The solution of the static deformation of a homogeneous, isotropic, perfectly elastic half-space caused by uniform movement along a long vertical tensile fracture is well known. In this paper, we study the problem of static deformation of a homogeneous, isotropic, perfectly elastic half-space caused by a non-uniform movement along a long vertical tensile fracture of infinite length and finite depth. Four movement profiles are considered: linear, parabolic, elliptic and cubic. The deformation corresponding to the four non-uniform movement profiles is compared numerically with the deformation due to a uniform case, assuming the source potency to be the same. The equality in source potency is achieved in two ways: One, by varying the depth of fracture and keeping the surface discontinuity constant and the other way, by keeping the depth of fracture constant and varying the surface discontinuity. It is found that the effect of non-uniformity in movement in the near field is noteworthy. The far field is not affected significantly by the non-uniformity in movement. In the first case, horizontal displacement is significantly affected rather than vertical displacement. In the second case, non-uniformity in movement changes the magnitude of the displacement at the surface. Also, the displacements around a long vertical tensile fracture for different movement profiles are plotted in three dimensions.
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The authors are thankful to the University Grant Commission, New Delhi for the financial support in the form of Junior Research Fellowship sanctioned to R C Verma and Major Research Project sanctioned to S Rani. They are also thankful to the reviewers for their suggestions in improving the manuscript.
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RANI, S., VERMA, R.C. Two-dimensional deformation of a uniform half-space due to non-uniform movement accompanying a long vertical tensile fracture. J Earth Syst Sci 122, 1055–1063 (2013). https://doi.org/10.1007/s12040-013-0325-8
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DOI: https://doi.org/10.1007/s12040-013-0325-8