What is the physics behind the Leaning Tower of Pisa?

in 1995 Engineers attempted to fix the leaning tower of pisa's dangerous 5° lean using large anchors to do this work the authorities first had to strengthen the marshy soil beneath the tower the solution inject liquid nitrogen can you predict what will happen here the engineers forgot that the water expands when it freezes the soil below the north side expanded worsening the building's tilt to 5.

 

 

 and extremely dangerous level despite this setback they eventually solved the issue with a brilliant technique the leaning tower of pisa's center of gravity is here a building topples when the center of gravity leaves the foot area we've all experienced it consider these simple examples here the center of gravity is within the foot area and it's outside for the second case unfortunately this explanation is completely wrong according to this analysis the Leaning Tower of Pisa is stable up to an angle of 18° to understand where we went wrong we

 

need to learn about a concept called leaning instability you might have observe this on a soft ground you can never build a tower more than a specific height it doesn't matter how straight to build it the Tower always fails after reaching a specific height that two a slow failure the tower is tilting very  slowly and it failed this is known as the Leaning instability let's introduce a small perturbation to this perfectly straight Tower while it is settling is the reaction torque larger on the right or

 

left side this will decide the stability of the tower the right side of the ground has compressed more than the left side producing more reaction force here's the trick the left side's reaction force has more distance from the center of gravity than the right side this makes predicting the bigger reaction torque values a tricky Affair at higher Tower Heights the left side reaction torque becomes greater than that of the right side causing the tower to fail this is exactly what happened to the Leaning Tower of Pisa the muddy soil

 

 

beneath it behaves similarly to soft ground at a height of 56 M the tower had already crossed the height of Leaning instability and slowly and gradually the tower began to lean with increase in lean the reaction torque on the left side continued to overpower the right side's reaction torque construction of the Leaning Tower of Pisa started in 1173 with full enthusiasm the engineers constructed a 3M deep foundation for the tower which was too shallow for the loose and Marshy soil of Pisa when the construction reached three

 

 

stories they had to stop the work due to war during this period of inactivity the building developed a lean most importantly the tower settled down due to its own weight squeezed and removed a lot of water out from beneath the foundation this increased the strength of the soil and prevented any further lean however when they resumed the construction after almost 100 years the Leaning instability kicked in again the lean kept increasing the engineers tried to solve this problem by using lighter construction material for the top floors

 

moreover they constructed the tower vertically not normal to the previous floor they also thought this technique would produce a visual illusion that the tower was not leaning as a result of these efforts the tower attained a banana likee shape despite this attempt the lean kept increasing after 6 years of construction when seven levels were completed they had to stop the construction again due to war the third stage of construction began in 1360 The Bell Chamber was constructed at this time The Artisans continued their trick of creating an

 

 

illusion of a straight tower for example at the bell tower region the north side has five steps and the South Side has six steps also The Architects brought the Bell Chamber a few degrees closer to the center axis again despite these strong attempts the lean kept increasing the construction of the Pisa tower was finally completed in 1372 it is estimated that the lean at this time was 1.

6 de you know the nature of Leaning instability once the instability starts it will never stop by 19 1934 the lean was around 4.5 de Bonito musolini the dictator of Italy at the time didn't like this lean he considered this imperfection an insult to Italian engineering musolini had a brute solution to this problem he drilled many holes in the north side of the foundation and poured concrete in the hole they injected concrete with a total weight of 90 tons into the foundation this this is what melini thought would happen what happened was

 

exactly the opposite the soil in the South Side got more compressed and the tower's tilt increased the lean reached 5° in the coming years the lean of the tower kept increasing and in 1990 the lean reached a dangerous level of 5.5 de the tower was closed to the public for the first time the authorities removed the tower's Bell they believed that doing so could reduce the stress on the tower it was a ticking Time Bomb waiting to fall at any moment to save the tower from an immediate collapse the engineers

