How often is a house packed into a tight neighborhood on a hill? How do you shift a mere yard of top dirt onto your urban back yard? I'll tell you how, unfortunately, you carry it in buckets. At least as far as I was concerned last year.
So why can't you pump it through a large flexible tube?
The tube could have an interior and exterior portion, the exterior being a sleeve in which the interior portion rotates. The rotation would have an inward facing screw-conveyor which drives the material along through the tube.
I think the tube should come in sections that snap together and there would have to be some sort of bearings that allow the inner driving tube to spin at relatively high speds to propel the aggregate through it.
As far as I am aware the only flexible tub conveyors in use are those in the grain and cereal industries and are no more than 15' long or so. I'm fairly sure that there are feasible designs providing the system could be powered from one end.
For instance you could have a motor on one end that spins the inner tubing from one end and is fitted with a hopper for loading the material. Or, possibly there could be a hydrolic motor at every junction allong the tubing that propels the thing so that the work is evenly distributed.
If anyone wants to fund this, say so, I'm always eager to actually test out an idea.
Addendum: I am aware of several pumps which require the material to be in a slurry(wet like mud, or concrete). I am also aware of systems that blow materials, (although, I wasn't aware small gravel is included). I still think a "screw-tunnel" is a markedly different concept.