Displacement Pattern in a Functionally Graded Transversely Isotropic, Half-Space Due to Dislocation

Document Type : Research

Authors

1 Ph.D. Candidate, Faculty of Civil and Environmental Engineering, Tarbiat Modares University, P.O. Box 14115-397, Tehran, Iran.

2 Ph.D., Civil and Environmental Engineering Program, Graduate School of Advanced Science and Engineering, Hiroshima University, Higashi-Hiroshima, 739-8527, Japan.

Abstract

The forward solution of dislocation on the fault plane is one of the most important issues for earthquake source slip inversion. The dislocation on the fault plane, explained by the Burgers vector which is called slip, plays a fundamental role in estimating displacement patterns in the whole medium. In addition, obtaining displacement values in any point of a medium is possible by using the slip function on the fault plane and Green’s function as medium properties. This study shows that various assumptions for earth materials result in significant differences in displacements. Therefore, due to the realistic ground motion simulations caused by future earthquakes, considering the properties of earth materials requires more attention. By implementing the elastostatic Green’s functions and based upon line integral representations due to an arbitrary Volterra dislocation loop, elastic displacements and strains due to finite fault dislocations in a functionally graded transversely isotropic (FGTI) half-space material is presented. Also, numerical examples are provided to demonstrate the effect of material anisotropy on the internal and surface responses of the half-space.

