1Frozen ground is soil or rock with a temperature below 0 C.The definition is based entirely on temperature and is indepen-dent of the water and ice content of the soil or rock. The largeincrease in soil strength on freezing has been utilized by engi-neers in the construction of frozen earth structures. The icebecomes a bonding agent, fusing together adjacent soil particlesor blocks of rock to increase their combined strength and makethem impervious to water seepage. Excavation and other workcan proceed safely inside, or next to, a barrier of strong, water-tight frozen earth. In cold regions, perennially frozen ground(or permafrost) remains at a temperature below 0 C continu-ously from year to year. Moisture in the form of water andground ice may or may not be present. Seasonally frozenground involves temperatures below 0 C only during the win-ter season. In the Northern Hemisphere, the southern limit ofcold regions extends to about the 40th parallel. Engineers iden-tify this southern limit by the depth of seasonal ground freez-ing, the 300-mm depth of frost penetration.

Several distinct terrain features are associated with perenni-ally frozen ground. The more important ones are ice wedgesand ice-wedge polygons, pingos, and thermokarst topography.These features are important in that they reflect special kindsof geomorphic processes, including frost action, patternedground, and mass wasting (downward movement of surfacematerials due to gravity). Complex glacial stratigraphy belowthese terrain features relates to potentially difficult and expen-sive construction problems. Engineering considerationsrequire an understanding of the freezing process, the effects ofthawing frozen ground, seasonal frost heave and settlement,and how useful aspects of frozen ground can be utilized by theengineer. Useful aspects include the stability, high strength,and impervious conditions that are utilized in frozen earthstructures for construction purposes. In cold regions, perenni-ally frozen ground can provide excellent bearing capacity forthe support of structural loads. For useful applications, someprecautions are necessary, the most obvious being to keep theground frozen.

1.1 Frozen Ground Support Systems

The use of ground freezing to form earth support systems hasworldwide applications. These systems are used on a variety ofconstruction problems, including frozen earth walls for deepexcavations, structural underpinning for foundation improve-ments, and temporary control over groundwater on construc-tion projects. Structural and thermal design considerationsinvolve the soil type, groundwater conditions, ground move-ment related to freezing, and possible thaw settlement on com-pletion of a project.

Frozen Earth Wall

Frozen soil structures are created by installing freeze pipes inwhich the cooling medium circulates down an inner pipe andreturns via the space between the pipes, as is illustrated in Fig.1-1a. The coolant is provided by a refrigeration plant locatedon the construction site. Heat extraction from the soil results incooling to 0 C, transformation of free water into ice, and addi-tional cooling of the frozen soil. Initially, the frozen soil forms acolumn around each freeze pipe. With continued heat extrac-tion, the frozen soil columns increase in diameter until theymerge and form a frozen wall. This frozen barrier is shown inFig. 1-1a as a circular wall surrounding the shaft excavation.Excavation limits may include a small portion of the frozenwall, giving a smooth soil face. During construction, insulationin the form of a thermal blanket or sprayed foam is normallyplaced against this wall surface to prevent deterioration bythawing and possible sloughing of the soil. Concrete for theshaft liner can be placed directly against the frozen soil or insu-lation. For deep shafts, prefabricated lining segments are nor-mally used to save construction time.

Based on geometry of the proposed structure and spaceavailable on site, the engineer selects the required excavationlimits and frozen earth wall system. Because of the relativelyhigh compressive and low tensile strengths of frozen soil, curved

1Frozen Ground

2 FROZEN GROUND ENGINEERING

arch walls, particularly circular wall sections, are a good solu-tion. An ellipse can be employed effectively for rectangularstructures if the ratio of length to width does not exceed about 2.If space or other site restrictions prevent the use of curved sec-tions, other structural configurations, including straight walls ormore complex shapes, can be used, as is described in Chapter 6.Various ground freezing applications are shown in Fig. 1-2, withdarker straight lines representing freeze pipes and adjacentshaded areas representing frozen ground. These illustrationsinclude deep excavations, underpinning of foundations adjacentto an excavation, temporary stabilization of a landslide duringremedial work, shafts, deep trenches, and tunnels.

Most ground freezing projects employ the circulating cool-ant freezing system illustrated in Fig. 1-1. Installation of thesystem includes site preparation, placement of freeze pipes, andsetup of the refrigeration plant. The coolant circuit includes abrine tank, a pump, and an insulated supply manifold for thesupply of coolant to the freeze pipes and return to the refrigera-tion plant. The normal freeze pipe spacing is close to 1 m. Flex-ibility in control of the coolant supply manifold allows foradditional heat extraction from individual freeze pipes asneeded. Soil thermal parameters are used to calculate the

energy to be extracted for freezingand the time required for formationof the wall, and to select the refrigera-tion plant capacity. Installation of acirculating coolant type of groundfreezing system for an open excava-tion routinely takes 2 or moremonths from the start of work untilexcavation can proceed.

Design Considerations

Site investigation must include bor-ings that extend well below theplanned excavation depth. These bor-ings provide information on the nat-ural soil strata and samples for soilclassification as well as undisturbedsamples for both frozen and unfrozenstrength tests. Ideally, a frozen wallshould be tied into an imperviousbottom layer to minimize watermovement under the frozen earthwall. Wall deterioration may occur asheat is introduced by flowing water.Soil type, densities, and water con-tents are needed for estimation of soilthermal properties. Thermal calcula-tions are described in Chapter 3.Ground temperatures and informa-tion on groundwater can be obtainedfrom the same borings. If groundwa-ter flow through the site is too large,greater than 1 to 2 m/day, heat fromthe water can prevent frozen soil col-

umns from merging, leaving openings in the completed wall.Possible solutions include reduced freeze pipe spacing or a sec-ond row of freeze pipes to increase the rate of heat extraction,and/or grouting during freeze pipe installation to reduce soilpermeability and water flow rates.

Ground movement may occur as a result of soil freezing,thawing, and removal of soil from the excavation. The freezingprocess involves conversion of water in the soil pores into ice,with an increase in volume of about 9%. Sanger and Sayles(1979) computed the resultant heave on the assumption thatone-half of the volume change occurs in the vertical direction.Ice lenses may also form along the vertical sides of the frozenwall, causing an increase in lateral frost pressures. Shuster(1972) explained how these pressures must exceed the lateralpassive earth pressure in unfrozen soil before vertical heave canoccur. More information is given in Chapter 6. Thaw settle-ment involves melting of ice lenses and settlement at the com-pletion of a project as the thawed soil volume adjusts to a newequilibrium void ratio. The concepts are described in Chapter4. Soil removal from the excavation involves unloading one sideof the frozen wall. Some horizontal movement occurs until newequilibrium conditions are reached. This introduction to fro-

FIGURE 1-1 Typical frozen ground support system: (a) shaft excavation; (b) freeze pipelayout; (c) refrigeration plant.

