Your query has peaked my curiousity so I have done a little research online. There are several articles on the Tennessee Civil War Sourcebook website concerning TN block houses in general. The one that particularly concerns the Columbia area is- 1 Oct 1864 Surrender of block houses at Carter's Creek, Columbia (OR Ser 1 vol 39 pt 1, pp 507-508).

I haven't looked into all the articles that came up in the search of "block houses", but here are 3 more that look promising:

24 April 1864 Federal situation report relative to status of construction of block-house defenses on the N & CRR from Bell Buckle to Poor Man's Creek (OR Ser 1 vol 32 pt 111, p 471). This concerns the Duck River south of Columbia from Bell Buckle to Tullahoma area.

8 April 1864 Estimate for number of troops to protect N & C RR (OR ser 1 vol 32 pt 111, pp 290-291)

28 April 1865 Report of the Office of Inspector- General of Fortifications, Military Division of the Mississippi, relating to Middle TN (OR Ser 1 vol 49 pt 11, pp 499-503

Hope this helps.