Abstract
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.
Highlights
The elasticity theory of dislocation was developed and applied by Steketee (1958), Rongved and Frasier (1958), and Maruyama (1964, 1966)
The problems related to seismic sources in elastic media have been studied extensively by many researchers (Burridge and Knopoff 1964, Singh and BenMenahem 1969, Singh 1970, Sato 1971, Singh et al 1973, Sato and Matsu’ura 1973, Jovanovich et al 1974a, b; Freund and Barnett 1976, etc.)
The detailed description about seismic sources is given in the classical texts: Aki and Richards (1980), Ben-Menahem and Singh (1981), Lay and Wallace (1995), and Stein and Wysession (2003)
Summary
The elasticity theory of dislocation was developed and applied by Steketee (1958), Rongved and Frasier (1958), and Maruyama (1964, 1966). Singh et al (1992) derived closed form expressions for displacements and stresses in two welded half spaces caused by two-dimensional sources. Some authors have considered mechanical sources ; e.g., Pan (1990) considered quasi-static governing equations of thermoelasticity and discussed the transient thermoelastic deformation in a transversely isotropic and layered half space by surface loads and internal sources. Quasi static deformation of a medium consisting of a homogeneous isotropic thermoelastic half space in welded contact with a homogeneous elastic half space, due to a line source and dip slip fault in an elastic half space, is studied. The present problem is useful in the field of geomechanics where the interest is about the various phenomena occurring in the earthquakes and measuring of displacements, stresses, and temperature field due to the presence of certain sources
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