Semnan University Press Journal of Transportation Infrastructure Engineering 2423-5350 11 4 2026 02 20 Investigating Mathematical Modeling for Determining Concrete Pavement’s Composite Foundation Reaction Modulus (K∞) Using Regression Optimization Concretes Investigating Mathematical Modeling for Determining Concrete Pavement’s Composite Foundation Reaction Modulus (K∞) Using Regression Optimization Concretes 29 47 10353 10.22075/jtie.2025.38579.1730 FA Mahdi Jokar Department of Civil Engineering, Yazd University Mohammad Mehdi Khabiri Civil Engineering Departement,Yazd University Sara Sarfaraz Department of Civil Engineering, Yazd University Masood Temory Department of Civil Engineering, Yazd University Journal Article 2025 08 07 The composite foundation reaction modulus (K∞) is a vital parameter in concrete pavement design, characterizing pavement-subgrade interaction behavior and directly influencing stress distribution and deformation in concrete slabs. Traditional determination methods relying on code-based design charts (Code 731 and AASHTO 1993) face data extraction challenges that limit modeling accuracy. This study develops an innovative numerical model for K_∞ using data extracted from these charts, assuming a semi-infinite subgrade. Primary objectives include precise chart data extraction, fitting regression models (linear, polynomial, exponential, power, logarithmic), and selecting the optimal mathematical relationship using rigorous statistical criteria. Model performance was evaluated via coefficient of determination (R²), adjusted R², standard error of estimate (SEE), and residual analysis. Results indicate that power model achieves superior statistical performance with R² = 97.41% and low SEE = 0.1308, alongside optimal residual behavior, explaining K∞’s nonlinear dependence on subbase thickness, subbase elastic modulus, and subgrade soil modulus. Analysis revealed that K∞ is critically influenced by: synergy between subbase thickness and elastic modulus; subbase’s protective effect on subgrade, and a subbase thickness threshold condition. These mechanical interactions govern pavement-subgrade system stiffness. The research provides an efficient methodology to convert design charts into analytical equations, enhancing accuracy, reducing human error, and enabling integration into sensitivity analyses and concrete slab thickness optimization under variable subbases. The composite foundation reaction modulus (K∞) is a vital parameter in concrete pavement design, characterizing pavement-subgrade interaction behavior and directly influencing stress distribution and deformation in concrete slabs. Traditional determination methods relying on code-based design charts (Code 731 and AASHTO 1993) face data extraction challenges that limit modeling accuracy. This study develops an innovative numerical model for K_∞ using data extracted from these charts, assuming a semi-infinite subgrade. Primary objectives include precise chart data extraction, fitting regression models (linear, polynomial, exponential, power, logarithmic), and selecting the optimal mathematical relationship using rigorous statistical criteria. Model performance was evaluated via coefficient of determination (R²), adjusted R², standard error of estimate (SEE), and residual analysis. Results indicate that power model achieves superior statistical performance with R² = 97.41% and low SEE = 0.1308, alongside optimal residual behavior, explaining K∞’s nonlinear dependence on subbase thickness, subbase elastic modulus, and subgrade soil modulus. Analysis revealed that K∞ is critically influenced by: synergy between subbase thickness and elastic modulus; subbase’s protective effect on subgrade, and a subbase thickness threshold condition. These mechanical interactions govern pavement-subgrade system stiffness. The research provides an efficient methodology to convert design charts into analytical equations, enhancing accuracy, reducing human error, and enabling integration into sensitivity analyses and concrete slab thickness optimization under variable subbases. https://jtie.semnan.ac.ir/article_10353_98d1fc1b9768acb786352154c606e304.pdf