The possibility of using, in seismic safety checks required by regulations, advanced numerical analysis methods, which realistically reproduce the structural response of concrete dams subject to earthquakes, is conditioned by the need to appropriately validate these methods. Furthermore, dam engineering needs to adopt advanced models of dynamic structure-foundation interaction, since traditional approaches, although reliable and consolidated, may significantly overestimate the seismic response.

The seismic wave propagation model we adopted delimits the foundation with artificial contours which reproduce, in the calculation domain, the behavior of an unlimited foundation: these contours allow both the entry of seismic waves (through the application of equivalent forces such that the numerical simulation provides the correct response in free field conditions, i.e. in the absence of the dam and the reservoir) and the exit of scattering waves caused by the dam-reservoir system.

The model, already tested in a two-dimensional context last year, was developed for three-dimensional cases. The equivalent seismic forces were calculated according to the procedure found in literature and based on a theoretical solution of the problem of vertical wave propagation in an elastic half-space.

Efficient use of the model in the numerical analysis of real problems required the implementation of pre-processing tools to calculate and apply forces to the contours of the three-dimensional domain and the experimentation of different types of continuous elements to simulate the absorbing contours made up of springs and/or dampers.

The effectiveness of the model and the adequacy of the pre-processing tools and artificial contours were verified by means of case studies on a three-dimensional numerical model representative of an elastic half-space: the results exactly matched the theoretical solution.

To ensure that the developed model also adequately represents foundations with canyons, case studies proposed in the literature for which an analytical or numerical solution is available were reproduced: the results were in line with the reference solutions.

Finally, the possibility of using explicit solution methods was considered, examining their advantages and disadvantages compared to implicit ones.