Modeling Cracking in Shell-Type Reinforced Concrete Structures

A three-dimensional (3D) hypoelastic material model for modeling material properties of cracked reinforced concrete is proposed. Material properties of multidirectionally cracked reinforced concrete are represented by the material properties of intact concrete and a number of uniaxially cracked concrete with their coupling solids. Cracking effects due to multiple nonorthogonal cracks are traced in each uniaxially cracked concrete. Tension softening and aggregate interlock occurring at the crack interface as well as tension stiffening and compression softening initiated in concrete between cracks due to multiple nonorthogonal cracks are all incorporated explicitly. RC panels under in-plane loading and RC slab under pure torsion have been analyzed. The developed 3D hypoelastic material model has been proved to be efficient and effective in modeling the material behaviors of cracked reinforced concrete in shell-type RC structures. The deformational response, the ultimate strength, and failure mode can be captured reasonably well.     

Longitudinal Cracking Distress on Continuously Reinforced Concrete Pavements in Illinois

The Illinois Department of Transportation (IDOT) initiated a failure investigation to determine the distress mechanisms causing premature longitudinal cracking on continuously reinforced concrete pavements (CRCP) on several Illinois interstates. The longitudinal cracking approximately followed the embedded reinforcement steel and occurred in both the driving and passing lanes. In this paper, the results from field visual surveys, coring, and petrographic analyses are reported along with a review of archival construction and material records of the distressed CRCP sections. A laboratory forensic study was also performed on several field extracted slabs. The results of the field and laboratory investigation show the cracking was not initiated by steel corrosion, deleterious reactions in the concrete materials, or an inadequate structural design. Rather, the cracking is related to settlement of the steel bars in the concrete. Settlement cracking is conventionally thought to occur only in concrete slabs and decks with plastic (high slump) concrete and small values of bar cover depth, while the studied CRCP sections have large values of cover depth and were cast with stiff (low slump) concrete. The settlement was likely caused by the relative settlement of heavy steel bars (22?mm diameter) within the lower density concrete during the original CRCP construction. The technique of placing the steel bars in the fresh concrete (called tube-feeding) further contributed to the development of this distress, and this practice is no longer employed by IDOT.     

Simulation of Crack Growth in FRP Reinforced Concrete

Experimental results show that the crack growth of fiber-reinforced polymer (FRP) reinforced concrete flexural elements experience a crack development stage followed by crack stabilization. The crack length and elastic crack mouth opening displacement (CMOD) increase during the crack development stage until reaching the crack stabilization stage. A finite-element representation was proposed to predict the initial CMOD. A debonded length was specified to account for the bond-slip between FRP bar and concrete. It was assumed that there was no tangential displacement between the reinforcement and concrete outside of the debonded length. A fatigue model was created using the Paris equation to simulate the growth of elastic CMOD. The model displayed good agreement with the test results. A size effect was also observed for the exponential parameter in the Paris equation.     

Probabilistic Approaches for Pavement Fatigue Cracking Prediction based on Cumulative Damage Using Miner’s Law

In mechanistic-empirical (M-E) pavement design, pavement damage is modeled as a random variable with a pre-specified distribution (normal or lognormal). The extent of fatigue cracking in terms of percentage cracking is computed as the probability of cumulative damage exceeding unity. This paper provides a methodological framework for characterizing damage distribution under mixed traffic loading (multiple strain levels) with an improved forecast of traffic spectrum based on renewal theory. Using the linear Miner’s law for damage accumulation, analytical representation of damage distribution is obtainable owing to the proportional relationship between maximum tensile strain of pavement and traffic load under linear elasticity condition. Numerical computation shows that percent of cracking from derived damage distribution is greater than that from hypothetical normal or lognormal distributions traditionally used in the M-E pavement design. The method developed here and the derived model can be used in pavement design and pavement management systems.     

