15498_06

137

Controlled ground freezing for construction and mining applica-tions has been in use for more than a century. Frozen ground maybe used to provide ground support, groundwater control, orstructural underpinning during construction. The frozen earthwall, which is constructed prior to excavation, for practical pur-poses eliminates the need for sheeting of the earth, site dewater-ing, soil stabilization, or concern for movement of adjacentground. It is a versatile technique that involves the use of refriger-ation to convert in situ soil pore water into ice. The ice becomes abonding agent, fusing together adjacent particles of soil or blocksof rock to increase their combined strength and make themimpervious to water seepage. Excavation and other work can thenproceed safely inside, or next to, the barrier of strong, watertightfrozen earth. But note that it is essential for groundwater to bepresent, supplied either by a high water table or artificially.

Ground freezing may be used in any soil or rock formation,regardless of structure, grain size, or permeability. Themechanical properties of frozen ground are more dependent ontime and temperature than on the geology of the strata. Henceit is less sensitive to advance geologic prediction than otheralternative construction methods. Only lateral groundwaterflow requires additional considerations. Freezing may be usedfor any size, shape, or depth of excavation, and the same refrig-eration plant can be used from job to job despite a wide varia-tion in these factors. The actual direct costs of freezing for aspecific project—excluding the contractor’s capability—willdepend largely on ground conditions, including groundwaterflow and impurities, spacing of freezing elements, time avail-able, and type of refrigeration system used. In this chapter, wedescribe the design considerations, freezing methods andinstallation, structural design, monitoring requirements, andother construction considerations.

6.1 Design Considerations

A review of typical applications of ground freezing includesshafts, deep excavations, tunnels, groundwater control, struc-

tural underpinning, containment of hazardous waste, and avariety of special projects. Planning and executing theseprojects involves getting information on the geometry of theexcavation or frozen barrier; soil and groundwater conditionsat the site; proximity of adjacent streets, utilities, and struc-tures; and known characteristics of the freezing method. Thesetopics are covered in subsequent sections.

Ground Freezing Applications

Frozen soil structures are created by installing freeze pipes inwhich the cooling medium circulates down an inner pipe andreturns within the space between the two pipes, as is illustratedin Fig. 6-1a. Heat extraction from the soil results in cooling to 0°C, transformation of free water into ice, and additional cool-ing of the frozen soil. Initially, the frozen soil forms a columnaround each freeze pipe. With continued heat extraction, thefrozen soil columns increase in diameter until they merge andform a frozen wall. This frozen barrier (Fig. 6-1a) serves as aretaining wall and permits soil excavation within the dashedlines. Utility lines in the area of soil freezing are appropriatelyinsulated to prevent either freezing of the utility or thawingwithin the frozen zone. The surface view of a shaft 6.7 m indiameter by 31.0 m deep immediately after excavation is shownin Fig. 6-2. Protective insulation on the walls has not yet beenplaced. Coolant supply and return connections to verticalfreeze pipes are clearly visible.

From the given geometry of the structure to be constructedand the available space on site, the designer must select a struc-tural system for the frozen earth wall. Because of the relativelyhigh compressive and low tensile strengths of frozen soil, curvedarch walls, particularly circular walls, are a good solution, as isillustrated in, Fig. 6-lb. In general, when possible, a circular,elliptical, or arched frozen wall should be chosen. An ellipse canbe employed effectively for rectangular structures if the ratio oflength to width does not exceed about 2.0 (Braun, Shuster, andBurnham 1979). The sections below provide information on thestructural calculations needed for wall design.

6Construction Ground

Freezing

138 FROZEN GROUND ENGINEERING

If space or other restrictions prevent the use of curved sec-tions, the designer may choose other structural elements. Agravity wall (Fig. 6-3a) has the advantages that it can be con-structed in a straight line and that the area inside the adjacentexcavation is free of any obstructions. A disadvantage of thegravity wall is that the soil volume that must be frozen for anygiven depth of excavation is from two to more than five times asmuch as that required for a structurally curved wall. The designof a gravity wall is governed by overturning and sliding criteria,not stress in the frozen wall. An anchored wall (Fig. 6-3c) hasthe same advantages as the gravity wall. Its design is highlysophisticated, and it requires very careful field control. The fro-zen wall may be damaged or destroyed by unanticipated waterflow during drilling of the anchors through the frozen soil,which together with localized thawing may result in unloadingof anchors and unacceptable movement of adjacent unfrozensoil. Braun, Shuster, and Burnham (1979) indicated that thetieback anchor design is too sensitive to be used reliably in thefield for most projects.

Ground freezing application to tunneling appears to berelated primarily to the construction of relatively thin frozensoil masses around the outer tunnel contours, as is shown inFig. 6-4. Three possibilities include support of the roof portionof an excavation, roof and sides, and the closed circular ring.Special technology has been developed to construct the tunnelfreeze wall in stages. Freeze pipes are placed starting from ashaft or from a cavern location in an excavated tunnel section(Fig. 6-5). This leads to a fanlike placement of freeze pipes sur-rounding each tunnel section. The freeze pipes are slightlyinclined outward with reference to the tunnel axis. To avoidgaps in the frozen wall, the drilling tube direction is controlledby a boring gauge, as is shown in Fig. 6-5. This equipment per-mits the placement of freeze pipes with sufficient accuracy fortunnel sections up to 60 m in length. Jessberger (1980) reportedthat precise borings of up to 115 m are possible with a steerabledrilling bit (Fig. 6-5). A permanent liner of concrete or prefab-ricated structural elements is placed in the tunnel immediatelyafter excavating a working section.

FIGURE 6-1 Ground freezing for support of excavation walls:(a) scheme of ground freezing; (b) curved frozen wall.Source: Reproduced with permission from Jessberger 1980. Copyright 1980Elsevier.

FIGURE 6-2 Exposed frozen earth immediately after excava-tion of a 6.7-m-diameter by 31.0-m-deep shaft.Source: Courtesy of Joseph A. Sopko, Jr., Layne-Northwest.

FIGURE 6-3 Open excavation supported by straight walls: (a)gravity; (b) cantilevered; (c) anchored.Source: Reproduced with permission from Jessberger 1980. Copyright 1980Elsevier.

CONSTRUCTION GROUND FREEZING 139

Soil Conditions

The site investigation should include borings that extend wellbelow the planned excavation depth. These borings must pro-vide samples for classifying the soil as well as undisturbed soilsamples needed for both frozen and unfrozen strength tests.Soil type, density, and water contents are needed to estimatesoil thermal properties. In situ permeability tests can provideinformation on the order of magnitude and variability for nat-ural pervious soil stratum. Ground temperatures and watertable measurements should be made after in situ conditionshave recovered from the disturbances caused by the boringoperation. Standard methods for investigating and samplingunfrozen soils and rocks are appropriate.

The soil profile shown in Fig. 6-6 illustrates the effect ofthermal properties on the probable shape of the frozen zone

and facilitates prediction of those areas that may be critical indesign. In the absence of flowing water, the shape of the frozensoil zone is dependent primarily on the frozen thermal conduc-tivity of the strata. This parameter may vary by a factor of 4 or5, with lower values for silts and clays and higher values forrock. For any given refrigerant temperature, the relatively thin-ner frozen zones will occur in the silts, clays, and organic soils.These are also the weaker strata; hence, structural analysis anddesign will often be dictated by these soils. When the freezepipe intersects the ground surface (Fig. 6-6), three-dimensionalheat flow as well as seasonal ground temperature effects willalter the shape of the frozen zone. In late summer, the surfacesoils will be appreciably warmer (to a depth of about 3 m) thandeeper strata. The combined seasonal and three-dimensionaleffects may result in the frozen zone having a conical shape nearthe surface, and it may be difficult to obtain closure betweenadjacent frozen soil columns at shallow depths. Surface insula-tion around the top of the freeze pipes will reduce this effect.During the winter months, this will not be a problem.

Soil conditions below the bottom of the excavation areextremely important. Ideally, a frozen soil wall should be tiedinto an impervious layer to develop a closed bottom condition.This eliminates the need for any significant pumping to controlgroundwater. In situations where an impervious layer does notexist at a reasonable depth and the excavation has an open bot-tom, extreme caution must be used to minimize water move-ment under the bottom of the frozen earth wall, as well as tosatisfy the usual concerns for piping or heaving at the bottomof the excavation. Deep wells outside the excavation have beenused to collect seepage for the open bottom construction(Braun, Shuster, and Burnham 1979). Continuous open sump

FIGURE 6-4 Tunnel supported by frozen soil: (a) roof; (b) roofand sides; (c) closed ring.Source: Reproduced with permission from Jessberger 1980. Copyright 1980Elsevier.

FIGURE 6-5 Freeze pipe installation for tunnels: (a) discontin-uous drilling from a cavern; (b) drilling with a steerable drill-ing bit.Source: Reproduced with permission from Jessberger 1980. Copyright 1980Elsevier.

FIGURE 6-6 Typical effect of thermal properties on the frozenzone.Source: Reproduced from Shuster 1972. Copyright 1972 American Society ofCivil Engineers.


pumping should not be used within a frozen earth wall becauseof the free water and relative lack of control. The movement ofwater to the pump brings heat toward the frozen soil and thusaggravates the condition.

In addition to seepage concerns, the location of the watertable is significant because of the importance of water contentand degree of saturation in determining the uniaxial compres-sive strength of frozen soil. Above the water table, the soil isnormally unsaturated. Unconfined compression tests on frozensilica sand (Alkire and Andersland 1973) indicated that thestrength approached zero for an ice saturation close to 15%. Ingeneral, the required degree of water saturation should be onthe order of 50–70% (Borkenstein, Jordan, and Schäfers 1992).It is possible to entrain water into coarse-grained soils at a siteduring construction, but questions may arise about waterretention up to the point of freezing. The presence of lenses ofless pervious materials will limit this form of water entrain-ment. Water combined with a drilling mud additive has beenused to form a viscous suspension for injection into the perme-able soil pores (Borkenstein, Jordan, and Schäfers 1992). Exper-imental results have shown that a high degree of saturation (Sr

> 70%) was obtained even in the more pervious gravel/sandlayers.

Groundwater Flow

Groundwater flowing through a proposed site adds heat, whichmay cause problems relative to the formation of a continuousfrozen wall. If the water flow velocity is too large—greater than1 to 2 m/day—the freezing columns will not merge, leavingopenings in the completed wall. For liquid-nitrogen systems,Shuster (1972) reported that flows as high as 50 m/day havebeen stopped. Using field data and Darcy’s law for the flow ofwater through soil, a heat balance equation has been developedthat accounts for the heat that can be removed by the flowingwater (Sanger and Sayles 1979). The freezing soil columns willnot merge for a critical groundwater velocity:

(6.1-1)

where ro (m) is the freeze pipe radius, kf (W/m · °C) the frozensoil thermal conductivity, S (m) the freeze pipe spacing, Vs (°C)the difference between the freeze pipe surface temperature andthe freezing point of water (°C), and Vo (°C) the differencebetween the ambient ground temperature and the freezingpoint of water. These seepage velocities agree very well withthose obtained by Khakimov (1957) and Hashemi andSliepcevich (1973) using the finite-difference method, and withfield observations.

