Abstract: To establish a quantitative relation between the fabric tensor and stress tensor of granular materials, a series of constant stress ratio biaxial compression tests were conducted in this paper using the discrete element method. Simulation results show that as the stress increases, contact normals between particles concentrate towards the major principal stress direction, so that the anisotropic degree of the sample gradually increases. When the stress is large enough, the fabric tensor defined by the contact normal direction no longer evolves, and its corresponding second partial invariant satisfies a quadratic function of the stress ratio approximately. Furthermore, if the fabric tensor and stress tensor are multiplied in a certain form, one can obtain a joint tensor that is independent of the stress ratio, which indicates that the relation between the fabric tensor and the stress tensor can be described by an implicit equation. Accordingly, under a specific condition where the particle arrangement of circular granular material reaches stable under constant stress ratio loading, quantitative relationship between macro and micro physical variables is determined, which provides a potential idea for the establishment of multiscale constitutive models.