Abstract
Strength of concrete is widely scattered because of the heterogeneity of this composite materials. So far, no generally accepted theory to describe the stochastic nature of concrete properties is available. In this paper, a stochastic theory for fracture of materials is presented. This theory is based on physically relevant models. It is possible to describe the fracture process and provide a realistic basis for a mathematical formulation of the variability of porous materials. Especially, the present paper is concerned about the size effect of concrete materials. It's clarified by theoretical consideration that the effect of specimen size on fracture strength is affected by the failure process. Therefore, the size effect is changed between tensile fracture and compressive fracture. The tendency of this theoretical consideration agrees with the results of past experimental investigations. This stochastic model is also available for the investigation of the fact that non-linear stress strain behavior is changed by the quantity of aggregates, or the degree of cracking arrest effect.
