The present research aims to examine the influence of stress anisotropy on the small-strain Young's modulus of granular materials. To this end, a series of numerical tests, including isotropic compression, isotropic extension, triaxial extension (TE), triaxial compression (TC), reduced triaxial extension, and reduced triaxial compression tests, were conducted using the 3D Discrete Element Method. The findings revealed the presence of a threshold value of stress ratio (SR) in both TE and TC stress paths. When the SR falls within the range between two threshold values, the fabric of the specimen, represented by the contact normal distribution, remains nearly constant. In this range, the anisotropy of small-strain Young's modulus is primarily attributed to the anisotropy of stress. However, it was observed that the small-strain Young's modulus in a specific direction is affected by the value of SR, contradicting the prevailing belief that it is solely influenced by the principal stress in that direction. A novel factor R-s was introduced and incorporated into Hardin's equation to capture the influence of the SR on the small-strain Young's modulus. In addition, a relationship was established between mechanical coordination number and small-strain Young's modulus during triaxial tests by considering both stress anisotropy and fabric anisotropy.