FROZEN GROUND 3

FIGURE 1-2 Ground freezing applications: (a) deep excavations; (b) underpinning; (c) landslides; (d) shafts; (e) deep trenches;(f) tunnels.Source: Shuster 1984.

4 FROZEN GROUND ENGINEERING

zen ground support systems and related design problems isexpanded on in the appropriate chapters.

1.2 Seasonally and Perennially Frozen Ground

Ground temperatures required to form seasonally and perenni-ally frozen ground are found in the cold regions of the North-ern and Southern hemispheres. Engineering design requires anunderstanding of the subsurface temperatures, the active layer,and permafrost in these cold regions.

Cold Regions: Definition

Cold regions of the world may be defined in terms of air tem-peratures, snow depth, ice cover on lakes, or depth of groundfreezing. Temperature and frost penetration are of greatestimportance to frozen ground engineering. The isotherm for 0C mean temperature during the coldest month of the year hasbeen used to define the southern limit of the cold regions in theNorthern Hemisphere (Bates and Bilello 1966). An arbitrarilyselected depth of seasonal frost penetration (300 mm) into theground once in 10 years is a generally accepted criterion foridentifying the southern boundary of cold regions, as is shownin Fig. 1-3. This boundary is similar to that defined by the 0 Cisotherm and with minor exceptions is approximated by the40th parallel. Major ocean currents such as the Gulf Streammay ameliorate the climate of adjacent land areas. Thisaccounts for the relatively mild climate of the northwest coastof Europe, Great Britain, and Ireland. Because actual observa-tions on the distribution and depth of frozen soil are scarceand because the freezing temperature of soils varies throughseveral degrees depending on the mineral, organic, and watercontentthe use of the 300-mm depth requires the estimationof frost penetration on the basis of a freezing index derivedfrom meteorological data. The 300-mm frost penetration isrepresented approximately by a freezing index of 55 C days (or100 F days). The intensity of a cold temperature or freezingindex is defined in Section 3.1. This application of the freezingindex is complicated by many factors, including the mineraland textural composition of the soil and the insulation effect ofvegetation and snow cover. It is possible that some areasexcluded by this definition can occasionally experience frostproblems. For these areas, local meteorological and soil datacan be used to provide accurate information on frost penetra-tion for a given site.

The cold regions are typically subdivided on the basis ofwhether the ground is only seasonally frozen, whether perma-frost occurs everywhere (continuous), or whether permafrostoccurs only in some areas (discontinuous) beneath the exposedland surface. This subdivision is used in Fig. 1-3, with the south-ern limit of seasonally frozen ground including a large portionof North America, Europe, and Asia. The division between sea-sonally frozen ground and discontinuous permafrost is based onan arbitrary selection of the 5 C isotherm measured at thedepth of zero annual temperature amplitude (Fig. 1-4). Frozenground in the discontinuous zone generally thickens from 10

cm or less to 100 m or more at the boundary with the continu-ous zone (Brown and Kupsch 1974). Gerdel (1969) stated thatan annual freezing index of at least 3,900 C (7,000 F) days isrequired to maintain a continuous permafrost regime. In polarregions, permafrost can exist to depths of more than 1 km. Thethickness, distribution, and temperature of permafrost are notconstant with present-day climates in many areas. It is usuallyassumed that the mean annual ground surface temperaturemust be at least 3 C for permafrost to exist.

Subsurface Temperatures

Ground temperatures are determined by air (or ground sur-face) temperatures, heat flow from the interior of the earth, andsoil thermal properties. Surface temperatures undergo approxi-mately simple periodic fluctuations (Fig. 1-4) on both a dailyand an annual cycle. Meteorological data for a given locationare used to provide the mean annual temperature (Tm) and thesurface temperature amplitude (As). The ground surface tem-perature (TS,t) can be reasonably estimated as a sinusoidal fluc-tuation that repeats itself daily and annually:

(1.2-1)

where t is time and p is the period, 24 hours or 365 days. If timet is measured from January 1 and the coldest time of the yearoccurs about 2 weeks into January, the surface temperaturecurve (Fig. 1-4a) will be shifted to the right. This can be accom-plished by replacing the sin term in Eq. (1.2-1) by cos(2pt/p 2pf/p). The term f represents a phase lag with the same units asthe period p. This temperature pattern is attenuated with depth(z) and, in a homogeneous soil with no change of state, the tem-perature (Tz,t) at any depth and time can be calculated as

(1.2-2)

where au is the soil thermal diffusivity and where heat flowfrom the earths interior is assumed to be negligible. Soil ther-mal properties are defined in Chapter 2. Equation (1.2-2) isthat of a wave motion whose amplitude Az decreases rapidlywith increase in depth (z) and is given by

(1.2-3)

The range in temperatures, or maximum variation, for anypoint below the ground surface is represented by the areabetween the trumpet-shaped curves in Fig. 1-4. These curvesare given by

(1.2-4)

Equation (1.2-4) represents the maximum and minimumground temperatures at depth z. The simple solution repre-

T T At

pS t m s,sin= +

2p

T T A zp

t

pz

pz t m s u u, exp sin= + -

-

pa

p pa

2

A A zpz s u

= -

exp

pa

T T A zpz m s u

= -

exp

pa

FROZEN GROUND 5

FIGURE 1-3 Cold regions of the Northern Hemisphere.Source: Reproduced with permission from Burdick, Rice, and Phukan 1978. Copyright 1978 McGraw-Hill.

6 FROZEN GROUND ENGINEERING

sented by Eq. (1.2-2) indicates the trends found in actualground temperatures. But in practice, they can be modified sig-nificantly by the effects of soil latent heat, differences in frozenand thawed soil thermal properties (conductivity and diffusiv-ity), nonhomogeneous soils, and nonsymmetrical surface tem-peratures because of seasonal snow cover, vegetation, and otherlocal climatic influences. No analytical closed form solutionexists that considers all these effects, but numerical computersolutions that take some of these factors into account arereadily available (see Goodrich 1973; Braley and Zarling 1991).Note that ground temperatures are not influenced by surfacetemperatures at the level of negligible (zero) annual tempera-ture amplitude.

EXAMPLE 1.2-1: Temperature varies between +20 and 0 Ceach day at the surface of a soil with thermal diffusivity of0.0049 cm2/s. Compute the temperature amplitude Az (or maximum temperature variation) at a depth of z = 30 cm.

