module 3 ice engineering

Arctic Engineering Module 3a

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Welcome to the lecture on river ice. This is Steve Daly of the US Army Engineer Research and Development Center. I work as a Research Hydraulic Engineer at the Cold Regions Research and Engineering Laboratory, in Hanover, NH and am also an affiliated Professor at UAA.


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In this lecture we will cover the important concepts of river ice. This lecture is an overview of a very broad area. We will concentrate on presenting a unified view of river ice, starting from its initial formation, through its final breakup, and the formation of ice jams.


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This is the schematic diagram I have developed to present the basic concepts of river ice. The diagram is meant to represent the ice conditions in a reach of river. The diagram starts at the top with open water, and proceeds downwards. The diagram is meant to represent the passage of time throughout the winter, but you cannot consider the distance from the top of the diagram to have a one-to-one correspondence with time. Rather, the diagram is meant to show how one stage of river ice development leads to another. Important alternate routes through the diagram are also shown.

The boxes that are highlighted with red in this slide show one alternative: no significant ice formation. This is a rather uninteresting alternative for us, and we will not discuss this after this slide. The point I want to make here is that the heat balance of the river controls ice formation. The river gains and looses heat through it surface. The river can also gain heat from warm water inputs such as ground water and artificial heat sources such as industrial, municipal, and commercial discharges. If the heat lost during the winter is not sufficient to overcome the heat gain and cool the water to 0°C (32°F), ice will not form.


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Now we will discuss ice formation. We are assuming that sufficient heat has been lost from the river to the atmosphere to cool the water to 0 °C (32 °F). Further heat loss leads to the production of ice.


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Slide script River water cools when heat is lost. If the heat loss continues long enough, the river water temperature will reach 0°C (32°F). We find that further heat loss will continue to cool the water temperature. When the water temperature is less than 0°C (32°F) it is said to be supercooled. Supercooled water is the precursor to the initial river ice formation.

Remember that when the water temperature is greater than 0 °C (32 °F) any ice in contact with the water will melt. Water at a temperature of 0 °C (32 °F) is in equilibrium with ice. Ice in contact with the water coexists without growing or melting. Water at a temperature less than 0°C (32°F) is considered supercooled. Ice in contact with the water grows.


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Nucleation is the processes sometimes cited as the source of the initial ice in rivers. Nucleation is a general term, referring to the formation of a new phase of a substance from a parent phase. In our case, the parent phase is obviously water, and the new phase that is appearing is, of course, ice. Heterogeneous nucleation refers to spontaneous appearance of ice from nucleating agents such as silver iodide, organic particles, bacteria, or bubbles. It is now known that the ice crystals in rivers do not “spontaneously” appear through heterogeneous or spontaneous nucleation in the water column.

We know now that seed crystals, which are ice crystals introduced from outside the river, start the initial ice formation. Seed crystals can come from a number of different sources: vapor evaporating from the water surface, upon encountering cold air, can sublimate into ice crystals, which fall back onto the water surface and are entrained by the turbulent motion of the flow; small water droplets generated by breaking waves, bubbles bursting at the water surface, and splashing; snow and sleet.


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There are two extremes under which ice can form in natural waterbodies. On one extreme is quiescent water. The other extreme is turbulent water. We will discuss ice formation under both extremes, however we will concentrate on formation in turbulent water, as this is the most common ice form in river and stream.

In quiescent water, the ice will form at the surface only. This type of ice is common in lakes, ponds and very slow moving rivers and streams. In quiescent water the heat loss from the surface stratifies water with coldest water at the surface. The surface water becomes supercooled, seed crystal are introduced and ice forms at surface.

In rivers, ice is mainly ice formed in turbulent water. Most rivers and streams are turbulent due to their flow velocity. Oceans, lakes and ponds can often be turbulent due to wind mixing. The type of ice formed in turbulent water is frazil ice.

Turbulence is a great mixer, and it produces a very uniform vertical temperature profile. This means that the entire depth of flow in rivers can becomes supercooled, and after seed crystals are introduced, ice can form throughout the entire depth of flow.


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Ice formation on water in which the flow velocity plays no role is called static ice formation. This includes ice formed on lakes and ponds during periods of low winds, and on rivers and streams in which the flow velocity is approximately 0.3 meter/sec (1 ft/sec) or less. Static ice formation starts in a very thin layer of supercooled water at the water surface and is probably initiated by the introduction of seed crystals. The ice grows at the ice/water interface as a result of heat transfer upwards from the interface, through the ice, to the atmosphere.


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• Rivers, streams and wind-blown lakes and ocean are turbulent.

• Heat loss can cause the entire turbulent region to become supercooled

• Frazil ice is formed in turbulent, supercooled water

• It is observed that once a very few seed crystals are introduced into turbulent supercooled water, very quickly, many new crystals are created through secondary nucleation. Secondary nucleation is the formation of new crystals through the presence of existing ice crystals The production of minute ice fragments through the collisions of existing crystals with hard surfaces (including other crystals) are thought to be the main mechanism through which new frazil ice crystals are formed. These new crystals can then further increase the rate of secondary nucleation with a multiplicative effect.

• Turbulence mixes and ice crystals grow throughout the turbulent region. Because the frazil ice crystals are suspended in supercooled water they are also growing in size. The water temperature will dynamically reflect the balance of the latent heat released by the growing crystals and the heat transfer from the water surface. Eventually, the rate of latent heat released is enough to return the water temperature to the ice–water equilibrium temperature (0 °C [32 °F]).


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This slide shows a typical measurement of water temperature with time during the formation of frazil ice. The water temperature falls at a constant rate at first, indicating that the heat transfer rate from the water body is constant. When the water temperaturereaches 32 °F (0 °C), it continues to fall. Remember that this is the water temperature of a turbulent body of water. When the temperature of the water is less than 32 °F we say that the water has become supercooled. Ice does not immediately appear. First, seed crystals must enter the water and secondary nucleation start. We can see that immediately after the first crystals are observed, the water temperature decline begins to moderate and soon stops. At this time the water temperature reflects a balance between the latent heat released by the growing ice and heat transfer away from the water body. After this time, the water temperature increases, indicating that the rate of latent heat release by the growing ice exceeds the heat transfer from the water body. Eventually the water temperature will return to near 32 °F (0 °C). Frazil ice will continue to be formed, but at this time, the latent heat released by the growing ice and the heat transfer away from the water body are in balance.

