Thin Ice

[CANPRO]

My parents have always drilled it in my head that ice has to be at least 6" thick before I could go skate...which was hard sometimes as a young child because I could see the older (and less supervised) kids out playing hockey on the thin ice.

I'm sure 6" is the safe number, and I'm not about to go jump around on 3" of ice...but this got me thinking..how would you go about figuring out on paper how thick the ice had to be?

I did some looking around on the internet and found a range of values for the tensile strength of ice...in the range of 1 - 3 MPa.

Any suggestions on how to do this...besides throwing the whole problem into some FEM software?

 

[dik]

There are so many variables with strength of ice... best to err on the safe side. The consequences can be ugly... it's not the sort of thing I would be looking for a minimum...

Dik

 

[CANPRO]

Agreed. I'm not looking to push any limits here...more of an academic question...just looking for an interesting problem to solve more than anything else

 

[SteelPE]

You must be really bored.

I would imagine this would be no different than designing a raft foundation with ice substituted for concrete and water substituted for the soil below.

 

[Teguci]

SG of ice = 0.92
Point Force = 400 lbs

From here, figure out the deflected shape (2-way action) and equate the volume displaced vs stiffness and varying thicknesses of ice. Not only is the ice buoyant but as the ice deflects down it displaces the water caulsing a resultant buoyant force up (minus the weight of the ice and skater).

Check stresses against bending and check 2-way shear. The biggest problem with ice is that it is brittle so no redistribution of loads after failure. Should probably have a safety factor of 4 or more.

 

[concretemasonry]

Any cracks in the ice surface will interrupt the continuity and vertical load transmission and lead to unpredictable results. The numbers mean little then.

Fresh ice is usually somewhat consistent and has few cracks or displacement areas, but as the season goes on more cracks and weak points occur, but not enough to disrupt skating activities but can support heavier loads.

The ice behaves like a beam on an elastic foundation once there are a few cracks that always occur as it goes through the season.

Dick



Engineer and international traveler interested in construction techniques, problems and proper design.

 

[JStephen]

Of course, the strength drops to zero as it approaches the melting point. I have seen ice that was 4" or so thick, but with VERY little strength.

 

[SkiisAndBikes]

I had a professor at University who studied ice engineering. I can remember calcs that were done to justify how thick the ice had to be to move construction equipment of various sizes to island project sites in the winter, etc... Unfortunately I don't have any specific references to provide. I remember being amazed at how strong ice actually was.

There is likely an obscure textbook somewhere with the data you seek. Also, the ice roads they use for trucking would be a source of information.

 

[concretemasonry]

As the ice freezes, there can be ice ridges that occur because of the expansion of the plates that act as individual members slightly connected. We have a lake near here where they routinely install arched wood bridges over the ice ridges for access to the week-end community of 10,000 or more people every week-end.

As far as the minimums, last week I saw a situation where an ice fisherman had an ice house/tent on a sled sitting on 4-6" of ice - new, pure, unfractured ice and you could see and identify the fish under the ice before it was pulled out or cut off. Once the ice expands and fractures, the load carrying capacity becomes variable. But, still generally depends on the general ice thickness since that eventually becomes the localized capacity unless you have an "ice road hauler".

Dick

Engineer and international traveler interested in construction techniques, problems and proper design.

 

[MiketheEngineer]

It's your butt - but 3'' seems at most the least!! Or have your brother go out there first - like I used to do!!!

Watch IRT - Ice Road Truckers - those guys are nuts!!

 

[bridgebuster]

THe USACOE has a manual on ice engineeering EM1110-2 1612. Chapter 8 gets into the thickness, along the lines of what Teguci wrote.

 

[CANPRO]

Teguci's approach made the most sense to me when I read it yesterday...I'm just starting to read through this army corps manual now and it seems to lay things out fairly clearly...thanks for the reference.

Concretemasonry and SteelPE, you are both saying to look at the water as an elastic foundation...if you were to take that approach how would you determine the stiffness of the water? Would it just be the buoyancy?

 

[Lemony]

Not what you are looking for, but we always used to do the potato test: you carefully walk out on the ice, you drop a potato from shoulder level, if it goes through you back off slowly.

