Non-Abelian gauge fields having a line-singularity of the Dirac type lead us to violation of the non-Abelian Bianchi identity (VNABI). VNABI as an operator is equivalent to violation of Abelian-like Bianchi identities corresponding to eight Abelian-like conserved magnetic monopole currents of the Dirac type in $SU(3)$ QCD. If these new Abelian-like monopoles exist in the continuum limit, the Abelian dual Meissner effect occurs, so that the linear part of the static potential between a quark-antiquark pair is reproduced fully by those of Abelian and monopole static potentials. Monte-Carlo studies of pure QCD using the Iwasaki gluonic action at various $\beta$ on $48^4$, the perfect Abelian dominance is reproduced fairly well, whereas the perfect monopole dominance seems to be realized for large $\beta$ when use is made of smooth lattice configurations in the maximally Abelian (MA) gauge. Making use of a block spin transformation with respect to monopoles, the scaling behaviors of the monopole density and the effective monopole action are studied. Both monopole density and the effective monopole action which are usually a two-point function of $\beta$ and the number of times $n$ of the block spin transformation are found to be a function of $b=na(\beta)$ alone for $n=1,2,3,4,6,8,12$ at 13 different $\beta $ on $48^4$. The scaling behaviors suggest the existence of the continuum limit, since $a(\beta)\to 0$ when $n\to\infty$ for fixed $b=na(\beta)$.