Crack Width Prediction Research Articles

Behavior of base restrained reinforced concrete walls under volumetric change

This study is conducted with the intention of modeling base restrained concrete walls subjected to volumetric deformation. To achieve this goal, an analytical study is carried out using the finite element method (FEM) of analysis. The overall crack pattern and the estimated crack widths, which are obtained by using the FEM along with a crack width prediction formula, are in a good agreement with the experimental observations. In addition, parametric studies are performed to investigate the effects of different factors such as wall height, wall length to height ratio, wall thickness, reinforcement ratio, shrinkage and temperature strain on the crack width. Consequently, design recommendations are provided for the minimum amount of reinforcement needed to keep the crack width within the allowable limitation, particularly for liquid containing structural walls. Finally, the results of this study are compared with the provisions of ACI 350 code.

Advanced Crack Width Analysis of Reinforced Concrete Beams under Repeated Loads

Presented is a method which can predict accurately the crack width in reinforced concrete beams under repeated loading. It is known that the crack widths increase with an increase of the number of load cycles. To evaluate the crack widths realistically, the bond stress-slip relation and the variation of transfer length under repeated loading have been modeled and incorporated in the analysis model for crack width. The present study indicates that the transfer length decreases according to the increase of load cycles, which is due to the increase of residual slip. The calculated crack widths from proposed method agree very well with test data available in the literature, while the existing method shows large deviation from the test data. The proposed method also allows the calculation of the residual crack width after repeated loading. The present study provides a realistic base for the prediction of crack width, which is important for the serviceability of reinforced concrete structures subjected to repeated loads.

Crack spacing and crack width investigation from experimental CRCP sections

Crack width (CW) and crack spacing (CS) data from full-scale continuously reinforced concrete pavement (CRCP) test sections were collected and analyzed for this study. In order to compare CWs obtained under different temperature conditions, the CRCP CW model presented in the new mechanistic–empirical pavement design guide (MEPDG) was utilized to standardize the measurements. The MEPDG CS model was compared first to the measured data due to its direct link to CW prediction. Based on the measured material properties, pavement geometry, and climatic conditions, the predicted CS and the CS distribution matched the observations on the three main CRCP sections. Using the same inputs provided in the CS prediction, the CW model in the MEPDG significantly over predicted the measured CW. The CW model was calibrated with the measured data in order to compare CWs between sections acquired at various temperature conditions. At the standard temperature condition, the measured CW varied from 0.031 to 0.116 mm and was smaller for higher reinforcement ratios. The CW formula was modified to allow computation of CW at any slab depth. A study of CW variability in one test section showed a skewed distribution with a right tail.

부식에 의한 부착저항감소를 고려한 콘크리트 교량의 균열폭 예측

The current design for crack width control in concrete bridges is incomplete in analytical models. As one of the important serviceability limit states, the crack width be considered with the quantitative prediction of the initiation and propagation of corrosion and corrosion-induced cracking. A serviceability limit state of cracking can be affected by the combined effects of bond, slip, cracking, and corrosion of the reinforcing elements. Considering life span of concrete bridges, an improved prediction of crack width affected by time-dependent general corrosion has been proposed for the crack control design. The developed corrosion models and crack width prediction equation can be used for the design and the maintenance of prestressed and non-prestressed reinforcements by varying time, w/c, cover depth, and geometries of the sections. It can also be used as the rational criteria for the maintenance of existing concrete bridges and the prediction of remaining life of concrete structures.

Prediction of Crack Width of Chloride Contaminated Reinforced Concrete Structures

Crack width is a significant parameter for assessing service life of reinforced concrete structures in chloride-laden environments. Corrosion-induced concrete cracking is a predominant causal factor influencing premature degradation of reinforced concrete structures, incurring considerable costs for repairs and inconvenience to the public due to interruptions. This gives rise to the need for accurate prediction of crack width in order to achieve cost-effectiveness in maintaining serviceability of concrete structures. It is in this regard that the present paper attempts to develop a quasi-brittle mechanical model to predict crack width of chloride contaminated concrete structures. Assuming that cracks be smeared uniformly in all directions and concrete be a quasi-brittle material, the displacement and stress in a concrete cover, before and after surface cracking, were derived respectively in an analytical manner. Crack width, as a function of the cover depth, steel bar diameter, corrosion rate and time, was then determined. Finally, the analysis results were verified by comparing the solution with the experimental results. The effects of the cover depth, steel bar diameter and corrosion rate on the service life were discussed in detail.

