacting effect by self-gravity without vibration during pouring. Because of its excellent fluidity, homogeneity, and stability, the application of self-compacting concrete in engineering can improve work efficiency and reduce project cost. The effects of loading rate on the fracture behavior of self-compacting concrete were studied in this paper. Three-point bend (TPB) tests were carried out at five loading rates of 1, 0.1, 0.001, 0.0001, and 0.00001 mm/s. The dimensions of the specimens were 100 mm × 100 mm × 400 mm. A precast crack was set in the middle of the specimen with a notch-depth ratio of 0.4. The experimental results show that the peak load on the load-CMOD (crack mouth opening displacement) curve gradually increases with the increase of the loading rate. Although the fracture energy a presented greater dispersion under the loading rate of 1 mm/s, the overall changes were still rising with the increase of the loading rate. Besides studying the softening characteristics of the self-compacting concrete, the constitutive softening curve of the self-compacting concrete was obtained using the bilinear model. Finally, curved three-point bending beams were simulated by using the extended finite element method based on ABAQUS. The fracture process of the self-compacting concrete under different loading conditions was analyzed more intuitively. The simulation results were compared with the experimental results, and the same conclusions were obtained.

Quantitative statistical analysis of the crack propagation and fracture process of self‐compacting rubber concrete based on acoustic emission

In this study, acoustic emission (AE) was used to monitor the whole process of tensile and fracture of the self-compacting rubber concrete (SCRC) under four-point bending. The AE activities of SCRC during the stretching and fracture process were analyzed by statistical methods to correlate the process of crack propagation with changes in mechanical properties. And by comparing the tensile and fracture properties, the change patterns of crack mode, the cumulative events and energy of AE in the bending process of SCRC with different rubber particles content, the influence of the incorporated rubber particles on the propagation of microcracks, and the macroscopic fracture mechanism were analyzed. Studies showed that with the incorporation of rubber particles, the ductility of the concrete before and after cracking was improved. Due to the weak bonding surface between the rubber particles and the matrix, the microcracks began to propagate at low-stress levels and developed steadily throughout the stretching process. As the rubber content increased, more rubber components participated in the tensile and fracture process. Because of the elastic stretching of rubber particles, the tensile deformation capacity and fracture properties of the concrete have been improved. And in the whole process of tensile and fracture, the cracking of the weak cemented surface of the matrix and the pulling of the rubber particles were more likely to cause shear mode cracks.

A localizing gradient enhanced isotropic damage model with Ottosen equivalent strain for the mixed-mode fracture of concrete

Standard isotropic damage models are simple to implement, but they may be inadequate for the mixed-mode fracture of concrete. A new equivalent strain based on the four-parameter failure criterion by Ottosen [1] is proposed here for incorporation into a standard isotropic damage model for mixed-mode fracture, and its performance benchmarked against three other commonly used equivalent strain definitions (Mazars, modified von Mises, Rankine). Departing from the original approach [1], shear failure is utilized here as one of the states for the determination of the four parameters. Numerically, mesh sensitivity is resolved by adopting the localizing gradient enhancement to obtain sharp damage profiles at failure [2]. For the numerical analysis, a series of tests done on Double-Edge-Notched (DEN) specimens of different sizes [3] and the interactive test with multi axial loadings for Single-Edge-Notched (SEN) specimen [4] are considered. These examples illustrate that a simple isotropic damage model in conjunction with new equivalent strain measure is able to capture mixed-mode fracture accurately.