## 3 Experiment Results and Analysis  
### Nonlinear Evolution Characteristics of Seepage-Erosion Process  
As the progress of water-sand inrush process, soil particles continue to erode away, which not only changes the soil skeleton, but also the flow pattern along with seepage-erosion process. The eroding ability of seepage flow is represented by sands erosion rate, namely the mass of eroded soil particles within a certain amount of time. The sands mass concentration of eroded sands in discharged fluid is also regarded as a crucial symptom herein, which can be obtained through equation below  
\[c_{i}=\frac{m_{i}}{\rho_{f}q_{i}+m_{i}}\times 100\%(i=1,2,3\ldots n) \tag{1}\]  
where \(m_{i}\) is the weight of collected sands, \(q_{i}\) is the volume of discharged fluid, \(\rho_{f}\) is water density, \({}_{i}\) is the serial number of time per minute. The test results of each group is calculated and shown in Tables 3-5 and Figure 6. The variation of water-outflow rate is well fitted through Boltzmann equation, the variation of sands erosion rate and sands mass concentration with time are depicted by the 7 th order polynomial equation. It can be observed that the test results exhibit obvious similarities among each group, the variation of water-outflow rate are all characterized with distinct non-linear feature, the variation of sands mass concentration and sands erosion rate are both in shape of wave with the existence of summit. In order to deeply analyze the experimental phenomena, the test result of group 2 is illustrated in detail in Figures 7 and 8. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Test**} & \multicolumn{1}{c}{**Time (min)**} & & & & & & & & \\
**Number** & **5 th** & **10 th** & **15 th** & **20 th** & **25 th** & **30 th** & **40 th** & **50 th** & **60 th** & **70 th** & **80 th** & **90 th** \\ \hline
1 & 3.94 & 8.84 & 17.52 & 12.41 & 15.62 & 2.26 & 5.54 & 3.20 & 1.07 & 1.13 & & \\
2 & 1.12 & 1.61 & 6.12 & 5.55 & 16.84 & 17.61 & 6.99 & 6.36 & 4.50 & 2.16 & & \\
3 & 0.43 & 1.71 & 2.03 & 1.64 & 2.02 & 3.28 & 12.48 & 11.63 & 6.36 & 3.42 & 1.22 & 0.54 \\
4 & 0.18 & 0.20 & 2.11 & 14.03 & 7.06 & 14.41 & 10.59 & 2.75 & 1.66 & 0.83 & & \\
2 & 1.12 & 1.61 & 6.12 & 5.55 & 16.84 & 17.61 & 6.99 & 6.36 & 4.50 & 2.16 & & \\
5 & 8.36 & 30.26 & 29.05 & 12.29 & 9.80 & 5.13 & 2.23 & 1.93 & & & & \\
6 & 1.60 & 1.43 & 6.24 & 5.95 & 5.34 & 15.38 & 12.20 & 4.29 & 1.95 & & & \\
2 & 1.12 & 1.61 & 6.12 & 5.55 & 16.84 & 17.61 & 6.99 & 6.36 & 4.50 & 2.16 & & \\
7 & 0.23 & 0.83 & 3.45 & 1.40 & 20.68 & 12.44 & 10.85 & 3.68 & 3.26 & 1.47 & 0.84 & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Variation of sands erosion rate with time (kg/h). \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Test**} & & & & & & & & & & \\
**Number** & **5 th** & **10 th** & **15 th** & **20 th** & **25 th** & **30 th** & **40 th** & **50 th** & **60 th** & **70 th** & **80 th** & **90 th** \\ \hline
1 & 0.47 & 1.21 & 4.16 & 6.48 & 6.81 & 7.66 & 7.76 & 7.70 & 7.80 & 8.26 & & \\
2 & 0.20 & 0.34 & 0.86 & 1.50 & 4.64 & 7.59 & 7.51 & 7.43 & 7.84 & 7.62 & & \\
3 & 0.03 & 0.29 & 0.56 & 0.33 & 0.59 & 0.70 & 4.25 & 5.82 & 6.32 & 5.98 & 6.49 & 5.98 \\
4 & 0.06 & 0.12 & 0.25 & 1.67 & 1.19 & 2.79 & 5.28 & 6.38 & 6.53 & 6.53 & \\
2 & 0.20 & 0.34 & 0.86 & 1.50 & 4.64 & 7.59 & 7.51 & 7.43 & 7.84 & 7.62 & & \\
5 & 0.76 & 2.99 & 6.28 & 8.89 & 8.20 & 8.97 & 8.05 & 9.00 & & & \\
6 & 0.60 & 0.72 & 1.21 & 1.39 & 2.98 & 4.00 & 5.91 & 5.76 & 5.25 & & \\
2 & 0.20 & 0.34 & 0.86 & 1.50 & 4.64 & 7.59 & 7.51 & 7.43 & 7.84 & 7.62 & & \\
7 & 0.19 & 0.72 & 0.53 & 0.55 & 1.75 & 3.40 & 8.18 & 7.77 & 8.26 & 8.35 & 8.67 & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Variation of water-outflow rate with time (m\({}^{3}\)/h). First, according to the variation curve of water-outflow rate, the water-sand inrush process is visually divided into three stages by Transition Point I, II, which are determined through the extremum analysis of water-outflow rate's fitted curve.