Cracks propagation and the friction coefficient belong to different research objectives and were seldom connected. The friction coefficient often come from experiments and lacked describing theoretically. Based on ‘Griffith ellipse cracks’

a ‘Griffith face cracks’ model which links the compression shear rupturing and microcrack friction is discussed. The macroscopic slit expectation

force

stress concentration that under uniaxial stress and three-axial stress situations is calculated. Because of locking

only cracks near the crack angle can extend. Larger stress ratio ( ) means smaller direction concentration ratio. The lock angle were increased with the increase of or confining pressure. Those tension cracks can not develop and transform into compression-shear cracks mode. Those convex-concave are from direction discrete of microcracks become the inclination angle of the asperities in a surface and affect the friction coefficient. The friction coefficient

direction concentration ratio and the stress ratio is a coupling relationship; on the one hand

large friction coefficient helps the direction concentrati

on the other hand

the direction concentration leads to the decrease of the average angle of asperities which in a macroscopic crack and decrease the friction coefficient furthermore. The coupling model reveals that the ambient pressure and stress is an important controlling factor of the friction coefficient. The stress ratio is often the conditions that allow the cracks developing. The friction coefficient were inversely proportional to the critical stress ratio. The average inclination angle of surface asperities and fractal dimensions of macrocracks have some memory function with respect to the stress condition and may thus be useful in characterizing the paleo-stress field.