When a suspension freezes, a compacted particle layer builds up at the solidification front with noticeable implications on the freezing process. In a directional solidification experiment of monodisperse suspensions in thin samples, we evidence a link between the thickness of this layer and the sample depth. We attribute it to an in-homogeneity of particle density that is attested by the evidence of crystallization at the plates and of random close packing far from them. A mechanical model based on the resulting modifications of permeability enables us to relate the layer thickness to this inhomogeneity and to select the distribution of particle density that yields the best fit to our data. This distribution involves an influence length of sample plates of about 11 particle diameters. Altogether , these results clarify the implications of boundaries on suspension freezing. They may be useful to model polydisperse suspensions with large particles playing the role of smooth boundaries with respect to small ones.