The magnitude and direction of water flow can be measuredin single bore holes with devices using fluorine ion or radioac-tive solutions (Grisak, Merritt, and Williams 1977; Drost et al.1974). If the groundwater seepage is greater than 1.5 m but lessthan 3.0 m/day, either reduced freeze pipe spacing or a secondrow of freeze pipes on the upstream side is a feasible solution. If

uk

SS

r

V

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o

s

o

=ÊËÁ

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44

ln

(m/day)

the groundwater flow exceeds 3 m/day, either the permeabilityof the formation or the groundwater gradient must be reduced.This can be accomplished by grouting prior to, or during, theinstallation of the freeze pipes. An alternative solution includesintercepting the water flow with wells. The relative cost anddegree of success for these methods depends largely on the uni-formity of the ground and the accuracy of the available subsur-face data used to plan the work. Extreme care must be exercisedin the handling of water around a frozen earth structurebecause poorly controlled pumping inside or outside a frozenearth cofferdam, or indiscriminate flooding of the excavation,may cause thermal erosion damage to the frozen earth wall.

■ EXAMPLE 6.1-1: A proposed circular frozen earth coffer-dam 20 m deep in a gravelly sand deposit will consist of a singlerow of freeze pipes spaced at 1.0 m. Groundwater flow acrossthe site is close to 0.9 m/day. Information about the site and thefreezing system to be used includes ground temperatures closeto 10 °C, average soil density of 1,968 kg/m3 with a water con-tent of 23.0%, freeze pipe diameter equal to 76 mm, and freezepipe surface temperatures close to –20 °C. Should the contrac-tor be concerned that the freezing soil columns may not merge?If a problem exists, what options are available to the contractor?

Solution: Compute the solid dry density [1,968/(1 + 0.23)] =1,600 kg/m3. Using Fig. 2-26, estimate the frozen soil thermalconductivity (kf = 3.2 W/m · °C). Determine Vs = To – TS = 0 –(–20) = 20 °C and Vo = Tg – To = 10 – 0 = 10 °C. Using Eq. (6.1-1), compute the critical flow velocity for the freeze pipe spacingof 1.0 m:

where uc = 0.85 m/day is close to the actual groundwater flowvelocity. The contractor should be concerned that wall closuremay not be attained. Grouting prior to freeze pipe installationis recommended. If necessary, liquid nitrogen (LN2) can beused to ensure wall closure.

Groundwater Quality

Contaminants in groundwater include a variety of constituents(inorganic, organic, radionuclides, and bacteriological). Manysubstances have a very low solubility in water. Other substances(immiscible fluids) exist in a liquid state in contact with waterin a manner that does not lead to mixing in a dissolved form.The presence of contaminated water in ground to be frozen canlead to several problems, including lower freezing temperatures(Fig. 2-3), reduced ice content (Fig. 5-31), and lower strength(Fig. 5-33). The salinity of groundwater should be determinedwhen there is doubt as to its freshness. Frozen strength proper-ties should be determined by laboratory tests. The extrapola-tion of existing strength data obtained for soils containing freshwater is not recommended. For partially ice saturated granularsoils, liquid contaminates with a low solubility in water and vis-cosities similar to water will flow through continuous soil voids

uk

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d

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42

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4 1 01 0

2 0 076

20

10ln

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( . )

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(Appendix C.7). This can create problems when frozen soil bar-riers are intended to contain liquid contaminants.

When soil pore water contains a significant quantity of sol-utes (often sodium chloride), the freezing point is depressed.The process is limited by their solubility in water, as is shown inFig. 2-12 for NaCl. Frozen soil barrier deterioration (i.e. thaw-ing of frozen soil) will involve ice erosion by contact with liquidcontaminants having a freezing point lower than the frozen soiltemperature. A contaminant with a small freezing pointdepression, say –5 °C, may cause erosion only in the outer por-tion of the frozen barrier where frozen soil temperatures areabove –5 °C. When ice erosion reaches the –5 °C isotherm,equilibrium conditions develop between the liquid contami-nant (brine) and ice. A colder average frozen wall temperatureand/or a thicker wall may be needed to avoid distress. If thefreezing point of the contaminant is lower than the freeze pipetemperature and if little or no dilution of the contaminantoccurs, slow ice erosion may lead to the complete disappear-ance of the frozen barrier. This behavior has been demon-strated using bench-scale frozen soil barriers (Andersland,Wiggert, and Davies 1996).

During slow freezing and the formation of a frozen wall insaline soils, solutes are excluded by the ice, forming a band infront of the frozen–unfrozen interface. This mechanismappears to be responsible for the ice banding in saline soilsobserved by Chamberlain (1983). Andersland, Wiggert, andLehner (1994) observed a similar banding in front of a verticalfrozen–unfrozen interface with decane as the contaminant. Theincrease in contaminant concentration will lower the freezingpoint and may prevent freezing in the band. With more heatextraction and lower temperatures, the freezing front will passthrough the contaminant-enriched band and continue with theformation of a series of bands until closure between freezepipes occurs. Baker and Osterkamp (1988) have shown that inuniform medium sand saturated with 35 parts per thousand(ppt) of sodium chloride solution, significant salt rejectionoccurred at a rate that increased with decreasing freezing rate.

Ground Movement

The design of temporary ground support systems involves pos-sible subsidence adjacent to the excavation and frost expansion.Subsidence after excavation can occur due to creep of the fro-zen barrier under prolonged loading. The amount of creep thatwill occur under any given stress can be predicted by finite ele-ment methods using parameters based on laboratory creepdata and will normally be accounted for during design. Thawsubsidence involves a volume change corresponding to thephase change of ice to water with no change in total water con-tent. Additional consolidation, which occurs with drainage,will be small if the soil was initially in a relatively dense statebefore freezing. (Details on computing thaw settlement weregiven in Chapter 4.) Ground movement due to frost expansionresults from two different phenomena: (1) expansion due to theconversion of soil pore water into ice during freezing (about9%), and (2) frost expansion due to pore-water migration andthe formation of ice lenses with time at the freezing isotherm.

These two phenomena occur simultaneously; however, theydiffer in predictability and magnitude. Vertical displacements(heave) due to a change in the phase of the pore water were esti-mated by Sanger and Sayles (1979) on the assumption that halfof the volume expansion is in the vertical direction. Thischange in soil column height (DH), based on a constant watercontent and only phase change, is

(6.1-2)

where n is soil porosity, H the frozen soil column height, and0.917 the specific gravity of ice. Equation (6.1-2) assumes thatthe effect of unfrozen water content will be very small for tem-peratures below –10 °C. This method is limited by several fac-tors. For partially water saturated soils, a portion of the iceexpansion will be absorbed by the available pore voids. In cleangranular soils with a high permeability, the excess pore waterwill drain ahead of the freezing front so that no volume changeoccurs. In cohesive soils, with a low permeability, drainage maynot occur during the freezing period and some heave can beexpected. In these soils, part of the water will remain unfrozen;the amount is dependent on soil type, temperature at eachpoint, and particle surface area characteristics. Unfrozen watercontents can be estimated using the methods described in Sec-tion 2.3.

Frost expansion with the formation of ice lenses is more dif-ficult to predict and may be much greater. It is related to soilpermeability; hence, this parameter can be used (as is shown inFig. 6-7) to provide a relationship with the rate of unconfinedexpansion due to ice segregation and the combined effectiveintergranular and potential expansion pressures. These curves(Fig. 6-7) do not represent a precise relationship; however, theydo approximate frost expansion behavior and provide a conve-nient means for discussing this problem. As a rule, fine silts andlean silty-clay mixtures usually represent the worst combina-tion of potential combined pressures and permeability. Notethat as the soil becomes more clayey the combined pressuresincrease exponentially. These pressures are also affected by tem-perature, being higher for colder temperatures (Hoekstra1969b). Note that for clay soil with a high combined pressure,the low permeability and/or confining pressure will limit therate of frost expansion. This is illustrated by the unconfinedexpansion rate curve in Fig. 6-7. The location and magnitudeof the expansion rate curve is dependent on the freezing rates.For higher freezing rates, the curve would be decreased in mag-nitude and displaced to the right (higher permeability). Forvery high freezing rates, such as those attained with a liquid-nitrogen system, frost expansion is greatly reduced duringactive freezing and may approach that corresponding to onlyphase change of the pore water.

A technique for determining potential frost expansion con-ditions at a freezing site is illustrated in Fig. 6-8. The threeintergranular stress curves represent the lateral (s3¢) and verti-cal confining pressures (s1¢) of undisturbed soil at rest and thelateral pressure (s3¢) required to mobilize the passive strengthof the undisturbed soil. Appropriate data for the potential com-

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ª2

1

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FIGURE 6-7 Typical effect of soil type on frost expansion pressures and rates.Source: Reproduced from Shuster 1972. Copyright 1972 American Society of Civil Engineers.

FIGURE 6-8 Technique for determining potential frost expansion conditions.Source: Reproduced from Shuster 1972. Copyright 1972 American Society of Civil Engineers.


bined pressures (Fig. 6-7) that could develop during freezing ofthe respective soils are superimposed on Fig. 6-8. If the poten-tial combined pressures are less than the actual intergranularpressure, no frost expansion will occur. If the combined pres-sures are greater than the at-rest lateral pressure, some ice seg-regation and frost expansion may occur. The direction ofexpansion will be lateral (displacing or consolidating unfrozensoil) until sufficient strength has been mobilized to attain thevertical at-rest pressure, or the potential combined pressure,whichever is least. If the potential combined pressures arelarger than the vertical at-rest intergranular pressure, frostexpansion will occur, both laterally and vertically. This expan-sion will continue until freezing is discontinued or the pressuredistribution is changed such that the intergranular pressureexceeds the potential combined pressures. This pressure crite-rion illustrates that freezing in the top 12 m (Fig. 6-8) wouldcause no expansion. Freezing would cause frost expansionbetween 12 and 17 m and to a lesser extent in the deeper clay toabout 25 m. The frost expansion potential of the hard clay isgreat; however, the clay is probably so impervious that the rateof expansion would be too slow to be of concern during theexpected duration of freezing. For the data and soils shown inFig. 6-8, it is probable that short-term freezing for temporaryground support of a tunnel would cause minimal frost expan-sion. These computations are not precise; however, they wouldenable the designer to evaluate whether or not a potential prob-lem exists, and the order of magnitude of movements that maybe expected.

6.2 Freezing Methods and System Installation

The cooling system normally consists of a primary refrigerationsource and a secondary distribution system needed to circulatecoolant or refrigerant to the freeze pipes that are extracting heatfrom the soil. Alternative expendable refrigerants include theuse of liquid nitrogen or carbon dioxide. Both systems are dis-cussed, along with installation of a refrigeration plant, coolantdistribution manifold, and freeze pipes.

