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As stated in the previous chapter, the Segregation Potential concept has been widely accepted and used in many engineering designs (e.g., highway, chilled pipeline). Konrad (1987) proposed a procedure to evaluate the SP value from frost heave tests. Ito et al. (1998) improved the test procedure to obtain more consistent and reproducible SP values by a more sophisticated frost heave test.
The purpose of this chapter is to measure the SP value of Fairbanks silt from the UAF experimental gas pipeline site by frost heave tests. Two different types of freezing mode were applied. The scope of the work includes: (1) a description of the test methods and test programs, and (2) an interpretation to determine the SP values.
In the following sections, the SP concept is described in detail. The frost heave test equipments are described next. A description of the undisturbed soil sample and frost heave tests follows. Finally, the results of the frost heave tests and determination of the SP value are presented.
Segregation potential concept
Laboratory frost heave tests
Laboratory frost heave tests are necessary for the SP concept to determine the frost heave susceptibility of a soil. Generally, there are three types of freezing tests: step-freezing test, ramp-freezing test, and the Japanese Geotechnical Standard Test (JGST) -freezing test.
In step-freezing, the cold and warm temperature boundary conditions are maintained at a constant level during the test. Figure 2.1a shows schematic ice lens distribution in the step-freezing test. In the early stages of freezing, there is no visible ice lens; rather, water expulsion due to the rapid change of temperature across the sample is visible. Then as the freezing front penetration slows down, very thin and diffusive visible ice lenses appear. The vertical spacing between ice lenses increases with a decreasing cooling rate of the frozen fringe during transient freezing. When the freezing front becomes stationary, the final ice lens starts to form.
Ramped-freezing (Figure 2.1b) consists of a linear reduction with time of the top and bottom temperature boundary conditions. The ramping boundary conditions can control constant freezing front penetration rate and temperature gradient.
The JGST-freezing test (Figure 2.1c) is the Japanese geotechnical standard test method to predict frost heave susceptibility (Japan Geotechnical Society 2003). The cold temperature boundary uniformly ramps down and the warm temperature boundary stays a constant temperature close to 0oC. JGST-freezing is developed to produce constant freezing front penetration rate. However, the freezing front does not penetrate steadily in response to the unsteady heat transfer condition. The final ice lens could form if the warm temperature boundary is slightly higher than 0oC.
Adsorbed unfrozen water exists around soil particles below the freezing temperature (T0). Water migration occurs through the unfrozen water films. The ice lens grows at slightly colder than freezing temperature, which is called the segregation freezing temperature (Ts). The partially frozen zone between T0 and Ts is termed the "frozen fringe" (Miller 1972).
Frost heave can be described as a moisture transfer problem to a growing ice lens past the layered frozen fringe and the unfrozen soil, called the hydrodynamic model (e.g., Taylor and Luthin 1978). The hydraulic conductivity of the frozen fringe should be determined in order to solve the layered moisture transfer problem. Williams and Burt (1974) measured the hydraulic conductivity over a range of temperatures simulating the frozen fringe temperature. Because of technical difficulty, a precise measurement of the hydraulic conductivity was not possible. Successful one-dimensional hydrodynamic models were reported verifying against laboratory frost heave test results (e.g., Selvadurai et al. 1999). However, the hydraulic conductivity of the frozen fringe used in the simulations was not directly measured. Furthermore, a trail-and-error approach was used to adjust the hydraulic conductivities in order to obtain a match of the result. The hydrodynamic model relies on the assumption that the generalized Clausius-Clapeyron equation, which relates ice and water pressure to temperature, holds true anywhere in the frozen fringe. However, it is noted that the dynamics of phase change and water flow in the frozen fringe make it impossible for the generalized Clausius-Clapeyron equation to remain valid anywhere but at the ice lens where water flow is halted (Miyata 1998). Therefore, it appears that precise measurements of hydraulic conductivity, temperature distribution, and suction within the frozen fringe would not ultimately be of direct value in a predictive frost heave model. To overcome the difficulty, Konrad and Morgenstern (1980; 1981) developed the SP concept. The SP concept explains theoretical considerations as following.