Solution: Compute the amplitude of surface temperaturechange As = (20 C 0 C) = 10 C. The period p = 1 day 24 h/day 60 min/h 60 s/min = 86,400 s. Substitution intoEq. (1.2-3) gives

EXAMPLE 1.2-2: The annual ground surface temperatureranges from 10 C on January 15 to +26 C on July 15 at alocation with relatively dry sandy soils. The soil has an averagethermal diffusivity of 0.06 m2/day, with essentially no phasechange for the soil system. Assuming a sinusoidal temperaturevariation, calculate the soil temperature at a depth of 0.5 m onApril 15 and July 15.

Solution: The ground surface temperatures will vary as isshown in Fig. 1-5, with t/p = 0 on April 15 and t/p = 1/4 on July

Az = -

=

10 300 0049 86 400

0 75

C cm cm /s s

C

2exp

. ,

.

p

FIGURE 1-4 Surface and ground temperatures: (a) sinusoidal fluctuations; (b)temperature attenuation with depth.

FROZEN GROUND 7

15. The surface temperature amplitude As = [26 (10)] = 18C and the mean surface temperature Tm = (26 18) = 8 C.Using Eq. (1.2-2), compute

Thus T = 8 2.80 = 5.20 C on April 15 at the 0.5-m depth.

Thus T = 8 + 14.63 = 22.63 C on July 15 at the 0.5-m depth.

Active Layer

The top layer of ground in which temperature fluctuates aboveand below 0 C during the year is defined as the active layer.Terms such as seasonally frozen ground, seasonal frost, andannually thawed layer are sometimes used as synonyms foractive layer. The thickness of this layer varies from as little as 15cm in the far north to as much as 1 m or more to the south. Inthe continuous permafrost zone (Fig. 1-3), it generally reachesthe permafrost table except in the vicinity of water bodies. Insome areas, the active layer is separated from the permafrost bya layer of ground that remains in the unfrozen state throughoutthe year. In the discontinuous permafrost zone, it extendsdownward to the permafrost table in some locations but not inothers. Its thickness depends on many factors, including theseverity of winter temperatures (freezing index), soil and rocktype, ground moisture content, snow cover, surface vegetation,drainage, and the degree and orientation of slopes.

Seasonal frost penetration is associated with an annual ther-mal cycle where the heat extracted in the winter is largely thatentering the ground in the summer. The depth of freezing (0 Cisotherm) is dependent on the surface freezing index and cre-ates a temperature profile as shown in Fig. 1-6. In the NorthernHemisphere, the active layer will increase, then decrease in

T = + -

-

8 18 0 50 06 365 25

2 0 0 50 06 365 25

exp .. ( . )

sin .. ( . )

p

p p

T = + -

-

8 18 0 50 06 365 25

2

40 5

0 06 365 25

exp .. ( . )

sin .. ( . )

p

p p

thickness as the mean annual temperature (Tm) is increased asone goes from north to south. Below the level of zero annualtemperature amplitude, ground temperatures will increasewith depth (Fig. 1-6) an amount dependent on the local geo-thermal gradient (dT/dz).

The annual freezing of the active layer is responsible for theheave that occurs with downward movement of the freezingsurface in a frost-susceptible soil. In situ pore water willincrease in volume by about 9+% on freezing. Additional heaveresults from the formation of ice lenses normal to the directionof heat flow as water migrates by capillary action through thesoil pores toward the freezing surface. When the water table isclose to the ground surface, water that migrates is continuallyreplenished and ice lenses grow continually during the freezingperiod. Most soils are not homogeneous; hence the heave pro-cess will not be uniform along the surface. Frost heaves up to150 mm are by no means uncommon in regions with a moder-ate winter climate.

Highway structures located above the frost heave zone usu-ally experience increased surface roughness and bumps. The0 C isotherm is superimposed on a highway section thatincludes the pavement structure and foundation soils in Fig.1-7. Frost heave will occur during the freezing period. With theapproach of spring and warmer temperatures, thawing willoccur. Thaw of a frozen soil involves disappearance of the ice,permitting the soil skeleton to adapt itself to a new equilibriumvoid ratio. Volume change (settlement) will result from boththe phase change and drainage of excess water away from thenewly thawed soil. As is shown in Fig. 1-7, the pavement struc-ture will be most susceptible to breakup during the periodwhen excess water cannot drain downward through still-frozensoil. The temporary high pore-water pressures combined withheavy vehicular loads result in damage to the pavement struc-

FIGURE 1-5 Surface temperature variation.

FIGURE 1-6 Temperature profile in perennially frozen soil.

8 FROZEN GROUND ENGINEERING

ture. Prevention or mitigation of this frost action in the activelayer is a typical problem for the highway engineer.

Permafrost

Permafrost, or perennially frozen ground, is defined as soil orrock having temperatures below 0 C during at least two con-secutive winters and the intervening summer (Brown and Kup-sch 1974). Moisture in the form of water or ice may or may notbe present. The formation and existence of this frozen condi-tion in earth materials is controlled primarily by climate andvarious terrain factors. Temperature conditions required forthe existence of permafrost are illustrated by the temperatureprofile shown in Fig. 1-6. The thickness of the frozen ground isdetermined by the mean annual surface temperature (Tm) andheat flow from the earths interior corresponding to the localgeothermal gradient. Measured gradients (Brown et al. 1981)range from 1 C per 22 m to 1 C per 160 m. In Fig. 1-6, theactive layer is shown at the surface and unfrozen soil existsbelow the permafrost, where temperatures are equal to orgreater than 0 C.

Geographically, permafrost is divided into two zones; con-tinuous and discontinuous, as is delineated on Fig. 1-3. Thetypical vertical distribution and thickness of permafrost at theircommon boundary is illustrated in Fig. 1-8a. In the discontinu-ous zone, permafrost occurs in scattered islands ranging in sizefrom a few square meters to several hectares. Its thickness willvary from a few centimeters at the southern limit to as much as100 m at the boundary with continuous permafrost. The crite-rion used to delineate the division between these zones is basedon the arbitrary selection of the 5 C isotherm of mean annualground temperature measured just below the level of annualvariation. A thermal balance is maintained in the continuouszone except where slow aggradation or degradation of the per-mafrost may be observed. Deeper frozen zones in discontinu-ous permafrost appear to represent relics of a colder climatefrom the past. A major factor affecting the thermal regime ofpermafrost is the presence of water bodies (Fig. 1-9). Smalllakes freeze completely in winter, so they do not have a majoreffect on permafrost. These lakes thaw more quickly in the

summer due to more efficient warming by water circulation,and as a result, permafrost thickness is reduced slightly. Lakesdeeper than 1.5 m normally do not freeze completely in the farnorth, and the result is an underlying thawed basin and upwardindentation of the lower permafrost surface. In large lakes(diameter permafrost depth), an unfrozen zone will extendcompletely through the permafrost beneath the lake (Fig. 1-9).In terms of its thermal effect, a river behaves like a long narrowlake and the ocean like a large deep lake. This short review illus-trates that a variety of frozen ground and groundwater condi-tions will confront the engineer working in permafrost areas.

