## 2 Theory of Slug Test on Determining Permeability Coefficient of Anisotropic Fractured Rock Mass
When \(\zeta<1\), the Equation (8) can be changed into the following after inverse transformation:  
Figure 1:2  
When \(\zeta=1\), the Equation (8) can be changed into  
Figure 1:3  
When \(\zeta>1\), the Equation (8) can be changed into  
Figure 1:4  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Dimensionless Variable** & **Dimensionless Transformation** \\ \hline Dimensionless water level variable & \(w^{\prime}=-\frac{w}{w_{0}}\) & \(w^{*^{\prime}}_{0}=-\frac{w_{0}^{*}}{w_{0}}\frac{t^{2}\mu_{s}}{k}\) \\ \hline Dimensionless water level & \(h^{\prime}=\frac{h_{0}-h}{w_{0}}\) & \(h^{\prime}_{s}=\frac{h-h_{0}}{w_{0}}\) \\ \hline Dimensionless time & \(t^{\prime}=\frac{h}{\tau_{s}^{\prime}\mu_{s}}\) & \(\hat{t}=\frac{t^{\prime}}{\hat{\beta}^{\frac{1}{2}}}=\frac{t\cdot k}{r_{s}^{ \prime}\cdot\mu_{s}\hat{\beta}^{\frac{1 Therefore, according to the Equations (10)-(12), the standard curves of the dimensionless water level change \(w^{\prime}\) and dimensionless time \(\hat{t}\) can be drawn with the relative damping coefficient \(\zeta\) of 0.05, 0.1, 0.2, 0.5, 0.7, 1, 1.5, 2, 3, 4, 5 and 10, as shown in Figure 1:5 In the semi-logarithmic paper of the same modulus with the standard curve, one can draw the measured curve of the water level changes \(w\) versus time \(t\), which are collected by the slug test. One must make sure the coordinate origin of the measured curve and standard curve are at the same height in the semi-logarithmic paper. By translating the measured curve time axis \(t\), one must match the measured curve with the standard curve; record the relative damping \(\zeta\) and dimensionless coefficients \(\alpha\) of standard curve; choose a matching point, record its \(\hat{t}\) and \(w^{\prime}\) on the standard curve, together with its \(t\) and \(w\) on the measured curve. According to the obtained fractured structural plane occurrence in the drilling, the dip direction \(\beta_{i}\), dip angle \(\varphi_{i}\) and the width of the fracture \(b_{ij}\), the fracture storage rate and the fracture permeability coefficient can be calculated by the following equations:  
Figure 1:6  
Figure 1:7  
The equivalent permeability coefficient \(K_{ei}\) within the length of test section of the same group fracture structural plane for some fractures of different width and spacing in the rock mass can also be calculated as follows:  
Figure 1:8  
where \(K_{eij}\) is the permeability parameter of No. \(j\) fracture in the No. \(i\) group fracture structural plane; \(m\) is the total number of fractures in No. \(i\) group fracture structural plane; \(b_{ij}\) is the width of No. \(j\) fracture in the No. \(i\) group fracture structural plane; \(L\) is the length of test section in the borehole. When the fractured rock mass has several groups' different occurrences fracture structural planes, one must choose \(ox1\), \(oy2\) and \(oz3\) in the cartesian coordinate system as north, east and the vertically upward direction. The permeability coefficient tensor \(K\) can be also calculated as follows:  
\[K=\sum_{i=1}^{n}K_{ei} \begin{bmatrix}1-\cos^{2}\beta_{i}\sin^{2}\varphi_{i}&- \sin\beta_{i}\sin^{2}\varphi_{i}\cos\beta_{i}&-\cos\beta_{i}\sin\varphi_{i} \cos\varphi_{i}\\ -\sin\beta_{i}\cos\beta_{i}\sin^{2}\varphi_{i}&1-\sin^{2}\beta_{i}\sin^{2} \varphi_{i}&-\sin\beta_{i}\sin\varphi_{i}\cos\varphi_{i}\\ -\cos\beta_{i}\sin\varphi_{i}\cos\varphi_{i}&-\sin\beta_{i}\sin\varphi_{i} \cos\varphi_{i}&1-\cos^{2}\varphi_{i}\end{bmatrix}  \tag{16}\]  
Figure 2: Slug test standard curve of determining different dip angle fracture permeability coefficients. where \(i\) is the number of No. \(i\) group fracture structural plane; \(K_{ei}\) is the equivalent permeability coefficient of No. \(i\) group fracture structural plane; \(n\) is the total groups of fracture structural planes in the rock mass. This proposed model is only applicable to the case where the dip angle \(\varphi\) is not zero. If it is a horizontal fracture, the Kipp model can be directly used.