# Dynamic Monitoring of the Water Flowing Fractured Zone during the Mining Process under a River
## 3 Materials and Methods
### Curve Fitting and Numerical Modeling Method  
To compare the change behavior of the water levels from TEM results more intuitively, the water levels of each survey station were extracted every day for curve fitting with MATLAB (R2014b, The  
Figure 5: The layout of the survey area. The red quadrangle refers to the survey area. The colored lines refer to the contours of the surface terrain of the 8101 longwall face. The black lines refer to roadways. The points in the lower left corner refer to the survey stations. In the lower right corner, the black coil is the transmitter loop, the orange coil is the receiver loop, and the yellow device is the TEM transmitter and receiver instrument. MathWorks Inc., Natick, MA, US 2014) We adopted the rational polynomials method, which had the best fitting result. The main advantage of the rational polynomials method is its flexibility with data that has a complicated structure. The rational polynomials equation is defined as:  
\[\mathrm{y}=\frac{\sum_{i=1}^{n}p_{i}x^{n-i}}{x^{m}+\sum_{i=1}^{m}q_{i}x^{m-1}} \tag{5}\]  
where \(n\) is the degree of the numerator polynomial and \(m\) is the degree of the denominator polynomial. Through comparison, we finally chose the cubic/linear rational equation as the governing equation of curve fitting. After comparing the change behavior of the water levels, a 2D finite-element numerical model developed with COMOSL (3.5a, COMSOL Inc., Stockholm, SWE 2018) Multiphysics was designed to study the lateral recharge and water seepage mechanisms of the aquifer. According to the geological conditions of the 8101 longwall face, the water seepage model was built based on the conservation of mass and the pressure equilibrium. The model consists of three parts, representing the overlying aquifer, the WFFZ and the roadway of the 8101 longwall face. The upper part is 100 m wide and 20 m thick, representing the K\({}_{\mathrm{lzh}}\) unconfined aquifer in the lower series of the Cretaceous and the middle Jurassic coarse sandstone aquifer, and the corresponding physical field is Darcy flow. The middle part is 10 m wide and 100 m thick, and the corresponding physical field is high-speed Forchheimer flow, representing the water flowing fractured zone. The middle part was set on the right side of the model to simulate the case that the WFFZ connected to the corner of the aquifer. The lower part is 100 m wide and 5 m thick, representing the roadway of the 8101 working face, and the corresponding physical field is Navier-Stokes flow. The model is shown in Figure 6. The finite element method with local mesh refine strategy was adopted, and the model was divided into 7314 triangular elements. Figure 6: The numerical model of water seepage in the water flowing fractured zone (WFFZ). The horizontal red dotted cut line was used to extract the corresponding water flow velocity in the aquifer, and the vertical one was used to extract the water flow velocity in the WFFZ and the corresponding aquifer area. The seepage of water in aquifers obeys [PERSON]'s law [28] as follows:  
\[\mathbf{u}=-\frac{k}{\eta}(\
abla p+\rho gZ) \tag{6}\]  
where \(\mathbf{u}\) is the flow velocity of water (m/s), \(k\) is the rock permeability (m\({}^{2}\)), \(\eta\) is the dynamic viscosity (Pa\(\cdot\)S), \(Z\) is the hydraulic head (m), \(\rho\) is the fluid density (kg/m\({}^{3}\)), \(g\) is the gravitational acceleration (9.8 m/s\({}^{2}\)), and \(\
abla\) is the gradient operator.