  We address the mechanical effect of rigid boundaries on freezing suspensions.
For this we perform the directional solidification of monodispersed suspensions
in thin samples and we document the thickness h of the dense particle layer
that builds up at the solidification front. We evidence a change of regime in
the evolution of h with the solidification velocity V with, at large velocity,
an inverse proportionality and, at low velocity, a much weaker trend. By
modelling the force balance in the critical state for particle trapping and the
dissipation phenomena in the whole layer, we link the former evolution to
viscous dissipation and the latter evolution to solid friction at the rigid
sample plates. Solid friction is shown to induce an analog of the Janssen
effect on the whole layer. We determine its dependence on the friction
coefficient between particles and plates, on the Janssen's redirection
coefficient in the particle layer, and on the sample depth. Fits of the
resulting relationship to data confirm its relevance at all sample depths and
provide quantitative determinations of the main parameters, especially the
Janssen's characteristic length and the transition thickness h between the
above regimes. Altogether, this study thus clarifies the mechanical implication
of boundaries on freezing suspensions and, on a general viewpoint, provides a
bridge between the issues of freezing suspensions and of granular materials.
