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My ancient golden dragon has a lot of time, since he doesn't die of old age in my world, and a lot of magical constructs that will tirelessly built a defensive mountain chain for him.

This chain will act as defense as well as a testament of his might.
It consists of blocks stacked on each other.
There don't need to be any rooms in it apart from maybe some small guard garrisons near the top. Other than that it can be solid stone blocks and as wide as need be.

The wall will be 3000 km long.
Earthquakes shouldn't be taken into account, wind can be a factor.
Bricks should preferably be made from materials easily available.
As long as it is easy to gather other materials can be used, as long as it's nothing like aerogel. Better ones can be constructed trough magic but then the "reward"/"cost" trade-off should be high enough.
One construct would be able to carry 1000 kg (2200 pounds) to the top of the wall in each trip.

I would like to know the height available when One side is as close to vertical as possible and the other can be sloped or when both sides are sloped.

Presume that simple resources are no problem.
Builder constructs created over estimated time frame should be the biggest thing to consider.

Addressing similar question - How quickly can I form a mountain chain?
This is focused on natural formation, I'm focused on man (construct) made formation

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    $\begingroup$ Class A engineering bricks have a crush strength of 125N/mm², though that could go as low as 50N/mm² for lower spec bricks $\endgroup$ – Separatrix Jan 22 at 8:17
  • $\begingroup$ Welcome to worldbuilding. Are you asking about how quick or how tall the wall can be built? Please take the tour and visit the help center to learn more about our community and its standards. $\endgroup$ – L.Dutch Jan 22 at 8:24
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    $\begingroup$ Tallness is the main concern. $\endgroup$ – turoni Jan 22 at 8:38
  • $\begingroup$ Hi turoni! I'd recommend waiting at least 24 hours before accepting an answer, even if you think it's the perfect one. It's quite possible someone will surprise you, and if not you can always award that check mark later. $\endgroup$ – Dubukay Jan 22 at 9:47
  • $\begingroup$ Please use vertical or steep instead of straight. The vertical side is going to be a pain as it makes the centre of gravity lopsided, which will limit the height of your mountain. EDIT: I made the change above, please roll back if needed $\endgroup$ – nzaman Jan 22 at 11:38
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A quick Google search says that a high-quality brick will have a compressive strength of around 100 kg per square centimeter. A similarly quick Google search says those high-quality bricks have a density of around 0.002 kilograms per cubic centimeter. Simple math says that a brick wall 500 meters tall will be heavy enough to crush the bottom layer of bricks.

In practice, I suspect that imperfections in the bricklaying, a desire for safety margins, and similar factors will limit your mountain of bricks to around 250 meters in height. Still taller than the Great Pyramid.

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    $\begingroup$ Well, that's disappointing, thanks. $\endgroup$ – turoni Jan 22 at 9:06
  • $\begingroup$ It seems these numbers refer to a single brick. Won't surrounding the brick with more bricks on all sides (as done by building a wall) stabilize it and increase it's compressive strength? $\endgroup$ – Elmy Jan 22 at 9:20
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    $\begingroup$ @Elmy, no. Making the wall thicker will make it less likely to fall over, but it won't do anything about reducing the pressure on the bottom brick. $\endgroup$ – Mark Jan 22 at 9:23
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    $\begingroup$ Mark, what are you talking about? you can definitely spread the pressure of a brick onto the underlying bricks. This won't increase the compressive strenght but will lighten the load onto more bricks. $\endgroup$ – Borgh Jan 22 at 12:45
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    $\begingroup$ @Demigan Crushed brick will flow, a little like a liquid. Building higher and higher gives you a mountain, not a wall, and mountians have slopes, not vertical km-high sections. Now, what you can do it terrace the wall; have 300-m tall walls, then a set back, then 300-m tall walls, then a set back, then 300-m tall walls. The "top" of each wall would be higher than the ground behind it. Drainage becomes a problem, but from a distance it is a solid tall wall. $\endgroup$ – Yakk Jan 22 at 14:58
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My search for numbers to support any conclusion to this question that included wind factors led me down a rabbit hole of interesting science. I'll try to keep the following answer as clear and concise as I can.

I started with a basic question: What are the limits of a wall? After some finagling of my Google search terms, I found what must be the most authoritative source of engineering formulae I've ever had the (mis)fortune to try to understand. This report on the Strength of Masonry Walls Under Compressive and Transverse Loads was both an eye-opener and informative, but incredibly dense to the point I spent over an hour trying to understand the equations and what they were telling me. (I'd relate them here, but there's a simplification later, so you can peruse if you want.)

