Each of the seismogenic locked segments in a well-defined seismic zone can accumulate high strain energy to bring about a major earthquake. Hence, better understanding the physical implication of self-organized criticality in the locked segment (rock) failure process is crucial to achieving insights into such issues as earthquake predictability and so on. We point out that there exist two critical points in the locked segment fracturing process. The first critical point is volume expansion point, which is the starting point of self-organization, at which a rupture event with high energy occurs. It can be regarded as the only identified precursor to macroscopic rupture of locked segment. The second critical point is the peak strength point, namely, the instability point, at which a major earthquake which is able to generate obvious surface rupture zones takes place. According to our previous research on the theoretical relationship of strain ratio between the two points as well as the constrained expressions concerning earthquake magnitudes and elastic strain energy, also known as the theory about the brittle failure of multiple locked segments in a seismogenic fault system, we can predict some characteristic earthquakes occurring at the first and the second critical point of locked segment, e.g., the 2004 Sumatra-Andaman MW9.0 earthquake in Indonesia, the 2008 Sichuan MS8.1 earthquake in China, and the 2011 Tōhoku MW9.0 earthquake in Japan. This was obtained by retrospectively analyzing the earthquake cases in 62 seismic zones covering the circum-Pacific seismic belt and the Eurasia seismic belt. The present results show that the self-organized process before the locked segment (rock) instability must arise due to its heterogeneity; there exists a causal link between the self-organization and criticality; it is possible to predict some large earthquakes (e.g. characteristic earthquakes) just because of the existence of self-organized process. We emphasize here that the damage process between the two critical points is not transient behavior, usually a long-term process; the evolution of characteristic earthquakes follows a deterministic rule; there is no probability with which small earthquakes can cascade into a large event (e.g. characteristic earthquakes). In summary, this study can help to comprehend the evolutionary mechanism of characteristic earthquakes, provide a physical basis of understanding the generation process of earthquakes, and clarify such issues as the identification of earthquake types and predictability of earthquakes.