This is a typical supercooling curve. It is important to note that the maximum levels of supercooling recorded are small, generally much less than 0.1 °C. This means that it can be quite difficult to measure supercooling in the field unless one is using laboratory grade equipment.


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This is an image of frazil ice crystals removed from supercooled water generated in the Ice Engineering Refrigerated Flume Facility at the US Army Corps of Engineers Cold Regions Research and Engineering Laboratory in Hanover, New Hampshire. These crystals have a major diameter of several tenths of a millimeter. Note the nearly perfect circular shape of the crystals.


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• Formed only in areas of open water

• Formed in turbulent water

o Flow velocity

o Wind mixing

• Formed in supercooled water

o -0.01 °C to -0.02 °C


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The evolution of river ice describes the transformation of individual and separate frazil ice crystals; suspended in turbulent flow, into large, stable, ice covers. The initial frazil ice crystals are quite small, on the order of millimeters; the final stable ice covers are quite large, on the orders of kilometers in length. The evolution can be seen as a dramatic change in the form of the ice.

I have divided the evolution into three Phases: formation, transformation and transport, and stationary ice covers. Dividing the evolution process into three phases ike this is somewhat arbitrary, but this approach makes clear the main processes that are occurring in each Phase.

During Formation, Seed crystals enter the supercooled water and the process of secondary nucleation produces many new, individual crystals.

The next phase is the transformation and transport phase. In this phase the individual crystals join together in a process known as flocculation. Several crystals to several dozen crystals may join together to larger units. These larger units are


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referred to as “flocs”. The actual mechanism(s) that cause(s) the crystals to join together is not known. Certainly if crystals come together in supercooled water they can freeze together. Sintering, the melding under pressure at temperatures at equilibrium or greater, may also play a role. Frazil crystals may also be deposited on the channel bottom. In this case they are referred to as anchor ice. The crystals that are not deposited on the bottom are transported downstream with the flow. At this point, the water temperature is no longer supercooled but has returned to the equilibrium temperature. The buoyancy of the flocs causes them to collect on the surface as frazil slush. There is always a tension between the buoyancy of the flocs, which tends to cause them to rise and remain at the surface; and the turbulence of the flow, which re-entrains the frazil ice into the depth of the flow. Frazil slush that remains at the surface becomes available to be formed into ice floes. This process is referred to as Floe formation and induration (hardening). Frazil slush that is exposed to cold air at the water’s surface will eventually form into floes, if the turbulent intensity is not too large.

The final phase is the formation of stable ice covers and under ice transport. We are all familiar with river ice covers. The mechanisms that form a stable ice covers depends on the depth and velocity of the flow at the leading (upstream) edge of the cover, and the form of the ice when it arrives at the leading edge. Large, thick ice floes in arriving at the leading edge at a point where the river is deep and slow moving will form a much different ice cover than frazil slush arriving at the leading edge where the flow is shallow and fast flowing. If the flow is high enough, all the ice may be swept under the leading edge and transported under the ice cover, perhaps for many kilometers.


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This cartoon also recapitulates the evolution of frazil, but shows how the different forms of ice appear. We start on the left with supercooled water. The flow is highly turbulent; gradients of temperature do not exist with depth and the water is supercooled from the surface to the bed. Seed crystals are introduced. Quickly many more crystals are created and grow in size. Crystals deposited on the bottom are anchor ice. The anchor ice can lift from the bottom and join the frazil collecting on the surface as slush. The surface slush can form floes. Eventually, the transported ice arrives at the leading edge of a stable ice cover, one that has formed spontaneously, or was formed through the use of ice control structure such as floating booms. Frazil ice can be transported a great distance under the ice cover and can be deposited on the bottom of the cover. Such depositions can become very thick, up to many meters.


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When frazil crystals stick to any underwater object we know that the water and the object must be supercooled. When frazil ice sticks to any underwater object, it is referred to as anchor ice. We see frazil ice that has stuck to an underwater chain that has been removed from the water in the upper image. The operators of a hydroelectric plant left this chain in the water. They would periodically remove it when they suspected the presence of frazil ice to see if ice was, in fact, present. You can imagine the difficulties of operating any water intake when the water is supercooled.


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Every water intake has a trash rack. The trash rack is a collection of bars in front of the intake to prevent debris from entering the intake. Generally, the bars are made from steel, and are spaced from ½ inch (12 mm) to 8 inches (203 mm) apart, although there are always exceptions. The trash rack spacing should be designed to keep material out that will damage downstream pumps, filters, etc. Frazil sticks to the trash rack when the water entering the intake is supercooled. The frazil continues to accumulate on the rack as long as flow passes through the rack. It is not uncommon for racks to become completely blocked. This can come as quite a surprise to the operators who only become aware of what is happening when the pumps trip out due to lack of water, alarm bells ring, and general pandemonium reigns. This image shows a hydroelectric intake trash rack that was removed after becoming completely blocked.


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Samples of frazil slush take on a characteristic white appearance when the water drains out of them. A micrograph taken of one floc of frazil slush shows how a number of crystals have come together to form this larger unit. There are hints of the original crystals, perhaps. Note also, the angular, rough outline of the floc. This angularity may encourage mechanical interlocking of flocs, allowing them to join together to form larger floes.


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This is a diagram of the formation of ice floes. In the top center is frazil slush, the basic material that forms all river ice floes. Across the bottom of the diagram I have indicated a continuum, from high velocity, high energy, mountain streams on the left; to slow flowing, low energy streams on the right. The type of floe formed will depend on where in this continuum the slush occurs. If it is in a steep mountain stream, the turbulent intensity may be enough to break apart any floe that tries to form, and the slush will remain as slush. In the middle part of the diagrams, floes form, but these floes will be of a relatively small size. These floes have a characteristic circular appearance and are known as pancake ice. Waves in oceans and large lakes can also create pancake ice. In slow moving rivers, the channel geometry can force large amounts of slush to converge in onearea to form very large floes, with a size equivalent to the width of the channel. These large floes can also be formed from pancake floes as well as slush, of course.


