Path with teenagers instead of grass.

How do I grow grass here?
There is a path on my property just outside my fence used by teenagers walking to highschool in one direction and JHS in the other. It's only about 30 feet long.
For 22 years that I have been here, the path alternated between periods of grass and periods of mud. As the kids got older and fewer still went to elementary school, more of them walked on this path and the grass situation got worse and worse.
Last fall I covered all the ungrassy areas and a bit of the grassy area with sod. It looked beautiful for weeks, until the snow. The kids continued to walk on it when it was covered with snow, so if there was a muddy period then, I don't know.
When spring came 95% of the grass in the sodded area was gone and there was less grass total then ever, THAN EVER! Much less than before I started last fall. My neighbor on the other side of the path thinks that it was caused by foot traffic, and that few if any times did any of them ride a bicycle over the area (for one thing, because they weren't riding bikes in the winter or in the snow to begin with.) And there were no tire tracks in the soft dirt.
What can I do to get grass to stick? School will be over soon, and it is very quiet in the summer. A couple kids a day. It was about 4 to 6 kids a day last fall, but when they noticed that it was no longer a slurpy mudpath, more kids started using this shortcut up to maybe 15 or 20 round trips per day.
The ground will be soaking wet for days after a heavy rain, even though it slopes downhill. Is this because of the heavy clay content in the soil?, because there is heavy clay content (Unless I am totally mixed up.) Is there any way I can get the earth to drain and dry more quickly, because their walking on it one day when it is wet, I don't think does that much damage. Four days in a row, wet from one rainstorm, does a lot of damage.
The foot of the path is at the edge of a small hill where I could vent a drain, if there were an easy way to lay an effective drain.
I don't want to do a lot of work, but there is a small chance I may be renting an excavator (like a small back hoe) this summer anyhow. Is there a way to scrape up the top 6 inches, mix them with something that will fix things, and spread the six inches out again.
Meirman -- If emailing, please let me know whether or not you are posting the same letter. Change domain to erols.com, if necessary.
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I used to endlessly read landscaping books, and although various authors have assorted opinions on plants and flowers, they all agree on one thing: Put pathways where people walk, not where you think they should be. If I were you, I'd take the cheapest route: Cover the pathways with shredded mulch, either hardwood or cedar. Cedar will last longer. Chunks get blown around on windy days, or flung by bike wheels and foot traffic. Shredded mulch tends to mat down more coherently, and stay put.
I'm seeing this done in quite a few parks here, probably because the towns have an endless supply of mulch from cutting down damaged trees after winter. You could use stones, but if kids are riding bikes on the path, the stones will be flung onto the grass, and the mower will fling them around. Might be harmless, but I just don't like that sound under my mower. If mulch gets moved, you just grab a rake.
Here (Rochester NY), the local garden center is selling 3 cubic foot bags of Canadian cedar or hardwood mulch for about $4.00. Each bag covers about a 5x10 foot area of my garden beds. Find a garden center where you can actually speak to the owner or manager, and see if you can make a deal for LOTS of bags.
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I like the idea of going ahead and making a path.
Some city landfills offer low-grade mulch free for the taking. You might check into that where you live too.
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need to be careful about free mulch like that. the free mulch that was available at wheaton plaza near where i used to live was a free ticket to having your house infested with roaches.
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Here in Central Florida our nurseries will sell cypress or other mulch in bulk, and deliver it as well. I have bought three yards at a time, before I worked out something with a local arborist. What I have done is make a deal with a local tree trimming firm, which uses a chipper when downing trees. Instead of taking their chippings to the land fill, for which they have to pay, they drop the chips off on my lot, and I share the mulch with neighbors. I also have a friend who is an extension agent (with a very large garden on several acres) who deals with the electric company. When they trim trees along the right-of-way they bring the chips to his property and he uses them in his garden. He gets about a truckload a week or so, and keeps the mulch in his garden beds at about 12" deep, even in his citrus grove. The plants respond vigorously, and he has no weed problems.
In Palm Beach County, the best profesional arborist company there dumps his wood chips on space he owns, free to anyone who wants to pick it up. Palm Beach County also operates a recycling compost facility which combines wood chips and treated sewage into compost that is available to any PBC resident for free pickup. I know that some northern areas (Arlington, VA, used to) have compost/mulch facilities to recycle wood material. You may want to check with your city or county, or the extension service to find out what's available, and local nurseries for bulk delivery.
If you're able to make a deal with a local arborist, make sure the tree trimmers know you want brown wood chips, not a lot of green leafy stuff, and no palm trees.

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