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Some Fibermesh brand fiber is considered wire replacement, but not rebar replacement. It will help control the cracking, but for actual strength you need rebar. They have some metal fibers that can be spec'd for rebar replacment in some applications, but the cost per yard is significant.
My only issue with traditional fiber mesh is the appearance. A company called buckeye makes a smaller mesh that can not be visually detected and seems to work well. Technically it is not considered a wire replacement, but we had a lot of happy customers use it. Especially decorative applications.
If you have alot of clay, that means it will expand and contract as it loses and takes on moisture. 4" with #4 rebar both ways @16" on center is good, but you probably want to make sure it will remain ridgid when the soil moves. It would probably be best to go with a deeper slab along the tire path and even thicker where the wheels and jacks will be sitting, like 6" or 8". You could even add another row of rebar along these areas. Do compact the area under the slab with road base to give it a good hard surface sit on. And like everyone has been saying, don't let the guys push the rebar down to the bottom of the concrete. Before they place the concrete everything should look nice and neat. Not like a mess of steel placed wherever they feel like it. I have done parking garages with 6" slabs and 5000# concrete, so don't worry about it too much, you could go with 3000# concrete and I think you'd be fine. Seal it to waterproof it and you're good to go.
Rezvani's Latest Post-Apocalyptic Monster Is a Ford F-150 Raptor Underneath
Slideshow: Called the Fortress, the 850-horsepower pickup combines Raptor underpinnings with military-inspired features, survival equipment, and a starting price of $285,000.