Quakes and a building's response

The following commentary by Dr Geoff Thomas from Victoria University's School of Architecture was originally published in the Dominion Post on 29 November.

A building's response to an earthquake is a function of the size of an earthquake, how far away it is, the frequencies at which shaking occurs at a building site, the height and mass of the building, and the type of structural systems and material of the buildings structure.  

The vibration emitted by an earthquake is over a range of frequencies and higher frequencies are absorbed more rapidly over distance than lower frequencies. The frequency of shaking at a site is critical to how a building responds, as, like a guitar string, a building has a natural frequency, and if the shaking is applied to it at the natural frequency the level of vibration in the building will increase.

Levels of shaking are measured using a strong motion accelerograph, a device that measures shaking that would send a seismograph off scale. The acceleration is reported as a decimal fraction of the acceleration due to gravity. So an acceleration of 0.5G on a 10 kilogram object would impose a force equivalent to 5 kilograms.  

The strongest motion recorded in the Kaikoura earthquake was 1.3G, recorded in Ward. In Wellington, the shaking reached a peak of about 0.8G on the waterfront, but only about 0.3G on the landward side of Thorndon, showing how much variation there can be over a very short distance. The level of shaking of 0.8G is close to what some buildings are designed for.

Not only did the peak acceleration differ between these two sites, but so did the frequency at which these peaks occurred. On the harbour front the maximum was about 0.7 Hertz (one cycle per second), but at the other site it was at about 1.7 Hertz.  

The response of buildings to shaking is normally described in terms of a period of vibration. The period is the inverse of the frequency, so a frequency of 0.7 Hertz corresponds to a period of about 1.4 seconds, and a frequency of 1.7 seconds corresponds to a period of about 0.6 seconds.  

Buildings are designed for the forces they would undergo during earthquake shaking at their natural period which corresponds to the natural frequency. The natural period of a building is roughly proportional to the number of storeys divided by 10. Hence a 10-storey building would have a natural period of about 1 second.

The fact that the strongest shaking was at a period of over one second on soft-soil sites explains why buildings on these sites that were about 10 storeys or more in Wellington were most susceptible to damage in this earthquake.  

As buildings are of many types and shapes, with different structural systems and materials, the period will differ between buildings. If the mass of a building is higher it will have a longer period, and if the building is more flexible it will have also have a longer period.

A longer period is more desirable, because over the range of earthquakes a building may be subjected to in its life, a longer period is associated with a lower level of acceleration. Low rise unreinforced masonry buildings and lightly reinforced concrete buildings, which are typically most of the earthquake-prone buildings, are very stiff and are therefore subjected to higher accelerations. As the forces on a building are directly proportional to mass, and these types of buildings are relatively heavy, they are subjected to relatively high earthquake loads that they were never designed to resist.  

Another complication that affects some types of buildings more than others, including unreinforced masonry buildings, is the duration of shaking. For every load cycle the strength of a building will deteriorate to a lesser or greater extent, so longer-duration earthquakes are more damaging.    

Modern buildings—that is those designed in New Zealand after 1976—are designed for two criteria.

One is the "strength" earthquake for which the building is expected to remain standing, but damage is acceptable and the building may not necessarily be able to be re-used.

The second criteria is the "serviceability" criteria, the level at which non-structural elements such as ceilings, partitions and glazing are expected to remain intact, and no damage to structural elements such as cracking should occur. The serviceability limit was reached for many buildings in Wellington during the Kaikoura earthquake. This means that damage to plasterboard walls in steel or concrete-frame buildings is to be expected, as is broken glazing. It also means that cracking may occur in beams (horizontal rectangular shaped elements) in reinforced concrete buildings.  

A crack in concrete means that the tension (stretching) strength of the concrete has been exceeded over part of the length of the beam, but it is the reinforcing steel that takes the tension load, and failure of the reinforcing steel occurs at a much greater level of stretching than when cracking starts to occur. Hairline cracks in beams should be checked out by a professional engineer as they may be a sign of something untoward, but they are highly unlikely to signify that a building is on the verge of collapse.    

Every earthquake is different, every building and site is different, so conclusions about how buildings might behave in another earthquake cannot be simply drawn from the experience of one earthquake. The high level of earthquake performance of New Zealand buildings is evidenced by the fact that many buildings in the 2011 Christchurch earthquake stood up to levels of shaking significantly greater than those they were designed for.