  We investigate the effects of the underlying quantum geometry in loop quantum
cosmology on spacetime curvature invariants and the extendibility of geodesics
in the Bianchi-I model for matter with a vanishing anisotropic stress. Using
the effective Hamiltonian approach, we find that even though quantum geometric
effects bound the energy density and expansion and shear scalars, divergences
of curvature invariants are potentially possible under special conditions.
However, as in the isotropic models in LQC, these do not necessarily imply a
physical singularity. Analysis of geodesics and strength of such singular
events, point towards a general resolution of all known types of strong
singularities. We illustrate these results for the case of a perfect fluid with
an arbitrary finite equation of state $w > -1$, and show that curvature
invariants turn out to be bounded, leading to the absence of strong
singularities. Unlike classical theory, geodesic evolution does not break down.
We also discuss possible generalizations of sudden singularities which may
arise at a non-vanishing volume, causing a divergence in curvature invariants.
Such finite volume singularities are shown to be weak and harmless.
