Easiest fix for this problem?
1. Remove the old damage fence boards. Easiest to do a whole section at once.
2. Remove excess dirt and earth from the fence line. Earth movement caused by water can be a challenge. You will often need to remove dirt and re-slope the yard to provide a relief gap under the fence.
3. Measure and cut replacement boards. Plan for about an inch gap under the fence. By leaving the gap you will help prevent future water damage to the wood. This will help avoid premature rot of the replacement boards.
Brian Jovag, owner of Jovag Home Inspection.