Hi Bobert89!
I'm no landscaping expert, but I have clay soil. (Plus, we have many maple trees, so leveling the ground lasts one year at most.) Water would remain for days after a normal rain and snow melt would remain until June. One area stayed under water nearly all year.
Here are some things that worked for me:
Trench-And-Pipe method
Basically a trench with drainage material in it and piping leading to an area with drainage material.
Big-Pit Method.
Basically a pit with drainage material. Water goes to the pit and can take its time seeping into the soil
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Details of how I did these are below:
Trench-
A) Dug trench about 8" wide x 18" deep from center of permanently wet area to a location suitable for water (back of yard). The trench pitches that way at about 1/16" per foot.
B) Lined the bottom & sides of the trench with polyester fabric. Cost came to 1 U.S. cent foot square at fabric store's close out pile. It lasts longer than landscape fabric.
C) Put slag sand in the bottom of the trench to about 3" deep.
I picked slag because is it a scrap product. No earth mining or stripping is used to get it.
D) Laid perforated Schedule 30 PVC pipes in the bottom of the trench. Didn't glue them together, just shoved a pipe into the belled end. I put the perforations at the 5 and 7 o'clock positions. (Facing down at an angle)
E) At the end of the trench, dug a larger diameter hole- Perhaps 24" diameter & 2 feet deep.
F) Lined the hole with dry stacked old concrete bricks & cinder blocks. (A scrap product)
G) Filled the hole with broken concrete. (A scrap product)
H) Made a "lid" for the hole out of a 1/4" thick steel plate & made sure it was about 4-6 " under final grade level (because it's ugly) Ground-Contact plywood would work & be much cheaper, but it isn't earth-friendly. The copper that leaches will kill insects & bacteria that live in the soil.
I) Wrapped the pipe with the fabric that is in the bottom of the trench. (Also made are "socks" for over the pipe instead)
J) Poured about 8" of small stone into the hole, over the pipe. I used crushed concrete & slag for the stone. The pieces range from about 1/2" diameter to 1". No jagged edges.
K) Laid fabric over the new stone layer
L) Filled the trench with what came out, then some top soil.
How Is It Working Out?
It surely solved the problem in that area. Water never pools and snow melt & ground freeze melt drain away.
Bad Aspect-
It is Not very environmentally friendly since PVC and Polyester are involved. Clay tiles might have been wiser, but $$$
Maybe I could have simply filled the hole with gravel instead of pipe.
Worse Way-
Made are long "socks" of polyester that are filled with foam peanuts. They are used instead of pipe. I can't think of any less earth-friendly way of building drainage. (I'd love to see a Styrofoam Nuisance Tax imposed- not that I'm Mister Innocent with my PVC pipe and polyester fabric.)
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In Another Area-
A 40 x 12 foot permanent puddle area lived all year at the back of the yard because the neighbor's yard dumps into my yard & we have clay soil.
The Fix-
I dug about 3 feet deep and 2 or so feet wider than the puddle.
I added about 2 feet deep of crushed concrete. Next, I laid polyester fabric. Then, back-filled.
How Is It Working Out?
Reasonably well. At ground thaw time of year, it does not drain quickly, but it's no longer permanently a puddle
Bad Aspect
Apparently either I didn't dig deep enough or I made the crush too tall. Some concrete chunks float up to the surface each spring.
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Combating Clay Soil-
I mix clay and sand or clay and slag sand to make garden soil.
On line one will read stuff like "clay and sand makes a brick". It doesn't. It makes nice, crumbly soil that things like to grow in. Worms love it, too.
One will also read that nothing grows in slag sand. That's wrong. I have a bit of a slag pile left from a project. Every year, I plant my extra seedlings- herbs, vegetables, etc. Everything* grows like crazy! Maple trees pop up, too. (*Never tried a root crop such as potatoes or carrots in slag sand.)
I hope a solution comes for your water challenges!
Paul