Soil behavior during freezing and thawing using variable and constant

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Soil behavior during freezing and thawing using variable and constant confining pressure triaxial tests Erik Simonsen and Ulf Isacsson

Abstract: Although variable confining pressure (VCP) triaxial tests are generally preferred to constant confining pressure (CCP) triaxial tests due to the more realistic stress application, VCP tests have never been utilized when investigating freeze–thaw effects on unbound road materials. In this study, three soils were investigated for resilient behavior during freezing and thawing utilizing both VCP and CCP triaxial testing. The soils were tested at selected temperatures between +20 and –10°C during one full freeze–thaw cycle. The results were analyzed in terms of the traditionally used resilient modulus and Poisson’s ratio, as well as volumetric and shear components, and indicate a significant difference in moduli computed from CCP and VCP data. However, resilient moduli display compatible values when interpreted in terms of mean values of deviator stress and mean normal stress. With regard to freeze–thaw effects on resilient moduli, the results are inconsistent with previous findings. However, this can be explained by the different test conditions applied. Key words: freeze–thaw, triaxial tests, unbound pavement materials, subgrade soils, resilient modulus. Résumé : Quoique des essais triaxiaux à pression de confinement variable (VCP) soient en général préférés aux essais à pression de confinement constante (CCP) à cause de l’application de contraintes plus réalistes, les essais VCP n’ont jamais été utilisés dans l’étude des effets de gel–dégel sur les matériaux routiers sans liant. Dans cette étude, trois sols ont été testés pour évaluer leur comportement résilient durant le cycle gel–dégel au moyen d’essais triaxiaux VCP et CCP. Les sols ont été testés à des températures choisies entre +20°C et –10°C durant un cycle complet de gel–dégel. Les résultats sont analysés en fonction du module de résilience et du rapport de Poisson utilisés traditionnellement, de même que des composantes volumétrique et de cisaillement, et indiquent qu’il y a une différence significative dans les modules calculés à partir des données des essais CCP et VCP. Cependant, ceci peut être expliqué par les conditions différentes d’essais appliquées. Mots clés : gel–dégel, essais triaxiaux, matériaux de chaussée non liés, module de fondation, module de réaction. [Traduit par la Rédaction]

Simonsen and Isacsson

Introduction Semimechanistic pavement design and evaluation procedures based on linear elastic theory have increased in popularity during recent decades. These procedures generally adopt the concept of resilient modulus and Poisson’s ratio as the fundamental material properties. It is widely observed, however, that unbound road materials display a highly nonlinear response under loading, and both resilient modulus and Poisson’s ratio are dependent on a large number of factors, of which stress level is generally regarded as the most important. In cold regions, a further dimension is added to the nonlinear material behavior through the introduction of freezing and thawing. In this case, the resilient properties are Received April 26, 1999. Accepted February 7, 2001. Published on the NRC Research Press Web site at http://cgj.nrc.ca on August 21, 2001. E. Simonsen. European Technical Support, Nynas AB, SE-149 82 Nynashamn, Sweden. U. Isacsson.1 Division of Highway Engineering, Royal Institute of Technology, SE-100 44 Stockholm, Sweden. 1

Corresponding author (e-mail: [email protected]).

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also severely affected by ice bonding between particles during freezing and excess moisture during thawing. These effects may in turn substantially reduce the structural capacity of pavement structures. Direct measurement of the apparent resilient moduli is generally performed using constant confining pressure (CCP) triaxial tests. However, the lateral stress in a pavement structure is not static. As a wheel moves over the structure, the materials experience both transient axial and lateral stress. In this sense, the variable confining pressure (VCP) triaxial test should be the preferred technique for obtaining the mechanical parameters for soils and unbound pavement materials. However, the VCP technique requires highly sophisticated equipment and the result is generally more difficult to evaluate, which in turn has led to wide acceptance of the simpler CCP test for practical purposes. Nonetheless, CCP and VCP tests are by nature different and do not produce similar soil deformations. Allen and Thompson (1974) compared the results obtained from CCP and VCP tests. Generally, they observed higher values of the resilient modulus computed from CCP data. However, the magnitude of the difference was found to be a function of the stress level and thus nonconstant. The authors also observed that Poisson’s

DOI: 10.1139/cgj-38-4-863

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Can. Geotech. J. Vol. 38, 2001 Table 1. Physical properties of the tested soils.

Soil

AASHTO classification

LuSi LinSa LinSub

A-4 A-3 A-1-a

Type

Optimum dry density (g/cm3)

Optimum moisture content (% by weight)

Particle density (g/cm3)

Sandy silt Fine sand Gravel

1.83 1.63 2.03

12.3 9.0 4.5

2.60 2.59 2.56

Fig. 1. Grain-size distribution of the investigated soils.

100

Sand (LinSa) Sandy Silt (LuSi) Gravel (LinSub)