Primary Plant and Pumped Loop Secondary Coolant

The main refrigeration source for a primary plant and pumpedloop secondary coolant freezing method is a conventional one-or two-stage ammonia refrigeration plant (two-stage for tem-peratures below –25 °C). These plants are commonly availablein a wide range of capacities and can frequently be rented com-pletely assembled in portable modules for field use. Theseplants use either diesel or electric prime movers, they have highthermal efficiency, and their technology is well understood(Shuster 1972). A schematic diagram (Fig. 6-9) illustrates thecooling plant in which the refrigerant is circulating. As thecompressor liquefies ammonia gas at about 0.8–1.2 MPa, thetemperature of the liquid ammonia rises to about 100 °C. Liq-uid ammonia is then pumped to a condenser under high pres-sure, where it is cooled to about 15 °C during passage through asystem of coils. Circulating water removes the excess heat.

Cooled liquid ammonia leaves the condenser and passesthrough an expansion valve, where ammonia is sprayed at con-stant high pressure through a fine nozzle into another coil at aconstant but lower pressure (Fig. 6-9a). With the decrease inpressure to about 0.15 MPa, the ammonia evaporates, causing adrop in temperature to about –25 °C. The brine cooler, or evap-orator, includes a series of coils for circulating the ammoniagas. The coils are surrounded by brine, which gives up its heatand helps convert any remaining liquid ammonia into vapor.This ammonia gas is again drawn in by the compressor for con-version into a liquid and a repeat of the cycle.

The brine circuit for the freezer system (Fig. 6-9a) includes abrine tank, a brine pump, an insulated coolant supply mani-fold, a number of parallel connected freezing elements in theground with inner supply and outer return lines, and an insu-lated return manifold. This system is simple but rather cum-bersome and thermally inefficient. Heat transfer occursbetween the coolant and the freeze pipes by convection; nophase change occurs. Because of this, large quantities of coolantmust be circulated to cause freezing, and an inherent thermalgradient exists in the system during active freezing periods.Large flows require large coolant volumes and large fixedplumbing systems. The flexibility to increase the capacity ofindividual freezing elements independently is desirable so as tofacilitate controlling localized wall conditions, including unex-

FIGURE 6-9 Refrigeration methods: (a) primary plant andpumped loop secondary coolant; (b) expendable liquid refrig-erant.Source: Reproduced with permission from Jessberger 1980. Copyright 1980Elsevier.


pected water flows. Different types of coolant have been usedwith the system (diesel oil, propane, glycol-water mixtures, andbrines); the most common is calcium chloride brine. Calciumchloride is added to water in sufficient quantities to depress itsfreezing point below that attainable by the refrigeration plantduring on-line operation. These brines have high specific heat;however, they are also dense, relatively viscous, and corrosive.Other fluids may have more attractive properties under thesame conditions, but flammable or toxic coolants should beavoided for obvious reasons.

Expendable Liquid Refrigerant

Expendable refrigerants, such as liquid nitrogen or carbondioxide, are very attractive for single projects of short duration(a few hours to a day or two) or for projects where the cost ofdelay is high. The characteristics of and relevant differencesbetween LN2 freezing and brine freezing are given in Table 6-1.No refrigeration plant is required. Liquid nitrogen is supplieddirectly or through a storage tank (Fig. 6-9b) into the freezepipes. After circulating through a few freezing pipes, nitrogen isreleased into the atmosphere. Uniform boiling of liquid nitro-

gen (LN2) throughout a series of freeze pipes represents thefastest, thermally most efficient means of ground freezing. Dif-ficulties encountered with the use of expendable refrigerantsinvolve control of the system. The unconfined venting of LN2 ina series of vertical or horizontal freezing elements frequentlyresults in a waste of refrigerant and a very irregular frozen zone.This irregularity occurs because the heat transfer coefficientvaries by an order of magnitude dependent on the quality ofthe liquid-vapor mixture and its velocity (Flynn, Draper, andRoss 1962). A supply and exhaust manifold with appropriatevalves at each end of a series of freezing elements permitsreverse flow, which tends to even out the irregular freezingcharacteristics. This is particularly true if no more than aboutfour freezing elements are connected in series (Shuster 1972).

When a series of open vertical freezing elements is filled withLN2 and allowed to boil (nitrogen boils at atmospheric pres-sure), the fluid may be ejected after a short period of boiling(Murphy 1965). The sudden geysering of supercold LN2 iswasteful and may be dangerous. This situation may be con-trolled by placing a supply tube with a slightly smaller diameterinside the freezing element (Shuster 1972). To ensure success,the supply tube should be nearly as large as the freezing ele-ment, and the supply of LN2 should be regulated to match therate of boil-off.

Sublimating carbon dioxide (CO2) is thermally less efficientthan LN2 and, except for the simple case of a row of verticalfreeze elements, is harder to control. If liquid CO2 is used as“snow,” it has a tendency to plug orifices, valves, and piping.Solid dry ice, even in pelletized form, is bulky and difficult tohandle. However, dry ice used with a mixing tank and a circu-lating secondary coolant is probably one of the most efficientways to use expendable CO2 on many projects (Shuster 1972).

When using expendable refrigerants, it is necessary to pro-vide positive exhaust for the vapor. Neither carbon dioxide nornitrogen is flammable or toxic. However, they are heavier thanair and in large quantities can cause suffocation. In addition toadequate ventilation, emergency oxygen should be available atthe site and protective gloves should be provided.

Installation of the Cooling System

Most ground freezing projects employ the circulating coolantfreezing system. The remainder employ expendable refrigerantsystems, particularly when rapid formation of the wall isimportant and only small earth volumes are to be frozen. Thetemperature, geometry, and performance of the frozen earthstructure formed by a given freeze pipe installation is depen-dent on the specific refrigeration plant and coolant distributionsystem employed. Construction operations necessary to com-plete any ground freezing project include site preparation, sub-surface installation of refrigeration pipes, and installation ofthe refrigeration plant and coolant distribution manifold.

Site Preparation. Site preparation must include grading toensure that surface water is collected and drained away fromthe planned frozen earth structure. Inadequate surface waterdrainage can result in severe damage to a frozen earth wall if the

TABLE 6-1 Characteristics of Liquid Nitrogen and Brine Freezing

Source: After Stoss and Valk 1979.

Item LN2 Brine

Site installation

Electric power Not required Required

Water for cooling Not required Required

Refrigeration plant Not required Required

Storage tank Required Required

Circulation pumps Not required Required

Pipe system for distribution of coolant

Supply only Supply and return

Low-temperature material for surface pipes, valves, etc.

Required Not required

Low-temperature material for freeze pipes

Not required Not required

Execution of freezing

Physical condition of coolant Liquid/vapor Liquid

Minimum temperature achievable (theoretical)

–196 °C –34 °C MgCl2–55 °C CaCl2

Reuse of coolant Impracticable Standard

Control of system Difficult Easy

Shape of freeze wall Often irregular Regular

Temperature profile in freeze wall

Great differences Small differences

Frost penetration Fast Slow

Impact on freeze wall in case of damage to freeze pipe

None Thawing effect

Noise None Little


water is allowed to pour over or to pond against it. Once thewall is eroded by water, it is generally difficult and costly torepair the affected area.

In urban areas, utility lines may traverse the frozen zone orbe located in close proximity to it. Although it is unlikely thatthe amount of energy removed will be sufficient to freeze themoving water in a water main or sewer, the potential must beconsidered. Most utilities are located close to the ground sur-face. Exposing the utility line in the affected area and insulatingthe pipe with sprayed polyurethane foam (instrumented withthermocouples) have proven effective in preventing freezing ofthe utility or thawing of frozen ground surrounding the utility.Steam pipes are the most sensitive utility lines. Any drop in sat-urated steam temperature will cause water buildup in the lines.Because of this, extreme caution should be exercised beforeground freezing is used in proximity to steam lines that mustremain in service.

Every site must have electric power unless the refrigerationplant is driven by an internal combustion engine. It is better toprovide temporary commercial power than to run a refrigera-tion plant with a motor-generator set (Shuster 1982). Routinestarting and stopping of the motor-generator for maintenanceand/ or fluctuations in the voltage generated can cause cumula-tive damage to electrical motors and even the compressors of arefrigeration plant. The damage may result in costs of compo-nent replacement and emergency repairs far in excess of thecost of providing temporary power in the first place. Backuppower is normally not required unless the frozen earth struc-ture is designed to function in a highly stressed state. The time-temperature response of frozen earth routinely permits refrig-eration downtime on the order of several days. When a poweroutage or component failure may result in downtime in excessof 72 h, backup refrigeration plant capacity should be consid-ered.

Subsurface Installation of Freeze Pipes. Ordinary ASTM A-120 or A-53 steel is commonly used for freeze pipes, includingliquid-nitrogen applications (Shuster 1982). When blasting isanticipated in the vicinity of the pipes, ASTM A-333 or 8%nickel steel pipe should be used. All subsurface connections ona refrigeration pipe should be welded. Threaded couplings arenot recommended. After the completion of all welding, butprior to installing the pipe in the ground, the pipe should bepressure tested to at least 125% of its working pressure toensure that no coolant leaks into the ground.

The techniques of pipe installation vary widely dependingon requirements of the particular application. Several factorsare basic regardless of the procedure used. The spacing ofrefrigeration pipes throughout their length should not exceedabout 13 times their diameter unless careful analysis indicatesthat a larger relative spacing will be acceptable for a particularapplication. The empirical data upon which this criterion isbased were derived from projects with freeze pipes varyingfrom 50 to 150 mm in diameter (Shuster 1982). More than anyother controllable variable, the relative freeze pipe spacing con-trols the time needed to complete satisfactory freezing. Theduration of time required to close a frozen wall, consisting of a

single row of freeze pipes, is exponentially proportional to therelative pipe spacing. For example, doubling the spacing withall other factors held constant will increase closure time by afactor of about 5. Because of this and the desire to maintainmore or less uniform temperatures in the frozen earth struc-ture, it is important that the alignment of all freeze pipes beverified after their installation. The alignment plots of verticalpipes can be obtained with a wide variety of downhole incli-nometer instruments. An example of freeze hole deviationsdetermined over a depth of 107 m is illustrated in Fig. 6-10.The 1.07-m spacing at the surface varies by a factor approach-ing 2 near the bottom for some adjacent holes. Note that hole14 intercepted core hole 7 at the 79.25-m depth, requiring thathole 14-A be drilled to get a freezable pattern. Horizontal andvertical deviations of horizontally driven pipes may also beobtained by using deflectometers. It is both unwise and unsafeto assume that pipe deviations are acceptable unless the pipesare short and the probability of deviation beyond tolerancelimits is very small. For pipes longer than 20 m, deviation mea-surements should be taken and the alignment verified. Wherespacing exceeds the criterion of 13 diameters of the freeze pipe,an additional pipe should be installed.

Installing a freeze pipe into a drilled hole requires a holelarger than the pipe diameter. In clays, rock, and some othersoils—especially above the water table—this results in an annu-lar void between the pipe and the surrounding soil. Under thesecircumstances, heat transfer between the pipe and soil is poor.If this condition is left uncorrected, it can lead to unexpectedcollapse or to the loss of a portion of the frozen earth wall.Attempts to backfill the annular void must be handled carefullyso as to ensure that the backfill material does not “bridge” nearthe surface before the hole has been filled completely. Groutingtechniques with bentonite, sand–bentonite, cement–bentonite,and plain cement have been used with good success. Wet sandcan be used for vertical holes if properly jetted with water dur-ing the backfilling process. Rotary mud drilling proceduresprovide one method to rapidly and efficiently install refrigera-tion pipes. Oil- or saltwater-based drilling muds should not beused, because they may prevent freezing of the soil or signifi-cantly reduce the frozen soil strength. Also, lost drill mud circu-lation below the water table indicates the potential for ground-water flow problems. When drill mud circulation is lost,remedial grouting is indicated to fill the void and reduce thesoil permeability. If it is necessary to set drill casings outside thefreeze pipe to advance a hole through soil strata, it is imperativeto carefully evaluate the potential for voids and groundwaterflow problems . It is easier and less expensive to conduct reme-dial grouting at this stage of construction than later.

