Rational transmitting boundaries for time domain analysis of dam reservoir interaction

Most existing arch dams have been designed for seismic loading using static methods with seismic coefficients. While no arch dams have been significantly damaged by earthquakes, the need for more realistic seismic analyses is increasingly recognized, particularly for evaluating the safety of existing structures. The finite element method offers engineers a robust tool for modeling the complex geometry and nonlinear material behavior of dams. However, a significant challenge remains: the interaction of the dam with the reservoir and foundation during seismic events. This interaction involves wave propagation, typically simplified in current engineering practice by treating water as incompressible and the foundation as massless. Although more advanced methods that consider compressible water and mass foundations have existed, they are limited to linear models operating in the frequency domain. Conversely, advanced nonlinear models for dams can only be applied in the time domain, often using simple transmitting boundaries. This report, derived from a doctoral thesis, introduces rigorous transmitting boundaries in the time domain, allowing for the integration of compressible water with nonlinear dam behavior. The new numerical model is grounded in a systems-theory approach, enhancing the accuracy of seismic analysis for arch dams.