Keywords

References

1. Lamb, H. (1904). I. On the propagation of tremors over the surface of an elastic solid. Philosophical Transactions of the Royal Society of London. Series A, Containing papers of a mathematical or physical character, 203(359-371), 1-42. [DOI:10.1098/rsta.1904.0013]
2. Steketee, J. A. (1958). On Volterra's dislocations in a semi-infinite elastic medium. Canadian Journal of Physics, 36(2), 192-205. [DOI:10.1139/p58-024]
3. Maruyama, T. (1964). 16. Statical elastic dislocations in an infinite and semi-infinite medium. Bull. Earthq. Res. Inst, 42, 289-368.
4. Robertson, I. A. (1966). Forced vertical vibration of a rigid circular disc on a semi-infinite elastic solid. In Mathematical proceedings of the Cambridge philosophical society (Vol. 62, No. 3, pp. 547-553). Cambridge University Press. [DOI:10.1017/S0305004100040184]
5. Apsel, R. J., & Luco, J. E. (1976). Torsional response of rigid embedded foundation. Journal of the Engineering Mechanics Division, 102(6), 957-970. [DOI:10.1061/JMCEA3.0002193]
6. Higashihara, H. (1984). Explicit Green's function approach to forced vertical vibrations of circular disk on semi-infinite elastic space. Journal of engineering mechanics, 110(10), 1510-1523. [DOI:10.1061/(ASCE)0733-9399(1984)110:10(1510)]
7. Okada, Y. (1985). Surface deformation due to shear and tensile faults in a half-space. Bulletin of the seismological society of America, 75(4), 1135-1154. [DOI:10.1785/BSSA0750041135]
8. Okada, Y. (1992). Internal deformation due to shear and tensile faults in a half-space. Bulletin of the seismological society of America, 82(2), 1018-1040. [DOI:10.1785/BSSA0820021018]
9. Thongchom, C., Roodgar Saffari, P., Roudgar Saffari, P., Refahati, N., Sirimontree, S., Keawsawasvong, S., & Titotto, S. (2022b). Dynamic response of fluid-conveying hybrid smart carbon nanotubes considering slip boundary conditions under a moving nanoparticle. Mechanics of Advanced Materials and Structures, 1-14. [DOI:10.1080/15376494.2022.2051101]
10. Moshtagh, E., Eskandari-Ghadi, M., & Pan, E. (2019). Time-harmonic dislocations in a multilayered transversely isotropic magneto-electro-elastic half-space. Journal of Intelligent Material Systems and Structures, 30(13), 1932-1950. [DOI:10.1177/1045389X19849286]
11. Wang, C. D., Tzeng, C. S., Pan, E., & Liao, J. J. (2003). Displacements and stresses due to a vertical point load in an inhomogeneous transversely isotropic half-space. International Journal of Rock Mechanics and Mining Sciences, 40(5), 667-685. [DOI:10.1016/S1365-1609(03)00058-3]
12. Pan, E., Yuan, J. H., Chen, W. Q., & Griffith, W. A. (2014). Elastic deformation due to polygonal dislocations in a transversely isotropic half‐space. Bulletin of the Seismological Society of America, 104(6), 2698-2716. [DOI:10.1785/0120140161]
13. Molavi Tabrizi, A., & Pan, E. (2015). Time-dependent displacement and stress fields due to shear and tensile faults in a transversely isotropic viscoelastic half-space. Geophysical Journal International, 202(1), 163-174. [DOI:10.1093/gji/ggv115]
14. Pan, E., & Chen, W. (2015). Static green's functions in anisotropic media. Cambridge University Press. [DOI:10.1017/CBO9781139541015]
15. Pan, E., Molavi Tabrizi, A., Sangghaleh, A., & Griffith, W. A. (2015). Displacement and stress fields due to finite faults and opening-mode fractures in an anisotropic elastic half-space. Geophysical Journal International, 203(2), 1193-1206. [DOI:10.1093/gji/ggv362]
16. Pan, E., Griffith, W. A., & Liu, H. (2019). Effects of generally anisotropic crustal rocks on fault-induced displacement and strain fields. Geodesy and Geodynamics, 10(5), 394-401. [DOI:10.1016/j.geog.2018.05.004]
17. Han, Z., Lin, G., & Li, J. (2015). Dynamic impedance functions for arbitrary-shaped rigid foundation embedded in anisotropic multilayered soil. Journal of Engineering Mechanics, 141(11), 04015045. [DOI:10.1061/(ASCE)EM.1943-7889.0000915]
18. Singh, A. K., Koley, S., Negi, A., & Ray, A. (2019). On the dynamic behavior of a functionally graded viscoelastic-piezoelectric composite substrate subjected to a moving line load. The European Physical Journal Plus, 134(3), 1-22. [DOI:10.1140/epjp/i2019-12444-2]
19. Attia, M. A., & El-Shafei, A. G. (2020). Investigation of multibody receding frictional indentation problems of unbonded elastic functionally graded layers. International Journal of Mechanical Sciences, 184, 105838. [DOI:10.1016/j.ijmecsci.2020.105838]
20. Azaripour, S., & Baghani, M. (2019). Vibration analysis of FG annular sector in moderately thick plates with two piezoelectric layers. Applied Mathematics and Mechanics, 40(6), 783-804. [DOI:10.1007/s10483-019-2468-8]
21. Yas, M. H., & Moloudi, N. (2015). Three-dimensional free vibration analysis of multi-directional functionally graded piezoelectric annular plates on elastic foundations via state space based differential quadrature method. Applied Mathematics and Mechanics, 36(4), 439-464. [DOI:10.1007/s10483-015-1923-9]
