So when we got my cat his first closed litter box and we would always hear this digging sound coming from it! we were sure he was just covering after himself but turned out he was scratching the walls of the box! till this day he still does this and he can go on for 10 minutes until we call him out! Now I've been searching for info about this behavior and only found info about cats pawing\scratching the air in their litter box, but he actually uses the walls to file his nails, I must mention he does not scratch anything else in the house, in fact he does not use his claws to attack either (people have asked me if he was de- clawed before!
)... non of my cats ever did this and I've never seen a cat do this so I don't know why he does this, it may be that's just where he likes to do it but it just seem's really odd to me ! did any of you ever hear of this or have a cat that does this? I've just always wondered..

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Another thing that occurs to me is the quality of the litter. Does it deal with the smell well enough? In the wild cats always bury their excrements so that other predators can't detect them so he may keep digging if he thinks there's still too much smell left...
By the way, does he do it only when pooping or both when peeing and pooping?
I did try an open litter box the problem is he thinks every open box shape item in the house is a litter box, so I had him pee in the trash can lid while I was cleaning and just pee in a box that he found so I try to avoid open boxes, although he did have one for a bit (he actually even had two for sometimes because we moved to a much bigger house so we wanted him to find them, but he would just pee in one and poo in the other) and he would scratch the walls there too...
he does not dig or even cover up anything he leaves it uncovered and just files his nails on the walls. I've never actually heard him digging in the sand it just sounded like that's what he was doing at first. as for the smell I did make a habit of peeking inside the box every time I visit the bathroom or just pass by and we have little diaper bags that are scented so we scoop after him every chance we get, and completely change the litter once every two weeks (we usually have to fill it up a bit before because its the clumping kind) and the actual plastic is clean because we use liners, so there's no smell absorbed in the plastic so I do keep it very clean for him.
I wonder if he just likes vertical space I am building him a cat tree with plenty of scratching posts but I honestly don't know if he would even use them though lol
It's good to hear that he's not the only one with that crazy habit !
he also has this real weird habit of dragging things to his litter box when something is bothering him or he just want's to make a statement, so when we moved to the new house he dragged all the bathroom carpets into his box (god knows how!!) and peed on them and when i went on vacation he took one of my little brothers socks placed it right in front of my bedroom door (it was closed) and pooped on it !
Barsik has another "ritual" to get our attention. He's toilet-trained, and every time he's finished his business he starts running around the rooms making as much noise as he can (this includes scratching the couch... he knows we won't stay calm when he's doing it, hehe). Now that he's older he's become less energetic but he had been doing that "Hey look at me, I peed!!" ritual for years.
Oh cats! You'll always find a key to your humans.