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2011-12-18T07:16:04Z

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'''Differential stress''' is the difference between the greatest and the least [[compressive stress]] experienced by an object. For both the [[geology|geological]] and [[civil engineering]] convention <math>\sigma_1</math> is the greatest compressive stress and <math>\sigma_3</math> is the weakest,

<math>\!\sigma_D = \sigma_1 - \sigma_3</math>.

In other [[engineering]] fields and in [[physics]], <math>\sigma_3</math> is the greatest compressive stress and <math>\sigma_1</math> is the weakest, so

<math>\!\sigma_D = \sigma_3 - \sigma_1</math>.

These conventions originated because geologists and civil engineers (especially [[soil mechanics|soil mechanicians]]) are often concerned with failure in compression, while many other engineers are concerned with failure in [[tension (physics)|tension]]. A further reason for the second convention is that it allows a positive stress to cause a [[Compressibility|compressible]] object to increase in size, making the sign convention self-consistent.

In [[structural geology]], differential stress is used to assess whether [[tensile failure|tensile]] or [[shear failure]] will occur when a [[Mohr circle]] (plotted using <math>\sigma_1</math> and <math>\sigma_3</math>) touches the failure envelope of the rocks. If the differential stress is less than four times the [[tensile strength]] of the [[rock (geology)|rock]], then extensional failure will occur. If the differential stress is more than four times the tensile strength of the rock, then shear failure will occur.<ref>Cosgrove. J. W. (1998) The role of structural geology in reservoir characterization. Geological Society, London, Special Publications, v. 127; p. 1-13</ref>

==References==

<references/>

{{DEFAULTSORT:Differential Stress}}
[[Category:Geology]]

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Paranormal operator - Revision history

en>Qetuth: more specific stub type