In this work, we analyze the characteristics of three-dimensional Mohr diagram. Based on this analysis, the conditions of reactivation of pre-existing planes on a Mohr diagram due to changes in applied stress state are investigated. Our results indicate that:

  1. On a three-dimensional Mohr diagram, one point, which is an intersection of three cycles (arcs) with direction angles θ1, θ2 and θ3, indicates a stress state in terms of shear and normal stresses, which represents four non-parallel planes due to the orthorhombic symmetry of the stress tensor. This implies that four planes may be reactivated, as long as a point on the diagram is located above the critical slip line;

  2. The reactivated planes that originally had the identical normal and shear stresses can have two different angles of pitch;

  3. If the planes represented by a point on the diagram rotate a magnitude about a certain axis, some of them could be reactivated, whereas the others could not be reactivated;

  4. Reactivation of a pre-existing plane is dependent on not only change in the maximum differential stress (σ1–σ3), but also the value of intermediate stress (σ2).

No matter what the maximum differential stress increases or decreases or maintains constant, a pre-existing plane may be reactivated due to changes in any principal stresses. (1) The range of the dips of the reactivated planes is larger for the smaller values of coefficient of friction μ and cohesion C. Also, the range of dip of the reactivated planes increases or decreases as the magnitudes of the principal stresses change.


Two-dimensional Mohr diagram is widely used in structural geology, seismology, soil mechanics, engineering geology etc (e.g. Sibson 1985, Streit & Hillis 2002). Crustal stress state could be considered as the result of superimposition from some sub-stress tensors.

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