Within the activities related to the development of the finite element model of the “Zavoj” dam for the seepage analysis and stability analysis, the first step was to develop the three-dimensional (3D) geometry of the dam with the surrounding rock-mass was formed. For 3D geometry development, the available two-dimensional (2D) documentation was used, while the Google Earth tool was used for surrounding rock-mass contours. The model has dimensions of 850x612x410 m and covers a wider area around the dam, in order to eliminate the influence of boundary conditions (Figure 1).
Figure 1 3D geometry of the “Zavoj” dam
Using 3D geometry, finite element (FE) model of the dam and surrounding rock-mass was developed (Figure 2).
Figure 2 FE model of „Zavoj“ dam
The model contains next elements: dam body (clay core, upstream and downstream multilayer filters, upstream and downstream slopes), grout curtain (Figure 3), overflow with three overflow fields and the surrounding rock-mass which is approximated by one quasi-homogeneous zone.
Figure 3 Dam body and grout curtain
The FE model was formed using tetrahedral finite elements with midside nodes (Figure 4). Model meets the set quality criteria in terms of Jacobians. All elements have a Jacobian value lower than 0.7, which eliminates the influence of numerical problems in stability analysis. The number of finite elements is optimized so the zones of interest, namely the dam with associated elements, are modeled by higher density mesh, while for the rock mass finite elements of larger dimensions were used. In this way, an optimal model was formed, consisting of 98 thousand elements and 140 thousand nodes.
Figure 4 Tetrahedral finite element
In order to analyze the influence of the flow change through the grout curtain on global stability of the structure, by changing the value of the filtration coefficient, the zoning of the grout curtain was performed (Figure 3b). The grout curtain is divided into 6 zones, in order to change the filtration coefficients in each zone independently.
To the seepage model boundary conditions by potentials was applied, where the potential is applied to all potentially wetted surfaces (Figure 5).
Figure 5 Applied hydraulic potential
To the stability model boundary conditions by displacements was applied, where the so-called natural boundary conditions are simulated, ie. displacement the lower base of the model is restricted, while nodes in the lateral sides of the model can translate in the plane. Hydrostatic pressure on all potentially wetted surfaces was applied (Figure 6).
Figure 6 Hydrostatic load
The hydrodynamic pressure on the upstream face of the dam was also applied, in order to simulate seismic influence. Contours for flow calculating are defined on the downstream face of the grout curtain (Figure 7).
Figure 7 Contours for flow calculation
The values of these flows are printed in a txt file. The loads of the stability model were applied in several phases: the 1st phase represents the initial stress state generating; the 2nd phase represents the birth of the dam elements. After this phase, all displacement is reset to zero. In phases 3 and 4, the load from the accumulation is applied.
For the purpose of testing the functionality of FE models and wrappers, preliminary material parameters were adopted. Some results of preliminary analysis of seepage and stability are presented below (Figure 8-Figure 9).
Figure 9 Total translation
In the fourth quarter of the project realization, a layer for managing numerical calculations (numerical wrappers) was formed and tested, for analysis of filtration and stress-strain processes (Figure 10).
Figure 10 Numerical wrapper for seepage and stress-strain analysis
Numerical wrappers are intended for managing numerical calculations, by enabling unbundled management of material parameters of the model (clay core, upstream and downstream multilayer filters, upstream and downstream slopes, grout curtain, overflow and the surrounding rock-mass). These wrappers also allow unbundled management of boundary conditions for the analysis of filtration and the analysis of stress-strain processes (Figure 11) from the rest of the data necessary for finite element analysis (data on nodes, elements, global constraints, numerical solvers, data for pre and post processing of results and more).
Figure 11 Material parameters and boundary conditions for stress-strain analysis
As rewarded previously, during the development of the “Zavoj” dam finite element model, the grout curtain was divided into six independent zones. This division was carried out in order to analyze the influence of the filtration coefficient change on the flows through the grout curtain, as well as on the change of the global safety factor of the structure. In this way, it is possible to simulate the penetration of the water from the reservoir through certain parts of the grout curtain, which can be the cause of an external disturbance such as an earthquake or poor quality of the injection curtain.
Figure 12 Flow through the contours of the grout curtain
In the first year of project implementation, a numerical analysis of the impact of functional failure of individual curtain zones on the flow was performed. This is also made possible by the application of a numeric wrapper that prints flows through defined contours into a separate text file (Figure 12).
This simulation obtained the dependence of the flow under the dam on the damage zone as well as function of the reservoir water level (Figure 13).
Figure 13 Influence of the grout curtain failure on flow change as a function of reservoir water level (KGV)
In the following period, an analysis of the impact of curtain failure (increased leakage) on the global dam safety factor is planned. Also, an analysis of the impact of seismic load on the functionality of the dam overflow will be conducted.