A multi-scale approach for crack width prediction in reinforced-concrete beams repaired with composites

The effects of externally bonded composite plates on the mechanical behaviour of a cracked RC beam loaded in flexure are modelled by a multi-scale approach. The problem of crack width prediction is addressed. Firstly, the state-of-the-art methods for crack width prediction in concrete beams are recalled. Then, they are confronted to experimental data obtained with a full-field optical method. It is shown that classical models are not suited for the prediction of crack widths in repaired beams. In order to improve the modelling, a new approach is considered: the structural behaviour of the beam is assessed from numerical computations conducted over a relevant representative volume element. The contribution of this multi-scale approach is that input parameters have a physical meaning and that the results are consistent with full-field measurements conducted on repaired beams. Finally, the paper focuses mainly on the validation of the model for computing displacement fields, crack widths and curvatures in repaired beams. The benefit for the identification of bonding properties between the composite sheet and concrete is also pointed out.

The influence of the parameter ?/?eff on crack widths

Many formulae for the prediction and control of crack widths in reinforced concrete members assume that the transfer length over which force is transferred by bond from the reinforcement to the concrete on either side of a crack is proportional to the parameter ϕ/ρeff, where ϕ is the bar diameter and ρeff is an effective reinforcement ratio. This paper aims to examine the validity of this assumption by comparing the predictions of the theory which leads to the derivation of the parameter ϕ/ρeff to data from experimental programmes where crack widths were measured. These comparisons strongly suggest that ϕ/ρeff has minimal influence on crack widths.

The influence of the parameterϕ/ρeffon crack widths

Many formulae for the prediction and control of crack widths in reinforced concrete members assume that the transfer length over which force is transferred by bond from the reinforcement to the concrete on either side of a crack is proportional to the parameter ϕ/ρeff, where ϕ is the bar diameter and ρeff is an effective reinforcement ratio. This paper aims to examine the validity of this assumption by comparing the predictions of the theory which leads to the derivation of the parameter ϕ/ρeff to data from experimental programmes where crack widths were measured. These comparisons strongly suggest that ϕ/ρeff has minimal influence on crack widths.

Experimental and numerical study of reinforced concrete specimens strengthened with composite plates

The present paper deals with the refined analysis of reinforced concrete specimens strengthened with composite plates and subjected to tension tests. A particular attention is paid to the characterization of cracks that develop in the concrete when tensile tests are carried out. A non-contact optical method based on image correlation is used to determine the displacement field onto the surface of the specimens during the tests. Both unstrengthened and strengthened specimens are tested in purely axial tension. The latter ones are first precracked, then repaired with composite plates bonded onto the concrete. The influence of the composite plates is studied in terms of distribution and width of cracks, especially in the vicinity of the composite. A model for the prediction of crack width in a repaired specimen is proposed. This model is validated by experiments and 3D finite element simulations.

Prediction of Crack Width for Fiber-Reinforced Polymer-Reinforced Concrete Beams

Use of fiber-reinforced polymer (FRP) bars to replace steel in reinforced concrete structures is being encouraged by many structural engineers, especially for its noncorrosive properties. The partial inferiority of the bond and mechanical properties for few commercial FRP bars, however, leads to wider, deeper cracks compared with those of steel-reinforced concrete structures. The characteristics of such cracks have significant interaction with the stresses and displacements induced in the concrete and the reinforcing bars crossing the crack (dowel action of bars), as well as on the contribution of the stirrups at crack location. Furthermore, because the dowel failure of FRP bars takes place in a brittle mode and lower magnitude of transverse displacement than steel, an accurate prediction of these characteristics is essential for a proper evaluation of beam serviceability, as well as its strength and failure conditions. Therefore, this paper presents an analytical formula that calculates the maximum crack width in FRP-reinforced concrete beams, taking into account both the bond and the mechanical properties of FRP bars.

