Nonlinear seismic response of arch and gravity dams including reservoir and foundation

Summary

The purpose of the project is to develop mathematical models for a realistic prediction of the seismic response of arch and gravity dams. Important aspects are the nonlinear behaviour of dams and the interaction of dams with their reservoir and their foundation. A key aspect of the project is the development of algorithms for the interaction problems in the time domain. These algorithms allow including nonlinear dam behaviour and interaction problems simultaneously in an analysis.

For arch dams, a model for the nonlinear behaviour of contraction joint with contact, friction, interlock, and tensile strength has been developed. This very sophisticated model will eventually be replaced by simpler one with an augmented Lagrangian method for contact and a radial return algorithm for friction. Transmitting boundaries are used based on a semi-analytical solution of an infinite channel. The semi-analytical solution is derived in the frequency domain and then approximated by a linear time-invariant system. The matrices of the linear system can be directly coupled to the finite element matrices. The combined global equations of motion can then be solved by standard time-stepping algorithms. A method for calculating the nonuniform earthquake input in a valley has also been developed.

For gravity dams, the formation of cracks in the dam body is modelled using a discrete crack model. This includes the strain softening of the concrete as well as the aggregate interlock between the rough crack sur-faces. Novel absorbing boundary conditions are used to consider the effects of radiation damping in the interaction model. These are very accurate because they are constructed from the dynamic stiffness matrix of the farfield. Their formulation as a system of linear differential equations simplifies considerably the coupling with the equations of motions derived from the finite element model of the near field. This allows an efficient numerical analysis of the overall system (near and far field).

The finite element program originally designed for arch dams has been further developed for both arch dams and gravity dams under the name CODA (formerly DANAID STRATUM). The program is written in the modern programming language C++ as an object-oriented program. Special attention was given to a flexible and well-structured implementation in the form of a class library. The rigorous separation of data and interfaces is an essential part of the general and flexible program structure. To simplify the software management, the classes are grouped into packages with minimal dependencies. The program handles linear and nonlinear, static and dynamic analyses as well as steady-state and eigenvalue computations. It includes the transmitting boundaries developed for arch and gravity dams. The implementation of nonlinear joints is also planned, using a model with an augmented Lagrangian method for contact and a radial return algorithm for friction. The implementation is still under development.

Staff

Dr. Benedikt Weber