Hybrid Bonding of FRP to Reinforced Concrete Structures

The adhesive attachment of fiber-reinforced polymers (FRP) laminate to the external face of reinforced concrete structures is currently one of the most popular and effective methods for retrofitting and strengthening concrete structures. With this method, the additional strength of the attached reinforcement is transmitted into the concrete members through adhesion. However, the relatively weak adhesive interface fundamentally limits the efficacy of the method. Much effort has been made in the research community to improve the bond strength and develop bond models, but a satisfactory solution has yet to be found. Mechanical fastening is another more traditional technology that is used to bond one material to another. This paper introduces a new hybrid bonding technique that combines adhesive bonding and a new type of mechanical fastening. The new mechanical fastening technique does not rely on bearing to transmit the interfacial shear, but instead increases the interfacial bond by resisting the separation of the FRP laminate from the concrete substrate. Experimental tests demonstrated that the bond strength with this new hybrid bonding technology was 7.5 times that of conventional adhesive bonding. Furthermore, the new bonding technique is applicable to all types of commercially available FRP laminate (fabric, sheet, plate, and strip), and in principle is also applicable to materials other than FRP.     

Numerical Cracking and Debonding Analysis of RC Beams Reinforced with FRP Sheet

Bonding a fiber reinforced polymer (FRP) sheet to the tension-side surface of reinforced concrete (RC) structures is often performed to upgrade the flexural capacity and stiffness. Except for upper concrete crushing, FRP sheet reinforcing RC structure may fail in sheet rupture, sheet peeloff failure due to opening of a critical diagonal crack, or concrete cover delamination failure from the sheet end. Accompanying the occurrence of these failure modes, reinforcing effects of the FRP sheet will be lost and load-carrying capacity of the RC structures will be decreased suddenly. This study is devoted to developing a numerical analysis method by using a three-dimensional elasto-plastic finite element method to simulate the load-carrying capacity of RC beams failed in the FRP sheet peeloff mode. Here, the discrete crack approach was employed to consider geometrical discontinuities such as opening of cracks, slipping of rebar, and debonding of the FRP sheet. Comparisons between analytical and experimental results confirm that the proposed numerical analysis method is appropriate for estimating the load-carrying capacity and failure behavior of RC beams flexurally reinforced with a FRP sheet.     

Structural Model to Predict the Failure Behavior of Plated Reinforced Concrete Beams

This paper presents a theoretical model, based on truss analogy, to analyze the structural behavior at failure of reinforced concrete beams with steel plates or fiber-reinforced polymer lamitates bonded to their tension faces. The analytical approach, incorporated in the framework of strut-and-tie models, takes into account the nonlinear behavior of materials and of the structural member. In addition, it includes the load transfer mechanism to reflect the plate-debonding phenomenon and associated cracking of concrete cover, both of which play a critical role in the failure process of plated beams. The model, which takes into consideration all the possible failure modes of plated beams, is capable of predicting the beam load-carrying capacity at ultimate and, also, of indicating the associated mode of failure. It aims to develop a rational engineering analysis in a field which until now has been studied with linear elastic approaches or empirical methods. The proposed model has been validated by comparing the results obtained in the present analysis with over a hundred experimental results available in published literature. Furthermore, the results obtained with the present analysis are compared with those obtained by two other models, and it is shown that the model proposed here provides a consistent and satisfactory correlation with a wide range of reinforced concrete beam tests strengthened with steel or polymer composite plates.     

Experimental Analysis of Crack Growth in GFRP Reinforced Concrete

For decades, bridge slabs have been troubled by the corrosion of steel reinforcement. The unique corrosion resistance of glass fiber-reinforced polymer (GFRP) bars makes them a promising alternative to steel bars. Experiments have been conducted to investigate the bond performance of GFRP reinforced concrete under constant amplitude cyclic fatigue loading. Each specimen was an identical length beam with a single GFRP bar at the bottom, intended to simulate a transverse strip of a typical bridge deck slab. The crack growth was monitored for specimens of different widths, simulating different transverse reinforcement spacings. Up to 2?million?cycles of cyclic loads were applied at 100% typical service load levels. No fatigue failure was encountered in the testing. The effects of moderate overloads were also investigated.     

