Lake Ice - Bearing Strength

The Bearing Strength of Ice for Recreational Activities

Summary: This article looks at the time tested Minnesota DNR recommendations for ice thickness for different recreational activities and compares them with three papers on the subject. Some of the recommended formulas for heavy loads on properly maintained ice roads are significantly less conservative than the MN DNR numbers and are not suitable for recreational activities. NOTE: Ice thickness is just one factor in the strength of an ice sheet. In particular, ice can weaken quickly in thaw conditions. With the rapid warming of the arctic and sub-arctic there were 18 fatalities in Alaska and Northern Canada in the 2019 ice season. In the previous 7 years there were, on average, less than one accident per season from these regions. There are also all sorts of weak points that can be found on ice. Pressure ridges and especially folded ridges are plentiful, essentially on larger lakes. Folded ridges can be hard to see. Holes of various types are sometimes common. This is described on the Ice Hazards section.

Detail: The origin of the Minnesota DNR recommendations is not clear, however, whoever developed them did so in a logical fashion. Tim Smalley, their recently retired water safety specialist, and his team have done and continue to do a particularly good job of coming up with practical advice on recreational ice use. Their work has been widely adopted by other states and towns across the ice belt. Their website is well worth a visit.

Ice roads in the Great White North

Ice roads are the best way to haul loads in parts of Canada. There has been a lot of work done toward making ice roads safer. Many papers have been written on various aspects of this problem. The three papers discussed here are:

Use of Ice Covers for Transportation by L. W. Gold, published in 1971. Gold's work is based largely on empirical data of what did or did not fall through and the ice conditions involved. His reports are the basis for much of the work that followed. His suggested formula for thickness if some risk was acceptable, gives values that are at or below the breakthrough thickness for weights involved with recreational activities.
BEST PRACTICE for Building and Working Safely on Ice Covers in Alberta This paper is an excellent look at working on ice. It offers basic advice for recreational activities.

Arithmetic:

The strength of a cold, black ice sheet increases with the square of the thickness: 2" ice will support four times more load than 1" ice, all other factors being equal.

The basic formula is:

P=Ah²This is sometimes referred to as 'Gold's Formula'.

Another form is:

P=CFh²

Where

P is the load
h is the thickness of the ice sheet
A is a constant which has units like pounds per square inch (psi), tons/square inch, kg/cm² or pascals (newtons/ square meter). For this discussion we will use units of pounds and inches. The numeric value of A can easily be converted to different units.
C is a proportionality constant between flexural strength and bearing strength
F is the flexural strength as measured in simple beam tests with the top in tension

In CRREL Report 78-9: Flexural strength of ice in temperate lakes the authors (A.J. Gow, H.T Ueda and J.A.Ricard) found below freezing ice strengths ranging from 130 to 230 psi (average 180 psi). Based on their work they concluded that the proportionality constant (C) is about 1, meaning C*F=F=A so 'A' is a reasonable estimate of the flexural strength of ice as they measured it on Post Pond and Cannan Street Lake in New Hampshire. This makes it simple to estimate bearing strength from flexural strength which is relatively easy to measure.

Their report also includes a few tests in warm conditions. They found strengths as low as 50 psi. We have measured much lower values in advanced thaw conditions (see 'Stage 5' on the Thawed Ice page). Thawing ice is much more variable and harder to assess. This is particularly true with early season warm spells that occur while the ice is still thin. Much thicker ice in the spring often masks its low specific strength. Thin new ice in the spring is especially vulnerable to the strong spring sun. Ice in the two to three inch range can dramatically weaken in a couple hours or less of sunny conditions.

Note: An example of strong ice I have tested was 286 psi from a single crystal of S1 ice. The ice sheet it was in was well thawed with a flexual strength in nearby S2 ice (small crystal size) was abouit 50 psi. A test of cold snow ice that had been through some thaw cycles tested at 280 psi (Lake Willoughby 2017). The measurement uncertainty is at least 5%.

Safety Factor: Ice sheets have several common features that reduce their strength. Examples include wet cracks, changes in thickness, areas that froze later than what you are presently standing on, etc. Snow drifts can inhibit ice growth and reef currents, gas holes, etc can thin the ice from underneath. Also the load you impose on an ice sheet might change very quickly if three friends skate up to you for a conversation. The safety factor is an effort to reduce the risk that any areas of weaker ice are below the breakthrough strength. A safety factor of 3 is common for recreational ice use. This seems to be adequate for people who are well prepared for dealing with falling through.

A formula for safety factor is: Safety factor (S) = the average body weight breakthrough strength of cold ice (150 psi) divided by the load (lbs) times the thickness squared (hxh, in inches).

S=150/P*h^2

Note: When using this formula a safety factor of '1' is the breakthrough thickness. Obviously you can't have a safety factor below the breakthrough force.

Thaw weakened ice is explicitly excluded in most minimum thickness recommendations. It is common to either not recognize that ice is being weakened by thawing or to not care. Although many people get away with it, it is pushing your luck. Reasonably well thawed black ice (stage 4) has a strength of about 50 psi (1/3 of the 150 psi that represents the average strength of cold ice).

Body Weight Breakthrough: In Vermont we have established that the 180 lb breakthrough thickness for black ice is about 1.1". This corresponds to a flexural strength of about 150 psi. Breakthrough strength in this weight range is obviously what skaters and fishermen (on foot) care about most. In a recent conversation with Tony Gow he suggested using using A=50 psi. This provides a cold ice safety factor of about three.