It has long been known that frost heave is caused not only by freezing of in-situ pore water but also by water flow suction to the frozen fringe. The SP concept clearly divides these two components into in-situ heave and segregation heave, respectively. To determine the frost heave susceptibility, Konrad and Morgenstern (1980) conducted step-freezing tests without overburden. When the final ice lens initiates, the cooling rate of the frozen fringe will decrease to a value near zero. It is assumed that the static phase equilibrium is available at the onset of the final ice lens. The SP concept is empirically demonstrated from the results that the water intake rate was related to the magnitude of the temperature gradient in the frozen fringe at the formation of the final ice lens in constant thermal boundary and no-overburden conditions, as shown in Figure 2.2.
Assuming that the variation of thermal conductivity within the frozen fringe is very little and very close to that of the unfrozen soil, the actual temperature profile can be fairly linear. Although detailed variation of the hydraulic conductivity below freezing temperature is still unknown, the hydraulic conductivity decreases in response to lowering temperature and the unfrozen water content of the frozen soil simultaneously. The actual hydraulic conductivity profile, therefore, adopts a non-linear trend. Also, the actual suction profile qualitatively becomes non-linear in response to the actual non-linear hydraulic conductivity as shown in Figure 2.3a.
The two fundamental assumptions made in the SP concept are that hydraulic conductivity of frozen fringe («ff) has an equivalent constant at the formation of the final ice lens and «ff and Ts are intrinsic parameters of the soil. According to Darcy's law, the suction profile adopts a linear trend corresponding to the equivalent constant hydraulic conductivity as shown in Figure 2.3b.
The assumptions are evaluated against step-freezing tests with different sample heights under different thermal boundary conditions at the formation of the final ice lens as shown in Figure 2.4. Thermodynamic equilibrium between ice and water at the onset of the ice lens is ruled by the generalized Clausius-Clapeylon equation (e.g., Biermans et al. 1976; Radd and Oertle 1973) as:
where Pw = pore water pressure; Pi = ice pressure; V_w = specific volume of water; V_i = specific volume of ice; T* = freezing temperature of pure water in K; „T0-s = difference between freezing temperature and segregation freezing temperature; and Lw = specific latent heat fusion of pure water.
It is emphasized that eq. [2.0] is valid for phase equilibrium and for solute-free water at the onset of the ice lens where the water flow ceases. When no external pressure is applied and self-weight of the soil is neglected, eq. [2.0] reduces to:
Atmospheric pressure is at the bottom of the soil sample. The total potential (H) at the onset of the final ice lens is defined as:
where ²w = density of liquid water; and g = gravitational acceleration.
Since Ts is assumed as instinct, „T0-s are same in the different sample height as show in Figure 2.5. Therefore, the suction potential developed at the onset of final ice lens is the same:
Geometrical considerations provide the following relations:
where d = the thickness of the frozen fringe; lu = the length of unfrozen soil; Twarm = the warm end temperature; and Tcold = the cold end temperature. Subscripts 1 and 2 denote the case numbers of the test.
Applying Darcy's law, the water intake rates for the two samples can be calculated as below:
where v = water intake rate; and « = the hydraulic conductivity. Subscripts ff and u denote frozen fringe and unfrozen soil, respectively.
From eqs. [2.0] through [2.0], the ratio between v1 and v2 is shown as:
Since the hydraulic conductivity of the frozen fringe is constant, eq. [2.0] becomes:
Therefore, eq. [2.0] indicates that the water intake rate inversely depends on the thickness of frozen fringe, and especially the temperature gradient of the frozen fringe, because Ts is assumed as instinct.
The following relationships could be satisfied based on the above considerations as shown in Figure 2.5:
where P0 = suction pressure at the freezing front; SP = segregation potential; and gradTff = temperature gradient of frozen fringe.
The applicability of gradTff has been questioned because gradTff produced in laboratory frost heave tests are much greater than in field conditions. Konrad and Nixon (1994) conducted the frost heave experiment using a 68.5cm soil sample. The experimental results obtained from the long soil sample proves that the SP concept is valid for gradTff as small as 4oC/m.
