On the similarity of shear deformation of a granular massif and a fragmented medium in the seismically active area
DOI:
https://doi.org/10.24028/gzh.v43i3.236386Keywords:
granular medium, shear deformation, earthquake, seismically active area, discrete element methodAbstract
In recent research, the dynamics of the medium located in the seismic region at the boundary of tectonic plates is considered as the behavior of a complex open system that is in a state of self-organized criticality. Such an approach results from the very laws of earthquake generation and the complex structure of these areas. The network of faults and cracks makes seismic zones significantly heterogeneous and fragmented. Therefore, discrete models are increasingly used to model the dynamics of these media. The basis for comparing the model and the full-scale object serves the statistical regularities of their dynamic deformation. Relying on this concept, in the paper it is modeled the shear dynamics of a granular massif composed of identical cubic granules and is compared system’s statistical characteristics with the similar characteristics obtained for the earthquake generation zone. Shear deformation is carried out by means of the box consisting of two parts — movable and immovable ones. The movable part possesses the cover which receives kinetic energy from the granular massif in the process of shear deformation. For numerical simulations of the shear dynamics, the discrete element method is applied. The numerical calculations result in the distribution of cover’s kinetic energy jumps simulating the perturbations transmitted from the granular system to an external medium. It turned out that the distribution for these perturbations is the power dependence with an exponent that is inherent in earthquakes (Gutenberg-Richter law). Before and after large perturbations it is observed the swarms of smaller perturbations which are the analogues of foreshocks and aftershocks. The distributions of element’s velocity fluctuations and the correlation of velocity fluctuations are calculated as well. It is revealed the similarity of distributions for velocity fluctuations in the model massif and in the seismically active region of California, which includes the San Andreas fault. Moreover, the similarity of corresponding correlation functions is shown. They both are the functions of the stretched exponent. The obtained result indicates that shear processes in granular massifs and natural seismic processes in the San Andreas Fault are statistically similar.
References
Beeman, D. (1976). Some multistep methods for use in molecular dynamics calculations. Journal of Computational Physics, 20(2), 130—139.https://doi.org/10.1016/0021-9991(76)90059-0.
Ben-Zion, Y., & Sammis, G. S. (2003). Characterization of fault zones. Pure and Applied Geophysics, 160, 677—715. https://doi.org/10.1007/PL00012554.
Beroza, G. C., & Ide, S. (2011). Slow earthquakes and nonvolcanic tremor. Annual Review of Earth and Planetary Sciences, 39, 271—296. https://doi.org/10.1146/annurev-earth-040809-152531.
Billi, A., & Storti, F. (2004). Fractal distribution of particle size in carbonate cataclastic rocks from the core of a regional strike-slip fault zone. Tectonophysics, 384, 115—128. https://doi.org/10.1016/j.tecto.2004.03.015.
Cundall, P. A. (1971). A computer model for simulating progressive large-scale movements in blocky rock systems. Proceedings of International Symposium Rock Fracture (pp. 2—8). ISRM, Nancy.
Forsythe, G. E., Malcolm, M. A., & Moler, C. B. (1977). Computer methods for mathematical computations. New Jersey: Prentice Hall, Inc., 259 p.
Geller, D. A., Ecke, R. E., Dahmen, K. A., & Backhaus, S. (2015). Stick-slip behavior in a continuum-granular experiment. Physical Review E, 92, 060201(R). https://doi.org/10.1103/PhysRevE.92.060201.
Gürlebeck, K., & Sprössig, W. (1997). Quaternionic and Clifford calculus for physicists and engineers. Chichester: Wiley, 384 p.
Kanamori, H., & Schubert, G. (eds.) (2015). Treatise on Geophysics: Vol. 4 Earthquake Seismology (2-d edition). Amsterdam: Elsevier, 653 p.
