Journal
PURE AND APPLIED GEOPHYSICS
Volume 157, Issue 6-8, Pages 1039-1057Publisher
BIRKHAUSER VERLAG AG
DOI: 10.1007/s000240050016
Keywords
boundary element; continuum mechanics; slope stability; stress analysis; topography
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Elastic stresses at ridges formed by (a) erosion and (b) volcanism are calculated here by the method of particular integrals with a displacement-discontinuity boundary element method. The two geologic scenarios require treating the far-field stresses in the analyses differently. For a continuous body, the elastic governing equation requires that the second partial derivatives of the Vertical and horizontal far-field normal stresses with respect to horizontal and vertical directions be defined throughout the solution domain. This constrains admissible solutions for continuous bodies in both two-and three-dimensional analyses. For example, if the horizontal far-field normal stress varies linearly with depth over any depth interval in a continuous body, then it must be continuous and vary linearly over the entire elevation range of the solution domain. This far-field stress distribution permits the description of a ridge formed by erosion of the surrounding material. A discontinuous or a piecewise linear distribution of horizontal far-field stresses does not yield admissible solutions for a continuous body but can apply to a ridge constructed by volcanism. Stresses induced by topography in volcanic ridges will inhibit dikes from propagating to the surface, favor the formation of near-surface magma chambers, and promote slope instability. The analyses demonstrate that topography and the extant tectonic stresses will not by themselves fully determine the stresses in a ridge; the geologic history is also important.
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