Quasi-static Planar Deformation in av Medium Composed of Elastic and Thermoelastic Solid Half Spaces Due to Seismic Sources in an Elastic Solid

• Autorzy: Vashisth A. K. , Rani K. , Singh K.

Identyfikatory

DOI

10.1515/acgeo-2015-0011

• Języki publikacji: EN

Abstrakty

EN

A two-dimensional problem of quasi static deformation of a medium consisting of an elastic half space in welded contact with thermoelastic half space, caused due to seismic sources, is studied. Source is considered to be in the elastic half space. The basic equations, governed by the coupled theory of thermoelasticity, are used to model for thermoelastic half space. The analytical expressions for displacements, strain and stresses in the two half spaces are obtained first for line source and then for dip slip fault. The results for two particular cases, adiabatic conditions and isothermal conditions, are also obtained. Numerical results for displacements, stresses and temperature distribution have also been computed and are shown.

Słowa kluczowe

EN

seismic sources; thermoelastic; quasi-static; deformation

PL

źródła sejsmiczne; termoelastyczność; quasi-statyczność; odkształcenie

• Wydawca: Instytut Geofizyki PAN ; Springer
• Czasopismo: Acta Geophysica
• Rocznik: 2015
• Tom: Vol. 63, no. 3
• Strony: 605--633
• Opis fizyczny: Bibliogr. 60 poz., rys., wykr.

Twórcy

autor

Vashisth A. K.

• Department of Mathematics, Kurukshetra University, Kurukshetra, India

autor

Rani K.

• Department of Mathematics, Government Post Graduate College, Hisar, India

autor

Singh K.

• Department of Mathematics, Guru Jambheshwar University of Science and Technology, Hisar, India

