# Failure Assessment of Embankment Dam Elements: Case Study of the Pirot Reservoir System
## 5 Results and Discussion
### Hypothetical Scenarios Results
#### 5.3.3 Analysis of Spillway Functionality (Scenario 3)  
Regarding the remaining load-bearing capacity field used to assess the partial stability of the structure parts, it can be seen that in case of seismic acceleration in the dam axis direction, this quantity has the lowest value at the junction of the dam and the rock mass on the left side of the structure (Figure 15a). This is expected because the maximum values of plastic strain occur at the same part. Additionally noted and important for the analysis of functionality of the overflow section, is that on the slope located just above the overflow, there is a significant zone where the remaining load-bearing capacity is almost consumed, along the entire length of the overflow (Figure 15b). As the plastic strain in this part of the structure does not have significant values compared to the values in the dam body, it is likely that for the considered load case there will be no loss of global slope stability. However, there is a real possibility of a partial loss of stability of the slope under the effect  
Figure 14: Overflow section for \(\mathrm{a_{y}}=0.19\) g: (**a**) total translation \(t\) (m), (**b**) remaining load-bearing capacity \(RC\) (%). Figure 13: Overflow section for \(\mathrm{a_{x}}=0.19\) g: (**a**) total translation \(t\) (m), (**b**) remaining load-bearing capacity \(RC\) (%). of seismic loading, which would lead to the collapse of part of the slope and reduce the capacity of the spillway. In the case of seismic load in the water flow direction, the remaining load-bearing capacity is almost non-existent in the clay core, to the left and right of the dam, as well as on the slope in the rock mass upstream of the dam (Figure 15(a)). As in the previous load case, the remaining load-bearing capacity is significantly reduced on the slope just above the spillway (Figure 15(b)). Plastic strain in this area is relatively small, so there will be no loss of global stability of this part. However, there is a real possibility of local instability, which would cause a part of the slope to collapse into the spillway and reduce its functionality. Such local instability can have serious consequences, as such a scenario could lead to water overflowing over the spillway walls, which would lead to erosion of the slope below the spillway and loss of global stability of the facility and uncontrolled release of water from the reservoir. The analysis of the influence of seismic load intensity on the spillway capacity reduction was performed for different values of seismic acceleration. The results of this analysis are presented as the dependence of the spillway capacity on the magnitude of the seismic acceleration, which is shown in Figure 17 for two seismic loading directions. Figure 16: Remaining load-bearing capacity \(RC\) (%) for \(\text{a}_{y}=0.19\) g: (**a**) whole model and (**b**) slope above spillway. Figure 15: Remaining load-bearing capacity \(RC\) (%) for \(\text{a}_{x}=0.19\) g: (**a**) whole model and (**b**) slope above spillway. Based on the dependence of the spillway capacity on the value of seismic acceleration in two orthogonal directions, the effective capacity was calculated, so the capacity for the worst case was used. The dependence of the effective spillway capacity on the seismic acceleration value is shown in Figure 18.  
The dependence formed in this way can be approximated by a third-degree nonlinear equation:  
\[C=1+0.0529a+0.0843a^{2}-0.7087a^{3}, \tag{17}\]  
where \(C\) represents the spillway capacity, and the quantity \(a\) represents the normalized value of the maximum seismic acceleration (from 0 to 1). This approximation (red line in Figure 18) represents a surrogate model of the FEM model behavior, which can be used in the assessment of dynamic resilience of the analyzed multipurpose reservoir system. Using the proposed procedure, the partial stability of the object is analyzed for load intensities (in this case earthquakes) that do not endanger the global stability of the object, but can compromise its long-term stability.