Introduction: Earthquake Ground Motion

Figure 1 : Ground Motion

Introduction: Earthquake Ground Motion

The dynamic response of the building to earthquake ground motion is the most important cause of earthquake-induced damage to buildings. Failure of the ground and soil beneath buildings is also a major cause of damage. However, contrary to popular belief, buildings are rarely, if ever, damaged because of fault displacement beneath a building.

To briefly review the basic of earthquake generation: Most earthquakes result from rapid movement along the plane of faults within the earth's crust. (See Figure 1.) This sudden movement of the fault releases a great deal of energy. which then travels through the earth in the form of seismic waves. The seismic waves travel for great distances before finally losing most of their energy. Figure 2 illustrates some of the basic features common not only to seismic waves but to all forms of wave motion.

At some time after their generation, these seismic waves will reach the earth's surface, and set it in motion, which we not surprisingly refer to as earthquake ground motion. When this earthquake ground motion occurs beneath a building and when it is strong enough, it sets the building in motion, starting with the building's foundation, and transfers the motion throughout the rest of the building in a very complex way. These motions in turn induce forces which can produce damage.

Complexity of Earthquake Ground Motion

Real earthquake ground motion at a particular building site is vastly more complicated than the simple wave form illustrated in Figure 2. Here it's useful to compare the surface of the ground under an earthquake to the surface of a small body of water, like a pond. You can set the surface of a pond in motion--by throwing stones into it, let's say. The first few stones create a series of circular waves, which soon begin to collide with one another. After a while, the collisions, which we term interference patterns begin to predominate over the pattern of circular waves Soon, the entire surface of the water is covered by a ripples; and you can no longer make out the original wave forms. During an earthquake, the ground vibrates in a similarly complex manner, as waves of different frequencies and amplitude interact with one another.

The complexity of earthquake ground motion is due to three factors: 1) The seismic waves generated at the time of earthquake fault movement were not all of a uniform character; 2) As these waves pass through the earth on their way from the fault to the building site, they are modified by the soil and rock media through which they pass; 3) Once the seismic waves reach the building site they undergo further modification which are dependent upon the characteristics of the ground and soil beneath the building. We refer to these three factors as

• source effects

• path effects

• local site effects

Ground Motion And Building Frequencies

The characteristics of earthquake ground motions which have the greatest importance for buildings are the duration, amplitude (of displacement, velocity and acceleration) and frequency of the ground motion. Frequency is defined as the number of complete cycles of vibration made by the wave per second. Here, we can consider a complete vibration to be the same as the distance between one crest of the wave and the next, in other words one full wavelength. (See Figure 2 above.) Frequency is often measured in units called Hertz. Thus, if two full waves pass in one second, the frequency is 2 hertz (abbreviated as 2 Hz).

Surface ground motion at the building site, then, is actually a complex superposition of vibrations of different frequencies. We should also mention that at any given site, some frequencies usually predominate. The distribution of frequencies in a ground motion is referred to as its frequency content.

The response of the building to ground motion is as complex as the ground motion itself, yet typically quite different. It also begins to vibrate in a complex manner, and because it is now a vibratory system, it also possesses a frequency content. However, the building's vibrations tend to center around one particular frequency, which is known as its natural or fundamental frequency. In general, the shorter a building is, the higher its natural frequency. The taller the building is, the lower its natural frequency.

Building Frequency and Period

Another way to understand this is to think of the building's response in terms of another important quantity, 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 time it takes for the building to make one complete vibration. The relationship between frequency f and period T is thus very simple math:

T = 1 / f

This means that a short building with a high natural frequency also has short natural period. Conversely, a very tall building with a low frequency has a long period. For example, it takes the Empire State Building a comparatively long time to sway back and forth during a strong gust of wind. (See Figure 3.) The table below gives a representative range of building heights and natural periods:

Resonant Frequencies

When the frequency contents of the ground motion are center around the building's natural frequency, we say that the building and the ground motion are in resonance with one another. Resonance tend to increase or amplify the building's response. Because of this, buildings suffer the greatest damage from ground motion at a frequency close or equal to their own natural frequency.

The Mexico City earthquake of September 19, 1985 provides a striking illustration of this. A majority of the many buildings which collapsed during this earthquake were around 20 stories tall--i.e., they had a natural frequency of around 2.0 Hz. These 20 story buildings were in resonance with the frequency contents of 1985 earthquake. Other buildings, of different heights and with different vibrational characteristics, were often found undamaged even though they were located right next to the damaged 20 story buildings.

Response Spectra

As we've just seen, different buildings can respond in widely differing manners to the same earthquake ground motion. Conversely, any given building will act differently during different earthquakes, which gives rise to the need of concisely representing the building's range of responses to ground motion of different frequency contents. Such a representation is known as a response spectrum. A response spectrum is a kind of graph which plots the maximum response values of acceleration, velocity and displacement against period and frequency. Response spectra are very important "tools" in earthquake engineering.
      

Figure 4 shows a highly simplified version of a response spectrum. Even though highly simplified, it does show how building response characteristics vary with building frequency and period: as building period lengthens, accelerations decrease and displacement increases. On the other hand, buildings with shorter periods (but higher natural frequencies), undergo higher accelerations but smaller displacements.

As the next page will describe in more detail, the amount of acceleration which a building undergoes during an earthquake is a critical factor in determining how much damage it will suffer. The spectra in figure 4 provides some indication of how accelerations are related to frequency 

characteristics--which shows one way in which response spectra can be useful, since identifying the resonant frequencies at which a building will undergo peak accelerations is one very important step in designing the building to resist earthquakes.

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