Category: Engineering

Stabilizing the leaning tower of Pisa

Post author By joachimsbach
Post date 31st March 2023
No Comments on Stabilizing the leaning tower of Pisa

In this blogpost we outline how engineers have been stabilizing the leaning tower of Pisa. We consider the history, techniques and end-result.

The leaning tower of Pisa

One of the major problems in civil engineering is getting the foundation of the building correct. Especially when the material which you are planning on building the building on consists water adhesive materials such as silt and clay. The problems with these types of characteristic materials particularly include differential settlement.

Differential settlement of the leaning tower of Pisa

Differential settlement is the procedure on which foundation weights presses water out of specific soils which adhere a large amount of water. This water is usually not easy to leave the soil of the foundation as this watery soil content, which is expressed through excess pore-volumes, contains water which when pressed over time, cause a slowly changing consolidation of the material.

The soil underneath foundations thus experience what is considered differential settlement as the water is pressed out unevenly across the foundation when pressured consistently over an excessive amount of time.

This causes the building to settle unevenly which in worst cases can form cracks along the foundation and in best situations cause lasting damages to the entire structure.

The geological composition underneath the leaning tower of Pisa

One, if not the most famous case when considering differential consolidation is the leaning tower of Pisa. The case of the leaning tower of Pisa is famous exactly because of this foundational engineering problem and have transformed from being a problem for frightening people, to be an memorable historic landmark which is cherished worldwide, see Figure 1.

The core ‘problem’ behind the leaning tower of Pisa, is the geological composition and the water tables high occurrence just below the foundation. The sandy clayey-silts which are the main source of concern is located just below the foundation. This particular composition of grain sizes is the root of the differential settlement observed.

The next layers consist of clay, followed by a small layer of intermediate sand and then once again clay. The sand is particularly problematic as water can be pressed out of the clays draining underneath water from clays to the sand content. The flow of water from the differential settlement of the leaning tower structure, allows the compression of the soil layers to easily form underneath the silty clayey top layer. Now to make things worse, the history of the leaning tower of Pisa, makes the stabilizing procedures a lot more challenging.

Figure 1: Left, the leaning tower of Pisa. Right, a cross-section of the geotechnical soil characteristics underneath the leaning tower of Pisa

History of the leaning tower of Pisa

The tower started out as a general massive construction planned to stand for multiple years. Construction of the main tower began in 1173 with expectations to finish later on during that century. However due to political unrest, recessions and expensive wars the construction of the tower was paused after finishing just four orders out of the originally planned eight cornices.

Financial and political unrest

This periodic influence of macroeconomic tendencies are typical of middle age construction projects where the first of the different projects are started in good periods, while most activities are cancelled or delayed during times of recessions.

The delay in construction of the at the time, Tower of Pisa, was quite significant as compared to similar buildings at the time. The delay was more than 100 years before financial and political stability was sufficient as for the funding of the building to continue onwards.

Second construction period of the tower of Pisa

The second construction period began completing three more cornices of the originally planned eight, before another interruption happened again due to political unrest and financial instabilities occurred.

Now by this time, the tower had already started tilting as the geological layers underlining the foundation had been exposed to excess pore-pressures for already 100 years more than any typical pre-consolidation theory usually encounters.

The now leaning tower of Pisa

Now the tower was leaning and construction continued until only the last order and top tower cornice needing to be finished. Work was then paused once more, due to political and financial unrest before finally the leaning tower of Pisa was finished with the tower and eight cornice completed.

It thus took almost 200 years from start to finish of the leaning tower of Pisa, a period which by many standards is quite significantly larger than any other major project under construction.

For comparison, the modern day one world trade took ‘only’ 13 years to complete but is simultaneously 104-storeys, 417 m’s high. This is in stark contrast to the 8’th orders corresponding to 57 m’s high leaning tower of Pisa.

For an example of the history of the leaning tower of Pisa, see Figure 3 from [1].

Figure 2: The history of the leaning tower of Pisa with indications of building mass and construction phases.

Modern day famous leaning tower of Pisa

The completed tower of Pisa remained standing for centuries, without any catastrophic events to occur. The result is that the tilt of the leaning tower of Pisa had reached levels which experts deemed to be critical, furthermore advanced measurement systems for monitoring the increase in the leaning tower of Pisa showed that the tilt was in matter of fact, accelerating slowly and if no measures were taken would lead to catastrophic failures within a matter of a lifetime.

Therefore it was decided to begin stabilization work in the 1990’s. At this point the the tilt was approximately 5.5 degrees, resulting in an overhang of the top cornices with about 4.1 m’s compared to the bottom of the structure, see Figure 3.

Figure 3: Cross-section of the Leaning tower of Pisa with inclination, cornices and geometric instances.

Modern day technologies have allowed for the restoration of the tilt ensuring that it is not accelerating as previously experienced. A number of different technologies were investigated. These include; placing heavy rocks on the side of the leaning tower of Pisa’s foundation, placing anchors on the leaning side and installing man pillars on the side of the leaning tower of Pisa.

