Issue 27

G. Kuidong et alii, Frattura ed Integrità Strutturale, 27 (2014) 43-52; DOI: 10.3221/IGF-ESIS.27.06 46 Figure 2 : Vertical mechanical model of rock fragment. Based on these assumptions, vertical mechanical model of rock fragment by conical pick is shown in Fig.2. According to the geometrical relationship in Fig.2, the force R is the resultant force of extrusion forces which acted on crush zone, and it has the relation with rock compressive strength and crush area. Meanwhile, the force R also increased with the height of crush zone ( a ), and it will reach a maximum when the torques caused by force T and force R on point C get balance. The force R can be expressed as: 90 c c (90 ) cos sin(2 ) sin a a R d               (9) where: γ is the cutting angle of conical pick; a is the height of crushing zone; σ c represents rock comprehensive strength;  is the cutting parameter of pick, and it equals to ( γ +  )/2. Rock will fracture along the arc AC when the force of conical pick applied on rock is big enough. However, the extreme state of rock fragment is determined by rock tensile strength, and the force T is the resultant force of tensile forces which acted on crack path. It can be expressed as: t t t cos 2 sin sin T d r d r               (10) where: r is the radius of the fracture arc AC;  stands for the complementary angle of vertical fracture angle. The force R and force T will reach a moment balance when the rock fragment forms. Therefore, an equation between them can be obtained according to geometrical conditions, and it can expressed as: sin cos( ) 0 sin 2sin d d R a T                (11) Submitting Eq.9 and Eq.10 to Eq.11, we have: 2 c t 2 cos( ) sin 0 sin sin 2sin a d d a                   (12) Changing Eq.12 to the form of quadratic equation: 2 t 2 c cos( ) 1 ( ) ( ) 0 sin sin 2sin w a a d d           (13) Solving Eq.13, the parameter a/d can be obtained and expressed as: