Simple Question: What does the subcontract with the excavator say? What is the method of measurement & payment for the work? Is it based on a price per cubic meter? Or is he being paid for the labor, equipment & materials ("Time and Materials") used for the work?
I assume, by the fact that you are posting the question as you have, that the subcontractor is paid Time and Materials: If that's the case, I would argue that the owner is only responsible for paying for the time the actual work is being performed, known as Productive Time. He would be eligible to be paid for his time to get his machine to and from the jobsite. He would not be responsible for paying for Non-Productive Time, assuming he was on-site with his equipment and labor forces not performing any work.
As
Dnyan Deshmukh points out, documentation in cases like this are important. A simple form, like the one I'm attaching a link to, can provide a real-time summary account of what occurred and can be used to generate the costs basis for payment. We use these forms all the time to log and track extra work when it occurs requiring us to pay a Contractor for work that does not have a clear method of measurement or basis of payment. Hope this helps.
Cheers!!