# Analysis of Shear Stress and Stream Power Spatial Distributions for Detection of Operational Problems in the Stare Miasto Reservoir

## Abstract

**:**

## 1. Introduction

^{3}. In Wielkopolska, there are also two large reservoirs with storage exceeding 5 hm

^{3}[1]. The number of reservoirs indicates the significance of the discussed problem. Additionally, it is worth noting the economic importance of the reservoirs.

## 2. Case Study System

^{3}. The lower part is the so-called main reservoir. This part is additionally split into two internal parts by highway A2 (Figure 1), running from Poznań to Warsaw [32]. The watershed area of the Stare Miasto reservoir in the cross-section of the main dam is 299.7 km

^{2}. The average depth of the reservoir is 2.4 m. The estimated length of this object is 4.5 km. The inundation area for the minimum headwater level (MinPP = 92.0 m a.s.l.) is 75.77 ha. For the normal headwater level (NPP = 93.5 m a.s.l.) the inundation area is 90.68 ha. The maximum headwater level (MaxPP) is 94.0 m a.s.l. The total reservoir capacity is 2.159 hm

^{3}. The active conservation storage is 1.216 hm

^{3}. The inundation area of the upper zone is 13.62% of the total water surface area. The land use in the neighborhood of the reservoir agriculture. Because the usefulness of the terrain is limited, crop production has been stopped in this region [32,33]. The reservoir is working in an annual compensation cycle, which may cause annual variation in the water level, from MinPP to NPP. The operational water level is from 92.00 m a.s.l. to 94.00 m a.s.l. The reservoir is filled in March and the water surface is kept at the level of NPP until the end of October. After October, the main reservoir is emptied to the level of MinPP. To protect the inlet part from degradation and sediment accumulation, the water surface in the upper part is kept at the NPP level for the entire year.

^{2}. The characteristic flows were determined on the basis of recorded observations at this gauge station during the period 1975–2017 [34]. The results are presented in Figure 2. The total minimum observed was 0.006 m

^{3}/s, while the total maximum was 42.6 m

^{3}/s. The mean flow was about 1.15 m

^{3}/s. During the time of reservoir operation, from 2006 to 2017, the maximum flow of 28.5 m

^{3}/s (Figure 2b) occurred in 2014. The minimum and mean flows did not differ much from those estimated for the entire period. In the analyzed period, the average annual outflow from the reservoir was 36.9 hm

^{3}.

#### Operational Problems in the Reservoir

^{3}. The soil removed was distributed more or less uniformly along the banks. The sluice gate was reconstructed in such a way that inverted elevation was decreased.

## 3. Materials and Methods

#### 3.1. Available Data

#### 3.2. Applied Methods

^{2}. The imposed cell size of rectangular cells was 2 × 2 m, but the cells near the boundaries may have different shapes. Hence, the minimum cell area was 1.74 m

^{2}and maximum was 7.87 m

^{2}, when the total average was 4.01 m

^{2}. The total number of cells covering the reservoir was 241,699. Three bottoms were tested, which were the reconstructions of the real reservoir for 2006, 2013, and 2018. The reconstruction process is described above. In all cases the flood wave observed in 2014 was simulated with constant head water kept in the reservoir outlet. The elevation of the head water simulated was 93.50 m a.s.l. This is the so-called normal head water level in the Stare Miasto reservoir. The simulation time step was chosen due to the stability requirements and it equaled 30 s. Because the semi-implicit scheme was used for time discretization, the weighting factor was set to 0.75.

_{h}is the hydraulic radius and k

_{s}is the absolute roughness. The second coefficient was defined theoretically as the average height of bottom irregularities. In practice its value was calculated on the basis of sediment characteristics, but a number of formulae have been proposed in literature for this purpose. The chosen and applied approaches are presented in Table 1 [40]. The symbol d

_{x}in this table means specific diameter of the grain sample determined on the basis of the sieve curve. The next step was calculation of Manning’s roughness coefficient n from the formula:

^{−1/3}, while the minimum and maximum values were 0.026 and 0.059 sm

^{−1/3}, respectively.

## 4. Results and Discussion

^{2}, while the stream power (SP) values reached about 100 W/m. The highest values of shear stress as well as stream power were observed for the reservoir in 2013. Supposedly, the accumulation of sediments in the period 2006–2013 changed the configuration of the bottom in such a way that there was an increase in these two factors. The values of shear stress and stream power were lower for the conditions in 2018. The removal of sediments in the pre-reservoir in 2014/2015 induced another kind of change. The next specific cross-section is shown in Figure 13b, at the internal dam with its sluice gate. The shear stresses as well as stream power in the sluice were increasing rapidly, independently of the bottom configuration tested. However, the sluice gate is made of concrete and it should be resistant to such forces. The huge values of the analyzed variable are more dangerous for the rest of the internal dam. The maximum values of shear stress were about 40 N/m

^{2}there, while the stream power reached about 200 W/m. The values of these two factors were relatively small for the conditions in 2006, but in other configurations of the bottom, 2013 and 2018, high shear stresses and stream power were noticed. These values were quite high, especially in the lowland reservoirs where fine sand is deposited with grain sizes smaller than 0.5 mm. It means that, irrespective of the dredging and rebuild of the sluice gate, the internal dam is still exposed to huge forces and is prone to break. In the cross-section of the bridge, the shear stresses were smaller, about 7 N/m

^{2}and seem to be stable. The same was noticed about the stream power values obtained there. The hydraulic conditions under the bridge seemed to be less dependent on the bottom configuration.

