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I may be using the wrong term then, it's essentially a big, open, concrete lined stream.
Gardens go right up to the edge.
Fairly comfortable with digging down, installing a retaining wall then back filling. My main concerns are A) what kind of wall? Will concrete posts and gravel boards work? B) I'll have to be careful not to undermine my neighbours fence. There's a small tree that might have to go and removing that could fuck their fence/retaining wall.
Edit: open culverts exist
Does your garden go all the way to the edge of the channel or is some of the land at the side owned by the council (or whoever)?
And doesn't a culvert run under something rather than being open?