Internal mechanical losses in gabbro under periodic impacts in low-frequency range

Internal mechanical losses are among the physical properties of rocks, which, alongside with elasticity, plasticity and strength, should be included in calculations and models but are sometimes discarded because of complexity of their determination. They count for much in estimates of seismic impacts exerted by earthquakes and rock burst, blasts and vibration sources on rock mass surrounding underground roadways and on underground structures. This article describes a laboratory system and a procedure for three-point bend testing of rock samples to determine a loss factor Q–1 (inverse Q-factor) as function of an impact frequency. The cyclic test results are presented for gabbro beams in deformation at different peak amplitudes and frequencies. The test procedure is described. The centered hysteresis loops are obtained for each cycle of beam bending increase and decrease in two series of tests. The averaged loss factors Q–1 and the Rayleigh ratios are calculated, which characterize the inverse and direct proportions of the losses and periodic impact frequencies in a frequency range from 0.001 to 0.05 Hz. The frequency values that lead to the minimum loss factors are found.

Salyukov V. S., Voznesenskii A. S., Kutkin Ya. O. Internal mechanical losses in gabbro under periodic impacts in low-frequency range. MIAB. Mining Inf. Anal. Bull. 2024;(11):64-74. [In Russ]. DOI: 10.25018/0236_1493_2024_11_0_64.

The study was supported by the Russian Science Foundation, Grant No. 24-27-00103.

V.S. Salyukov¹, Graduate Student, e-mail: m1605021@edu.misis.ru, ORCID ID: 0009-0003-0343-7056,
A.S. Voznesenskii¹, Dr. Sci. (Eng.), Professor, e-mail: asvoznesenskii@misis.ru, ORCID ID: 0000-0003-0926-1808,
Ya.O. Kutkin¹, Cand. Sci. (Eng.), Assistant Professor, e-mail: kutnew@mail.ru, ORCID ID: 0000-0003-2644-3371,
¹ University of Science and Technology MISIS, 119049, Moscow, Russia.

A.S. Voznesenskii, e-mail: asvoznesenskii@misis.ru.

1. Liu Y., Dai F. A review of experimental and theoretical research on the deformation and failure behavior of rocks subjected to cyclic loading. Journal of Rock Mechanics and Geotechnical Engineering. 2021, vol. 13, no 5, pp 1203—1230. DOI: 10.1016/j.jrmge.2021.03.012.

2. Zhang Q., Dai F., Liu Y. Experimental assessment on the dynamic mechanical response of rocks under cyclic coupled compression-shear loading. International Journal of Mechanical Sciences. 2022, vol. 216. DOI: 10.1016/j.ijmecsci.2021.106970.

3. Zhang C., Wang Y., Ruan H., Ke B., Lin H. The strain characteristics and corresponding model of rock materials under uniaxial cyclic load/unload compression and their deformation and fatigue damage analysis. Archive of Applied Mechanics. 2021, vol. 91, no. 6, pp. 2481—2496. DOI: 10.1007/ s00419-021-01899-0.

4. Chunde M., Shan L., Xibing L., Zelin L., Weibin X. Research and microscopic analysis of seepage characteristics of sandstone under low-frequency cyclic loading. IOP Conference Series: Earth and Environmental Science. 2020, vol. 570, no. 5, article 052048. DOI: 10.1088/1755-1315/570/5/052048.

5. Zhou Z., Zhang J., Cai X., Wang S., Du X., Zang H., Chen L. Permeability evolution of fractured rock subjected to cyclic axial load conditions. Geofluids. 2020. DOI: 10.1155/2020/4342514.

6. Mashinskii E. I. Amplitude-dependent hysteresis of wave velocity in rocks in wide frequency range: an experimental study. Mining Science and Technology (Russia). 2021, vol. 6, no. 1, pp. 23—30. [In Russ]. DOI: 10.17073/2500-0632-2021-1-23-30.

7. Tang J., Fang B., Lan Y. Analysis of rock nonlinear deformation behavior with loading and unloading hysteresis effect. Oil Geophysical Prospecting. 2014, vol. 49, no. 6, pp. 1131—1137.

8. Cao L., Zhang P., Zhang J., Lin G., Jiskani I. M., Chen Z., Wang Z., Li M. Experimental study of hysteresis characteristics of water-sediment mixture seepage in rock fractures. Geofluids. 2021. DOI: 10.1155/2021/6692388.

9. Chen L., Wang D., Jiang Y., Luan H., Zhang, G., Liang B. Experimental study on mechanical properties and acoustic emission characteristics of dry and water-saturated soft rocks under different dynamic loadings. Sustainability (Switzerland). 2023, vol. 15, no. 17, article 13201. DOI: 10.3390/ su151713201.

10. Han J., Zhao D., Zhang S., Zhou Y. Damage evolution of granite under ultrasonic vibration with different amplitudes. Shock and Vibration. 2022. DOI: 10.1155/2022/8975797.

11. Guo H., Ji M., Zhang Y., Zhang M. Study of mechanical property of rock under uniaxial cyclic loading and unloading. Advances in Civil Engineering. 2018. DOI: 10.1155/2018/1670180.

12. Pan Y., Wang C., Wang Y. Mechanical degradation mechanism of rock under seismic disturbance stress. Quarterly Journal of Engineering Geology and Hydrogeology. 2022, vol. 55, no. 4. DOI: 10.1144/qjegh2022-007.

