ls *.txt | xargs -t -n 1 -P10 -J % curl -u username:password -T % https://mywebdav.server/
This does the upload with 10 parallel cURL processes which can make uploading a large set of files much faster.
ls *.txt | xargs -t -n 1 -P10 -J % curl -u username:password -T % https://mywebdav.server/