Functions of the SP
There are many factors affecting frost heave of soil. Likewise, the SP will depend upon the following factors:
where ³ov = overburden pressure at the segregation freezing front; OCR = overconsolidation ratio; and N = the number of freeze-thaw cycles.
The first three factors in the list relate basically to properties of the porous medium. Soil type includes all of the physical properties such as gradation, mineralogy of the fines fraction, surface area, and surface charge density. The porosity reflects the degree of soil density. The pore fluid reflects the concentration of solute.
As show in eq. [2.0], the water intake rate decreases with decreasing suction pressure at the freezing front, and the SP decreases as well. Seto and Konrad (1996) directly measured the suction pressure at the freezing front during step-freezing frost heave tests with applied back-pressure, and verified the effect against SP.
A relationship between cooling rate (or frost penetration rate) and heave rate has been studied. Conclusions from these studies showed contradictions. Beskow (1935) concluded that, at a constant load on the soil, the heave rate is independent of the cooling rate. Loch (1979) showed that the heave rate did depend on the cooling rate for Norwegian silty soil. There existed a peak heave rate obtained at a certain value or range of cooling rate. Konrad and Morgenstern (1982b) defined the cooling rate as the change in average temperature of the frozen fringe per unit time. The SP for Devin silt showed a dependency on the cooling rate in step-freezing tests. The data indicated that the SP for Devin silt increased with increasing the cooling rate to some maximum value and then began to decrease as shown in Figure 2.6. It has been well documented that applied external load inhibits frost heave susceptibility ever since Beskow's work (1935). Konrad and Morgenstern (1982a) confirmed that Ts decreased with increasing overburden pressure in step-freezing frost heave tests at the formation of the final ice lens. It is reasonable to define Pi equal to ³ov for laboratory frost heave tests. eq. [2.0] is changed as:
With decreasing Ts due to the overburden loads, the thickness of the frozen fringe increases; therefore, overall hydraulic conductivity of the frozen fringe decreases according to the SP concept. The effect of overburden pressure against SP is accounted for empirically as:
where SP0 = the maximum value of segregation potential; and b = a soil constant.
With increasing overconsolidation ratio (OCR), smaller SP values were determined by laboratory frost heave tests (Konrad 1989b). This trend was explained as the result of a decrease of Ts and a concomitant decrease of overall hydraulic conductivity of the frozen fringe. In addition, with increasing OCR, the void ratio decreases and the pore pressure at the freezing front increases. However, if all other factors are the same, the SP increases with increasing OCR. Konrad (1989b) explained the mechanism using the following simple model. The unfrozen water increases when the particles packed closer together as OCR increases. The more unfrozen water exists, the more water is possibly migrated within the frozen fringe.
Repeated freeze-thaw cycles reduced the SP value of saturated clay, and the SP converged to a certain value (Konrad 1989a). Although consolidation is induced in unfrozen soil during freezing due to frost heaving, the effect of freeze-thaw cycles is different from overconsolidation. The freeze-thaw cycles showed dependency over a range of OCR. Konrad (1989a) concluded that freeze-thawed cycles caused significant changes in the soil structure; therefore, the change of the soil structure reduced the SP values.
Improvements to the SP frost heave test equipment
Two frost heave test equipments, which are composed of single- and quadric-cell, respectively, were used in this study.
Single-cell frost heave test equipment
The single-frost heave test equipment used in the study is shown in Figure 2.7. The equipment consists of the following components:
Frost heave cell,
Two thermal baths to control pedestal temperatures,
One thermal bath to apply ice-nucleation,
Laser displacement transducer,
Differential pressure transducer,
Air pressure loading system, and
Data acquisition system.
The single-frost heave cell was fabricated by the University of Laval, Quebec, Canada to determine the SP values by step-freezing frost heave tests. The single-cell was modified for this study as follows:
The single-freezing cell consists of a 102mm inner diameter PVC cylinder, which has 50mm wall thickness and 337mm length. Stainless steel porous plates are used to improve thermal response. Overburden pressure is applied to the sample using an air pressure cell. The inside of the cell wall is greased with silicon vacuum grease to minimize friction during frost heave tests. Top and bottom pedestal temperatures are controlled by circulating anti-freeze fluid from the thermal bathes, respectively.
