# Particle Packing Optimization for CCR-GGBS-FA Binder Stone Waste pavement Base Material
## 1 Introduction  
Stone waste is generated from the process of mining and stone processing to the finished products that are not used resourcefully. Due to the poor engineering nature of stone waste, it cannot be directly used resourcefully, and the disposal method is mainly centralized stockpiling [1]. In addition to consuming a large amount of land resources and raising the operating costs of enterprises, the stacking of stone waste has a high content of fine particles, which can cause dust pollution, and there is also the safety hazard of landslides, which poses a threat to human safety, after it is stacked into a mountain. calcium carbide residue, ground granulated blast-furnace slag, fly ash, and other industrial solid waste piling processes also exist in the ecological environment. In the field of resource utilization, concrete or other materials for geotechnical filling can be prepared by mixing cement and other cementitious materials with rock waste, which is one of the main ways of rock waste resource utilization at present [2; 3; 4; 5]. Stone waste can be mixed with other geotechnical materials or cementitious materials to be used as geotechnical filling materials, and its application and research have mainly focused on pavement base engineering, while the current research mainly focuses on the laying of pavement base and pavement subgrade [6]. In pavement base layer materials, the strength of the skeleton plays an important role in their mechanical properties, and the strength of the skeleton is, in turn, determined by the grading of coarse and fine aggregates. Due to the wide distribution of the particle-size gradation of primary stone waste, which leads to its poor engineering properties, the grading of primary stone waste will need to be optimized and designed to improve the mechanical and durability properties of the stone waste pavement base material so as to meet the engineering requirements of the pavement base layer. In 1892, the French scholar [PERSON] confirmed that the strength of concrete is mainly related to the volume contents of cement, water, and air, and based on this, he proposed a theoretical equation for calculating the strength of concrete, as shown in Equation (1) [7]:  
\[f_{c}=k(\frac{c}{c+v+a})^{2}. \tag{1}\]  
where \(f_{c}\) represents the compressive strength of concrete; \(c\), \(v\), and \(a\) represent the volumes of cement, water, and air in the wet mix, respectively; and \(k\) is a constant. In order to optimize the gradation and improve its close-packed pile, [PERSON] published the Fuller gradation curve in 1907 [8], as shown in Equation (2). \[Y=100(\frac{D_{0}}{D_{\max}})^{n}. \tag{2}\]  
where \(Y\) denotes the number of particles passing through the \(D_{0}\) aperture; \(D_{\max}\) denotes the maximum particle size in the system; and \(n\) is a coefficient related to the aggregate type. The Fuller gradation curve is regarded as a semi-empirical and semi-theoretical model that has been successful in improving the close packing and compressive strength of concrete by optimizing the aggregate gradation. However, there is a large error in the prediction of this curve when large flowability or other types of concrete need to be formulated. [PERSON] and [PERSON] proposed the classical model of continuous particle packing in 1930 [9], called the A-A model, as shown in Equation (3). Among the many ultra-high-performance concrete proportion design methods based on the theory of closest packing, the design method based on the MAA model is more accurate due to its advantage of considering the particle-size distribution [10]. \[P(D)\,=\,(\frac{D}{D_{\max}})^{q} \tag{3}\]  
where \(P(D)\) is the percentage of total solids (including concrete aggregate and cementitious materials) less than a certain particle size \(D\), %; \(D\) is the particle size, \(\mu\)m; \(D_{\max}\) is the maximum particle size, \(\mu\)m; and \(q\) is the distribution modulus.