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{mu}m Spitzer infrared spectrograph (IRS) spectra and broad-band photometry from the optical to the mid-infrared are available. From the modelling, we find mass-loss rates in the range ~8x10^-8^-5x10^-6^M_{sun}_/yr, 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.