Empress Catherine II Saint-Petersburg Mining University, Saint-Petersburg, Russia

A. V. Mysin, Senior Lecturer, Department of Geoecology, Candidate of Engineering Sciences, mysin_av@pers.spmi.ru
V. N. Kovalevskiy, Associate Professor, Department of Basting, Candidate of Engineering Sciences

One of the factors determining the nature of the fracture process is the physical and mechanical properties of a medium. The nature of propagation and reflection of elastic waves determines the structure of stress fields arising in rock mass under dynamic loading, and therefore has a significant impact on the rock mass behavior and destruction. Particular attention in this term deserves anisotropy of rock mass properties, which significantly affects the blast-induced fragmentation quality, pit wall stability, design perimeter preservation, etc., caused, as a rule, by stratification and fracturing. This study used mathematical modeling methods to reveal peculiarities of influence of stratification on the behavior of complex-structured rock mass under blast-induced impact. This article presents the results of numerical calculation of stress wave propagation as a case-study of a layered section of rock mass. The Ansys/Autodyn software package was used to simulate the borehole charge explosion. According to the results, layering has influence on the stress distribution in rock mass and on the nature of fractures. The empirical analysis of interaction of plane elastic waves with the interface between two elastic isotropic half-spaces determined reflection and propagation coefficients for the incident P-wave. For waves propagating in rocks, a positive value of the reflection coefficient indicates a compression wave, while a negative value indicates a tensile wave. The dependences of the incident wave reflection coefficient at the interface on the angle of incidence and acoustic impedance are given.

1. Flyagin A. S., Zharikov S. N. Contour blasting in underground mining. Problemy nedropolzovaniya. 2016. No. 3(10). pp. 70–73.
2. Overchenko M. N., Tolstunov M. N., Mozer S. P., Belin V. A. Optimal parameters of process flows in air-decoupling blasting. MIAB. 2022. No. 4. pp. 87–99.
3. Sokolov I. V., Smirnov A. A., Rozhkov A. A. Technology of blasting of strong valuable ores with ring borehole pattern. Journal of Mining Institute. 2019. Vol. 237. pp. 285–291.
4. Shevkun E. B., Leshchinskiy A. V., Lysak Yu. A., Plotnikov A. Yu. Long-period delay loosening blasting in open pit mines. MIAB. 2020. No. 10. pp. 29–41.
5. Alenichev I.A., Rakhmanov R.A. Empirical regularities investigation of rock mass discharge by explosion on the free surface of a pit bench. Journal of Mining Institute. 2021. Vol. 249. pp. 334–341.
6. Dolzhikov V. V., Ryadinsky D. E., Yakovlev A. A. Influence of deceleration intervals on the amplitudes of stress waves during the explosion of a system of borehole charges. MIAB. 2022. No. 6-2. pp. 18–32.
7. Saadoun A., Fredj M., Boukarm R., Hadji R. Fragmentation analysis using digital image processing and empirical model (KuzRam): a comparative study. Journal of Mining Institute. 2022. Vol. 257. pp. 822–832.
8. Fedoseev A. V. Validation of borehole drilling design in blasting layered enclosing rock mass of ferruginous quartzites : Dissertation of Candidate of Engineering Sciences. Saint-Petersburg, 2014. 136 p.
9. Serebryakov E. V., Gladkov A. S. Geological and structural characteristics of deep-level rock mass of the Udachnaya pipe deposit. Journal of Mining Institute. 2021. Vol. 250. pp. 512–525.

10. Afanasev P. I., Makhmudov K. F. Assessment of the Parameters of a Shock Wave on the Wall of an Explosion Cavity with the Refraction of a Detonation Wave of Emulsion Explosives. Applied Sciences. 2021. Vol. 11, Iss. 9. ID 3976.
11. Goncharov S. A., Dugartsyrenov A. V., Klyuka O. F. Development and substantiation of rock mass softening technique in blasting ferruginous quartzites in open pit mines. MIAB. 2003. No. 6. pp. 5–8.
