Tag: Extreme weather

Earthquake proofing buildings

Post author By joachimsbach
Post date 14th February 2023
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In this blogpost we will try and answer some questions in relation to earthquake proofing buildings using different materials and tools.

Earthquakes in short

Earthquakes are disastrous events influencing people, infrastructure and houses. The most prone areas to earthquakes are lie at fault lines where epicenters of earthquakes usually happen, see Figure 1 and 2 for epicenters and tectonic plates respectively.

Figure 1: Location of earthquakes epicenters across the globe. This distribution of epicenters supports the hypothesis of tectonic plates present across the globe.

Figure 2: Location of the tectonic plates across the globe. Illustration of the different types of plate tectonics including subduction, lateral sliding and spreading events.

The exact locations of when and where earthquakes will happen varies as the nature of these events is chaotic. However they usually follow patterns as outlined by the fault lines where tectonic plates meet and exchange information. In addition, the frequency of occurrence alongside with magnitude of earthquakes are completely unpredictable in nature.

This fundamental description of earthquakes causes problems for engineers and scientists alike. Engineers are faced with the challenge of accurately creating safe and sound buildings able to withstand the next earthquake, while scientists are faced with the problems of understanding the different phenomena which are chaotic in nature.

When engineers are facing the problems of designing buildings in earthquake prone areas It is often necessary to find solutions for the moving and differential settlement for which buildings are subjected to.

Earthquake proofing buildings – blocks

One solution to earthquake proofing buildings is for the building to move together with the earth during the earthquake. In order for the building to easily move together with the earthquake the foundation of the building needs to be placed on elastic blocks. See Figure 3 for an illustration.

Figure 3: Illustration of the spring mats utilized for stabilizing the foundations beneath the floor of buildings. Illustration is not to scale.

The movement blocks allow the foundation to absorb some of the shearing movements caused by the earthquakes surface waves, the so-called Rayleigh and Love waves. This allows them to withstand stronger more devastating movements when compared to houses without mats.

Related read: earthquake epicenters

Earthquake proofing buildings – tuned mass damper

Another example of a way to earthquake proof buildings and larger structures such as bridges, towers and walkways is through the use of a tuned mass damper.

The tuned mass damper is a special type of damper designed specifically to the building in question. It works by adding a suspended mass into towers or structures. The suspended mass works by shifting the buildings eigenfrequency sufficiently higher than before such that earthquake vibrations are damped out before destroying the building. The dampening works by absorbing the deformation inside the tuned mass damper. For an illustration of the concept of a tuned mass damper see Figure 4 and Gallery 1 for real life counterparts.

Figure 4: Illustration of a tuned mass damper located inside the top of a tall building. The illustration is not to scale.

Tuned mass damper on the millennium bridge.

Tuned mass damper on the Taipei 101 tower

As we can see the different types of tuned mass dampers varies in shape, form and size from the relatively small discrete ones underneath walkways till the large heavy ones inside the Taipei 101 and Shanghai towers.

Earthquake destruction in Turkey-Syria

Recently the Turkish earthquake Kahramanmaras lead to a massive destruction of buildings, infrastructure and railroads alike. The destruction of buildings was massive as can be seen when comparing the a before and after image from Kahramanmaras, see Gallery 2.

**Gallery 2:** *Before and after pictures of the Turkeys earthquake in Kahramanmaras reproduced from: source.*

The destruction led to massive amounts of death and homelessness in the thousands of numbers, see source. This destruction is terrible for the population of Turkey and Syria where the death tool is immense alongside with the cold winter coming showing degrees below freezing during the cold nights.

What are the best materials for earthquake-proof buildings

The best materials for earthquake proofing buildings are steel and elastic materials. The strength of steel allow it to absorb stresses from the earth foundation strains.

Steel as a building material

Furthermore the elasticity of steel is sufficient for deformations to remain elastic as compared to plastic. Elastic deformations are important as the destructive forces usually occur due to permanent shifting of loads during the plastic deformation of bearing members of the structure.

Since steel is an exceptionally strong material with large elastic and plastic bearing capacities it makes it ideal as a construction material for earthquake prone buildings. For an example curve of the strength of steel see Figure 5 for an example of a steel loading curve.

Figure 5: Stress-strain illustration of typical steel with indications of elastic (linear deformation) and plastic deformations.

