# An FDM-Based Dynamic Zoning Method for Disturbed Rock Masses above a Longwall Mining Panel
###### Abstract
Several methods have been employed to study the development characteristics of the four zones in overlying strata, such as field measurements [5,8,9], physical modeling [4,10,11], and numerical modeling [3,6,7,12,13,14]. Numerical modeling can be considered a promising and effective tool to reflect the overburden movement process and predicting the heights of disturbed zones in longwall mining. Various examples of numerical modeling have been reported in the literature. Researchers have used different numerical modeling methods, including the finite element method (FEM) [12], finite difference method (FDM) [7,10], discrete element method (DEM) [3,6], and mesh free method (MFM) [13]. There are several types of zoning methods introduced in the literature. The commonly used zoning methods are outlined below. In the first method, rock masses are considered elastoplastic materials while employing a strain-softening model, and the process of caving is simulated after determining the parameters in the strain-softening model when rock masses fail using an empirical formula [12,15]. As the failed rock masses freely fall from the roof during caving, [PERSON] et al. assumed that the stresses of the rock masses suddenly drop to almost zero after failure [12]. After satisfying the yielding condition, the material fails, and its properties are updated to those of the damaged material. In this method, the differences in the mechanical characteristics of roof rock masses before and after caving are considered, and it is feasible to simulate strata caving by adjusting the mechanical characteristics of failed rocks. However, this method considers rock mass yielding as the caving criterion without clearly defining the scope of the caved zone, which may lead to a misjudgment of the scope. In the second method, the heights and shapes of the caved zone and fractured zone are calculated according to an empirical formula, and then the scopes of the two zones above the mined-out area and the corresponding mechanical parameters are determined before conducting a simulation of longwall mining. [PERSON] [16] assumed that the caved zone existed with a height _lz_ and a shape similar to a trapezoid above the mined-out area. Moreover, the fractured zone existed with a height _lts_ and a shape similar to a half-ellipse above the caved zone. The heights depended on the mechanical properties of the rock mass layers and the thickness of the excavation. The parameters of the two zones were determined with laboratory tests and the GSI (geological strength index). In this method, the differences between different zones are considered, and the scope of disturbed rock masses is clearly determined. However, the determination of the scope of the caved zone and the fractured zone is strongly impacted by expert judgments, and the roof strata development process from the elastic-plastic deformation stage to the cracking and falling stage is ignored. In the third method, the height of the caved zone is determined according to the empirical bulking factor, and in the simulation, if the strain or displacement of the falling rock mass reaches the caving criterion, it is considered a new loose material. [PERSON] and [PERSON] used the principal plastic strain to identify the caving boundary and the bulking  
Figure 1: The four zones of disturbance in the overlying strata resulting from longwall mining. factor to determine whether the roof strata of the panel entirely filled the mined-out area. After the caving process stops, the mechanical properties of caving materials are changed to a double-yield model [17; 18]. In this method, the caving criterion is used to determine whether the surrounding rock falls in a mining simulation, which avoids misjudging the yielded noncaving rock as caved rock. The roof strata development process from elastic-plastic deformation to cracking and caving can be dynamically reflected. Moreover, the change in mechanical parameters of caved rock can also be well reflected.