Creep Deformation of Fiber Reinforced Plastics-Plated Reinforced Concrete Tensile Members

The problem of long-term creep deformation of reinforced concrete tensile elements strengthened by external fiber reinforced plastic (FRP) plates is studied. Formation of discrete cracks in concrete under tension is taken into account. A kinematic model is used, where relative slips between concrete, steel bars, and FRP plates are considered, governed by viscous interface shear stress–slip laws. Bazant’ solidification theory and exponential algorithm are used to obtain incremental constitutive equations for concrete as well as for steel-concrete and FRP-concrete interface laws. Moreover, cohesive normal stresses across transverse cracks in concrete are considered. The incremental differential system of equations is transformed into a nonlinear algebraic system by a finite difference discretization with respect to axial coordinate. Several numerical examples are presented, concerning both short-term and long-term loadings. It is shown that reinforcing by means of FRP plates or sheets has significant beneficial effects on the behavior of reinforced concrete elements under service loadings because (1) it increases concrete tension stiffening effect and (2) it strongly reduces crack width. The present study shows that these beneficial effects are preserved also in the case of long-term loadings.     

New Approach for Estimating the Deflection of Beams Reinforced with FRP Reinforcement

Due to concerns with corrosion, the use of fiber-reinforced polymer (FRP) as a replacement to conventional steel reinforcement has greatly increased over the last decade. Researchers have identified the distinctive mechanical and bond properties of FRP reinforcement that prevent the use of existing relationships to establish serviceability of concrete structures reinforced with such products. Although studies have modified these empirical relationships to describe the behavior of structures reinforced with FRP reinforcement, this paper will provide a new approach to estimate deflection of concrete beams by considering material properties of the reinforcement and incorporating the effects of tension stiffening. Accuracy and precision of the approach was established by performing a statistical analysis on a database containing 171 FRP-reinforced concrete beams. Results were compared to those from existing proposed relationships and indicate the potential of the method to estimate deflection at various service conditions.     

Control of Corrosion-Induced Damage in Reinforced Concrete Beams Using Carbon Fiber-Reinforced Polymer Laminates

This paper presents the results of an experimental study conducted to investigate the effect of carbon fiber-reinforced polymer (CFRP) confinement on the cracking damage induced by impressed current-accelerated corrosion of reinforced concrete beams. The beams were 254?mm deep by 152?mm wide by 3,200?mm long. Two different corrosion configurations, namely uniform and shear-span corrosion, were investigated in eight specimens at three different degrees of corrosion (5, 10, and 15% theoretical mass loss). Uniform corrosion along the whole length of the beams (3,000?mm) and shear-span corrosion (900?mm from each beam end) were considered. The different degrees of corrosion were induced using an accelerated corrosion technique with an impressed current. Based on the results, it was concluded that CFRP laminate confinement reduces corrosion expansion by up to 70% and slows the rate of corrosion through decreasing the corrosion mass loss by up to 35%.     

Stiffness Degradation and Time to Cracking of Cover Concrete in Reinforced Concrete Structures Subject to Corrosion

Corrosion-induced cracks in reinforced concrete (RC) structures degrade the stiffness of the cover concrete. The stiffness degradation is mainly caused by the softening in the stress-strain relation in the cracked concrete. Limited efforts have been made to model the cracking and the corresponding effects on the cover concrete, despite of its importance in assessing and modeling the behavior of RC structures. This paper proposes a stiffness degradation factor to model the stiffness degradation of the cover concrete subject to cracking. The proposed factor is computed in terms of the cracking strain corresponding to the maximum opening of the concrete cracks based on an energy principle applied to a fractured RC structure. The time to cracking of the cover concrete is then determined as the time from the corrosion initiation needed by the crack front to reach the outer surface of the cover concrete. The proposed stiffness degradation factor and the method to compute the time to cracking are illustrated through two numerical examples. The times to cracking of the cover concrete that are predicted using the proposed method are in agreement with the measured values from laboratory experiments.     

