This study investigates the phenomenon of soil arching in stone column–improved loose silty sand, which critically affects stress distribution and settlement in geotechnical applications. Traditional design methods often ignore arching effects, leading to uncertainties in predicting stresses and deformations. Laboratory-scale physical model tests were conducted to examine the system’s behavior under varying surcharge loads and fill heights. Results show that increasing the normalized fill height relative to stone column spacing improves arching efficiency, stress concentration, deformation, and column loads, all amplified by surcharge. Existing stress equations were evaluated, and new stress–settlement relationships were developed using multivariate statistical analysis via Design-Experts software. The study provides illustrative charts and a preliminary predictive framework, offering guidance for estimating settlements and improvements, though further validation with full-scale tests or advanced numerical modeling is required.