12. Paramonov G. P., Fedoseev A. V., Gaponov Yu. S. Assessment of cracked area to its destruction in the production of blasting. Journal of Mining Institute. 2013. Vol. 204. pp. 294–296.
13. Wang L., Wu C., Fan L., Wang M. Effective velocity of reflected wave in rock mass with different wave impedances of normal incidence of stress wave. International Journal for Numerical and Analytical Methods in Geomechanics. 2022. Vol. 46, Iss. 9. pp. 1607–1619.
14. Daehnke A., Rossmanith H. P. Reflection and refraction of plane stress waves at interfaces modelling various rock joints. Fragblast: International Journal for Blasting and Fragmentation. 1997. Vol. 1, Iss. 2. pp. 111–231.
15. Xu P., Yang R.-S., Guo Y., Chen C., Kang Y. Investigation of the effect of the blast waves on the opposite propagating crack. International Journal of Rock Mechanics and Mining Sciences. 2021. Vol. 144. ID 104818.
16. Fan L. F., Ma G. W., Li J. C. Nonlinear viscoelastic medium equivalence for stress wave propagation in a jointed rock mass. International Journal of Rock Mechanics and Mining Sciences. 2012. Vol. 50. pp. 11–1 8.
17. Lei M., Liu J., Lin Y., Shi C., Liu C. Deformation characteristics and influence factors of a shallow tunnel excavated in soft clay with high plasticity. Advances in Civil Engineering. 2019. Vol. 2019. ID 7483628.
18. Sun Z., Zhang D., Li A., Lu S., Tai Q. et al. Model test and numerical analysis for the face failure mechanism of large cross-section tunnels under different ground conditions. Tunnelling and Underground Space Technology. 2022. Vol. 130. ID 104735.
19 . Kausel E., Roësset J. M. Stiffness matrices for layered soils. Bulletin of the Seismological Society of America. 1981. Vol. 71, No. 6. pp. 1743–1761.
20. Kotikov D. A., Shabarov A. N., Tsirel S. V. Connecting seismic event distribution and tectonic structure of rock mass. Gornyi Zhurnal. 2020. No. 1. pp. 28–32.
21. Perino A., Orta R., Barla G. Wave propagation in discontinuous media by the scattering matrix method. Rock Mechanics and Rock Engineering. 2012. Vol. 45, Iss. 5. pp. 901–918.
22. Kholodilov A. N., Gospodarikov A. P. modeling seismic vibrations under massive blasting in underground mines. Journal of Mining Science. 2020. Vol. 56, Iss. 1. pp. 29–35.
23. Isheyskiy V., Marinin M., Dolzhikov V. Combination of fracturing areas after blasting column charges during destruction of rocks. International Journal of Engineering Research and Technology. 2019. Vol. 12, No. 12. pp. 2953–2956.
24. Huang F., Zhu H., Xu Q., Cai Y., Zhuang X. The effect of weak interlayer on the failure pattern of rock mass around tunnel—Scaled model tests and numerical analysis. Tunnelling and Underground Space Technology. 2013. Vol. 35. pp. 207–218.
25. Huang L., Ma J., Lei M., Liu L., Lin Y. et al. Soil-water inrush induced shield tunnel lining damage and its stabilization: A case study. Tunnelling and Underground Space Technology. 2020. Vol. 97. pp. ID 103290.
26. Tripathy G. R., Gupta I. D. Prediction of ground vibrations due to construction blasts in different types of rock. Rock Mechanics and Rock Engineering. 2002. Vol. 35, Iss. 3. pp. 195–204.
27. Esen S., Onederra I., Bilgin H. A. Modelling the size of the crushed zone around a blasthole. International Journal of Rock Mechanics and Mining Sciences. 2003. Vol. 40, Iss. 4. pp. 485–495.
28. Bohloli B. , Hoven E. A laboratory and full-scale study on the fragmentation behavior of rocks. Engineering Geology. 2007. Vol. 89, Iss. 1-2. pp. 1–8.
