The destructive potential of earthquakes is infamous. The root cause of earthquakes is the build-up of stress within rocks due to forces pushing different parts of the earth to try and move relative to each other. The resulting deformation in the rocks under this stress stores a huge amount of elastic energy. At some point the stress exceeds the strength of the rock, which then breaks along a fault. The breaking of the rock along the fault releases a good part of the stored elastic energy within the rock, which then emanates outwards from the fault as vibrating seismic waves. The length of the fault plane can range from a few metres for a small earthquake to over a hundred kilometres for a huge earthquake.

Apart from the destruction in the narrow area of the fault zone where the rock movement occurs, the sudden release of energy from fault rupture can cause certain types of soil to lose their physical strength and act more as liquids than solids. Such “liquefaction” can cause a phenomenon known as “flow failure” where liquefied soil (or still solid soil riding on a layer of liquefied soil), at high-speed, flows large distances – sometimes dozens of kilometres. Soil movement or liquefaction of the soil under a building can cause the building to tip or collapse.

However, the greatest damage from earthquakes is caused by the vibration waves radiating out from the earthquake fault zone. These seismic waves travel at speeds many times the speed of sound, meaning that earthquakes will damage buildings and equipment long before people hear the sounds of falling structures from areas that the waves have already passed through. Earthquake-induced ground shaking can trigger landslides – including both soil and rock avalanches. In rarer cases, earthquakes cause catastrophic tsunamis. However, other than for those cases where earthquakes cause such large tsunamis, the greatest destruction from earthquakes is usually due to the ground vibration that it causes transmitting vibration to structures through the latter’s support points on the ground.

The Nature of Earthquake-Induced Ground Vibration

Although the rupture along a fault typically occurs within a fraction of a second, the period of most intense ground vibration of an impacted area from an earthquake can last up to 30 seconds, although it more typically lasts from between 4 to 15 seconds. The relatively long duration of intense ground shaking compared to the duration of rock failure occurs for two reasons. Firstly, the different types of seismic waves that radiate from a fault rupture – including compression body waves (known as P waves), shear body waves (known as S waves) and Rayleigh and Love surface waves – travel at different speeds. Secondly, because the seismic waves are reflected – often several times – from the boundaries between different layers of the earth, they reach an impacted area after travelling different distances from their source. Typically, the ground shaking from an earthquake involves a rapid build-up to peak levels, a period of “strong motion” of several seconds and then a slow decay.

Ground vibration from an earthquake occurs simultaneously in all directions, with vibration in a horizontal direction usually more intense than vertical vibration. Typically, the maximum vertical vibration is 50% to 90% of the magnitude of maximum horizontal vibration. The level of ground vibration is greater in size the closer one is to the fault rupture. However, the level of earthquake-induced ground shaking also depends on the type of rock within the propagation path between the fault rupture and the affected area and the nature of the rock and soil within the impacted region itself. Therefore, the amount of damage from the same earthquake can vary considerably for different areas that are the very same distance from the fault rupture.

The ground shaking caused by an earthquake is of a random vibration character involving simultaneous motion at multi-frequencies and the components of the individual frequency narrow bands vibrating at different randomly-distributed phases. The magnitude of the vibration can be measured by the ground displacement, the ground  velocity or the ground acceleration. Scientists record one of these three quantities through instruments placed at various locations called seismographs. However, the destructive potential of an earthquake depends on not only the maximum magnitude of its vibration but also on the frequency distribution of the vibration. That frequency content of earthquake-induced ground shaking in turn depends on not only the type of earthquake but on the propagation path between the fault rupture and the particular impacted area.

