Seismic Ground Motion - Dynamic Behavior of Concrete and Seismic Engineering - page 114

3.4.3.1. Effects of topographic relief
After destructive earthquakes, the damage reported is significantly worse at the
hilltop than the base. The most outstanding French examples took place in Rognes
and Vernegues (1909 earthquake) and in Castillon (1887 earthquake). This
“qualitative” observation has been confirmed by numerous instrument
measurements, which revealed amplitude relationships between the summit of a
relief and its foot which sometimes reach a 3 to 4 factor difference in their time
maximum (PGA, PGV) and a factor higher than 10 in the spectral field (Figure 3.4).
The number of experimental studies on the subject is extremely low compared with
the studies dealing with the underground amplification, so it is not yet possible to
derive statistically significant empirical laws. Theoretical and numerical models also
predict a seismic motion systematic amplification perpendicular to the convex parts
of a topographical relief (cliff edge, hilltop), in addition to sensitivity to the field
characteristics of the incident wave (wave types, azimuth, incidence). The sensitivity
of seismic motions to the topographic relief seems to be linked to three physical
phenomena:
- sensitivity of surface motion to the incidence angle, especially around the limit
angle for SV waves;
- focusing of seismic waves in a convex relief (summit) and defocusing in a
concave relief (foot);
- volume and surface wave diffraction over all the surface irregularities, which
generates interferences (constructive and/or destructive depending on the position
and the frequency).
The known facts on this topic can be summarized as follows:
- as far as quality is concerned, agreement between theory and observations is
quite satisfactory;
- a convex relief generates amplification whereas a concave relief brings about
de-amplification;
- the amplification is generally higher for horizontal component forces than for
vertical component force. In the case of 2D reliefs (ridges), the horizontal
component perpendicular to the crest's axis is often more amplified, and the
transverse stiffness is weaker than the longitudinal stiffness;
- amplification level is linked to the topographic slenderness (height/width): the
stiffer the average slope, the higher the summit amplification;
- summit amplification (as well as base de-amplification) shows a strong
frequency dependency. The maximum effects correspond to wavelengths similar to
the relief's horizontal dimensions, favoring an interpretation of the topographic