Glacier crevasse - 2D cross-section

Stress in the ice

Far from the crevasse the ice is pulled apart by a longitudinal resistive stress R_xx, while the weight of the overlying ice squeezes it with ρ_igz. The net opening stress at depth z is σ(z) = R_xx − ρ_igz. The crevasse is a crack, so the ice at its tip feels the stress intensity factor K_I = ∫₀^d σ(z) m(z, d) dz computed with an edge-crack weight function m; the crack grows while K_I exceeds the fracture toughness K_Ic (about 0.1 MPa√m for glacier ice).

Nye depth and water

Nye's zero-stress argument gives a dry crevasse depth d = 2R_xx/(ρ_ig) (dashed red line). A proper fracture-mechanics balance stops the crack a little shallower, where K_I drops back to K_Ic (yellow line). Meltwater changes everything: water of density ρ_w pushes outward with ρ_wg(z − z_w) below its surface, which is nearly as big as the ice overburden, so a full crevasse has an almost depth-independent K_I growing with √d, and it can cut all the way to the bed (hydrofracture, the mechanism behind moulins and ice-shelf collapse).

Honest simplifications: a two-dimensional vertical slice with one isolated crevasse; uniform R_xx with no creep relaxation, no firn layer density change, no crevasse interaction; the growth speed law (a few metres per sim-minute above K_Ic) is illustrative, not a measured subcritical-crack law; the opening width drawn is exaggerated and scales only qualitatively with K_I; the weight function is the semi-infinite edge-crack form, so it ignores the finite thickness H until the tip nears the bed; inflow is a simple level rise, not a hydrological model.

• Run Dry crevasse: it stops near the yellow line, shallower than Nye.
• Run Meltwater fills it: the water raises K_I and the crack runs to the bed.
• Raise K_Ic to the Tough cold ice preset and see how much more water it needs.
• Watch the last graph: water-filled depth jumps to the full thickness even at low tension.