Abstract: In order to study the rock localization phenomenon, based on the examples of the stability of axial pressure bar, applied the mathematical and mechanical knowledge, according to Drucker-Prager criterion, a universal formula can be derived based on the bifurcation theory. On this basis, combined with the finite difference theory, the judging criterion of bifurcation in rock mass in FLAC3D calculation can be worked out. Then under the assistant of own FISH compile language, using the Drucker-Prager criterion, a numerical analysis model is established in FLAC3D to study the rock localization phenomenon and its development process. The results show that in FLAC3D the imbalance force ratio model system came from the 20 000 steps interval gradually tends to be stable, the unbalanced force ratio gradually reduces; the localization phenomenon gradually expands the scale to its stability; and the clarity increases gradually, which confirms that the bifurcation theory can effectively analyze the rock localization phenomenon. The rock bifurcation criteria of rock localization phenomenon and numerical verification given by this paper more scientifically and reasonably expound the origin of the universal bifurcation condition, so as to provide the theoretical support for the explanation of the mechanism and process of the rock localization phenomenon to play a promoting role.

Key words: bifurcation theory, localization phenomena, FISH language