From what I can see in the pics it seems like good non-expansive soil. There seems to be enough clay to bind it well when compacted. There is way to much to use a plate compactor. I would employ some one with road compaction equipment to do this or just rent the equipment. As dry as the soil is water is going to have to be applied for proper compaction. The use of steel at today's prices may be cost prohibitive. Fiber Mesh should do you a good job if expansion joints are used. I also feel that beams would not be necessary.(Assuming heavy equipment will not be used on top of it.) Again, you may want to talk to a post tension company in your area and get a price to compare with. (If there is one)
How do you intend to address the side walls? When the bunk is full there should be no problem. When it is not you may get some cave inns especially where there is a lot of gravel in the foreground of the pic. A very good positive slope away from to bunker for drainage will help. Even better if you can compact it too.
You mentioned that when it rains it is usually very heavy. Going back to the pic., showing the gravel in the foreground, it comes close to the surface with a small layer at the top. When the rains come this will act as a drain so to speak allowing water to travel down and for an underground spring, thus putting water into your silo. Not good and should be addressed. This may be to technical, sorry. But I think it should be sealed if it was me building it. I would dig it out a compact clay into it.
As an added note, not only for you but other that may be reading this, concrete is not poured it is placed. Most subcontracted concrete want to water down the concrete so it will flow. This make there job easier but also make for weaker concrete. Concrete should be placed with not more than a 5" slump. Again this may be technical but it is important. Google up slump on concrete.
I am not a design engineer and my recommendations are only an opinion.
For any of you that think that I am going overboard on this, I would like you to consider this. As cattlemen we are all concerned with longevity of our cattle that may produce for 20 or so years if we are lucky. So why shouldn't we be just as concerned about concrete which should last 20 or more lifetimes, wither it be a sidewalk, driveway silo floor, or multi story building. If you don't think so I would like you to meet my friend, Mr. Jackhammer.