 

[Teguci]

So we have RISA, STAAD, SAP and countless other finite element anlyses programs. We've taken Calculus 4, Linear Algebra and Differential Equations. We understand static and dynamic loading and many of us have designed buildings that are more than 4 stories tall...and you're advocating the use of a potato drop test?!? (Smile!) Potatoes are for frying!

 

[CANPRO]

I think my first step in the potato test would be throwing it from shore...and it would have to be a giant potato.

The army corps reference was excellent...exactly what I was looking for. Thanks again!

 

[SAIL3]

Teguci...you seemed to have supplied the only coherent solution to a very interesting problem.
The buoyant force you mention I would assume is local,however there also seems to be a confinement mechanism in the body of water occuring at the same time. As the ice deflects locally it displaces a certain vol of water which in turn tries to displace surrounding ice upwards...the ice acts or tries to act to contain the vol of water...very complicated to get a handle on..
CANEIT..I don't have that army corp manual and would be interested in a synopsis of the solution you discovered...thanks

 

[CANPRO]

Here is a link to the manual

http://140.194.76.129/publications/eng-manuals/em1110-2-1612/toc.htm

chapter 8 relates to this discussion...but I've read through a couple of other chapters as well and it is all very interesting.

 

[dhengr]

An interesting subject.... and several of the posts seem to be headed in the right direction. But ice is a very fickle material in its mechanical and physical properties. So, be very careful; just a few practical additions to the thread....

We always talked in terms of about 4" of ice for safe walking or skating. But I’ve walked on much thinner ice with some trepidation, in not too deep a water situation. You can feel and see it flexing just before you fill your boots with water. This is very dangerous where there is any moving water since it can keep the ice from forming despite cold weather, it melts it from below. Rivers or streams are an example of this all season long. You must know the lake, because a lake bottom spring entering the lake, 20' below the ice will stir the water enough to keep the ice very thin. With no guarantees, we thought: about 5" of ice for snowmobiles and ATVs; about 8" for compact cars; about 12" for light trucks, spacing of these heavier loads are at your own risk.

Snow acts as an insulator, so if you get ice and then snow too quickly, the ice will not develop thickness very quickly. The weight of the snow may actually depress the thin ice, slowly, with water coming up through cracks or weak ice and forming an inferior (not strong) ice/snow mix. Some compressive strength once it freezes, but no tensile strength. For ice roads, as quickly as you can get a light plow on the ice, you want to plow the ice road very wide, so the ice will continue to form a nice wide, and thick, roadway.

There is a buoyant force (the elastic found.), force/stress transfer through the ice and away from the point load area as Teguci suggests, and there is a confinement/pressure mechanism going on as the ice deflects under load as Sail3 suggests. This shows up in the form of water geysers or artesian like water, flowing up through cracks in the ice in the vicinity of a heavy load like a car. This must be in the form of a ice stress/deflection and buoyancy/pressure wave moving along under the moving load. And, you can see the two sheets of ice displace w.r.t. each other as the wheel goes over a fresh crack. I have had ice crack right under my feet, suffice-it-to-say I was glad I relieved myself before I left the house. I have had ice cracking behind me, with water welling up through the cracks, using a snowmobile. If you keep moving, you can stay ahead of it and get off the ice. I’m sure that if I had stopped I would have been fishing the snowmobile out of the lake. This happened during an age where I thought I was more invincible than I know I am now.

 

[BadgerPE]

Lemony,

Is that where the term "spud bar" came from?

 

[concretemasonry]

A "spud bar" is a very portable chisel that can be use to determine the thickness of the ice (before and more portable than augers) for exploring fish spots.

Ice is a very flexible medium that can be amazingly strong and resilient. I can remember numerous times when you could hear the ice crack (for hours earlier) and shift as you were ice fishing out of the front door of your car. You just moved to give the cracks to heal and freeze and come back a day or so later because it is not permanent. The more permanent deformations are the ice ridges where they usually place bridges over the problems even when there is 4' of ice or more.

Ice is not a static condition. I spent many days of spring ice fishing on 6" of "soft/melting" ice where we were on skis and pulled a canoe in case there was a shift. - It is not a scienticif subject.

Engineer and international traveler interested in construction techniques, problems and proper design.