The architectural challenges

It was of utmost importance not to completely fix the tilt of the tower as this was now considered a historical monument whose perseverance was valuable.

Furthermore most of the proposed solutions such as installing pillars on the side of the leaning tower and subjecting the far most side to extra load resulting in a stabilizing moment were disregarded due to the imprint on the architectural expression the building incurs in its users.

The solution to these architectural constraints was an expensive horizontal drilling action, where specific amounts of soil were excavated deep under the existing foundation in amounts carefully outlined as to provide sufficient stabilizing actions to the now already strained foundation.

Stabilization measures for the leaning tower of Pisa

Most of the proposed remedies to the tilting of the leaning tower of Pisa were tossed in the bin, as a result of the architectural expression of the leaning tower of Pisa. However some of them were utilized with great success. These measures are outlined in the following.

Horizontal directional drilling

The horizontal directional drilling equipment utilized for the procedure is outlined in figure 4-5. This type of equipment is specialized towards the excavation of small exact amounts of soils deep underneath the foundation.

Furthermore, it is also possible to see the stones and counterweights placed on the side of the foundation as a counterweight ensuring that any potential miss excavations which could resolve in destabilizing of the entire building would be counteracted by the weight of the blocks and tower combined.

The surgical procedure allows engineers and scientists to control exactly how much of the soil underneath which needed to be excavated before the tilt-acceleration is stopped.

Figure 4: Horizontal directional drilling boreholes underneath the leaning tower of Pisa. Counter weights placed away from the tilt providing a stabilizing moment. Source: Wikipedia commons.

Figure 5: Pan view of the restoration process of the leaning tower of Pisa. The view is showing the horizontal drilling action and the counterweights placed on the tower. Source: Wikipedia commons

Drainage of foundation soils

The stabilization of the leaning tower of Pisa is furthermore complicated by the excessive amount of water filled soil contents which caused the differential settlement to begin with.

The differential settlement thus occurs as a result of where the water content is pushed out from the inner core samples. This water leaks from the soil as the excess pressure from the entire building is pressing on the soil causing consolidation.

Drain pumps installed

In order to combat this phenomena, drain pumps was installed allowing the excess water contents to spill out from the soil and drained away before causing problems. The result is increased strength of the soil as water is drained causing compaction and consolidation.

The drainage pumps have been constantly pumping throughout the entire restoration process of the leaning tower of Pisa. This allowed for engineers and scientists to easily calculate and ensure safe soil consolidation while simultaneously ensuring that equipment was kept dry at all operation phases.

Cable strays for temporary stabilization

As a final installment of the renovation operation procedures ensuring that the tilting of the leaning tower of Pisa was stabilized in a sufficient manner was cables.

The cables wrap around the construction in the lower decks of the tower and was afterwards pre-strained ensuring that the Tower had gotten sufficient support ensuring that the tower was stabilized to a degree that catastrophic failure was not an issue.

Open for public usage

All the above measures were sufficient as to stabilize the tower tilt by approximately 50 cm’s from the top of the tower. The stabilizations incorporated ensured that the leaning tower of Pisa could safely be opened to the public after being closed for more than a decade in the 1990’s.

The safety of the structure was increased significantly while simultaneously ensuring that the leaning tower of Pisa remained a leaning tower. This was important as a catastrophic failure event was absolutely unacceptable by authorities while authorities simultaneously recognized the need for keeping the leaning tower of Pisa leaning.

In fact, this purposely insufficient recovery of the leaning tower of Pisa’s tilt, was incorporated with the purpose of keeping the beloved tourist attraction alive without destroying the historical value which the tower had amazed throughout its history of more than 800 years.

In conclusion

Visitors can now climb to the top of the tower and witness the beautiful views of the city of Pisa without fear or concern for their safety. The restoration project has helped to preserve the tower for future generations to enjoy, ensuring that the historical significance of this iconic structure is not lost.

Thanks to the diligent efforts of the team behind the stabilization project, the leaning tower of Pisa will continue to lean for many years to come, delighting tourists from all over the world with its fascinating story and captivating beauty.

References

[1] Burland, John & Jamiolkowski, Michele & Viggiani, C.. (2003). The Stabilization of the Leaning Tower of Pisa. Soils and Foundations. 43. 63-80. 10.3208/sandf.43.5_63.

Tags Engineering

Engineering

Earthquake proofing buildings

Post author By joachimsbach
Post date 14th February 2023
No Comments on Earthquake proofing buildings

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

Engineering

Gas leak at Nord stream 1 and 2

Post author By joachimsbach
Post date 7th November 2022
No Comments on Gas leak at Nord stream 1 and 2

The gas leak at Nord stream 1 and 2 undersea pipelines have been observed on the 26’th of September 2022.

Nord stream gas pipelines

The Nord Stream 1 and 2 pipelines are undersea pipelines capable of supplying the European union with gas from Russia. The pipelines, location of leaks and dates can be seen on Figure 1 while a picture of the emissions can be seen on Figure 2.

