The representation and calculation of the deviatoric component of the geological stress tensor

A new diagram for the representation of stress states is proposed and compared with Nadai's stress diagram. The diagram is a graph whose axes are labelled as the differences of the principal stresses (σ₂-σ₃ as ordinate axis, σ₁-σ₂ as the abscissa; where σ₁ > σ₂ > σ₃ are the principal stresses). The design of the plot has been deliberately modelled on that of the ‘log Flinn’ diagram which is used to represent finite strain ellipsoids. The position of the plotted stress state on this diagram depends on the nature of the deviatoric (non-hydrostatic) component of the stress tensor. The distance of the plotted stress from the origin corresponds broadly to the departure of the stress from a hydrostatic state and the parameter R, defined as the gradient of the line joining the plotted state to the origin, expresses the type of symmetry possessed by the stress tensor.It is explained how the diagram can be used to represent calculated palaeostresses and, in particular, how the parameter R can be found directly from some existing methods of stress analysis currently in use.Besides its proposed function to represent the results of such analyses it is felt that the use of the diagram may make clear the essential elements of the definitions of well-known terms used to describe particular stress states (e.g. plane stress, triaxial stress, axial compression, etc.).