The soil temperature profiles are measured by seven evenly spaced thermistors mounted at an 18.3mm interval along the cell sidewall. All of the thermistors are calibrated in an ice bath, in which a mixture of distilled ice and water co-exist to maintain a constant temperature of precisely 0oC. There was some uncertainty of temperature measurements in the original frost heave cell, because the original thermistor setup measured the inner walls of the frost heave cell, not exactly the temperature inside the specimen. With that in mind, the thermistors are directly attached to the soil sample. Furthermore, the frost heave cell is covered with insulation, consisting of fiber glass and a sheet of aluminum-coated insulation to prevent lateral heat flow and radiant effects.
Total sample displacement is recorded with a laser displacement transducer (Keyence LK-081), which has a precision of 0.003mm. A double-walled burette is connected to the top pedestal. Water intake/outtake is measured using a differential pressure transducer (Validyne DP-10). The accuracy of the differential pressure transducer is 0.05ml. This is approximately equal to 0.006mm heave for a 100mm diameter sample. These precise measurements make it possible to assess the formation of the final ice lens using both total heave and water intake data.
Sample temperature, water intake/outtake, and soil displacement are recorded by a data acquisition system at 5-minute intervals.
Quadric-cell frost heave test equipment
The configuration of the quadric-frost heave cell is shown in Figure 2.8. It is located in Hokkaido University, Japan. The quadric-cell was originally fabricated to make frozen sand samples in similar temperature conditions by Professor Akagawa. The equipment consists of the following items:
Quadric-frost heave cell,
Two thermal baths to control pedestal temperatures,
Differential pressure transducer,
Free weight loading, and
Data acquisition system.
The quadric-freezing cell consists of 50.2mm inner diameter acrylic cylinders, which have 7.5mm wall thickness and 100mm length. Porous stone plates are placed above and below the soil sample. An overburden pressure can be applied to the sample using deadweight. The inside of the cell wall was greased to minimize friction during frost heave tests. The top and bottom pedestal temperatures were controlled by circulating anti-freeze fluid from the thermal baths, and measured by platinum resistance temperature detectors.
Total sample displacement is recorded with a LVDT. A double-walled burette is connected to the bottom pedestal. Water intake/outtake is measured using a differential pressure transducer. The sample temperature, water intake/outtake, and soil displacement are recorded by a data acquisition system at 5-minute intervals.
Sample preparation and properties
Undisturbed soil samples were taken from the UAF frost heave experiment site on the Chena Hot Spring Road twice. Initial sampling was conducted during the site construction in December 1999. Undisturbed soil samples were taken from just beneath the pipe. Frost heave tests were conducted using those undisturbed soil samples (Kim 2003). After the frost heave tests, the undisturbed soil samples were remolded at 60kPa consolidation pressure. The remolded soil samples were trimmed for the quadric-frost heave cell. Figure 2.9 shows grain size distribution curve and Table 2.1 shows the soil properties of the first soil samples in December 1999, respectively.
The second sampling was conducted after operation of the UAF frost heave experiment in September 2005. The undisturbed soil sample was taken along the thermal fence TFA-S1. The sample location was at 1.8m depth, and 1m south from the center of the pipe. The sample was fully-saturated by applying vacuum pressure. The fully-saturated sample was trimmed to 100mm diameter and 115mm initial height for the single-frost heave cell. The average gravimetric water content from the excess trims was 32.5%.
Testing program and procedures
The single-cell frost heave test equipment was used for a series of step-freezing tests (STEP), and the quadric-cell frost heave test equipment was for the JGST-freezing tests (JGST), respectively. Using the undisturbed soil sample, four step-freezing tests were conducted by changing thermal boundary conditions (e.g., temperature gradient, cooling rate) and overburden conditions. The undisturbed soil sample was enclosed in the single-frost heave cell, and then cooled to approximately the warm-end pedestal temperature. An overburden pressure was applied to the top pedestal in each test. After consolidation, falling head hydraulic conductivity test was conducted in the single-frost heave cell. The frost heave cell was covered with insulation consisting of fiber glass and a sheet of aluminum coated insulation. The frost heave cell was placed in a refrigerator, which was maintained at 1.5±0.25oC.
