The following quote is more historical, referring to the Central Pacific [Railway], which would indicate considerably less than an absolute minimum in later years.
From a book "Railway Track & [Maintenance: A manual of maintenance-of-way and structures formerly published under the title of railway track and track work]" by E E Russell Tratman [a McGraw-Hill book Co; 4th ed edition was published in 1926] (reprint NMRA), 'A Manual of [Maintenance] of Way and Structures', page 168:
'In the standard tunnel section of the Central Pacific [Railway], the height is 14 ft 3 inches from top of rail to springing line (base of 'cat tails?") , with a roof radius of 8 foot giving a clear width of 16 feet, and a total height of 22ft 3inches.'
Earlier it states "Overhead structures (not tunnels) must be 22 ft above the rails, in order to clear men standing on [top] of box cars [... "]
Thoought this might be of historical interest.
[from the R&LHS Newsgroup]
... SP raised the roof of Summit Tunnel at Norden to accommodate autoracks in the 1970's, but doublestacks are too high for it. They closed the line rather than raise the roof again since traffic was down and CTC permitted them to use the other track of former double track.
Tom Irion [from the R&LHS Newsgroup]