Fiber Bragg grating (FBG) based sensors are one of the most studied optical fiber sensors in harsh environments. The effects induced on gratings by the radiation depend on the gratings' properties and on the irradiation conditions, such as temperature, dose and dose-rate. Only few studies dealt with the dose-rate dependence of the response of some particular gratings and observed that the higher is the dose-rate, the larger is the radiation-induced Bragg wavelength shift (RI-BWS) at a same accumulated dose. In this work, we verify this behavior in a larger dose-rate range, from 5 to 50 Gy/s, for different grating types and from our results we find an empirical law that describes the RI-BWS. Moreover, a comparison between the radiation-induced refractive index variation values calculated from the RI-BWS and from attenuation measurements performed at the same irradiation conditions allows us to propose a candidate for the RI-BWS origin: the Ge(1) defect.