A study of wave propagation and stiffness anisotropy in anisotropically loaded granular material-synthetic fiber binary systems

Abstract

The influence of polypropylene fiber inclusion on the wave propagation parameters and stiffness anisotropy of granular materials was examined through vertically and laterally positioned bender elements, by which, shear wave velocities were measured leading to the quantification of elastic stiffness Gmax(vh), Gmax(hv) and Gmax(hh) (the first subscript corresponds to the direction of wave propagation and the second subscript corresponds to the direction of particle perturbation as v:vertical and h:horizontal). Various stress paths were considered to comprehensively study stiffness anisotropy of the specimens and grain-scale laboratory tests were additionally performed to provide, partly, some multi-scale insights into the mechanisms of wave propagation of the sandfiber granular composites. For the back-calculation of elastic stiffness from the wave propagation experiments, Biot's theory was adopted, in which case an equivalent density was used to interpret the high-frequency test results taking into account the relative movement of the solid and fluid phases, which approach provided much better convergency of the results from bender elements and resonant column tests. In this case we assumed that the solid skeleton is composed of the sand particles and the fibers. The test results indicated that when subjected to isotropic stress state, the presence of fibers led to a decrease of Gmax(vh) and Gmax(hv) but an increase of Gmax(hh). The extent of Gmax(hh) increase was dependent on the characteristics of the host sand and could be attributed to the structural anisotropy with preferred horizontal orientation of the fibers leading to more pronounced development of rigid-soft contacts in the vertical direction. The contribution of the rigid-soft contacts in stiffness reduction could be linked to the microscopic influence of the softer synthetic fibers in reducing the normal contact stiffness and increasing the energy dissipation of the granular system as the grain-scale experiments suggested. When subjected to anisotropic stress state, the stiffness anisotropy was affected by fiber content in a way that with increasing amount of fiber inclusion, the reduction of the stiffness anisotropy became larger. The stiffness anisotropy of the sand or sand-fiber binary system increased with the increase of the stress ratio. Further analysis of the test results revealed that stress induced anisotropy was directly linked to the influence of deviatoric stress on the volumetric strain.