13. Leonov M. G., Kocharyan G. G., Revuzhenko A. F., Lavrikov S. V. Tectonics of rock loosening: geological data and physics of the process. Geodynamics and Tectonophysics. 2020, vol. 11, no. 3, pp. 491—521. [In Russ]. DOI: 10.5800/GT-2020-11-3-0488.

14. Taheri A., Faradonbeh R. S., Munoz H. Experimental study on progressive damage evolution in rocks subjected to post-peak cyclic loading history. Geotechnical Testing Journal. 2022, vol. 45, no. 3, pp 606—626. DOI: 10.1520/GTJ20210109.

15. Kulagina M. A., Rychkov B. A., Stepanova Yu. Yu. Determination of elastic constants of rocks. Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki. 2019, vol. 23, no. 2, pp. 284—303. [In Russ]. DOI: 10.14498/vsgtu1595.

16. Lou P., Li C., Liang S., Feng M., Pan B. Hysteresis characteristics of brittle rock deformation under constant load cyclic loading and unloading. Tehnicki Vjesnik. 2020, vol. 27, no. 3, pp. 906— 911. DOI: 10.17559/TV-20180705053718.

17. Chen Y., Wang S., Wang E. Quantitative study on stress-strain hysteretic behaviors in rocks. Chinese Journal of Rock Mechanics and Engineering. 2007, vol. 26, no. 2, pp. 4066—4073.

18. Fu H., Li J., Li G., Li D. Hysteresis Behavior Modeling of Hard Rock Based on the Mechanism and Relevant Characteristics. Sustainability (Switzerland). 2022, vol. 14, no. 16. DOI: 10.3390/ su141610412.

19. Chen Y. P., Xi D. Y., Xue Y. W. Hysteresis and attenuation of saturated rocks under cyclic loading. Acta Geophysica Sinica. 2004, vol. 47, no. 4, pp. 672—679. DOI: 10.1002/cjg2.3547.

20. Liu H. P., Peselnick L. Mechanical hysteresis loops of an anelastic solid and the determination of rock attenuation properties. Geophysical Research Letters. 1979, vol. 6, no. 7, pp. 545—548. DOI: 10.1029/GL006i007p00545.

21. Golovin I. S. Vnutrennee trenie i mekhanicheskaya spektroskopiya metallicheskikh materialov [Internal friction and mechanical spectroscopy of metallic materials], Moscow, 2012, 247 p.

22. Mochugovskiy A. G., Mikhaylovskaya A. V., Zadorognyy M. Y., Golovin I. S. Effect of heat treatment on the grain size control, superplasticity, internal friction, and mechanical properties of zirconium-bearing aluminum-based alloy. Journal of Alloys and Compounds. 2021, vol. 856. DOI: 10.1016/j.jallcom.2020.157455.

23. Lebedev A. V., Ostrovskii L. A., Sutin A. M., Soustova I. A., Dzhonson P. A. Resonant acoustic spectroscopy at low Q factors. Acoustical Physics. 2003, vol. 49, no. 1, pp. 81—87. [In Russ]. DOI: 10.1134/1.1537392.

24. Voznesensky A. S., Kutkin Y. O., Krasilov M. N. Interrelation of the acoustic q-factor and strength in limestone. Journal of Mining Science. 2015, vol. 51, no. 1, pp. 23—30. DOI: 10.1134/ S1062739115010044.

25. Morozov I. B., Deng W., Cao D. Mechanical analysis of viscoelastic models for Earth media. Geophysical Journal International. 2020, vol. 220, no. 3, pp. 1762—1773. DOI: 10.1093/gji/ggz445.

26. Petrushin G. D., Petrushina A. G. Determination of the area of mechanical hysteresis loop using mathematical models. Industrial laboratory. Diagnostics of materials. 2020, vol. 86, no. 5, pp. 59—64. [In Russ]. DOI: 10.26896/1028-6861-2020-86-5-59-64.

27. Rayleigh B. The theory of sound. Vol. 2. New York, 1945, 504 p.

28. Galvez F., Sorrentino L., Dizhur, D., Ingham J. M. Damping considerations for rocking block dynamics using the discrete element method. Earthquake Engineering and Structural Dynamics. 2022, vol. 51, no. 4, pp. 935—957. DOI: 10.1002/eqe.3598.

29. Voznesenskii A. S. Modelirovanie fizicheskikh protsessov gornogo proizvodstva [Modeling of physical processes of mining production], Moscow, 2023, 291 p.

30. Salyukov V. S. Internal mechanical losses in rocks in the low-frequency range. Problemy osvoeniya nedr v XXI veke glazami molodykh. Materialy 16-y mezhdunarodnoy nauchnoy shkoly molodykh uchenykh i spetsialistov [Problems of subsoil development in the XXI century through the eyes of young people. Materials of the 16th international scientific school of young scientists and specialists], Moscow, 2023, pp. 140—142. [In Russ].

31. Ouchterlony F., Franklin J. A., Zongqi Sun, Atkinson B. K., Meredith P. G., Rummel F., Mfiller W., Nishimatsu Y., Takahashi H., Costin L. S., Ingraffea A. R. Suggested methods for determining the fracture toughness of rock. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts. 1988, vol. 25, no. 2, pp. 71—96.