Numerical Model for Time-Dependent Fracturing of Concrete

A finite-element formulation for the analysis of time-dependent failure of concrete is presented. The proposed formulation incorporates: (1) the viscoelastic behavior of uncracked concrete through a Maxwell chain model; and (2) the inelastic behavior of damaged concrete, characterized by a modified version of the microplane Model M4 which includes the rate dependence of fracturing. The proposed formulation is applied to the simulation of quasi-static concrete failure in the time domain. The different effects of creep and rate dependence of crack growth and their role in the lifetime of concrete structures are studied. The influence of different loading rates on the size effect is also analyzed with reference to single notched specimens, revealing the link between the size of the fracture process zone and the loading rate. The capability of the proposed numerical formulation is also verified for the case of sustained uniaxial compressive loads.     

Fatigue Fracture of Concrete Subjected to Biaxial Stresses in the Tensile C–T Region

In this paper cyclic quasi-static and constant amplitude fatigue responses of concrete subjected tensile compression–tension (C–T) biaxial stress are presented. In the tensile C–T region within the biaxial stress space, magnitude of the principal tensile stress is larger than or equal to that of the principal compressive stress. An experimental program consisted of subjecting hollow, cylindrical concrete specimens to torsional loading. Failure in both quasi-static and fatigue is due to crack propagation. It is shown that the crack propagation resulting from the biaxial loading can be predicted using Mode I fracture parameters. The fatigue crack growth is observed to be a two-phase process: an acceleration stage that follows a deceleration stage. The crack length where the rate of crack growth changes from deceleration to acceleration is shown to be equal to the crack length at the quasi-static peak load. Analytical expressions for crack growth in the deceleration and acceleration stages are developed in terms of the mechanisms that influence quasi-static crack growth. The model parameters obtained from uniaxial fatigue tests are shown to be sufficient for predicting the biaxial fatigue response. Finally, a fracture-based fatigue-failure criterion is proposed, wherein the fatigue failure can be predicted using the critical Mode I stress intensity factor.     

Simulation of Crack Propagation in Asphalt Concrete Using an Intrinsic Cohesive Zone Model

This is a practical paper which consists of investigating fracture behavior in asphalt concrete using an intrinsic cohesive zone model (CZM). The separation and traction response along the cohesive zone ahead of a crack tip is governed by an exponential cohesive law specifically tailored to describe cracking in asphalt pavement materials by means of softening associated with the cohesive law. Finite-element implementation of the CZM is accomplished by means of a user subroutine using the user element capability of the ABAQUS software, which is verified by simulation of the double cantilever beam test and by comparison to closed-form solutions. The cohesive parameters of finite material strength and cohesive fracture energy are calibrated in conjunction with the single-edge notched beam [SE(B)] test. The CZM is then extended to simulate mixed-mode crack propagation in the SE(B) test. Cohesive elements are inserted over an area to allow cracks to propagate in any direction. It is shown that the simulated crack trajectory compares favorably with that of experimental results.     

Shrinkage in Concrete Masonry Walls: Case Study

In spite of our understanding and knowledge of the properties of concrete masonry as a material, shrinkage continues to be a problem affecting the performance of concrete masonry walls. A case study is presented which suggests that the behavior of concrete masonry walls subjected to the shrinkage of units is not completely understood. The paper discusses causes in material standards, design specifications, manufacture and construction practice which may contribute to shrinkage cracking of concrete masonry walls.     

Determining the Tensile Stress-Crack Opening Curve of Concrete by Inverse Analysis

The determination of the fundamental stress versus crack opening (σ-w) response of concrete under uniaxial tension is performed in this study through inverse analysis using data from notched beam tests. The procedure used for optimizing the parameters of the σ-w relation using the load versus crack mouth opening displacement response of the notched beam is described. Satisfactory comparisons have been obtained between the σ-w curves obtained through the inverse analysis and those directly measured in uniaxial tension tests. The use of weighting functions in the inverse analysis may be necessary when large crack widths are to be considered.     

Modeling the Structural Effects of Rust in Concrete Cover

Vast governmental budgets are spent annually to face corrosion problems of steel reinforcement in concrete bridges attributable to the extensive use of deicing salts. Corrosion controls the lifetime of a bridge, which has two distinct periods. During the first period, chlorides diffuse through the cover. When sufficient chlorides are formed at the rebars, corrosion initiates. This marks the start of the second period, during which rust with higher volume to bare steel is produced. The rust puts pressure on the cover, which finally leads to cover spalling. In this paper, a model is developed to determine the time span of the second period. The model includes a volume compatibility condition that allows for the proper introduction of compaction of all materials that contribute to cover spalling, including the rust. A new condition for marking failure of the cover is also established, based on fracture mechanics and strain energies. Finally, a new formula is proposed for the rate of rust production, which allows for the constant rust production at early and nonlinear diffusion dependant rates at latter stages of corrosion.     

Simplified Model for Wall Deflection and Ground-Surface Settlement Caused by Braced Excavation in Clays

Accurate prediction of ground-surface settlement adjacent to an excavation is often difficult to achieve without using accurate representation of small-strain nonlinearity in a soil model within finite-element analyses. In this paper a simplified semiempirical model is proposed for predicting maximum wall deflection, maximum surface settlement, and surface-settlement profile due to excavations in soft to medium clays. A large number of artificial data are generated through finite-element analyses using a well-calibrated, small-strain soil model. These data, consisting of wall displacements and ground-surface settlements in simulated excavations in soft to medium clays, provide the basis for developing the proposed semiempirical model. The proposed model is verified using case histories not used in the development of the model. The study shows that the developed model can accurately predict maximum wall deflection and ground-surface settlement caused by braced excavations in soft to medium clays.     