1.3 Terrain Features in Permafrost Areas

Ground surface features are indicative of underlying frozenground conditions. Construction in or on this frozen groundmust accommodate related changes in the ground thermalregime, which may cause thaw settlement or other unfavorablesoil conditions. The more important features (Price 1972), par-ticularly with respect to ground ice, include ice wedges, pingos,and thermokarst terrain. Patterned ground includes such formsas polygons, circles, and stripes.

Ground Ice Features

Ice Wedges. These vertically oriented masses of relatively pureice occur close to the permafrost surface, as is shown in Fig. 1-10. They are wider at the top (13 m) than at the bottom andrange in height from 1 cm to 10 m. Formation of the initialopen crack is related to falling winter temperatures. During thisperiod, superficial layers try to contract but are constrainedby more stable lower layers. Low temperatures and rapid cool-ing rates favor larger tensile stresses. The thermal strain is gen-erally higher where ice content is high because the expansioncoefficient for ice is about five times that of most soil particles.Rupture and crack formation occur when tensile stressesexceed the frozen soil tensile strength. The cracks are usuallyonly a few millimeters wide but may extend downward severalmeters. In the spring, water from melting snow fills thesecracks, freezes, and forms a vertical ice vein that penetrates thepermafrost. As temperatures rise in the summer, the perma-frost expands, causing horizontal compression and upturningof adjacent soil. The following winter renewed thermal con-traction reopens the crack, because it is now a zone of weak-ness, and in the spring another increment of ice is added asmeltwater enters the crack and freezes. The ice wedge formsbelow the active layer and would normally not be visible at thesurface. Recurring cracks that cause growth of ice wedgesappear to initiate near the permafrost surface, whereas the orig-inal cracks that start ice wedges and determine their locationprobably initiate at the ground surface. This cycle, operating forseveral hundred years, creates ice wedges of the form illustratedin Fig. 1-10 and shown exposed by a highway cut in Fig. 1-11.Soils in the photo consisted of fine-grained solifluction depos-its derived from glacial till.

FIGURE 1-7 Seasonal ground freezing beneath a pavementstructure.

FROZEN GROUND 9

FIGURE 1-8 Permafrost in cold regions: (a) vertical distribution and thickness; (b) typical profile.Source: Reproduced with permission from Brown et al. 1981. Copyright 1981 John Wiley & Sons.

10 FROZEN GROUND ENGINEERING

Ice wedges may occur singly but most frequently are con-nected at the surface by a system of ice-wedge polygons. Thepolygons form a surface pattern similar to that formed bycracks in drying mud. The polygon diameters are probablydetermined by two factors: (1) variation in the strength of thefrozen surface soils from place to place, and (2) the width of thestress relief zone adjacent to individual cracks. Lachenbruch(1963) stated that crack spacing will be on the order of a fewcrack depths (550 m in northern Alaska). Ice-wedge growthcauses the upturning of surface strata within 3 m of the wedge,creating a ridge at the surface. A prominent ridge with lowpolygon centers is associated with actively growing ice wedges.If thawing and erosion are more prevalent, small stream chan-nels form along the ice wedges and create high-centered poly-gons. As temperatures increase in the discontinuous zone, theice wedges become inactive and eventually disappear. Mostactively growing ice wedges and ice-wedge polygons arerestricted to the continuous permafrost zone.

Pingos. A conical, more or less asymmetrical mound or hill,with a circular or oval base and commonly fissured at the sum-mit, occurring in the continuous and discontinuous permafrostzones is defined as a pingo (Brown and Kupsch 1974). The coreconsists of massive ground ice covered with soil and vegetation,as is shown in Fig. 1-12. This 26-m-high pingo is partly sur-rounded by a lake. A collapse of one side shows the exposed icecore near the top. The term pingo includes mounds with verti-cal dimensions of 10 m or more and horizontal dimensions of100 m or more. Most pingos are restricted to thick alluvial, del-taic, or glaciofluvial sands with negligible fractions of coarseror finer grain sizes. The typical sands are not frost susceptible,lacking sufficient fines to produce either frost heave or thick icelenses. Large areas in the arctic although thermally suitable,have no pingos, because they are too hilly or rocky or are

veneered with too thin-, coarse-, or fine-grained soil for pingoformation.

The two main pingo types include the closed and open sys-tems. The closed-system pingos from the Mackenzie delta ofCanada are the best documented (Price 1972) and occur infairly level, poorly drained shallow lake basins. The distinctionbetween a shallow and a deep lake is based arbitrarily on thesize of the winter unfrozen pool. If the lake is deeper than themaximum winter ice thickness over much of the lake bottom,the lake is defined as deep; otherwise, it is shallow. Typicaldevelopment (Fig. 1-13) involves a drop in the lake basin watertable with a change in the heat balance system. The lake freezesto the bottom, permitting encroachment of permafrost on thelake bed. A closed system forms when permafrost has formedover the entire lake basin. As more water freezes and expands, aconsiderable uplift pressure is created. The result is gradual for-mation of a conical mound consisting of massive ground icecovered with soil and vegetation. Single pingos tend to developwhen freezing to the lake bottom occurs for small lake basinsbecause the small size can nourish only one pingo.

The open-system pingo (East Greenland type) usuallyoccurs on slopes rather than in level areas. Water is supplied bysprings where artesian pressure has developed in unfrozen per-mafrost zones. Differences in elevation provide the hydraulicgradient; discontinuous permafrost permits the entrance ofsurface waters into the ground; granular materials allowgroundwater flow; and an impervious yielding permafrost layercan be arched to form a pingo. As the water reaches the surface,it freezes. The continual water supply allows the buildup of aconsiderable ice mass, which domes the ground surface upwardduring a period of many years.

Thermokarst. A variety of surface features resulting from thedifferential melting of ground ice in permafrost fall under theterm thermokarst. These features include mounds, caverns, dis-appearing streams, funnel-shaped pits, elongated troughs, andlarge flat-floored valleys with steep sides. A disruption of thepermafrost thermal regime by broad-scale climate or localenvironmental changes creates thermokarst features. Climatechanges may involve a rise in the mean temperature, leading towarmer summers. Local changes favoring thermokarst devel-opment include cyclic changes in vegetation, shifting of streamchannels, fire, and human-made changes involving farming orconstruction activities. Clearing trees and vegetation for agri-cultural purposes near Fairbanks, Alaska, in the 1920s led tothe development of thermokarst mounds varying from 3 to 15m in diameter and 0.3 to 2.4 m in height (Rockie 1942). Withthe removal of vegetation, the ice-wedge polygons began tothaw, causing the overlying soil to collapse in a polygonal pat-tern resulting in mounds.