Refrigeration Plant and Coolant Distribution Manifold.Ground freezing refrigeration plants are designed as low-tem-perature machines. They should be routinely capable of rapidlyachieving and maintaining suction temperatures between –30and –40 °C under warm, humid, ambient air conditions. Alarge refrigeration compressor and motor must have an ade-quate condenser. The refrigeration plant must be evaluated andsized as a complete operating system, not on the basis of the


heat rejection capacity of an individual component. The heatextraction of the system at about –30 °C suction should be onthe order of 100–230 W/m of freeze pipe in the ground (thisassumes adequate insulation of the surface distribution mani-fold). The refrigeration plant should be instrumented so as toshut down automatically on any one of three criteria: (1) highhead pressure, (2) low suction pressure, or (3) loss of hydraulicpressure in the coolant circulating system.

A coolant distribution system is normally assembled in aseries-parallel configuration. The amount of freeze pipe in asingle series should usually not exceed about 50 m2 of heattransfer area in the ground (Shuster 1982). The parallel supplyand return temperatures of each group of pipes in series arenormally monitored by thermocouples to determine energyremoval in the group. The difference between inlet and outlettemperatures (commonly called “the split”) should vary moreor less proportionally to the number of pipes in the series (e.g.,more pipes, larger split; fewer pipes, smaller split). Each group

of pipes in series is connected in parallel between an insulatedcoolant supply manifold and a coolant return manifold. Themanifold configuration around the perimeter of the area to befrozen (Fig. 6-11) should be arranged so that multiple sectionsare of approximately equal length to ensure approximatelyequal coolant distribution. Manual valves should be insertedinto the main supply and return manifold system at a numberof predetermined locations. The intent of these valves is toenable a portion of the system to be disassembled for repair orcorrection without the loss of coolant in the entire system orthe need to shut down the remainder of the system. It should bepossible to isolate hydraulically each group of pipes in series, aswell as each major section of the manifold, without having todiscontinue refrigeration operations. It is not possible to com-pute the hydraulic flow in each section of the coolant distribu-tion manifold because the length and configuration of the pip-ing and hoses vary too widely. In the absence of externalsources, balanced flow is accomplished more effectively by bal-

FIGURE 6-10 Freeze hole deviations for 107-m-deep shaft.Source: Adapted from Gail 1973.


ancing the coolant split temperatures. When the split tempera-tures are more or less equal (proportional to the number ofpipes in each group), so is the hydraulic flow. Although it istechnically possible to measure coolant flow in each series ofpipes, it is not practical or necessary for most applications. Themain supply and return temperatures of the coolant, togetherwith the split temperatures for each group of pipes in series,normally provide adequate control over coolant distribution inthe system.

Each freeze pipe and each group of pipes in series should beprovided with positive air-bleed valves to allow relief of trappedair in the system during operation. A temperature differencebetween inlet and outlet pipes of 4–5 °C often indicates thepresence of air pockets. If this is not checked continuously dur-ing the initial operation of the system, some freezer pipes prob-ably will not be properly cooled—even though the refrigerationplant is functioning normally and the main coolant supply andreturn temperatures are reasonable. One air bleeding is usuallynot sufficient. In addition to air entrapped in the system at thetime it is started, there is also air in solution in the coolant.Although air in the latter situation is not normally a problemon start-up, it is a problem subsequently if the compressor loadis reduced and the coolant is allowed to warm, causing air tocome out of solution and forming airlocks in the system.Inspectors should routinely check and bleed any suspiciousfreeze pipes to ensure adequate coolant flow. The tops of indi-vidual freeze pipes should not be insulated, to enable theinspector to see the amount and quality of ice that has formedon the pipe. To the trained eye, this is a very quick and effectiveindicator of the performance of the system.

The frozen earth mass formed by a vertically installedground freezing system tapers toward the refrigeration pipe asit nears the ground surface, much like the neck of a bottle (Fig.6-6). This results in the frozen mass being somewhat thin, evendiscontinuous, near the ground surface. This situation cancause problems because the thin top of the wall has little resis-

tance to deterioration in the presence of construction loads,thermal erosion, and adverse weather. To overcome this prob-lem, the use of a ring line is recommended. A ring line is typi-cally a 4- or 5-cm PVC hose buried 25–30 cm deep completelyaround the perimeter of the area to be excavated immediatelyinside the freeze pipe perimeter. The ring line is connected tothe coolant manifold and forms a strong continuous beam offrozen earth around the perimeter of the excavation at the sur-face, completely eliminating the bottleneck effect and resultingin a much more stable, impervious frozen earth wall.

During excavation, it can be anticipated that from time totime excavation machinery may damage or break exposed por-tions of the coolant distribution system. Aside from the imme-diate need to turn off the nearest valve, isolating that portion ofthe system, there is normally no cause for alarm. The damagedcomponent merely needs to be replaced, additional coolantmixed to replace that which was lost at the time of the break,and the system put back on line. Damage of this type, althoughnot desirable, is certainly common and should not be a causefor undue concern. The single exception is the breakage of afreeze pipe deep in the ground, which would allow concen-trated coolant to penetrate the earth, potentially destroying theadjacent frozen earth wall and preventing it from being frozenexcept with expendable low-temperature refrigerants. Becauseof this, underground blasting or excavating with mechanicalequipment in close proximity to the freeze pipes must always bemonitored carefully by an alert operator prepared to close off avalve immediately if the pipe is inadvertently broken.

6.3 Structural Design of Frozen Earth Walls

On the basis of required excavation limits and the availablespace on site, the designer must select the frozen earth wallgeometry. Because of the relatively high compressive and lowtensile strengths of frozen soil, curved arch walls, particularlycircular walls, are the best solution from a structural point ofview. Space permitting, they normally will result in the mosteconomical design. An ellipse may be employed effectively forrectangular structures if the ratio of length to width does notexceed about 2. If space or other restrictions prevent the use ofcurved structural elements, straight walls provide an alterna-tive. Complex structures may involve combinations of curvedor straight walls, along with some form of bracing system. Thestructural sections associated with tunneling involve relativelythin frozen soil masses to support the roof portion of the exca-vation, roof and sides, or a closed circular ring.

Curved Walls

The normal procedure for designing a frozen earth wall is todetermine the thickness based on the creep strength of the fro-zen soil and then compute the amount of deformationexpected during the life of the structure. Design loads havebeen assumed to vary between at-rest and passive pressureswithin about 2 to 4 h after excavation to at-rest and active pres-sures for periods greater than one work shift. Ladanyi (1982c)

FIGURE 6-11 Refrigeration system supply and return mani-fold; each vertical freeze pipe is individually connected to themanifold.Source: Courtesy of Joseph A. Sopko, Jr., Layne-Northwest.


has shown, by an approximatemethod, the magnitude of pressureincrease during freezing based onlyon the phase change of the soil porewater. Ice lens formation in the fro-zen wall during and after freezingcan generate additional volumechange and pressures. The groundhorizontal effective and hydrostaticpressure variation with time on afrozen clay wall at a depth of 200 mis illustrated in Fig. 6-12. Calcula-tions show that during the excava-tion process, due to freezing pre-stress, ground pressures can be closeto the at-rest ground pressures.Installing a rigid permanent liningwill stop the displacements andkeep the ground pressure fromdecreasing with time. If the frozenwall deformation predicted is exces-sive for the loading period, thedesign can be modified by changingthe structural geometry, increasingthe wall thickness, or lowering the wall temperature. It is essen-tial to know the strength and deformation behavior of frozensoil that is representative of the site for the expected loads inorder to determine the most economical design and to avoidpossibly unsafe conditions.

Design Based on Time-Dependent Strength. Consider firsta thick, hollow, circular frozen soil cylinder. Stress conditionsare shown in Fig. 6-13 for a vertical cylinder wall. The innerwall surface with radius a has no pressure, and the outer frozensoil surface with radius b is acted upon by the soil pressure p.The soil element at radius r is acted upon by the horizontalradial stress sr , the horizontal circumferential stress sq, and thevertical stress sz , all of which are normal stresses. Becauseshearing stresses on vertical sections through the centerline ofthe cylinder are equal to zero, the circumferential stress sq is aprincipal stress. Sanger and Sayles (1979) assumed that theradial stress sr was almost identical to the minor principalstress. Considering forces in the radial direction, the equilib-rium equation can be written as

(6.3-1)

The condition for plastic equilibrium in frozen soil, as based onthe geometry of the Mohr–Coulomb diagram (Fig. 6-13b),becomes

(6.3-2)

where the cohesion c is given by Eq. (5.3-46) and the flow valueNf by Eq. (5.3-47). Equations (6.3-1) and (6.3-2) may be solvedusing the boundary conditions sr = 0 at r = a and sr = p at r =b: thus

rd

drr

rs

s sq= =

s sq f f= +2c N Nr

FIGURE 6-12 Ground pressure variation with time after excavation on a frozen clay shaftwall at a depth of 200 m. Php, freezing prestress pressure; Ph¢, horizontal effective pres-sure; Uw , hydrostatic water pressure.Source: Reproduced with permission of B. Ladanyi from Ladanyi 1982c.

FIGURE 6-13 (a) Thick wall cylinder section (P = externalpressure); (b) Mohr–Coulomb diagram showing the stressrelationships.


(6.3-3)

where

H = c(t, q) cot f (6.3-3a)

and

(6.3-4)

For a circular frozen wall without lining, Sanger (1968) pre-sented the design chart shown in Fig. 6-14. In cases where pri-mary creep dominates the deformation behavior, Sanger andSayles (1979) recommended using for p the at-rest lateral earthpressure to determine the required wall thickness, d = b – a.

Klein and Gerthold (1979) have extended this solution tothe case where the internal pressure acting on the wall pi > 0, inwhich case, for the Mohr–Coulomb failure condition, Eqs.(6.3-3) and (6.3-4) become

(6.3-5)

and

(6.3-6)

where pe and pi are external and internal pressures acting on thefrozen cylinder. The internal pressure pi is supplied by the lin-ing, which should be able to support the soil with a sufficientfactor of safety against failure.

■ EXAMPLE 6.3-1: A 1,000-m-deep shaft is being sunk by theground freezing method. Its internal radius a = 5 m, and it willbe lined with concrete that can safely support a pressure pi =2,700 kPa. The wall thickness at a depth of 500 m must bedetermined. The groundwater table is at the surface. The soil isa dense silt with unit weight g = 20.5 kN/m3, water content w =20%, and porosity n = 0.36. Its at-rest earth pressure coefficientKo = 0.33. The frozen soil at –10 °C has a friction angle f = 15degrees and a long-term cohesion c = 1,700 kPa.

