In order to determine the composition of the dust in the circumstellar envelopes of oxygen-rich asymptotic giant branch (AGB) stars we have computed a grid of modust radiative-transfer models for a range of dust compositions, mass-loss rates, dust shell inner radii and stellar parameters. We compare the resulting colours with the observed oxygen-rich AGB stars from the SAGE-Spec Large Magellanic Cloud (LMC) sample, finding good overall agreement for stars with a mid-infrared excess. We use these models to fit a sample of 37 O-rich AGB stars in the LMC with optically thin circumstellar envelopes, for which 5$-$35-$μ$m Spitzer infrared spectrograph (IRS) spectra and broadband photometry from the optical to the mid-infrared are available. From the modelling, we find mass-loss rates in the range $∼ 8\times10^{-8}$ to $5\times10^{-6}$ M$_{⊙}\ \mathrm{yr}^{-1}$, and we show that a grain mixture consisting primarily of amorphous silicates, with contributions from amorphous alumina and metallic iron provides a good fit to the observed spectra. Furthermore, we show from dust models that the AKARI [11]$-$[15] versus [3.2]$-$[7] colour-colour diagram, is able to determine the fractional abundance of alumina in O-rich AGB stars. ; Comment: 22 pages, 17 figures, accepted MNRAS