| Abstract: | Explicit time integration schemes provide an efficient solution to non-linear dynamic finite element analyses of geotechnical problems especially when high frequency response is important. Such explicit time integration schemes require one of two distinct transmitting boundary formulations to overcome the problem of radiation damping. These are the superposition boundary approach, which involves the cancellation of the reflected waves by combining the solutions of two different boundary conditions and the viscous boundary approach, which involves the absorption of incident wave energy by frequency independent viscous dashpots. The theoretical justification of these two approaches and their means of implementation are reviewed. The solutions obtained using the two different boundary approaches to the problem of a rigid massless circular footing vibrating on an elastic half-space are compared with an independent theoretical solution. The performance of the boundaries for problems involving step loading is also examined and the implications for any loading pattern with a non-zero time average are discussed. |
