A brief possible definition for the phrase "under the viaduct" is offered in the book, "Words and Songs of Bessie Smith, Billie Holiday, and Nina Simone: Sound ..." By Melanie E. Bratcher found here: http://books.google.com/books?id=EAR4HFatIWQC&lpg=PA98&ots=9-muxNpr-R&dq=%22under%20the%20viaduct%22%20song&pg=PA98#v=onepage&q=%22under%20the%20viaduct%22%20song&f=false
        
Guest, Guest- When you realize that a viaduct is the bridge structure containing several spans, it will suddenly make sense that activity takes place under, rather than in, the viaduct. Make sense? :)