Calculation method for rock fracture under impacts

Designing of impact tools with rational parameters requires calculating indicators of a destruction process based on the analysis of the process dynamics using mathematical models which take into account the piston–tool interaction and the change in the stress state of rocks in time. This article presents such method. In actual practice, the method consists in calculation of indicators of rock fracture under impact loads depending on various factors. The load of an impact tool depending on its elastic properties, geometrical parameters and impact velocity is found. The time–load relationships are determined. It is shown that these relationships demonstrate a step-wise behavior governed by propagation of elastic waves along a rod. A case-study of calculation of rock fracture parameters under impacts is presented, and the volume of a broken material is determined using the Morozov–Petrov strength criterion. The volume of rock destruction by an impact tool is correlated with the compressive strength of rocks, the height and width of chips, and the load angle. To sum up, the calculation method developed for rock fracture parameters under impacts enables determination of kinetics of dynamic loading and destruction of rock mass, and provides the values required for the efficiency evaluation. 

Zhabin А. B., Lavit I. M., Polyakov Аn. V., Polyakov Аl. V. Calculation method for rock fracture under impacts. MIAB. Mining Inf. Anal. Bull. 2026;(7):5-19. [In Russ]. DOI: 10.25018/0236_1493_2026_7_0_5.

А.B. Zhabin¹, Dr. Sci. (Eng.), Professor, e-mail: zhabin.tula@mail.ru, ORCID ID: 0000-0001-5305-4908,
I.M. Lavit ¹, Dr. Sci. (Phys. Mathem.), Professor, e-mail: IgorLavit@yandex.ru, ORCID ID: 0000-0002-8683-5943,
Аn.V. Polyakov², Dr. Sci. (Eng.), Assistant Professor, Expert, e-mail: polyakoff-an@mail.ru, ORCID ID: 0000-0002-0067-6954,
Аl.V. Polyakov², Cand. Sci. (Eng.), Expert, e-mail: polyakoff-al@mail.ru, ORCID ID: 0009-0006-6076-6958,
¹ Tula State University, Tula, Russia,
² United Consulting Holding LLC, Moscow, Russia.

А.B. Zhabin, e-mail: zhabin.tula@mail.ru.

1. Shcherbakov I. P., Vettegren V. I., Mamalimov R. I. Fracture mechanism of the rock under the action of shock waves. Izvestiya, Physics of the Solid Earth. 2020, no. 5, pp. 23—35. [In Russ]. DOI: 10.31857/S0002333720050099.

2. Ushakov L. S., Kotylev Yu. E., Kravchenko V. A. Gidravlicheskie mashiny udarnogo deystviya [Hydraulic impact machines], Moscow, Mashinostroenie, 2000, 416 p.

3. Kamanin Yu. N., Redelin R. A., Kravchenko V. A. Simulation of fracture rock hydraulic equipment of percussion. Mining Equipment and Electromechanics. 2017, no. 2 (129), pp. 30—34. [In Russ].

4. Zhornik A. I., Kirichek V. A. The dynamic problem of a semi-infinite crack moving in elastic space. Journal of Applied Mechanics and Technical Physics. 2018, no. 2, pp. 209—217. [In Russ]. DOI: 10.15372/PMTF20180221.

5. Atageldiev K. T., Bahtybaev N. B., Abil' O. A. Dynamic destruction of rocks: experimental and numerical methods. Mining Magazine of Kazakhstan. 2025, no. 1, pp. 12—16. [In Russ]. DOI: 10.48498/minmag.2025.237.1.008.

6. Zhukov I. A., Timofeev E. G. Mathematical and computer simulation of impact processes in rod system of impact machines. Modern High Technologies. 2020, no. 12 (1), pp. 43—49. [In Russ]. DOI: 10.17513/snt.38409.

7. Lyaptsev S. A., Stepanova N. R. Parameters multimass shock mechanism for the destruction of rocks. Fundamental research. 2014, no. 12 (8), pp. 1649—1651. [In Russ].

8. Klishin V. I., Opruk G. Y., Pavlova L. D. Active prefracture methods in top coal caving technologies for thick and gently dipping seams. Journal of Mining Science. 2020, vol. 56, pp. 395—403. DOI: 10.1134/S1062739120036689.

9. Li T., Marigo J. J., Guilbaud D. Numerical investigation of dynamic brittle fracture via gradient damage models. Advanced Modeling and Simulation in Engineering Sciences. 2016, vol. 3, article 26. DOI: 10.1186/s40323-016-0080-x.

