Managing waste tires presents a significant challenge globally, particularly in regions experiencing high temperatures and shortage of landfill sites. This issue is affecting countries like Kuwait, where the abundance of waste tires is a major source of environmental and safety risks, particularly during the intensely hot summer months. This extreme heat has sparked numerous fires, leading to substantial air pollution due to thick black smoke. Given the limited disposal options, recycling waste tires and finding practical applications for ground tire rubber (GTR) is essential. To address the challenge, a comprehensive laboratory testing program was conducted, using locally produced rubber aggregates as an additive to Kuwait's local surface sands. Two new variables were examined namely the size and gradation of the GTR, and the density of the compacted mixes. For this purpose, two different sizes of rubber aggregates, fine and coarse produced locally, were utilized, and the impact of relative compaction on the strength and compressibility of the mixtures was investigated by testing samples compacted to the maximum density and to 95% of the maximum density. The results suggest that combining local surface sands with rubber tire additives results in a lighter, more permeable, and compressible material, contributing significantly to sustainable waste management. With 20% rubber additive the maximum dry density decreased by nearly 20%, and the permeability increased by 1.74–3.11 times and the compression index increased by 6.15 and 3.8 times with fine and coarse rubber respectively. The angle of friction remained unchanged at 36° with the addition of coarse rubber and decreased by 3°–4° with fine rubber. The change in behavior although not an increase in the strength and stiffness, offers a range of suitable practical applications in civil engineering and environmental management, including use as a drainage layer, embankment construction on soft ground, earth fill around retaining walls, an additive in asphalt mixes, and in manufacturing compressible tiles for sports facilities.