Brush the dirt away from the exposed root ends, and hip some glue over them. Supper glue, gorilla glue, even white glue. Its just something to keep moisture from coming out the cut ends to fast, which is what promotes cracking.
Personally, I can't get enough carving files, rasps and rifflers. I have ones big enough and coarse enough that they almost can be used as saws, and tiny diamond coated rasps for detail work.
If you don't want to spend a huge amount, Nicholson makes good rasps and files, some under $10. Stanley Subform blades are decent. But by the best you can afford. I had a Nicholson that I bought for around $8, and it is still usable after 30 years. I do have much better ones now, and I suppose that they will eventually belong to someone else after I'm not using them anymore. In the long run, they are cheaper and less of a mess than sand paper. I had one carbide rasp, very aggressive cutter, about 60 grit, and I used it a lot for at least 8 years before it dulled down. Wish I had bought a handful, as the line was discontinued and was on clearance.