Crack-tip plastic zone and initiation mechanism of rock based on Eshelby stress

Abstract

The crack initiation and propagation mechanism of rock is significantly related to characteristics of the crack-tip plastic zone due to energy dissipation. In this paper, conservation integral and configurational stress/force is derived by the Noether’s method. The crack-tip configurational stress field is then deduced and analyzed. Additionally, the Drucker–Prager yield criterion of configurational stress is derived and it is used to predict the crack-tip plastic zone of rock. The fracture criteria of rock are also developed based on the critical area and minimum polar radius of the crack-tip plastic zone. Subsequently, the effects of bedding dip angles and porosity on rock mixed mode fracture are investigated, and the fracture resistance of rock is assessed using the resistivity and wave velocity. It is shown that the configurational force as the crack driving force is induced by the invariant transformation of an action integral with respect to translation of a defect. It is also found that the crack-tip plastic zone assessed by Drucker–Prager yield criterion of Cauchy stress is discontinuous at the crack surface while that predicted by yield criterion of configurational stress is continuous. The present fracture criteria take into account the internal friction angle, and the predicted initiation angles and fracture loads are in good agreement with those determined by the maximum tensile stress (MTS) fracture criterion and experiments. The fracture loading envelope decreases with the porosity, bedding dip angles and resistivities of rock, but increases with wave velocity.