PSI - Issue 32

S.S. Andreiko et al. / Procedia Structural Integrity 32 (2021) 3–9 V.Anikin / Structural Integrity Procedia 00 (2021) 000–000

5

0,612 ⁄ ∙ ,

(0) =

3

(7) where is the reduced initial pulse duration, ms/m; (0) is the initial pulse duration, s; is the explosive detonation velocity of E, m/s; 2.3. Initial Explosion Strain The initial explosion strain depends on the properties of used E (charge density, detonation velocity), physical and mechanical properties of the rock (density, speed of sound). These parameters in total determine the value of the reflection coefficient of the detonation blast wave from the walls of the charging cavity due to different acoustic stiffness of E and the rock of the exploded mass and are calculated by the following formulas [6, 8]: = ∙ ∙ 2 (1 + ) ⁄ (8) = 2 ∙ ∙ ( ∙ + ∙ ) ⁄ (9) = 2,1 ∙ (0,001 ∙ ) 0 , 73 (10) where is the reflection coefficient; is the rock density, kg/m 3 ; is the speed of propagation of the longitudinal wave in the rock, m/s; is the Grüneisen parameter of used E [3, 6, 8]; is the density of E, kg/m 3 . Formula (10) is an approximation of the empirical data of the dependence of the strain at the front of the detonation wave at the known explosive density and the velocity of its detonation, given in [6, p. 76]. Formula (1) mathematically does not allow calculating the initial explosion pulse of the borehole-rock boundary. Its value is calculated by expression [7]: 0 = ∙ (0) , (11) The strain damping rate in the rock mass is found experimentally. At the same time, the determination process itself is very laborious and costly; therefore, it is proposed to determine the damping rate for the studied rock by calculation based on the similarity of the curves of the rocks and the known curve of the reference rock, i.e. granite according to equation [6, 8]: ⁄ = ∙ ∙ ∙ ∙ 1 , 69 ⁄ (12) where is the initial strain in the studied rock, Pa; is the initial strain in granite, Pa; is the dimensionless distance from the blast center, expressed in the radii of the borehole; , , , are the density and velocity of propagation of longitudinal vibrations, respectively, in the studied rock and granite, kg/m 3 , m/s; is the degree of strain damping with the distance in the studied rock. Strain damping value is determined by the method of successive approximations until the equality of both sides of equation (12) is established. The experimental curve of the strain damping in granite in the range of 40-160 relative charge radii is approximated by a power law with a defining initial number of 54∙10 9 and a decay rate of 1.85 [6]. If the determining initial number is given the physical meaning of threefold initial strain in granite (8.169·10 9 Pa with ammonite 6ZhV), then it will become equal to 24.51∙10 9 and, accordingly, the degree of the strain damping will decrease to 1.69. This value is most typical for this type of rocks [5]. In this case, the calculated strain values at a distance in the range of 40-150 borehole radii converge with the experimental results with an error of less than 7 % [6]. At large where 0 is the initial explosion pulse, Pa·s; 2.4. Strain Damping Rate in the Rock Mass