Mathematical model of piston/bit interaction in percussive destruction of rocks

The mathematical model of percussive destruction of rocks is represented by a set of two sub-models. The first sub-model simulates piston/bit interaction and allows finding the bit force on rocks as a function of time. The second sub-model describes the temporal variation of stress state and estimates strength of rock mass. Integration of the sub-models enables determining the influence exerted by the rock-breaking tool parameters and by mechanical characteristics of rock mass on the volume of destruction. The tool affects rock mass by concentrated load along the tool axis. The time variation of the loading modulus is obtained from the first sub-model. The input dimension data are set as the depth of shear cut, torque angle and loading step. The stress state of rocks mass is determined from the numerical solution of an initial– boundary value dynamic problem of elasticity by integration of the method of lines (Crank– Nicolson approach) and the method of finite elements. The strength assessment of rocks uses the criteria of Mohr–Coulomb and Morozov–Petrov, which make it possible to find volume of rock destruction. The calculation is exemplified by a case-study of Rammer G100 hydraulic hammer, Finland.

Keywords: rock mass, percussive tool, mathematical model, method of lines, finite element method, Mohr–Coulomb criterion, Morozov–Petrov criterion.
For citation:

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;(11):140-150. [In Russ]. DOI: 10.25018/0236-1493-2020-11-0-140-150.


The study was supported by the Tula State University, R&D Project No. 2019-18.

Issue number: 11
Year: 2020
Page number: 140-150
ISBN: 0236-1493
UDK: 622.23.05:622.235
DOI: 10.25018/0236-1493-2020-11-0-140-150
Article receipt date: 23.06.2020
Date of review receipt: 13.07.2020
Date of the editorial board′s decision on the article′s publishing: 10.10.2020
About authors:

A.B. Zhabin1, Dr. Sci. (Eng.), Professor, e-mail:,
I.M. Lavit1, Dr. Sci. (Phys. Mathem.), Professor, e-mail:,
A.V. Polyakov1, Dr. Sci. (Eng.), Professor, e-mail:,
Z.E. Kerimov1, Graduate Student, e-mail:,
1 Tula State University, 300012, Tula, Russia.


For contacts:

A.B. Zhabin, e-mail:


1. Kravchenko V. A. Obosnovanie gidravlicheskikh ustroystv udarnogo deystviya s ponizhennoy udel'noy metalloemkost'yu dlya razrusheniya gornykh porod [Justification of hydraulic impact devices with reduced specific metal content for rock destruction], Candidate’s thesis, Orel, 2004, 23 p.

2. Dobroborskiy B. S., Ovcharov A. A. Research impact machine with movable hammer mechanism. Modern problems of science and education. 2014, no 5, available at: 5/ 468.pdf (accessed: 24.09.2014). [In Russ].

3. Abramenkov D. E., Abramenkov E. A., Dedov A. S., Krutikov E. I. Pneumatic hammer mechanism with a combination of the air. Izvestiya vysshikh uchebnykh zavedeniy. Stroitel'stvo. 2014, no 4, pp. 114—118. [In Russ].

4. Gorodilov L. V. Analysis of the dynamics of two-way hydropercussion systems. Part II: Influence of design factors and their interaction with rocks. Journal of Mining Science. 2013. Vol. 49. No 3. Pp. 465—474. DOI: 10.1134/S1062739149030143.

5. Oparin V. N., Timonin V. V., Karpov V. N., Smolyanitsky B. N. Energy-based volumetric rock destruction criterion in the rotary–percussion drilling technology improvement. Journal of Mining Science. 2017. Vol. 53. No 6. Pp. 1043—1064. DOI: 10.1134/S1062739117063114.

6. Redelin R. A., Kravchenko V. A., Kamanin Y. N., Panichkin A. V., Bozhanov A. A. Study of effect of in-line hydropneumatic accumulators on output characteristics of hydraulic hammer. IOP Conference Series Earth and Environmental Science. 2017. Vol. 87. No 2. Article 022016. DOI: 10.1088/1755-1315/87/2/022016.

7. Tian Jialin, Yang Zhi, Li You, Yang Lin, Wu Chunming, Liu Gang, Yuan Changfu Vibration analysis of new drill string system with hydro-oscillator in horizontal well. Journal of Mechanical Science and Technology. 2016. Vol. 30. No 6. Pp. 2443—2451. DOI 10.1007/s12206-016-0504-z.

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

9. 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.

10. Ushakov L. S., Klimov V. E. Modern trends in the development of tunneling equipment for strong mountain ranges. Innovatsii na transporte i v mashinostroenii: sbornik trudov IV mezhdunarodnoy nauchno-prakticheskoy konferentsii [Innovations in transport and engineering: proceedings of the IV international scientific and practical conference], Vol. II. Saint-Petersburg, NMSU «Gornyy», 2016, pp. 63—68. [In Russ].

11. Kamanin Yu. N., Ushakov L. S. Development of new technologies for tunneling in solid rock. Transportnye sistemy i tekhnologii. 2016, no 4(6), pp. 77—86. [In Russ].

12. Li X., Wang S., Ge S., Malekian R., Li Z. A theoretical model for estimating the peak cutting force of conical picks. Experimental Mechanics. 2018. Vol. 58. Pp. 709—720. DOI: 10.1007/S11340-017-0372-1.

13. Timoshenko S. P., Gudier J. Teoriya uprugosti [Elasticity theory], Moscow, Nauka, 1979, 560 p.

14. Ladyzhenskaya O. A. Kraevye zadachi matematicheskoy fiziki [Boundary value problems in mathematical physics], Moscow, Nauka, 1973, 408 p.

15. Strange G., Fix J. Teoriya metoda konechnykh elementov [An analysis of the finite element method], Moscow, Mir, 1977. 349 s.

16. Zenkevich O. Metod konechnykh elementov v tekhnike [The finite element method in engineering science], Moscow, Mir, 1975, 541 p.

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

18. Baron L. I., Khmel'kovskiy I. E. Razrushaemost' gornykh porod svobodnym udarom [Destructibility of rocks by free percussive impact], Moscow, Nauka, 1971, 203 p.

Our partners

Подписка на рассылку

Раз в месяц Вы будете получать информацию о новом номере журнала, новых книгах издательства, а также о конференциях, форумах и других профессиональных мероприятиях.