Compressive fracture process of rock under the uni-axial compression is discussed, as a result of the sub-critical crack growth in it. A numerical procedure for the failure prediction is presented and discussed, basing upon the critical pressure-crack elongation curve (pc - a curve) for the pure mode I crack propagation (KII = 0, KI = KIC) in the homogenized joint model, which is analyzed by means of the Stress Compensation-Displacement Discontinuity Method (SC-DDM). The crack elongation rate (da/dt) is formulated by the empirical equation of the form of da/dt ∝ KIn, where n: the sub-critical crack growth index. The applied stress-crack elongation curve (p - a curve) in the uni-axial compression test is analyzed to clarify the strain rate dependency of the macroscopic compressive strength (Sc), and the time-crack elongation curve (t - a curve) in the creep test of the uni-axial compression is analyzed to evaluate the effect of applied stress upon the lifetime (tF). It is concretely shown that the non-linearity of stress-strain curves and time-strain curves is deeply associated with the sub-critical crack growth in rock. Moreover the significant influence of heterogeneity and in-homogeneity of rock is discussed by presenting a parallel plate model to assess the damage effect and so on.