Solution: The external pressure (pe) acting on the frozen wallat the 500-m depth includes both water pressure and effectivelateral pressure pg , thus pe = pw + pg where

pw = gw · h = 9.81(500) = 4,905.0 kPa

pg = Kog ¢h = 0.33 (10.69)500 = 1,763.85 kPa

with

g ¢ = g – gw = 20.5 – 9.81 = 10.69 kN/m3

Now compute pe :

pe = 4,905.0 + 1,763.85 = 6,668.85 kPa

Compute H and Nf using Eqs. (6.3-3a) and (5.3-47):

H = c(t, q) · cot f = 1,700 cot 15° = 6,344.5 kPa

b

a

p H

H

N

= +ÊËÁ

ˆ¯ >

-1 1

0/( )f

ffor

b

a

p

c t= È

ÎÍ˘˚

=exp( , )2

0q

ffor

b

a

p H

p He

i

N

=++

ÊËÁ

ˆ¯

>-1 1

0/( )f

ffor

b

a

p p

c te i=

-ÈÎÍ

˘˚

=exp( , )2

0q

ffor

Using Eq. (6.3-5), compute the ratio b/a, thus

Compute the required wall thickness

Nt

tff qf q

=+-

=1

11 6984

sin ( , )

sin ( , ).

b

a=

++

ÊËÁ

ˆ¯

=6 668 85 6 344 5

2 700 6 344 51 684

1 4318, . , .

, , ..

.

FIGURE 6-14 Design chart for circular frozen walls: (a) designcurves; (b) definitions.Source: Reproduced with permission from Sanger and Sayles 1979. Copyright1979 Elsevier.


Design Based on Creep Displacements. Assuming a frozensoil cylinder, very long in proportion to its diameter, with inter-nal and external radii a and b (Fig. 6-14b), acted upon by inter-nal and external pressures pi and pe, respectively, the radial dis-placement ui of its internal surface can be determined from theformula (Vialov 1962; Ladanyi 1980a; Klein 1985):

(6.3-7)

where B is the parameter b in Table 5-3,

(6.3-8)

(6.3-9)

The reference stress sc q = sco f (q), a function of the referencestrain rate, ec , is defined as in Chapter 5.

For creep closure of frozen circular shafts in a frictional fro-zen soil (f > 0, c > 0), Klein (1985) has given closed-form solu-tions for cases where the creep exponent n = 1 or 2.

■ EXAMPLE 6.3-2: An 8.0 m diameter circular shaft, pro-tected by a 6.0 m thick frozen wall, is excavated deep in Callov-ian sandy loam. Creep properties from Table 5-3 include B =0.37, n = 3.70, w = 0.89, and sco = 0.31 MPa for ec = 10–5 h–1. Atthe excavation level of the shaft, the external pressure acting onthe frozen wall pe = 4.9 MPa. Determine the radial closure of thewall, u i , 12 hours after excavation, considering that the shaft isunlined for this period. Use a freezing temperature of –15 °C.

Solution: Using Eqs. (5.3-17), (5.3-20), (6.3-7), (6.3-8), and(6.3-9) gives

This displacement is clearly unacceptable. A lining will berequired with placement closely following the shaft excavation.

The stability of frozen earth walls for deep (mine) shaftswith unsupported wall heights (h) of 1.5–6 m below a perma-nent shaft lining have been described by Vialov (1962) andVyalov, Zaretsky, and Gorodetsky (1979). The unlined portionis short in comparison with the shaft diameter, and the wall is

d = ÊËÁ

ˆ¯ -È

ÎÍ˘˚

= =ab

a1 5 0 684 3 418( . ) . m

u aKp p

tie i

c

n

B=-Ê

ËÁˆ¯ws q

Kn B

nc

B

= ÊËÁ

ˆ¯

ÊËÁ

ˆ¯

ÊËÁ

ˆ¯

3 3

2

�e

w = - ÊËÁ

ˆ¯1

2

a

b

n

s qc = + =0 31 1 15 3 6560 89. ( ) .. MPa

K = ÊËÁ

ˆ¯

ÊËÁ

ˆ¯

ÊËÁ

ˆ¯

=-3

3 7

3

2

10

0 370 00107

3 75 0 37

. ..

. .

w = - ÊËÁ

ˆ¯ =1

4

100 3906

23 7.

.

ui =¥

ÊËÁ

ˆ¯ =4 0 0 00107

4 9

3 65 0 390612 1 028

3 70 37. ( . )

.

. .( ) .

.. m

restrained at the ends. The wall must be sized so as to guaranteeagainst failure or cracking, and the inward deformation mustbe limited to a value that does not interfere with construction.For full and equal restraint at both ends, the wall thickness(Vialov 1962) is

(6.3-10)

where h is the unsupported height of frozen soil (Fig. 6-15), p isthe lateral soil pressure, and sfu is the creep strength in uniaxialcompression (Eq. 5.3-48). For fixity at one end only,

(6.3-11)

The frozen wall behavior is more closely characterized by inter-mediate conditions of fixity. Vialov (1962) recommended using

(6.3-12)

Considering displacement of the inner frozen wall surface, theequation for determination of the safe wall thickness (Vialov1962) becomes (in the notation of Chapter 5)

(6.3-13)

ds1

3

2= - = Ê

ËÁˆ¯

b aph

fu

d s2 3= - =ÊËÁ

ˆ¯

b aph

fu

ds3

1 3= - =b a

ph

fu

.

b

aK

n

n

ph

a

a

B

t

c

n

c

B= + -Ê

ËÁˆ¯

ÊËÁ

ˆ¯

ÊËÁ

ˆ¯

ÊËÁ

ˆ¯

ÊËÁ

ˆ¯

+

11

31

s

eq D

�

ÈÈ

Î

ÍÍÍÍÍ

˘

˚

˙˙˙˙˙

Ï

Ì

ÔÔÔ

Ó

ÔÔÔ

¸

˝

ÔÔÔ

˛

ÔÔÔ

-1 1n

nn( )

FIGURE 6-15 Diagram of ice-soil retaining structure: 1, frozensoil; 2, surrounding soils; 3, liner; 4, refrigeration pipes; 5, opera-tional unsupported part of shaft; 6, lateral soil pressure diagram.Source: Reproduced from Vialov 1962.


where D is the permissible deflection of the unsupported wallsection at mid-height, K

–is a coefficient describing the degree of

fixity at the end planes of the unsupported wall section, the creepparameters are defined as in Chapter 5, and p is the lateral soilpressure. Vialov (1962) reported that K

–falls within the limits

(6.3-14)

A value of K–

= 1 is recommended when soil inside the radius r£ a remains unfrozen and p corresponds to the condition ofelastoplastic equilibrium in the unfrozen soil surrounding thefrozen wall. The lower value

(6.3-15)

corresponds to the condition where soil inside r £ a is frozen,and p corresponds to the hydrostatic pressure of unfrozen soil.On the basis of experimental work, Vialov (1962) used

(6.3-16)

where x represents a coefficient taking partial fixity into consid-eration. The computed wall thickness depends, to a largeextent, upon the accuracy of lateral earth pressures. The safeworking height h depends on several factors, including wallthickness as determined by the freezing method, lateral earthpressures on the frozen wall, the frozen soil creep parameters,and the time t required for soil excavation and placement of theshaft liner. Prefabricated permanent lining segments are nor-mally used to save time during construction. Klein (1988) hassummarized the engineering design of shafts that involve fro-zen walls during construction.

■ EXAMPLE 6.3-3: A shaft 600 m deep and 8 m in diameter isto be constructed through sandy loam (silt) using the groundfreezing method. Lateral soil pressures are estimated at 4.9MPa. For a working height h = 2 m, an allowable inner wallsurface displacement of 5 cm, a soil temperature of –15 °C, anda 12-h work period, determine the required wall thickness.

Solution: Soil parameters from Table 5-3 for the Calloviansandy loam include: B = 0.37, n = 3.70, w = 0.89, and sc q = 0.31MPa for e c = 10–5 h–1. It is also assumed that K

–in Eq. (6.3-13) is

equal to 0.75. For a freezing temperature of –15 °C, sc q = 3.656MPa. Now compute the ratio b/a using Eq. (6.3-13)

b/a = 2.40 and d = 4.0(2.4 – 1) = 5.6 m.A different manner of considering the effect of an elastic lin-

ing interaction with the frozen wall was shown by Jessberger,Klein, and Ebel (1979) for a linear-viscoelastic ground behav-ior, and by Ladanyi and Gill (1984) and Ladanyi (1992) for anonlinear viscoelastic behavior of frozen ground. The latter

2 11 1-( )+ < <n K

K n= -( )+2

1 1

Kn

=-1

21

x

b

a= + Ê

ËÁˆ¯

ÊËÁ

ˆ¯ ¥

ÊËÁ

ˆ¯

1 0 752 7

3 7

4 9

3 656

2 3

4

0 01250 37

4 7

..

.

.

..

.

.

112 10 5

0 37

13 7

3 72 7

¥ÊËÁ

ˆ¯

È

Î

ÍÍÍÍÍ

˘

˚

˙˙˙˙˙

Ï

Ì

ÔÔ

Ó

ÔÔ

¸

˝

ÔÔ

˛

ÔÔ-

.

.

..

solution, which is based on the power-law creep equation, isable to follow the buildup of pressure on the lining with time. Ittakes into account the time of lining installation (or the gap leftbetween the lining and the frozen wall) and the elastic rigidityof the lining. Some essential results of this solution, modifiedso as to be applicable to a frozen wall of finite thickness, arepresented in the following.

An increase of pressure on the lining, pc, at a time t after thelining-frozen wall contact has been established, is given by

(6.3-17)

where the dimensionless time t* is defined by

(6.3-18)

where K and w are defined by Eqs. (6.3-8) and (6.3-9), and Ksc

is the elastic rigidity of the concrete lining, given by

(6.3-19)

where ri and re refer to the internal and external radii of the lin-ing, and Gc and mc are the elastic constants of the lining mate-rial. The corresponding creep closure after installation of thelining is then

(6.3-20)

If the lining is installed after a certain delay at a distance x ≥ 4aabove the shaft bottom, or if a gap D (filled with a compressiblematerial) is left behind the lining, the total closure will be

(6.3-21)

where Kss is the elastic rigidity of the frozen wall, given by

(6.3-22)

where a, b, G, and m now refer to the frozen soil cylinder.Finally, the solution shows that the lining will fail in compres-sion when the external pressure attains the value

(6.3-23)

where fc¢ denotes the compressive strength of massive concrete.According to theory, this will happen when the time after con-tact between the wall and lining attains

p p tc en= - +[ ]- -1 1 1 1( *) /( )

t K K n tp

scB e

n

cn

* ( )( )

( )

= --

11

s wq

K

Gr

r

r

r

sc

ci

e

ci

e

=-

ÊËÁ

ˆ¯

È

ÎÍÍ

˘

˚˙˙

- +ÊËÁ

ˆ¯

2 1

1 2

2

2

m

uap

Kic

sc

=

u

a

p

K a

p

Ki e

ss

c

sc

= + +D

K

G a

b

a

b

ss =- Ê

ËÁˆ¯

È

ÎÍ

˘

˚˙

- + ÊËÁ

ˆ¯

2 1

1 2

2

2

m

p p fr

rc cf c

i

e

= = ¢ -ÊËÁ

ˆ¯

È

ÎÍÍ

˘

˚˙˙

12

12


(6.3-24)

In ground freezing, this kind of solution may be found use-ful for evaluating the behavior of a primary lining, such asshotcrete, because, for the final shaft lining, the original unfro-zen ground and water pressure will be more relevant.