Bibliografia

• [1] Abd-Alla, A.M. (1995), Thermal stress in a transversely isotropic circular cylinder due to an instantaneous heat source, Appl. Math. Comput. 68, 2-3, 113-124, DOI: 10.1016/0096-3003(94)00085-I.
• [2] Ahrens, T.J. (ed.) (1995), Mineral Physics and Crystallography: A Handbook of Physical Constants, American Geophysical Union, Washington, D.C.
• [3] Aki, K., and P.G. Richards (1980), Quantitative Seismology: Theory and Methods, Vol. I and II, W.H. Freeman & Co., San Francisco.
• [4] Attetkov, A.V., I.K. Volkov, and S.S. Pilyavskii (2009), Temperature field of a solid body containing a spherical heating source with a uniformly moving boundary, J. Eng. Phys. Thermophys. 82, 2, 368-375, DOI: 10.1007/ s10891-009-0185-x.
• [5] Ben-Menahem, A., and S.J. Singh (1981), Seismic Waves and Sources, 2nd ed., Springer Verlag, New York.
• [6] Burridge, R., and L. Knopoff (1964), Body force equivalents for seismic dislocations, Bull. Seismol. Soc. Am. 54, 6a, 1875-1888.
• [7] Dziewonski, A.M., and D.L. Anderson (1981), Preliminary reference Earth model, Phys. Earth Planet. In. 25, 4, 297-356, DOI: 10.1016/0031-9201(81)90046-7.
• [8] Freund, L.B., and D.M. Barnett (1976), A two-dimensional analysis of surface deformation due to dip-slip faulting, Bull. Seismol. Soc. Am. 66, 3, 667-675.
• [9] Garg, N.R., and S.J. Singh (1987), 2-D static response of a transversely isotropic multilayered half-space to surface loads, Indian J. Pure Appl. Math. 18, 8, 763-777.
• [10] Garg, N.R., D.K. Madan, and R.K. Sharma (1996), Two-dimensional deformation of an orthotropic elastic medium due to seismic sources, Phys. Earth Planet. In. 94, 1-2, 43-62, DOI: 10.1016/0031-9201(95)03095-6.
• [11] Garg, N.R., R. Kumar, A. Goel, and A. Miglani (2003), Plane strain deformation of an orthotropic elastic medium using an eigenvalue approach, Earth Planets Space 55, 1, 3-9, DOI: 10.1186/BF03352457.
• [12] Ghosh, M.K., and M. Kanoria (2007), Displacements and stresses in composite multi-layered media due to varying temperature and concentrated load, Appl. Math. Mech. 28, 6, 811-822, DOI: 10.1007/s10483-007-0611-5.
• [13] Heaton, T.H., and R.E. Heaton (1989), Static deformations from point forces and force couples located in welded elastic Poissonian half-spaces: Implications for seismic moment tensors, Bull. Seismol. Soc. Am. 79, 3, 813-841.
• [14] Hou, P.-F., A.Y.T. Leung, and C.-P. Chen (2008a), Fundamental solution for transversely isotropic thermoelastic materials, Int. J. Solids Struct. 45, 2, 392-408, DOI: 10.1016/j.ijsolstr.2007.08.024.
• [15] Hou, P.-F., A.Y.T. Leung, and C.-P. Chen (2008b), Green’s functions for semiinfinite transversely isotropic thermoelastic materials, ZAMM J. Appl. Math. Mech. 88, 1, 33-41, DOI: 10.1002/zamm.200710355.
• [16] Hou, P.-F., L. Wang, and T. Yi (2009), 2D Green’s functions for semi-infinite orthotropic thermoelastic plane, Appl Math. Model. 33, 3, 1674-1682, DOI: 10.1016/j.apm.2008.03.004.
• [17] Hou, P.-F., S. He, and C.-P. Chen (2011), 2D general solution and fundamental solution for orthotropic thermoelastic materials, Eng. Anal. Bound. Elem. 35, 1, 56-60, DOI: 10.1016/j.enganabound.2010.04.007.
• [18] Jovanovich, D.B., M.I. Husseini, and M.A. Chinnery (1974a), Elastic dislocations in a layered half-space - I. Basic theory and numerical methods, Geophys. J. Int. 39, 2, 205-217, DOI: 10.1111/j.1365-246X.1974.tb05451.x.
• [19] Jovanovich, D.B., M.I. Husseini, and M.A. Chinnery (1974b), Elastic dislocations in a layered half-space - II. The point source, Geophys. J. Int. 39, 2, 219-239, DOI: 10.1111/j.1365-246X.1974.tb05452.x.
