Limit analysis with anisotropic fibre-reinforced soil

Fibre reinforcement is a technology to improve the strength of soils used as fill in geotechnical structures. The properties of the fibre-reinforced sand are anisotropic because of the distribution of orientation of the fibres, which is characterised by a preferred bedding plane. The development of an anisotropic yield condition for fibre-reinforced sand is presented. Application of the kinematic approach of limit analysis to anisotropic frictional materials is demonstrated. An interesting implication of anisotropy is a lack of uniqueness in the internal friction angle along a shear surface with given orientation. The anisotropic internal friction angle was found to be a function of the major principal strain rate direction, and not just a function of the orientation of the shear surface. While the inclination of principal strain rate directions can be inferred from the kinematics of the mechanism for a given boundary value problem, the internal friction angle cannot be determined a priori as a unique function of orientation in space. Two examples are presented to illustrate the use of the kinematic approach for anisotropic frictional materials: retaining wall loading, and the bearing capacity of a footing.