We have constructed a numerical model of basal ice formation for glacier ice in contact with subglacial sediment. The model predicts four different ice facies whose formation is controlled by availability of subglacial water to satisfy the basal freeze-on rate. Clean (or clotted) facies may result from congelation (or frazil) ice growth occurring when (supercooled) meltwater separates ice base from substrate or if a groundwater source can supply water to the ice base at a velocity equal to the freezing rate. Laminated facies develops when the supply of subglacial water is sufficiently constrained for cryostatic suction to raise the subglacial effective stress above a threshold for intrusion of ice into sediment by regelation. Debris laminas (~1 mm) are entrained by short, periodic regelation events (of a few hours) separated by longer periods (days to months) of congelation. Further meltwater limitation produces a massive dirty ice facies due to stacking of debris laminas. The model predicts growth of solid dirty ice facies when the bed is meltwater-depleted with fast freezing (5 mm yr-1) causing enhanced erosion (30 mm yr-1). We find that basal ice facies and sediment entrainment are controlled mainly by the ratio of freezing rate to water supply rate. The predicted ice facies compare favorably with borehole camera imagery of the basal ice layer in Kamb Ice Stream, West Antarctica. Facies variability in this layer suggests complex hydrologic history for the West Antarctic Ice Sheet with significant changes occurring over a period of several thousand years.