Hi badger1992...welcome to wab
Question is a bit of a tricky one to answer here mate, your guess would probably be as good as ours. It all depends on where you are in the country and if the site is still being used. If its abandoned, then for how long and has the flora started to take hold. These sort of quarries are fairly hostile environments for many inverts, colonization can take a great length of time... How indepth are going to be, do you need to get to species level or doesn't it matter?
I have just started to take a look at an abandoned one near me, my first look at the site was late last year. I spent just under an 1hr looking about and found the species listed below. The ground is frozen there at the moment so i'm waiting for things to warm up before i start making regular visits.
Androniscus dentiger / Rosy woodlouse
Oniscus asellus / Common shiny woodlouse
Porcellio scaber / Common rough woodlouse
Trichoniscus cf. pusillus / Common pygmy woodlouse
Nebria brevicollis / Ground Beetle
Bembidion stephensii / Ground Beetle
Pterostichus madidus / Ground Beetle
Olisthopus rotundatus / Ground Beetle
Pyramidula rupestris / Rock Snail
Discus rotundatus / Rounded Snail
Oxychilus cellarius / Cellar Snail
Oxychilus alliarius / Garlic Snail
Candidula intersecta / Wrinkled Snail
Tachypodoiulus niger / White-legged Snake-millipede
Lithobius melanops / Centipede
Lithobius variegatus / Centipede
Coelotes atropos? / Spider (yet to be determined)
Megabunus diadema / Harvestman
Hopefully someone else can offer more insight to what i have...but do let us know how you get on. If you get stuck in identifying any, take a photo and post it on Wab, there are plenty of experts on here that will help you out.