■ EXAMPLE 6.3-4: A shaft 5 m in diameter must be sunk 50m deep through water-bearing sands. The shaft will be sunkunder protection of a 3.5-m-thick frozen wall kept at a temper-ature of –15 °C. The shaft will be continuously lined with a0.20-m-thick concrete lining. The lining will be installed at adistance of 10 m above the shaft bottom, 24 h after excavation.Determine the shaft closure at the 50-m level, when left unlinedfor 24 h, and the buildup of pressure on the lining after installa-tion. The lateral ground pressure acting on the frozen wall isassumed to be isotropic, with pe = 1.0 MPa. Properties of thefrozen soil correspond to those of frozen Ottawa sand (Table 5-3). They include G = 200 MPa, m = 0.30, B = 0.45, n = 1.28, w =1.0, sc q = 1.05 MPa for e c = 10–5 h–1, and f = 30 degrees. Theproperties of the concrete include Ec = 26 GPa, mc = 0.20, andthe compressive strength fc¢ = 30 GPa.

Solution: At T = –15 °C and with f = 30 degrees, use Eq.(5.3-53) to compute sc q = 1.05(1 + 15) + 1.0(3 –1) = 18.8 MPa.Equation (6.3-8) gives

Eq. (6.3-9) gives

Compute the time-dependent closure with Eq. (6.3-7):

For t = 24 h, ui = 0.00366 m. To determine the instantaneousclosure, compute Kss using Eq. (6.3-22):

Total closure before installation of the lining is then

ui = 4.34 + 3.66 = 8.00 mm

tp p p

K B nf

e cfn

en

sc

B

=- -

-È

ÎÍ

˘

˚˙

- - - -( )

( )

( ) ( )1 1

1

1

K = ÊËÁ

ˆ¯

ÊËÁ

ˆ¯

ÊËÁ

ˆ¯

=-3

1 28

3

2

10

0 450 01027

1 285 0 45

. ..

. .

w = - ÊËÁ

ˆ¯ =1

2 50

6 000 74536

21 28.

..

.

u t

u

i

i

= ÈÎÍ

˘˚

=

2 50 0 010271 0

18 8 0 74536

0 000087

1 28

0 45. ( . ).

. ( . )

.

.

.

55 0 45t .

Kss =- Ê

ËÁˆ¯

È

ÎÍ

˘

˚˙

- + ÊËÁ

ˆ¯

=2 200 1

2 5

6 0

1 2 0 30 2 5

6 0

576

2

2

( ) .

.

( . ) .

.

..3 MPa

uap

kie

ss

= = =2 5 1 0

576 30 00434

. ( . )

.. m

To determine the buildup of pressure on the lining, computethe lining rigidity according to Eq. (6.3-19):

Using Eq. (6.3-18), compute

t* = 0.22537(t0.45 – 240.45)

Now compute the increase in pressure on the lining using Eq.(6.3-17)

The resulting time-dependent wall closure and the correspond-ing buildup of pressure on the lining (Fig. 6-16) tends veryquickly toward the original ground pressure of 1.0 MPa.According to Eq. (6.3-23), the lining would fail only when pc

attains about 2.3 MPa; hence, there is sufficient safety againstlining failure.

Shaft Bottom Heave. As has been shown by Ladanyi (1981a,1992), the shaft bottom heave due to frozen soil creep can beestimated by comparing the bottom of the circular shaft with acontracting hemispherical cavity. For the power-law type ofcreep equation, as used previously, one gets the average time-dependent bottom heave

(6.3-25)

where po is the average total ground pressure acting at the bot-tom level, and

(6.3-26)

takes into account the limited thickness of the frozen soil belowthe bottom, b ¢ ≥ b.

■ EXAMPLE 6.3-5: Under the same conditions as in Example6.3-4, and assuming that the frozen soil thickness below thebottom is equal to the thickness of the wall, i.e., b ¢ = b = 3.5 m,compute the bottom heave.

Solution: Using Eq. (6.3-26) compute

Now compute the bottom heave using Eq. (6.3-25)

Ksc =- Ê

ËÁˆ¯

È

ÎÍ

˘

˚˙

+ - + ÊËÁ

26 000 12 3

2 5

1 0 20 1 2 0 202 3

2 5

2

, .

.

( . ) ( . ).

.ˆ¯

È

ÎÍ

˘

˚˙

=2

2 300, MPa

tt

* , ( . )( . )( . ). ( . )

..

.= -

[ ]2 300 0 01027 1 28 1 1 0

18 8 0 745360 28

0 45

1 28

p tc = - + -[ ]{ }-1 0 1 1 0 22537 4 180 45 357

. . ( . ).

s aB n

ptc

B no

c

n

B= ÊËÁ

ˆ¯

ÊËÁ

ˆ¯ ¢

ÊËÁ

ˆ¯

�es wq

3

2

¢ = -¢

ÊËÁ

ˆ¯w 1

3a

b

n

¢ = - ÊËÁ

ˆ¯ =w 1

2 5

6 00 87151

31 28.

..

.


giving s = 2.87 mm after 1 day, 8.10 mm after 10 days, and 40.9mm after 1 year.

Straight Walls and Combinations

Straight walls include gravity, cantilevered, and anchored walls,as illustrated in Fig. 6-3. They are a massive, relatively rigidstructure formed before excavation takes place. The design ofthe gravity wall is governed by overturning and sliding criteria,not stresses in the wall. Conventional earth pressure theoriesmay be used in design for wall sliding and overturning. Thecantilevered and anchored walls involve highly sophisticateddesigns and require careful field control. Unanticipated waterinflows during drilling of the anchors through the frozen earthtogether with localized thawing can seriously damage ordestroy the frozen wall. As a practical matter, the gravity wall isfavored when a straight wall is required on a project.

A braced wall has all the advantages of a gravity or anchoredwall. It is much less sensitive to field installation procedures andit can be readily packed or rebraced should the need arise. Tech-nically, bracing is more desirable than anchors for use with fro-zen earth, but it may be more awkward and difficult for the con-tractor to deal with during other subsurface work. Both

s = ÊËÁ

ˆ¯

ÈÎÍ

˘˚

¥ È-2 5

10

0 45

3

2 1 28

1 0

18 8 0 8715

5 0 45 1 28

.. ( . )

.

. ( . )

. .

ÎÎÍ˘˚

=

1 28

0 45

0 450 00069

.

.

..

t

s t

anchored and braced walls must incorporate steel or concretebearing elements to distribute concentrated stresses. For the con-struction of deep, wide trenches, such as those required for sub-ways or large sewers, a combination of soldier beams, bracing,and frozen earth can be an attractive construction alternative.

For frozen earth structures involving irregular geometries,arches, and various curved shapes, a two- or three-dimen-sional, nonlinear elastic, finite-element analysis is the most use-ful method for design. Both the surrounding unfrozen soil andthe frozen soil are modeled with linear or nonlinear modulus ofelasticity and Poisson’s ratio (Sopko 1990). Time and tempera-ture are considered indirectly in the modeling techniquethrough selection of the elastic modulus used for the frozensoil. Next, the action of gravity forces and applied loads isallowed to act through the unfrozen soil to develop pressureson the frozen wall. Soil excavation is represented by forcingnormal and shear stresses to zero on the inside surface of thewall. New stresses in the wall are computed and compared withthe long-term frozen soil strength. Wall displacements are com-puted and compared with permissible displacements. Braun,Shuster, and Burnham (1979) stated that these procedures havebeen used successfully on numerous projects. More recently, atime-dependent finite element program (TEMP-W) designedfor geothermal solutions of problems with phase change ofwater to ice is being used (Sopko 2001). Its introduction signif-icantly advances the science of structural analysis and designinvolving frozen soils.

FIGURE 6-16 Wall closure and pressure build-up curves for the freeze-shaft, example 6.3-4.


Tunnels

Frozen earth tunnels may involve circular or elliptical configu-rations with a partial (back or back and ribs) or total ring offrozen soil. The refrigeration pipes may involve horizontalplacement, as is shown in Fig. 6-4, or they may be inclinedfrom the ground surface in the form of an inverted V. Thedesign combination will depend on soil conditions, tunnel con-figuration, site constraints, and other project requirements.The wall thickness will depend on permissible wall displace-ments and strength requirements, but in some cases it can be assmall as 1 m (Jones and Brown 1979) for shallow depths.

The stresses that act on an annular frozen tunnel wall areillustrated in Fig. 6-17. The static system includes both verticalloads and horizontal soil and water pressures. These loads maybe combined, giving the radial pressure distribution shown inFig. 6-17. Bending moments within the structure will alter thestress distribution. Consider a wall section of thickness d locatedat point A. Normal stresses across the section are linear when lin-ear elastic behavior is assumed for the frozen wall. Recognizingthat temperature will vary from warm (0 to –5 °C) at the wallsurface to cold (–20 to –25 °C) at the freeze pipe, some stressredistribution will occur across the wall section with time. Amean temperature of –15 °C is shown for the section in Fig. 6-17.

A system for static calculations (Fig. 6-18) is based on theassumption that unfrozen soil is bedded against the annularfrozen soil structure. It is assumed that the frozen soil behaveslike an elastic mass. The relevant Young’s modulus of elasticitymust be selected for different stages of performance and for theeffective service life of the annular structure. Time-dependentstress-strain curves for frozen soil are illustrated in Fig. 6-19.

This approach, using a linear stability analysis, is sufficient fordesign in some cases (Jessberger 1991). Calculated stresses arecompared with the time- and temperature-dependent strengthof the frozen soil. Deformations can be estimated using a repre-sentative modulus of elasticity. To account for creep, nonlinearelastic behavior, the geometry of the frozen soil structure, andvariation in parameters with temperature, the finite elementmethod must be used for a thermal and stability analysis.

Finite-Element Method

Finite-element models are suitable for structural analysis andfor designing frozen earth support systems with complex wall

FIGURE 6-17 Stresses acting on an annular frozen soil structure.Source: Reproduced from Jessberger 1991.

FIGURE 6-18 Design method based on static calculation.Source: Reproduced from Jessberger 1991.

FIGURE 6-19 Time dependent stress-strain curves for frozen soil.


geometry and that involve multiaxial stress states. Details of thefinite-element method (FEM) are given in various textbooks.Applications to frozen earth structures have been described byKlein and Jessberger (1979); Klein (1981); Jessberger (1982);Soo (1983); Soo, Wen, and Andersland (1987); Meissner(1988); and Sopko, Shuster, and Andersland (1991). Its use foranalyzing frozen earth structures has increased with the avail-ability of FEM programs that can handle the time-dependentbehavior and material properties, which vary with temperatureand stress (tensile and compression).