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The upper image is a stream in northwestern PA and lower image is a river in China. Both show frazil ice moving downstream. There is the suggestion that surface floes are forming in the PA picture and we can see the definite formation of floes in the China image. The ice in the China picture has traveled much further than the ice in PA. The image in PA was taken in early morning and the ice seen here was undoubtedly formed the night before.


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The upper image shows pancakes on the Green River in Utah. The Green River is very steep in the reach immediately upstream. Pancake ice is formed in this steep reach and then travels for many miles downstream. The lower image shows frazil slush entering a slow moving section on Oil Creek in PA. The presence of shore ice and the low flow velocity causes the slush to converge. The flow velocity exerts a drag force that causes large separate floes to break off of the converged slush. This can be seen on the right side of the image. In fact, a regular progression of relatively large floes can be seen moving to the right away from the converged frazil slush. So in this case, we have a continuous supply of slush entering on the left and a regular progression of discrete, large floes leaving on the right.


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Border ice is ice that is formed along the banks of a river channel. Border ice can be formed in two different ways: floes and frazil slush can be deposited along each shore; or ice can spontaneously grow away from the bank into flow. This second means is possible if the flow velocity is very low near the bank and the depth is shallow. We really do not have a good way of predicting the growth rate of border ice at this time.


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Now we are going to turn our attention to the formation of stable ice covers. Stable ice can last for long periods of time through the winter. The ice covers impacts the hydraulics of the river flow.


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The type of ice cover formation we are going to consider is called dynamic ice formation, that is formation that is dominated by the interaction of ice floes and the flowing water. Once an ice cover has formed dynamically, however, it can then thicken due to heat lossto the atmosphere.

The flow conditions of depth and velocity determine the type of process that occurs when ice floes reach the leading edge of a stationary ice cover. Starting with the lowest flow velocity, each successive process occurs under higher and higher flow velocities.

Bridging describes “spontaneous” formation of stationary ice covers. At the present time, we cannot predict if an ice cover will form spontaneously at any location. Certainly, it is more likely in river reaches where the flow velocity is very low, and the width is relatively narrow. Ice control structures are sometimes used to promote or ensure that an ice cover will, in fact, form at a particular location.


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Slide script Here are some important points to remember about river ice covers. First of all: river ice covers are always floating at hydrostatic equilibrium. The pressure at the base of the cover exactly balances the weight of the ice cover. If you drill a hole through the cover, water does not shoot up in the air like a geyser. Of course, if you park your pickup on the ice next to your fishing hole, you may see water come up through the hole and flood the ice surface. This is due to the additional weight of the vehicle and I suggest you drive your truck off the ice as soon as possible. If the water level of the river changes, the ice cover will respond to the change. During this period of time that the ice cover is responding to the change in water level, it may not exactly be floating at hydrostatic equilibrium. In fact, it can’t be because there has to be an unbalanced pressure force to cause the ice to move to its new position. However, these periods tend to be short and the amount of the unbalanced pressure force small, and so for all intents and purposes, the ice can be considered to be at hydrostatic equilibrium.

Next are listed the three important ways in which an ice cover, floating at hydrostatic equilibrium can influence steady flow in a river.

• Blocks flow area

• Reduces hydraulic radius (area/wetted perimeter)

• Modifies effective channel roughness (Manning’s n)


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We know that every year the ice covers formed during the cold of winter will breakup and disappear. Breakup transforms a completely ice-covered river into an open river. Two example forms of breakup bracket the types of breakup commonly found throughout most of North America. At one extreme is thermal meltout. During an ideal thermal meltout, the river ice cover deteriorates through warming and the absorption of solar radiation and melts in place, with no increase in flow and little or no ice movement. At the other extreme is the more complex and less understood mechanical breakup.

Actual breakups take place most often during warming periods, when the ice cover strength deteriorates to some degree and the flow entering the river increases because of snowmelt or precipitation. Therefore, most river ice breakups actually fall somewhere in between the extremes of thermal meltout and mechanical breakup. As a general rule, the closer that a breakup is to being a mechanical breakup, the more dramatic and dangerous it is because of the increase in flow and the large volume of fragmented ice produced.


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Every river in North America will experience a thermal meltout every spring unless a mechanical breakup occurs first. The ice cover melts in place because of heat transfer into the ice cover from the flowing water and the atmosphere. Direct sunlight can play an important role, but because the surface of the ice is often white much of the sunlight will be reflected. The absorption of sunlight can be promoted if the surface color can be modified, such as by dusting with a dark material. The creation of meltwater on the surface will also help the ice absorb sunlight. The ice cover can also deteriorate internally without much of a loss of thickness if solar radiation is able to penetrate it. The absorbed solar radiation causes melting in the interior of the ice that results in a loss of structural integrity of the cover.


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The process of mechanical breakup of the river ice cover can lead to spectacular and dangerous ice jams. The formation of an ice jam is the last of step of a process that starts with the mechanical breakup of the ice cover. The individual pieces are the carried downstream. Ice jams form at locations where the capacity of the channel to transport ice floes is exceeded.


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A pure mechanical breakup occurs when the hydrodynamic forces acting on cover exceed cover strength. The increases in the hydrodynamic forces arise because of the increase in the river flow. The flow increase will generally result from a precipitation event, snowmelt, or the opening of gate at a dam.

The increased force on the ice cover fractures the ice covers. The fractures free the ice cover from the constraints of the channel banks and the ice pieces are transported downstream. A rough rule of thumb is that the water level must rise 1.5 to 3 times the ice thickness before the ice cover will be begin to breakup

The breakup process follows a rough progression: first shore cracks are seen, then lateral crack across the channel; then transport of the ice pieces; and then fracture of the moving ice into smaller piece sizes.


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Shore cracks are longitudinal cracks running parallel to the banks of the rivers. Shore cracks form when the magnitude of the water level change in the river channel exceeds a limit determined by the material properties of the ice, the ice thickness, channel width, and the type of attachment of the ice cover to the channel bank (hinged or fixed). Only a small increase or decrease in discharge is necessary to cause shore cracks, and they are usually common soon after runoff into a river has begun to increase. The presence of shore cracks does not necessarily indicate the immediate onset of breakup. They may be present throughout the winter season.


