Prediction of Fatigue Strength in Plain and Reinforced Concrete Beams

ACI Structural Journal, Sep/Oct 2007 by Sain, Trisha, Kishen, J M Chandra

A fatigue crack propagation model for concrete is proposed based on the concepts of fracture mechanics. This model takes into account the loading history, frequency of applied load, and size effect parameters. Using this model, a method is described based on linear elastic fracture mechanics to assess the residual strength of cracked plain and reinforced concrete (RC) beams. This could be used to predict the residual strength (load carrying capacity) of cracked or damaged plain and reinforced concrete beams at a given level of damage. It has been seen that the fatigue crack propagation rate increases as the size of plain concrete beam increases indicating an increase in brittleness. In reinforced concrete (RC) beams, the fracture process becomes stable only when the beam is sufficiently reinforced.

Keywords: fatigue; fracture toughness; residual strength; stress.

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INTRODUCTION

In recent years, condition monitoring, repair, and retrofitting of existing structures such as buildings and bridges have been among the most important challenges in civil engineering. The primary reasons for condition assessment and consequent maintenance/strengthening of structures include enhancement of resistance to withstand underestimated loads, increase in the load-carrying capacity for higher permit loads, restoration of lost carrying capacity due to corrosion of structural steel or reinforcing bars, and cracking of concrete or other types of degradation caused by aging. Whereas a lot of research has been done in the area of repair and retrofitting of aged structures, not much has been reported on the assessment of current structural condition so as to estimate the residual capacity at present-day enhanced load levels. The assessment requires that any damage in the structure be detected before it has developed to a dangerous size. The concepts of fracture mechanics may be used as a mathematical tool for assessment of residual strength for providing equations that can be used to determine how cracks grow and how cracks affect the fracture strength of a structure.

It is well known to designers that fatigue accounts for a majority of material failures. In metallic structural components, fatigue is a well understood phenomenon, causing irreversible material damage (Paris and Erdogan 1963). In the case of concrete, the fatigue mechanism is different from that in metals due to dissimilar fracture behavior. In plain and reinforced concrete structures, fatigue may lead to excessive deformations, excessive crack widths, debonding of reinforcement, and rupture of the reinforcement or cement mortar matrix leading to structural collapse (Perdikaris and Calomino 1987).

Fracture of concrete is characterized by the presence of a fracture process zone (FPZ) at the crack tip as shown in Fig. 1. In this figure, the effective crack length aeff is longer than the true crack but shorter than the true crack plus the FPZ. The FPZ is a zone where the cement mortar matrix is intensively cracked. Along the FPZ, there is a discontinuity in displacements but not in the stresses. The stresses are themselves a function of the crack opening displacement (COD). At the tip of the FPZ, tensile stress is equal to tensile strength ft' of the material and it gradually reduces to zero at the tip of the true crack. It is assumed that under low-cycle fatigue loading, the resulting damage, that is, the decrease in load-carrying capacity and stiffness, occurs primarily in the FPZ and not in the undamaged material (Foreman et al. 1967). In most of the nonlinear material models for fatigue of concrete, it is assumed that only the FPZ is responsible for the variation of material properties during cyclic loading. If the fracture process zone exhibits greater sensitivity to fatigue loading than the surrounding material, then the fatigue behavior can be considered to be dependent on loading history (Slowik et al. 1996). Furthermore, the size, shape, and fatigue behavior of the FPZ are dependent on specimen size and geometry (Zhang et al. 2001). Thus, loading history is of paramount importance in fatigue behavior of concrete and only a nonlinear fracture mechanics model can rigorously explain it. Therefore, the cumulative damage theory based on Palmgren-Miner's hypothesis is not applicable for the fatigue behavior of concrete specimens (Oh 1991). A method for residual life prediction of plain concrete has been proposed by Zhang and Wu (1997), but it is based on the S - N curve approach, where S is the cyclic stress level and N is the number of cycles to failure.

In this study, a fatigue crack propagation model is proposed by modifying the one proposed by Slowik et al. (1996). The proposed modification includes the development of a closed form expression to compute the sudden increase in crack growth due to overloads. Furthermore, the crack growth rate can be computed for any frequency of applied loading that was not possible in the original model. This improved fatigue law is used in the assessment of residual strength for plain and reinforced concrete beams.