  The discovery of the Higgs boson at $\sim 125$ GeV indicates that the scale
of weak scale supersymmetry is higher than what was perceived in the pre-Higgs
boson discovery era and lies in the several TeV region. This makes the
discovery of supersymmetry more challenging and argues for hadron colliders
beyond LHC at $\sqrt s=14$ TeV. The Future Circular Collider (FCC) study at
CERN is considering a 100 TeV collider to be installed in a 100 km tunnel in
the Lake Geneva basin. Another 100 km collider being considered in China is the
Super proton-proton Collider (SppC). A third possibility recently proposed is
the High-Energy LHC (HE-LHC) which would use the existing CERN tunnel but
achieve a center-of-mass energy of 28 TeV by using FCC magnet technology at
significantly higher luminosity than at the High Luminosity LHC (HL-LHC). In
this work we investigate the potential of HE-LHC for the discovery of
supersymmetry. We study a class of supergravity unified models under the Higgs
boson mass and the dark matter relic density constraints and compare the
analysis with the potential reach of the HL-LHC. A set of benchmarks are
presented which are beyond the discovery potential of HL-LHC but are
discoverable at HE-LHC. For comparison, we study model points at HE-LHC which
are also discoverable at HL-LHC. For these model points, it is found that their
discovery would require a HL-LHC run between 5-8 years while the same parameter
points can be discovered in a period of few weeks to $\sim 1.5$ yr at HE-LHC
running at its optimal luminosity of $2.5\times 10^{35}$ cm$^{-2}$ s$^{-1}$.
The analysis indicates that the HE-LHC possibility should be seriously pursued
as it would significantly increase the discovery reach for supersymmetry beyond
that of HL-LHC and decrease the run period for discovery.
