We have constructed a high-resolution numerical model of heat, water, and solute flows in sub-ice stream till subjected to basal freeze-on. The model builds on quantitative treatments of frost heave in permafrost soils. The full version of the Clapeyron equation is used. Hence, ice-water phase transition depends on water pressure, osmotic pressure, and surface tension. The two latter effects can lead to supercooling of the ice base. This supercooling, in turn, induces hydraulic gradients that drive upward flow of pore water, which feeds the growth of segregation ice onto the freezing interface. This interface may progress into the till and form ice lenses if supercooling is sufficiently strong. Hence, the ice segregation process develops a stratified basal ice layer. In our model, a high basal temperature gradient (~0.054¿C m-1) triggers ice stream stoppage, and the loss of basal shear heating leads to relatively high basal freeze-on rates (~3--5 mm a-1). In response, the subglacial till experiences comparatively rapid consolidation. Till porosity can decrease from 40% to 120 kPa, approximately within one century. Basal supercooling arising from redistribution of solutes and ice-water interfacial effects amounts to ca. -0.35¿C below the pressure-melting point. Fine-grained till is in our model associated with widely spaced, thick ice lenses. Coarse-grained till yields thinner ice lenses that are more closely spaced. Our model results compare favorably, although not in all details, with available observational evidence from borehole studies of West Antarctic ice streams.