I've got my stone mages who can manipulate earth (let's define earth as silicon dioxide). They can form protective barriers, raise platforms for them to stand on, or lift entire boulders to lob at those who look at them funny. Now they do not conjure up earth out of nothing - they have to pull it up from the ground.
Some more details regarding the manipulation:
- At its core this is nothing but telekinesis. A stone mage can achieve anything a bulldozer can. But the mage has precision, they can control individual grains if necessary. Of course when picking up those grains, water and other impurities will go with it by virtue of sticking to the sand.
- Rocks are manipulated just as well as grains of sand (really just tiny rocks). There's a great deal of force behind the magic; any novice can expel 500 Newtons on a bad day, experts can briefly channel 200 kilo-Newtons. Force can generally be maintained for up to ten seconds, and there's also a limitation on how much force can be applied to a mass of rock (otherwise one could accelerate pebbles to relativistic speeds).
- Rocks can be turned into sand by essentially grinding them down; however this takes energy and there's usually enough sand around. Sand can be turned into rock, but only kinds of sedimentary rock that are created via pressure (and desiccation as pressure can push the water out).
- The range of the effect is 10 meters omnidirectional (regardless of line of sight), and 50 meters within line of sight. Of course you can throw something farther if it is given all required energy within the range.
That being said, simply lifting up soil vertically is not going to create a lasting barrier because there's a void below it, where the barrier was. It would fall right back down. So, my solution is that the earth they manipulate becomes "fluffy". There's a lot of air inside the barrier and in the sub-surface ground holding it up.
According to Banach and Tarski, this can be done without difference in properties. But we are dealing with discrete particles: the grains of sand making up the dirt being used. So this becomes a stacking problem. Using the fewest grains possible, construct a wall with sufficient compressive strength to hold a person and stop a projectile. Using too much earth would make the ground around one's magic activities too fluffy! Then we could have our fighters end up sinking in quicksand.
The strength requirement for the fluffy barrier is a value judgement, so I looked around for materials that are about as sturdy as what I imagine the barrier requires at a minimum. I landed on water ice; which according to Wikipedia has a compressive strength of 3 megapascals. That compares to 60 for sandstone and 7 for light bricks. Ice is also a fun comparison value given the broader context of the setting, which I'm afraid may not be mentioned by name.
So the question becomes; assuming a typical mound of earth to source from, and the magical manipulation of each individual grain (but no strength holding it up after the deed is done). How much earth, in weight, is required for a given volume of fluffy earth barrier to be as strong as water ice? In other words, what is the density of this barrier?
I understand if nobody has ever stacked grains of sand in perfect configurations and a lot of the knowledge is unknown. But I would still really appreciate an order-of-magnitude approximation, if it can be provided, so that I know whether my stone mages would need to worry about creating quicksand below their footing during an extended fight scene.
One other strategy, thanks to the contributions of AdrianColomitchi and PcMan in the comments, is to take as much soil as necessary from the ground (becoming fluffy in the process), and compress that into hard rock for your barrier. Again, only sedimentary rock is possible here.
So for the second version, one needs to know the ratio of the densities of the barrier and of (standard soil minus fluffy soil = removed earth) to get the picture of how much sand is required for a barrier.