Stress and strain from striated pebbles. Theoretical analysis of striations on a rigid spherical body linked to a symmetrical tensor

Abstract

Striations on a pebble are interpreted as resulting from slip due to either a homogeneous stress state or a small homogeneous coaxial deformation in the matrix. In terms of stress, striations are assumed to be parallel to the applied shear stress. In terms of strain, striations are considered to be parallel to the relative tangential displacement between the pebble and adjacent matrix particles. Slip on the surface of a spherical rigid body enclosed in a deformable matrix (brittle or ductile) is theoretically analysed for different stress and strain regimes. The analysis predicts the topology of the resulting striations and singularity distribution on the sphere. Both in terms of stress and strain, the tangential vector field on the sphere's surface derives from a potential function proportional to the magnitude of the normal vector field. Tangential and normal vectors represent either shear and normal stresses, or displacement components (in terms of strain). The plot of continuous curves parallel to striations (integral curves) and of equipotential curves on the sphere, allows simultaneously the magnitude and orientation of the tangential and normal vector fields to be visualized. Close to singular points, the integral curves correspond to power laws and the equipotentials correspond to conic sections. This theoretical analysis allows graphical method for estimating the stress ratio (σ 2 − σ 3) (σ 1 − σ 3) from striated faults to be proposed, once the orientations of the principal stress directions are known (i.e. by means of other graphical methods).