This question contains two parts going in different directions.

The typical answer (the one supplied by most building codes) is 1/4″ per foot for drainage. The actual minimum slope for drainage is closer to 1/64″ per foot. At that slope gravity stops becoming the driving force behind water. Air movement, surface tension, and capillary flows start dominating water movement.

At what point does concrete become a slip hazard? This varies a great deal. Again, if we go by values supplied by code it gets placed at 6% slope (6′ per 100′). Actually, a lot of codes use roughly this slope to warn about a number of conditions.

Basically, water drainage we predict, slipperiness is dependent on specific conditions of you walking on the concrete.

I’m not sure these are the ”main” obstacles, but certainly major ones.

Supply.

A bridge or any infrastructure project would require many many many times more carbon fiber than other objects that use it. A single bridge would likely require the entire annual output or more just for the bridge due to volume alone.

The filler/matrix.

Carbon nanotubes are so long compared to their cross-section that they are considered to be a tension only material. To solve this they are placed/woven into resin, or plastic, or some other type of material. But, none of these materials come close to the strength of the carbon fiber especially when compared to the weight of the resin. So, in high strength applications you’re still looking at tension only applications.

Cost.

At the sheer scale of material involved you can’t even come close to how cheap steel and concrete are compared to carbon nanotubes. By volume, the cost is thousands of times more expensive to build with carbon nanotubes.

There are a number of other items I have heard brought up but I have less knowledge about:

Abrasion resistance – Either the nanotubes themselves or the matrix that holds them.

Fire resistance – I believe the concern is the matrix material degrading and no longer holding the nanotubes.

We seem like we have a long way to go on this material before it becomes a primary construction material.

First lets define a courtyard. A courtyard would be outdoor space enclosed sufficiently by a building or structures to create a clearly defined area. Sometimes it can be an indoor space that is treated as if it is an outdoor space.

An underground courtyard could imply two different versions, as I see things. First, a courtyard depressed into the ground, or secondly, an enclosed space below the plane of your ground floor.

For the first version it may not seem any different from a traditional courtyard. The edges would be defined by walls of the edge. They could be sloped or vertical, but an occupier of the space may never know they are underground unless the edges were quite tall compared to the other dimensions of the courtyard.

For the second version, it would be an indoor space being used as if it were outdoors. Unless handled well most occupiers would probably identify it as an atrium or greenhouse than a courtyard unless it was large and tall.

In most cases the size and depth of the spaces would have a huge impact on the difference. As would the access to sky/outside. Either way try to avoid the concept of being at the bottom of a hole. Unless that was the concept.

Hopefully this helped.

Architecture school pretty much revolves around a class called studio which you take each semester with a different topic. By design all other courses you take in architecture school feed directly into studio, or are best taken away from studio.

Studios can take nearly any form from lectures to field trips to 1000 page essays of assigned reading for the week. Regardless you are given a project that has something to do with the studio topic. This project will result in a formal presentation called a critique. Note that at no time have I mentioned design or buildings as they may or may not be part of your project. In a given studio semester you might have only one critique or you may have 15. You will scramble to setup materials for the critique typically with a fraction of the amount of time you feel the subject requires. At a minimum, you will need a custom built model with context and graphic drawings to describe what you’ve done. It is common that you’d also need a presentation panel of some kind, an audio/visual display or rendered illustrations (yes, these are all different). Written material is looked down upon unless it can all be displayed on a presentation panel.

As part of studio you are given a space usually called a cubical. It will have a table or desk, access to power, and some kind of controlled access like a classroom. A room could contain 4 cubicals or 60. You get access to this space 24/7, and they mean that. I regularly had professors who would pick a random day, even Sunday, at between 1 am and 3 am. If you were there working you got extra points or time with the professors. Likewise, if you weren’t there you might get minus points or lost time with the professor. It was common knowledge that if you didn’t spend at least one or two nights a week working through the night every week you were not likely to pass.

