# Predicting the Pillar Stability of Underground Mines with Random Trees and C4.5 Decision Trees
## 1 Introduction  
Pillars are essential structural units of most underground mines, used to ensure safety and economically maximize the extraction of the ore body. [PERSON] [1] defined the pillars as \"the in-situ rock between two or more underground openings\". Their primary purpose is to provide safe access to the working area and to support the weight of overburden material between adjacent underground openings temporarily or permanently, and drilling room of ceilings during excavation and mining [2; 3; 4; 5; 6; 7]. Instable pillars may significantly increase workers' safety hazards and sudden roof collapse [8]. Additionally, with the increase in mining depth, the failure of the pillar becomes more frequent and critical owing to increased ground stresses. The determination of pillar stability is, therefore, important for attaining efficient and safe mining. Several researchers have developed numerous methods for understanding and predicting pillar failures in thee past several decades. Pillar stability is generally evaluated using a factor of safety (FoS), which is the ratio between the pillar strength and the load imposed on the pillar structure. Theoretically, when the \(FoS\) ratio is greater than 1, the pillar is considered stable. However, studies suggest that pillar with \(FoS\) above this threshold may still fail due to non-regular geometries, uncertain material properties, and differences in mining operations [7; 9]. In literature, numerical simulation methods are mostly used to predict the pillar stability that allows for consideration of material properties and complex boundary conditions. [PERSON] et al. [10] used FLAC3D with mining sequence scenarios to predict pillar stability. [PERSON] et al. [11] integrated the random field theory coupled with an elasto-plastic finite element method (FEM) for predicting pillar stability. In their study, [PERSON] et al. [12] used three-dimensional FEM analysis to investigate the stress-strain behavior of coal pillars. [PERSON] et al. [13] developed the Finite-Discrete Element Method (FDEM) to examine the failure modes and mechanical behavior of pillars. [PERSON] et al. [14] used the fast Lagrangian analysis of continua (FLAC) to investigate the pillar failure mechanism of pillar and non-linear rock behavior. Owing to the anisotropic nature of rock mass and complicated non-linear characteristics, it is difficult to accurately evaluate the model inputs and constitutive equations in the numerical simulation techniques [11]. With the increasing availability of pillar stability cases, machine learning (ML) algorithms have been successfully applied for pillar stability assessment with greater accuracy compared to most available methods. [PERSON] and [PERSON] [15] in their study, utilized artificial neural networks (ANN) to explore the stability characteristics of the surface crown pillars. [PERSON] et al. [16] examine the applicability of the stochastic gradient boosting (SGB) model for predicting pillar stability. Study results demonstrated that the proposed model outperformed random forest (RF), multilayer neural perceptron (MPNN) and support vector machine (SVM). [PERSON] [9] presented the multinomial logistic regression (MLR) for predicting the pillar's stability. [PERSON] et al. [17] used SVM and J48 algorithms to develop pillar stability plots. Both models acquired acceptable prediction performance. [PERSON] et al. [18] used SVM and fishery discriminant analysis (FDA) for determining the pillar stability of underground mines. [PERSON] et al. [19] compared six different supervised machine learning algorithms for pillar stability analysis. Study results showed that SVM and RF performed much better. While most of the implemented ML techniques have been implemented successfully to predict the stability of the pillar, they also have some shortcomings. For example, the optimum model structure (such as the number of hidden layers and model inputs, training algorithms, and transfer functions) the a priori requirements when adopting the ANN approach.