Hi Workshoppers,
Earlier I started the below thread on the same topic, but wanted to add a project diary to share my fix.
https://www.workshop.com.au/t5/Gardening/Suggestions-to-fix-a-muddy-lawn/m-p/12931/highlight/true#M1680
In the end it involved a little more than sticking a pitchfork into the lawn over and over, in an attempt to aerate. When the first pitchfork entry sunk effortlessly all the way down the forks without resistance I knew I had a bigger issue. New drainage and connection to existing grated drains meant this project was beyond me.
It was time to call in the experts - here are the photos
Photo 1 - The before shot. Muddy mess, drainage lines marked.

Photo 2 - drainage channels being dug out. Left end is shallow, right end is deeper - water will drain to an existing draining point

Photo 3 - Agi pipe with a filter sock laid into drainage channels

Photo 4 - Intersection of pipes as they lead around to the existing drainage pit

Photo 5 - Agi pipe / filter sock shallow end

Photo 6 - with agi pipe laid, drainage gravel poured into the channels and top soil spread across the top.

Photo 7 - freshly laid turf and the finished product. We decided to lay turf above existing ground level so that the grass level was flush with edge of patio.
Previously the patio floor sat about two inches higher than the grass.
Kids now pace back and forward on the patio trying to work out how to get to the trampoline! 😂
