  Employing the concept of three-body radial distribution function and using
the two-body correlation functions, calculated based on the lowest order
constrained variational method, we investigated the effect of the three-body
force (TBF) on the nuclear matter properties, for Argonne and Urbana
$\it{v_{14}}$ potentials. As such, the results for nuclear matter density,
incompressibility, energy per nucleon, and symmetry energy are presented at the
saturation point. The inclusion of a phenomenological TBF resulted in closer
values of the saturation density, incompressibility, and symmetry energy to the
empirical ones for the symmetric nuclear matter. This is especially the case
for the Urbana $\it{v_{14}}$ potential. In addition, an empirically-verified
parabolic approximation of the interaction energy was utilized to perform an
approximate study of the nuclear matter with neutron excess. Hence, at
densities higher than about 0.3~fm$^{-3}$ and for proton-to-neutron density
ratios close to the symmetric nuclear matter, the inclusion of TBF resulted in
an extra attraction for the Argonne as compared to the Urbana $\it{v_{14}}$
potential.
