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The stress–strain relationship of a homogeneous specimen in triaxial compression test allow to estimate a suitable understanding of stiffness parameters. However, when a two-layered specimen is tested the characterization of the stress–strain behavior for two-layered soil is mainly complex due to the nonlinearity of the deformations. A homogenization approach was adopted to determine the initial Young’s modulus of the supposed cross-anisotropic linear elastic medium. Triaxial compression tests were carried out on both homogeneous and two-layered specimens under a low effective confining pressure of 30 kPa. A model 3D printed geogrid was fabricated to fit in the interaction between aggregate and sand–rubber mixture. The nonlinear stress–strain relationship for unreinforced and reinforced homogenized two-layered triaxial specimens was formulated by a well-known hyperbolic model which involves Mohr-Coulomb strength parameters. The initial Young’s modulus for the cross-anisotropic medium was used in the hyperbolic model to characterize the stress–strain behavior of unreinforced and 3D printed geogrid reinforced soils specimens. In this study was proposed analysis of a well-known nonlinear model involving effect of unreinforced and reinforced homogenized two-layered specimen.