Peak strength of replicated and real rocks containing cracks

This paper studies the peak strength of cracked solids using real rocks (e.g. marbles and granites) and replicated rock (a sandstone-like modelling material by Wong & Chau [12]) under uniaxial compressive stresses. Sandstone-like specimens, which contain various number of parallel frictional cracks ranging from eighteen to forty-two (i.e. with varying initial crack density εo), are used to study the failure mechanism of the cracked solids. Two main observations for replicated rock are: (1) the overall failure angle θ (the angle between the fracture plane and the direction of uniaxial compression) is ≤ 1/2tan-1(1/μ) (μ is the frictional coefficient on the crack surfaces); and (2) peak strength of the specimens does not depend on the initial crack density εo but depends on the total number of cracks involved in the coalescence process. For real rocks, the normalized peak strength of rock drops rapidly with εo then remains roughly constant with the crack density if εo > 0.03. Our experimental observations on replicated rocks provide a plausible explanation on this experimental observation that the peak strength of real rocks is roughly constant when a threshold value of crack density is exceeded. To reinforce our speculation, we show that the peak strength prediction by Ashby-Hallam [7] agrees with our experimental data.