A Systematic Evaluation of the Empirical Relationships Between the Resilient Modulus and Permanent Deformation of Pavement Materials

The resilient modulus (Mr) and permanent deformation of subgrade soils are key indicators for assessing pavement performance under repeated traffic loads. Although numerous studies have confirmed their importance in pavement design and performance prediction, a systematic review of empirical relationships and scientific knowledge is lacking, resulting in insufficient integration and application of current findings. To address these issues, this study systematically reviews laboratory and field-testing methods based on over 200 published papers, summarizes common empirical equations, and focuses on the feasibility and advantages of integrating AI to predict Mr. Meanwhile, by examining the main factors that influence Mr and permanent deformation, this study synthesizes and evaluates existing research to identify potential gaps. Findings indicate that laboratory and field tests effectively capture the mechanical behavior of pavement materials, and incorporating AI technology in modulus prediction enhances accuracy and efficiency while managing complex influencing factors. However, existing empirical equations have not been fully integrated with emerging technologies for validation and optimization, and some predictive models remain limited in terms of applicability and generalizability. This review highlights the need to refine empirical relationships for the resilient modulus using stochastic methods and AI techniques, thereby facilitating a more comprehensive integration of the latest testing technologies and computational tools. This research is of great significance for advancing sustainable pavement design, optimizing maintenance strategies, and guiding future research directions.

This creative work has been published under the Creative Commons Attribution 4.0 International (CC-BY 4.0) license which allows copying, and redistribution as well as adaptation of the original work provided appropriate credit is given to the original author and the conditions of the license are met.