## 1 Introduction  
The block caving method exploits the distribution characteristics of joints and the low-strength properties of the ore/rock. Undercutting--blasting at the base of the ore block--creates a free surface, inducing gravity-driven caving of the ore [1]. This process involves stages including undercutting, initial caving, and continuous caving until the collapse propagates to the surface. Block caving is an efficient underground mining method well suited to specific geological conditions, offering significant economic benefits and technical advantages [2]. However, its successful implementation depends critically on precise draw control strategies. Understanding draw theory and its associated control techniques is paramount for elucidating the movement laws of caved ore within the surrounding rock cover. Furthermore, it plays a vital role in predicting ore loss and dilution, thereby enhancing economic outcomes [3, 4]. Numerous researchers have conducted extensive indoor experiments, numerical simulations, and theoretical studies on draw problems in metal mines. Various ore draw theories have been developed to date, including the ellipsoid theory, quasi-ellipsoid theory, random medium theory, and inverted drop theory. Concurrently, indoor draw experiments have garnered significant interest among scholars, and their findings have proven indispensable in mining research. For instance, [PERSON] (2016) developed a large-scale ore draw test apparatus and utilized it to investigate the influence of moisture content and particle size on extraction zone (EZ) morphology. [PERSON] (2016) and [PERSON] (2017) systematically conducted three-dimensional physical draw experiments using gravel as a granular medium to examine the morphological evolution of the extraction zone and ore flow patterns under 3D conditions. [PERSON] et al. (2018) performed multiple laboratory experiments to quantify variations in internal stress within the drawpoint structure under consistent rock mass gradation but different draw strategies. Their results revealed that the vertical stress during drawing fluctuated between 0.3 and 2.8 times the initial vertical stress, with variations closely linked to factors such as the draw strategy and spatial location within the draw zone. [PERSON] (2018) conducted isolated draw experiments, the results of which demonstrated a distinct longitudinal asymmetry in the EZ shape, deviating from a standard ellipsoid. The migration zone (MZ) exhibited an inverted droplet shape, corroborating the inverted drop theory. Building on this, [PERSON] proposed a novel method for characterizing EZ geometry and development. [PERSON] and [PERSON] et al. (2018, 2019) constructed a physical model featuring a draw funnel and tested various coarse-to-fine material ratios, coarse particle distributions, and material heights to assess the effects of key variables on fine particle migration. [PERSON] (2019) examined the migration patterns of caved ore and rock under different influencing factors, such as draw column height, drawpoint size, and vertical stress. Furthermore, with the continuous advancement of computer technology and ore draw theory, numerical simulation methods are poised to play an increasingly critical and indispensable role in studying ore draw problems. Among these methods, PFC (particle flow code) is particularly well suited for investigating ore draw phenomena due to its unique capability to analyze the movement laws of granular media, such as caved ore, from a microscopic perspective ([PERSON] _et al._, 2016; [PERSON] _et al._, 2016). Currently, researchers have achieved significant results in studying near-field mining issues in metal mines using PFC software. For instance, [PERSON] (2019) investigated the shape of the Isolated Extraction Zone (IEZ) and its key influencing factors through isolated physical draw experiments.