Abstract: Two classifications of gradient plasticity theory and their differences are introduced. Subsequently, the general constitutive relation of gradient plasticity theory is established by introducing the gradient term of hardening parameter into material's yielding function. Considering the particularity of rock material, a gradient plastic model with plastic bulk strain as internal variable is established by introducing its gradient term to Drucker-Prager yield model. The expression of plastic bulk strain is presented based on the classical plasticity theory, and the increment constitutive relation of rock's strain localization is derived. At last, rock's strain localization in uniaxial stress is analyzed in the condition of the plane strain. As a result, the expression of the strain localization band width is deduced, and the band width variation when the localization band parameter changes is derived.

Key words: rock fracture, strain localization, gradient plasticity theory, internal variables, shear band