29. Marysyuk V. P., Sabyanin G. V., Trofimov A. V., Kirkin A. P. Designing blast patterns by calculation of fracture zones and ore zoning by physical and mechanical properties. Gornyi Zhurnal. 2020. No. 1. pp. 58–62.
30. Belytschko T., Moës N., Usui S., Parimi C. Arbitrary discontinuities in f inite elements. International Journal for Numerical Methods in Engineering. 2001. Vol. 50, Iss. 4. pp. 993–1013.
31. Zhuang X., Augarde C. E., Mathisen K. M. Fracture modeling using meshless methods and level sets in 3D:Framework and modeling. International Journal for Numerical Methods in Engineering. 2012. Vol. 92, Iss. 11. pp. 969–998.
32. Vignollet J., May S., De Borst R., Verhoosel C. V. Phase-field models for brittle and cohesive fracture. Meccanica. 2014. Vol. 49, Iss. 11. pp. 2587–2601.
33. Toraño J., Rodríguez R., Diego I., Rivas J. M., Casal M. D. FEM models including randomness and its application to the blasting vibrations prediction. Computers and Geotechnics. 2006. Vol. 33, Iss. 1. pp. 15–28.
34. Miehe C., Welschinger F., Hofacker M. Thermodynamically consistent phase-field models of fracture:Variational principles and multi-field FE implementations. International Journal for Numerical Methods in Engineering. 2010. Vol. 83, Iss. 10. pp. 1273–1311.
35. Wu J.-Y. A unified phase-field theory for the mechanics of damage and quasi-brittle failure. Journal of the Mechanics and Physics of Solids. 2017. Vol. 103. pp. 72–99.
36. Wu J.-Y., Nguyen V. P. A length scale insensitive phase-field damage model for brittle fracture. Journal of the Mechanics and Physics of Solids. 2018. Vol. 119. pp. 20–42.
37. Cundall P. A. A computer model for simulating progressive, large-scale movements in blocky rock system. Proceedings of the International Symposium on Rock Mechanics. Nancy, 1971. pp. 129–136.
38. Yang Y., Wei C., Chen Z., Yao Y., Chen X. et al. Multi-dimensional numerical simulation and experimental investigation of Monel alloy/Cu explosive cladded rod. Journal of Materials Science. 2022. Vol. 57, Iss. 46. pp. 21363–21377.
39. ANSYS Autodyn User’s Manual. Canonsburg : ANSYS, Inc., 2013. 502 p.
40. Mysin A., Kovalevskiy V. Creation and verification of numerical model of explosive charge blast in the ansys software system, for the purpose of substantiating the optimal parameters of drilling and blasting operations. Proceedings of V International Innovative Mining Symposium. 2020 E3S Web of Conferences. 2020. Vol. 174. ID 01046.
41. Pan C., Li X., Li J., Zhao J. Numerical investigation of blast-induced fractures in granite: insights from a hybrid LS-DYNA and UDEC grain-based discrete element method. Geomechanics and Geophysics for Geo-Energy and Geo-Resources. 2021. Vol. 7. DOI: 10.1007/s40948-021-00253-6
42. Onederra I. A., Furtney J. K., Sellers E., Iverson S. Modelling blast induced damage from a fully coupled explosive charge. International Journal of Rock Mechanics and Mining Sciences. 2013. Vol. 58. pp. 73–84.
43. Bonet J., Wood R. D. Nonlinear Continuum Mechanics for Finite Element Analysis. 2^nd ed. Cambridge : Cambridge University Press, 2008. 318 p.
44. Donea J., Huerta A. Finite Element Methods for Flow Problems. Chichester : John Wiley & Sons Ltd, 2003. 350 p.
45. Courant R., Fridrichs K., Lewy H. Über die partiellen Differenzengleichungen der mathematischen Physik. Mathematische Annalen. 1928. Vol. 100. pp. 32–74.