From a geomorphological point of view, the origin ofthermokarst can be divided into two groups: lateral permafrostdegradation (backwearing) and permafrost degradation fromabove (downwearing) (Czudek and Demek 1970). Backwearingis due largely to fluvial, lacustrine, or marine erosion. Rivers inpermafrost areas undercut their banks during the spring thawand expose ground ice, which subsequently melts and col-

FIGURE 1-9 Schematic representation of permafrost distribu-tion in a continuous-permafrost region where the meanocean bottom temperature is greater than 0 C.Source: Reproduced with permission from Gold and Lachenbruch 1973. Copy-right 1973 National Academies Press.

FROZEN GROUND 11

lapses. If ice-wedge polygons are present, conical mounds maydevelop. Another example of backwearing is the developmentof thaw lakes (Hopkins 1949). The lakes are characterized byundercutting along their margins due to thawing of perma-frost. These dynamic features are constantly changing in shape,coalescing, and often migrating across the tundra (Tedrow1969). These oriented lakes are a type of thaw lake rangingfrom small ponds to bodies more than 16 km long and coveringmore than 65,000 km2 on the Alaskan Arctic slope. Their orien-tationapparently due to prevailing wind directionsis con-sistently toward the north-northwest.

Permafrost degradation from above (downwearing) isrestricted primarily to fairly level areas. Thermokarst featuresdepend on the amount and type of ground ice present; where

the amount is small, the result is often flat with shallow depres-sions. After a small forest fire (Czudek and Demek 1970), theactive layer increased in thickness from 40 to 80 cm and theground surface settled 20 cm. Where ice wedges occur, the heatof water accumulating in the summer often causes thawing andcreates troughs. The continuation of this process leads to thedevelopment of beaded drainage, which consists of a series ofsmall ponds connected by short, straight water courses. Thepools forming at the intersection of ice wedges range from 0.6to 2.4 m deep and up to 30 m in diameter. Thermokarst devel-opment may also be very extensive and give rise to large, flat-floored basins (Czudek and Demek 1970) that are 340 m deepand 100 m15 km long. Occasionally, these basins coalesce toform thermokarst valleys of considerable length.

FIGURE 1-10 Schematic representation of ice-wedge evolution according to thermalcontraction theory.Source: Reproduced with permission from Lachenbruch 1963. Copyright 1963 National Academies Press.

12 FROZEN GROUND ENGINEERING

FIGURE 1-11 Ice wedges exposed in a highway cut, Alaska.Source: Courtesy of Jerry Brown, U.S. DOT, and R. L. Berg, U.S. Army, ColdRegions Research and Engineering Laboratory.

FIGURE 1-12 Pingo located about 100 km north of Inuvik,Northwest Territories, Canada.Source: Courtesy of J. Ross Mackay, University of British Columbia, Vancouver.

FIGURE 1-13 Schematic drawings of pingo growth: (a) lake with an unfrozen basin beneath it;(b) growth of permafrost after lake drainage; (c) growth of a pingo at the site of a residualpond.Sources: Reproduced with permission from Mackay 1985; Mackay 1992. Copyright 1985, 1992 National Research Councilof Canada.

FROZEN GROUND 13

Patterned Ground

Patterned ground is a collective term for the characteristic geo-metric ground surface patterns common to periglacial environ-ments. Patterned ground can be divided on the basis of circles,polygons, or strips, and also on the presence or absence of sort-ing, (i.e., separation of stones and fines) (Fig. 1-14). These twocharacteristics form the basis of Washburns (1956) classifica-tion of patterned ground. The principal geometric formsencountered, although some are gradational in both patternand sorting, include (1) circles, (2) polygons, (3) nets, (4) steps,and (5) strips. Drying and/or frost cracking are probably theinitiating processes in the creation of polygonal patterns,whereas local differential heaving is probably important in cre-ating circular patterns (Price 1972). Sorting of materials is dueprincipally to frost heaving and thrusting. The theory (Price1972) is that in heterogeneous material there will be some areasin which there is a greater concentration of fines than in others.The accumulation of fines results in a greater water-holdingcapacity; upon freezing, greater expansion will occur. Uponcontraction during thawing, the fines are drawn back togetherby surface tension forces; the coarser material does not contractas much. After many freezing and thawing cycles, the amountof fines grows and the coarse material is forced farther out. Theprocess continues, forming sorted circles or polygons.Although these statements hold primarily for horizontal sur-faces, the same processes apply to slopes, except that the fea-tures will be elongated, due to mass wasting (downslope move-ment of surface materials due to gravity).

Nonsorted circles are bare circular areas with a vegetativeborder. These circles may occur singly or in groups, are mostoften found on relatively level ground, and are commonly 0.53 m in diameter. Sorted circles involve finer material sur-

rounded by a circular accumulation of stones. Sorted circlesvary in diameter from a few centimeters to more than 3 m andoften extend to a depth of about 1 m. Stone size tends toincrease with circle size, with the largest stones at the surface.Sorted circles may occur singly or in groups and are most com-mon on nearly horizontal surfaces. A slope will cause elonga-tion into stripes (Fig. 1-14).

Nonsorted polygons involve polygonal-shaped surface fea-tures, which are often delineated with a crack or furrow andwithout a border of stones. Vegetation concentrated in the fur-row helps emphasize the pattern. Nonsorted polygons are bestdeveloped on nearly horizontal surfaces but may also be foundon slopes. They never occur singly and range from a few centi-meters up to 100 m in diameter. Excellent examples occur inmiddle latitudes, where they are associated with desiccationcracking. They are typically observed in a mud hole that hasdried up. The largest nonsorted polygons occur in permafrostand are associated with ice wedges (Fig. 1-10). The ice wedgeforms the border, which may be raised or depressed withrespect to the central area depending on whether the wedgesare actively growing or whether thawing and erosion are moreprevalent. High-centered polygons are shown in Fig. 1-15, withsquare patterns (more or less) along the river reflecting the evo-lution of ground ice along the bends in the river.

Sorted polygons are surface features defined by a border ofstones surrounding a central area of finer material. Like non-sorted polygons, they are best developed on nearly levelground and range in size from about 10 cm to 10 m across.They never occur singly, and the size of stones in the bordersincreases with polygon size and decreases with depth. Rocks inthe border are often on edge and oriented parallel to the bor-der, which may or may not be coincident with crack patterns.

FIGURE 1-14 Schematic diagram of patterned ground development.Source: Reproduced with permission from Sharpe 1938. Copyright 1938 Columbia University Press.