• [20] Kit, H.S., B.E. Monastyrs’kyi, and O.P. Sushko (2001), Thermoelastic state of a semiinfinite body with plane surface crack under the action of heat sources, Mater. Sci. 37, 4, 610-614, DOI: 10.1023/A:1013272721094.
• [21] Kumar, A., S.J. Singh, and J. Singh (2005), Deformation of two welded elastic halfspaces due to a long inclined tensile fault, J. Earth Syst. Sci. 114, 1, 97-103, DOI: 10.1007/BF02702012.
• [22] Kumar, R., and R.R. Gupta (2009), Plane strain deformation in an orthotropic micropolar thermoelastic solid with a heat source, J. Eng. Phys. Thermophys. 82, 3, 556-565, DOI: 10.1007/s10891-009-0220-y.
• [23] Kumar, R., and L. Rani (2004), Deformation due to mechanical and thermal sources in generalised orthorhombic thermoelastic material, Sadhana 29, 5, 429-447, DOI: 10.1007/BF02703254.
• [24] Kumari, G., S.J. Singh, and K. Singh (1992), Static deformation of two welded elastic half-spaces caused by a point dislocation source, Phys. Earth Planet. In. 73, 1-2, 53-76, DOI: 10.1016/0031-9201(92)90107-7.
• [25] Lanzano, P. (1986a), Thermoelastic deformations of Earth’s lithosphere: A mathematical model, Earth Moon Planets 34, 3, 283-304, DOI: 10.1007/ BF00145087.
• [26] Lanzano, P. (1986b), Heat conduction within an elastic Earth, Earth Moon Planets 36, 2, 157-166, DOI: 10.1007/BF00057608.
• [27] Lay, T., and T.C. Wallace (1995), Modern Global Seismology, Academic Press, San Diego.
• [28] Madan, D.K., K. Singh, R. Aggarwal, and A. Gupta (2005), Displacements and stresses in an anisotropic medium due to non-uniform slip along a very long strike-slip fault, ISET J. Earthq. Technol. 42, 1, 1-11.
• [29] Mallik, S.H., and M. Kanoria (2008), A two dimensional problem for a transversely isotropic generalized thermoelastic thick plate with spatially varying heat source, Eur. J. Mech. A 27, 4, 607-621, DOI: 10.1016/j.euromechsol.2007.09.002.
• [30] Maruyama, T. (1964), Statical elastic dislocations in an infinite and semi-infinite medium, Bull. Earthq. Res. Inst. Univ. Tokyo 42, 2, 289-368.
• [31] Maruyama, T. (1966), On two-dimensional elastic dislocations in an infinite and semi-infinite medium, Bull. Earthq. Res. Inst. Univ. Tokyo 44, 811-871.
• [32] Nowacki, W. (1975), Dynamical Problems of Thermoelasticity, PWN Polish Sci. Publ., Warszawa, Noordhoff Int. Publ., Leyden.
• [33] Okada, Y. (1985), Surface deformation due to shear and tensile faults in a halfspace, Bull. Seismol. Soc. Am. 75, 4, 1135-1154.
• [34] Okada, Y. (1992), Internal deformation due to shear and tensile faults in a halfspace, Bull. Seismol. Soc. Am. 82, 2, 1018-1040.
• [35] Pan, E. (1989a), Static response of a transversely isotropic and layered half-space to general surface loads, Phys. Earth Planet. In. 54, 3-4, 353-363, DOI: 10.1016/0031-9201(89)90252-5.
• [36] Pan, E. (1989b), Static response of a transversely isotropic and layered half-space to general dislocation sources, Phys. Earth Planet. In. 58, 2-3, 103-117, DOI: 10.1016/0031-9201(89)90046-0.
• [37] Pan, E. (1990), Thermoelastic deformation of a transversely isotropic and layered half-space by surface loads and internal sources, Phys. Earth Planet. Int. 60, 1-4, 254-264, DOI: 10.1016/0031-9201(90)90266-Z.
• [38] Rani, S., S.J. Singh, and N.R. Garg (1991), Displacements and stresses at any point of a uniform half-space due to two-dimensional buried sources, Phys. Earth Planet. Int. 65, 3-5, 276-282, DOI: 10.1016/0031-9201(91)90134-4.
• [39] Rongved, L., and J.T. Frasier (1958), Displacement discontinuity in the elastic halfspace, J. Appl. Mech. 25, 125-128.
• [40] Rundle, J.B. (1982), Some solutions for static and pseudo-static deformation in layered, nonisothermal, porous media, J. Phys. Earth 30, 5, 421-440, DOI: 10.4294/jpe1952.30.421.
