Essentially, you want the intersection of the meshes. You may try duplicating the edge of the excavation mesh to get a curve that you can use to trim the exterior of the grade surface, then stitch the two meshes together to close the excavation mesh into a volume you can measure. I tried this quickly but the volume tool didn't like some inconsistencies in the grade surface mesh...to fix it would take a little time to manually clean up the holes/overlapping faces. The Mesh Audit tool will mark these faces. If the excavation mesh were closed and larger (extended above grade), you could try trim mesh or if both were closed elements you could just intersect meshes directly and avoid having to project the duplicated boundary curve. Maybe others here have a more direct route.
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Makai Smith
Director, MicroStation Product Line
Bentley Systems, Inc.