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Field/french drain in backyard

Hi, I've got a flat back yard at the bottom of a bank, the soil is mostly clay and it gets boggy and wet in winter. I am wanting to have it well draining so that I can plant trees along the back without them having wet feet. There is already a very slight ditch along the bottom of the bank, it looks like some might have had a go at fixing the drainage previously. I am interested in solutions any landscapers might have. I had considered a french drain might be the best approach. We are hoping to have it completed in April - May. Please see photos of back yard. The width of the yard from the shed to the fence is about 11.5 m. Access to the lawn is up some stairs from a driveway. Please get in touch if you are interested or need more information.