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Transverse cracks (across the channel) will appear soon after the river stage has begun to increase. The first cracks will generally create relatively large ice floes, a river-width wide, and many river-widths long, but sometimes the ice covers are immediately broken into much smaller floes. The actual mechanisms responsible for creating the individual floes have not yet been positively identified.


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As the stage continues to increase, the ice floes will begin to move. If the floes are relatively large, they may be kept from movement by geometric constraints, such as sharp bends, constrictions, the presence of bridge piers, etc., until a substantial increase in stage is reached. If the floes are relatively small, and there are no constraints, they may begin to move after a small stage increase. As a rule of thumb, the stage must rise 1-1/2 to 3 times the ice thickness before the ice moves. Once the floes begin moving, they are quickly reduced in size, eventually arriving at a size that is roughly 4 to 6 times the ice thickness.


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Ice jams form when the moving ice floes reach a location in the river where its ice transport capacity is exceeded. This is most likely at places where an intact ice cover remains, the slope of the river decreases, a geometric constraint exists, etc. At these locations, the ice stops moving and jams. This type of ice jam is a breakup ice jam. Ice jams substantially reduce the channel flow conveyance. As a result, water levels upstream of an ice jam can rise substantially and quickly, causing flooding and transporting ice into the flood plain. The probable maximum thickness and roughness of ice jams can be estimated and used to estimate the probable flood stages (see Chapter 3).


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Look at the two images. On the left, we see a very rough field of ice. This is obviously a jam. The relief in the ice is large, certainly on the order of the height of the two individuals standing on the ice, say 6 feet (2 meters). Now look at the image on the right. The ice cover looks smooth. This may not be reported as a jam. But this is an ice jam as well, and has a dramatic effect on the hydraulics of the river


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The International Association of Hydraulic Research (IAHR) put together a working group of international ice experts to decide on common definitions for all ice terminology, including ice jams. After literally years of discussion, they arrived at this simple definition of a river ice jam: “ An ice jam is a stationary accumulation of fragmented ice or frazil that restricts flow.” There are several key concepts here. The first is that an ice jam is stationary. The second is that a jam is formed from fragmented pieces of ice or frazil ice. And finally, that an ice jam restricts the flow.


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Lets now turn our attention to the two main types of ice jams. The first we are going to cover are freezeup jams. Freezeup jams occur during the ice formation process.


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These are the general characteristics of a freezeup jam. Freezeup jams are formed largely from frazil ice. We know that the formation of frazil ice requires open water and subfreezing air temperatures. Freezeup jams happen when so much frazil ice is transported into a reach of river that it substantially blocks the channel cross section.

Freezeup jams are fairly robust once they are in place. Often this causes problems when the ice cover upstream of the freezeup jam breaks up and runs downstream. The location of the freezeup jam is a classic location for a breakup jam to occur.

The river flow rate is usually fairly constant or slowly decreasing during the formation of freezeup jam. There is usually a rise in water level upstream of the jam as the flow capacity of the channel is reduced as ice fills the channel cross section.

A freezeup jam will have porosity of about 50%. Heat loss from the surface of the jam will quickly freeze the water in the interstices of the ice. The jam will then exhibit cohesion. The undersides of freezeup are not particularly rough. As a result, the jams are not particularly rough hydraulically.


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This is a schematic diagram of a freezeup jam. This diagram is simplified in that it shows the jam with a flat, horizontal bottom across the width of the channel. This is not likely. Usually, the bottom of the ice cover will be very uneven, and the flow area may be limited to small section of the river cross section. In fact, it may be difficult to locate the actual flow area under the ice.


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This image is of a freezeup jam. The surface has the characteristic white appearance of drained frazil ice. There are also characteristic shear lines where the ice cover successively shoved and thickened as it was formed.


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Shear wall is the term used to describe the ice left along the channel banks after an ice jam has blown out or melted out. This image shows the shear wall left in place after a freezeup jam melted out. The frazil ice deposits in this jam were quite thick compared to the channel depth. In the background is a small hydroelectric station that was flooded out by the jam.


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Let’s turn our attention to breakup jams.


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Slide script Where do breakup jams tend to occur? Breakup jams occur at locations where the river’s ability to transport the broken ice floes is exceeded. These locations are:

• Upstream edge of an intact ice cover

• Sharp bends

• Decreases in channel slope

• Constrictions, such as at bridges, islands

• Confluences.


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Slide script These are the general characteristics of breakup jams. Breakup jams must form after the river ice cover has formed so this means the jams occur relatively late in the season. This is especially true in Alaska, where most breakup jams occur in May. However, in the continental US, warm fronts can occur at any time, so as soon as a cover has formed, the potential for a breakup jam exists.

Breakup jams are formed from pieces of fragmented ice covers, which implies that the ice cover was mechanically broken up. Mechanical breakup, in turn, results from increases in river flows. Increases in flow occur during precipitation events, snowmelt events, or when the outflow from a dam or hydraulic control structure was increased. Certainly the first two situations require that the temperature be above freezing.

Breakup jams are formed from broken pieces of the ice cover. Typically, the average diameter of broken ice pieces is three to five times their thickness.

Breakup jams can form quickly causing upstream water levels to rise rapidly. As the upstream level rises, the net pressure acting on the jam increases. At some point, the jam may suddenly release, sending a large wave of water downstream. It is not possible to predict the conditions under which a breakup jam will release. It is very dangerous to walk on breakup jams once they have gone into place. As a result, we have not been able to make many measurements of ice jams once they are in place. The pieces of a breakup jam exhibit little cohesion. This reflects the relatively warm air temperatures under which they formed. The underside of breakup jams can be very rough in appearance and also be very rough hydraulically.


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This is a schematic diagram of breakup jam. This diagram is simplified in that it shows the jam with a flat, horizontal bottom across the width of the channel. This is not likely. Usually, the bottom of the ice cover will be very uneven, and the flow area may be limited to small section of the river cross section. It is my opinion that breakup jams are often grounded on the channel bottom over a portion of the downstream “toe” of the jam, especially in smaller channels.


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This image is an example of a breakup jam. The individual pieces can be clearly seen.


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These images show the ice left when a breakup jam has moved out. Especially interesting are the shear walls left in place. These walls can be quite dramatic, with thickness of several to many meters, depending on the size of the channels and conditions when the ice jam formed. Measurements made in Canada indicate that the thickness of the shear wall is a pretty good estimate of the actual thickness of the jam.


