DOUGHNUT DIAGRAMS FOR STRESS, STRAIN, AND KINEMATIC ANALYSIS IN DEFORMED ROCKS

 

Recent developments in stress, strain, and kinematic analysis have greatly expanded the range of problems that can be solved using constructions based on the classical Mohr diagram, albeit at the cost of increased complexity. It remains difficult to solve simultaneously for both magnitudes and spatial orientations of stresses or strains. This paper presents new alternative constructions that build on the structural geologist's familiarity with stereonets. The Mohr circle (which has a diameter equal to the difference in the principal values) is moved to the center of a tracing overlay which revolves on a polar grid with the aid of a central thumb-tack. A second, concentric circle is drawn with diameter equal to the sum of the principal values. The two circles constitute the doughnut diagram. Simple geometric rules are used to solve for normal and shear stresses, longitudinal and angular strains, or strain rates and vorticities. The diagrams represent stress and strain data with correct magnitudes and spatial orientations, without recourse to complex off-axis or pole constructions. A set of interactive Flash™ animations are available for automated application using any version 4 or higher web browser.