  We describe the taming effect induced by soft gluon $k_t$-resummation on the
rapid rise of QCD mini-jet contributions to the total cross-sections.This
results from an eikonal model in which the rise of the total cross-section is
due to mini-jet contribution. We perform the calculation with current Parton
Density Functions (PDFs). The impact parameter distribution we use is obtained
as the Fourier transform of the resummed $k_t$-distribution of soft gluons
emitted from the initial state during the collision.The emission, which is
energy dependent, destroys the initial collinearity of partons.In this model,
the strong power-like rise due to the increasing number of low-x gluon
collisions is tamed by the acollinearity induced by soft gluon kt-resummation
down to zero gluon momenta. It explicitly links a singular soft gluon coupling
in the infrared region to the behaviour dictated by the Froissart bound for the
total cross-section. The model describes well both proton and photon processes
at present accelerator energies and gives predictions in the TeV range. For
photons the model predictions agree with fits by Block and Halzen based on
Finite Energy Sum Rules (FESR) at low energy and an asymptotic behaviour
consistent with the Froissart bound.
