)1 State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China; [EMAIL_ADDRESS] (Q.S. ); [EMAIL_ADDRESS] (S.L)1 State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China; [EMAIL_ADDRESS] (Q.  
often used to control the physical and mechanical behaviours of these materials. The success of similarity model tests heavily depends on the mechanical properties of similar materials, particularly those simulating weak rock masses, as failures in tunnels and support systems frequently occur in such conditions. The preparation of similar materials involves selecting appropriate aggregates and binders, with a mixture of fine and coarse aggregates often used to achieve high density and strong friction characteristics. Commonly used coarse aggregates include river sand and quartz sand, while fine aggregates may consist of iron powder and barite powder. Binders such as paraffin, gypsum, cement, and rosin-alcohol solutions are also employed [7; 8; 9; 10]. Extensive proportioning tests are the prerequisite for achieving the satisfying physical and mechanical parameters of similar materials. Numerous researchers have investigated the effects and correlations of different proportions on the mechanical parameters of similar materials. For example, [PERSON] et al. [11] found that as the barite content increased, the density of the material significantly increased, and the strength of the material increased with an increase in binder content [11; 12]. The concentration of the binder can effectively enhance the strength and elastic modulus of the material [12]. Additionally, the type of binder also has a significant influence on the strength and elastic modulus of the material but has less noticeable effects on the internal friction angle of the material [13]. Current studies present a similar result; the strength and elastic modulus of the material can be effectively adjusted by modifying the binder ratio [14]. However, it was found that current studies have different opinions on the influence of the aggregate ratio to similar materials. Based on numerous tests, [PERSON] et al. observed that higher proportions of fine aggregates in the aggregate mixture result in higher material strength [15]. [PERSON] et al. concluded that the angle of the internal friction of the material, as well as the cohesion, gradually decreases when the content of fine aggregate is greater [16]. [PERSON] et al. [17] found that with the increase in fine aggregate content, the internal friction angle of the material showed a tendency of decreasing, while the cohesion showed a tendency of increasing and then decreasing. These findings indicate that further investigation is required to understand the impact of aggregate ratios on the mechanical properties of similar materials. Currently, many proportioning tests have qualitatively investigated the influences of different component proportions of similar materials on mechanical behaviour. To solve this, several studies proposed a qualitative relationship between component proportion (i.e., proportions of fine and coarse aggregates, binder content, binder concentration) and the mechanical property (i.e., density, uniaxial compressive strength, elastic modulus, cohesion, and internal friction angle) [18; 19; 20]. However, as repetitive proportioning tests require a significant investment of time and financial resources, these empirical equations often only apply to specific sets of components and lack generality. Their results fall short of meeting the detailed requirements of model materials for prototypes in wide ranges. Discrete element analysis provides a convenient method for analysing the mechanical behaviour of granular materials [21]. This allows for optimisation of the design of component proportions of similar materials by simulating the components as granular materials.