Gap under patio slab
Any inorganic gravel or sand will do the job. The trick is packing it in tightly enough to eliminate all gap. As you can imagine, concrete doesn't flex, and any gap will eventually result in a crack and settling of the concrete.

Fill the gap by tamping horizontally with a piece of lumber or similar tool, and work your way out. A little bit of moisture might help compact things as you work. Once you have the void completely filled, landscape around the patio to retain the material you've installed. This is critical to long-term success.

You may need to hire a "mud jacking" company to inject concrete through the slab to fill the void where it's inaccessible. They'll drill small holes and patch them when they're done.