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　T5hoku　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.