Analysis of fan waves in a laboratory model simulating the propagation of shear ruptures in rocks
DOI:
https://doi.org/10.7242/1999-6691/2016.9.1.4Keywords:
fan-shaped mechanism, Lagrange equations, Euler equation, traveling waves, computational algorithmAbstract
The fan-shaped mechanism of rotational motion transmission in the system of elastically connected plates on a plane base is analyzed. This mechanism governs the propagation of shear ruptures in super brittle rocks of the Earth’s crust at seismogenic depths. A laboratory physical model was created which demonstrates the process of fan wave propagation. Equations of the dynamics of a fan system as a mechanical system with a finite number of degrees of freedom are obtained. A computational algorithm taking into account contact interaction between plates is worked out. Within the framework of a simplified continuous model, the approximate estimates of the length of a fan depending on the velocity of its propagation are obtained. It is shown that in the absence of friction a stationary fan can move with any velocity that does not exceed the critical value, which depends on the size, the moment of inertia of plates, the initial angle and the coefficient of elasticity of connection, and that the length of a fan decreases with increasing velocity. In the absence of distributed shear stress, when the system of plates is in a horizontal position, the fan stops due to the friction forces. The action of distributed shear stress leads to the incomplete disclosure of a fan, and besides the angle of opening decreases with increasing friction. In a system with friction the velocity of a traveling fan is uniquely determined by the opening angle, and in the case of neglecting friction it can take any value within an allowable range. On the basis of a discrete model, the computations demonstrating the incomplete disclosure of fans with different opening angles due to rapid or slow change in the velocity of rotation of the first plate are performed. Comparison of the results of computations of the length and velocity of the fan by means of a discrete model with computations based on analytical formulas and laboratory observations showed a good correspondence between the results.
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References
Reches Z., Lockner D.A. Nucleation and growth of faults in brittle rocks // J. Geophys. Res. - 1994. - Vol. 99, no. B9. - P. 18159-18173. DOI
2. Peng S., Johnson A.M. Crack growth and faulting in cylindrical specimens of Chelmsford granite // Int. J. Rock Mech. Min. - 1972. - Vol. 9, no. 1. - P. 37-86. DOI
3. Ortlepp W.D. Rock fracture and rockbursts: an illustrative study. Monograph Series M9. - Johannesburg: South African Institute of Mining and Metallurgy, 1997. - 98 p.
4. Ortlepp W.D., Armstrong R., Ryder J.A., O’Connor D. Fundamental study of micro-fracturing on the slip surface of mine-induced dynamic brittle shear zones // Proc. of 6th Int. Symp. on Rockburst and Seismicity in Mines. RaSiM6 - Controlling Seismic Risk, Perth, Australia, March 9-11, 2005 / Eds.: Y. Potvin, M. Hudyma. - Perth: Australian Centre for Geomechanics, 2005. - P. 229-237.
5. King G.C.P., Sammis C.G. The mechanisms of finite brittle strain // Pure Appl. Geophys. - 1992. - Vol. 138, no. 4. - P. 611-640. DOI
6. Scholz C.H. The mechanics of earthquakes and faulting. - Cambridge: Cambridge University Press, 2002. - 471 p.
7. Stavrogin A.N., Tarasov B.G. Experimental physics and rock mechanics: results of laboratory studies. - Lisse/Abingdon/ Exton/Tokio: A.A. Balkema Publishers, 2001. - 356 p.
8. Tarasov B.G., Randolph M.F. Frictionless shear at great depth and other paradoxes of hard rocks // Int. J. Rock Mech. Min. - 2008. - Vol. 45, no. 3. - P. 316-328. DOI
9. Tarasov B.G. Intersonic shear rupture mechanism // Int. J. Rock Mech. Min. - 2008. - Vol. 45, no. 6. - P. 914-928. DOI
10. Tarasov B.G. Hitherto unknown shear rupture mechanism as a source of instability in intact hard rocks at highly confined compression // Tectonophysics. - 2014. - Vol. 621. - P. 69-84. DOI
11. Tarasov B.G. Superbrittleness of rocks at high confining pressure // Proc. of 5th Int. Seminar on Deep and High Stress Mining, Keynote Address. Deep Mining 2010, Santiago, Chile, October 6-8, 2010 / Eds.: M. Van Sint Jan, Y. Potvin. - Perth: Australian Centre for Geomechanics, 2010. - P. 119-133.
12. Tarasov B.G., Randolph M.F. Superbrittleness of rocks and earthquake activity // Int. J. Rock Mech. Min. - 2011. - Vol. 48, no. 6. - P. 888-898. DOI
13. Tarasov B., Potvin Y. Universal criteria for rock brittleness estimation under triaxial compression // Int. J. Rock Mech. Min. - 2013. - Vol. 59. - P. 57-69. DOI
14. Tarasov B.G. Fan-structure shear rupture mechanism as a source of shear rupture rockbursts // J. S. Afr. I. Min. Metall. - 2014. - Vol. 114. - P. 773-784.
15. Tarasov B.G. Depth distribution of lithospheric strength determined by the self-unbalancing shear rupture mechanism // Proc. of Int. Symp.: Rock Mechanics for Resources, Energy and Environment. EUROCK 2013, Wroclaw, Poland, September 21-26, 2013 / Eds.: M. Kwasniewski, D. Lydzba. - London: Taylor & Francis Group, 2013. - Ch. 21. - P. 165-170. DOI
16. Tarasov B.G., Randolph M.F. Improved concept of lithospheric strength and earthquake activity at shallow depths based upon the fan-head dynamic shear rupture mechanism // Tectonophysics. - 2015. - Vol. 667. - P. 124-143. DOI
17. Tarasov B.G., Guzev M.A. New insight into the nature of size dependence and the lower limit of rock strength // Proc. of 8th Int. Symp. on Rockbursts and Seismicity in Mines. RaSiM8, Saint Petersburg-Moscow, Russia, September 1-7, 2013 / Eds. A. Malovichko, D. Malovichko. - Obninsk/Perm: GS RAS & MI UB RAS, 2013. - P. 31-40.
18. Sadovskaa O.V., Sadovskij V.M. Matematiceskoe modelirovanie v zadacah mehaniki sypucih sred. - M.: Fizmatlit, 2008. - 368 s. DOI
19. Glovinski R., Lions Z.-L., Tremol’er R. Cislennoe issledovanie variacionnyh neravenstv. - M.: Mir, 1979. - 574 s.
20. Sadovskij V.M., Cencov E.P. Analiz rezonansnogo vozbuzdenia sloistyh i blocnyh sred na osnove diskretnyh modelej // Vycislitel’nye metody i programmirovanie. - 2015. - T. 16, No 2. - S. 318-327.
21. Marcuk G.I. Metody vycislitel’noj matematiki. - M.: Nauka, 1989. - 608 s.
22. Novikov E.A. Avnye metody dla zestkih sistem. - Novosibirsk: Nauka, 1997. - 192 s.
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