Estimation of the dependence of the dynamic modules of elasticity on the porosity of limestone samples by the method of pulse diagnostics

The paper addresses a study of the mineral and elemental composition of limestone specimens. On average, the specimens contain 97.5 % calcite, 2 % quartz, 0.5 % dolomite; the concentration of other minerals is less than 0.1 %. For limestone of this composition, analytical expressions are found to connect the measured density of specimens and longitudinal wave velocity with the density and longitudinal wave velocity in pore-free limestone specimens with the same mineral composition. This functional relationship is used to determine the density and longitudinal wave velocity in limestone with no pores; these values are verified using a GreenChristoffel equation for a medium consisting of chaotically oriented trigonal crystals of calcite, quartz, and dolomite. All specimens are characterized in terms of total porosity, including closed and open ones. Longitudinal and shear wave velocities are precisely measured (with an error of less than 0.2 %) by means of laser-ultrasonic structuroscopy. The measured velocities are used to calculate the dynamic elastic moduli. It is found that Young’s and shear moduli depend on porosity in a quasilinear manner; there is no distinct connection between porosity and Poisson’s ratio. It is demonstrated that the methods of mineral analysis of specimens and laser ultrasonic testing are able to determine the correlation between dynamic elastic moduli and total porosity of heterogeneous media.

Galunin A. A., Gapeev A. A., Pospichal V. Estimation of the dependence of the dynamic modules of elasticity on the porosity of limestone samples by the method of pulse diagnostics. MIAB. Mining Inf. Anal. Bull. 2021;(4-1):98—107. [In Russ]. DOI: 10.25018/0236_1493_2021_41_0_98.

Galunin A. A.¹, Graduate student, galunin.andrew@yandex.ru;
Gapeev A. A.¹, engineer;
Václav Pospíchal², Ph.D;
¹ National Research Technological University «MISiS» Mining Institute, Moscow, Russia.
² Czech Technical University in Prague, Czech Republic.

1. Marinoni N., Pavese Al., Bugini R., Silvestro G. Di. Black limestone used in Lombard architecture. Journal of Cultural Heritage, 2002. Vol. 3, Issue 4, pp. 241—249. DOI: 10.1016/ S1296—2074(02)01233—5.

2. La Russa M. F., Belfiore C. M., Ficherа G. V., Maniscalco R., Calabro C., Ruffolo S. A., Pezzino A. The behaviour to weathering of the Hyblean limestone in the Baroque architecture of the Val di noto (SE Sicily): An experimental study on the «calcare a lumachella» stone. Construction and Building Materials, 2015. Vol. 77, pp. 7—19. DOI: 10.1016/j.conbuildmat.2014.11.073.

3. Dreyfuss T. Artificially induced calcium oxalate on limestone in urban environments — New findings. Journal of Cultural Heritage, 2020. Vol. 42, pp. 56—63. DOI: 10.1016/j. culher.2019.06.011.

4. Gaylarde Chr. C, Gaylarde P. M., Beech Iw. B. Deterioration of limestone structures associated with copper staining. International Biodeterioration & Biodegradation, 2008. Vol. 62. Issue 2, pp. 179—185.

5. Vaisberg L. A., Kameneva E. E. Investigation of changes in the structure of porosity of rocks at different stages of loading. Ore and Metals. 2019, no. 3, pp. 37—42. [In Russ].

6. Yakushina O. A., Ozhogina E. G., Khozyainov M. S. Microtomography of technogenic mineral raw materials. Vestnik. 2015, no. 11, pp. 38–43. [In Russ].

7. Vaisberg L. A., Kameneva E. E., Pimenov Yu. G., Sokolov D. V. Study of the structure of the pore space of gneissic-granite by X-ray computer microtomography. Ore and Metals. 2013, no. 3, pp. 37—40. [In Russ].

8. Martinez-Martinez J., Fusi N., Galiana-Merino J. J., Benavente D., Crosta G. B. Ultrasonic and X-ray computed tomography characterization of progressive fracture damage in low-porous carbonate rocks. Engineering Geology, 2016, Vol. 200, pp. 47—57.

9. Kravcov A., Svoboda P., Konvalinka A., Cherepetskaya E. B., Sas I. E., Morozov N. A., Zatloukal J. Evaluation of crack formation in concrete and basalt specimens under cyclic uniaxial load using acoustic emission and computed X-Ray Tomography. Key Engineering Materials, 2017, Vol. 722, pp. 247—253.

10. Chawre B. Correlations between ultrasonic pulse wave velocities and rock properties of quartz-mica schist. Journal of Rock Mechanics and Geotechnical Engineering, 2018, Vol.10, Issue 3, pp. 594—602. https://doi.org/10.1016/j.jrmge.2018.01.006.

11. Gheibi A., Hedayat A. Ultrasonic imaging of microscale processes in quartz gouge during compression and shearing. Journal of Rock Mechanics and Geotechnical Engineering, 2020, Vol. 12, Issue 6, pp. 1137—1151. DOI:10.1016/j.jrmge.2020.03.011.

12. Scales J. A., Malcolm A. E. Laser characterization of ultrasonic wave propagation in random media. Physical Review E, 2003, Vol. 67, pp. 67—73. DOI: 10.1103/ PhysRevE.67.046618.

13. Karabutov A. A., Podymova N. B., Cherepetskaya E. B. Determination of uniaxial stresses in steel structures by laser-ultrasonic method. Journal of Applied Mechanics and Technical Physics. 2017, no. 3, pp. 146—155. DOI: 10.15372/PMTF20170315 [In Russ].

14. Shibaev I. A., Cherepetskaya E. B., Bychkov A. S., Zarubin V. P., Ivanov P. N. Evaluation of the internal structure of dolerite specimens using X-ray and laser ultrasonic tomography. International Journal of Civil Engineering and Technology, 2018, Vol. 9, Issue 9, pp. 84—92.

15. Shibaev I. A., Morozov D. V., Dudchenko O. L., Pavlov I. A. Estimation of local elastic moduli of carbon-containing materials by laser ultrasound. Key Engineering Materials, 2018, Vol. 769, pp. 96—101. https://doi.org/10.4028/www.scientific.net/KEM.769.96.

16. Grigoriev K. S., Kuznetsov N. Yu., Cherepetskaya E. B., Makarov V. A. Second harmonic generation in isotropic chiral medium with nonlocality of nonlinear optical response by heterogeneously polarized pulsed beams. Optics Express, 2017, Vol 25, Issue 6, pp. 6253—6262. DOI: 10.1364/OE.25.006253

17. Aleksandrov K. S, Prodajvoda G. T. Anizotropiya uprugih svojstv mineralov i gornyh porod [Anisotropy of elastic properties of minerals and rocks], Krasnoyarsk, SB RAS, 200, 349 p. [In Russ].