“…According to tensile strength criterion, hydraulic fractures on the wellbore wall initiate when the principal tensile stress within the rock (due to the fluid pressure within the rock) exceeds the minimum principal stress plus the tensile strength of the rock (Haimson, 1967;Hossain, Rahman, & Rahman, 1967, 2000Hubbert & Willis, 1957). A series of lab experimental studies have been conducted in the past to investigate the influence of natural fracture on the fracture initiation and propagation under different reservoir conditions (Beugelsdijk, De Pater, & Sato, 2000;Blanton, 1986;Dehghan, Goshtasbi, Ahangari, & Jin, 2014Gu et al, 2012;Olson, Bahorich, & Holder, 2012;Suarez-Rivera, Burghardt, Stanchits, Edelman, & Surdi, 2013;Tie, Wei, & Xueliang, 2011;Warpinski & Teufel, 1987;Zhou, Chen, Jin, & Zhang, 2008;Zhou, Jin, & Chen, 2010). Some experimental investigations (Blanton, 1982;Daneshy, 1974;Lamont & Jessen, 1963) have demonstrated that the advancing induced hydraulic fracture crosses the natural fracture without any significant change in its direction, turns into the natural fracture and dilates it or, in some cases, turns into the natural fracture and beside the dilation of natural fracture, breaks out again by a fracture or flaw along the natural fracture.…”