Most of the frequency content of earthquake vibration is typically within a range of 0.2 Hz to 33 Hz (that is vibrations of periods between 5 seconds down to 0.03 seconds). However, in more recent times, earthquake-induced vibration in some hard rock regions of the U.S. have been detected with content up to frequencies of 100 Hz. It is important to note that the vibration experienced by equipment or other type of product in an earthquake-impacted area will depend not only on the ground vibration but its own exact location relative to the ground. For example, ground shaking may have to pass through the soil then through the building foundations, then onto the floor of a building and then through any substructure holding the equipment before it is transmitted to a piece of equipment on the floor of a building. The dynamic characteristics (in particular the natural frequencies and damping properties) of each of the soil, foundations, building floor and substructure – as well as of any vibration damping and seismic isolation structures deliberately introduced into a building to mitigate earthquake damage – will filter the ground vibration in a way that may amplify the vibration transmitted onto the product at some frequencies and attenuate it at other frequencies. Therefore, the vibration experienced by a product in a structure during an earthquake may be quite different to the ground vibration.

The Damage Potential of Earthquake-Induced Ground Vibration

The damage-causing potential of earthquake vibration depends on not only its own magnitude and frequency content and the dynamic characteristics of the vibration transmission path between the ground and the product but on the dynamic characteristics of the product itself. Put simply, if the resonant frequencies of a product match those of the most intense frequencies transmitted into it from earthquake-induced ground vibration, then the product is more likely to be damaged during the earthquake.

For low and medium height buildings, the most damaging components of ground vibration are those with frequencies between 0.5 Hz to 1.0 Hz (that is with periods from 2 seconds down to 1 second). These are frequencies lower than that which are most strongly felt by humans, which tend to be frequencies above 1.0 Hz. Therefore, an earthquake that causes ground vibration that is most strongly felt by humans may not necessarily be the type of earthquake that is most likely to cause buildings to collapse. When it comes to very tall buildings, it is frequency content that is below 0.5 Hz that is most destructive. Seemingly counter-intuitively, some super high buildings may not be catastrophically affected by earthquakes. This is because their resonant frequencies may be less than 0.3 Hz, frequencies at which earthquake-induced ground motion is not strong. Such super-high buildings are more susceptible to failure from high winds and wind gusts.

Most equipment does not have natural frequencies below 3 Hz. Therefore, it is the frequency content of ground shaking above 3 Hz that is most likely to damage equipment. Given that the frequency content of most earthquake vibration is below 33 Hz, a quite low frequency, it tends to be heavier equipment and products that are most susceptible to earthquake vibration damage. Additionally, even lighter, powered equipment on vibration mounts can be prone to earthquake damage. This is because, in order to minimise the vibration transmitted to floors – and thus to humans – of electrically powered equipment, which often have natural frequencies at 50 Hz or 60 Hz, vibration mounts are typically designed so that the fundamental natural frequencies of the assembly that they hold are around 3 Hz to 15 Hz. Frequencies within this range have high content during earthquake vibration.

Vibration Acceleration Response Spectrum

Since the damage potential of earthquake vibration is closely related to the natural frequency of the structures or products being impacted, the vibration of an earthquake is usually represented as an acceleration response spectrum. This spectrum is based on the maximum acceleration of a single degree of freedom, spring-mass system oscillator of varying natural frequency when subjected to the earthquake vibration. The spectrum plots this maximum acceleration response for each discrete oscillator natural frequency. Different acceleration response spectra can be produced for spring-mass systems with different amounts of damping. It is most common to produce the response spectrum for oscillators with 5% of critical damping.

Once determined, the response spectrum enables one to estimate the maximum acceleration that a product or component will experience from the earthquake by knowing the product or component’s natural frequency, provided that the spectrum has been determined for a damping level comparable to that of the product or component and provided that the natural oscillatory motion of the product or component can be approximated as a single degree of freedom system. Since the latter is usually the case, the representation of earthquakes by acceleration response spectra helps engineers to design their products in a way that makes them resilient to earthquake damage.

Earthquake Vibration Test Criteria

For the same reason that acceleration response spectra provide the best means of characterising earthquake-induced ground vibration, they are also used as the criteria for vibration testing of products to determine their resilience to earthquake vibration. The product under test is required to be subjected to vibration on a vibration shaker table such that the acceleration response spectrum of the applied vibration waveform envelopes the response spectrum of the earthquake that the item is designed to withstand. That means that the acceleration response spectrum of the test vibration waveform must exceed that of the design earthquake at basically all frequencies but not by too much to ensure that product damage is not produced in the vibration test that would not occur during the actual designed-for earthquake. It is up to the test house to derive the random vibration profile that will produce the required acceleration response spectrum. Different vibration waveforms can meet a particular required acceleration response spectrum. The test house should produce ones that match the capabilities of their vibration testing apparatus.

