# Evolution Mechanism of Volume Parameters and Gradation Optimization Method for Asphalt Mixtures Based on Dual-Domain Fractal Theory

## TL;DR

This study uses fractal theory to improve asphalt mixture design, leading to better durability and performance in harsh environments.

## Contribution

A dual-domain fractal framework is introduced to optimize asphalt mixture gradation and volume parameters.

## Key findings

- Optimized gradation improves dynamic stability by 112% and average film thickness by 75%.
- Dc is the main factor controlling VMA, while binder content governs VFA.
- Robust Design methodology enhances volumetric stability and mechanical performance.

## Abstract

The primary objective of this study is to bridge the gap between descriptive geometry and mechanistic design by establishing a dual-domain fractal framework to analyze the internal architecture of asphalt mixtures. This research quantitatively assesses the sensitivity of volumetric indicators—namely air voids (VV), voids in mineral aggregate (VMA), and voids filled with asphalt (VFA)—by employing the coarse aggregate fractal dimension (Dc), the fine aggregate fractal dimension (Df), and the coarse-to-fine ratio (k) through Grey Relational Analysis (GRA). The findings demonstrate that whereas Df and k substantially influence macro-volumetric parameters, the mesoscopic void fractal dimension (DV) remains structurally unchanged, indicating that gradation predominantly dictates void volume rather than geometric intricacy. Sensitivity rankings create a prevailing hierarchy: Process Control (Compaction) > Skeleton Regulation (Dc) > Phase Filling (Pb) > Gradation Adjustment (k, Df). Dc is recognized as the principal regulator of VMA, while binder content (Pb) governs VFA. A “Robust Design” methodology is suggested, emphasizing Dc to stabilize the mineral framework and reduce sensitivity to construction variations. A comparative investigation reveals that the optimized gradation (OG) achieves a more stable volumetric condition and enhanced mechanical performance relative to conventional empirical gradations. Specifically, the OG group demonstrated a substantial 112% enhancement in dynamic stability (2617 times/mm compared to 1230 times/mm) and a 75% increase in average film thickness (AFT), while ensuring consistent moisture and low-temperature resistance. In conclusion, this study transforms asphalt mixture design from empirical trial-and-error to a precision-engineered methodology, providing a robust instrument for optimizing the long-term durability of pavements in extreme cold and arid environments.