*rubs chin*
8" double wall culvert, 55 gallon drum. and good size strong piece of grate. that will fit a few inches on all sides over 55 gallon drum top.
prefer double wall vs single wall culvert, due to double wall culvert has a nice smooth inside, and less chance of sticks and other muck getting stuck inside of the culvert.
if you can burry the culvert 1 foot or deeper so when done there is a foot or more of dirt over culvert, you should be ok, when you drive over the top of it.
the 55 gallon drum. cut hole in lower side of drum to side culvert part way into. cut the top out of 55 gallon drum ((top out, not cut the top off. leave 1 to 2 inches around the edge, this adds a lot of extra strength to the drum so it does not cave in on itself))
drill some holes in bottom of drum. ((this is to make it so, drum will not act like a boat and come up and out of the ground on you))
drill some holes around side of drum. this will allow water to soak into the drum. ((all holes say 1/4" size))
get yourself some spray foam "closed cell type" (example "great stuff, in red can") and spray in between culvert and drum. and let it cure for a couple days. this will give you a descent seal. with some flexing.
put say 6" of gravel below drum, and 1 foot or so wide around drum. ((drainage rock, crushed rock, something to allow water to soak into drum))
at the very top pour concrete say 8" thick 1 foot or side wide all way around drum. ((top of concrete should be level with lowest spot of area))
place a good size / strength grating over top of 55 gallon drum / concrete. so if you drive over spot you do not fall into it. also make sure grating has small enough holes. so no child or animal can fall down into drum. might suggest anchoring the grating down with "concrete anchors and some bolts"
the goal of above, would be like having a bath tub drain. were all water for area runs down into. and exits out into the creek. and there would be no ditches, or ravens, or major wash outs happening. or you could look at it like an "overflow" on a pond or lake. but in this case, you are not wanting any water.
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you can do the french drain setup as your diagram posted as well.
or just do a standard culvert, like a culvert underneath a driveway. but between creek and low spot. and just have a larger hole at end of culvert in low spot you will have to watch out for.
if you are not planning on lake / pond. i would say just re-slope / grade the entire area first. and if having mush areas. i might suggest running a french drain / field tile up near bottom of hill sides. so the french drain / field tiles run parallel to the hill side, so water coming down hills hits the french drain / tiles and then every so often run a pipe from french drain down to creek. so the water hits the french drains first. vs water running across flat areas of land.
multi ways of going about it. no wrong or right way. perhaps one would work better for you than another.