I have accepted a PhD offer a month ago, and have since decided not to go ahead with it. I feel terrible about accepting it in the first place, but at the time I was convinced it was the right project for me. Will I get into alot of trouble if I decline this acceptance and accept another at a different institution?

i know that your situation is a little bit tough, but if you really think it is better for you to not to accept the offer, just tell them and give them your reason. i think every institution has this kind of experience, and they will understand. Keep in mind that you are not the only and the first person to do so, and it is very common. So do not feel too humiliated if you want to refuse an offer

The people your about to turn down will probably be annoyed, but it's unlikely to be the first time it's happened to them and it won't be the last. You're not going to be in trouble and they'll get over it. The important thing is that you are honest with them and let them know as quickly as possible about your decision, so that they can re-advertise the position.