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

December 10, 2020

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 ubroutines 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.