We can see that the strength of steel during the elastic part of the curve is linearly proportional to the displacement, meaning that we can load up and down the displacement curve without loss of strength.

This curve is representative of all axial strains meaning that steel is isotopic and thus able to withstand forces with equal strength in all directions.

Wood as a building material

Unlike steel there is wood. Wood is a natural material whose properties depend on the type of wood, the age and location to name a few. In fact, wood is not isotopic since fibers are growing upwards from the stem.

The mechanical properties of wood therefore varies from tree to tree and depending on the force direction of loading including axial and torsional directions. An example of a typical axial stress-strain loading curve is shown in Figure 6.

Figure 6: Stress-strain relationship for the axial loading of wood. Indications of plastic regions have been made. Reproduced from sourc e.

As we can see when comparing the curve from wood with the curve from steel we can see that the elastic region is followed by a small plastic period with increased strength for steel while the wood curve is flattening out directly after yield stresses are observed.

In both cases the axial strength increases in a short period before failure for steel, which is the hardening period, while tree follows densification before failure.

Comparing wood vs steel

For steel the hardening period is followed by increasingly plastic deformation and loss of material strength throughout the necking period. This period allows buildings to deform providing a warning sign before failure. The behavior of deformation before failure is known as ductility and is a particular sought after characteristic for building materials.

For wood the linear elastic period of deformation in the axial direction is followed by plastic continual deformation. This means that the wood will compress without gaining strength up until the point of densification. Densification is the happening where tree fibers are compressing increasing the capacity of the wood before failure occurs due to cracking fibers.

With these considerations when trying to earthquake proof buildings it is important to make the bearing elements strong and elastic. For this purpose steel is an excellent material.

Building earthquake-proof buildings

In conclusion utilizing different measures such as tuned mass dampers or spring mats increases the foundation bearing capacity in regards of vibrational stressors from earthquakes.

For the building materials it should be performed in steel for the load bearing parts of the structure ensuring that maximum elasticity and strength against materials is achieved.

Steel unlike wood, is isotopic meaning that shear forces from earthquakes are easily absorbed in a manner similar to axial compression while wooden structures will act differently depending on the mode of deformation and earthquake surface waves.

References

Stress-strain curve for wood https://doi.org/10.1016/j.jobab.2020.07.004

Number of casualties in earthquake Turkey-Syria – https://www.theguardian.com/commentisfree/2023/feb/15/earthquake-turkey-corruption-buildings-collapse

Tags Engineering, Extreme weather

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Earthquake epicenters

In this blogpost we will try and explain how to calculate earthquake epicenters with examples of measurement systems and methodologies.

Tectonic plates

The Earth can be subdivided into different ‘floating’ parts called tectonic plates. This subdivision follows three different main mechanism as explained in the figure below outlining the tectonic plates.

Figure 1: illustration of tectonic plates and their individually driving mechanisms dividing the subdivision zones.

These tectonic plates move around on the earth in unpredictable patterns that build up stress throughout the solid medium. When the built up stress releases the earth moves and we have an earthquake.

These event are extremely energetic releasing immense amounts of energy. The release of energy causes widespread destruction as seen in the Turkey earthquake from February 2023, the Kahramanmaras earthquake.

Definition of a p(ressure)-wave

Firstly, lets define the definitions of pressure and shear waves, the so-called p and s-waves.

The definition of the pressure, p-wave is a pressure type underlying wave moving through the solid medium. The direction of propagation is dominated by compression\expansion pressures. The particle path is first compressed and then elongated.

GIF 1: illustration of the p-type (pressure) wave

The p-wave is the fastest moving pressure wave throughout the solid medium. The initial disturbance moves quickly through the solid medium. It emanates from the area of interest; the epicenters of earthquakes.

Definition of a s(hear)-wave

The shear type, s-waves, is different from the p-wave. Contrary to p-waves, shear waves moves in the direction of propagation through shearing motions. Shearing waves causes particle motions to move in a up-and-down type of fashion. In addition to this, the s-wave is slower than the pressure waves as shearing of solid medium poses more resistance.

GIF 2: illustration of the s-type (shear) wave

The shearing causes changes in the underlying soil characteristic and in extreme cases causing earth ruptures. These waves emanate in all-directions arising from the epicenters of earthquakes.