Characterization of Transverse Cracking Spatial Variability: Use of Long-Term Pavement Performance Data for Continuously Reinforced Concrete Pavement Design

Mechanistic-empirical design procedures for continuously reinforced concrete pavement (CRCP) require characterization of variations in major design parameters so that a new or rehabilitated pavement can be designed for a desired level of reliability. Transverse cracking is an important CRCP design parameter affecting the prediction of crack width, crack load transfer efficiency, and critical stresses leading to longitudinal cracking and punchout development. The primary focus of this study was to investigate spatial characteristics of transverse cracking occurring in CRCP and to develop a theoretical model that would provide a means for systematic characterization of transverse crack spacing variability along the pavement length. Long-term pavement performance distress data were utilized to analyze transverse crack spacing characteristics for CRCP sections. From the results of the field data analysis, a theoretical model utilizing a Weibull distribution was developed to characterize the along-the-section transverse crack spacing frequency distribution. This theoretical model could be incorporated into the mechanistic-empirical procedures for CRCP structural design. The relationship between transverse crack spacing characteristics and punchout development and the location of the longitudinal cracks, which are a punchout precursor, were also analyzed using field survey data. Conclusions derived from field data analysis and the theoretical model presented here will be of interest to practicing engineers and researchers involved in CRCP design and performance modeling.

Deflection and crack-width prediction of concrete beams reinforced with glass FRP rods

Concrete beams reinforced with fiber reinforced polymer (FRP) bars exhibit large deflections and crack widths as compared to concrete beams reinforced with steel due to the low modulus of elasticity of FRP. Current design methods for predicting deflections at service load and crack widths developed in concrete structures reinforced with steel bars may not be used for concrete structures reinforced with FRP bars. Thus, the ACI 440 Committee has provided design guidelines for concrete beams reinforced with FRP bars. Verification of the ACI 440 methods for predicting deflections and crack widths for glass fiber reinforced polymer reinforced concrete beams are presented in this paper. In addition, improvement to the crack width equation was suggested to account for 2 layers of reinforcement. This study shows that ACI 440.1R-01 can be effectively used to predict deflections in concrete beams reinforced with FRP bars and crack width in beams with one-layer FRP bars. However, when FRP bars are placed in two layers, ACI 440.1R-01 can be used after some parameters are modified. Six full concrete beams reinforced with different GFRP reinforcement ratios were load tested and the measured deflections and crack widths were analyzed and compared with those predicted by the proposed models. The experimental results compared well with those proposed by the model.

외부부착 보강된 교량 바닥판 균열폭의 반경험적인 예측

외부부착 보강된 교량 바닥판 균열폭의 반경험적인 예측

鋼管・コンクリート複合構造橋脚における温度ひび割れの発生機構とその評価方法に関する研究

Time-dependent changes in the temperature, strain, and crack width of a steel pipe-concrete composite pier structure were measured. These were then numerically simulated by 1-D and 2-D thermal stress analysis to elucidate the mechanism of thermal cracking and formulate a method of assessing measuresagainst thermal cracking including crack width prediction. Gaps between the internal and surface temperatures were found to cause surface cracking during the rising phase of temperatures. It was also found that the presence of concrete in the pipes and its rigidity affect the temperature history anddegree of restraint, which cause effective strain on the surfaces. Prediction of the changes in the temperature and effective strain, as well as the resulting crack width, was found feasible using a simple 1-D model by setting adequate physical property values for the internal pipe elements. The crack-inhibiting effect of moderate-heat portland cement was verified by this method.

