Do retaining walls require a planning permit?

Yes, it's still a wall/fence. It fits into the same category, as defined by the Richmond Municipal Code Definitions Section:

Fence-Related Terms:

  • Fence. A horizontal or vertical barrier that functions as a means of protection or confinement or obscures sight to provide privacy, including a wall, hedge, or structure made of metal, wood or similar material.

  • Opacity. The proportion of a fence construction that is opaque, including pilasters and pickets.