The High Luminosity LHC (HL-LHC) phase is designed to increase by an order of magnitude the amount of data to be collected by the LHC experiments. The foreseen gradual increase of the instantaneous luminosity of up to more than twice its nominal value of $10times10^{34} {rm cm}^{-1}{rm s}^{-2}$ during Phase I and Phase II of the LHC running, presents special challenges for the experiments. The region with high pseudo rapidity ($eta$) region of the forward muon spectrometer ($2.4 > |eta| > 1.9$) is not equipped with RPC stations. The increase of the expected particles rate up to 2 kHz cm$^{-1}$ ( including a safety factor 3 ) motivates the installation of RPC chambers to guarantee redundancy with the CSC chambers already present. The current CMS RPC technology cannot sustain the expected background level. A new generation of Glass-RPC (GRPC) using low-resistivity glass was proposed to equip the two most far away of the four high $eta$ muon stations of CMS. In their single-gap version they can stand rates of few kHz cm$^{-1}$. Their time precision of about 1 ns can allow to reduce the noise contribution leading to an improvement of the trigger rate. The proposed design for large size chambers is examined and some preliminary results obtained during beam tests at Gamma Irradiation Facility (GIF++) and Super Proton Synchrotron (SPS) at CERN are shown. They were performed to validate the capability of such detectors to support high irradiation environment with limited consequence on their efficiency.
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