Probabilistic Capacity Models and Fragility Estimates for Reinforced Concrete Columns based on Experimental Observations

A methodology to construct probabilistic capacity models of structural components is developed. Bayesian updating is used to assess the unknown model parameters based on observational data. The approach properly accounts for both aleatory and epistemic uncertainties. The methodology is used to construct univariate and bivariate probabilistic models for deformation and shear capacities of circular reinforced concrete columns subjected to cyclic loads based on a large body of existing experimental observations. The probabilistic capacity models are used to estimate the fragility of structural components. Point and interval estimates of the fragility are formulated that implicitly or explicitly reflect the influence of epistemic uncertainties. As an example, the fragilities of a typical bridge column in terms of maximum deformation and shear demands are estimated.     

Design Proposal to Avoid Peeling Failure in FRP-Strengthened Reinforced Concrete Beams

According to the available experimental work, the most common failure in existing structures strengthened by plate bonding is the laminate peeling off. In the last few years, an important effort in the development of mathematical models to avoid premature peeling failures has been made. However, a suitable and reliable design method to predict debonding due to the shear flow between crack discontinuities or at the laminate end is still not available. This paper describes a new design procedure for structures strengthened by plate bonding to avoid peeling failure at any location. After calculating the laminate area required for flexural strengthening, a two-step procedure to prevent peeling failure is proposed. The first step, to avoid peeling failure along the span, is based on a shear-bending interaction diagram associated with the theoretical maximum transferred force between laminate and support along the crack spacing before laminate debonding. This interaction diagram can be obtained through the application of nonlinear fracture mechanics. The second step consists of checking for peeling failure at the laminate end. The bonded length between the laminate end and the nearest crack should be enough to transfer the laminate tensile force acting on this crack. The proposed method has been verified with available experimental results assembled in a database. A good agreement between the experimental and predicted failure load has been obtained. Finally, an application example is presented to show the applicability of the method.     

Deflection Calculation of FRP Reinforced Concrete Beams Based on Modifications to the Existing Branson Equation

Fundamental concepts of tension stiffening are used to explain why Branson’s equation for the effective moment of inertia Ie does not predict deflection well for fiber reinforced polymer (FRP) reinforced concrete beams. The tension stiffening component in Branson’s equation is shown to depend on the ratio of gross-to-cracked moment of inertia (Ig/Icr), and gives too much tension stiffening for beams with an Ig/Icr ratio greater than 3. FRP beams typically have an Ig/Icr ratio greater than 5, leading to a much stiffer response and underprediction of computed deflections as observed by others in the past. One common approach to computing deflection of FRP reinforced concrete beams has been to use a modified form of the Branson equation. This paper presents a rational development of appropriate modification factors needed to reduce the tension stiffening component in Branson’s original expression to realistic levels. Computed deflections using this approach give reasonable results with the right modification factor, and compare well with a more general unified approach that incorporates a realistic tension stiffening model. Comparison is made with the existing and past correction factors recommended by ACI 440 for predicting deflection of FRP beams. The method presently used by ACI 440 gives reasonable estimates of deflection for glass and carbon FRP reinforced beams. However, this method underestimates deflection of aramid FRP reinforced beams and is restricted to rectangular sections. A proposal is made for adoption of a simple modification factor that works well for all types of FRP bar and beam cross-sectional shape.     

High-Cycle Fatigue of Diagonally Cracked Reinforced Concrete Bridge Girders: Field Tests

Large numbers of conventionally reinforced concrete deck–girder (RCDG) bridges remain in-service in the national highway system. Diagonal cracks have been identified in many of these bridges, which are exposed to millions of load cycles during service life. The anticipated life of these bridges in the cracked condition under repeated service loads is uncertain. RCDG bridges with diagonal cracks were inspected and instrumented. Strain and crack displacement data were collected under ambient traffic conditions and controlled test trucks. Results indicated relatively small stirrup stresses and diagonal cracks exhibited opening and closing under truck loading.     

