Fracture mechanics criteria

Fracture mechanics is the theory dealing with propagation of cracks, based on the concept of energy dissipation by the structure undergoing fracturing process. It has been recognized only recently that the failure mechanism in concrete structures is different from the usual strength based concept, due to the progressive growth of a fracture process. The fracture mechanics of concrete has drawn significant attention of the research community over the last decade; as a consequence, the literature on the subject is voluminous. Here, only the principal developments in fracture mechanics, relevant to the seismic analysis of concrete dams, are reviewed.

Figure 5.1: Modes of failure: (a) mode I - Tensile fracture; (b) mode II -planar shear fracture; (c) mode III - tearing fracture

Three elementary modes of failure are recognized in the fracture theory (Figure 5.1). For two- dimensional idealizations, modes I and II (the opening mode and the planar shear mode) are usually considered. The third one, the tearing mode (mode III), is considered for three- dimensional fracture propagation studies. Fracture mechanics crack propagation models can be broadly classified into two categories the linear elastic fracture mechanics (LEFM) models and the nonlinear fracture mechanics (NLFM) models.

According to LEFM, the fracture process occurs right at the crack-tip and the entire volume of the material remains elastic (Figure5.2-a). The stress field around the tip of a sharp crack is characterized by the stress intensity factors, Ki, determined from linear elastic solutions:

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