# Utilizing Soft Computing Techniques to Estimate the Axial Permanent Deformation of Asphalt Concrete
###### Abstract  
Rutting is a crucial concern impacting asphalt concrete pavements' stability and long-term performance, negatively affecting vehicle drivers' comfort and safety. This research aims to evaluate the permanent deformation of pavement under different traffic and environmental conditions using an Artificial Neural Network (ANN) prediction model. The model was built based on the outcomes of an experimental uniaxial repeated loading test of 306 cylindrical specimens. Twelve independent variables representing the materials' properties, mix design parameters, loading settings, and environmental conditions were implemented in the model, resulting in a total of 3214 data points. The network accomplished high prediction accuracy with an R\({}^{2}\) of 0.93 and a mean squared error (MSE) of 0.0039. Results based on the sensitivity analysis and variable importance techniques showed that the percentage of aggregate passing the 4.75 mm sieve and the (rice) theoretical maximum specific gravity (Gmm) were the most significant factors in predicting axial permanent strain (cp). Furthermore, the connection weight method highlighted input variables' distinct positive and negative impacts on permanent deformation. r 2025 8 26 2025 8 202  
indicates the urgency for developing new and efficient approaches for putting prediction with high accuracy and confidence. Recent developments in the field of artificial intelligence (AI) have introduced machine learning (ML) techniques as revolutionary tools that can be used to address challenging issues in pavement construction, maintenance, and distress prediction. In this regard, significant focus has been given to Artificial Neural Networks (ANNs) due to their exceptional ability to predict complex relationships and perform well with varying datasets [8]. Furthermore, ANNs do not have any explicit mathematical equation formulation as they are driven purely by the data, unlike the conventional empirical models that require a predetermined understanding of the problem at hand [9]. This mainly makes them useful for complicated problems such as permanent deformation resulting from the interaction between the used materials, loading, and environmental factors. Several efforts have been reported to implement the predictive capabilities of ANNs to estimate some essential concrete pavement performance indicators, including fatigue life and moisture susceptibility [10; 11]. However, studies on using ANNs to predict permanent deformation parameters under relevant conditions are scant, creating a knowledge gap in the existing body of literature. The incorporation of Artificial Neural Networks (ANN) in pavement engineering has various benefits, including the capacity to work with large and complex data sets, less reliance on extensive experimental testing, and the ability to provide predictions under a wide range of conditions [12; 13; 14; 15]. These attributes will not only improve rutting predictions but also provide information that can be used to develop a reliable design of asphalt mixtures that can resist deformation. Accordingly, this research proposes an effective ANN-based model that predicts the permanent deformation of asphalt concrete. The employed input variables are based on combining the primary mix design and material properties such as aggregate gradation, asphalt content, air voids, and other specific parameters, including the temperature and the applied load repetitions. Moreover, the ANN model has been accurately trained, validated, and tested for prediction purposes. Sensitivity analysis was also performed to establish the degree of variation in the parameters and define the most significant factors affecting rutting by means of axial permanent strain of asphalt concrete, which could be utilized to optimize asphalt mix designs and improve the future performance of asphalt pavement. Both academia and practice may benefit significantly from the findings herein in this research.