About the zone of reduCed seismiC hazard in the transition from mountainous to flat terrain
Abstract
The relevance of the work lies in the need to search for areas with reduced seismic hazards in areas where mountain ranges turn into plains. There are few rigorous mechanical and mathematical approaches to studying seismicity in such areas, due to the fact that they require solving some problems in the theory of inte- gral equations. The aim of the research was to identify a reduced seismicity zone in the area of transition from a mountainous territory to a flat one. Methods. The solution of the contact problem on the concentration of contact stresses in the transition zone of a mountain range to a flat terrain was used for the study. It is assumed that the mountain range towering above the plain is modeled by a deformable stamp, which is located on an anisotropic half-space characteristic of granite layer structure in the lithospheric plate. The work takes into account tidal lunar impacts described by the time function. The task required constructing a solution to the two-dimensional Wiener- Hopf integral equation with an anisotropic symbol for the kernel of the integral equation. To describe a deformable stamp, the solution of the boundary value problem for a stamp of complex rheology is decomposed into solutions of boundary value problems for stamps of simplified rheology given by the Helmholtz equations. Results. In the process of study, a representation of the distribution of contact stresses under a deformable die was obtained. It is established that in the boundary zones of the deformable stamp, an increase in contact stresses occurs as it approaches the rectilinear boundary. To identify the zone of decreasing contact stress concentration, the case of a stamp with an internal angle was studied. It contains a sector that includes the first two quadrants and part of the third quadrant on the plane. The fracture zone of the stamp boundary, called the inner corner, is the least dangerous, and safety increases as the stamp sector solution increases, as shown in the table. A further increase in the mortar sector of the stamp may lead to the opposite location of the gorge boundaries approaching parallel ones, which may lead to I.I. Vorovich resonances.
References
Бабешко В.А., Евдокимова О.В., Бабешко О.М., Евдокимов В.С., Зарецкая М.В., Хрипков Д.В. О предвестнике повышенной сейсмичности в области перехода горной территории в равнинную. // Геология и геофизика Юга России. – 2025. – Т. 15. № 1. – С. 45–55. DOI: 10.46698/VNC.2025.25.51.004.
Бабешко В.А., Евдокимова О.В., Бабешко О.М., Уафа С.Б., Лозовой В.В., Евдокимов В.С. О предвестнике землетрясения в сейсмоопасной горной территории. // Геология и геофизика Юга России. – 2024. – Т. 14. № 2. – С. 33–44. DOI: 10.46698/VNC.2024.21.47.003.
Ворович И.И., Бабешко В.А. Динамические смешанные задачи теории упругости для неклассических областей. М.: Наука, 1979. – 320 с.
Гамбурцев Г.А. Перспективный план исследований по проблеме «Изыскание и развитие прогноза землетрясений». // В сборнике: Развитие идей Г.А. Гамбурцева в геофизике. М.: Наука, 1982. – С. 304–311.
Заалишвили В.Б., Мельков Д.А., Габараев А.Ф., Мерзликин Т.И. Нелинейные колебания грунтовой толщи по инструментальным и численным данным. // Геология и геофизика Юга России. – 2021. – Т. 11. № 4. – С. 70–82. DOI: 10.46698/VNC.2021.77.59.006.
Садовский М.А., Болховитинов Л.Г., Писаренко В.Ф. Деформирование геофизической среды и сейсмический процесс. М.: Наука, 1987. – 104 с.
Чернов Ю.К. Сильные движения грунта и количественная оценка сейсмической оценки территории. Ташкент: Фан, 1989. – 296 с.
Arhore E.G., Yasaee M., Dayyani I. Comparison of GA and topology optimization of adherend for adhesively bonded metal composite joints. // International Journal of solids and Structures. – 2021. – Vols. 226–227. Art. No. 11107. DOI: 10.1016/j.ijsolstr.2021.111078.
Awrejcewiez J., Krysko V.A., Mitskievich S.A., Zhigalov M.V., Krysko A.V. Nonlinear dynamics of heterogeneous shells. Part 1: Statics and dynamics of heterogeneous variable stiffness shells. // International Journal of Non-Linear Mechanics. – 2021. – Vol. 130. Art. No. 103669. DOI: 10.1016/jijnonlinmec.2021.103669.
Chernov Yu.K., Zaalishvili V.B., Chernov A.Yu. Strong ground motion simulation for forecasting the probable seismic impacts in the territory of the Republic of North Ossetia-Alania. // Izvestiya. Physics of the Solid Earth. – 2020. – Vol. 56. No. 5. – pp. 644–655. DOI: 10.1134/S1069351320050018.
Di Toro G., Han R., Hirose T., De Paola N., Nielsen S., Mizoguchi K., Ferri F., Cocco M., Shimamoto T. Fault lubrication during earthquake. // Natire. – 2011. – Vol. 471. Issue 7339. – pp. 494–498. DOI: 10.1038/nature09838.
Fernandez L., Novotny A.A., Prakash R., Sokołowski J. Pollution sources reconstruction based on the topological derivative method. // Applied Mathematics and Optimization. – 2021. – Vol. 84. – pp. 1493–152. DOI: 10.1007/s00245-020-09685-0.
Gonçalves J.F., Moreira J.B.D., Salas R.A. et al. Identification problem of acoustic media in the frequency domain based on the topology optimization method. // Structural and Multidisciplinary Optimization. – 2020. – Vol. 62. – pp. 1041–1059. DOI: 10.1007/s00158-020-02638-9.
Huang M., Lim X., Lei Y., Gu J. Structural damage identification based on modal frequency strain energy assurance criterion and flexibility using enhanced Moth-Flame optimization. // Structures. – 2020. – Vol. 28. – pp. 1119–1136. DOI: 10.1016/j.istruc.2020.08.085.
Lu X., Lapusta N., Rosakis A.J. Pulse-like and crack-like ruptures in experiments mimicking crustal earthquakes. // Proceedings of the National Academy of Sciences of the United States of America. – 2007. – Vol. 104. Issue 48. – pp. 18931–18936.
Mitchell E., Fialko Y., Brown K. Frictional properties of gabbro at conditions corresponding to slow slip events in subduction zones. // Geochemistry, Geophysics, Geosystems. – 2015. – Vol. 16. – pp. 4006–4020.
Mitchell E., Fialko Y., Brown K. Temperature dependence of frictional healing of westerly granite: Experimental observations and numerical Simulations. // Geochemistry, Geophysics, Geosystems. – 2013. – Vol. 14. – pp. 567–582.
Pena M., Rapun M.L. Application of the topological derivation to post-processing infrared time-harmonic thermograms for defect detection. // Journal of Mathematics in Industry. – 2020. – Vol. 10. DOI: 10.1186/s13362-020-0072-9.
Scholz C.H., Sykes L.R., Aggarwal Y.P. Earthquake prediction: a physical basis. // Science. – 1973. – Vol. 181. No. 4102. – pp. 803–810.
Xavier M., Van Goethem N., Novotny A.A. Hydro-mechanical fracture modeling governed by the topological derivatives. // Computer Methods in Applied Mechanics and Engineering. – 2020. – Vol. 365. Art. No. 112974. DOI: 10.1016/j.cma.2020.112974.
Xia K., Rosakis A.J., Kanamori H. Laboratory Earthquakes: The Sub-Rayleigh-toSupershear Rupture Transition. // Science. – 2004. – Vol. 303. – pp. 1859–1861.
Xia K., Rosakis A.J., Kanamory H., Rice J.R. Laboratory Earthquakes along Inhomogeneus Faults: Directionality and Supershear. // Science. – 2005. – Vol. 308. – pp. 681–684.
English
Русский
