Compressive Strength of Sintered Snow

Say the honest thing first: this is an empirical fit with very wide scatter, and it is not a law. Measured compressive strengths of snow at a single density routinely span a factor of five. Published exponents for sintered snow range from about 3 to over 4, and across the density range of ordinary snow that spread alone is a factor of two or three in the answer. A number out of this equation is an order of magnitude. Nothing should be designed to it, and a page that pretended otherwise would be worse than no page.

What the fit does capture, and captures correctly, is the direction and the steepness. Strength rises far faster than density. Going from 200 to 400 kg/m³ — a doubling — multiplies the strength by roughly eleven at an exponent of 3.5. That extreme sensitivity is why snow is either useless or genuinely structural with very little middle ground, and why the same shovelful of material is a nuisance one hour and a building block the next.

And that last sentence points at what the equation cannot see, which is time. Snow gains strength by sintering: water vapour leaves the convex surfaces of the ice grains, where the vapour pressure is slightly higher, and deposits in the concave necks between touching grains, where it is slightly lower. The necks thicken. The heap becomes a bonded solid. This happens at essentially no change in density whatever, over a timescale of hours, and it can raise the strength of disturbed snow by an order of magnitude while the mass and the volume sit still. Density is on one axis of this equation and the other axis is missing entirely.

This is the entire principle of a quinzhee, and it is why the waiting is the manufacturing step rather than a tradition. You shovel snow into a pile, which breaks every bond it had — freshly shovelled snow is weak no matter what it weighs. Then you leave it, typically one to three hours and longer in very cold snow, and during that wait the grains weld to each other. Only then is it hollowed. Skip the wait and the roof is a heap of loose grains with a hole cut in it. The shovelling also does something the equation can see, by mixing snow of different grain types and temperatures so the pile ends up more uniform than the layered pack it came from — but the strength arrives with the sintering, not with the shovel.

Three more limits worth carrying. This is unconfined compressive strength: snow in tension is far weaker and fails far more suddenly, and a roof span is in tension across its underside, which is the failure mode a shelter actually has. Snow is strongly rate-dependent — a slow squeeze it accommodates by creeping, a fast one it answers brittlely — so a strength measured on a press at one strain rate does not transfer to another. And the reference strength $\sigma_i$, the fitted intercept at solid ice, is not a measured property of ice: it is where the line lands when extrapolated to zero porosity, and real ice fails by a different mechanism at a strength that depends on grain size, temperature and strain rate. Fit the pair together on your own snow, or do not quote either.