Definition of a love wave

Thirdly, we have the Love type surface waves. Contrary to p and s-type waves, this is a surface wave. In other words surface waves have particle motions varying with depth, where deeper particles move less, than upper surface particles. As an example of the L-type wave, see the figure below.

GIF 3: Illustration of the love-type wave

Important to realize is that Love type waves are slower than both p- and s-type waves and are present at the surface. In particular the particle motions which are horizontally varying with depth causes a diagonally shearing with depth. Thus L-waves require a solid material in order to be able to propagate. Conversely L-type waves are unable to propagate through liquid media. Therefore does the presence of L-type waves throughout the earth constitute an underlying measure for the existence of a liquid earth core. This is one of the reasons why we believe the core of the earth is liquid due to the absence of L-waves across the earths solid media.

Definition of a Rayleigh wave

Fourthly, we have the Rayleigh wave. This type of wave is similar to the love wave in the sense that it is a surface wave traveling across the globe emanating from the epicenters of earthquakes.

The Rayleigh waves propagate in a fashion similar to ocean waves with horizontal displacements in direction of propagation varying with depth. An illustration explaining the wave propagation is shown in the figure below.

GIF 4: illustration of Rayleigh-type wave

The Rayleigh waves are slower than love type waves but are also causing surface changes and therefore affects buildings, infrastructure and people alike.

The particle motion is orbital meaning that it changes with depth. The Rayleigh waves are able to happen across liquid and solid media alike, thus differing significantly from L-type waves.

Now that we have introduced the four types of earthquake waves we now move further into measuring these different types of waves. For this scientists and engineers utilize the physical instrument called the seismograph.

Seismograph

The seismograph is an instrument utilized in measurement engineering when trying to estimate and predict the onset of earthquakes. It works by having giant ear-like sounding equipment directed towards the earth. The resulting vibrations ‘heard’ are measured with high accuracy and mapped onto a seismogram see Figure 2.

Figure 2: A Seismograph device showcased with measured earthquake vibrations on a seismogram paper.

From the picture you can see the characteristic black line indicating differences in surface vibrations measured in time. The vibrations consist of a superposition of p-, s-, L- and R-waves all mixed together onto the seismogram. The amplitude and phases differs based on the type of waves allowing engineers and scientists to differentiate individual wave types.

Seismogram

The seismogram allows us to analyze the differences in amplitude period and type of vibrations. In addition it allows interpretation by seismologists geologists or similar experts. Furthermore the interpretation include the characterization of individual waves. An example of wave characterizations is shown in Figure 3.

Figure 3: an illustration of interpreted seismogram where p-, s- and surface-waves are marked with an red arrow.

From Figure 3, we can see that the earliest sign of an earthquake is the p-wave, followed by the s- and surface waves (Love and Rayleigh). Amplitudes of the surface waves compared with the p- and s-waves are significantly larger making them easily felt by people on the ground. Furthermore the p and s-waves are barely measurable and have significantly faster arrival times compared with surface waves.

With the introduction of the seismograph and seismogram we now continue with the mathematical description of the distance calculations following the narrative with Euclidean distances.

Euclidean distance

An Euclidean distance is the observed straight-line connection between points. It is calculated in two dimensions as the difference between points x1, x0 and y1, y0 denoting end and startpoints respectively.

(1) $\begin{equation*} s = \sqrt((x_1-x_0)^2 + (y_1-y_0)^2) \end{equation*}$

Now as we live and breathe in three-dimensions, (four counting time) we need to include a third coordinate in our calculations of distance. For this purpose we include the coordinate z1 and z0 in a similar manner.

$s = \sqrt((x_1-x_0)^2 + (y_1-y_0)^2 + (z_1-z_0)^2)$

Now we can calculate the distance between two points in space. Finally we need to compare different locations in time to accurately calculate the earthquake epicenters.

Triangulation methodology

With the knowledge of how to calculate a distance between points, now we can move on to calculating the epicenters location through use of time-dependent triangulation methodologies. The location of epicenters in three-dimensional space corresponds to accurately figuring out a location based on satellite measurements. As the medium we consider is solid state matter, we need estimations of sound speeds through the media and for this we need seismologists, geologists and similar experts.

