We inherited a house and the basement leaks profusely. It has a half basement and when we crawled under the main floor to check things out the back of the half basement foundation was left open with a moat like trench instead of being filled with soil. The trench has a sump pump that does not keep up with the amount of water entering during the recent big rain we had and large amounts of water were in the trench which then leaked into the basement. Should we fill in around the back of the basment wall or get a bigger pump or is there another solution.

Sounds like the trench is there to carry water to the sump pump. Is the trench just a ditch dug in the soil or has it been lined with something, like concrete. The average sump pump can move quite a bit of water if it doesn't have to pump it too high. If it couldn't keep the water pumped out you may have to install an additional one. Don't fill in the trench. Look at gutters and down spouts to insure that they are clear and functioning. Look at grading to make sure water runs away from the house. Consider piping down spouts to carry water away form the house.

I would do as Harold suggests. There must be a problem with your grading for this to be happening. I'll bet Harold's last sentence says it all. You mention a moat, a sump pump but did not mention a sump pump pit. If this pump is not in a pit its efficiency is cut way down. Is there a pit, if so how high does the water get befire the pump float kicks in?

The trench is just a ditch, not lined with anything. There are no gutters but we're getting them installed soon. Thank you for your help... with this info and the gutters hopefully we can get things dried out.

When you get gutters you'll get down spouts, they need to be connected to horizontal discharge tubes to carry the water about 5' from the foundation. I think you will see a big improvement.