Winter's Bane: The Angle of Repose

This year has been increasingly warm and not particularly snowy here in Minnesota. However, I'm still having problems finding places to put snow. My driveway is flanked by garages giving me a tiny footprint to pile snow on either side . The other night, while shoveling powder onto the existing piles and watching it spill back down, I pondered an engineering concept I stumbled upon one time called the angle of repose. According to Wikipedia, the angle of repose, or critical angle of repose, of a granular material is the steepest angle of descent relative to the horizontal plane to which a material can be piled without slumping. What I thought would be a simple Google Search turned into an evening going down the rabbit hole. While I never found the answer I was seeking in a satisfactory manner, the journey was far more interesting.

Frictional Forces

A few years ago while researching making adobe from native soil, I ran across a video from The Practical Engineering YouTube channel about reinforced earth. I had been researching what purpose straw serves in making adobe and if other fibrous materials were suitable. The video was fascinating on several fronts. Most fascinating for me was the idea that freeway retaining walls are mostly for decoration since the ground they hold back is actually layered with geotechnical cloth the give the soil greater structural stability. Without the added stability, the soil would easily exert too much outward force and collapse the retaining wall.  To demonstrate this, the video uses paper towels (and later mesh) to create a freestanding block of sand stable enough to support the weight of a car.

The video discusses the types of forces that hold stuff together. Unlike molecular bonds that give steel its strength, sand is held together with frictional forces of the grains rubbing against each other. At a certain angle, gravity overcomes sand's frictional forces and the pile "slumps".  Fascinating stuff. Watch the video at the bottom of this post. The website, structx.com has a great article listing the angle of repose for various soils and moisture content. In general, wetter materials can be piled steeper than dry ones, and it seems finer materials can be piled steeper than course ones. However, no mention of snow.

Tiny Avalanches

I then thought about avalanches. Surely, there must be tons of research on angle of repose with respect to avalanches. 

According to the National Snow and Ice Data Center's Avalanche Awareness doc, the quality of the snow pack is the most significant factor in avalanches. Different layers of snow will bind to the subsequent layer of snow dependent on the type of snow falling and the qualities of the snow pack. Snow crystals within the snow pack become more rounded due to melting/re-freezing and settlement. This allows the crystals to compress and form stronger bonds with the other layers. Whereas, on the surface of the snow pack, the melting/re-freezing cycle creates a smoother and less stable area for subsequent snow fall to bind to. It goes on to talk about a type of snow pack called depth hoar (aka sugar snow), which is a course form of crystaline snow (compared to dry sand in structure). Snow pack with a layer depth hoar is more likely to result in an avalanche. Finer, more tightly packed snow crystals are less likely. 

Finally, the article reveals that most avalanches occur when slope angles are between 30 and 45 degrees, which from the structx.com article, is the range of most soils. However, the article also suggests wet snow will lubricate the snow pack and cause avalanches at lower angles - somewhat counter to the effects of moisture in soil. Think of a mudball holding its shape vs. slush "slumping".

As a side note, Cambridge University had an article focused primarily on graupel (course snow) causing avalanches in Japan, which suggests sleet will not form a layer if the snow slope angle is greater than 45.
We may have found an answer!

 

Walls of Snow

When I was in 7th grade, our class did the first Winter Survival unit (now in its 23rd year). We spent three nights at the Camp Phillips Boy Scout Camp. Among other things, we built Quinzhees to sleep in. Differing from Igloos, Quinzhees are a type of shelter made by digging out snow piles. Snow obviously has some structural integrity.  Then I remembered those roads cut through thick snow packs in Japan. Obviously, a 45 degree angle of repose doesn't come into play with sheer vertical cuts through layers of snow pack. Which brings us back to the beginning - layers of snow pack act like the geotechnical cloth with the density of the snow being the biggest factor - much like with avalanche.

Chapter 10 of The Interconnected Arctic does a fairly thorough analysis of using snow as a construction material in Finland. For designing structures, it suggests the density of snow should be between 400 and 820 kg/m3. For comparison, the density of pure water just above the freezing point is approximately 1000 kg/m3.  The Science Learning Hub of New Zealand lists out several different types of snow and their densities ranging from fresh snow (50-70kg/m3) to glacial ice (830-917 kg/m3). Estimating based on the other types, my snow piles are somewhere between 200 and 400 kg/m3.

 

So while, 45 degrees is probably the max slope I can pile snow, I can maximize the amount of snow I can pile but packing it down to get it to a density point where it won't slump. Neat. Meanwhile, I need to keep an eye on the potential avalanche on the roof...
 

Take A Ways

• Snow is weird. 
• Packing snow into dense layers seems to be the optimal way to pile snow. 
• Depth Hoar needs to be my next band name.
• Shoveling is not fun.
   

Related Links
 

• A fun classroom activity exploring the angle of repose of different materials sciencebuddies.org
• Avalanche Awareness - Facts about avalanches from the National Snow and Ice Data Center
• Types of Snow - An exhaustive list of types of snow fall, snow formations and more. 

Title Image Credit: The towering snow walls of Tateyama. PIETRO ZANARINI/CC BY 2.0