An innovative 'Eco-rubber geotechnical seismic-isolation foundation system’ has been proposed to help address New Zealand’s waste tyres problem. This foundation system combines gravels with granulated tyre chips to take advantage of rubber’s damping properties, providing seismic-isolation beneath low-rise buildings during earthquake shaking. In support of the laboratory geotechnical characterisation of this new synthetic geomaterial, this thesis presents the findings of a numerical study dealing with understanding the micromechanical behaviour of gravel-rubber mixtures under direct shear loading conditions using the three-dimensional discrete element method (DEM). The work done was organised into three phases: (1) development of a robust DEM direct shear model for rigid (high moduli) gravel particles; (2) development of a new DEM particle model capable of describing the highly compressible behaviour of soft (low moduli) tyre chip; and (3) use of the two previous models to investigate the shear response of gravel-rubber mixtures with 10%, 25% and 40% volumetric rubber content (VRC) and evaluate the effects of increasing rubber content on the engineering behaviour of these mixtures. The calibrated DEM models produced good agreements with the experimental stress-strain-volumetric macro-response under different VRCs and confining pressures (30 kPa, 60 kPa and 100 kPa). Micro-scale information such as coordination number, fabric and force anisotropy, and strong-force chains were obtained and analysed throughout the shearing process to compare the micromechanical behaviours for varying VRCs. This study revealed that the magnitude of fabric and normal force anisotropy were closely related to the shear strength of the granular mixture, and decreased with increasing VRC. Analysis of the strong-force network suggests that strong-force chains are predominantly carried by the gravels (gravel-like behaviour) up to 30% VRC, which tied in well with the trends observed in the macro- and micro-responses. Furthermore, this study demonstrates the capabilities of DEM simulations in realistically capturing the interaction between rigid and soft particles and accurately describing their assembly-level behaviours.