# Modeling of Water Losses in Hydraulic Tunnels under Pressure Based on Stepwise Regression Method
## 4 Case Study
### Measurements in the Tunnel  
In the hydrotechnical tunnel measurements of the temperatures of concrete and water in the tunnel, the water level in the upper reservoir, the water level in the piezometers, and measurements of the width of the crack openings in the tunnel's concrete lining are conducted approximately two times per month. Measurements of the total water losses are conducted 2-4 times per year depending on the weather conditions and the tunnel exploitation regime.  
Measurement of total water losses is carried out under conditions when the tunnel is closed both at the entrance building at the upper reservoir and at the outlet towards the pipeline. One session of measurements of total water loss is performed in several phases. A single phase includes the rapid reduction of the water level in the surge tank down to some level, \(H_{i}\), and then, a measurement step. In the measurement step, it is measured how much the water level \(H_{i}\) has lowered in the observed time interval. The decrease in water level is the result of water loss from the tunnel. At the end of the measurement step, the water level is \(H_{i+1}\). Based on the difference, \(H_{i}-H_{i+1}\), the resulting volume of lost water \(\Delta V\) from the tunnel is obtained according to (8) [4].  
\[\Delta V=(H_{i}-H_{i+1})\cdot\frac{D^{2}\pi}{4}, \tag{8}\]  
The total water loss is calculated according to (9):  
\[q=\frac{\Delta V}{\Delta t}, \tag{9}\]  
where \(q\) [L/s], \(\Delta V\) [I], and \(\Delta t\) [s] are the total water loss, water volume decrease in the surge tank with a circular cross-section (diameter D = 12.0 m), and time interval, during  
Figure 3: Longitudinal tunnel profile with a schematic view of the upper lake, pipeline, PSHPP, and HPP “Bajina Basta” (**a**) and cross-section of tunnel (**b**).  
Figure 2: Map of Serbia showing the river Drina and the position of the PSHPP Bajina Basta.  
a single measurement step, respectively. The measuring is stopped when the total water loss \(q\) becomes negative--\(\Delta V\) becomes negative, i.e., water volume in the surge tank starts increasing and water loss turns into water inflow. The duration of one measurement step is usually 30 min. According to the same principle, the procedure repeats in the next phases in the session.  
Figure 4 shows a diagram of water level change in the surge tank during one session of total losses measurement (in this case, the 75 th session, 17 August 2015).  
During the session of measurement of total water losses, measurements of concrete temperature on the extrados of the concrete lining, water temperatures, width of the crack openings, water level in the upper reservoir, and water level in piezometers are also measured at the same time.  
For measuring the temperatures of the water and the concrete, thermometers are installed in the tunnel lining (on the extrados and intrados of the tunnel). The instruments are isolated from the effects of water and the measurements are conducted twice a month via a portable measuring station. For measuring the width of the crack openings electroacoustic deformeters are installed in the concrete in the zone of the crack. The instruments are isolated from the effects of water and the measurements are conducted twice a month via a portable measuring station (outside the tunnel).