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A new fracture criterion of the shear failure for the geomaterials is presented which predicts a straight extension of a crack in an elastic plastic material under compressive loads called “The maximum frictional shear stress criterion”. Weexamine the criterion by using both the singular and the constant terms in the asymptotic expansion of the crack tip stress fields for a non-associate linear hardening Drucker-Prager elastic-plastic material. As a result, we find that the confining pressure, the friction along the crack surfaces, the internal material friction, and the dilatancy effect are the lowering of the extensive hoop stress: Then they cause the maximum frictional shear stress to extend a crack straigh

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On a shear failure based on the maximum frictional shear stress criteria by using an asymptotic solution for a non-associate Drucker-Prager elastic-plastic material