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The upper image is of a shear wall left in place when an ice jam moved out. The lower image documents the erosion that can be caused by an ice jam. The erosion can be caused by direct scour of the bank by ice and because the ice jam directed the flow against the bank itself.


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Slide script This is a diagram that displays the forces acting on an ice jam that is composed of small, individual pieces. The jam in this diagram can be considered to be composed of a granular material. This is a typical breakup jam. Breakup jams cause a considerable amount, if not the vast majority, of flooding associate with ice jams. This type of jam will turn out to be important for us because we can describe the material properties of the jam in engineering terms. This allows us to estimate the jam thickness that is required to resist the applied forces.

In the bottom diagram the forces acting on the jam are shown. These are the water drag force acting on the bottom of the jam and the component of the gravity force that acts in the downstream direction due to the slope of the water surface. (The wind drag is also shown but the wind drag is hardly ever significant and is almost always ignored.)

In the top diagram, the force resisting the downstream force is shown. This is the shear force developed between the ice cover and channel banks. This is the only force that can balance the downstream forces. The internal shear stress in the cover arises because the downstream forces may not be exactly balance by the bank stress at every section along the channel. If the downstream forces are in balance with the bank stress at every section, the jam is referred to as an equilibrium jam. Equilibrium jams are rare in nature, but the concept of the equilibrium jam has proved fruitful to ice jam analysis.


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Slide script This is an important diagram that describes the various sections of a wide river jam that contains an equilibrium section. The downstream end of the jam is the “toe.” The ice thickness changes rapidly immediately upstream of the toe. This portion of the jam cannot be in equilibrium because of the rapid changes in jam thickness along the length of the jam. That is why it is referred to as a “transition” section. The actual ice conditions at the toe are generally not known.

The equilibrium section begins above the downstream transition. In the equilibrium section, the ice thickness is constant and the forces are in balance. In nature, equilibrium sections exist about as often as uniform flow exists in open channels. Changes in the channel width, depth, and slope will all lead to new transition sections. However, ice jam equilibrium is a powerful concept that can provide a lot of insight in ice jam force balance analysis.

The upstream end of an ice jam ends in another transition from the equilibrium section to the leading edge of the ice cover.

This is a classic ice jam: start at the toe with a transition section leading to the equilibrium section. The equilibrium section extends upstream for most of the length of the jam. At the upstream end of the jam another transition section exists before the upstream end of the ice jam.


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Arctic Engineering Module 3b

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This is Jon Zufelt welcoming you to Module #3B – Physical and Mechanical Properties of Ice. This presentation will provide information on the properties of water, river ice, lake ice, and sea ice. The reading assignment for this module is in the Course Texts, EM 1110-2-1612 Ice Engineering Manual Chapter 2 and “River and Lake Ice Engineering” Chapter 2.


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In ice engineering, ice is almost always in contact with liquid water, whether it is the ice in a jam on a river or the bottom of the growing ice sheet on a lake. To understand ice, we should look at water a bit, also. Water molecules are composed of one oxygen atom and two hydrogen atoms. The structure of the water molecule arises from the covalent bond or sharing of an electron between the hydrogen and oxygen atoms. A covalent bond is one of the strongest molecular bonds there is and gives rise to some of water’s unique properties. The hydrogen atoms attach to the oxygen atom at a 105-degree angle between them which gives rise to an electrical polarity, the oxygen side of the molecule has a negative charge while the hydrogen side has a positive charge.


Page 3 of 27

Slide script

The electrical polarity of the water molecules gives rise to hydrogen bonding in which the positive hydrogen sides are attracted to the negative oxygen sides of neighboring molecules. Water and ice have this hydrogen bonded structure where each oxygen atom is associated with two hydrogen atoms but with the restriction that only one hydrogen atom can be located between any pair of oxygen atoms. The slide shows this arrangement of covalent (strong) bonds and hydrogen (weaker) bonds.


Page 4 of 27

Slide script

The effect of the hydrogen bonds results in some interesting and important properties for water. It has a high heat capacity or the ability to absorb a large amount of heat with little increase in temperature. This is why dry air (like in a desert) heats up and cools down much more rapidly than humid air. Water also has a high latent heat of fusion or the amount of heat that must be lost before change of liquid to solid state occurs. Think of how dangerous it would be to be out on the lake ice skating on a sunny day if the latent heat of fusion was the same as the amount of heat required to raise the temperature of water one degree (80:1 ratio). Water also has a very high latent heat of vaporization which acts to keep the water in our lakes instead of the atmosphere. Finally, water has a very high surface tension, important in droplet formation, crystal formation, and capillary wave formation.


Page 5 of 27

Slide script

The specific heat is a measure of the quantity of heat that must be added to a unit mass of substance to raise its temperature one unit degree under constant pressure. Water has a high specific heat meaning that a relatively large amount of heat must be added or extracted to change the temperature. The specific heat of water is a function of temperature and is given in the following empirical equations for SI and English units.


Page 6 of 27

Slide script

The density of water is temperature dependent and even though the changes in density over the range of water temperatures normally encountered in nature are small, the effects are very important. Unlike most substances, the density of water increases with decreasing temperature only to about 4 °C. Further decrease in temperature actually results in a decrease in density as the hydrogen-bonded molecules begin to align into a regular crystalline pattern. Upon freezing, the crystalline structure takes up much more room and the density decreases significantly.


Page 7 of 27

Slide script

This slide gives the empirical formula for the density of water as a function of temperature at standard atmospheric pressure. The maximum density of freshwater (at 4 °C or 39.2 °F), is 1000 kg/cubic meter or 62.4 lbs/cubic foot.


Page 8 of 27

Slide script

In the summer, natural water bodies will have warmer and lighter water at the surface with cooler denser water at the bottom. As the surface water in the lake cools and becomes more dense, it will sink to the bottom. As the water continues to cool, the entire lake reaches a uniform temperature of 4 degrees Celsius. The surface will continue to cool but the water will remain at the surface since it is now less dense. Ice eventually forms at the surface. The denser water at the bottom forms a thermal reserve for the lake which is insulated from further heat loss by the ice sheet and snow on the lake surface. Windy conditions prior to freeze-up will result in significant mixing of the water, thereby reducing the water temperature near the bottom and the potential thermal reserve.


