Extending the BKT Memory-Efficient Displacement-Based Internal Friction Model for Representing Attenuation in Wave Propagation Simulations

Md Monsurul Huda, & Ricardo Taborda

Published 2015, SCEC Contribution #6223

Energy losses in the form of anelastic attenuation due to material internal friction plays a major role in wave propagation problems and earthquake ground motion simulation. These attenuation effects are typically represented through the characterization of the quality factor, Q. There have been several studies in which Q is modeled using viscoelastic devices, where the effects of internal friction are represented by springs and dashpots. A recently introduced model, called the BKT model (after authors Bielak, Karaoglu and Taborda), proposed the use of two Maxwell elements (each made of a spring and a dashpot connected in series) in combination with a Voigt element (consisting of a spring and a dashpot connected in parallel). The BKT model showed very good adherence to intended values of constant Q = Qo. The BKT model, however, depended on a set of parameters that needed to be computed a priori for a fixed set of Qo values. The model, as well, was limited to problems under the assumption of frequency independent attenuation. In this work we show that the internal parameters used in the BKT model can be determined using exact expressions formulated based on a numerical optimization of the model’s fit with Qo. This formulation holds for any value of Qo > 5, with errors less than 5 percent. In addition, we show that using three Maxwell elements substantially improves the accuracy of the model and increases its flexibility, allowing one to model problems with frequency-dependent Q = Q(f). This latter extension of the BKT model is of critical significance for deterministic physics-based earthquake simulations done at frequencies of engineering interest (f > 1 Hz).

Key Words
ground motion simulation, attenuation, wave propagation

Citation
Huda, M., & Taborda, R. (2015). Extending the BKT Memory-Efficient Displacement-Based Internal Friction Model for Representing Attenuation in Wave Propagation Simulations. Poster Presentation at 2015 SCEC Annual Meeting.