22. Martin, P. A., Richardson, J. D., Gray, L. J., & Berger, J. R. (2002). On Green's function for a three-dimensional exponentially graded elastic solid. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 458(2024), 1931-1947. [DOI:10.1098/rspa.2001.0952]
23. Roshanbakhsh, M. Z., Tavakkoli, S. M., & Neya, B. N. (2020). Free vibration of functionally graded thick circular plates: An exact and three-dimensional solution. International Journal of Mechanical Sciences, 188, 105967. [DOI:10.1016/j.ijmecsci.2020.105967]
24. Thongchom, C., Jearsiripongkul, T., Refahati, N., Roudgar Saffari, P., Roodgar Saffari, P., Sirimontree, S., & Keawsawasvong, S. (2022a). Sound transmission loss of a honeycomb sandwich cylindrical shell with functionally graded porous layers. Buildings, 12(2), 151. [DOI:10.3390/buildings12020151]
25. Çömez, İ. (2015). Contact problem for a functionally graded layer indented by a moving punch. International Journal of Mechanical Sciences, 100, 339-344. [DOI:10.1016/j.ijmecsci.2015.07.006]
26. Eskandari, M., & Shodja, H. M. (2010). Green's functions of an exponentially graded transversely isotropic half-space. International Journal of Solids and Structures, 47(11-12), 1537-1545. [DOI:10.1016/j.ijsolstr.2010.02.014]
27. Eskandari-Ghadi, M., & Amiri-Hezaveh, A. (2014). Wave propagations in exponentially graded transversely isotropic half-space with potential function method. Mechanics of Materials, 68, 275-292. [DOI:10.1016/j.mechmat.2013.09.009]
28. Kalantari, M., Khaji, N., & Eskandari-Ghadi, M. (2021). Rocking forced displacement of a rigid disc embedded in a functionally graded transversely isotropic half-space. Mathematics and Mechanics of Solids, 26(7), 1029-1052. [DOI:10.1177/1081286520979351]
29. Kalantari, M., & Khaji, N. (2022). Torsion vibration of foundation in a functionally graded transversely isotropic, linearly elastic half-space. Forces in Mechanics, 100082. [DOI:10.1016/j.finmec.2022.100082]
30. Kalantari, M., Khaji, N., Eskandari-Ghadi, M., & Keawsawasvong, S. (2022). Dynamic Analysis of a Vertically Loaded Rigid Disc in a Functionally Graded Transversely Isotropic Half-Space. Transportation Infrastructure Geotechnology, 1-25. [DOI:10.1007/s40515-022-00234-6]
31. Yuan, J. H., Pan, E., & Chen, W. Q. (2013). Line-integral representations for the elastic displacements, stresses and interaction energy of arbitrary dislocation loops in transversely isotropic bimaterials. International Journal of Solids and Structures, 50(20-21), 3472-3489. [DOI:10.1016/j.ijsolstr.2013.06.017]
32. Kalantari, M., Khojasteh, A., Mohammadnezhad, H., Rahimian, M., & Pak, R. Y. S. (2015). An inextensible membrane at the interface of a transversely isotropic bi-material full-space. International Journal of Engineering Science, 91, 34-48. [DOI:10.1016/j.ijengsci.2015.02.004]
33. Aster, R. C., Borchers, B., & Thurber, C. H. (2018). Parameter estimation and inverse problems. Elsevier. [DOI:10.1016/B978-0-12-804651-7.00015-8]
34. Shahmohamadi, M., Khojasteh, A., Rahimian, M., & Pak, R. (2017). The frictionless axial interaction of a rigid disk with a two-layered functionally graded transversely isotropic medium. Mathematics and Mechanics of Solids, 22(6), 1407-1424. [DOI:10.1177/1081286516635871]
35. Nirwal, S., Sahu, S. A., Baroi, J., & Saroj, P. K. (2021). Analysis of wave scattering in 3-layer piezo composite structure [Pb [Zr x Ti1-x] O3-ALN-Pb [Zr x Ti1-x] O3]. Mechanics Based Design of Structures and Machines, 49(3), 307-328. [DOI:10.1080/15397734.2019.1686991]
36. Ding, H., Chen, W., & Zhang, L. (2006). Elasticity of transversely isotropic materials (Vol. 126). Springer Science & Business Media.
37. Godfrey, N. J., Christensen, N. I., & Okaya, D. A. (2000). Anisotropy of schists: Contribution of crustal anisotropy to active source seismic experiments and shear wave splitting observations. Journal of Geophysical Research: Solid Earth, 105(B12), 27991-28007. [DOI:10.1029/2000JB900286]
38. Vajedian, S., Motagh, M., Mousavi, Z., Motaghi, K., Fielding, E., Akbari, B., ... & Darabi, A. (2018). Coseismic deformation field of the Mw 7.3 12 November 2017 Sarpol-e Zahab (Iran) earthquake: A decoupling horizon in the northern Zagros Mountains inferred from InSAR observations. Remote Sensing, 10(10), 1589. [DOI:10.3390/rs10101589]
39. Wang, Z. (2002). Seismic anisotropy in sedimentary rocks, part 1: A single-plug laboratory method. Geophysics, 67(5), 1415-1422. [DOI:10.1190/1.1512787]
40. Kalantari, M., & Khaji, N. (2022). Response of rigid circular plate in a functionally graded transversely isotropic, half-space under horizontal steady-state excitation. Mechanics Based Design of Structures and Machines, 1-24 (in press). [DOI:10.1080/15397734.2022.2098762]
Numerical Methods in Civil Engineering
Volume 7, Issue 2
December 2022
Pages 42-49

Files

History

  • Receive Date: 26 April 2022
  • Revise Date: 02 June 2022
  • Accept Date: 04 June 2022

Share

How to cite

Statistics