The observation of very-high-energy (VHE; > 10 GeV) γ-ray emission from γ-ray bursts (GRBs), especially in the prompt phase, will provide critical information for understanding many aspects of their nature including the physical environment, the relativistic bulk motion, the mechanisms of particle acceleration of GRBs, and for studying Lorentz invariance violation, etc. For the afterglow phase, the highest-energy photons detected to date by the imaging atmospheric Cherenkov telescopes extend to the TeV regime. However, for the prompt phase, years of efforts in searching for the VHE emission has yielded no statistically significant detections. A wide field of view and large effective area above tens of GeV are essential for detecting the VHE emissions from GRBs in the prompt phase. The High Altitude Detection of Astronomical Radiation (HADAR) experiment has such merits. In this paper, we report the estimates of its expected annual GRB detection rate, which are obtained by combining the performance of the HADAR instrument with the theoretical calculations based on a phenomenological model to generate the pseudo-GRB population. The expected detectable gamma-ray signal from GRBs above the background is then obtained to give the detection rate. In the spectral model, an extra component is assigned to every GRB event in addition to the Band function. The results indicate that if the energy of the cutoff due to internal absorption is higher than 50 GeV, the detection rate for GRBs for the HADAR experiment is approximately two or three GRBs per year, which varies slightly depending upon the characteristics of the extra component.

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