Creeks and culverts are a very tricky situation. You run into several problems. First, if determining how big it needs to be. This is determined by the worse case scenerio. Do not make the mistake of figureing what it will handle during a heavy rain, that's not nearly enough. Remember this, the experts, cities, highway departments have years and years of experience at this, and they are always replacing washed out culverts.
You don't need rock around our culvert. Clean dirt or sand works great. The idea is to get is compacted evenly on both sides. Compaction is what gives teh culvert it's strenghth. What you need to protect your fill material and keep your culvert in place is a headwall. That can be built up of lots of rock that't too big to wash away during a heavey storm, or sacks of concrete stacked on each other, or concrete poured into a solid wall. If water can get past the pipe, it will wash out your culvert. Since it never stops trying, 24/7, it will succeed unless you do it right.
The other option is a wet crossing, or a combination of a smaller culvert with a wet crossing on top of it. If you put in a small culvert that will handle the day to day water flow, then pour concrete along the sides and top so that water can flow over it when you have heavy rains, that wold also work. It's not as simple as it sounds because the water will eat out all the supporting material around the concrete over the years unless you dig down your footings really deep. I've never done this, but have seen it done on others ranches. Some have failed because they cut a corner, others are working just fine. You just have to realize that on heavy rains, you cannot cross the creek.
Buy the next larger culvert then you will ever need and pray that you are right. Whatever it costs, it's cheaper then having to redo it again.
Eddie