ABSTRACT
ABSTRACT:A probabilistic model for failure of brittle materials under compression, based on Linear Elastic Fracture Mechanics (LEFM), is proposed herein. Crack length is taken as the model random variable. Phenomena like axial crack propagation, stable fracture propagation, interaction between cracks and tensile stresses induced by compressive load are considered. New parameters are introduced, explaining the development of the shear band and the decrease in length of critical cracks, both observed when confinement is present. The model has been analyzed under very simple situations, and compared to laboratory test results, applied to scale effect on compressive strength. A new technique was used in order to generate and control cracks in the interior of cast specimens employing polyester film strips. It was thus possible to obtain specimens with crack lengths both constant and proportional to specimen dimensions. These simulations proved that the model, under the particular conditions analyzed, as well as LEFM, are applicable to the prediction of scale effect on the compressive strength of brittle materials.1 INTRODUCTIONFracture mechanics has been frequently used for the analysis of different rock mechanics problems. Explanations have been found for some important phenomena in rock behavior (e.g. creep, fatigue, scale effect, aspects related to the stress-strain curve, etc.). Classical failure theories based on a limit stress were unable to explain those phenomena. In addition, the basic concept for the theoretical formulation of fracture mechanics involves a mechanism which is easily observed in brittle rock: crack propagation during failure process. However, questions have been raised with respect to the applicability of LEFM for the analysis of problems in rock and concrete because of discrepancies observed in the results of tests on small dimension specimens or cracks. This is usually attributed to the presence of the process zone at the crack tip (Hoagland et al. 1973; Rossmanith 1983; Labuz et al. 1987; Whittaker et al 1992). Another difficulty for the application of LEFM to geotechnical problems has to do with the type of load. Whereas LEFM requires the existence of tensile stress at the crack tip for crack propagation, typical loads in geotechnical problems lead to average compressive stresses. A probabilistic failure model for compressive load, based on LEFM was proposed by Bortolucci (1993). Its fundamental idea is that intrinsic material cracks are responsible for the two above mentioned aspects. The complexity of the phenomena involved during failure requires the model to be probabilistic. Only the most important variable (the length of cracks present in the sample) is considered as a random variable. All the other model parameters are considered to be deterministic. Because most of these parameters have not been adequately characterized yet, the model has just been calibrated by means of peculiar condition laboratory analysis of scale-effect on unconfined compressive strength of brittle materials. Rock-like material (Portland cement mortar with polyester film strips to simulate cracks) was used for the physical simulation. Crack length and density could be easily controlled in the beginning of the tests.