With this in mind, Table 1 looks at the Minnesota DNR thickness recommendations.

Ice road operators can get away with much higher values of 'A' as they have many rules and procedures for building, assessing and maintaining their roads. Values up of up 250 psi have been suggested if some risk of breaking through is acceptable (eg military transport).

Some of the criterion are:

Non-moving loads need more ice than moving loads
Concentrated loads need more thickness than spread out loads.
There is a range of acceptable speeds over the ice. Ice can be significantly weakened by loads moving at the the wrong speed.
Snow ice is included at 1/2 its thickness in some studies. This appears to come from studies done in Russia before 1956. (See discussion point 4 below)
Sudden and large decreases in air temperature warrant more conservative 'A' values or a 'stay off the ice for a day' recommendation.
Warm weather is the behind many ice fatalities.
Wet cracks are treated as reducing the bearing strength by 1/2 at the edge of the crack for perpendicular cracks and 1/4 the strength for cracks parallel to the direction of travel and next to the vehicle.
Layered ice (frozen snow ice over slush over black ice): Only the strongest layer is considered.
Ice road construction, monitoring and maintenance: The Alberta report goes into considerable detail about building and managing ice roads. Doing this well has a lot to do with how reliable the road will be.

Table 2 lists looks at the various recommendations for minimum ice thickness needed to support a 200 lb person on foot. The 'Alberta' and 'Gold' numbers are calculated with their ice road formulas. They are included here to show why they should not be used for recreational activities. The safety factor is based on the approximately 150 psi flexural strength we found in our body weight breakthrough tests.

Note: Using this formula a safety factor of 1 is the breakthrough thickness.

Reference links and comments:

Ref D: Article on Body Weight Breakthrough Thickness.

Ref G: Use of Ice Covers for Transportation by L. W. Gold, published in 1971. This paper is an excellent and widely used perspective on transporting heavy loads over ice sheets in Canada. The numbers 50 and 250 in Table 1 refer to values of 'A' (in psi). Gold found in his surveys that there were very few breakthroughs below 50 psi and that, if some risk was acceptable, that 250 psi was OK, at least at the heavy loads/thick/cold ice situation that he was most focused on. As you can see above, using 250 psi at body weight is pretty much a guarantee of a swim.

Gold's 1960 Paper. This paper has more detail on the circumstances involved in different breakthroughs and safe passages.

Ref A: BEST PRACTICE for Building and Working Safely on Ice Covers in Alberta This is a modern, comprehensive look at practical bearing strength. The numbers 4 and 7 are values of 'A' in units of kg/cm2. Table 3 below looks at their Figure 14 and TABLE 5: MINIMUM ICE THICKNESS FOR LIGHTER LOADS. These numbers may look conservative but for foot travel it is common to have two or more people stand near each other. For snowmobiles, the 7" minimum is concervative but reasonable.

Discussion:

1) The Minnesota DNR recommends 4" as the minimum ice thickness for any ice activity. Ice thinner than 4" is more likely to have thin spots or weak ice. It is especially important that people going out on ice between 2" and 4" thick be experienced with lake ice, be equipped for assessing the ice and be fully prepared to fall through and rescue themselves and each other if they misjudge the situation.

2) Most recreational breakthroughs occur at local thin or weak (thawed) spots that can be found on almost any ice sheet (mostly pressure ridges, recently frozen open water and holes of various types). Knowing the ice sheet thickness is just a starting point. Identifying and avoiding thin/weak ice is the bigger part of staying on top. Even more important is being equipped and skilled at rescue of yourself and others: ice claws, test pole/drill, life jacket, throw rope, buddies to through their rope to you, knowledge about escaping from a sinking car or truck, etc.

3) None of these recommended thickness numbers apply in thaw conditions (see note above).

4) Snow ice in many papers on bearing strength is rated at half the strength of black ice. In CRREL Report 78-9 they found cold, fully saturated snow ice to be stronger than black ice. Snow ice can weaken dramatically in thaw conditions, probably faster than small grain ice. The authors of CR 78-9 suggest that the half strength consideration may make sense in warm conditions.

5) Contrary to often stated advice on the www, old ice is generally not significantly weaker than new ice if the ice type, degree of thaw and other factors are the same. This may be a case of writers of advice confusing 'old ice' with 'thawed ice'.

6) If you are thinking of driving anything on ice, keep in mind that this is a high risk endeavor. In Minnesota from 1976 to 2013 vehicles account for 60% of fatalities (70% in the early part of the season). Read the Vehicles and Ice page for perspective and suggestions for maximizing your chances of living through a breakthrough. The best bet is to leave your vehicle on shore.

Conclusions:

Use the Minnesota DNR recommendations as a starting point for minimum thicknesses for recreational activities on ice that is below freezing. Of course, thicker is better.

If you would like a formula, either of these will work :

Don't use the minimum thickness formulas for ice roads for recreational activities (unless they have an 'A' value of 50 psi or less).

These recommendations do not apply to ice that is or has recently been exposed to temperatures above freezing. Strong sunlight can weaken ice at temperatures a little below freezing and speed up weakening at above freezing temperatures. This is more pronounced at lower latitudes and near the end of the ice season.

For a more comprehensive treatment bearing strength see Ice Engineering (by Lennart Fransson) or River Lake Ice Engineering (Edited by George Ashton). These sources take into account how concentrated the load is, static vs moving loads, etc.

Bob

Last updated April 11, 2020