Regarding the anisotropic elastic modulus of sands

the effect of various stress states on the compressional wave (P-wave) and shear wave (S-wave) velocities along multi-directions measured using two pairs of horizontal and vertical bender elements installed on the sample is investigated. A cross-anisotropic stiffness matrix is fully determined based on the measured elastic wave velocities and the evolution of the anisotropy degree of elastic wave velocity with stress ratio is presented. The test results indicate that there exists a power relationship between the elastic wave velocities and the confining pressure in isotropic stress states. Meanwhile

the elastic stiffness of Toyoura sands in the horizontal direction is less than that in the vertical direction

indicating an initial fabric anisotropy. During anisotropic consolidation along a triaxial compression path

the velocities of elastic wave propagating along the vertical direction increase

while those propagating along the horizontal direction first remain constant then decrease as the ratio of vertical stress to horizontal stress increases. Moreover

the anisotropy degree of the stress normalized elastic wave velocity in the sands first keeps almost constant then increases with the increase of the ratio of vertical to horizontal stress

which is attributed to the evolution of soil micro fabric during anisotropic loading.