Is it a mac by any chance? There seems to be a few problems with this on macs(and occasionally Toshibas according to EA). There's a couple of help guides with stuff you can try: https://help.ea.com/article/the-sims-3-disc-authorization-failure-workaround & https://help.ea.com/article/what-steps-can-i-take-to-attempt-to-correct-a-disc-authentication-error
Changing nothing and just repeatedly trying to load the game has worked for some people, but I can imagine that gets annoying after a while. I'd do a clean install(no mods or downloads or anything), check you have all the latest updates and uninstall & redownload origin then install that again as well(the origin client seems to be a delicate flower and is easily upset, imho).
Oh and if it's not a mac, register your games on the sims 3 site and then you should be able to download them through the origin client and play them that way(it treats it as a digital copy of the game then, so it shouldn't give disc errors, I'm thinking). Sadly, EA doesn't have a digital version for mac users, so this will only work if you're using windows(if you have a windows partition, you could try this method on there, even using the discs with your windows partition might work better as EA's "mac version" of the sims is just a windows emulation of sorts).
If all else fails, you could always contact customer service here: https://help.ea.com/contactus :B
