  We study the local curvature estimates of long-time solutions to the
normalized K\"ahler-Ricci flow on compact K\"ahler manifolds with semi-ample
canonical line bundles. Using these estimates, we prove that on such a
manifold, the set of singular fibers of the semi-ample fibration on which the
Riemann curvature blows up at time-infinity is independent of the choice of the
initial K\"ahler metric. Moreover, when the regular fiber of the semi-ample
fibration is not a finite quotient of a torus, we determine the exact curvature
blow-up rate of the K\"ahler-Ricci flow near the regular fiber.
