Thx to all,
This is what I have done:
cp backint.log backint.log_19.01.2016
cat /dev/null > backint.log
The file will get empty and after starting a backup, the file will be re-used.
Now, I will create a script, to perform this operation, automatically, so that the file does not became more than 50 GB big.
No problem so far :-)
cheers