Advice regarding hutch dampness

I have two bunnies housed outside. The enclosure is fairly big, and is covered with two tarpaulins for protection from the weather. It has no bottom so is placed directly on the ground( is an Omlet hutch). It is constantly damp. I have just placed barley hay on the front part, but am concerned this will get constantly messy, and due to the size of the hutch it is hard to place this everywhere. Looking for ideas for this situation. Housing inside is not an option.
Thanks

Photos of your setup may help

If you are having issues with the area being consistently damp, then it's a good idea to try to address it. Your climate, it seems, isn't helping the situation. It would be a good idea to consider some modifications or changes to your setup.

Having some hardscape in their area could help somewhat. This could be pavers or bricks to provide a non-grassy (ie. hopefully drier) area for them to be on. I'd also consider enlarging their area and raising their "roof." The way it is now-- so low to the ground -- the moisture is just getting trapped in there. A larger area with a solid roof but with airy sides would allow the moisture to escape. You can see some examples of such outdoor housing at the following thread on this forum:
https://www.rabbitsonline.net/threads/outdoor-cages-post-your-photo.96732/

I remembered another video of an outdoor setup in a rainy climate. This is a video tour of her setup which might get you thinking outside the box (so to speak) for ways to provide a dry home for your rabbits.