  Dark matter that interacts strongly with baryons can avoid the stringent dark
matter direct detection constraints, because, like baryons, they are likely to
be absorbed when traversing the rocks, leading to a suppressed flux in deep
underground labs. Such strongly interacting dark matter, however, can be probed
by dark matter experiments or other experiments operated on the ground level or
in the atmosphere. In this paper we carry out systematic analysis of two of
these experiments, XQC and CSR, to compute the experimental constraints on the
strongly interacting dark matter in the following three scenarios: (1)
spin-independent and spin-dependent interactions; (2) different velocity
dependent cross sections; (3) different dark matter mass fractions. Some of the
scenarios are first analyzed in the literature. We find that the XQC exclusion
region has some non-trivial dependencies on the various parameters and the
limits in the spin-dependent case is quite different from the spin-independent
case. A peculiar region in the parameter space, where the XQC constraint
disappears, is also found in our Monte Carlo simulations. This occurs in the
case where the interaction cross section is proportional to the square of the
velocity. We further compare our XQC and CSR limits to other experimental
constraints, and find that a large parameter space is allowed by various
experiments if the dark matter mass fraction is sufficiently small,
$f_\chi\lesssim 10^{-4}$.
