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Physics of ice-cold liability: Conduction

  • SIMA
- Posted: July 27, 2016
By George Melchior
In my last article, I discussed “snow bias” in the snow and ice management industry, and I reinforced the most important covenant of wintertime premises liability: Ice is dangerous. In this piece, and ensuing articles, I will describe the physics of ice formation and persistence as it pertains to winter operations.

If you’re recognized by SIMA as an ASM or CSP, or you’ve participated in formal training for snow and ice management in recent years, then you know that ice management is heavily influenced by surface temperature. Surface temperature is the temperature of the ground surface (whether asphalt, concrete, stone, dirt, or another material) at a specific time and location and is the result of heat transfer from the Earth out to the atmosphere or vice versa. When surface temperatures are below freezing, any moisture that comes in contact with the surface will cool on contact and freeze to form ice. Therefore, effective ice management requires owners and contractors to have a practical familiarity with heat transfer and its effect on surface temperature.

There are three forms of heat transfer: conduction, convection and radiation, and they all affect surface temperature. This article focuses on conduction. Conduction, simply put, is the transfer of heat through matter. The most important and oft misunderstood concept to remember with conduction is that heat travels from hot to cold. Often, property owners and contractors confuse heat with hot air. Hot air rises, but heat flows from hot to cold, regardless of direction. Heat will continue to flow through matter, from hot to cold, until there is no longer a difference in temperature between hot and cold, a condition known as thermal equilibrium. Most importantly for owners and contractors is that equilibrium is not instantaneous. Just because the air temperature outside is 40° doesn’t mean the surface temperature is 40°. In fact, all factors considered, a region could experience a 40°-plus day and the surface temperature may never rise above the freezing point.

Heat transfer
Ground surface equilibrium takes time, and, when heat is transferred by conduction, the time it takes for the surface to equilibrate is best described by Fourier’s Law. According to Fourier, three attributes govern the rate of heat transfer through matter: temperature difference between hot and cold; material thickness; and the thermal conductivity of the material. The first two factors do not require much discussion. The higher the temperature differential, the faster ice melts (cold drinks get warm, etc.). Likewise, the thicker the walls of a cooler, or your house insulation, the longer it takes for heat to transfer through those walls. Thermal conductivity, however, requires discussion.

The ground surface on the Earth’s crust is the subject of heat transfer between the Earth’s core and the surrounding atmosphere. While the temperature of the Earth’s core is tens of thousands of degrees, most of the United States experiences a steady state temperature of approximately 55°F below about 8 to 15 feet in depth from the surface. In the layer of Earth between the steady state temperature and the atmosphere at the surface, there are myriad soil types. Each soil type conducts heat at a different rate depending on conductive mineral density and water content. For example, loose soil with a lot of air, like gravel, will conduct heat slower than dense clay with a high moisture content. The rate at which soils allow the transfer of heat through their body is known as thermal conductivity.

This illustration depicts a typical soil profile and corresponding temperature profile based on relative thermal conductivity.

Why is this important to owners and contractors? Remember, surface temperature has the highest influence on the formation of ice. The typical construction of sidewalks and parking lots includes a porous sand and/or gravel subbase with low conductive mineral density, and virtually no moisture content. While this subbase is great for its primary intent, which is to provide underslab structure and drainage, it also encumbers heat transfer, thus extending the time it takes for the pavement surface to reach thermal equilibrium. Why? Because the subbase insulates heat transfer from the steady state of 55°F.

Going back to Fourier’s Law, the temperature differential is only between the frozen ground and the air, with virtually no help from the Earth. The difference between, say, 28°F surface temperature and 40°F air temperature is 12°F. For an asphalt or concrete surface, with no wind (convection) or sunlight (radiation), such as on the north side of a building, the time it would take for the asphalt to warm to a temperature above freezing can be as much as 6 to 8 hours. As such, it is common for surface temperatures to stay below freezing all day, despite air temperatures at or above 40°F.

Chart 2 shows a week of air and ground temperatures, measured hourly, last winter in southern New Hampshire. Despite three days where the air temperatures were above freezing, the ground temperatures never went above 31°F. So, any moisture that touched the surface on those days would have cooled to form ice. 
Despite three days where the air temperatures were above freezing, the ground temperatures never went above 31°F. Any moisture that touched the service on those days would have formed ice.

Case study/Temperature differential
A premises liability case that I consulted on recently demonstrates a common mistake that owners and contractors make when it comes to surface temperature. In this case, a woman slipped while walking to her car and fell on untreated ice in the parking lot of her apartment complex. The air temperatures for the two weeks leading up to the fall never rose above 30°F, though, on the day of the fall, they rose to a high of 42°F throughout the morning, under overcast skies. The parking lot was asphalt and nominally flat. The owner and snow management contractor had a residual pile of snow just off the edge of the pavement from a snow event five days earlier. 

Over the course of the morning, the snow pile began to melt in the warmer air. The melt flowed from the pile and well into the parking lot. As the moisture remained in contact with the asphalt surface, which was still below freezing, the water refroze into a thin sheet of ice. The tenant, while walking to her car, was unaware of the ice, and she did not anticipate the presence of ice on a day where air temps were in the 40s. She slipped, fell, and injured her knee, hip and shoulder. Testimony revealed that neither the owner nor the contractor were aware of the influence that surface temperature has on ice formation. The case settled with payment of damages to the plaintiff in excess of $55,000. If the owner and/or contractor had known about the effects of surface temperature on ice formation, they would have recognized the dangerous condition and properly mitigated it for less than $100.

Other factors influence the rate at which heat will conduct through matter and the corresponding time it will take to achieve thermal equilibrium (e.g., specific heat, thermal diffusivity). However, the factors most important to the snow and ice manager are those in Fourier’s Law: temperature differential; thickness of material; and material thermal conductivity. If owners and contractors pay attention to those three attributes, they will quickly learn the time-rate characteristics of the surfaces that they manage, and can more effectively prevent or treat the formation of ice.
George Melchior, ASM, is a registered architect and professional engineer and owns GVM Consulting, based in Portsmouth, NH. Contact him at
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