When stress measurements are made in rock masses, there is an implicit assumption that the magnitudes of the three principal stresses (s1, s2 and s3, known in this paper as a ‘triple’) are independent. However, there is evidence from stress measurements made in different parts of the world that there seem to be relations between the principal stresses; in particular, s1/s2 ˜ 1.5, s2/s3 ˜ 1.5 and s1/s3 ˜ 2.3. In order to explore these potential relations, we present Australian, Chilean, Finnish and UK stress data in the form of principal stress component versus the first stress invariant, and then we evaluate the mean ratios s1/s3 and s2/s3. In order to assess whether the ratios represent a mechanical phenomenon or a mathematical artifact of the ordered triples, we generate sets of ordered random numbers and determine the ratios associated with these. This leads to the conclusion that the observed relations between the principal stresses could not be fully explained through the ordered triple hypothesis. This means that the observed ratios must arise as a function of some controlling mechanism, probably the constraint induced by rock failure. Accordingly, we found that those simulated principal stress triples satisfying a Mohr-Coulomb type relation between s1 and s3 did, in fact, follow similar trends to the stress ratios observed in situ. Thus, we conclude that this is entirely consistent with the hypothesis that the Earth’s crust is in a state of limiting equilibrium and we consider some of the ramifications for stress measurement campaigns.


The three principal values of a stress tensor are theoretically independent, and so, in general, there is no reason to expect any particular relation between them.

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