The overall macroscopic behaviour of granular media is strongly influenced by their fabric tensor. This serves as a micromechanical state variable. During a granular mass flow event, the combined action of compression and shear deformations induces anisotropy in the granular ensemble, which further changes with the flow kinematics and the subsequent interactions with a rigid obstacle. Evolution of fabric anisotropy along with the fabric orientations can be closely monitored to decipher its connection to the macroscopic response of the granular material, i.e., the impact force on the rigid barrier. To this end, this study investigates the fabric evolution with the aid of the fabric tensor in 2D and 3D spaces. Several numerical investigations examine fabric tensor descriptions up to second and fourth-order terms. However, the accuracy analysis of fabric tensors of higher orders is often overlooked. This study evaluates the fabric anisotropy obtained from higher-order fabric tensor analysis for dry granular flow down an inclined flume interacting with a rigid barrier. Within the discrete numerical setting, the effect of particle shape - a micromechanical feature, on fabric anisotropy has also been studied by incorporating non-spherical particle shapes, namely ellipsoid, dodecahedron, cylinder, octahedron, and tetrahedron. The results indicate that the goodness of fit is dominated by the higher-order fabric tensors, potentially increasing the accuracy in calculating the values of fabric orientation and degree of anisotropy induced within the system. This phenomenon is consistently observed across all particle shapes considered in this study, with sphericity as a metric used for various particle shapes. Additionally, our study is further aimed at establishing a formal relationship between the fourth-order fabric tensor and the fourth-rank elasticity tensor that has physical origins at the micromechanical particulate level in granular media.