Context.Studying absorption and scattering of X-ray radiation by interstellar dust grains allows us to access the physical and chemical properties of cosmic grains even in the densest regions of the Galaxy.Aims.We aim at characterising the dust silicate population which presents clear absorption features in the energy band covered by theChandraX-ray Observatory. Through these absorption features, in principle, it is possible to infer the size distribution, composition, and structure of silicate in the interstellar medium. In particular, in this work we investigate magnesium and silicon K-edges.Methods.We built X-ray extinction models for 15 dust candidates using newly acquired synchrotron measurements. These models were adapted for astrophysical analysis and implemented in the SPEXspectral fitting program. We used the models to reproduce the dust absorption features observed in the spectrum of the bright low mass X-ray binary GX 3+1, which is used as a background source.Results.With the simultaneous analysis of the two edges we test two different size distributions of dust: one corresponding to the standard Mathis-Rumpl-Nordsieck model and one considering larger grains (n(a) ∝a_i^−3.5with 0.005μm <a₁< 0.25μm and 0.05μm <a₂< 0.5μm, respectively, withathe grain size). These distributions may be representative of the complex Galactic region towards this source. We find that up to 70% of dust is constituted by amorphous olivine. We discuss the crystallinity of the cosmic dust found along this line of sight. Both magnesium and silicon are highly depleted into dust (δ_Z= 0.89 and 0.94, respectively), while their total abundance does not depart from solar values.