10. Nhon Nguyen-Thanh, Hung Nguyen-Xuan, Weidong Li Phase-field modeling of anisotropic brittle fracture in rock-like materials and polycrystalline materials. Computers & Structures. 2024, vol. 296, article 107325. DOI: 10.1016/j.compstruc.2024.107325.

11. Garanin V. N., Unitsky A. E., Artyushevsky S. V., Ovsyanko V. A., Pronkevich S. A. Development of a computer model of destruction heterogeneous material. Proceedings of BSTU. Series 3, Physical and mathematical sciences and Computer science. 2022, no. 1 (254), pp. 28—37. [In Russ].

12. Ming Zhou, Lan Qiao, Qingwen Li, Shuang Yang and Zhenping Huang Research on the conversion relationship between dynamic point load strength and dynamic compressive strength based on energy system. Shock and Vibration. 2022, vol. 2, p. 10.

13. Kozyrev A., Kasparyan E., Fedotova Iu., Kuznetcov N. The specificities of deformations and failures of highly stressed hard rock massifs. E3S Web of Conference. 2019, vol. 129, article 01010. DOI: 10.1051/e3sconf/201912901010.

14. Laura De Lorenzis, Alexander Düster Modeling in engineering using innovative numerical methods for solids and fluids. CISM International Centre for Mechanical Sciences. Courses and Lectures. 2020, vol. 599, 220 р. DOI: 10.1007/978-3-030-37518-8.

15. Gerasimov T., Römer U., Vondřejc J., Matthies H. G., De Lorenzis L. Stochastic phase-field modeling of brittle fracture: Computing multiple crack patterns and their probabilities. Computer Methods in Applied Mechanics and Engineering. 2020, vol. 372, article 113353. DOI: 10.1016/j.cma.2020.113353.

16. Shi H., Chen W., Zhang H., Song L., Li M., Wang M., Lu P. Dynamic strength characteristics of fractured rock mass. Engineering Fracture Mechanics. 2023, vol. 292, no. 15, article 109678. DOI: 10.1016/j.engfracmech.2023.109678.

17. Zhang L., Wang E., Liu Y., Yue W., Chen D. Experimental research into the dynamic damage characteristics and failure behavior of rock subjected to incremental repeated impact loads. Engineering Geology. 2024, vol. 331, article 107435. DOI: 10.2495/SUSI140311.

18. Zhabin A. B., Lavit I. M., Polyakov A. V., Kerimov Z. E. Mathematical model of piston–tool interaction in rock fracture by impact. MIAB. Mining Inf. Anal. Bull. 2020, no. 7, pp. 94—103. [In Russ]. DOI: 10.25018/0236-1493-2020-7-0-94-103.

19. Zhabin A. B., Lavit I. M., Polyakov A. V., Kerimov Z. E. Mathematical model of piston/bit interaction in percussive destruction of rocks. MIAB. Mining Inf. Anal. Bull. 2020, no. 11, pp. 140—150. [In Russ]. DOI: 10.25018/0236-1493-2020-11-0-140-150.

20. Mohammadnejad M., Liu H., Chan A., Dehkhoda S., Fukuda D. An overview on advances in computational fracture mechanics of rock. Geosystem Engineering. 2021, vol. 24, pp. 206—229. DOI: 10.1080/12269328.2018.1448006.

21. Geller Yu. Factors affecting the process of soil and rock massif destruction. Transbaikal State University Journal. 2021, vol. 27, no. 5, pp. 17—25. [In Russ]. DOI: 10.21209/2227-9245-2021-27-5-17-25.

22. Azimov A. M., Zhukov I. A. Increasing energy efficiency of hydraulic hammers used for secondary breaking based on the geometry effect of the impactor parts. Russian Mining Industry Journal. 2025, no. 3, pp. 71—79. [In Russ]. DOI: 10.30686/1609-9192-2025-3-71- 79.

23. Linnik Yu. N., Linnik V. Yu. Analysis of methods for assessing rock fracture resistance under dynamic load application. Mining Equipment and Electromechanics. 2025, no. 1 (177), pp. 39—46. [In Russ]. DOI: 10.26730/181-4528-2025-1-39-46.

24. Kramarenko N. V. Metody podobiya v mekhanike. Analiz razmernostey [Similarity methods in mechanics. Dimensional analysis], Novosibirsk, 2020, 212 p.

25. Morozov N. F., Petrov Yu. V. Problemy dinamiki razrusheniya tverdykh tel [Problems of dynamics of destruction of solids], Saint-Petersburg, 1997, 132 p.