Seismologists, geologists and experts

An important parameter is the time-aspect of figuring out exactly how to do the determination of the individual epicenters. By comparing measurements of seismograms through time, one can calculate the arrival time of individual p-, s-, L-, and R-waves. As the speed of sound is assumed through specific soils this leaves the only unknown to be distance which is solved for numerically.

This type of analysis is carried out by seismologists, geologists and similar experts with knowledge about wave propagation speeds throughout solid state media and how to interpret the individual seismograms. Now lets consider the epicenters themselves

Epicenters of earthquakes

With the advent of seismographs, seismograms and specialized scientific methodologies for accurately calculating the measured distances and time-variation of seismograms allows the calculation of epicenters of earthquakes.

The epicenters are important parameters to understand as they allow for the construction of the tectonic plates. They are characterized by experts whose knowledge is used to construct the tectonic plate theory. Finally understanding epicenters help when trying to understand the earths complex composition of solid state matter.

References

https://en.wikipedia.org/wiki/Epicenter

Tags Extreme weather

Extreme weather Natural phenomena

Tsunami measurements

Locations of the NDBC Buoys, epicenter of the earthquake and Terrain\bathymetric features of the eastern pacific basin

This blog-post dives into the measurements of the 2011 11’th March Tsunami from the ‘Great Sendai Earthquake’. The Great Sendai Earthquake, caused a loss of lives in the order of 20.000 and insurmountable amounts of economic damages.

Tsunami measurements from NDBC buoys

Lets focus on measuring the Tsunami itself. We do this to try and understand how the tsunami spread across the globe. To investigate this we will have a look into some wave buoy measurements from the National Data Buoy Center in short, NDBC.

The NDBC wave buoy measurement equipment, are located at different distances from the earthquake epicenter across the Pacific Ocean. Figure 1, showcases all buoy measurement locations of the NDBC Tsunami program within the pacific ocean. These buoys are specifically designed for Tsunami detection purposes.

Figure 1: NDBC NOAA wave buoy locations with historic, recent and decommissioned stations.

The water depth and distances vary with thousands of kilometers between the buoy observation stations. However we will see that measuring a tsunami is still possible even across the vastness of the pacific ocean.

Measurements from the (National Data Buoy Center) NDBC buoys – (North Oceanic and Atmospheric Administration) – NOAA

Measurements are extremely valuable for understanding the natural world in general and in particular the oceans dynamics.

Although the vastness and shear scale of the oceans makes such a task almost implausible we still try and measure wave heights, wind speeds and current speeds by placing buoys out at sea.

Buoy data and placements

The NDBC-buoys are located offshore and for this exercise we will specifically look into buoys 43451, 21418 and 21413 which was in place during the March 11’th 2011 Tsunami. The driving mechanism behind the Tsunami was the “Great Sendai Earthquake”. We can see the Earthquake epicenter and aftershock locations in Figure 2.

In order to showcase the differences in measured surface elevations between the NDBC-buoys. I have created Figures 3-8 where measurements are shown and GIS (Geographical Information System)-figures are created of the buoy locations in question. Here we can see that the measurements of the Tsunami are occurring at different times across the pacific ocean.

Figure 2: Epicenter of the magnitude 8.9 Earthquake “Great Sendai Earthquake” prior to the Tsunami hitting shores of Japan among other locations.

Figure 3: NDBC Buoy 43451 de-trended measured surface elevations across the Tsunami event where the high-frequent disturbance is clearly available.

Figure 4: NDBC Buoy 21418 de-trended measured surface elevations across the Tsunami event where the high-frequent disturbance is clearly available.

Figure 5: NDBC buoy 21413 de-trended measured surface elevations across the Tsunami event where the high-frequent disturbance is clearly available.

Figure 6: All NDBC buoy measurements of the Tsunami from the “Great Sendai Earthquake” on 11’th of march 2011. Each have been individually de-trended.

Figure 7: NDBC-buoys across the western part of the pacific ocean with locations of buoys 21418, 21413 and the epicenter of the Great Sendai Earthquake. Terrain heights and water depths are displayed following GEBCO and google-maps imprinting

Figure 8: NDBC-buoy across the eastern part of the pacific ocean with locations of buoys 21418, 21413 and the epicenter of the Great Sendai Earthquake. Terrain heights and water depths are displayed following GEBCO and google-maps imprinting

Tsunami wave celerity

The Figures above show that there are differences in the Tsunami surface elevations. The Tsunami wave disturbance develops and travel across the globe changing underway.