 

kept lead counterweights on the North side they had to First construct a concrete ring at the base to keep these weights in place they added a total of 600 tons of lead counterweights to the north side this effort reduced the Tilt by one 100th of a degree for the first time the tower leaned towards the correct direction remember the lead counterweight method was only a temporary method the engineers still had to find a permanent solution we already learned about their next attempt to stabilize the tower the liquid nitrogen

method of 1995 this straightening method was such an elegant solution the idea was to go 40 m deep and connect the foundation of the Tower with the hard strata using anchor bolts tightening anchor bolts seemed like a perfect solution to straighten the tower P's soil is so watery and loose not ideal for such construction activities strengthening the soil by injecting liquid nitrogen is a proven method in construction engineering however the liquid nitrogen method backfired in the soil of Pisa the soil had high water content and water expands

when it freezes the soil in the north side expanded and leaned towards the wrong direction the the authorities immediately added another 300 tons of lead ingots to stop the tower from falling they couldn't even try the anchor bolt method this idea had to be abandoned in the very first phase of the project the soil strengthening phase by this time the tower's lean had reached dangerous levels Engineers calculated that a mere increase of 7% weight would topple the tower a factor of safety of 1.07 engineer John Berlin a geotechnical

engineer and the leader of the leaning tower of pza stabilization project believed that the masonry at the south side of the tower could explode at any time the reason the masonry in this region was fragile and the lean created an extra stress on them now comes the solution which finally saved the tower most of the experts by this time accepted that a method called under excavation was the best method to straighten the tower this method looks so simple in this animation remove the soil from the north side the hole will

collapse and the tower will straighten however if the position and angle of the drill are in the wrong direction the tower will tilt towards the wrong direction to perfect the method of underere excavation the engineers first experimented with it on a 7 m diameter concrete footing which was built on a similar soil condition near the Tower of Pisa their initial attempts were not fruitful however after a few trials they finally got the correct angle and depth needed for the drill these results were exciting however the engineers didn't want to

 

 

 

take any risk at this time they first decided to do a small level underere excavation at the actual site they removed soil in only 12 locations they even attached a pair of Steel steak cables for safety purposes look at the way they connected these massive cables and attached them with counterweights they didn't penetrate more than 1 meter beneath the foundation the idea was just to prove their method in the actual site not to straighten the tower the result was encouraging between February and June 1999 they were able to

 

 

straighten the tower by. 1° after the success of the trial the committee decided to undertake the final underere excavation this time they attached 41 guide drills and went for the maximum penetration of 2 m a total of 38 M cubed of soil was removed in this process 69% of soil was from below the foundation the tower leaned towards the right direction consistently if the engineers wanted they could have made the tower perfectly straight but would you like a perfectly straight Tower of Pisa in order to preserve the tower's unique tourist

 

attracting feature the engineers kept a tilt of 3.9 7° after more than 10 years of renovation work the tower was finally open to tourists this is how the Leaning Tower of Pisa achieved the current angle we see today the water table on the North side was higher than that of the South some Engineers believe that this could cause complications in the future imagine what could happen during the winter months no more risks were to be taken they drilled three Wells on the North side and drained the water from the north Foundation to the Wells this

 

guaranteed that the North and South water tables are almost the same climbing the Leaning Tower of Pisa is a fun experience as you climb up because of the lean the steps feel steeper or shallower depending on where you are in relation to the Tilt it's quite disorienting but fascinating once you climb up 251 steps you reach the first viewing gallery from here you can enjoy spectacular views of the city nearby Hills and the Patza de miroli below don't forget to enjoy the beauty of the historic bells in the Bell

 

Chamber they are still functional and are rung on special occasions this is how you reach the very top of the tower the marshy soil around the tower may be a villain that caused the Tilt to the Tower but the same soil acted as a hero and saved the tower from at least three major earthquakes the 1846 earthquake was of high intensity the marshy soil around the tower acted as a buffer and saved the tower from failing this phenomenon is called Dynamic soil structure interaction a tower surrounded by a rigid environment would have failed

under the same seismic condition we learned in 2001 the engineers reduced the lean to an angle of 3.97 De and stopped their straightening operation surprisingly from 2001 to 2018 the tower reduced the angle on its own a self-correction a reduction of lean of 4 cm was noticed during this period however the engineers do not believe that the tower will be able to self-correct to 0° according to them this self-correction would settle down very soon now it's time to clear a major misconception regarding laning Tower of

Piza the misconception is that the soil below the tower was non uniform in nature more specifically the soy of the south side of the tower was weaker than that of the north side such situations will lead to a phenomenon called differential settlement this is a misconception we have all already seen that the water C below the north side was much higher than the the South Side as we have already studied the reason behind the lean of the tower was not defal settlement but the Leaning instability according to the analysis