We consider the special case that the dark matter (DM) candidate is not detected in direct-detection programs when the experimental sensitivity reaches the neutrino flux background. In such circumstance the DM searches at the colliders impose constraints on the DM relic abundance if the DM candidate is a WIMPs type. Specifically, we consider the triplet (quintet and septet) DMs in the framework of minimal DM model and explore the potential of discovering the DM candidate in the mono-jet, mono-photon and vector boson fusion channels at the Large Hadron Collider (LHC) and future 100 TeV hadron collider. If the DM candidate in such a scenario is discovered at the LHC, then additional DM candidates are needed to explain the observed relic abundance. On the other hand, null results in those DM searching programs at the colliders give rise to lower limits of DM relic abundance.