Page 9 of 27

Slide script

As water freezes, the molecules arrange themselves in a more open, more regular, hexagonal crystalline structure. The oxygen atoms occupy the points of the hexagonal lattice in which each oxygen atom is tetrahedrally coordinated with four other oxygen atoms. The oxygen atoms are concentrated in planes, called basal planes which are situated perpendicular to the hexagonal axis or c-axis. In the figure on the right, the view is along the c-axis and looking down through the hexagonal basal planes.


Page 10 of 27

Slide script

The density of freshwater ice at 0 degrees Celsius is 916.8 kg/cubic meter or 57.2 lbs/cubic foot. Like most solids, ice contracts with decreasing temperature, thereby increasing the density. Its density is most affected by impurities such as air bubbles (which can reduce the density) or pockets of liquid water (which can increase the density). For most ice engineering applications in the temperature ranges expected, a value of 915-917 kg/ cubic meter or 57.1-57.2 lb/cubic foot is a good value for freshwater ice density.


Page 11 of 27

Slide script

Thermal conductivity is the measure of the ability of ice to transmit heat under a unit temperature gradient. The values of thermal conductivity for freshwater ice are given here in the slide for both SI and English units. Ice is less of a heat conductor than copper or aluminum (which have thermal conductivities of 388 and 209 Watts/meter-degree °C) but a greater heat conductor than wood or concrete. Impurities, unfrozen water, and air bubbles can affect the thermal conductivity. The latent heat of freezing, or that amount of heat that must be lost for water to change into ice, is much higher than the specific heat of ice, which is the amount of heat which much be lost to drop the temperature of ice by one degree Celsius. The specific heat of ice is roughly half of the specific heat of liquid water.


Page 12 of 27

Slide script

Mechanical properties of ice are important parameters that determine the forces that ice may exert on structures or the way that ice deforms under loading conditions. Depending on the crystalline structure of ice, its behavior can range from brittle to ductile, also being influenced by the loading rate, temperature, testing technique, and testing conditions. Detailed explanations of ice properties can be found in Chapter 2 of “River and Lake Ice Engineering” our course text.


Page 13 of 27

Slide script

Strength is mechanical property of ice that comes to mind in engineering terms since it determines the ice forces acting on a structure or the load bearing capacity of an ice sheet. Strength tests are relatively easy to perform and as such, ice strength has been extensively tested. Strength is defined as the maximum stress that a specimen can support. Failure is described as brittle when the specimen ruptures or breaks with an instantaneous drop in stress and ductile if the strain continues to increase with no further increase in stress. Strength values must be fully qualified in their description since they depend on temperature, ice type (crystal structure), grain size, air bubble content, loading rate, orientation, end conditions, and specimen size.


Page 14 of 27

Slide script

Compressive or crushing strength is the maximum load that can be supported due to loads perpendicular to the c-axis. These type of loadings usually occur normal to the floe thickness, such as a floe being pushed against a vertical wall or crushing against a bridge pier. The main factors affecting crushing strength are the crystal size, rate of loading, and ice temperature. For snow or frazil ice and columnar ice at a temperature of -10 °C, the average crushing strength ranges between 8 to 10 Mega Pascals or 1.1 to 1.5 thousand psi. The formula given here for crushing strength is from experiments by Michel and includes the variables of temperature and crystal size.


Page 15 of 27

Slide script

Tensile strength is much harder to measure due to the difficulty of attaching the specimen to the loading device. As such, only limited test data exists on tensile strength. In the brittle failure region, strength appears to be mainly a function of grain size with very little influence of temperature. There seems to be no impact of strain rate on the results. For snow ice (small grains) at –7 °C, values of 1.8 to 2.2 Mega Pascals have been measured. Larger columnar-grained ice showed strengths of 1 to 1.2 Mega Pascals. There is not much call for values of tensile strength, mainly in ice breaker performance and forces on inclined structures.


Page 16 of 27

Slide script

Shear strength implies a lateral movement within the material or forces that cause breakage along a plane. Since the different testing methods approach shear in various ways (torsion, direct shear, and punch tests) values can vary widely. Russian literature gives shear strength ranges of 0.2 to 4 Mega Pascals depending on temperature, ice type, specimen size, and loading rate.


Page 17 of 27

Slide script

Flexural strength has been investigated both in the laboratory and in the field and applies to performance of ice breakers, ice forces on inclined structures, rubble mound and ridge building, and determining safe bearing capacities on ice sheets. The flexural strength is the maximum vertical load that can be supported by an ice sheet at its edge. The results of many tests show that the strength reported depends on the size of the test specimen, the type of test performed, crystal size, and whether the top or bottom of the ice sheet is put into tension. Values for competent freshwater columnar ice ranges from 0.5 Mega Pascals for large cantilever beam specimens to 1.2 Mega Pascals for small specimens in simple beam tests.


Page 18 of 27

Slide script

Breakthrough loads are discussed later in the course but for short-term duration loads, the allowable load P that a floating ice sheet can withstand is proportional to the square of the ice thickness. This slide presents the formula representing this relation. The value of A depends on the system of units used.


Page 19 of 27

Slide script

The Elastic Modulus or E represents the relationship between stress and strain. It depends on the ice temperature, ice crystal structure, and the rate of stress application. Creep, or stress deformation, can occur at high stress levels and can cause the strain to vary during a test. As a result, the values of Elastic Modulus can vary widely. For natural freshwater ice, values have been measured between 0.4 and 9.8 GigaPascals (55 to 1350 thousand psi). For large laboratory tanks of freshwater ice, values have been measured of 4.3 to 8.3 GigaPascals (600 to 1150 thousand psi).


Page 20 of 27

Slide script

The characteristic length, L sub-c, of a floating ice sheet is a measure of the zone of deformation when the sheet is subjected to a vertical load. It is also a measure of the initial size of ice floes upon breakup of a cover. Field measurements have shown that the characteristic length of competent freshwater ice is 15 to 20 times the thickness. The formula for characteristic length is given in this slide.


