Mixtures of small rigid sand particles Ds and large soft rubber particles Dr are prepared at different volume fractions and tested to investigate their small-strain and zero-lateral strain responses (Dr /Ds ≈ 10). Both data sets are simultaneously gathered in an oedometer cell instrumented with bender elements. Data are analyzed in the context of mixture theory and with the aid of numerical simulations. Results show that the sand skeleton controls the mixture response when the volume fraction of rubber particles is Vrubber ≤ 0.3, while the rubber skeleton prevails at Vrubber ≥ 0.6. The large size and incompressibility of rubber particles provides high stress-induced stiffness in the sand skeleton near the equatorial plane of rubber particles. The corresponding increase in local small-strain shear modulus Gmax results in earlier wave arrivals in mixtures with Vrubber ≤ 0.3 than in pure sand, while the quasi-static constrained modulus is highest in pure sand. The constrained modulus and shear wave velocity are power functions of the applied effective stress in all mixtures. Results from this study (Dr /Ds ≈ 10) and from a previous complementary study with small rubber particles (Dr /Ds = 0.25) show that the development of internal fabric, particle level processes, and the associated macroscale response of sand–rubber mixtures depend on the relative size between the soft rubber chips and the stiff sand particles Dr /Ds and their volume fractions.