Stone or dirt can be placed along new or existing asphalt to create a sound and stable berm.  A berm will allow better drainage and support the edges of the asphalt in most cases.  This will also keep water from pooling right next to the asphalt, which can cause the stone base to soften and allows for premature failure.

Before DirtAsphalt MaintainerPlaced DirtBerm with Grass

Existing driveway that was bermed with dirt.                 (Click on pictures to enlarge)