A thorough understanding of fracture and scaling of quasi-brittle materials is important for engineering practice. The quasi-brittle materials include a broad range of widely used materials such as concrete, rock, ceramic, and some polymer matrix composites. However, the fracture and failure criteria of these materials are not yet completely understood. This dissertation attempts to clarify these criteria. It consists of four parts: (1) A numerical study of fracturing damage behavior in column stability. The basic phenomena in inelastic column buckling under flexible end restraints are explained. The so-called 'naively optimal' elastic bracing is analyzed and is shown to occur when the critical loads for the symmetric and antisymmetric buckling modes coincide. The study reveals that the ACI approach is quite conservative in most but not all cases and suggests some simple ways to improve it. (2) A study of the size effect law for the compression failure of concrete columns. The reduced-scale reinforced concrete columns which were tested by Bazant and Kwon (1994) are analyzed from the viewpoint of energy release. A simplified model of compression failure is developed and used to simulate the test results, and the size effect is predicted. (3) A numerical study of a constitutive model for the general nonlinear triaxial behavior of concrete. The study deals with a new form of the well-known microplane model, in which the new concept of stress-strain boundaries is introduced. The model is generalized to finite strain. The formulation obtained is simpler than the previous microplane model, yet more realistic, especially for the post-peak strain-softening. The new formulation is verified and calibrated by test data on tensile, compressive, shear and triaxial deformations and failure. (4) An experimental study of time-dependent concrete fracture. Two groups of notched fracture specimens of concrete, with a normal strength and a higher strength, are tested, using different sizes and load levels. The test results are modeled and three different stages of response are distinguished. The effects of creep in the bulk as well as rate-dependent breakage of bonds at the fracture front are considered. It is shown how Bazant's size effect law can be generalized to predict the life-times.
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