### Tech Briefs

Dam Safety in an Earthquake

An earthquake can cause a dam to crack or dislocate, or even cause its component blocks to detach. The damage can result in uncontrolled water release or a catastrophic flood. Numerical methods such as finite element analysis play an important role in assessing the possible seismic damage to dams. In this Brief, we show how ADINA is used by a team of engineers in Switzerland for this challenging task.

The dam considered is the Gigerwald dam in the Canton of St. Gallen, Switzerland, see Figure 1. It is an arch dam comprising 24 vertical monoliths (blocks) made of concrete. Since concrete has low tensile strength, the dam is designed such that the water pressure and self-weight cause compression, also between the monoliths, thereby preventing them from separating.

Swiss regulations require that the dam must not allow uncontrolled release of water for an earthquake of 8.0 MSK intensity at its location, with a return period of 10,000 years.

 Dam type: double-curvature arch dam Number of blocks: 24 Max height: 147m Crest length: 430m Dam thickness: 7.0m (crest) to 22m (base) Figure 1  The Gigerwald dam

The ADINA model of the dam is shown in Figure 2. Seismic shaking is applied in the ADINA model as acceleration loading. The seismic load is combined with the dam’s self-weight and the reservoir water pressure on the upstream side of the dam.

Figure 2  Finite element model of the dam. (Left) The dam and the rock base.
(Right) Detail of a central monolith, no. 11, of the dam

The engineers first conducted a linear dynamic analysis to determine if the blocks separate during an earthquake of the prescribed magnitude. In this analysis, the dam was modeled as a single piece consisting of monoliths that are glued together. The results show that the maximum tensile stress indeed exceeds the separation limit, and therefore the monoliths are very likely to separate (see Figure 3).

Figure 3  Principal tensile stresses obtained from linear dynamic analysis

To determine whether this separation poses a safety threat, a nonlinear dynamic analysis was conducted. For this analysis, contact is defined between the monoliths. The results show that the maximum separation and sliding displacements occur at the crest level of the dam. The separations are in the order of several millimeters (see Figure 4 and Figure 5).

Figure 4  Block separation under earthquake shaking. Note that the deformation is magnified by 1000 times

Figure 5  Maximum opening and sliding displacements between monoliths at crest level

When the blocks are separated from each other at the crest level, it is possible that the upper portion of a monolith will be fully detached from its base due to fracture. The engineers evaluated this possibility using a 3D model with several pre-existing horizontal cracks. The results showed that the final crack opening and the movement of the detached portion are well within the safety margins. For example, when the assumed crack is 27 meters below the crest level (the highest vertical tensile stress occurs at this point), the crack opening is 6 millimeters.

Figure 6  Deformation of the dam with a detached upper portion in central monolith

From the results of these extensive analyses, the engineers concluded that the dam is safe during an earthquake, based on the Swiss regulations.

This application demonstrates just a few of the powerful features of ADINA that make it an ideal tool for solving structural problems. In particular, it is seen that a complex nonlinear analysis including contact using the same finite element discretization, if necessary, can be directly carried out after a linear analysis.

Reference

• S. Malla, "Comparison between 2D and 3D analyses of seismic stability of detached blocks in an arch dam", Proceedings of the Second European Conference on Earthquake Engineering and Seismology, Istanbul, Aug. 25-29, 2014.

Keywords:
Linear dynamic analysis, nonlinear dynamic analysis, stability, dam, earthquake, concrete, crack, fracture

Courtesy of Dr. S. Malla, Axpo Power AG, Switzerland