Relating elastic and plastic fabric anisotropy of clays

Abstract

A relationship between elastic anisotropy, as typically observed in clayey soils subjected to shear wave propagation tests, and plastic anisotropy, detected at yielding and leading to rotated yield loci, is proposed. Such a relationship is expected because both elastic and plastic anisotropies can be ascribed to the same directional ingredients that characterise the fabric of the soil at the microscale. The relationship takes the form of an analytical relation between an elastic and a plastic fabric tensor, the former entering a hyperelasticity theory while the latter is the rotational hardening variable of a clay plasticity theory. The elastic anisotropy can be measured experimentally by wave propagation along orthogonal planes, identifying the ratio of the corresponding elastic shear moduli while a sample is compressed at fixed stress ratio, and paired with plastic anisotropy obtained by the integration of its plastic fabric tensor evolution equation during the foregoing compression. Such experiments were available and used to calibrate and validate the proposed elastic–plastic anisotropy relationship. The findings have a two-way beneficial effect for the solution of a geotechnical boundary value problem, where one can easily measure initial elastic clay anisotropy in the field, which can be used to initialise the plastic anisotropy for the subsequent analysis of the problem, while the evolving plastic anisotropy can be used to update the elastic fabric tensor during deformation.