Seismic Analysis and Design of Concrete Dams

By Kianoosh Hatami, PhD, PEng

There is a growing worldwide interest in building new dams due to increasing demands on water supply, irrigation and clean hydropower energy. The safety of dams and their potential risks to their downstream region, particularly in seismically active areas, are serious concerns for governments, private owners of dams and affected communities. The hydrodynamic load of the reservoir subjected to ground motion can increase to the magnitudes that are comparable to hydrostatic load behind the dam and therefore, jeopardize the structural safety of the dam. A thorough understanding of the effects of reservoir boundary conditions on the magnitude of reservoir hydrodynamic load is essential for a safe and economical design of concrete dams in geographical areas with high seismic risk. The author's research work has addressed the quantitative evaluation of the effects of reservoir size and boundary conditions (including the effects of sediments) on hydrodynamic pressure in the reservoir and seismic response of concrete dams (Figure 1).

Highlights of the author's research on seismic analysis of concrete dams are listed in the following:

Figure 1: Two-dimensional analytical model of a dam-reservoir-foundation system with general reservoir boundary conditions

1) A finite element program has been developed to calculate the hydrodynamic pressure in the reservoir and dynamic response of concrete gravity dams to ground motion. The program has been verified against the results of analytical solutions for hydrodynamic pressure due to harmonic ground motion (Figures 2 and 3).

Figure 2: Frequency response of hydrodynamic force on the dam subjected to horizontal ground motion for different reflection coefficients, ab, of the reservoir bottom. (a) FEM (b) analytical solutions after Fenves and Chopra (1984)
Figure 3: Frequency response of hydrodynamic force on the dam subjected to vertical ground motion for different reflection coefficients, ab, of the reservoir bottom. (a) FEM (b) analytical solutions after Fenves and Chopra (1984)

Actual measurement of hydrodynamic pressure wave amplitudes in reservoirs of selected dams using different vibration techniques will provide a valuable database of recorded response that can be used to refine the assumptions of analytical approaches and, to calibrate the results of numerical simulation studies. The calibrated models can then be used to propose simplified methodologies for evaluating the hydrodynamic load of the reservoir for given reservoir shape, size and boundary conditions.

2) The possibility of seismic response reduction of dams with hydrodynamic isolation is investigated. The concept of hydrodynamic isolation addresses the engineering modification of the dam-reservoir interface boundary condition in order to reduce the transferred hydrodynamic load to the upstream face of the dam structure. Results of the author's analytical and numerical simulation studies indicate that the seismic response of a dam with hydrodynamic isolation can be notably lower (e.g., as high as 35%) than the response of an otherwise identical, unprotected dam (Figure 4).

Figure 4: Contours of maximum tensile stress across the monolith cross section with full reservoir subjected to 1940 Taft ground motion. Notes: Height of dam=91.5 m (300 ft); stress values in kPa. (a) unprotected dam; (b), (c) dam with hydrodynamic isolation: (b) dam face reflection coefficient = 2/3 (c) dam face reflection coefficient = 1/3

Further studies on the subject including reduced-scale experimental modeling as well as instrumentation of selected dams that are in service can provide a valuable approach for enhancing seismic safety of dams in a practical and economical manner.

3) A structural response index is introduced that correlates well with ground motion intensity measures and can be conveniently used to evaluate the stress level in a gravity dam monolith under different loading conditions. In addition, it can be used as an auxiliary design index for selecting the dam cross section geometry. The applicability of the proposed index can be expanded to include different types of dams and structural nonlinearity. Some modifications in the definition of the index may be required to account for nonlinear material behavior including crack initiation and propagation in the dam.


  1. Fenves GL and Chopra AK, 1984. Earthquake Analysis and Response of Concrete Gravity Dams. Report No. UCB/EERC-84/10, University of California, Berkeley, CA, USA.
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