When determining the required acceleration response spectrum that a product must survive during testing, manufacturers and end users must consider the geographical spread that the product is expected to be mounted in. The earthquake in the most severely affected region among the different possible use areas should be chosen as the basis for determining the acceleration response spectrum that will be used as the test criteria. However, since earthquakes occur sporadically in time and different earthquakes in the one area are of different intensity, a decision must be made about what probability of earthquake intensity in the designed-for-use region that the product should be designed to withstand. Often manufacturers and end users will want the product to survive an earthquake with an intensity that would likely only be reached once in a hundred years – or once in a hundred and fifty years – in the designed-for-use region. However, if the product is one where failure during an earthquake could have catastrophic consequences, such as equipment essential for the safe operation and shutdown of nuclear reactors, then designers would want the item to survive an earthquake of intensity only probable to be reached once in ten thousand years.

The required acceleration response spectrum that the product must survive during testing should then be modified for the filtering effects of the vibration transmission path – which depending on the item’s location within a structure may include the soil, foundations, the building floor and substructure – between the ground and the mounting point of the product within a structure. If the product can be located at different points relative to the ground, then the required acceleration spectrum should be chosen assuming the location of the product relative to the ground is that which subjects it to the most damaging vibration.

Since earthquakes induce ground vibration in a number of directions simultaneously, the vibration environment that products are subjected to during an earthquake is most accurately represented by vibration testing in two principal horizontal axes and the vertical axis simultaneously. However, vibration shaker tables that can perform such tri-axial testing are rare and mostly found in university and government laboratories that prioritise their use for research rather than product development. Therefore, most earthquake vibration testing standards allow for testing to be performed through uniaxial testing conducted consecutively in each of the three directions. This generally achieves a somewhat conservative test in terms of determining the resilience of products to low-cycle fatigue.

The Challenges of Earthquake Vibration Testing

Since the vibration induced by earthquakes is not only potentially very intense but also highly complex, the resilience of a product to earthquake vibration cannot be determined with great confidence by modelling alone. Therefore, the verification of the resilience of products to earthquake-induced vibration is best performed by vibration testing of the products.

The problem is that the conduct of earthquake vibration testing is not easy. This is the case for three reasons. Firstly, commonly used earthquake vibration testing standards require the test house to determine the parameters of the random vibration profile that will produce the required acceleration response spectrum. It is a challenge to design the required random vibration profile in such a way that it both achieves the required acceleration response spectrum and ensures that there is not excessive over-test at particular frequencies. Secondly, because each particular earthquake vibration test typically lasts a very short duration and involves a rapid ramp to the “strong motion” full level, followed by a dwell at this level for typically only 15 to 30 seconds, controlling the vibration shaker table so that it achieves the desired vibration profile, even if the latter is correctly derived, can be challenging.

Thirdly, earthquake vibration tests typically involve very high displacement. Recognising the displacement limitations of many vibration-testing machines, earthquake vibration standards do allow for some minimisation of the required displacement for testing of items with higher natural frequencies. For example, IEE344 and AC156 only require the test vibration to exceed the required acceleration response spectrum down to frequencies that are respectively 70% and 75% of the lowest natural frequency of the item being tested. Nevertheless, both standards stipulate that the required acceleration response spectrum must still be met down to a frequency of 3.5 Hz regardless of the lowest natural frequency of the item being tested. Moreover, it is not uncommon for resiliently mounted equipment, heavy equipment or their components to have natural frequencies as low as 3 Hz, meaning that earthquake vibration tests on equipment may sometimes need to meet acceleration response spectra down to as low as 2.1 Hz. For these reasons, earthquake vibration tests may be of very high displacement despite the clauses in test standards aimed at reducing required shaker displacement levels. For this reason, commonly used electrodynamic shakers, which typically have maximum peak-peak displacements of between 25 mm to 50 mm are unsuitable for most earthquake vibration testing.