A feasibility study of a tunnel support system (Jones andBrown 1979) involved the use of the finite-element method tocalculate stress levels and wall displacements. The plane strainfinite-element model, which is shown in Fig. 6-20, illustratesthe 23-m-wide tunnel with a frozen earth roof in the form of anarch. Linear elastic stress-strain moduli corresponding to a verylong loading time were used in the analysis to model the frozensoil behavior. The first step in analyzing the tunnel involved thedetermination of geostatic stresses and the stress increase dueto surface loads prior to excavation. Next, the finite-elementmethod was used to compute the stress induced during excava-tion by forcing the final shear and normal stresses around theinside tunnel perimeter to equal zero. Calculated maximum

shear stresses were all less than 450 MPa. A comparison withstrength results, from laboratory tests on frozen soils represen-tative of the site, showed acceptable compressive stresses at alllocations except point A in Fig. 6-20. High principal stresses,both in tension, indicated the need for a change in the tunnelcross section so as to reduce or eliminate any tensile stresses.

Another example, reported by Sopko, Shuster, and Ander-sland (1991), involved the construction of a drop shaft andapproach structure intended to transfer storm runoff waterfrom a surface collector system to a deep large-diameter tunnel.The overall dimensions of the structure, which are shown inFig. 6-21, indicated that a rectangular excavation would beappropriate. Lateral earth support using straight frozen wallsgenerally involves high tensile stresses and bending momentsthat are not acceptable for frozen soils. More conventional fro-zen walls are typically circular or elliptical in cross section so asto create a structure with only compressive stress. The use of asingle elliptical cofferdam would require a large number offreeze pipes, making the single elliptical cofferdam economi-cally unfeasible.

To minimize the frozen wall length, reduce the requiredrefrigeration capacity, and limit the excavation volume, a seriesof four separate but interconnected frozen soil structures were

FIGURE 6-20 Finite-element model of the Georgia tunnel.Source: Reproduced with permission of P. E. Frivik from Jones and Brown 1979.


selected (Fig. 6-22). Each unit was a curved compressive struc-ture and could be frozen independently. The linearly elasticStructural Analysis Program (SAP) IV was used to determineboth internal stresses for individual cofferdams and forcestransferred to buttress sections (Fig. 6-22). A four-node shellelement was used for the analysis because it could model thethree-dimensional geometry of the cofferdam while limitingthe total number of nodes and required computer time. Moredetails are given by Sopko, Shuster, and Andersland (1991).Required wall thicknesses were significantly less than thoseindicated by conventional analysis (Sanger and Sayles 1979).High compressive stresses at the cell 1 wall/drop shaft intersec-tion indicated a potential problem. To compensate for thesehigh stresses, an additional row of freeze pipes was installed soas to increase the wall thickness at critical areas.

The next concern (Sopko, Shuster, and Andersland 1991)involved buttress sections (Fig. 6-22) and the potential for hightensile stresses, when openings were excavated through the wallbetween two cells. A three-dimensional elastic model was usedto determine (1) nodal deflections, (2) the magnitude and loca-tion of maximum compressive and tensile stresses, and (3)reaction forces on the buttress section. The eight-node brick(type 5) element available in the SAP IV program was used.The results of the analysis showed (1) excessive tensile stressesnear the face of the opening through the buttress sections, (2)

acceptable compressive stresses within the buttress sections,and (3) negligible inward deflections at the sides of the exca-vated opening. High tensile stresses showed that modificationof the cofferdam design was needed. A review of several optionsindicated that reinforcement members, designed and placed soas to transfer loads to less critical areas, were the most practicalsolution.

A two-dimensional plane strain linear elastic model wasused for initial evaluation of nodal displacements adjacent tothe wall opening between cells and the magnitude of shearstresses developed between the frozen soil and a steel/concretebeam embedded in the frozen soil adjacent to the wall opening.Loads applied at nodal points were those obtained fromboundary element forces for the previous analysis. The resultsof this analysis indicated that load transfer to the reinforcementmembers eliminated the high tensile stresses. Shear stresses atthe interface between frozen soil and reinforcement memberswere acceptable with no danger of adfreeze bond failure. Fur-ther analysis of the reinforced section considered the time-dependent properties of the frozen soil. It was confirmed thatmost of the displacement at the sides of the wall openingbetween cells occurred during the initial elastic phase. The totalwall displacements were very small, less than 2 mm, and didnot interfere with construction.

6.4 Monitoring Requirements

Monitoring requirements for ground freezing are normallylimited to freeze hole deviation, temperatures within the cool-ant distribution system and frozen wall, frost boundary loca-tion, and wall thickness.

Freeze Hole Deviation

Soil freezing is achieved by a system of freeze pipes placed in acertain pattern (e.g., in a circle around a shaft, in a semicircularscreen above an adit, or in lines to form a straight wall). For allthese cases, the distance between pipes (boreholes) is of consid-erable importance because deviations may result in poorly fro-zen zones or in frost gaps. Borehole inclinometers can be usedto trace the freeze pipe locations, as is shown in Fig. 6-10. Com-parison with repeated measurements provides information ondisplacements associated with freezing and subsequent thaw-ing. According to different requirements for vertical and hori-zontal boreholes, a number of instruments and techniques havebeen developed.

To describe the trace of a vertical borehole in space, both thecoordinates of the borehole collar and the deviation of theactual borehole axis from the vertical (including the azimuth)must be known. These data can be obtained using a measuringdevice positioned within the borehole by means of centralizingdevices arranged at both ends of this instrument and having ameasuring base of 1 m. By moving this instrument downholealong the borehole axis in increments of 1 m, a vector sequenceis obtained that shows the simplified borehole trace as an openpolygon (Fig. 6-23). Measurement accuracy of deviation

FIGURE 6-21 Proposed underground structures.Source: Reproduced from Sopko 1990.


between the borehole direction and the vertical depends on theexactness with which the inclinometer is centralized within theborehole casing and on the sensitivity of the instrument. Theinclinometer may be centralized with a skid, with springs, orwith three-point centralizers. The sensor consists of a mechani-cal pendulum or an accelerometer. To control the deviationdirection (i.e., of the azimuth), there are several possibilities.The magnetic compass measures the angle of distortion of theinclinometer in relation to magnetic north. The gyrocompass(north-seeking gyroscope) will orient the instrument sus-pended from its framework in the direction of the meridian.Accuracies for the casing axis of 10 mm per 100 m of depthhave been reported by Heinrich, Müller, and Voort (1979). Theinert gyroscope maintains its direction, as preset at the surface,even after insertion into the borehole.

To describe the trace of a horizontal or an inclined boreholein space, a number of vectors are required. Starting from aknown reference section outside the borehole—which may bethe connecting line of two guide sockets for the drilling pipe oran outside guide tube—an open polygon trace is continuedalong the axis of the borehole casing by measuring the bendangles in both the horizontal and vertical directions in relationto the preceding element of the polygon. For this purpose, atwo-armed measuring device with a pivoting point in betweenis used, one arm of which is placed (at the beginning of a mea-surement) in the guide sockets or the guide tube mentioned,while the second arm rests in a measuring section of equallength within the borehole casing. By moving the instrumentagain and again for the length of the measuring distance (i.e.,half the instrument length along the casing), the vector

FIGURE 6-22 Three-dimensional illustration of the proposed frozen earth structures; frozenwalls formed by installing 76-mm-diameter steel freeze pipes on approximately 0.9-m centers.Source: Reproduced with permission from Sopko, Shuster, and Andersland 1991. Copyright 1991 A. A. Balkema.


sequence that follows gives the borehole trace as an open poly-gon (Fig. 6-24). Two different ways of determining the amountof horizontal and vertical bending of the two arms in relationto each other have been reported (Heinrich, Müller, and Voort1979). The optical probe for horizontal deviation measure-ments uses a light beam traveling parallel to the longitudinalaxis of one arm toward the second arm, where its image oncross wires is photographed, together with a pinpoint-shapedpendulum end. The maximum accuracy obtainable is 3 mmon a 10-m-long borehole, 10 mm on a 20-m-long one, and 30mm on a 30-m-long one (Heinrich, Müller, and Voort 1979).In the electrical probe, the position of a tensioned wire or of arod on both sides of the pivoting point between the twoinstrument arms is determined with the use of inductive trans-ducers.

Temperature

Temperature measurement provides the simplest way to moni-tor frost advance in ground freezing. Several ways to do this areavailable, differing only in accuracy and cost. Temperature sen-

sors may be used either to monitor cooling liquid at the refrig-eration plant and in the freeze pipes or to measure soil temper-atures in specific observation holes. Sensors may be stationaryas well as movable, and they may have a direct readout with aneventual recording system. Examples of temperature monitor-ing of a freezing shaft are given in Fig. 6-25.

Temperature sensors for the cooling liquid may be used forboth stationary and mobile measurements. They can either beplaced inside a flange welded to the feed and return pipes orscrewed into the pipes with fittings. More complicated sensorversions allow them to be placed in the center of the pipe, withan insulating spacer to prevent thermal flow through the steelpipe. Remote indication and automatic recording of tempera-ture data guarantee constant control of the freezing progressand allow an estimate of thermal energy released by the soil.

■ EXAMPLE 6.4-1: Temperature measurements of the brineinflow and return for a 30-m-long freeze pipe shows a tempera-ture drop of 2 °C. Brine properties include a specific gravity of1.26 and a heat capacity of 2.85 kJ/kg · °C. The flow ratethrough the freeze pipe is about 0.00158 m3/s.

FIGURE 6-23 Deviation measurement and tracing of a vertical borehole.Source: Reproduced with permission of P. E. Frivik from Heinrich, Müller, and Voort 1979.


(a) Determine the average heat removal per meter of freezepipe per day.

(b) Would a temperature drop of 4–5 °C between brine inflowand return be indicative of heat removal? Explain.

Solution: (a) Heat removal (J/m day) = brine flow rate (m3/s) × brine specific gravity × water density (kg/m3) × time con-version (s/day) × brine heat capacity (J/kg · °C) × temperaturedrop (°C) × 1/ freeze pipe length (m).

(b) A temperature drop of this magnitude would be indicativeof an air lock that has reduced brine flow through the freezepipe. Immediate correction is needed in the form of airremoval through the appropriate air-bleed valve.

Heat removalm

s

kg

m

s

3

3= Ê

ËÁˆ¯

¥ ¥ ÊËÁ

ˆ¯

¥

0 00158 1 26 1 000

86 400

. . ,

,dday

kJ

kg C

C)1

30 m

kJ

m day

ÊËÁ

ˆ¯

¥◊∞

ÊËÁ

ˆ¯

¥ ∞ ¥

=◊

ÊËÁ

ˆ¯

2 85

2

32 68

.

(

.

