## Continuum crack propagation models CCPM

The continuum crack can be divided into Smeared crack propagation model (SCPM) and Damage mechanics crack propagation model. In these models the fracture is idealized to propagate as a blunt front smeared over an entire element or a certain band width of the element. After initiation of the fracture process, determined by a suitable constitutive model, the pre-crack material stress- strain relationship is replaced by an orthotropic relationship with material reference axis system aligned with the fracture direction. The tension stiffness across the crack plane is either eliminated suddenly or a gradual stress-release criterion is applied. Thus, only the constitutive relationship is updated with propagation of cracks and the finite element mesh is kept unchanged. The advantage of the models lies in its simplicity and cost effectiveness, although the physical nature of crack representation is questionable. The tendency of the model to cause diffused crack pattern and the directional bias caused by slanted finite element mesh are still significant computational difficulties. However, the model has been extensively used in the seismic response study of concrete gravity dams.

### 5.3 Constitutive models for crack propagation

To conduct a comprehensive fracture propagation analysis, the selected constitutive model should describe the prefracture material stress-strain behavior, the fracture initiation and propagation criteria, and the post-crack behaviour. It is a usual practice in concrete structure analysis to presume linear elastic behaviour before the onset of tensile fracture process. The behaviour of concrete under high compressive loading is predominantly nonlinear. Several models based on the concepts of elastoplasticity and elasto-viscoplasticity have been proposed, to study the nonlinear behaviour of concrete under compression. However, the compressive stresses in concrete gravity dams are expected to be low even under severe ground excitations. A reasonable assumption of linear elastic behaviour under compressive loading has been applied in almost all previous investigations. It is almost universal in the constitutive models of fracture analysis to assume the initiation of new cracks in a homogenous structure when the principal tensile stress reaches the tensile strength of concrete. Diversity in various models lies in the definition of the fracture propagation criteria after the crack has been introduced in the structure. Major developments in the realms of crack propagation analysis and their relative merits are presented in the following sections.

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