Coupled Mechanical and Chemical Damage in Calcium Leached Cementitious Structures

Long-term durability of concrete structures must be faced both from the point of view of cracking and physical degradations. In this paper, the relevance and the sensitivity of an existing constitutive relation aimed at modeling mechanical and chemical damage is examined. This constitutive relation is based on a scalar continuum damage model. The chemical degradation mechanism is calcium leaching. It is observed that the model predictions, i.e., the lifetime of cement-based beams subjected to leaching, are very sensitive on the tensile strength and fracture energy of the sound material. The existing model predicts the response of bending beams subjected to various states of leaching prior to any mechanical loading. The simulation of the size effect tests shows that the mechanical internal length and the damage threshold of the material cannot be considered to be constant. The internal length ought to decrease and the damage threshold should increase.     

Mode II Fracture Localization in Concrete Loaded in Compression

As an alternative to a series-coupling model for localization of deformations under uniaxial and confined compression, an approach based on Mode II crack growth is proposed. Such a model appears to be in closer agreement to experimental observations than the presently used series-coupling model, and has the advantage that both material and structural aspects of softening are incorporated directly. Similarities to tensile fracture exist that would make the approach universal.     

Assessment of Retrofit Dowel Benefits in Cracked Portland Cement Concrete Pavements

A parametric study was conducted using the finite-element rigid pavement program ISLAB2000. For cracks that utilize aggregate interlock as the sole means of load transfer, the integrity of the cracks was initially modeled using the aggregate interlock factor. A subsequent analysis was then performed on the same cracks for the case where both dowel bars and aggregate interlock were available for load transfer purposes. The latter scenario represents the case where dowel bar retrofitting (DBR) has been performed on the cracks. In both cases, the deflection load transfer efficiency and critical slab tensile stresses were computed in order to examine the immediate theoretical benefits of the dowel bars. The validity of these theoretical benefits was tested using data from falling-weight deflectometer testing on DBR sites in both Michigan and Washington. It was found that installation of dowel bars did not increase the load transfer efficiency for cracks that had levels greater than 89–95%, depending on pavement parameters. When temperature gradients were not considered, little change in tensile stress due to a load at the crack was exhibited when DBR was performed on cracks that had load transfer efficiency levels less than 70–80%.     

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.     

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.     

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.     

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.     

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.     

Permeability due to the Increase of Damage in Concrete: From Diffuse to Localized Damage Distributions

Experimental tests exhibit a strong interaction between material damage and transport properties of concrete. There are at least two asymptotic cases where some theoretical modeling exists: in the case of diffuse cracking, the material permeability should be controlled by damage, e.g., by the decrease of average stiffness due to microcracking. In the case of localized microcracking, and after a macrocrack has formed, permeability should be controlled by a power function of the crack opening (Poiseuille flow). For quasi-brittle materials with evolving microstructure due to mechanical loads, a transition regime on the evolution of permeability between these two asymptotic cases is expected. In this contribution, we define a relationship between permeability and damage that is consistent with the two above configurations. One of the key issues is to relate the crack opening to the state variables in the continuum approach, so that the two asymptotic cases are expressed in the same variable system and can be matched. A simplified approach is used for this purpose. The permeability law is then derived using a mixing formula that weights each asymptotic regime with damage. To illustrate the influence of the matching law on structural response, finite-element simulations of a Brazilian splitting test and a comparison with existing test data are presented.     

IC Debonding of FRP NSM and EB Retrofitted Concrete: Plate and Cover Interaction Tests

The use of fiber-reinforced polymer (FRP) externally bonded (EB) plates is widely accepted as an efficient and unobtrusive retrofitting technique. FRP near-surface mounted plates are now also gradually gaining acceptance due to their substantial increase in debonding strains over EB plates. However tests have shown that the intermediate crack (IC) debonding resistances of FRP plates can be reduced by their interaction with adjacent parallel plates and with parallel free surfaces, that is the cover; this is often reflected in design rules where the IC debonding resistance of individual plates depends on the width of the plate as a proportion of the width of the concrete specimen and on the cover. In this paper, 22 new pull tests are reported that study the IC debonding interaction with adjacent plates and cover. The results are encouraging as they show that there is little reduction in the IC debonding resistance until the lateral cover or gap between plates is relatively small.     

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.     

Long-Term Deflection and Cracking Behavior of Concrete Beams Prestressed with Carbon Fiber-Reinforced Polymer Tendons

This paper discusses the experimental result on the long-term deflection and cracking behavior of concrete beams prestressed with carbon fiber-reinforced polymer (CFRP) tendons, under sustained long-term service load, including cracked and uncracked sections. Six full-scale beams were cast and tested. The experimental parameters included the level of prestress, the level of sustained service loading, and concrete strengths. The experimental results showed that the performance of concrete beams prestressed with CFRP tendons meets the serviceability criteria in terms of deflection and cracking. The test results also showed that the long-term performance of concrete beams prestressed with CFRP tendons was comparable to those prestressed with steel tendons. Furthermore, the test results showed that with the increase of concrete strength, the serviceability performance also improved with concrete beams prestressed with CFRP tendons.