When the specimen temperature reached a steady state, anti-freeze fluid (-10oC) was circulated from the ice nucleation thermal bath through the bottom pedestal. After the ice nucleation was observed by temperature increase due to latent heat release, the test program started. After the freezing test, the sample was thawed by raising the temperature at the cold end to the warm end temperature and the temperature in the refrigerator to the room temperature (approximately 25oC). The applied load was maintained during thawing. After thawing, the next step-freezing test was conducted by the same procedure.
A complete test on the sample consists of four cycles of freezing, thawing, and over-consolidation. Table 2.2 lists the conditions of a series of step-freezing tests.
Using the remolded soil samples, twelve JGST-freezing tests were conducted by changing the thermal boundary (cooling rate) and applied load. The remolded soil samples were enclosed in the quadric-frost heave cell. The quadric-frost heave cell was placed in a cold room, which was maintained at 4±1.5oC. The soil samples were cooled to approximately the warm-end pedestal temperature. After the ice nucleation was determined by temperature rise due to latent heat release, the test programs started. Table 2.3 summarizes the test conditions of a series of JGST-freezing tests. The quadric-frost heave cell has an advantage to evaluate the effect of overburden pressure, because four freezing tests in different overburden conditions can be operated in the same thermal boundary condition.
General results and pressure dependency at the formation of final ice lens
The step-freezing test results at a 20kPa overburden pressure, STEP-3, are shown as an example of a series of step-freezing tests. Figure 2.10a presents the total heave (ht), segregation heave (hsp), and in-situ heave (hin), respectively. The total heave is obtained directly from the laser displacement transducer reading. The water intake rate (vsp) (Figure 2.10e) at time t can be directly calculated using the reading from the differential transducer as:
where V(t) = volume of the water in the burette at time t; and A = cross section area of the soil sample (7.85x103mm2).
The segregation heave, which is the heave due to water migration through the unfrozen soil, is calculated by multiplying 1.09 to vsp as:
Using the total heave and the segregation heave, the in-situ heave is calculated as:
On the other hand, the water intake rate base on the reading from the laser displacement transducer (vt) (Figure 2.10e) is calculated as:
The temperature distribution (Figure 2.10b) can be used to calculate the temperature gradient of the frozen fringe (gradTff) (Figure 2.10d) and frozen depth (X0) (Figure 2.10c).
Within a wide range of Ts, the SP itself is insensitive, and shows an acceptable accuracy for engineering purposes (Konrad and Morgenstern 1980). Therefore, assuming Ts = -0.1oC, gradTff is calculated.
The cooling rate of the frozen fringe (Tff) is calculated as:
SP is defined as (Konrad and Morgenstern 1980):
The SP is evaluated using the relationship between vt and vsp as shown in Figure 2.10e. In step-freezing test, when freezing front penetration stops, there is no further in-situ heave. The time in-situ heave stops is considered as the formation of the final ice lens. After the formation of the final ice lens, further total heave is mainly caused by freezing of migrating water. The vt almost equals vsp at 31hr. Furthermore, the in-situ heave, frozen depth, cooling rate reaches to asymptotically constant at 31hr, simultaneously. Therefore, it is reasonable to assume that the final ice lens formed at 31hr. The SP value is evaluated as approximately 33x10-5mm2/(sec x oC) at the formation of the final ice lens as shown in Figure 2.10g.
As the pore water pressure at the freezing front (P0) is concerned. The suction pressure at the freezing front is calculated by applying Darcy's law to the unfrozen soil as:
where «u = the hydraulic conductivity of the unfrozen soil; and lu = the length of unfrozen soil.
The pressure head difference between inside the burette and pedestal is approximately 80cm (= 7.8kPa). Pore pressure at the end of the soil sample is assumed to be equal to atmospheric pressure, because the pressure head difference is canceled out with the friction between the pedestal and the cell wall. P0 is nearly zero due to the high hydraulic conductivity of the unfrozen soil during the operation as shown in Figure 2.10h.
