Advancing the mechanical properties of naturally weak clayey soils is crucial in geotechnical engineering and is often achieved through targeted stabilization techniques. This research focuses on reinforcing clayey soil by integrating inert material, specifically aeolian sand collected from roadside deposits, in varying proportions from 2.5 to 30%. An experimental approach is adopted to analyze the improvement in geotechnical properties resulting from the addition of aeolian sand to clay through a series of geotechnical tests. These tests include the methylene blue test (MBV), the determination of Atterberg limits (LL, PL, PI), compaction characteristics (MDD and OMC), direct shear testing (C and ϕ), and oedometer tests (Cc and Cs). Furthermore, an optimization approach based on response surface methodology (RSM) and a central composite design (CCD) is implemented to determine the optimal mixture composition and accurately predict the evolution of the geotechnical properties of the soil. The experimental findings demonstrate significant improvements in the mechanical characteristics of the soil following the incorporation of aeolian sand, with the best performance achieved at a 30% sand content. The MBV decreased by 34.98%, the LL decreased by 39.62%, the PL decreased by 37.50%, and the PI decreased by 45.45%. In contrast, the MDD increased by 12.25%, enhancing the compaction and load-bearing capacity of the soil. A reduction of approximately 7.59% in the OMC was observed, lowering the water demand. The internal friction angle (ϕ) increased significantly by up to 233.33%, improving the shear strength, whereas the cohesion decreased by 49.78%. Additionally, the Cc and Cs decreased by 16.15 and 54.45%, respectively, which reduced the sensitivity of the soil to volume changes. Mathematical models are developed and statistically validated using the clay and aeolian sand contents as predictive variables, while key parameters such as the maximum dry density (MDD), cohesion (C), internal friction angle (ϕ), compressibility coefficient (Cc), and swelling coefficient (Cs) serve as response metrics. By applying analysis of variance (ANOVA) and refining the quadratic model via RSM, the study demonstrated significant results, with a coefficient of determination (R2) exceeding 0.97 for all the responses. The alignment between R2 and adjusted R2, along with the observed P values for critical parameters, highlights the robustness of the model. These findings pave the way for practical applications in foundation and road infrastructure projects, particularly in arid regions where water management and soil stability are critical concerns. The integration of 30% sand proves to be an effective and sustainable solution for enhancing the strength and stability of clayey soils in moisture-sensitive environments.