Rocks are quasi-brittle materials that inherently contain different types of flaws, microcracks and inhomogeneity, which are weak under tensile loading. The tensile strength of rock is significant parameter for rock mechanics designers, which plays the dominant role in rock cutting, fracturing and fragmentation on blasting. In general, fractures in rock initiate from tiny cavities and micro-fractures, then coalescence to form macro-fractures, and finally fail. Most of the well-known failure criteria address only the ultimate stage of failure and ignore progressive damage on loading of the rock. To take account of the effect of micro-fractures in quasibrittle materials such as rocks, Continuum Damage Mechanics (CDM) has been used in this study. Recently, micro-fracture effects in rock and concrete have been investigated by using damage evolution in conjunction with thermodynamics theory. As micro-cracking and damage directly influence the rock elastic properties and elastic wave velocities, the ultrasonic properties of rock under loading provide a clear view of the development of micro-fracturing. The Brazilian test has been used to apply indirect tensile loading and has been coupled with the measurement of ultrasonic P and S-wave velocities.

1.1 Fracture mechanics and rock mechanics

Fracture mechanics is one the most significant key parameter in rock mechanics design analyzing for underground and on the ground civil and road construction projects. The major reason of fracturing and damage in rocks is contributing to a significant degradation of rock road-bearing capability. Furthermore knowledge of rock fracture mechanics and fatigue damage is significant source for rock cutting practices and fragmentation's industry. Unlike the other material in other engineers filed, rock normally suffers from different type of inhomogeneity and discontinuity to be dealt with. These parameters directly effect on rock strength value and hence influence on the rock support size in one hand and size of the rock cutting machinery in the other hand. Since the prior experiments and studying, fracture mechanics has been employed in deep mining hard rock analyzing. The structural parameters are shown to be the other important factor in rock fracturing which includes; rock grain sizes and characteristics, pre induced cracks, micro and macro fractures before loading and during loading process, dimension and physical condition of environment involving in rock testing time. The third and also most significant key role in the rock fracture is studying mechanical behavior induced by different loading that cause different types of fracture pattern in rock matrix. Different approaches have been developed from the linear elasticity and fracture mechanics by (Bieniawski & Tonder 1969) and (Brady & Brown 2006) to the several developed numerical methods to simulate fracturing process in rocks (Anderson 1995). Based on the different numerical methods, FEM is more common methods using different techniques for re-meshing and applying different small elements for modeling fracture initiation and growth through (Jing & Hudson 2002).

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