Some assumptions are made in a series of step-freezing tests. The Fairbanks silt used in the tests exhibits low compression characteristic as shown in Table 2.1. Because of the low frost heave susceptibility and the high hydraulic conductivity of the unfrozen soil, pore water pressure is nearly zero at the freezing front as shown in Figure 2.10e. For the reasons above, the effects of OCR, freeze-thaw cycle, and consolidation in the unfrozen zone are negligible.
The test results from each step-freezing test are presented in Appendix B and summarized in Table 2.4, respectively. The correlation between the SP value and overburden pressure is shown in Figure 2.11. The SP parameters for the undisturbed Fairbanks silt are SP0 = 41.3x10-5mm2/(sec x oC) and b = 0.0156kPa-1 and both are determined at the formation of the final ice lens.
The SP values also were determined by a series of JGST-freezing tests. One of the JGST-freezing test results at a 30kPa overburden pressure, JGST-9, is shown here as an example.
Figure 2.12a shows the total heave (ht), segregation heave (hsp), and in-situ heave (hin), respectively. The total heave is obtained directly from the LVDT reading. The segregation heave is calculated from the reading of the differential transducer multiplied by 1.09 and divided by the cross sectional area of the soil samples (approximately 1.96x103mm2). The in-situ heave is calculated by eq. [2.0]. Figure 2.12b shows the top and bottom pedestal temperatures, Tcold and Twarm, respectively. The top pedestal temperature uniformly ramped down and the bottom pedestal temperature set constant. The water intake rates base on the reading from the differential transducer and the LVDT were calculated by eqs. [2.0] and [2.0], respectively (Figure 2.12c). vsp started to overlap with vt at 21.5hour. Contrary to the step-freezing test result, vsp does not equal to vt but is slightly smaller than vt. The in-situ heave keeps increasing after 21.5hour as shown in Figure 2.12a. Mageau and Morgenstern (1980) found that moisture transfer is much reduced in passive-frozen system due to very low hydraulic conductivity of the frozen soil and the effect to total heave is negligible in laboratory conditions. It is considered that a small amount of unfrozen water in the frozen soil and frozen fringe gradually decreases in response to the JGST-freezing mode after the formation of the final ice lens.
Since soil temperatures are not measured in a series of JGST-freezing tests, an assumption is made to evaluate gradTff. When a ramped temperature below freezing is applied to the top of a soil sample, unsteady heat flow is initiated. The progress of freezing front is a function of the imbalance of the heat removed. Heat associated with cooling is assumed to be negligible as compared with that associated with the latent heat of freezing water. The thermal conductivities (¬f = thermal conductivity of frozen soil, and€ ¬u = thermal conductivity of unfrozen soil) are determined based on thermal conductivity needle probe method (Kim 2003). Satisfying continuity of temperature and heat flux at frozen fringe, the relationship is shown as:
where ¬f = 2.11W/(m x K); ¬u = 1.19W/(m x oC); Xs(t) = the location of segregation freezing front; h0 = the initial height of the soil sample; ¤ = a fraction taking into account the portion of unfrozen water in frozen soil; w0 = unfrozen water content at freezing point; and L = volumetric latent heat.
The right-hand term represents the heat liberated by freezing of water intake and in-situ water in the frozen fringe. When the final ice lens forms, the heat due to in-situ water on the right of the equal sign is assumed as zero. The location of the segregation freezing front is determined based on the assumptions above. Since thermal conductivity of the frozen fringe is assumed to be equal to that of the unfrozen soil, the temperature gradient of the frozen fringe is equal to that of the unfrozen soil at the start of the final ice lens formation as:
The gradTff at the formation of the final ice lens is calculated as 0.11oC/mm, and the SP is determined as 21x10-5mm2/(sec x oC).
The test results from each JGST-freezing test are presented in Appendix A and summarized in Table 2.5, respectively. The SP values for the remolded Fairbanks silt were defined as SP0 = 37.3x10-5mm2/(sec x oC) and b = 0.0157kPa-1 and both were determined at the formation of the final ice lens.
