Issue 27

G. Kuidong et alii, Frattura ed Integrità Strutturale, 27 (2014) 43-52; DOI: 10.3221/IGF-ESIS.27.06 47 2 t 2 c cos ( ) cos( ) 2 2sin 4 sin ( ) sin a d               (14) In this paper, the derivation process of theoretical model takes Evans work as reference. So, the energy of cutting system will be minimum at the moment of rock broken presumed by Evans as an equilibrium situation. For this reason, this paper can use the ‘minimum energy theory’ as theoretical basis. According to the minimum energy theory: d( / ) / d 0 a d   (15) Now, the relationship between  and  can be obtained and expressed as: 2 2 2 t t 2 2 c c 2 sin( ) cos( )sin( ) 2sin cos ( ) cos ( ) cos( ) 4 sin ( ) cos ( ) 2 2 2sin 4 sin 4 sin 0 sin sin                                       (16) B represents the ratio of rock compressive strength to tensile strength. From Eq.16, we can conclude that it is difficult to get the analytical solution of Eq.16. Consequently, the effects of cutting parameter  and ratio B on vertical fracture angle ψ are investigated, and the change law of ψ along with  and B is shown in Fig.3. Fig.3 shows that ψ increases with  and B . In order to get intuitive relationship among ψ ,  and B , the data points of numerical solution in Fig.3 are regressed based on space surface regression method. The regression formula of vertical fracture angle ψ can be expressed as Eq.17, and the correlation coefficient of formula is 0.994. 2 48.87 0.526 0.224 0.994 B R       (17) Figure 3 : Variation law of vertical fracture angle of rock fragment. V ERIFICATION OF THE MODEL orizontal fracture angle of rock fragment is directly related to the optimal intercept of conical picks. The optimal intercept of conical picks in rock cutting process is 3.46 times the cutting depth according to Evans calculate method [1]. Optimal intercepts of 22 different rock types have been obtained through rock cutting experiments by Bilgin [5], and their values are very close to 3.23 times the cutting depth. In view of 7% difference between Evans calculated result and Bilgin experimental result, Evans calculate method is considered reliable and correct. So, in this paper, horizontal fracture angle of rock fragment in the mathematical model for predicting the peak cutting force will adopts Evans calculate model, which means that horizontal fracture angle is equal to 60 degree. Verification of vertical fracture angle In order to verify the correctness of vertical mechanical model of rock fragment in this paper, rock cutting experiments are carried in laboratory as shown in Fig.4. The semi-angel of conical pick is 40 degree, cutting angle of conical pick is selected in range of 45~55 degree according to actual working condition, and the mechanical properties of marble is H