Page 21 of 27

Slide script

Two techniques can be used in the field to measure elastic modulus and flexural strength with minimal equipment. The cantilever beam test is shown on this slide. A beam is cut in the ice sheet with a length L that is about 5 to 8 times the sheet thickness, h. The width should be about 2 ice thicknesses. The load P is applied to the tip of the beam and the deflection delta is measured. The failure load P prime is used to determine the flexural strength. Formulas are provided in the slide. The saw cuts at the root of the beam (inside corners) should be rounded to avoid local stress concentrations that may cause early beam failure.


Page 22 of 27

Slide script

In the simple beam test, a beam of length L and width B is cut from the ice sheet and placed on two supports. It is loaded at its center with the load P and the deflection delta is measured. Formulas are provided in the slide. For both the cantilever and simple beam test, the top or the bottom of the ice specimen can be put into tension.


Page 23 of 27

Slide script

The properties of sea ice differ from those of freshwater ice mainly due to the presence of brine and air pockets within the ice structure. As sea ice freezes, the impurities are rejected to the crystal boundaries, resulting in brine pockets where the salt concentration is high enough to prevent further freezing. The volume of the brine in parts per thousand is given here as a function of salinity and temperature.


Page 24 of 27

Slide script

The volume of the air voids in the ice structure can be found after measuring the bulk density, ρ of the ice containing salt and air. This relation also depends on the salinity and two functions of temperature.


Page 25 of 27

Slide script

The two functions of temperature are provided here in graphical form and are derived from a phase equilibrium table developed by Cox and Weeks. The total porosity in the ice ν sub-t, and the brine volume fraction of the porosity, ν sub-b are used to calculate values of compressive and flexural strength of sea ice.


Page 26 of 27

Slide script

Timco and Frederking analyzed over 400 samples to come up with the relations for compressive strength presented here as a function of the total porosity (in parts per thousand) and strain rate. The range of applicable strain rates for these equations is 10 to the -7th to 10 to the -4th per second. Relations are given for horizontally loaded columnar sea ice, vertically loaded columnar sea ice, and granular sea ice.


Page 27 of 27

Slide script

Timco and O’Brien analyzed over 900 flexural strength measurements to come up with this relation for flexural strength of sea ice which is only a function of the brine volume fraction. If the brine volume is set to zero, the equation results in a flexural strength of 1.76 Mega Pascals, which agrees very well with the average value of 1.73 Mega Pascals for freshwater ice.

Arctic Engineering Module 3c

Page 1 of 18

Slide script

This is Jon Zufelt welcoming you to Module #3C – Bearing Capacity of Floating Ice Sheets. The floating part is important because it is the material properties of the ice that determine strength and therefore bearing capacity.


Page 2 of 18

Slide script

The most idealized and simplest case of bearing capacity is given in this figure with a point load acting perfectly in the center of a floating ice block. The block has buoyancy due to its density being less than that of water. If the block did not have an extra load on it and you didn’t know its density, you could figure out the density by knowing that the weight of the block must be equal to the weight of the volume of water that is displaced. As in the case shown, if the block has an area of A and has a depth of submergence z, then its weight is equal to A times z times the unit weight of water (gamma sub w). Since we usually can assume a density or unit weight of ice, we can calculate the maximum load that a floating block can hold. For the maximum loading case, the block submergence depth z, is equal to its thickness, h and the maximum load P is given by A times h times the difference between the ice and water density. If the load is not perfectly centered, however, the block will have an induced moment and tip or flip over.


Page 3 of 18

Slide script

This figure shows a load applied to an idealized infinite ice sheet. By infinite, we mean that there are no effects due to attachment at the edges of the sheet. Think of it as a load out in the middle of a lake as opposed to the load on a small puddle ice sheet where the attachment at the edges provides additional support. Away from the load, the buoyancy force supports the ice sheet and is given as a pressure on the underside of the sheet equal to the unit weight of the ice times the ice thickness (or density times gravity times ice thickness). Closer to the load, deflection occurs due to the load and an additional pressure is required to keep the load afloat. This additional pressure is equal to the unit weight of water times the local deflection. The sheet can act as a membrane and deflect below the piezometric head line but any cracks will allow water onto the surface of the sheet which results in additional load on the sheet. Ice sheets respond to loads by elastic and creep deformations depending on the strain rate. If the load is too great (or too concentrated) the tensile strength of the ice will be exceeded at the lower surface and cracks will begin to form, lessening the load carrying capacity of the ice sheet.


Page 4 of 18

Slide script

The loading type is really dependent on the strain rate. At low strain rates, deformation is by creep, while at high strain rates the sheet deforms elastically. Short term loads allow the sheet to deform elastically. These loads might be due to slow moving loads on an ice cover (like a person walking across a frozen pond). Moving loads are characterized by movements that are quick enough to cause the ice sheet to deflect and then return to normal, possibly setting up a resonance. Problems with moving loads often occur as a vehicle traveling across an ice sheet approaches the shore. Finally, long-term loads are those that allow the ice sheet to deform under creep, such as a drill rig on the ice or long-term storage of materials on the ice.


Page 5 of 18

Slide script

Under a short-term load, the ice sheet behaves as an elastic, brittle material. If we assume that the ice cover can be described as an elastic plate on an elastic foundation, we can solve the bearing capacity and deflection analytically (or through a theoretical solution). As long as the elastic stresses under the load are less than the tensile strength of the bottom of the sheet, this analytical solution is valid. If the tensile strength is exceeded, however, the sheet cracks. Further loading causes radial cracks to form extending from the loading point out for a distance of about 2-3 characteristic lengths. Then circumferential cracks form around the loaded area. Eventually, the sheet will break through.


Page 6 of 18

Slide script

The next few slides show some break-through experiments conducted in the test basin at CRREL with fresh water ice. You can see the break-through at the point of loading, the radial cracks extending out from the loading point, and the circumferential cracks.


Page 7 of 18

Slide script

This plot shows the loading (in kiloNewtons) vs. deflection at the loading point (in mm). You can see a reduction in the loading before the break-through which could be due to cracks allowing water onto the ice surface (which would increase the total load on the ice but reduce measured load applied).


Page 8 of 18

Slide script

These two photos show the significant micro cracking between the major radial cracks.