14 FROZEN GROUND ENGINEERING

Small sorted polygons may occur in mountainous middle-lati-tude areas. Large sorted polygons are best developed in perma-frost areas.

Nonsorted stripes consist of parallel lines of vegetation andintervening strips of relatively bare ground. They range in sizefrom a few centimeters to 12 m wide and can extend down-slope several tens of meters. Sorted stripes are elongated accu-mulations of stones with intervening areas of fine material.They do not occur singly and are often formed from thedownslope extension of sorted polygons. Sorted stripes rangein size from a few centimeters to 1.5 m or more wide, with theintervening fine material commonly several times wider. Theycan be more than 100 m long and tend to be straighter on steepslopes. The size of stones increases with the size of the stripe.Price (1972) reported stone size up to 1 m in length for stripeslocated in the Ruby Range, Southwest Yukon Territory. Stonesdecrease in size with depth and are commonly turned on edgeand oriented parallel with the stripe.

1.4 Engineering Considerations

The physical properties of frozen ground are dependent on thefreezing process, thawing of frozen ground, and seasonal orlong-term temperature changes. In the frozen state, most soilsbecome relatively impervious and develop high strength. Theseproperties are important and must be considered in engineer-ing design.

Freezing Process

Water contained in the voids of a moist or saturated sand orgravel freezes in situ when the temperature is lowered below thefreezing point. The freezing is associated with volume expan-sion of the water by about 9+%. This expansion does not nec-essarily lead to a 9+% increase in the voids of a saturated sandor gravel, because part of the water may be expelled duringfreezing. For a saturated silt or silty sand, the effects of freezingdepend on the rate at which the temperature is lowered. Rapidcooling of a saturated specimen in the laboratory causes thewater to freeze in situ. If the temperature is lowered gradually, alarge part of the frozen water accumulates in the form of layersof clear ice oriented parallel to the surface exposed to the freez-ing temperature. As a consequence, the frozen silt or silty sandconsists of a series of layers of frozen soil separated from eachother by layers of clear ice.

Under field conditions, ice layers formed in silty soilslocated adjacent to a frozen wall or in the active layer can growto several centimeters or more in thickness. In perennially fro-zen silt, these ice lenses can grow to several meters in thickness.Ice lenses develop only in fine-grained soils. Formation of thesemasses of clear ice requires that water migrate through the soilvoids toward the freezing front. This freezing behavior is illus-trated in Fig. 1-16, which shows three cylindrical samples ofsilt. Sample A rests on a firm base, and samples B and C havetheir lower ends immersed in water. The temperature at theupper surface of each sample is lowered below the freezing

FIGURE 1-15 Patterned ground along a river.Source: Courtesy of Frederick E. Crory, U.S. Army, Cold Regions Research andEngineering Laboratory.

FIGURE 1-16 Ice formation in soils: (a) closed system; (b) open system; (c) pea gravel layer changesupper part of specimen into a closed system.Source: Reproduced from Terzaghi 1952. Copyright 1952 Boston Society of Civil Engineers.

FROZEN GROUND 15

point. In sample A, ice layer growth is limited by the waterdrawn out of the lower part of the specimen. The lower partconsolidates as if the water were pulled by capillarity toward anevaporation surface at the top of the sample. The ice layergrowth may continue until the water content in the lower partis reduced to the shrinkage limit. The sample is referred to as aclosed system because all water entering the ice layers comesfrom within the specimen. The volume increase does notexceed 9+% of the pore water contained in the system.

In sample B, the water required for initial ice layer growth isalso drawn out of the silt. As consolidation progresses in thelower part of the sample, water is drawn from the free waterlocated below the sample. Finally, both the rate of flow towardthe zone of freezing and the water content of the unfrozen zonethrough which the water percolates become constant. Sample Bconstitutes an open system. Ice lens formation in such a systemcan, at least theoretically, increase to several meters in thick-ness. Inserting a layer of coarse-grained material between thefreezing zone and the water table transforms the open system(sample B) into a closed system (sample C). Water cannot riseby capillary action through the coarse layer; hence the upperpart of sample C represents a closed system. If the frost pene-trates below the coarse layer, the lower part of sample C will besubjected to frost action. In clay specimens, the low permeabil-ity limits the rate of water migration toward the freezing front,resulting in a reduced ice lens formation.

In field situations, open systems are encountered whereverthe vertical distance between the water table and the freezingdepth is smaller than the height of capillary rise of the soil. Themaximum capillary rise, hc (Holtz and Kovacs 1981) can beapproximated by the relation

(1.4-1)

where d, the effective pore diameter, is about 20% of the effec-tive grain size, D10. The D10 size is defined in Section 2.1.Because the water that migrates from the water table is replen-ished continually, ice lenses grow continually during the freez-ing periods and the ground surface located above the freezingzone rises. This behavior is known as frost heave. Frost heavesup to 150 mm are by no means uncommon in regions with amoderate winter climate. Variations in the underlying soil per-meability control the ice lens thickness; hence frost heave isusually nonuniform. Highway structures located above thefrost heave zone usually experience increased surface roughnessand bumps. As warmer spring weather arrives, the frozen soiland ice lenses are transformed into a zone of supersaturatedmaterial with a mushy consistency. The resultant loss in bear-ing capacity can severely impair the pavement performance.The use of insulation to control these problems is outlined inSection 11.3.

Thawing of Frozen Ground

Frozen ground will contain ice in several forms, ranging fromcoatings on individual soil particles and small lenses to large

hdc

(m) (mm)

=0 03.

inclusions and massive deposits. All forms of ice segregationcan occur in the same material, including granular soils. Onthawing, the ice will disappear and the soil skeleton must adaptitself to a new equilibrium void ratio. The amount of waterresulting from ice melting may exceed the absorption capacityof the soil skeleton. Until drainage is completed, excess porepressures may develop temporarily in fine-grained soils withlow permeabilities. If thawing occurs fast enough, frozenground may be transformed into a slurry of soil particles andwater that is unable to support any significant load. Volumechange will result from both the phase change and flow ofexcess water out of the soil. This volume change due to thawingof a fine-grained soil is illustrated for a frozen soil element inFig. 1-17. Line bc represents thawing at 0 C followed by con-tinued-drainage (consolidation) equilibrium until conditionsdevelop in the soil skeleton for the overburden pressure (so)plus any additional loads (Ds).