Effect of Fiber-Reinforced Polymer Wraps on Corrosion Activity and Concrete Cracking in Chloride-Contaminated Concrete Cylinders

This paper presents the results of an experimental study designed to investigate the effect of fiber-reinforced polymer (FRP) wraps on corrosion activity and concrete cracking in chloride-contaminated concrete cylinders. Thirty-five concrete cylinders, each having 102?mm diameter and 204?mm height, concentrically reinforced with one steel reinforcing bar, were subjected to accelerated corrosion exposure for 80?days. Test parameters included level of applied potential, presence of FRP wraps, and bar diameter. The corresponding current and concrete expansion were continuously monitored throughout the corrosion exposure. At the end of the test, the steel bars were extracted, cleaned of rust, and weighed to determine the actual steel mass loss. The results showed that, for the same applied fixed potential, FRP wraps effectively reduced the corresponding current, the concrete expansion, and the steel mass loss. For the same applied potential, the current density increased as the bar diameter decreased. For the same corrosion depth, the circumferential expansion of the cylinder caused by corrosion decreased as the concrete cover-to-bar diameter ratio (c/d) increased.     

Concrete Contribution to the Shear Resistance of Fiber Reinforced Polymer Reinforced Concrete Members

Seven beams were tested in bending to determine the concrete contribution to their shear resistance. The beams had similar dimensions and concrete strength and were reinforced with carbon fiber reinforced polymer bars for flexure without transverse reinforcement. They were designed to fail in shear rather than flexure. The test variables were the shear span to depth ratio, varying from 1.82 to 4.5, and the flexural reinforcement ratio, varying from 1.1 to 3.88 times the balanced strain ratio. The test results are analyzed and compared with the corresponding predicted values using the American Concrete Institute, the Canadian Standard, and the Japan Society of Civil Engineers (JSCF) fiber reinforced polymer design recommendations. Based on these results and previous experimental data, it is shown that the ACI recommendations are extremely conservative whereas the Canadian and JSCE recommendations, albeit still conservative, are in closer agreement with the experimental data. Overall the Canadian Standard’s predictions are in better agreement with experimental data than the JSCE predictions.     

Rehabilitation of Cracked and Corroded Reinforced Concrete Beams with Fiber-Reinforced Plastic Patches

The behavior under static loading of fiber-reinforced plastic (FRP) retrofitted reinforced concrete beams, possessing a high chloride content and rebar corrosion, was studied both experimentally and analytically. The test beams were characterized as falling into three different groups according to the state of their corrosion damage: (1) natural corrosion, (2) cathodic protection, and (3) accelerated corrosion. The load carrying capacities of the beams, with or without FRP patching, were tested in the laboratory. The experimental results show that the state of corrosion of the steel, the water/cement ratio of the concrete material, and the arrangement and the number of FRP patches all affect the strength as well as the failure mechanisms of retrofitted RC beams. Some simple analytical models and a design concept for retrofitting cracked and corroded RC beams with FRP sheets are also presented and discussed.     

Cracking and Reinforcement Corrosion in Short-Span Precast Concrete Bridges

A nationwide survey revealed 14 states having bridges comprised of precast, nonprestressed, concrete channel beams. Currently, the Arkansas State Highway and Transportation Department (AHTD) bridge inventory includes approximately 389 in-service bridges using 5.79?m precast channel beams that were constructed using 1952 AHTD bridge details. Results from a statewide inspection of these bridges conducted by the writers revealed bridges with extensive concrete longitudinal cracking at the flexural reinforcing steel level and exposed reinforcing steel. Approximately 2,000 beams in 95 precast concrete channel beam bridges were inspected during a statewide investigation; longitudinal cracking at the reinforcing steel level was observed in 60.4% of the beams and exposed flexural reinforcement in 21.2%. A combination of flexure cracking from the live-load overloads and the presence of moisture has led to this high level of beam deterioration. The source of this moisture is humidity and water seepage at joints between adjacent beams. This paper examines the causes of longitudinal cracking deterioration by examining the influences of water permeation and humidity on the corrosion of flexural reinforcement in precast concrete channel beams.