Differential geometric approach to the stress aspect of a fault: Airy stress function surface and curvatures |
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| Authors: | Kazuhito Yamasaki Takahiro Yajima |
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| Institution: | 1. Department of Earth and Planetary Sciences, Faculty of Science, Kobe University, Nada, Kobe, Japan
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| Abstract: | We considered the two-dimensional stress aspect of a fault from the viewpoint of differential geometry. For this analysis,
we concentrated on the curvatures of the Airy stress function surface. We found the following: (i) Because the principal stresses
are the principal curvatures of the stress function surface, the first and the second invariant quantities in the elasticity
correspond to invariant quantities in differential geometry; specifically, the mean and Gaussian curvatures, respectively;
(ii) Coulomb’s failure criterion shows that the coefficient of friction is the physical expression of the geometric energy
of the stress function surface; (iii) The differential geometric expression of the Goursat formula shows that the fault (dislocation)
type (strike-slip or dip-slip) corresponds to the stress function surface type (elliptic or hyperbolic). Finally, we discuss
the need to use non-biharmonic stress tensor theory to describe the stress aspect of multi-faults or an earthquake source
zone. |
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| Keywords: | |
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