46. Peng J., Zhang F., Du C., Yang X. Effects of confining pressure on crater blasting in rock-like materials under electric explosion load. International Journal of Impact Engineering. 2020. Vol. 139. ID 103534.
47. Huo X., Shi X., Qiu X., Zhou J., Gou Y. et al. Rock damage control for large-diameter-hole lateral blasting excavation based on charge structure optimization. Tunnelling and Underground Space Technology. 2020. Vol. 106. ID 103569.
48. Dehghan Banadaki M. M., Mohanty B. Numerical simulation of stress wave induced fractures in rock. International Journal of Impact Engineering. 2012. Vol. 40-41. pp. 16–25.
49. Wang Z., Wang H., Wang J., Tian N. Finite element analyses of constitutive models performance in the simulation of blast-induced rock cracks. Computers and Geotechnics. 2021. Vol. 135. ID 104172.
50. Gao F., Li X., Xiong X., Lu H., Luo Z. Refined design and optimization of underground medium and long hole blasting parameters—A case study of the Gaofeng Mine. Mathematics. 2023. Vol. 11, No. 7. ID 1612.
51. Yi C., Johansson D., Greberg J. Effects of in-situ stresses on the fracturing of rock by blasting. Computers and Geotechnics. 2018. Vol. 104. pp. 321–330.
52. Xie L. X., Lu W. B., Zhang Q. B., Jiang Q. H., Chen M. et al. Analysis of damage mechanisms and optimization of cut blasting design under high in-situ stresses. Tunnelling and Underground Space Technology. 2017. Vol. 66. pp. 19–33.

53. Liu K., Li Q., Wu C., Li X., Li J. A study of cut blasting for one-step raise excavation based on numerical simulation and field blast tests. International Journal of Rock Mechanics and Mining Sciences. 2018. Vol. 109. pp. 91–104.
54. Borrvall T., Riedel W. The RHT concrete model in LS-DYNA. Proceedings of the 8^th European LS-DYNA Users Conference. Strasbourg, 2011.
55. Seokwon J., Tae-Hyun K., Kwang-Ho Y. Characteristics of crater formation due to explosives blasting in rock mass. Geomechanics and Engineering. 2015. Vol. 9, Iss. 3. pp. 329–344.

56. Preece D. S., Chung S. H. Blasting induced rock fragmentation prediction using the RHT constitutive model for brittle material. Proceedings of the 29^th Annual Conference on Explosives and Blasting Technique. Nashville : International Society of Explosives Engineers, 2003.
57. Weng M.-C. A generalized plasticity-based model for sandstone considering timed ependent behavior and wetting deterioration. Rock Mechanics and Rock Engineering. 2014. Vol. 47, Iss. 4. pp. 1197–1209.
58. Tian H.-F., Bao T., Li Z., Peng H., You S. et al. Determination of constitutive parameters of crystalline limestone based on improved RHT model. Advances in Materials Science and Engineering. 2022. Vol. 2022. ID 3794898.
59. Artero-Guerrero J., Pernas-Sánchez J., Teixeira-Dias F. Blast wave dynamics: The influence of the shape of the explosive. Journal of Hazardous Materials. 2017. Vol. 331. pp. 189–199.
60. Hu Y., Lu W., Chen M., Yan P., Zhang Y. Numerical simulation of the complete rock blasting response by SPH–DAM–FEM approach. Simulation Modelling Practice and Theory. 2015. Vol. 56. pp. 55–68.
61. Pramanik R., Deb D. Implementation of smoothed particle hydrodynamics for detonation of explosive with application to rock fragmentation. Rock Mechanics and Rock Engineering. 2015. Vol. 48. pp. 1683–1698.
62. Sanchidrián J. A., Castedo R., López L. M., Segarra P., Santos A. P. Determination of the JWL constants for ANFO and emulsion explosives from cylinder test data. Central European Journal of Energetic Materials. 2015. Vol. 12, No. 2. pp. 177–194.