## 1 Introduction  
With the continuous progress and development of technology, human activities are expanding into increasingly complex environments, including the deep sea and the Earth's interior. This expansion has led to a significant increase in the number and complexity of underground engineering projects. As a result, the evaluation of the mechanical properties of rock masses has become increasingly crucial [1, 2, 3]. Rock masses play a dominant role in the performance of engineering structures built on them [4, 5, 6, 7]. Traditionally, field sampling and laboratory tests have been employed to determine the mechanical parameters of rock masses. However, due to the existence of the rock size effect, the test results obtained from rock specimens of different sizes are inconsistent, making it impossible to accurately characterize the actual strength parameters of engineering rock masses using small-scale rock strength [8]. Extensive research on the rock size effect has been conducted by experts, yielding numerous valuable findings. [PERSON] and [PERSON] [9] found that with the increase in joint length, the peak shear strength and dilatation angle gradually decrease, peak shear displacement gradually increases, and the failure mode changes from brittle failure to plastic failure. In addition, the influence of the size effect is weakened with a decrease in joint roughness. [PERSON] and [PERSON] [10] believe that the shear behavior of small-size specimens is controlled by a small and sharp rough solid on the joint surface, while the shear behavior of large-scale specimens is controlled by a large and non-sharp fluctuation. [PERSON] and [PERSON] [11] reported an innovative method to sample large-size rock with rough joints. Some scholars [12; 13; 14] pointed out that the size effect only exists in a specific size range, and the mechanical parameters will no longer be affected by size when the size is larger than a certain value. On this basis, the representative sizes of rock under different loading conditions are obtained through numerical simulation [15; 16; 17; 18]. Scholars have made a lot of efforts in the study of the rock size effect and have reached many important and useful conclusions [19; 20; 21]. However, a key challenge in studying the mechanical behavior of rock while considering the size effect is that large-scale or in situ tests require substantial human and material resources. In this context, numerical simulation emerges as a cost-effective, convenient, and efficient method for investigating the rock size effect. [PERSON] and [PERSON] [22] proposed a new method for the relationship between the uniaxial compressive strength and specimen size, and used particle flow simulation to study the influence of the size effect on rock shear strength. [PERSON] and [PERSON] [23] used Particle Flow Code (PFC) software to conduct a simulation of rough joint specimens of different sizes, and the results showed that the shear strength and peak dilatancy increased and the shear stiffness decreased with an increase in size, which verified the correctness of the test by [PERSON] and [PERSON] [9]. The degradation mechanism of roughness under different sizes is also studied. It is suggested that the motion of the micro-convex surface of a rough joint is the cause of the size effect. [PERSON] and [PERSON] [24] studied the influence of microscopic parameters on the direct shear strength of the joint. In particle flow simulation, the settings of the particle size and particle size ratio are always based on experience or other scholars' research [25; 26; 27; 28]. For natural rocks with a known particle distribution, [PERSON] and [PERSON] [29] and [PERSON] and [PERSON] [30], studied the influence of the mineral grain size variation on the macroscopic mechanical properties of rock.