Effects of shrinkage on tension stiffening and cracking in reinforced concrete

Basic concepts of tension stiffening behaviour of reinforced concrete members under tension are reviewed, and different approaches to account for this behaviour are linked together. This includes a "load sharing" approach, where the average load carried by the cracked concrete is used to determine the post-cracking stress–strain response of concrete in tension, and a "tension stiffening strain" approach, which evaluates changes in member stiffness to obtain a reduction in member deformation by including the stiffening effect of the tension carried by concrete between cracks. Shrinkage strains are then included in an analysis of tension stiffening and the results of this analysis are validated with experimental data. The experimental study was carried out for symmetrically reinforced axial tension members having reinforcing percentages between 1% and 2% and shrinkage strain values up to 230 µε. Failure to account for initial member shortening caused by shrinkage leads to an apparent reduction in tension stiffening, which becomes more predominant as the percentage of reinforcement increases. Corrected results indicate that tension stiffening is independent of the reinforcing steel ratio, ρ (within the studied field for 1% < ρ < 2%) and continues to decrease during loading after cracking has stabilized. Test results are also compared with a number of proposals made by other researchers in the past. Prediction of crack widths based on results from axial tension member tests is not significantly affected by shrinkage.Key words: bond, cracking, crack widths, reinforced concrete, shrinkage, stress-strain response, tension, tension stiffening.

A New Formula for Prediction of Crack Widths in Reinforced and Partially Prestressed Concrete Beams

A new formula for predicting the average crack widths in reinforced and partially prestressed concrete beams has been developed incorporating four governing parameters. The performance of the proposed formula is checked using the authors' test results which includes crack spacing and crack width measurements from 18 reinforced and 12 partially prestressed concrete beams. Also included in the comparison are published data on 76 beams from other laboratory investigations. The comparative study indicates that the predictions are accurate. The performance of the proposed formula is also compared with three major code formulas, viz those recommended in the ACI Building Code, the British Standard and the Eurocode. It is concluded that better correlation with test data is achieved by the proposed formula.

Crack-Width Prediction for High-Strength Concrete Fully and Partially Prestressed Beam Specimens Containing Steel Fibers

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Effects of FRP Reinforcement Ratio and Concrete Strength on Flexural Behavior of Concrete Beams

Corrosion of the steel reinforcement in a cold and saline environment leads to the overall deterioration of reinforced concrete structures. To avoid such deterioration, fiber-reinforced polymers (FRP) rebars are used in place of steel reinforcement. In the present paper, test results of 12 concrete beams reinforced with FRP rods are reported. The main parameters investigated in the study include the reinforcement ratio and the concrete strength. Theoretical models are proposed for the prediction of crack width, crack spacing, load-deflection response, ultimate capacity, and modes of failure. The concept of deformability is also discussed.

Cracking behaviour of concrete beams reinforced with fiber reinforced plastic rebars

This paper presents the results of an experimental investigation on the cracking behaviour of concrete beams reinforced with fiber reinforced plastic rebars. The effects of reinforcement ratio on the cracking pattern, crack spacing, cracking moment, and crack width are investigated. The test results indicate that the reinforcement ratio has no meaningful effect on the cracking moment, which can be calculated as recommended by the ACI code. Also, the use of the equations adopted by ACI and the European codes for the prediction of crack width of conventionally reinforced concrete members is investigated and due modifications are made. Both relationships show good correlation with the test results; and the prediction of crack width of concrete beams reinforced with these two types of fiber reinforced plastic rebars is now possible. Key words: beam, cracking behaviour, cracking moment, crack width, fiber reinforced plastic, flexure, rebars, reinforced concrete, reinforcement ratio.

Failure in plain and reinforced concrete—an analysis of crack width and crack spacing

The proper prediction of crack widths in plain concrete and the spacing of primary cracks in reinforced concrete are the subject of this paper. Attention is focused on the influence of the crack concept. A comparison has been made between the standard crack model, the crack model with the fracture energy as a separate parameter, the rate-dependent crack model and the gradient crack model. It is shown that for reinforced concrete, use of one of the first two models results in a random location of primary cracks and consequently in a random value for the crack spacing. The effect of the inclusion of a length scale parameter in the latter two models has been determined with respect to the crack width in plain concrete and the crack spacing in reinforced concrete. Furthermore, attention is paid to the crucial role of the bond-slip characteristic in predicting crack spacing in reinforced elements.