The Mohr-Coulomb criterion has two shear strength parameters commonly known as the cohesion and the friction angle. The peak shear strength of granular materials obtained from direct shear tests has common non-linear strength envelopes due to particle crushing. The effective cohesion continues to increase while the effective friction angle decreases with the increase of effective stress in direct shear tests. Particle crushing of granular materials in direct shear tests leads to a power-law distribution of fragment sizes, and is accurately characterized by the fragmentation fractal dimension drawn from the power exponent. Based on the fractal model for particle fragmentation, a power function is advocated to represent the shear strength criterion of granular materials involving only two constant parameters. The exponent of power-law shear strength criterion is found to express using the fragmentation fractal dimension. The proposed power-law shear strength criterion is validated with experimental data of municipal solid waste incineration (MSWI) bottom ashes from direct shear tests. (C) 2018 Elsevier B.V. All rights reserved.