Kumar, P., Korkolis, E., Benzi, R., Denisov, D., Niemeijer, A, Schall, P., Toschi, F., &Trampert, J. (2020). On interevent time distributions of avalanche dynamics. Scientific Reports, 10(1), 626. https://doi.org/10.1038/s41598-019-56764-6.
Lherminier, S., Planet, R., Levy ditVehel, V., Simon, G., Vanel, L., Måløy, K. J., & Ramos, O. (2019). Continuously sheared granular matter reproduces in detail seismicity laws. Physical Review Letters, 122, 218501.https://doi.org/10.1103/PhysRevLett.122.218501.
Loveless, J. P., & Meade, B. J. (2011). Stress modulation on the San Andreas fault by interseismic fault system interactions. Geology, 39(11), 1035—1038. https://doi.org/10.1130/G32215.1.
McCaffrey, R. (2005). Block kinematics of the Pacific-North America plate boundary in the southwestern United States from inversion of GPS, seismological, and geologic data. Journal of Geophysical Research, 110, B07401. https://doi.org/10.1029/2004JB003307.
Meade, B. J., & Hager, B. H. (2005). Block models of crustal motion in southern California constrained by GPS measurements. Journal of Geophysical Research, 110, B03403. https://doi.org/10.1029/2004JB003209.
Meroz, Y., & Meade, B. J. (2017). Intermittent granular dynamics at a seismogenic plate boundary. Physical Review Letters, 119, 138501. https://doi.org/10.1103/PhysRevLett.119.138501.
Mykulyak, S. V. (2019). The regularities of the dynamics of structured geomedia: theory, model, experiment. Extended abstract of Doctor’s thesis. Kyiv, 37 p. (in Ukrainian).
Mykulyak, S., Kulich, V., & Skurativskyi, S. (2019a).Simulation of shear motion of angular grains massif via the discrete element method. In Z. Hu, S. Petoukhov, I. Dychka, M. He (Eds.), Advances in Computer Science for Engineering and Education. ICCSEEA 2018. Advances in Intelligent Systems and Computing (Vol. 754, 74—81). Springer. https://doi.org/10.1007/978-3-319-91008-6_8.
Mykulyak, S. V., Polyakovskyi, V. O., & Skurativskyi, S. I. (2019b). Statistical properties of shear deformation of granular media and analogies with natural seismic processes. Pure and Applied Geophysics, 176, 4309—4319. https://doi.org/10.1007/s00024-019-02209-0.
Mykulyak, S. V., Polyakovskyi, V. O., & Skurativskyi, S. I. (2021). Experimental study of shear deformation of the medium formed by the massif of ribbed grain. Geofizicheskiy zhurnal, 43(2), 178—188. https://doi.org/ 10.24028/gzh.v43i2.230197.
Nassauer, B., & Kuna, M. (2013). Contact forces of polyhedral particles in discrete element method. Granular Matter, 15(3), 349—355. https://doi.org/10.1007/s10035-013-0417-9.
Olami, Z., Feder, H. J. S., & Christensen, K. (1992). Self-organized criticality in a continuous, nonconservative cellular automaton modeling earthquakes. Physical Review Letters, 68, 1244. https://doi.org/10.1103/PhysRevLett.68.1244.
Shakarji, C. V. (1998). Least-squares fitting algorithms of the NIST algorithm testing system. Journal of Research of the National Institute of Standards and Technology, 103(6), 633—641.
Scholz, C. H. (2019). The mechanics of earthquakes and faulting (3-d edition). Cambridge: Cambridge University Press, 700 p.
Shelly, D. R., Beroza, G. C., Ide, S. & Nakamula, S. (2006). Low frequency earthquakes in Shikoku, Japan, and their relationship to episodic tremor and slip. Nature, 442, 188—191. https://doi.org/10.1038/nature04931.
Zhao, S., Zhou, X., & Liu, W. (2015). Discrete element simulations of direct shear tests with particle angularity effect. Granular Matter, 17(6), 793—806. https://doi.org/10.1007/s10035-015-0593-x.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
