According to Urban (2002), some relationships have been established based on differences in the length, width or height of the topography. Others such as Mulas de la Peña (1995) approached this from the point of view of geometry from the base of a riverbed or ravine. He concluded that the maximum amplification factors were obtained at the crests of the slopes with higher inclination. Castro (1999) correlated geometry with the damage observed from ABCDEFGplainvalleyedge of valleycrestalluvial depositrock
51the 1999 Armenia-Colombia earthquake collected as the part of the Rapid Inventory of Earthquake Damage (RIED) project (ITC, TU Delft et al. 2000). There are differences of opinion related to the maximum distances from the borders of hillsides or scarps where building damage is above average. For example, Geli et al. (in Urban 2002) consider that the effects exist up to a distance of 200 m, whereas Castro (1999) considers that the distance is 70 m. Despite the differences of opinion related to the figures, there is consensus about the correlation between damage of buildings and borders of hillsides or scarps. As Sauter (1989) pointed out, despite recognition of the effect of topography on the intensity of ground motion, no appropriate methods to quantify this have been developed and therefore building codes currently lack this consideration. 3.2.7 Building Response The response of a building to ground motion is as complex as the ground motion itself, yet typically quite different. Buildings also begin to vibrate in a complex manner and, because this is a vibratory system, it also possesses a frequency content. The building's vibrations, however, tend to centre around one particular frequency, which is known as its natural or fundamental frequency. In general, the lower a building is, the higher its natural frequency; the taller the building is, the lower its natural frequency. An important quality of a building’s response is the building's natural period. The building period is simply the inverse of the frequency: whereas the frequency is the number of times per second that the building will vibrate back and forth, the period is the time it takes for the building to make one complete vibration. This means that a very tall building with a low natural frequency has a high natural period. For example, it takes a skyscraper a comparatively long time to sway back and forth during strong wind (see Figure 3.10). Table 3.3 below provides a representative range of building heights and natural periods: Height (in storeys) Typical Natural Period (s)Typical Frequency in cycles/second (Hz) 2 0.2 5.0 5 0.5 2.0 10 1.0 1.0 20 2.0 0.5 30 3.0 0.3 Table 3.3: Natural Periods and Frequencies per Building Height
52When the frequency content of the ground motion is centred on the building's natural frequency, resonance occurs which tends to increase or amplify the building's response.