^{2}and median stream power of 27.97 W/m over the internal dam. The median results obtained for bathymetry 2018 were 7.77 N/m

^{2}and 19.27 W/m, respectively. Hence, the decreases were 2.2% and 31.1% for shear stress and stream power, respectively. The same results indicate significant increases of the maximum values in the case of these two factors. The maximum shear stress and stream power values for bottom for 2013 were 28.63 N/m2 and 653.78 W/m, respectively. The results for the bathymetry 2018 gave maximum values of the same variables equaling 36.75 N/m

^{2}and 815.12 W/m. Hence, the increase of shear stress was 28.4% and the increase of the stream power was 24.7%. It confirms the previous conclusion that the rebuild of the internal dam and sluice gate did not improve the safety of this object.

^{2}. The course of the channel, meandering or straight, influenced the obtained values greatly. The results were also dependent on the type of model applied. They compared results of 1D, 2D, and 3D models. It is obvious that shear stresses are impacted by the roughness of the channel bed and flow velocities. In the Stare Miasto reservoir maximum velocities up to 10 m/s (Figure 14a) generated huge shear stresses, reaching values of 90 N/m

^{2}(Figure 13b). Such magnitudes were noted in the internal dam and near the sluice installed there. Huge velocities and shear stresses caused huge values of stream power. In the sluice it was 900 W/m (Figure 13b). During the flood wave propagation in the reservoir, the most critical location was the reservoir inlet. The velocities simulated there equaled 5 m/s (Figure 11), which was related to huge shear stresses reaching values of 25 N/m

^{2}(Figure 13a).

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Chosen case study—Stare Miasto reservoir on the Powa river: (

**a**) The reservoir and its main elements—internal dam, highway bridge, and main dam; (

**b**) the watershed with main elements—river, reservoirs, and gauge station.

**Figure 2.**Variability of discharge at the Posoka gauge station, (

**a**) for the period 1971–2017; (

**b**) for the year 2014.

**Figure 3.**Stare Miasto reservoir in the Powa river: (

**a**) The internal dam in 2011; (

**b**) the internal dam destroyed after the flood wave propagation in 2014; (

**c**) the uncovered reservoir bottom near the internal dam (author: J. Wicher-Dysarz).

**Figure 4.**Stare Miasto in the Powa river: (

**a**) The bridge with highway A2; (

**b**) the sluice in the internal dam in 2011; (

**c**) the sluice in the internal dam in 2014 (author J. Wicher-Dysarz).

**Figure 5.**Examples of data used for the reconstruction of the reservoir bathymetries: (

**a**) Location of the selected area; (

**b**) design map from 2006; (

**c**) measurement points from 2013; (

**d**) measurement points from 2018.

**Figure 6.**Main ideas of the bathymetry reconstruction with RiverBox [37]: (

**a**) Scheme of interpolation; (

**b**) applied algorithm.

**Figure 7.**Estimation of roughness coefficients: (

**a**) Statistics of roughness coefficients calculated on the basis of approaches presented in Table 1; (

**b**) sieve curves applied for the calculation of roughness coefficients.

**Figure 8.**Elements used in the analyses: (

**a**) Parts of the reservoir and location of cross-sections; (

**b**) location of sample points.

**Figure 9.**Analysis of depth distributions over the reservoir bottom in the Stare Miasto reservoir: (

**a**) Bathymetry 2006; (

**b**) bathymetry 2013; (

**c**) bathymetry 2018.

**Figure 10.**Selected cross-sections: (

**a**) Bottom and water surface elevations for three bathymetries; (

**b**) difference in bottom elevations between 2006 and 2013, as well as between 2006 and 2018.

**Figure 11.**Spatial distributions of velocities in the Stare Miasto reservoir for three bathymetries: (

**a**) Bathymetry 2006; (

**b**) bathymetry 2013; (

**c**) bathymetry 2018.

**Figure 12.**Shear stress calculated for the Stare Miasto reservoir and three bathymetries: (

**a**) Bathymetry 2006; (

**b**) bathymetry 2013; (

**c**) bathymetry 2018.

**Figure 13.**Shear stress and stream power in chosen cross-section: (

**a**) inlet; (

**b**) internal dam; (

**c**) bridge.

**Figure 14.**Characteristic values of analyzed hydraulic parameters simulated for bathymetries 2006, 2013, and 2018, and recorded at random points: (

**a**) Velocity; (

**b**) shear stress; (

**c**) stream power.

Methods | Absolute Roughness (k_{s}) |
---|---|

Nikuradse | k_{s} = 2.3d_{80} |

Einstein | k_{s} = d_{65} |

Engelung-Hansen | k_{s} = 2d_{65} |

van Rijn | k_{s} = 3d_{90} |

Kamphuis | k_{s} = 2d_{90} |

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**MDPI and ACS Style**

Wicher-Dysarz, J.
Analysis of Shear Stress and Stream Power Spatial Distributions for Detection of Operational Problems in the Stare Miasto Reservoir. *Water* **2019**, *11*, 691.
https://doi.org/10.3390/w11040691

**AMA Style**

Wicher-Dysarz J.
Analysis of Shear Stress and Stream Power Spatial Distributions for Detection of Operational Problems in the Stare Miasto Reservoir. *Water*. 2019; 11(4):691.
https://doi.org/10.3390/w11040691

**Chicago/Turabian Style**

Wicher-Dysarz, Joanna.
2019. "Analysis of Shear Stress and Stream Power Spatial Distributions for Detection of Operational Problems in the Stare Miasto Reservoir" *Water* 11, no. 4: 691.
https://doi.org/10.3390/w11040691