The SP0 from the JGST-freezing tests is slightly higher than that of the STEP-freezing tests. However, the difference varies less than 1%. The difference can be due to the assumption in calculating gradTff in a series of JGST-freezing tests. The SP values of JGST-freezing tests are more scattered than that of STEP-freezing tests as shown in Figure 2.13 because of the inherent uncertainty in temperature distribution. However, similar SP values were determined at the formation of the final ice lens despite different freezing modes.
For a standard test to determine frost heave susceptibility, the selected cooling rate should reflect the filed condition. In the UAF frost heave experiment, freezing front penetration rates are very small. They are approximately 0.28mm/hr during the first 150 days and only approximately 0.07mm/hr after 500days (Kim et al. 2008). The actual temperature gradients of frozen fringe were also very small, ranging from approximately 0.002 to 0.0005oC/mm. Using these results, the cooling rate is calculated at 0.00056oC/hr or less. Penner (1986) conducted a ramped-freezing test simulating the cooling rate in a field condition. The cooling rate was approximately 0.0008oC/hr. It took 240 to 360hrs using 10cm high sample. The ramped-freezing test was expensive to conduct considering the long operational time involved.
There are two advantages of using step-freezing tests. One is the short duration of testing, and the other is the simplicity of frost heave test apparatus and testing procedure. It should be emphasized that step-freezing test provides full ranges of cooling rates. The cooling rate is very high at the beginning of freezing, decreases rapidly with time, and approaches zero asymptotically as shown in Figure 2.10f. Therefore, it is reasonable for the SP value at the formation of the final ice lens to be applied to frost heave prediction in field conditions. The formation of the final ice lens is evaluated by the continuous soil heave and water intake measurements.
A series of step-freezing and JGST-freezing tests were conducted to determine the SP values. Significant findings were from this study are:
1) Improvements were made to a step-freezing test to facilitate a consistent and reproducible evaluation of the SP values. The improvements include the use of a differential transducer to measure precise water intake rate, the well-controlled environmental chamber and insulation for precise temperature measurement, and an additional thermal bath for ice nucleation.
2) The SP values were determined using the undisturbed Fairbanks silt sample by a series of step-freezing tests. The SP values were the most expensive and reliable parameters for SP predictions.
3) A series of JGST-freezing tests were conducted using remolded Fairbanks silt samples. Consistent SP values were obtained at the formation of the final ice lens compared with step-freezing tests.
Overall, it is concluded that step-freezing test should be conducted with a continuous water intake/outtake, soil heave, and temperature distribution monitoring system. With these improvements, consistent SP values were obtained for the UAF frost heave experiment. The obtained SP values will be used for a proposed frost heave model presented in following chapter.
Figure 2.1 Schematic temperature distribution and ice lens formation in different freezing-mode
Figure 2.2 Relation between water intake velocity and temperature gradient in frozen fringe at the end of transient freezing (Konrad and Morgenstern 1980)
Figure 2.3 Characteristics of frozen fringe: a)actual; b)simplified shape (modified from Konrad and Morgenstern 1981)
Figure 2.4 At the formation of final ice lens for two different samples in step-freezing tests (modified from Konrad and Morgenstern 1980)
Figure 2.5 Schematic of condition in a freezing soil (modified from Konrad 1999)
Figure 2.6 Characteristic frost heave surface for Devin silt (Konrad and Morgenstern 1982b)
Figure 2.7 Schematic diagram of single-frost heave cell
Figure 2.8 Schematic diagram of quadric-frost heave cell
Figure 2.9 Gradation distribution of Fairbanks silt (Kim 2003)
Figure 2.10 Results from step-freezing test, STEP-3
Figure 2.11 Segregation potential of undisturbed Fairbanks silt by step-freezing tests at the formation of the final ice lens
Figure 2.12 Results from step-freezing test, JGST-9
Figure 2.13 Segregation potential comparisons between step-freezing tests and JGS-freezing tests at the formation of final ice lens
Table 2.1 Soil properties (Kim 2003)
Table 2.2 Conditions of a series of step-freezing tests
Table 2.3 Conditions of a series of JGST-freezing tests
Table 2.4 Results of a series of step-freezing tests
Table 2.5 Results of a series of JGST-freezing tests