Validating Nonlinear Seismic Analysis of Dam-Foundation-Reservoir System with Foundation Cyclic Symmetry

Evaluating the seismic performance of a concrete (or rockfill) dam requires a set of
nonlinear time-history simulations on a representative model that includes the dam and an
extension of the rock foundation underneath (with mass). The reservoir is either modeled
as a body of water or represented with equivalent hydrodynamic masses on the upstream
face of the dam (Westergaard, 1933).

Two of the major challenges in modeling procedure are:

(1) accounting for the seismic input, which is the free-field earthquake motion; and

(2) elimination of the reflected seismic waves from the dam into the foundation, i.e.
radiation damping.

One analysis procedure uses the effective seismic input method (ESIM) to apply the freefield
earthquake records, as well as using the perfectly matched layers (PML) to eliminate
the reflected waves. While the combination of these two methods have proven to be very
effective in the proper simulation of earthquake response (LSTC, 2019), they are not
readily implemented in most of the available commercial codes.

A second analysis procedure applies the standard viscous damper absorbing boundaries at
the cut boundaries of the foundation. The earthquake excitation is applied at the bottom
and side cut boundaries as traction stresses, which are functions of both elevation and
time, and could be computed based on the free-field earthquake motions (Nielsen, 2006).
While this method could be used with some commercial codes, the proper application of
the solution would require either extra analyses and extensive book-keeping and data
transfer, or proper subroutines for those purposes.

A third, simpler analysis procedure, which implements proper boundary conditions, is
further reviewed in this study. In this method, the nodes on the opposing vertical cut
boundaries of the foundation are tied together to form cyclic symmetry boundary
conditions (Zienkiewicz, 1989). The viscous damper boundary condition and the traction
forces, on the other hand, are applied only to the base cut boundary of the foundation,
and, hence, the tractions will not be depth-dependent.

These three solutions have been used in the industry for dam studies. The first procedure
is gaining wide popularity within the dam engineering community, especially using the
commercial software LS-Dyna (LSTC, 2019). Additionally, the author has evaluated the
seismic performance of the culvert gates (Rasekh, 2012) using the commercial software
Abaqus (Dassault Systèmes, 2011), where the second procedure was implemented using
user-defined elements. He also has used the second procedure in an evaluation of the
seismic performance of a major tailings dam (Oviedo, 2016) using the commercial
program FLAC (Itasca, 2011). The author has also evaluated the seismic performance of
an old concrete arch dam using the third procedure (Rasekh, 2019).

Although the third procedure has been used in the dam industry, it is least known in the
dam engineering community, and, hence, this study would compare dam response using
the third procedure with the ESIM + PML solution.

Rasekh, A. 2020. “Validating Nonlinear Seismic Analysis of Dam-Foundation-Reservoir System with Foundation Cyclic Symmetry,” in Proceedings of the United States Society of Dams Annual Conference, 20-24 May. Denver, CO: USSD, 2020