## 1 Introduction  
Excavation design in underground mining must predict and control rock displacements within and around excavations to prevent fractures of intact rock, excessive roof and floor deflections, and rock sliding along weakness planes, all of which significantly impact mine stability. Consequently, the stability of underground excavations is closely linked to the stability of their walls, where stope and room characteristics significantly influence overall mine stability. The design of these excavations must anticipate rock mass behavior and consider slope stability, a fundamental aspect of underground mining projects due to their complexity and interdependencies. Additionally, the design must predict dilution,defined as waste rock mixing with ore, thereby reducing its grade. Planned dilution consists of unavoidable waste rock within the stope, whereas unplanned dilution refers to waste rock outside the stope boundaries due to blasting or poor rock stability. Unplanned dilution significantly increases operational costs in underground mining [1; 2; 3; 4]. Figure 1 illustrates various sublevel stoping methods, including drift layouts, drillhole configurations, and differences between designed and actual stope shapes due to overbreak (dilution) and underbreak (ore loss). [PERSON] [4] states that stope stability and dilution depend on factors such as rock mass classification, in situ stress, stope geometry, blasting techniques, geological structures, and stope exposure time. Empirical [5; 6] and numerical methods, such as finite element [7] and boundary element [8] methods, are commonly used to assess dilution and stability in underground excavations. However, both approaches have limitations, e.g., empirical methods do not account for hanging wall geometry, exposure time, blasting effects, and stress variations, while numerical methods may overlook the impact of exposure time, blasting, and rock mass strength properties, depending on the input data [4]. The geological structure of the rock mass, including the location, persistence, and mechanical properties of faults and fractures, is typically assessed using rock quality designation (RQD) [9; 10; 11]. The most relevant rock mass classification schemes include rock mass rating (RMR) [12; 13; 14], the Q-system [15], and the geological strength index (GSI) [16; 17]. In situ stress evaluation generally involves borehole disturbance, followed by measurements of strain, displacement, or hydraulic pressure. Analytical techniques aid in predicting rock mass responses to mining conditions and proposed stope geometries. [PERSON] et al. [18] introduced the D factor in the generalized Hoek-Brown criterion to quantify detonation-induced damage to the rock mass. Stope exposure (stand-up) time for unsupported spans can be estimated using the RMR system or the stress reduction factor (SRF) [19]. Various methods are used to design slopes in underground mining and predict stability and dilution. Analytical methods [11; 20; 21] assess excavation instability based on stress criteria for stress-driven failures and limit equilibrium analysis for structurally controlled failures. However, these methods often yield unrealistic results due to assumptions and simplifications [22]. Numerical modeling [7; 23; 24] simulates stope mechanical responses but requires an extensive modeling effort, particularly for complex conditions, and relies on accurate rock mass property data. Back analysis [25; 26] can enhance numerical modeling accuracy. Empirical tools [5; 6; 27; 28; 29], such as the Mathews stability graph method [27], are widely used due to their simplicity but struggle to define stability zone limits objectively. Furthermore, physical modeling using equivalent materials can be employed to emulate  
Figure 1: Different sublevel stoping methods, including drift layouts, drillhole configurations, and variations between designed and actual stope shapes due to overbreak (dilution) and underbreak (ore loss).