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Living with two cats and ALWAYS having about a foot radius of catlitter outside the box...I understand the irritation.
The reason for observing is to truly determine behavior vs. problem. Many times cats that are having excessive straining in urinating (bladder infection) or defecating (constipation/diarrhea) they spend lots of time digging...
I imagine it is in efforts to make things work better...so they strain and then dig some more.
Let me know...
Maybe you need a hidden litterbox cam...to see if it is the cat...or someone/thing else in the house...dog? kid?