Within the activities of the finite element model of the embankment dam “Zavoj” development for the seepage and stability analysis, a 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.
Using 3D geometry, finite element (FE) model of the dam and surrounding rock-mass was developed (Figure 1). The model contains next elements: clay core, upstream and downstream multilayer filters, upstream and downstream slopes (Figure 2), grout curtain (Figure 3), overflow with three overflow fields and the surrounding rock-mass which is approximated by one quasi-homogeneous zone.
The FE model was formed using tetrahedral finite elements with midside nodes. 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 about 98 thousand elements and about 140 thousand nodes.
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 3). 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 4). 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 5). 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 6). 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 simpler management of calculation process, boundary conditions and material parameters, the so-called numerical wrappers were created. 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 7-Figure 10).
Figure 1 FE model of „Zavoj“ dam
Figure 2 Dam body
Figure 3 Grout curtain
Figure 4 Applied hydraulic potential
Figure 5 Hydrostatic load
Figure 6 Contours for flow calculation
Figure 7 Depth of water
Figure 8 Hydraulic gradient
Figure 9 Total translation
Figure 10 Plastic strain