Page 9 of 18

Slide script

The deflection is described in the analytical solution by a differential equation that is presented and solved in both of our texts. The solution results in an expression for the Characteristic Length of the ice sheet as shown here. The factor D is further defined as well with gamma sub w equal to the unit weight of water, capital E is the Elastic Modulus of the ice, h is the ice thickness, and nu is the Poisson ratio for the ice sheet. The figure provides characteristic length versus sheet thickness for several values of Elastic Modulus and a Poisson’s ratio of 0.3.


Page 10 of 18

Slide script The maximum tensile stress, before the first crack appears, can be calculated with the formula shown here. As noted before, characteristic length depends on the Elastic Modulus and thickness of the ice sheet. So, as the loaded area radius increases (as a/L increases in the figure), the value of C and hence the maximum tensile stress decreases. The effect is that for a given maximum tensile stress, the lower C allows a larger load P for a given ice sheet. This means that as you distribute the load over a larger radius, the sheet can carry a larger load. Also shown on the plot is the value of C if the load is placed over a square area at the edge of a semi-infinite ice sheet (think of this as the edge of an ice sheet with open water beyond). Values of C are higher, indicating a lower allowable value of load which is what you would expect at the edge of an ice sheet.


Page 11 of 18

Slide script

Experience with floating drilling platforms in the arctic has resulted in accepted values of maximum allowable tensile stress. For sea ice, 550 kPa (or 80 psi) is customary while a value of 690 kPa (or 100 psi) can be used for freshwater ice. The values customarily used for elastic modulus were obtained by measurements using strain gages embedded in very thick ice platforms (ice islands). 690 MPa is used for calculations of deflections immediately after a load is placed on an ice sheet. The Elastic Modulus decreases with time due to creep deformation and thus for long term loads, a value of only 55 MPa is used.


Page 12 of 18

Slide script

A long data history of break-through loads and ice thicknesses has resulted in some very good empirical relations for short-term bearing capacity. The Army actually did a series of experiments where different sized vehicles were loaded until an ice sheet failed. The form of the empirical relation is P=A * h-squared where P is the load, h is the allowable thickness and A is a coefficient that depends on the condition of the ice, ice temperature, factor of safety desired, and the units used. For a load in tons and ice thickness in inches, the relation is P=h-squared/16 or h=4*P to the 1/2 power. The relation for load in metric tons and thickness in centimeters as well as the relation for load in megaNewtons and the thickness in meters are given in this slide. Of course these values are for clear competent ice. White, bubble-filled, or snow-ice should be considered to be only half as strong or equivalent to half as much clear ice.


Page 13 of 18

Slide script

This slide shows a plot of actual break-through loads for short-term loadings vs. ice thickness. The best fit lines to this data show P=1.93 * h-squared or P=1.75 * h-squared which is a bit higher than the formula on the previous slide of P=h-squared. This difference could be due to the ice sheets not being clear, or not being strong ice.

Table 8-1 on page 8-9 of the Ice Engineering EM provides additional information to assist in vehicle operations on an ice sheet. The table gives values of ice thickness required for different weights of tracked and wheeled vehicles for two different ambient temperature ranges. There is also a recommendation for the distance between vehicles. As the air temperature rises above freezing, the ice sheet will begin to lose its strength (especially at the surface). Continued warm temperatures significantly reduce the bearing capacity.


Page 14 of 18

Slide script

Moving loads present additional difficulties due to the inertia of the ice and water. A load on an ice sheet deflects the sheet in a bowl-shaped area. As the load moves across the sheet, the deflection bowl (and the water that is being displaced) is also moving. Just as with a boat moving through the water, the moving deflection bowl sets up a gravity wave. If the deflection is great enough and the speed is high enough, a wave begins to form in front of the moving load. While this is less evident in deep water, as the water depth decreases, the wave grows and attempts to break as it nears the shore (similar to a beach wave). The most critical time is when a moving vehicle approaches the shore line. Not only does the critical speed become less, the ice thickness near the shore is often less as well. The slide shows the formulas for critical speed (which is really the wave speed) for both deep water and shallow water conditions.


Page 15 of 18

Slide script

Long term loads are characterized by creep deformation. When a load is initially placed on the sheet, deflection occurs. The effect of creep is that this vertical deflection increases with time due to the Elastic Modulus and characteristic length decreasing with time. The maximum deflection of an elastic ice sheet (but still less than the freeboard of the sheet) is given by w-max=P/(rho-water times g times the characteristic length squared). As stated before, the Elastic Modulus for an initially loaded ice sheet would be 690 megaPascals while that of a long-term loaded sheet would only be 55 megaPascals. It is important to limit the long-term deflection of the ice sheet to its freeboard. That way, even as the sheet continues to creep, water shouldn’t leak up onto the surface through cracks (causing additional loading). By limiting the deflection to the freeboard, the effects of creep are that the long-term load is about 3 to 4 times smaller than the allowable short-term load.


Page 16 of 18

Slide script

What if you’re not sure how long you’re going to load the ice sheet, or not certain of the Elastic Modulus? One of the best ways to ensure that you don’t deflect more than the freeboard is to drill a hole in the sheet near your load. As long as the water doesn’t come up onto the ice, you should be safe. This is the ice fisherman’s rule: if your truck tires are getting wet, its time to move.


Page 17 of 18

Slide script

We often need to significantly load an ice sheet, whether for construction or safe passage across a river. Methods to increase the bearing capacity of the ice sheet include distributing the load over a larger area. This might be done by spreading out your items to be stored rather than stacking them up. Other ways to increase the bearing capacity include increasing the Elastic Modulus or increasing the ice thickness. The latter can be accomplished by removing the snow cover (which is really an insulation layer) from the ice sheet to induce ice growth or by periodically flooding the ice sheet in thin layers, thereby building up the thickness. A final method of increasing bearing capacity is to reduce the time of loading such that you maintain short-term loading conditions.


Page 18 of 18

Slide script

So in summary, the bearing capacity of floating ice sheets depends on the type of loading, whether short-term , moving, or long-term. Many parameters influence the bearing capacity including the Elastic Modulus, characteristic length, ice thickness, loading area, and time of loading. Creep deformation and cracking can accelerate the failure of ice sheets and the available freeboard of the sheet should also be monitored.

The homework assignments look at some practical aspects of bearing capacity. It can be found under the assignments section of the website and will be due on April 24th.

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