Figure 1: Nord Stream 1 and Nord Stream 2 explosions and locations, source Wikipedia.

Figure 2: Picture of one of the Circular gas leaks

Investigation of the gas leaks

To investigate what caused the sudden eruption of the undersea pipeline leakages. An underwater remote operated vehicle (ROV), see Figure 3, was sent down to one of the undersea pipelines.

Authorities and the general public assumed the coherent leakages to be the result of sabotage as the likelihood of four coherent ruptures seemed highly unlikely.

Pictures from one of the leakage sites where made publicly available and elucidating that the leaks were caused by explosives placed on the pipeline where a small explosive could lead to a zip-line effect of damage on the pipeline.

Close-ups of the undersea pipelines from the remote operating vehicle can be seen in Figure 4.

Figure 3: Example of a ROV vehicle. Source: https://reachrobotics.com/blog/what-is-an-underwater-rov/

Figure 4: ROV picture of the Nord-stream 1 leakage – Closeup of the damage at one of the locations source: Reuters

To understand where the leaks occur and to get a sense of the depth at the site of the occurrence, I have created a map overviewing the depth-map and pipeline lines at the sites in the figure below.

Figure 5: Bathymetry map with pipelines Nord Stream 1 and 2 marked as black lines. Bathymetry contours are differentiated utilizing color coding, light-blue shallow dark-blue deep locations.

This bathymetry maps allows users to see how far down the charges would need to be placed in order to be clamped onto the pipelines.

Local mixture ratio of Gas at the leakage sites – A ballpark estimate

The ambient mixture ratio of methane to atmospheric air is approximately 1.896 ppb (parts per billion) according to recent studies from the National Oceanic and Atmospheric Administration.

Lets try and uphold this value with an estimated local value at the site based on scientist estimates of the amount of gas leaked.

Approximately 300,000 – 500,000 tons of methane gas is estimated to have been released during the period of the gas leak.

Ball park estimate of gas concentration

Now lets try and estimate the concentration of methane gas at the surface assuming that we have released the scientist estimates through a period of 7 days, assuming a constant emission flux.

The volume of gas emitted is calculated utilizing the density from Table 1, and methane gas density assuming that methane gas suppress all other gas concentrations.

$v = \fraq{m}{\rho}$

Chemical compound	Density [kg/m³] (25^o Celsius, 1 atm)
CH₄ (gas)	0,657

Table 1: Density of gaseous methane at room temperature

The max volume of gas leaked can then be estimated to be 7,61 * 10⁸ m³ which happening over a period of 7 days corresponds to a mean flux of 1.258 m³/s.

Assuming that the amount is released and spread out evenly in a circular cylinder, spanning 10 m’s above the surface of the water with a radius of 700 m’s. We can first calculate the volume of the cylinder and next calculate the volume concentration.

$V = \pi \cdot r^2 \cdot h$

Where, r is the radius [m], pi is the Pythagorean constant, h is the height [m] and V the volume of the cylinder. Plugging in the numbers provide an estimate of the volume to be 1.54 * 10⁷ m³.

The ratios of these two volumes provide an estimate of the local volume concentration at the gas leak sites that is estimated to be:

$\frac{V_{gas}}{V_{air}} = \frac{1.258 \cdot 10^3}{15.400 \cdot 10^3} \approx 80.000 ppb$

This gives a ballpark estimate of the local enhancement of methane gas concentration at the leakage sites.

News agencies provide leverage to ESA

News agencies was quick to deliver headline news of the gas leakages near Bornholm island. Not long after posting the headlines, the European Space agency caught on and quickly utilized their high resolution satellites network to make remote sensing measurements of the methane gas concentrations.

Coupled with the visual inspections from ROV, overflight pictures and nearby vessel accounts. These concentration measurements allowed the construction of a safe zone around the leakages to be constructed easily.

Measurements of the enhanced Methane gas concentration from space

The European Space Agency has released satellite images measuring the methane gas concentration enhancement at one of the leakage sites. See Figure 6.

Figure 6: Methane plume enhancement as observed by high-resolution satellite images from GHGSat.

Now compare the satellite measurements with our ball-park estimate. We can see that our estimate is wrong with an order of magnitude 80. Given the rough estimates of dispersion characteristics and gas volume leaked this estimate is quite precise.

Concluding remarks

The allegedly sabotage happening at the pipelines are critical for the supply of Russian gas to the Europeans. The gas leakages are investigated with ROV enabling visual documentation, the overflight pictures capture the visual zone of emulsion and satellite remote sensing measurements capture the concentration estimates.

The conclusion is that the leakages are caused by explosive charges placed on the pipelines. In addition, the damages are substantial and it will be a while before the pipelines are fully operational again.

Lets hope that the incoming winters are sufficiently warm such that heating through gas won’t be the dominating factor going into the winter.

Links and references

https://weirdwonderfullworld.com/ESA-GSG-methane-plume-detection-Nord-Stream

https://weirdwonderfullworld.com/NOAA-methane-gas-ambient-concentrations