In your case, I would simply add more break-lines to define the bottom face.

Using these lines I got this bottom surface:

The volume calculation then looked like this:

This result depends a bit on how we define the bottom surface with break-lines. For best results, we would ideally take a first measurement of the terrain with no material, and then take a second measurement when the material is present. Of course, this is not always possible. In this case, we then have to define the underside as well, if possible with broken lines and points that are still visible.