  We combine high-level theoretical and \emph{ab initio} understanding of
graphite to develop a simple, parametrised force-field model of interlayer
binding in graphite, including the difficult non-pairwise-additive
coupled-fluctuation dispersion interactions. The model is given as a simple
additive correction to standard density functional theory (DFT) calculations,
of form $\Delta U(D)=f(D)[U^{vdW}(D)-U^{DFT}(D)]$ where $D$ is the interlayer
distance. The functions are parametrised by matching contact properties, and
long-range dispersion to known values, and the model is found to accurately
match high-level \emph{ab initio} results for graphite across a wide range of
$D$ values. We employ the correction on the difficult bigraphene binding and
graphite exfoliation problems, as well as lithium intercalated graphite
LiC$_6$. We predict the binding energy of bigraphene to be 0.27 J/m^2, and the
exfoliation energy of graphite to be 0.31 J/m^2, respectively slightly less and
slightly more than the bulk layer binding energy 0.295 J/m^2/layer. Material
properties of LiC$_6$ are found to be essentially unchanged compared to the
local density approximation. This is appropriate in view of the relative
unimportance of dispersion interactions for LiC$_6$ layer binding.
