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Leaning Tower of Pisa | The Incredible Physics behind its Lean

To straighten the leaning tower of Pisa, the engineers came up with a brilliant solution in 1999 - under excavation. If the under excavation is not done correctly, a disaster is guaranteed. Here are the two cases of underexcavation. What do you think? Which one will save the tower? To answer this tricky question we should have a clear understanding about the tower’s foundation. Did you notice a strange structure called Catino around the foundation? Also some other strange things around the foundation? The support from the Catino in fact saved the tower from toppling. The foundation constructed for the tower was a mere 3-meter deep, which was too shallow for the loose and marshy soil of Pisa. When the construction reached 3 storeys, they had to stop the work due to war. During the period of inactivity, the building developed a lean - a lean due the phenomenon called ‘leaning instability’. 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. They resumed construction after almost 100 years. Unfortunately, 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 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-like 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 5 steps and the south side has 6 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 degrees. Did you know that the Leaning Tower of Pisa looked like this in the 1800s? The foundation was completely below ground. In 1838, the architect Alessandro Della Gherardesca took the initiative to dig out the ground and create a walkway called the Catino. He believed this would allow people to walk around and appreciate the intricacies of the architecture and observe the foundation's details. However, this excavation caused the tower to tilt by more than 0.25 degrees. Interestingly, according to many engineers, the Catino actually provided structural support against leaning. One significant improvement Della Gherardesca made was adding a 0.7 meter thick concrete ring beneath the Catino, possibly to reduce water inflow to the foundation. We will learn it later, once the ‘leaning instability’ starts, it will never stop. By 1934, the lean was around 4.5 degrees. Benito Mussolini, the dictator of Italy at the time, didn’t like this lean. He considered this imperfection an insult to Italian engineering. Mussolini 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 tonnes into the foundation. This is what Mussolini 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 degrees. In the coming years, the lean of the tower kept increasing, and in 1990, the lean reached a dangerous level of 5.5 degrees. The tower was closed to the public for the first time. The authorities removed the tower’s bells. 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 on the north side. This effort reduced the tilt by 1 by 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. Now, it’s time to learn about the phenomenon of ‘leaning instability’ - the phenomenon of which tilted the tower of Pisa. You might have observed this. On a soft ground, you can never build a tower more than a specific height. It doesn’t matter how straight you build it, the tower always fails after reaching a specific height. That too is 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 is 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. At a height of 56 meters, the tower has 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. The engineers came up with an innovative solution in 1995 - the liquid nitrogen method. This straightening method was such an elegant solution. The idea was to go 40 meters 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. Pisa’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 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 has 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 Burland, a geotechnical engineer and the leader of the leaning tower of Pisa’s 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. The engineers took their next steps with extra precaution. 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 under excavation, the engineers first experimented with it on a 7-meter 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 under excavation at the actual site. They removed soil only in 12 locations. They even attached a pair of steel stay 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 0.1 degrees. After the success of the first trial, the committee decided to undertake the final under excavation. This time, they attached 41 guide drills and went for the maximum penetration of 2 meters. A total of 38 m3 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 3.97 degrees. After more than 10 years of renovation work, the tower was finally open to the 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 believed 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 Piazza dei Miracoli 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 3 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 that 2001 the engineers reduced the lean to an angle of 3.97 degrees and stopped their straightening operation. Surprisingly from 2001 till 2018 the tower reduced angle by 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 zero degree. According to them this self correction would settle down very soon. Now, it’s time to clear a common misconception regarding the leaning tower of Pisa. The misconception is that the soil below the tower was nonuniform in nature. More specifically, the soil below the south side of the tower was weaker than that of the north side. Such situations lead to a phenomenon called differential settlement. This is a misconception. We have already seen that the water content below the north side was much higher than that of the south side. As we have already studied the reason behind the lean of the tower was not differential settlement, but the leaning instability. According to the analysis of Prof. John Burland, if the tower was shorter by a few meters, it would have leaned a little bit, but would have stabilized and stayed there forever. And if the tower was taller by a few meters, it would have collapsed many centuries ago. The current height of the Leaning tower of Pisa is just perfect enough to create this beautiful civil engineering phenomenon.
I hope you enjoyed this video.