The melting of ice introduces a thaw-settlement phenome-non important to frozen ground support systems, permafrost,and seasonally frozen ground. Roads and highways are particu-larly vulnerable to damage under heavy traffic loads, whenthawing produces excess water content in the subgrade andbase materials. On completion of a ground freezing project, thefrozen wall will be allowed to thaw, followed by removal of thefreeze pipes. Initial wall formation in a saturated soil with und-rained conditions (i.e., with no change in moisture content)will involve an increase in volume by an amount correspondingto the phase change for water. When this soil is thawed, itreturns to its original volume and consolidates further if drain-age is permitted. This additional consolidation will be small ifthe soil was initially in a relatively dense state. In natural soils,this situation occurs only in coarse-grained frozen soils withvery little segregated ice. For fine-grained soils, some ice segre-gation will always occur, even under undrained conditions.Slow freezing of frost-susceptible soils such as silts and clayey

FIGURE 1-17 Relation between volume and pressure for afrozen soil subjected to thawing.

16 FROZEN GROUND ENGINEERING

silts at low pressures with free access to capillary water gives riseto the formation of ice lenses. Usually, the total moisture con-tent of these frozen soils considerably exceeds the moisturecontent corresponding to their unfrozen state. Therefore, whensuch ice-rich soils are thawed under drained conditions, theyundergo volume change and settlement under their ownweight. As a result, the total thaw settlement will originate fromthree sources: (1) phase change, (2) settlement of the soilsunder their own weight, and (3) settlement of the soils underapplied loads. Knowledge of thaw-settlement and consolida-tion behavior is a basic design requirement when dealing withfrozen ground.

Frost Action

The term frost action is used to describe the detrimental processof frost heaving resulting from the formation of ice lenses at thefreezing plane in soil during the freezing period followed bythaw weakening or decrease in bearing strength when season-ally frozen soil thaws. Three basic conditions required for frostaction to occur include a frost-susceptible soil, a supply ofwater, and soil temperatures sufficiently low to cause some ofthe soil water to freeze. The process of ice formation has beenillustrated in Fig. 1-16. The major concerns to the engineer arethe damaging effects (Fig. 1-18) of ice lens growth at the freez-ing front, heave of the pavement surface, and then thaw weak-ening of the foundation soils in the spring. Surface movementsof 150200 mm during a single season are not unusual. Thepavement is most susceptible to breakup during thawing of thefoundation soils (Fig. 1-7). Although water may drain laterally,poor internal drainage and no drainage through the underlyingfrozen soil create conditions that lead to a loss of strength insome active layer soils. After complete thawing in seasonal frostareas, the moisture becomes part of the groundwater system. Inpermafrost areas, the thaw period lasts throughout the entiresummer, and the water released upon thawing is retainedwithin the active layer.

The heterogeneous nature of most soils results in a verynonuniform heave, which seriously affects the riding qualityand use of traffic surfaces. Differential heave of foundationsresults in the distortion of structures. The effect can be cumula-tive over several years, so that a foundation or wall can be dis-placed permanently. Thaw weakening is of special concern forhighways and railroads. Thawing of ice lenses at a rate fasterthan meltwater can drain leads to a large decrease in bearingcapacity. These factors require the engineer to evaluate the frostsusceptibility of available soil materials. Both frost heaving andthaw weakening, indicators of the soil frost susceptibility, mustbe addressed in evaluating soil materials for use in road andrunway foundations. Classification methods based on particlesize, together with laboratory frost heave tests, have been usedextensively to assess frost susceptibility (Chamberlain 1981).The details are given in Chapter 2.

Useful Aspects of Frozen Ground

Frozen ground properties useful to engineering projectsinclude high strength in compression, excellent bearing capac-ity, and the impervious nature of frozen ground relative towater seepage. These properties are used by engineers in thedesign of ground support systems, foundations, earth dams,and other frozen earth structures.

High Strength. The strength of frozen ground involves a com-bination of frictional resistance and interference between soilparticles, a dilatancy component, and interaction between theice matrix and the soil skeleton. Stress-strain curves for a frozenquartz (Ottawa) sand and a frozen (Sault Ste. Marie) clay (Fig.1-19) illustrate comparative compressive strengths for two soiltypes at 12.0 C. The clay, with smaller particles and more sur-face area, has a larger unfrozen water content. It displays a moreplastic behavior in comparison with the more brittle sand, withessentially no unfrozen water. The frozen sand, with a compres-sion strength close to that of a weak Portland cement concrete,is stronger than the clay by a factor approaching 2. Strengthcomparisons with the same soil material in the unfrozen condi-tion are very significant. Sand, with no confinement, will haveno strength in compression. With confinement (s3 = 0.62 MN/m2), no cohesion, and a friction angle f of 30 degrees, theunfrozen sand will give a stress difference (sl s3) of 1.24 MN/m2. Frozen sand with the same confinement and temperaturehas a strength close to 8.5 times greater than that of the con-fined unfrozen sand. A similar but less dramatic increase in fro-zen clay strength is shown in Fig. 1-19. High strength, in turn,will increase bearing capacity as required for foundationsplaced on frozen soil materials. Foundation schemes for per-mafrost areas are outlined in Section 7.1.

Low Permeability. Unfrozen clean sand and gravel mixtureswill have a permeability approaching 1 cm/s (864 m/day). Thepermeability of the same saturated soil in the frozen conditionwill approach zero. For large excavations, this reduced perme-ability can remove the need for a dewatering system when thefrozen earth support system extends down into an impermeable

FIGURE 1-18 Damaging effects of frost action on a city street.Source: Courtesy of E. J. Chamberlain, U.S. Army, Cold Regions Research andEngineering Laboratory.

FROZEN GROUND 17

soil layer. For groundwater remediation projects, a subsurfacefrozen soil wall can provide a temporary impermeable barrieraround and under the contaminated site. Within the barrier,groundwater levels can be temporarily raised to the surface asneeded and the remediation process can be conducted withoutdanger of spreading the contamination to a larger area.

In poorly drained areas where excavation below the watertable is required, it can be advantageous to do the work in winterwhen the ground is frozen. Higher frozen soil strengths will per-mit access by heavy equipment to sites that would normally besoft and marshy during the summer. The imperviousness of fro-zen soil can remove the need for pumping, greatly reducing cost.Excavations up to 3 m below the existing groundwater table havebeen reported by Moore and Sayles (1980) for a site near Fair-banks, Alaska. More information is given in Section 9.2.

Ice as a Construction Material

In cold regions, ice and snow can be used as a substitute forconventional soil materials in the construction of temporaryaccess roads, landing pads, airfields, grounded ice islands, ther-mal or wind barriers, and containment dikes (Crick andMcClellan 1983). Freshwater ice is a relatively strong materialthat will resist deformation from short-term loadings much aswould conventional embankment soils. Seawater ice will varyin its physical properties due to brine concentrations commonto a saline solution. Ice and snow embankments provide a

usable driving surface and structural support. On land, theseembankments provide protection from physical damage to theunderlying organic layer. The limiting factor in the use of iceand snow as a construction material involves temperature con-straints common to cold regions in winter. Duthweiler and Utt(1985) stated that grounded ice islands will, in general, not sur-vive the Arctic summer.

