The paper analyses the effect of structure size on the nominal strength of the structure that is implied by the cohesive (or fictitious) crack model proposed for concrete by Hillerborg et al. A new method to calculate the maximum load of geometrically similar structures of different sizes without calculating the entire load-deflection curves is presented. The problem is reduced to a matrix eigenvalue problem, in which the structure size for which the maximum load occurs at the given (relative) length of the cohesive crack is obtained as the smallest eigenvalue. Subsequently, the maximum load, nominal strength and load-point displacement are calculated from the matrix equilibrium equation. The nonlinearity of the softening stress-displacement law is handled by iteration. For a linear softening law, the eigenvalue problem is linear and independent of the matrix equilibrium equation, and the peak load can then be obtained without solving the equilibrium equation. The effect of the shape of the softening law is studied, and it is found that the size effect curve is not very sensitive to it. The generalized size effect law proposed earlier by Ba~ant, which describes a transition between the horizontal and inclined asymptotes of strength theory and linear elastic fracture mechanics, is found to fit the numerical results very well. Finally some implications for the determination of fracture energy from the size effect tests are discussed. The results are of interest for quasibrittle materials such as concrete, rocks, sea ice and modem tough ceramics.
A simple analytical model is developed to predict the average crack spacing and crack depth in highway pavements due to thermal loading. The pavement is modeled as a beam on a Winkler elastic foundation. The effect of cracks on the pavement is considered on the basis of compliance functions. A simple method is introduced to describe the behavior of the pavement material according to nonlinear fracture mechanics. It is shown that the material length in the fracture model should be defined by the total fracture energy, rather than the effective fracture energy. The effect of nonlinearity in the distribution of thermal stress across the pavement depth is also analyzed. The foundation of the pavement is found to have little importance. The theoretical predictions are shown to compare well with field observations on asphalt pavements.
The cohesive (or ficticious) crack model, characterized by softening stress-displacement relations, provides a good description of fracture of quasibrittle materials such as conrete, rock, or tough ceramics. The cohesive crack model is formulated in terms of compliance influence functions and the failure is analyzed as a stability problem. The size effect is determined by means of an eigenvalue problem. In this problem, the structure size for which a given relative crack length yields the maximum load is the eigenvalue. The model is further generalized to time dependence. The opening displacement is considered as a function of the cohesive stress and the opening rate of the crack. Finally, applications to rock and concrete are discussed.
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