The Target Absorbers for Neutrals (TANs) represent one of the most radioactive regions in the Large Hadron Collider (LHC). Seven 40 cm long fused silica rods with different dopant specifications, manufactured by Heraeus, were irradiated in one of the TANs located around the ATLAS experiment by the Beam RAte of Neutrals (BRAN) detector group. This campaign took place during the Run 2 p+p data taking, which occurred between 2016 and 2018. This paper reports a complete characterization of optical transmission per unit length of irradiated fused silica materials as a function of wavelength (240 nm - 1500 nm), dose (up to 18 MGy), and level of OH and H\(_2\) dopants introduced in the manufacturing process. The dose delivered to the rods was estimated using Monte Carlo simulations performed by the CERN FLUKA team.