How were the Pyramids built?
Just ask a civil engineer.
JUNE 30, 2023
Part 1. Background.
Introduction
Built around 2400 BCE the great pyramid of Giza was the tallest man-made structure in the world for the following 3400 years. Originally clad in polished white limestone it would have dazzled all who looked upon it, and was a fitting tomb for the Egyptian fourth dynasty pharaoh Khufu, for whom it was apparently built. (See Fig 1).
Fig 1. The Great Pyramid at Giza
You would think that in the intervening 4400 years we would have developed a definitive idea of how such a huge structure could have been built by a people who lacked the wheel and possessed only copper tools, but we’re still no nearer to answering the question in any practical way. It was after watching a documentary about the building of the great pyramid that it occurred to me that none of the programme’s experts had consulted with, or were themselves, a civil or structural engineer. (Which you would think is a key skill in building big things). Having pointed this out to my partner Heather, who is the in-house ancient Egypt enthusiast, she asked me how I would go about doing it.
“Leave it with me” I said.
That was 15 years ago, and in the intervening period I’ve kept a casual check on the latest research and theories. The problem is that, although many ideas look promising in theory, they fail when faced with the practicalities of construction. Now retired with time on my hands I thought it may be fun to take a look at the building of the great pyramid from a civil engineering perspective, applying my 40+ years of experience in planning, designing, and constructing large projects to the problem, and to see if I could develop a sensible and practical solution.
After approximately 12 months of studying the challenges presented, I’ve developed a method of construction which satisfies all the parameters, chief of which is the problem of handling a large number of huge stone blocks. I call it “The Rising Culvert” method.
The Great PyramId - A Brief Description.
Located approximately 7 kilometres west of Cairo the great pyramid stands on the northern edge of the Giza plateau, which it shares with two other large pyramid tombs, the Sphinx, and numerous smaller structures. What is seen today is the core structure, as the original facing blocks are missing. The great pyramid contains a number of internal chambers, passages and shafts, some of which were cut into the underlying bedrock. See Fig 2.
Fig 2. Section through the great pyramid.
Although today the river Nile lies 9 kilometres to the east of Giza, at the time of construction it was only 400 metres east of the great pyramid, and during the annual inundation the river would flood to a height sufficient to cover the Giza plateau up to the pyramid’s base.
It is very difficult to find a definitive set of dimensions for the great pyramid. Weathering, erosion and the absence of the original facing blocks make exact measurements difficult. Experts can’t even agree on the exact size of a royal cubit, the Egyptian unit of measurement in 2400 BCE. Currently, it is thought to be between 523mm and 530mm. With this in mind, here are some statistics;
Height = 280 royal cubits. (145 metres)
Plan size = 440 royal cubits on each side (230 metres)
Angle of the faces = 52 degrees.
Total volume = 2.56x106 m3
Construction:- Current Thinking.
It’s worth summarising the current construction narrative of the pyramid.
The great pyramid was constructed over a 30 year period using approximately 2.3 million blocks of stone each weighing between 2 and 70 tonnes. The core and support blocks were yellow, fossiliferous, limestone from local quarries at Giza. The polished limestone facing blocks originate from the quarries at Tura, 20 kilometres south east of Cairo. The granite blocks used in the various chambers were quarried at Aswan, 900 kilometres upstream from Cairo. All the blocks were quarried, shaped, and dressed using copper tools, dolerite hammers, and wooden mallets. Each block was then mounted on a timber sled and man-hauled up an inclined ramp before being placed. This ramp was extended as work progressed, with the core blocks being installed as the ramp ascended, and the facing blocks being installed as the ramp was dismantled.
This all sounds plausible and practical, and is a narrative rarely challenged. Even the current Egyptian Minister of Antiquities, Khaled al-Anani, (and his predecessor Zahi Hawass) see this as the answer. Unfortunately, it would appear that neither of these two gentlemen has given any consideration to the practicalities. Let’s take a look at just two elements of this theory; the number of blocks and the ramps.
I should point out here that any calculations stated are derived from documented evidence or, when this is absent, realistic assumptions based on my experience.
Counting Blocks.
