PSI - Issue 32

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

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distances, the error doubles or more. The strain damping degree for other rocks was determined from expression (12) in the near explosion zone at a distance of 10 borehole radii, in which the main cracks originate and form. 3. Criterion of Destruction With a new destruction factor, a new destruction criterion should be used, i.e. the normalized crushing pulse, which is actually a characteristic of the dynamic strength of rocks. Its value is determined experimentally in laboratory conditions on standard rock samples by the impact crushing method [9, 10]. However, for the rocks indicated in Table 1, the values of this criterion are unknown. To simulate the dynamic resistance of a rock mass to the impact of an explosion, taking into account their physical and mechanical properties ( ρ , С , σ ), characteristics of explosives ( , D ) and the duration of the minimum destructive pulse of the explosion strain (0) , it is proposed to use the calculated dynamic strength index, which physically responds to the normalized crushing pulse [8-10]: = ∙ ∙ ∙ ∙ (0) ⁄ ∙ ∙ 0 2 (13) where is the theoretical design indicator of the dynamic strength of the rock, Pa∙s; is the empirical coefficient, depending on the type of E, for ammonite 6ZhV = 8; is the rock strength under uniaxial compression, Pa; 0 is the degree of crushing of the samples, corresponding to its stable destruction. Here, the crushing degree is defined as the ratio of the initial average sample size to the average diameter of a piece of the resulting crushed product. Mathematically, it is equal to the cube root of the number of pieces with uniform crushing of the sample into equal fragments. To determine the radius of the crack formation zone in a springing explosion, the stable crushing degree was taken equal to 1.3. At this degree, the sample is theoretically divided into two equal pieces and a number of small pieces, which make up 1/5 of the volume of one piece. For crack initiation in the sample, it is sufficient to carry out minimal crushing: into 2 pieces. However, in the rock mass under conditions of еру all-round compression, the rock resistance to fracture increases and a larger impact pulse is required for the crack initiation, which creates a correspondingly more intense crushing. 4. The Radius of the Crack Formation Zone The radius of the crack formation zone (m) is calculated from the value of the relative dimensionless radius , determined by the formula: ( ) = 1 ⁄ , (14) where ( ) is the explosion strain pulse at a relative distance , at which it becomes equal to the dynamic strength of the rock. At the same time, at a greater distance, the initial compression wave, due to its damping, ceases to destroy the rock mass. This equation has no analytical solutions, since the sought value is included in the argument. This equation is figured numerically by the approximation method until the equality is satisfied with a given accuracy. The initial value , equal to 1 , is set from the physical considerations based on the known experimental data of similar conditions. The radius of the crack formation zone is calculated by the formula: = 0 ∙ , m. (15) 5. Modeling Results Based on the calculations results using formulas (1-15) for 17 types of rocks, a graph of the dependence of the radius of the crack formation zone on the strength of rocks under uniaxial compression for 6 ZhV ammonite explosives with an explosive charge length of 1.6 m, is shown in the figure. In this case, the resulting regression