Soil temperature measurement is almost always carried outin observation boreholes. The use of a movable probe involveslowering it by cable into a vertical borehole. In a horizontalborehole, it is inserted with positioning rods or placed at theposition required with a cable, pully, and retracting cord. Whengreater measurement accuracy is required, stationary probesare used so as not to cause any disturbing flow of the liquid inthe borehole. Stationary sensors may be installed temporarily,or they can be installed permanently when the borehole is notprovided with a casing but is filled with the soil originallyremoved from it. The permanently installed sensors will yieldthe most reliable and accurate temperature data. The datarecorded from stationary probes give the temperature as afunction of time for a particular point. An example utilizingtwo probe holes is given in Fig. 6-26. Measured temperaturesare plotted versus radial distance from the freeze pipe. Curves,representing days after the start of freezing, have been drawnthrough the data points. These data illustrate the approximateminimal thickness of the freeze wall when probe holes areinstalled at locations midway between freeze pipes. A sufficientnumber of measuring points—depending on soil type andcomposition, on water content, and on groundwater move-ment and level changes—will provide an overall picture of thetemperature field of the frozen soil mass.

FIGURE 6-24 Deviation measurement and tracing of a horizontal borehole.Source: Reproduced with permission of P. E. Frivik from Heinrich, Müller, and Voort, 1979.


■ EXAMPLE 6.4-2: Temperature data at the 10-m depth fortwo freeze pipes and a probe hole are given in Fig. 6-27. Esti-mate the radius of the frozen soil columns (location of the zero-degree isotherm).

Solution: Assume a linear variation in temperature betweenthe freeze pipes and the probe hole. The calculations are asgiven in Table 6-2.

Comment: More accurate methods for calculating the extentof freezing around a freezing element are available. Theyrequire accurate information on the frozen soil properties.Without this information, it is normally assumed that a lineartemperature variation gives a reasonable estimate of the loca-tion of the zero-degree isotherm.

Frost Boundary Location and Wall Thickness

Seismic measurements provide a means for observing the frostadvance in water-bearing soil or rock on the basis of an increasein the velocity of the compression waves after water haschanged into ice. The test procedure is similar to that used forcrosshole seismic testing (ASTM D-4428). In water, these wavestravel at a velocity of about 1,500 m/s, in comparison withabout 4,000 m/s in ice. This change in velocity gives a directindication of the change in state, from liquid to solid, for waterin the soil pores. Soil and rock subjected to freezing may betested in situ by measurements between boreholes by placing aseismic (energy) source in one borehole and a receiver (geo-phone) in a second one. The increase of frozen soil is deter-

FIGURE 6-25 Temperature control system for a freezing shaft.Source: Reproduced with permission of P. E. Frivik from Heinrich, Müller, and Voort, 1979.


mined by comparing travel times for compression waves afterdifferent periods of freezing. The so-called zero measurement(Fig. 6-28) is made at positive temperatures reflecting theunfrozen stage. Several repeat measurements are performed atconvenient time intervals after freezing has started. Theprogress of freezing (i.e., movement of the frost boundary orincrease of frozen wall thickness), can be seen on a particularcontrol section by a reduction of travel time for compressionwaves due to the higher wave velocity in ice. The amount ofvelocity increase indicates the amount of pore water that hasbeen transformed to ice (Fig. 6-28). The presence of frost gapsbetween adjacent boreholes is shown by lower velocities atthose particular locations. Subsequent closure corresponds tohigher wave velocities, which will approach an upper limit forthe soil type and temperatures at the site.

6.5 Other Construction Considerations

The exposed frozen wall surface is susceptible to deteriorationand possibly unstable conditions due to several factors, includ-

FIGURE 6-26 Temperature versus radial distance from freezepipe.Source: Reproduced with permission from Lacy and Floess 1988. Copyright1988 Transportation Research Board.

FIGURE 6-27 Probe hole location relative to freeze pipes for Example 6.4-2.

TABLE 6-2 Calculations for Example 6.4-2

Freeze pipe A Freeze pipe B

Temperature gradient

Distance to 0 °C isotherm (R)

5 6 17 8

7110 03291

. ( . ).

- -= ∞

mmC/mm

5 6 17 8

7870 02973

. ( . ).

- -= ∞

mmC/mm

17 8541

. ∞∞

=C

0.03291 C/mmmm

17 8599

. ∞∞

=C

0.2973 C/mmmm


ing (1) thermal load from sun, rain, and moving ambient air;(2) sloughing of partially saturated frozen granular soils due tosublimation of the ice; and (3) improper construction methodsinvolving water and soil removal from the excavation. Theplacement of concrete against frozen earth involves possiblefreezing and a reduced curing rate, which can prevent the con-crete from developing adequate strength. These topics are dis-cussed in this section.

Protection of Exposed Frozen Earth

The location and type of support system has a major influenceon the cost of maintaining a frozen wall because of thermal loadfrom sun, rain, and moving ambient air on the exposed excava-tion surface. Because most construction work in open excava-tions is completed between spring and fall, the exposed frozenwall surface is normally insulated. An exposed wall, if left unin-sulated, will slough a small amount daily until it deteriorates toan unstable condition. A single layer of reinforced reflectiveplastic is frequently sufficient to prevent sloughing. If greaterprotection is required, fiberglass or foam insulating blanketswith reflective plastic on both sides are used. Weighted lines or

other methods must be employed to hold the fabric close to thewall. For open excavations, old automobile tires tied to ropesand hung over the side of the excavation have been used to forma flexible method of retaining the insulating fabric.

Excavation of unfrozen soil and rock adjacent to a frozenearth structure may normally proceed without delay, employ-ing any one of numerous excavation methods. The material tobe excavated should not be allowed to remain piled against theface of a frozen earth structure, because it will freeze, greatlyincreasing the difficulty of excavation. Soils that were saturatedwhen frozen are relatively insensitive to exposure to the atmo-sphere and elements during the excavation process. In contrast,unsaturated soils, particularly coarse clean sands and gravels,will become unstable and slough due to sublimination of thesmall amount of ice bonding them together. For most applica-tions, these materials must be protected and/or mechanicallystabilized immediately after excavation.

Flooding of an excavation supported by a frozen wall mayresult in severe damage and possible wall collapse due to ther-mal undermining. Shuster (1982) reported this problem to beparticularly bad in cohesionless soils. Extreme care must beexercised in removing water from an excavation protected byfrozen earth. When pumping is required from inside the exca-vation, steel or plastic piping should be employed. Rubber orfabric discharge hoses should not be used, except for temporarydaytime applications that are closely supervised. Dischargehoses usually hang on the face of the excavation, and because oftheir potential to leak or break, they represent a distinct threatto a frozen earth wall. A small hole in a discharge line can emita jet of water sufficient to thaw, erode, and ultimately destroy afrozen earth wall.

Frozen earth can be excavated by jetting with water, blastingwith explosives, cutting with rotating hardened metal bits, orbreaking with pneumatic or hydraulic impact tools. Of thesealternatives, blasting and water jetting represent the greatestdanger to the frozen earth. Poorly controlled blasting mayresult in the fracturing of refrigeration pipes and a loss of cool-ant into the soil. If a relief hole or free face is available for theblast to relieve into, controlled blasting may be completed with-out difficulty. Water jetting requires closer supervision thanblasting. Improperly supervised workers can inadvertently jet ahole through a frozen earth wall in a matter of minutes.

Concrete Placement against Frozen Earth

Concrete can be placed directly against frozen earth when neces-sary—despite the fact that low temperatures reduce the curingrate. Experience (Braun, Shuster, and Burnham 1979) hasshown that for concrete placed at 15–18 °C, the adjacent frozensoil will thaw to a depth approximately equal to 50–100% of theconcrete section thickness, and with more time the soil will startto refreeze. Temperature change with time and location is illus-trated in Fig. 6-29 for a deep shaft lined with concrete. Brine cir-culation was maintained continuously during placement andcuring of the concrete. If refrigeration is stopped after concreteplacement, the earth will not refreeze, and it is frequently possi-ble to do this. In view of these observations, the major technical

FIGURE 6-28 Increase of compression wave velocity due tosoil freezing between freeze-pipes.Source: Reproduced with permission of P. E. Frivik from Heinrich, Müller, andVoort 1979.


concerns for any application involving concreting against frozenearth include the following: (1) that the ground and concretewill refreeze before the concrete hydrates sufficiently to achieveits initial set; and (2) that the reduced curing rate of the concretewhen frozen will prevent it from developing adequate strengthbefore it must carry working stresses.

Normally, neither freezing nor the reduced curing rate pre-sents any problem for ordinary concrete placed in sectionsthicker than about 250 mm (Braun, Shuster, and Burnham1979). For marginal or thinner sections, the heat of hydrationand/or rate of set must be increased by using more or less, inorder of economy and desirability, any of the following: (1) alower water–cement ratio; (2) a richer mix design; (3) highearly or regulated-set cement; (4) accelerating additives; (5)aluminous cement; or (6) high concentrations (9–15%) of cal-cium chloride. The use of high concentrations of a calciumchloride additive (in comparison with the 2% limit recom-mended by the American Concrete Institute) or regulated-setcement will allow concrete to set up and cure if it is mixed,placed, and cured below freezing temperatures (down to –10°C). Calcium chloride additives in large concentrations havenot been widely used and may have other undesirable sideeffects, such as increased rebar corrosion potential, decreaseddurability, and so on, which are not directly related to compres-sive strength. An obvious alternative to elaborate mix designsfor thin sections is placing some type of insulation on the fro-zen earth surface prior to pouring the concrete. The proposedconcrete mix can be tested after 48 h in a 4–10 °C environment(refrigerator) to determine if it will achieve a minimumstrength in this initial period prior to any danger of freezeback.If the mix performs satisfactorily and the section is more than250 mm thick, no additional special measures need be taken. In

some situations, it may be desirable to use a concrete mix mod-ified by one of the previously mentioned methods to hastenhardening and to increase the heat of hydration. For example,concrete may be subjected to higher working stresses before thestructural frozen earth wall has thawed and been allowed ade-quate normal curing, or for thinner sections. Cores taken frominitial pours may be tested to confirm this approach.

Problems

6.1 A cross section of a frozen wall in a layered soil strata isshown in Fig. 6-6. Relative values of thermal conductivity andstrength are given for the rock and for each soil type. Brieflydescribe five problems that a contractor may encounter duringthe design and freezing of this wall. Suggest a solution for eachproblem.

6.2 All freeze pipes at the ground surface in Fig. 6-10 arespaced at 1,070 mm. Inclinometer measurements show a spac-ing of more than 2 m for some pipes at the 107-m depth. For afreeze pipe diameter of 150 mm, what is a desirable upper limiton pipe spacing? What freezing problems should the contractoranticipate for the project as represented in Fig. 6-10?

6.3 Measurements give an average brine flow velocity of 3.0 m/min in the annulus between the feed pipe (50 mm diameter)and a 150 mm inner diameter, 15.0 m long freeze pipe. A tem-perature drop of 1.4 °C was observed between the brine inflowand return. The calcium chloride brine at –22 °C has a specificgravity close to 1.26 and a heat capacity of 2.80 kJ/kg · °C.Compute the average heat removal per meter of freeze pipe perday.

FIGURE 6-29 Temperature variation of concrete lining and soil adjacent to shaft. Concrete data: 7 sack-mix, type II cement, W/Cratio = 0.45, no additives, placing temperature = 16.1 °C, concrete wall thickness = 355 mm; shaft data: shaft diameter = 9.1 m,frozen shaft depth = 249.3 m, circulating brine temperature = –25 to –26 °C, brine circulation maintained continuously duringplacement and curing of concrete.Source: Reproduced from Shuster 1984.

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