Consider the estimate as to the number of blocks used in the great pyramid, currently 2.3 million. With a 30 year timeframe and working 12 hours per day, 365 days days per year, the Egyptians would have to quarry, shape, dress, transport and place one stone block approximately every 4 minutes. I’m not sure that even the Egyptian’s massive workforce could achieve this rate of construction, so either the block count is wrong or the timescale is incorrect. As there is documented evidence as to the timescale, the problem must lie with the block count.
The current paradigm is that the great pyramid is solid stone all the way through, but from a civil engineering perspective there’s isn’t any reason to make the pyramid solid. It wouldn’t serve any purpose, and would be a huge waste of time, effort and resources. All that is required is an outer ’shell’ of facing blocks with a couple of rows of ‘support’ blocks behind, with the resulting internal void filled using rubble and construction debris. I estimate that this construction method could reduce the block count to approximately 250,000. Working 12 hours a day, 365 days per year would result in a block being placed approximately every 30 minutes; still quick, but a more realistic rate of installation.
The Ramp.
The idea of using ramps to construct the great pyramid is one that is generally accepted by both academics and archaeologists alike, and there are currently a number of different suggestions, but only two are taken as seriously by the ‘experts’. The first is a ‘straight’ ramp, the second is a ‘wrap around’ ramp.
The ‘straight’ ramp would be huge. (See Fig 3)
Fig 3. The ‘straight’ ramp.
Taking a height of 145 metres, an gradient of 5 degrees, a ‘road’ width of 10 metres, and sides battered at 52 degrees (to match the pyramid sides), would result in a ramp which extended approximately 1.7 kilometres out from the top of the pyramid, with a volume of 9.6x106 m3. This is nearly four times the volume of the pyramid itself! It would consume considerable effort and materials, and would never fit the timeframe.
The ‘wrap around’ ramp is even more impractical than the ‘straight’ variety (see Fig 4), and it has two main problems. The first is, again, the size. With a 10 metre road width, and a maximum gradient of 5 degrees, the ‘wrap around’ ramp would be in the region of 1.8 kilometres long and contain 1.7x105 m3 of material. Not as huge as the ‘straight’ variety, but still a drain on effort and materials, not to mention the time required.
Fig 4. The ‘wrap around’ ramp.
The second problem is that there are areas of the pyramid face which the ‘wrap around’ ramp would not reach. Ascending would not be a problem, but descending means removing the ramp as you go. With reference to fig 5, it would not be possible to place the orange facing blocks for example, as either the ramp would be in the way or it would not allow access to these locations. Bear in mind that, not only are the higher blocks placed first (we are descending), but each block has to be slotted and coursed under the two above it, meaning that it has to be positioned underneath and lifted into position.
Fig 5. The ‘wrap around’ ramp does not give access to some areas
Neither could the blocks be placed when the ramp ‘wraps around’ once more, as it would be too low down the face to reach these areas. This is exacerbated by the fact that, as the ramp ascends the pyramid the height of each ‘lift’ is slightly less than the previous one because each ramp leg gets shorter. You can keep the ‘lift’ height but only by increasing the gradient. (Isn’t geometry wicked!).
The other ramp designs have problems so severe, that they are not worth considering, (one is a ‘wrap around’ type which is inside the pyramid!), and as I’ve demonstrated above the ‘straight’ and ‘wrap around’ types both suffer from serious shortcomings resulting in them both being impractical. Fortunately, my ‘Rising Culvert’ method does not require the construction of huge ramps. It does, however, require lots of water.
The Causeways.
Originally the great pyramid had a ‘causeway’ which extended from the its east face down to the valley temple located on the west bank of the Nile. It has been suggested that this ‘causeway’ would have been very similar to the one at Saqqara. See fig 6.
Fig 6. The causeway at Saqqara
In fact, all three pyramids on the Giza site have causeways leading down to the Nile, and current thinking is that these causeways were used for ceremonial purposes. However, studying the features in the photographs suggested to me a different purpose. For example, why sink the pavements when it would have been far easier and quicker to lay the paving over the top of the existing ground? Also, some of the walls are thicker at the bottom, and had been built to a greater height before being reduced to their current level. To a civil engineer this suggests that these had been retaining walls.When I consider the installation of paving to specific levels irrespective of the terrain and walls designed to be retaining it is obvious that this was a culvert for transporting and retaining water.
