DivineHeretic
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Your final understanding is fairly correct. Your analogy, unfortunately, is not. Your have to consider Force due to buoyancy as well in case of water.Ok, I will try to put it in simple way, if I'm right.. and please feel free to correct me if needed.
You can make afloat a needle(thin ones used for sewing cloths) on water surface due to water surface tension(imagine surface tension like very very thin strings covering the water surface, similar to badminton racket). one can easily experiment it at home, put a tissue paper in water and at top of it a needle. In a few seconds the tissue will go under water once it gets wet, but the needle will keep floating, due to tension of water surface. But when you try to put a similar shaped but bigger and heavy needle it will go under the water, even if it is made of same material & the design is same(meaning same pressure on surface), as that tension(imaginary strings) can no longer take the weight.
In case of ground each different layers(soil character varies as you go deeper, even by a few inches), acts similar to water surface tension, and hence once the weight of a vehicle reaches a critical stage it will sink irrespective of its ground pressure.
If you wish to get a basic idea of soils under load, check this thread out.
http://defenceforumindia.com/forum/members-corner/56139-suitablity-soils-vehicle-movement.html
Lets keep this thread on Arjun only.