The prerequisites for ice and snow construction includewater in sufficient quantity at appropriate locations, suitableterrain, proper cold-weather conditions, and specialized con-struction equipment. Ideally, the terrain should be flat and levelso as to ease construction problems with the placement of a liq-uid construction material, to reduce quantities of water and icerequired for fills, and to reduce maintenance requirements. Atemperature of 20 C is considered optimum for ice embank-ment construction (Crick and McClellan 1983). During mar-ginal temperature conditions, work during the colder nighttimeperiod gives more rapid freezeback. Duthweiler and Utt (1985)reported on an investigation showing the freezing rates of sea-water over a range of temperatures and wind speeds (Fig. 1-20).The wind-chill effect is important in the freezing process. Note

FIGURE 1-19 Stress-strain curves for compression tests onfrozen Ottawa sand and Sault Ste. Marie clay.Source: Al-Nouri 1969.

FIGURE 1-20 Ice growth prediction chart for layered floodingwith seawater.Source: Reproduced from Duthweiler and Utt 1985. Copyright 1985 AmericanSociety of Civil Engineers.

18 FROZEN GROUND ENGINEERING

that at a temperature of 20 C and a wind speed of 10 mph (16km/h), a 2-in. (51-mm) ice layer will freeze in 12 h.

Guidelines for the design and construction of various ice andsnow projects are summarized in Table 1-1.Project types are separated as to purpose (light,single-use, and extended-use roads; bridgecrossings; and airstrips) with different thick-nesses depending on subgrade type (onshore,freshwater, or saltwater). On land, temporaryembankment construction involves filling gul-lies and depressions with ice, placement of snowas a leveling course, and as a medium to holdwater in place. The water serves to saturate,freeze, and bind the ice-snow mixture into adense structural layer. A single-use heavy-dutyroad on land would typically be constructedwith a water spray over a single lift of snow, withno compaction, resulting in an 80-mm-thickstructural layer. A heavy-duty, extended-usehaul road, constructed in several lifts, requires a150-mm ice structural layer (Crick and McClel-lan 1983). Emphasis is given to compaction andhigh watersnow ratios to minimize long-termmaintenance requirements.

Water-supported ice embankments requirea much thicker section to support both thedirect wheel-loading and the dynamic plate-loading characteristics created by a vehiclemoving over a floating ice sheet. For freshwa-ter, 1.2 m of existing and built-up ice is consid-ered adequate (Crick and McClellan 1983).For floating saltwater ice, 2.4 m of existing andbuilt-up combined ice thickness is required forstructural support. River crossings are gener-ally constructed the same as offshore ice roads,with a thickness of 1.22.4 m. Erosion at thebank-water interface by vehicle-generatedwaves must be given special attention. The useof snow berms to form successive layers of ice

during construction of a grounded ice island is illustrated inFig. 1-21. Similar ice structures can also be used as protectivebarriers for other bottom-founded platforms. A large groundedice mass will transfer forces from floating ice to the sea bottomrather than to the main structure. Maintenance for extended-use haul roads, pads, and airfields constructed of ice and snowprimarily involves filling potholes and clearing drifting snow.During warmer periods, additional ice and snow may berequired for repairs.

Problems

1.1 Point A in Fig. 1-22 represents the mean annual groundsurface temperature. The curves represent limits of maximumand minimum ground temperatures. Three site locations (rela-tive to the curves) are indicated by points (a), (b), and (c).Which locations are in permafrost regions? Sketch and label theactive layer and depth of permafrost (if any) for each site loca-tion: (a), (b), and (c).

TABLE 1-1 Typical Ice Construction Specifications

a Combined thickness.N/A, not applicable. Source: Crick and McClellan 1983; reproduced with permission.

Thickness [ft (m)] for various subgrade types

Type of project Onshore Freshwatera Saltwatera

Light-duty road or pad 0.1 (0.03) 1.0 (0.3) 3.0 (0.9)

Single-use, heavy-duty road or pad

0.25 (0.08) 4.0 (1.2) 5.0 (1.5)

Extended-use, heavy-duty road or pad

0.5 (0.15) 4.0 (1.2) 8.0 (2.4)

Bridge crossings N/A 4.08.0(1.22.4)

8.0 (2.4)

C-130 Hercules airstrip 1.0 (0.3) 4.0 (1.2) 6.0 (1.8)

FIGURE 1-21 Grounded ice island formed using snow berms.Source: Reproduced from Duthweiler and Utt 1985. Copyright 1985 American Society of Civil Engi-neers.

FROZEN GROUND 19

1.2 Annual ground surface temperatures of a sand depositrange from a low of 11 C to a high of 21 C. The soil thermaldiffusivity equals 0.8 106 m2/s. Consider the system to bewithout phase-change effects and neglect the geothermal gradi-ent. Calculate the maximum and minimum soil temperaturesat a depth of 0.6 m.

1.3 The surface temperature of a 2.44-m-thick concrete slabvaries from +15.5 to 40 C during the year. Determine themaximum temperature at the base of the slab assuming a ther-mal diffusivity of 0.09 m2/day for the concrete. Neglect latentheat effects.

1.4 Describe the processes involved in the formation of an icewedge. What factors influence the spacing of these ice wedges?Explain.

1.5 Explain how thermokarst mounds are formed. What initialfield conditions are necessary for their development?

1.6 Several basic conditions are required for frost action todevelop in highway subgrade soils. What are these conditions?Describe the effects of frost action on a pavement structure rel-ative to the traffic surface and the pavement support capacity.

1.7 The heave of a soil upon freezing can be more than is esti-mated based on the initial soil water content and the knownvolume increase during conversion of water to ice. Explain howthis is possible.

1.8 What useful aspects of frozen soil are important to theengineer relative to frozen ground support systems? Explainhow they might enter into the design of a frozen wall for a deepshaft.

FIGURE 1-22 Ground temperature limits for Problem 1.1.

Front MatterTable of Contents1. Frozen Ground1.1 Frozen Ground Support Systems1.1.1 Frozen Earth Wall1.1.2 Design Considerations

1.2 Seasonally and Perennially Frozen Ground1.2.1 Cold Regions: Definition1.2.2 Subsurface Temperatures1.2.3 Active Layer1.2.4 Permafrost

1.3 Terrain Features in Permafrost Areas1.3.1 Ground Ice Features1.3.2 Patterned Ground

1.4 Engineering Considerations1.4.1 Freezing Process1.4.2 Thawing of Frozen Ground1.4.3 Frost Action1.4.4 Useful Aspects of Frozen Ground1.4.5 Ice as a Construction Material

Problems

AppendixesReferencesAuthor IndexSubject Index