We present the results of a variability study of broad absorption lines (BALs) in a uniformly radio-selected sample of 28 BAL quasars using the archival data from the first bright quasar survey (FBQS) and the Sloan Digital Sky Survey (SDSS), as well as those obtained by ourselves, covering time scales $\sim 1-10$ years in the quasar's rest-frame. The variable absorption troughs are detected in 12 BAL quasars. Among them, five cases showed strong spectral variations and are all belong to a special subclass of overlapping iron low ionization BALs (OFeLoBALs). The absorbers of \ion{Fe}{2} are estimated to be formed by a relative dense (\mbox{$n\rm _{e} > 10^6~cm^{-3}$}) gas at a distance from the subparsec scale to the dozens of parsec-scale from the continuum source. They differ from those of invariable non-overlapping FeLoBALs (non-OFeLoBALs), which are the low-density gas and locate at the distance of hundreds to thousands parsecs. OFeLoBALs and non-OFeLoBALs, i.e., FeLoBALs with/without strong BAL variations, are perhaps to be the bimodality of \ion{Fe}{2} absorption, the former is located in the active galactic nucleus environment rather than the host galaxy. We suggest that high density and small distance are the necessary conditions what causes OFeLoBALs. As suggested in literature, strong BAL variability is possibly due to variability of the covering factor of BAL regions caused by clouds transiting across the line of sight rather than ionization variations.
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