  The observation of very-high-energy (VHE, $\rm >10~GeV$) $\gamma$-ray
emission from $\rm \gamma$-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 (FOV) 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.