Water Supply.
My ‘Riser Culvert’ method of construction would require huge amounts of water independent of the Nile supply, and available at the top of the great pyramid. So where would this supply come from?
The river Nile’s annual inundation period runs from August to October, and before the Aswan dam was constructed, this inundation took the water level from a low of 20 metres above mean sea level (AMSL) to almost 60 metres AMSL. At its highest, the water level almost reaches the Giza plateau.
In addition, under the Sahara lies the Nubian Sandstone Aquifer System. The system has three major aquifers; strata of saturated sandstones and limestones that retain water like a sponge. The eastern most of these, extending over two million square kilometres, underlies all of Egypt west of the Nile, all of eastern Libya, and much of northern Chad and Sudan. It contains 375,000 cubic kilometres of water, which is the equivalent of 3750 years of Nile River flow.
If a well could be bored down through the upper layer to tap into this aquifer then the water in the well will rise up to a level known as the “potentiometric height”, which is equal to the highest level of water in the underlying aquifer. If the top of the well is above this level it is known as an “oasis”, of which there are many in the Sahara. If the top of the well is below this height it is known as an artesian well, and the water will exit from the well under the pressure created by the head of water in the aquifer. See Fig 7.
Fig 7. Typical Aquifer System.
There are a number of artesian wells on the Giza plateau, one of them within the footprint of the great pyramid. In 1856 the French hydrologist Henry Darcy published an equation which provided the flow rates for such artesian wells, and in 2010 Samuel R. Sampson and Michael N. Read developed the model further demonstrating that “the potentiometric height at the Giza Plateau was such that the natural artesian flow……had the potential to reach the topmost courses of the pyramid at about 200 meters (sic) AMSL”.An interesting aside; buried in the bedrock under the great pyramid is a subterranean chamber, which is approximately 30 metres below ground level. In the chamber’s floor there is a descending vertical shaft. It is filled with rubble to within approximately 5 metres of the top, but nobody is sure how deep it extends. If this was an artesian well it would have had sufficient water pressure to fill all the chambers and shafts throughout the great pyramid, making for an excellent water distribution system during construction. See fig 2.
Part 2 - Preperations
Temporary Works
Temporary works are any works built to facilitate the construction of the main structures. They are normally removed when the project is finished, but it’s often more expedient and/or cheaper to leave them in-situ, or re-task them.
Over the last 30 years the Ancient Egypt Research Associates (AERA) have carried out the The Giza Plateau Mapping Project, the purpose of which is “…..to create a high-precision map of the natural and cultural features at Giza to better understand the social and economic forces that supported pyramid construction.” They have developed a detailed and comprehensive map of the Giza plateau at the time of the great pyramid building. See Fig 8.
Fig 8.
The AERA survey has confirmed that there was a large complex of harbours, marinas, canals, and culverts at Giza built to support the building of the pyramids and temples. Along with the confirmation of a culvert running from the valley temple to the base of the great pyramid, this provides the infrastructure and temporary works needed to support my. “Rising Culvert” construction proposal.
Methods and Materials.
The Egyptians would have used those materials to hand and with which they had experience. These included granite, limestone, sandstone, water, timber, sand, rope, papyrus, animal skins, bentonite clay and gypsum. They were experts in the mass production of bricks and blocks, and in the quarrying, shaping and dressing of many kinds of rock and stone. They were also expert tunnellers and boat builders. They had access to copper and bronze tools, but they did not have the wheel (which was not introduced into Egypt until 1650 BCE).
In addition to the materials mentioned above, my “Rising Culvert” method would have required the following;
Mortar:
Made from gypsum, it could also be used as a lubricant to enable the blocks to slide more easily.
