Captive columns are columns that have been partially restrained against lateral movements by strong infill walls; therefore instead of showing a ductile flexural failure they exhibit a brittle shear failure. Captive columns can be found in many buildings mainly due to the fact that the majority of structural engineers do not seek for them in the architectural drawings when designing buildings for earthquakes. They are widely found in the staircases, toilets area and rooms with windows (see figures shown below).
It is highly unlikely to repair a damaged captive column because of the presence of axial force in the column and its lateral sway.
Another point about captive columns is that it has been shown the equations provided in the main design codes like ACI 318 and Eurocode 2 cannot accurately predict their shear capacity (the difference can be as large as 150%). Therefore, we need to avoid their presence in the buildings using different methods.
The figure below show a damaged short column (the yellow column) during 2015 Sabah earthquake in Malaysia with a magnitude of 5.9 (Mw). As can be seen a medium intensity earthquake can significantly damage a short captive column