  We show that the onset and rise of QCD mini-jets provide the dynamical
mechanism behind the appearance of a soft edge in pp collisions around ISR
energies and thus such a soft edge is built in our mini-jet model with soft
gluon resummation. Here the model is optimized for LHC at $\sqrt{s} = 7, 8 TeV$
and predictions made for higher LHC and cosmic ray energies. Further, we
provide a phenomenological picture to discuss the breakup of the total
cross-section into its elastic, uncorrelated and correlated inelastic pieces in
the framework of a one-channel eikonal function.