Flotation devices
In the British Museum there is a sculpted gypsum panel from 850 BCE depicting Assyrian soldiers swimming across a river whilst holding onto inflated animal skins to keep them afloat (See Fig 10), and animal skin flotation devices can still be seen in India. A flotation bag with a volume of 1m3 would displace 1m3 of water, which weighs 1000 kg. So a 1m3 capacity float can support 1 tonne. It would be relatively straightforward for the Egyptians to employ a number of animal skins of varying sizes to enable them to ‘float’ everything from small bricks to large stone blocks. Barges and flotation boxes could also be used. The floats would be bound to the cargo using ropes.
Waterproofing.
This would required in the ‘rising culvert’ and the perimeter construction channel to prevent the pressure forcing water through the joints. It could be made from Bentonite clay, or a type of mud-clay render could be applied and left to bake in the sun. Animal fats also make a decent waterproofing layer, and it may be that they used a combination of any of the materials.
Scaffolding.
A small amount of timber scaffolding would be required.
Bricks/blocks.
These would be made from Nile mud mixed with chopped up dried grass or straw. They would squeeze the mixture into brick shapes and leave them to dry in the sun.
Levers.
Used for easing the blocks into position, these would be made from a piece of wood similar to a brush handle and fitted with a flat stone wedge bound to the handle using rope. The wedge could not be made from copper or bronze as these would bend.
Lock gates.
My proposed construction method requires a system of lock gates at key locations to control the water levels. Although the majority of these could be made using timber, some doors would be under considerable hydrostatic pressure, which may make them difficult to move. In these locations, the doors could be made from a slab of stone, and raised and lowered using oxen aided by counterbalance weights. The design of the door seals could be such that it offered minimum contact area and would be lubricated using animal fats.
The final pieces of the jigsaw.
So now we’re ready to start construction of the great pyramid, but we need to install the final pieces required to carry out the most important task; lifting the stone blocks into position. This is the single, most important task in the entire undertaking, and is the one subject most hotly debated. Just how do you raise up and place 250,000 blocks of stone?
At the valley temple location on the Nile, a set of lock gates would be required at the entrance to the culvert. These would retain the water in the culvert at the correct level. At the top of the culvert a second set of lock gates would be constructed. See Fig 10. These would need to be substantial enough to resist considerable hydrostatic pressure.
Fig 10.
Finally, between the final culvert lock gate and the pyramid’s base, the builders would start to build the ‘rising culvert’.After quarrying, the larger stones would be dressed and finished, and fitted with sufficient flotation devices to make them buoyant. The smaller bricks would be loaded onto pallets and fitted with similar floats. All the blocks, regardless of size, would utilise the waterways, canals and locks to travel to Khufu’s marina. (See Fig 9). Here they would enter Khufu’s culvert and travel to the lock gates at the base of the ‘rising culvert’. For most of the year the difference in water level between the Nile and the base of the pyramid (approximately 40 metres) would require water from the artesian wells and the use of a series of locks in the culvert. The blocks arrival at the entrance to the ‘rising culvert’ would trigger the sequence of tasks described next.
Part 3 - How it Works
The Story of a Single Course
The following is a step-by-step account of how a single course of blocks is installed. The method is the same for all courses regardless of height above the ground. However, a slight variation would be required for the final few courses and the capstone. More on this later.
1. Temporary scaffolding is erected around the top of the rising culvert walls.
2. At the bottom of the rising culvert, the first lock door is opened and the bricks/blocks required for the next course in the rising culvert are pushed into the intermediate chamber.
3. The first lock door is closed and the second one opened, allowing the cargo to rise up the rising culvert.
4. On reaching the top of the rising culvert the bricks/blocks are used to raise the height of the rising culvert walls by a height equivalent to one pyramid block course.
5. The scaffolding is struck.
6. A high level culvert front wall is built to the same height as the rising culvert wall i.e one pyramid block course. The toe of the wall is positioned at the top edge of the previous course of facing blocks.
7. An inner wall is built to match the height of the front wall, forming the high level culvert around the perimeter of the pyramid. This and the rising culvert are then filled with water. A series of sluice gates in the high level culvert will be used to control the water.
11. The blocks required for the pyramid’s next course pass through the gates at the bottom of the rising culvert, float up the riser, and are floated into position using the high level culvert.
12. Once the blocks are in their approximate position the builders drain the water from the high level culvert, dropping the blocks on the floor, then remove the floats.