We can calculate the average wave celerity using the time difference of the measured wave disturbance between individual buoys. The arrival time of the wave at the eastern NDBC buoy 43412 is approximately 30 hours after the first measured signal. See Figures 7 and 8 for locations.

The approximate distance between NDBC buoy 21418 and 43412 is 15.000 km’s. Using this approximate distance together with the time difference of 30 hours and we get that the celerity of the Tsunami wave is approximately 500 km/hr!

In conclusion, the Tsunami moves with approximately 500 km/hr across the deep ocean of the Pacific. That is faster than a racing formula 1 car!

Meme 1: Tsunamis move faster than an Formula 1 car across the deep oceans

lets now try and examine the wave-shape of the Tsunami itself.

Tsunamis – Single or multiple waves?

Lets investigate Figures 3-6 more in-depth. In all figures, we can see that the initial wave disturbance comprises of multiple individual waves with different frequencies. Each of these waves travel independently and exchange energy with one-another. For instance, Figure 6 show individual wave buoy signals plotted together. In order to process the wave buoy data to reach the above signals we do the following steps:

Firstly, we download the individual raw wave data.
Secondly, we preprocess the data series removing unwanted data.
Thirdly, we detrend the data removing mean water depths from the equation.
Finally, we plot the results against each other with date-stamps.
In conclusion we can now investigate the Tsunami wave amplitude individually.

We can see that the large amplitude in buoys 21418 and 21413 are smoothed out in buoy 43412. This confirms the hypothesis that the wave dispersion relation transforms energy from bound high frequency harmonics towards carrier low frequency harmonics resulting in the smoothing out the of wave signal across distance.

Tsunami wave trains

In reality, Tsunamis consist of a plethora of waves with different amplitudes, frequencies and directions, all interacting resulting in what we call a Tsunami. When we think of an individual Tsunami wave, in reality we think of a wave-train of multiple waves with different frequencies, amplitudes and directions whose sum and difference make up the Tsunami.

In linear wave theory, we assume that these individual waves are all travelling independent of one-another, resulting in a wave-train of motion where the net wave train moves at speeds different from the individual frequencies.

This agrees with the above measured wave celerity as the individual tsunami wave-train moves with 500 km/hr while the incoming individual Tsunami wave frequency only travels of few tens of kilometers an hour.

Tsunami amplitude

Lastly lets look into the tsunami wave amplitude. We have now concluded that the Tsunami wave consists of a train of individual waves whose frequencies and directions all interact. We have also concluded that the wave-train travels across the ocean with approximately 500 km/hr whenever the water depth is large O(4000 m’s). The last interesting piece of the puzzle is the most feared one, the Tsunami amplitude.

We can see that the amplitudes out in the deep sea are O(1/10 m’s) above figures and small compared to the amplitudes experienced near the shore O(10 m’s). Now one may wonder why are there so large differences in the observed wave amplitude between the deep and shallow ocean?

Why are Tsunamis wave heights increasing at shorelines?

The answer lies in the dynamical nature of wave shoaling. As waves near the shore, the wave-energy transforms from the sub-harmonic space into the super-harmonics. Shoaling causes the wave to slow down and transform increasing the wave amplitudes of the incoming wave until breaking occurs. Check out this blogpost explaining shoaling in detail.

The wave period of the Tsunami wave endures throughout the breaking causing the water to keep rushing in over shores, low breakwaters damaging infrastructure and potentially people.

Conclusion

In this blogpost we have examined the measurements of the 11’th March 2011 Tsunami caused by the Great Sendai Earthquake.

We have looked into the placements of NDBC buoys along with measured amplitudes of the Tsunami.

We have estimated the wave celerity at deep water O(4000 m’s) to be 500 km/hr, faster than a racing formula 1 car.

We have explained in short details why wave heights at nearshore is substantially different from the deep water measurements.

References

https://www.ndbc.noaa.gov/

https://www.britannica.com/event/Japan-earthquake-and-tsunami-of-2011

https://www.sciencelearn.org.nz/resources/596-tsunami-shoaling

Tags Extreme weather, GIS, Measurements, NDBC, Tsunami