I am currently attempting to remove a bunch of dead grass in a roughly 5'x5' plot. When the grass fully grows sometime in early-to-mid summer, they are like very small, long-grassed shrubs, sort of like this but smaller and closer to the ground. It basically covers the area in numerous bunches.
The area also has a lot of of weeds - some sort of thistle, I think - which I also would like to remove.
I tried doing it by hand but it took a lot of effort to remove the sod, particularly because the roots are thicker than the average lawn grass root and because they extend around 4"-6" into the soil.
I was wondering what the best method would be to go about doing this. I was thinking about renting a soil tiller to rip up the roots, since I have another clear plot on which I plan on using. If I do it this way, should I remove all the weeds first before tilling or can I rake them out after the roots are pulled up? (The weeds have just emerged and will not go to seed soon.)
Additionally, if I should remove the roots by continuing to use a grub hoe, how can I loosen the sod of its soil so that only the roots remain? I'd like to leave as much matter in the area as possible. I also noticed the roots had nodules, which I assume are for nitrogen fixation. Is there any way to take advantage of that, perhaps leaving them in the dirt to decompose?
Or should I just smother the area with tarp/cardboard/newspaper/mulch and make a "lasagna garden"?
Pictures for clarity: Section that I've already removed, with the suggested tool; removed sod; roots; close up of roots with nodules.