Page 297 - Numerical Analysis and Modelling in Geomechanics

278 THE 2-D CHEBYSHEV SPECTRAL ELEMENT METHOD

Figure 9.10 Resonant scattering of the Rayleigh wavefield. The letters indicate the
incoming Rayleigh wave (R), and the scattered pressure (P), shear (S), and Rayleigh
waves (R'), respectively. The picture also shows part of the computational mesh near the
massive structure (from Chiaruttini et al. (1996)).
tackling real cases has been demonstrated by two case histories, i.e. the
estimation of ground shaking in the area of Catania (Sicily, Italy), and the study
of the influence of a massive structure on the nearby ground motion. In the
present implementation, the approach has some drawbacks (Priolo, 2001), such as
the difficulty of generating the quadrangular mesh, the sporadic occurrence of
numerical instabilities resulting in large problems, as well as the heavy
computational needs related to the use of global matrices. However, recent work
carried out by several authors clearly shows the still large possibilities of
improvement.

Acknowledgements
This work has been partially funded by the National Group for the Defence
Against Earthquakes (GNDT). Figure 9.2 was made by GMT software (Wessel
and Smith, 1995). I wish to thank Giovanna Laurenzano for her recent
contribution to the improvement of the method.
Figure 9.3 is reprinted Journal of Seismology, Vol 3, 2001, pp. 289–309,
Priolo, E., ‘2-D spectral element simulations of destructive ground shaking in
Catania (Italy)’, Figure 2, with kind permission of Kluwer Academic Publishers.
Figures 9.9, 9.10, 9.11 and 9.12 are reprinted from Soil Dynamics and
Earthquake Engineering, Vol 15, Chiaruttini, C., Grimaz, S., and Priolo E.,
‘Modelling of ground motion in the vicinity of massive structures’, Figures 3, 5,
9 and 14, pp. 75–82, 1996, with permission of Elsevier Science.