After seeing the term "cavity wall" in that report, I decided to do some digging on what kinds of walls were out there and what their limits were. That led me to a Study on Stress Performance and Free Brickwork Height Limit of Traditional Chinese Cavity Wall. This report indicated that traditional Chinese cavity walls could survive a 6.0-magnitude earthquake if they weren't more than 12.79 meters tall and they could survive a 20-meter-per-second wind if they weren't more than 7.5 meters tall. (Note: handy tool for calculating wind pressure.)

But what about other kinds of walls, like a solid wall? Back to the drawing board. Looking for the limits of a structure, in general, led me to this question on our sister site, Physics SE: How high can be tower or building? (sic) The OP's research led them to a simple equation:

$$ h = \dfrac{\sigma}{\rho g} $$

The OP did some additional research after asking the question, which produced another equation that for shapes other than a cylinder or cone, $\sigma$ is constrained by

$$ \sigma \geq \dfrac{\rho g V}{S} $$

where $\rho$ is the density of the structure, $g$ is acceleration due to gravity, $V$ is the volume of the structure, and $S$ is the surface area.

But wait, there's more! From comments on that question, I made my way over to this answer to a question about ice walls. There, the answerer indicated that

[t]he most heavily solicited cross section will be the one at the very bottom, which will be supporting a compressive pressure of $\rho h g$, where $\rho$ is the density of the ice, $h$ the height of the wall, and $g$ the acceleration of gravity.

Comparing that resulting value to the compressive strength of the material in question will indicate at which point the wall will fail. However, s/he also noted:

As an aside note, if you are willing to sacrifice perfectly vertical walls, having a wall with width growing as $A e^{by}$, where $y$ is vertical distance from the top of the wall, will have every cross section of it standing the exact same compressive pressure.

This would allow you to make the wall as high as you wanted.

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  • $\begingroup$ I'm not sure about your last paragraph. The OP specified that "The wall will be 3000 km long"; and presumably this wall is to be on a planet; so the width of the base is presumably limited to the hundreds or at most thousands of kilometers. (Not to mention the requirement that the materials be "easily available", which limits the total volume of the wall.) Unless the value of $b$ is much smaller than I expect, this will sharply limit the height. (Also, I believe that -- as Mark alludes to in a comment above -- that approach would require a shear strength far greater than bricks'.) $\endgroup$ – ruakh Jan 23 at 1:47
  • $\begingroup$ @ruakh I could argue that the OP wants the wall to be 3k km long, so its height is constrained by the OP's desires, but I understand your point. I think $b$ in this case refers to the size of the base, but I'm not sure; the other answer didn't clarify the equation. $\endgroup$ – Frostfyre Jan 23 at 12:56
  • $\begingroup$ I don't think $b$ can be the size of the base, because then the units would be wrong. (The exponent $by$ has to be dimensionless, so $b$ needs to have units of $\text{m}^{-1}$.) $\endgroup$ – ruakh Jan 23 at 21:31
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Even though the footing of the Monadnock Building in Chicago extends 11 feet into the street, the walls of its six foot thick base have sunk 20 inches. It's 197 feet tall.

The Monadnock's final height was calculated to be the highest economically viable for a load-bearing wall design, requiring walls 6 feet (1.8 m) thick at the bottom and 18 inches (46 cm) thick at the top. Greater height would have required walls of such thickness that they would have reduced the rentable space too greatly.

I don't know what the upper limit is, but if you keep it under 200 feet, you can still even go inside it. It is reinforced with wrought iron, but that's for wind loading because it's hollow.

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If you release the "one side has to be vertical" requirement and build a basically trapezoidal wall (a smooth wall with a 60 degree angle is bloody hard to climb) the weight of the top bricks will be better distributed over the lower bricks. If I take the number from mark's answer, the 500m height should be easy, replacing the safety margin with a slope.

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  • $\begingroup$ See comments on Mark's answer, addressing what you state in your answer $\endgroup$ – L.Dutch Jan 22 at 12:40
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    $\begingroup$ The comments are incorrect, you can definitely spread out the pressure of a brick onto the underlying bricks. See for example the walls on medieval cathedrals: massive on the bottom and as thin as possible on top. $\endgroup$ – Borgh Jan 22 at 12:43
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    $\begingroup$ Agreed. That's why there's a 200' tall building with 6 foot thick walls at the bottom, and 18" at the top... and why the previous record holder is shaped like a pyramid. $\endgroup$ – Mazura Jan 22 at 13:23
  • $\begingroup$ ... and why one of them is Bent Pyramid $\endgroup$ – Mazura Jan 23 at 3:52

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