First describe the selecting rule of the C-M and D-P failure criterion and the rule and the relations of the D-P criterion parameter with the rock mass fracture toughness; then through overlapped stresses in the end region of crackle, the total stresses about end region of tensile and sheared crackle can be obtained. The results are introduced into D-P failure criterion and C-M failure criterion, the relation between criterion D-P failure criterion, and rock fracture toughness KⅠc,KⅡc. can be derived. Compared with the results of experiments, which proved the validity of the derivation.Through overlapped stresses in the end region of crackle, the total stresses about end region of tensile and sheared crackle can be obtained. The results are introduced into D-P failure criterion and C-M failure, the relation between criterion D-P failure criterion, and rock fracture toughness KⅠc, KⅡc. can be derived. Compared with the results of experiments, which proved the validity of the derivation.