ANALYSIS OF LOCALIZED DEFORMATION IN SHEAR BAND CONSIDERING DEGRADED STIFFNESS BASED ON GRADIENT-DEPENDENT PLASTICITY

Distributed shear strain and displacement in localized shear band were investigated considering degraded stiffness in the strain-softening process based on gradient-dependent plasticity. Shear band was treated as a one-dimensional shearing problem and constitutive relation between shear stress and shear strain was bi-linear elastic and strain softening. Elastic shear strain in shear band was dependent on shear elastic modulus, damage variable and residual shear modulus. The bi-linear constitutive relation determines the total shear strain in shear band. Subtracting the elastic strain from the total strain yields the non-local plastic shear strain that depends on the flow stress and the damage variable. A yield function was proposed to consider damage in the context of classical plastic theory. The second-order shear strain gradient was introduced into the yield function. Analytical solution of the local plastic shear strain in shear band was derived and then the local plastic shear displacement was obtained by integrating the local plastic shear strain. Analytical results show that after the degraded stiffness is involved in the present model, elastic shear strain (or displacement) increases while plastic part decreases. Degraded stiffness has no influence on the stability of the system composed of shear band and elastic rock. Present analytical solutions can be simplified as earlier results without the degraded stiffness. Compared with in situ observation for localized shear deformation of rock, the validity of the proposed analytical solutionsconsidering degraded stiffness and strain gradient was verified.