13. The front perimeter wall is removed, and the resulting debris used to fill the void behind the rear perimeter wall.
14. The blocks are eased into their final positions using levers, starting with the facing blocks. Wet mud would be used as a lubricant, and the masons would be on hand to prepare and finish the joints.
15. The rear wall is removed and the resulting debris used to fill the void behind the rear perimeter wall.
16. Repeat as required.
Topping out.
There will come a point towards the top of the pyramid where there is no need to build the rear high-level culvert wall; the entire area can have one perimeter wall and be flooded. Then we have the capstone to install, and here’s the real rub. Not only does it have to line up with the same setting out point as the perimeter wall i.e. the outside edge of the last course of blocks, but, according to current information, it’s big and heavy.
The capstone was a 3 metre high limestone pyramid, coated in gold. The angle of the sides would’ve matched that of the pyramid’s i.e. 52°. These figures give a base size of approximately 4.7 m for each side of the base, and produce a volume of approximately 22 m³. The density of limestone is approximately 2700 kg/m³, thus producing a capstone weight of 60 metric tons. To this figure needs to be added the weight of the gold finishes, but as we do not know the thickness of the coating, we need to make some educated guesses.
The total surface area of all four side of the capstone will be approximately 133m2 The gold coating would have been thick enough to allow inscriptions, so let’s assume it was 3mm thick. This gives a volume for the gold of 0.4m³, and with the density of gold being 19,320 kg/m³, the weight of the gold coating is 7,730 kg, or 7.73 metric tonnes. This gives a total capstone weight in the region of 68 tonnes.
Of course, the capstone does not need to be a single piece of stone; it could have been assembled from, for example, four individual pieces. Each piece would still be 17 tonnes, but the work to shape, coat, inscribe and install each piece would be much easier. However, whether it was one piece or four pieces, we still have the ‘problem’ of installation, this being that the capstone will cover the entire top surface area, making it impossible to place the perimeter wall on the toe of the previous course of blocks as per our current method. So how was it done?
The easiest way would be to raise the rising culvert walls up to the required height. (See Fig 11). Then scaffolding would be installed on the remaining three sides. The supports for this could have been slotted into the joints between blocks, similar to the modern process of fixing scaffolding members into inserts in brickwork.
Fig 11. Topping Out.
Next, sized and shaped stone slabs would have been installed on the scaffolding, providing not only a working platform, but an impervious floor. The perimeter wall would then be built up off the stone bases, and coursed into the rising culvert brickwork. The entire internal area would have the joints caulked and a waterproof lining applied. The area would then be flooded and the capstone floated into position.
Final Thoughts.
The method of placing the blocks in the great pyramid is the most important question in the entire undertaking, and until now all the currently proposed methods may work in theory, but they fail when subjected to the practicalities of actual construction.
There’s’ nothing about my ‘Rising Culvert’ method which cannot be done by people who use copper tools and do not have the wheel. It uses methods and materials which we know the Egyptians had access to, and were very good at. Ultimately, they were required to build some very tall brick walls, manage large quantities of water, and transport large, heavy items. This was all well within their capabilities.
So there you have it; We now not only know how the pyramids were built, but that the methods used were achievable.
But, as Mr Steve Jobs was fond of saying “There’s just one more thing………..”.
In researching this paper, I did come across an intriguing question. In the Serapeum, there are a number of granite boxes. Nothing remarkable you may think, and, at first glance, you would be correct. However, the degree of precision to which these boxes have been worked and finished is remarkable. In one box the underside of the lid and the inside wall of the box were found to be square, and not just on one side of the box but on both sides. (See Fig 12.).
Fig 12. The precision square shown was calibrated to .00005 inch
This requires that the inside walls would have to be parallel to one another along the vertical axis. Also, the top of the box would need to establish a plane that is square to the sides. The makers of these boxes not only created inside surfaces that were flat when measured vertically and horizontally, they also made sure that the surfaces were square and parallel to each other, with one surface, the top, having sides that are 5 feet and 10 feet apart from each other.All in all, this is a remarkable feat of precision engineering. After all, this is granite we’re talking about! So how did they do it?
I’ll get back to you!