• [41] Sato, R. (1971), Crustal deformation due to dislocation in a multi-layered medium, J. Phys. Earth 19, 1, 31-46, DOI: 10.4294/jpe1952.19.31.
• [42] Sato, R., and M. Matsu’ura (1973), Static deformations due to the fault spreading over several layers in a multi-layered medium. Part I: Displacement, J. Phys. Earth 21, 3, 227-249, DOI: 10.4294/jpe1952.21.227.
• [43] Schapery, R.A. (1962), Approximate methods of transform inversion for viscoelastic stress analysis. In: Proc. 4th U.S. National Congress of Applied Mechanics, 18-21 June 1962, Berkeley USA, Vol. 2, 1075-1085, American Society of Mechanical Engineers, New York.
• [44] Shevchenko, V.P., and A.S. Gol’tsev (2001), The thermoelastic state of orthotropic shells heated by concentrated heat sources, Int. Appl. Mech. 37, 5, 654-661, DOI: 10.1023/A:1012364530719.
• [45] Singh, K., D.K. Madan, A. Goel, and N.R. Garg (2005), Two-dimensional static deformation of an anisotropic medium, Sadhana 30, 4, 565-583, DOI:10.1007/BF02703280.
• [46] Singh, S.J. (1970), Static deformation of a multilayered half-space by internal sources, J. Geophys. Res. 75, 17, 3257-3263, DOI: 10.1029/ JB075i017p03257.
• [47] Singh, S.J., and A. Ben-Menahem (1969), Displacement and strain fields due to faulting in a sphere, Phys. Earth Planet. In. 2, 2, 77-87, DOI: 10.1016/ 0031-9201(69)90003-X.
• [48] Singh, S.J., and N.R Garg (1985), On two-dimensional elastic dislocations in a multilayered half-space, Phys. Earth Planet. In. 40, 2, 135-145, DOI: 10.1016/ 0031-9201(85)90067-6.
• [49] Singh, S.J., and N.R. Garg (1986), On the representation of two-dimensional seismic sources, Acta Geophys. Pol. 34, 1, 1-12.
• [50] Singh, S.J., A. Ben-Menahem, and M. Vered (1973), A unified approach to the representation of seismic sources, Proc. Roy. Soc. London A 331, 1587, 525-551, DOI: 10.1098/rspa.1973.0006.
• [51] Singh, S.J., S. Rani, and N.R. Garg (1992), Displacements and stresses in two welded half-spaces caused by two-dimensional sources, Phys. Earth Planet. In. 70, 1, 90-101, DOI: 10.1016/0031-9201(92)90164-Q.
• [52] Singh, S.J., G. Kumari, and K. Singh (1993), Static deformation of two welded elastic half-spaces caused by a finite rectangular fault, Phys. Earth Planet. In. 79, 3, 313-333, DOI: 10.1016/0031-9201(93)90112-M.
• [53] Singh, S.J., A. Kumar, and J. Singh (2003), Deformation of a monoclinic elastic half-space by a long inclined strike-slip fault, ISET J. Earthq. Technol. 40, 1, 51-59.
• [54] Small, J.C., and J.R. Booker (1986), The behaviour of layered soil or rock containing a decaying heat source, Int. J. Numer. Anal. Meth. Geomech. 10, 5, 501-519, DOI: 10.1002/nag.1610100504.
• [55] Stein, S., and M. Wysession (2003), An Introduction to Seismology, Earthquakes, and Earth Structure, Blackwell Publishing, Oxford.
• [56] Steketee, J.A. (1958), On Volterra’s dislocations in a semi-infinite elastic medium, Can. J. Phys. 36, 2, 192-205, DOI: 10.1139/p58-024.
• [57] Tomar, S.K., and N.K. Dhiman (2003), 2-D deformation analysis of a half-space due to a long dip-slip fault at finite depth, J. Earth Syst. Sci. 112, 4, 587-596, DOI: 10.1007/BF02709782.
• [58] Youssef, H.M. (2006), Problem of generalized thermoelastic infinite medium with cylindrical cavity subjected to a ramp-type heating and loading, Arch. Appl. Mech. 75, 8-9, 553-565, DOI: 10.1007/s00419-005-0440-3.
• [59] Youssef, H.M. (2009), Generalized thermoelastic infinite medium with cylindrical cavity subjected to moving heat source, Mech. Res. Commun. 36, 4, 487-496, DOI: 10.1016/j.mechrescom.2008.12.004.
• [60] Youssef, H.M. (2010), Two-temperature generalized thermoelastic infinite medium with cylindrical cavity subjected to moving heat source, Arch. Appl. Mech. 80, 11, 1213-1224, DOI: 10.1007/s00419-009-0359-1.