# Small Dam Drainage with Nonwoven Geotextile after 40 Years of Exploitation
## 2 Materials and Methods
### Numerical Calculations  
In this research, we used the well-known software HYDRUS (2D/3D) Standard to predict pressure heads in the earth dam [16]. This program is a computer package that allows one to simulate the flow of water and pollution, mass and heat [22] through saturated and unsaturated porous media [23]. The two-dimensional model was built with a mixed flow regime, using the finite element method. Water flow under unsaturated conditions was calculated in the presented 2D model using the Richards equation [24]. The simulations were made in the schematic model presented in Figure 7.  
The second kind of boundary condition \(q_{n}=0\) (no flow) was assumed on the base of the aquifer layer. A drainage pipe along the air-side embankment from the level of the bench to the end of the ditch a seepage face condition was used. In this case, the length of the seepage face is not known a priori, and its length is determined iteratively by the software. In the HYDRUS (2D/3D) software it is assumed that the pressure head is constant and equal to zero along the seepage face. The boundary condition of type I (marked in red) defined the constant maximum water level (3.32 m) in the reservoir equilibrium from the lowest located nodal point. Similarly, the initial condition, defined for the entire seepage area, was established using the hydrostatic pressure equilibrium from the lowest located nodal point at the bottom, equal to 8.7 m. Soil parameters in Table 1 were estimated using Rosetta software [25] based on textural and literature data [26].  
Calculations were performed with a varying time step in the range of \(1\cdot 10^{-5}\) to 5 days. The model was run for 30 days.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Material**} & \(\mathbf{\Theta_{r}}\) & \(\mathbf{\Theta_{S}}\) & \(\mathbf{a}\) & \(\mathbf{n}\) & \(\mathbf{K_{s}}\) & \(l\) \\  & **(m\({}^{3}\)/m\({}^{3}\))** & **(m\({}^{3}\)/m\({}^{3}\))** & **(l/m)** & **(c)** & **(m/day)** & **(c)** \\ \hline Sand & 0.045 & 0.43 & 14.5 & 2.68 & 7.78 & 0.5 \\ \hline Gravel & 0.05 & 0.4 & 175 & 2.8 & 86.4 & 0.5 \\ \hline Concrete & 0 & 0.069 & 0.000248 & 1.917 & 4.089\(\cdot 10^{-8}\) & 0.5 \\ \hline Silty Loam & 0.067 & 0.45 & 2 & 1.41 & 0.108 & 0.5 \\ \hline Clogged A & 0.045 & 0.43 & 14.5 & 2.68 & 129 & 0.5 \\ \hline Clogged B & 0.045 & 0.43 & 14.5 & 2.68 & 345 & 0.5 \\ \hline Clogged C & 0.045 & 0.43 & 14.5 & 2.68 & 259 & 0.5 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Filtration properties of used soils.  
Figure 7: Numerical scheme built in software package HYDRUS (two-dimensional/three-dimensional (2D/3D)).  
To simulate clogged nonwoven geotextile located around the gravel and sand near the drainage pipe, we adopted the following assumptions, presented in Figure 8:  
1. The nonwoven geotextile permeability was adopted in accordance with the measurement from the sample taken,
2. The permeability of nonwoven geotextile lying below the drainage pipe was taken similarly to geotextile A. This assumption was made because the research should be conducted in future and taking a sample below the drain would cause a disturbance in the drainage pipe. The geotextile sample can only be taken without distribution above a drainage pipe.