At this point, you get to stand up in front of everyone to give your presentation to the professors (there are typically two professors in studio), invited professors, invited professionals, and your fellow classmates. The professors and professionals get to ask you any questions they want about the project, even questions that go beyond the scope of the project at hand. You are expected to adapt and answer their questions fully. Keep in mind that every time the project was set up by the school so that you are up there with a partially completed project because they intentionally gave you insufficient time, you are likely very tired for the same reason. Lastly, most questions will not have correct answers. Much of these projects are about convincing persons, who know a great deal more than you on your subject, that you know what you’re doing, could succeed at completing it, and that they like the look of the results.

Many people freeze up in front of an audience. Your audience is allowed to interrupt you at any time. They can demand that you prove a point in the middle of your presentation. They can change the meaning of your subject which you now must apply your project towards. Professional architects are rather known for their egos which show up in full force during critiques. Again I’ll mention that you may not have slept in the last day or two during this. Hurtful comments, demands remove or change the project pieces on the spot are commonplace. Most students and graduates will admit to being brought to tears in frustration of a critique either in front of everyone or alone in their car.

The process is meant to be unfair and stacked against you. There are no right answers, but endless wrong answers. You need to figure out, on the fly, what your audience likes and dislikes so that you can steer them to the conclusion you want, or at least can accept. You will be called names, you will be humiliated, and they will change the rules on you.

This why architecture school is so hard. And once you go through that first critique only to be smashed. You work yourself to death to make sure they can’t do that to you again.

In some cases it adds to the binder material, but for most cases it acts as aggregate (same as the rock or gravel added to concrete).

In principle, you need a structural material (aggregate) and a binder (asphalt or cement). Rock is a plentiful strong material for aggregate, but broken up concrete, glass or plastics works as well.

I’m not seeing what the point of the low melting point metal would be unless your description is to use metal and plastic as some combination of aggregate and binder. If that is the case, then current materials will be far more economical.

That amount of water would probably heat up the mountain and wash away a fair portion of it.

If the water was slowly put on the mountain cold enough to be snow or ice it would continue to roll/slide down the mountain to melt at lower elevations. The height would not increase by much. Maybe 50 to a couple hundred feet.

If the water was somehow retained and frozen in place… The Capsian Sea is much larger in volume than Mount Everest, so let’s imagine three scenarios.

1. Very wide block of ice. The Caspian Sea is considered to contain 19,000 cubic miles of water, Everest is something like 5.5 miles high. As such a block of ice 5.5 miles high with the volume of the Caspian Sea would cover about 3,500 square miles.
2. Roughly cubic block of ice. Cube root of 19,000 puts us at about 26.7 miles on each side. That about 140,000 feet high. Commercial jets fly at about 30,000 feet. Most ice couldn’t take this configuration and would crumble.
3. Very tall block of ice. With this scenario, we could easily get to space which roughly starts at 82 miles up. This would still be 230 square miles across. Again this would likely quickly break up due to the stress imposed on the ice.

Most likely you are using a higher voltage on your circuit. You should be pulling the same number of volt-amps regardless.

There is a huge amount of research going into laminates and composites of various materials (structural).

Foamed homogenous materials (structural).

Sapphire as a structural material.

Various grown crystalline structures that behave like metals.

Glass as a structural material.

Memory metals that behave differently under various conditions like heat or electricity.

Strand bundled sections that change strength profiles as loading increases.

Solid materials that are lighter than air (insulation).

Materials that become more fire resistant as they are exposed to fire.

Materials that are opaque or reflective to certain frequencies of light (thermal barriers).

Phase changing materials (insulation).

These are just items off the top of my head. This can be a very long list.

Simple answer, yes.

Real answer, asphaltic binders come in quite a range of workable temperatures while your urethane pellets will likely work in a fairly narrow temperature range. Under lab conditions, this would be doable. If this were to be done in the field, you’d likely have a rocky road ice cream problem.