Percent passing

90 80 70 60 50 40 30 20 10 0 100

10

1

0.1

0.01

0.001

Grain size [mm] ratio, computed from CCP tests, was greatly overestimated compared with that from VCP tests. Brown and Hyde (1975) also observed a significant difference in Poisson’s ratio. They found that Poisson’s ratio, determined from CCP tests, increased with an increase in the ratio of deviator stress to mean confining stress, whereas results from VCP tests yielded the inverse relation. However, Brown and Hyde also suggested that CCP and VCP tests would display similar values for the resilient modulus, assuming that the mean value of mean normal stress was the same in both tests. They further concluded that CCP and VCP test results were compatible when interpreted in terms of volumetric and shear stress/strain relationships. With respect to freeze–thaw effects on resilient properties, previous research is limited. Johnson et al. (1978), Cole et al. (1986), and Berg et al. (1996) investigated the resilient properties of granular materials from frozen to thawed conditions. Basic findings from these investigations include significant loss of strength upon thaw for most soils tested, a gradual regain of strength as moisture drained from the soil during the recovery period, and a two to three orders of magnitude increase in strength of all materials at subfreezing temperatures. Fredlund et al. (1975) found a significant reduction in matric suction after freeze–thaw cycling which was associated with a reduction in resilient modulus. The reduction in matric suction was substantial below optimum water content, but diminished above optimum. Bergan and Fredlund (1972) found similar behavior in undisturbed subgrade samples during spring thaw. Lee et al. (1995) in-

vestigated the resilient properties of cohesive soils and found that soils with low unconfined compressive strength exhibited negligible freeze–thaw effects, whereas the opposite effect was observed in soils with high compressive strength. Simonsen et al. (2000) investigated freeze–thaw effects in resilient properties on various fine- and coarsegrained soils. A substantial decrease in the resilient modulus of soils that generally would not be regarded as frost susceptible was observed. However, Simonsen et al. observed a net volume increase after freeze–thaw, indicating a looser soil structure than that prior to freezing. Although the VCP test is recognized as the preferred test procedure, in the sense of a more realistic application of stress, this procedure has, to the author’s knowledge, never been utilized in combination with freeze–thaw effects on unbound materials. This paper presents the results from laboratory testing of soil behavior during freezing and thawing using variable and constant confining pressure triaxial tests.

Method and materials Two subgrade soils and one subbase material were investigated with regard to resilient behavior during freezing and thawing. Classification and certain physical properties of the soils are given in Table 1 and the grain-size distribution is shown in Fig. 1. The subgrade sand and subbase gravel (LinSa, LinSub) were acquired from the Heavy Vehicle Simulator (HVS) test sections in Linköping, Sweden, and the subgrade silt (LuSi) © 2001 NRC Canada

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Fig. 2. Closed-loop servohydraulic test apparatus. LDT, linear displacement transducer.

was acquired from the Björsbyn test road, located outside Luleå in the northern part of Sweden. The soils were tested in a closed-loop servohydraulic test apparatus. The test equipment is illustrated in Fig. 2. The major components of this system are the digital controller, actuators for axial and lateral stress, and fully automated software for equipment control and data acquisition. Temperature control is achieved by an automated closed-loop controller, which regulates the circulation of liquid nitrogen through an internal heat exchanger. The controller also regulates the internal heater. To avoid temperature gradients in the triaxial cell, the confining fluid (silicone oil) is constantly circulated by means of a pressurized external pump. The triaxial cell temperature accuracy is 0.1°C. Axial deformation was monitored using both internally and externally mounted devices. External measurements were obtained with a short-stroke linear variable displacement transducer (LVDT) mounted on the actuator push rod. Axial deformation was also measured using dual DC based endcap to endcap strain-gauged extensometers and radial deformation with a strain-gauged extensometer. The radial extensometer is clamped on the specimen using an adjustable steel ring and measures the diameter change in one direction. The axial load is measured with a base-mounted load cell. The samples were compacted to a size of 100 mm by 200 mm with varying density according to Table 2 to inves-

Table 2. Degree of compaction of the tested soils. Degree of compaction (%) Soil

Specimen 1

Specimen 2

Sandy silt Fine sand Gravel

93 102 100

100 105 102

tigate the effects of density on freeze–thaw behavior. For lower densities, the samples were compacted in five layers using a vibrating hammer. However, a gyratory compaction technique was required to achieve the target density for the high-density specimen. The degree of compaction is defined as the ratio of actual dry density to optimum dry density. Each sample was generally tested at five temperatures (+20, +1, –1, –5, and –10°C) during freezing and thawing. The samples were exposed to closed-system freeze–thaw. However, during loading the drainage valves were opened and water was allowed to drain if necessary. The specimens were tested using both CCP and VCP tests, applying a 0.1 s haversine pulse and a 0.9 s rest period both for deviator and confining pressure. The stress paths used for the CCP and VCP tests are illustrated in Fig. 3. In accordance with the nature of the CCP tests, the slopes of the stress paths in p – q space are always constant and equal to 3. For the VCP © 2001 NRC Canada

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Fig. 3. Stress paths in p–q space for the CCP and VCP tests at nonfreezing temperatures. 80 70

VCP CCP

q [kPa]

60 50 40 30 20 10

0

10

20

30

tests, the slopes of the stress paths are dependent on the actual stresses applied. At nonfreezing temperatures, the CCP tests were generally performed according to American Association of State Highway and Transportation Officials (AASHTO) TP46-94. A minimum axial contact pressure of 10% of maximum deviator stress was maintained throughout the test sequence. The maximum axial and radial stress levels during the VCP testing were also applied in accordance with the TP46-94 procedure. In this case, the confining pressure was cycled from a base pressure of 4 kPa. At subfreezing temperatures, the applied stress levels were increased to account for the increase in sample stiffness. In this case, the actual applied stress levels varied with temperature and material according to the current sample stiffness. However, the same maximum axial and radial stress levels were always used in the CCP and VCP testing. Once mounted and instrumented, the sample was preloaded approximately 500 times to ensure uniform response. At each temperature, sequences of CCP tests were performed, applying generally 9–12 stress combinations. Each loading sequence contained 100 cycles, and data were recorded during the last five cycles. The CCP test was immediately followed by a sequence of VCP tests, using the corresponding maximum stress levels and number of load applications. After completion of the CCP and VCP tests, the temperature of the silicone oil was lowered to the subsequent target temperature. The sample was then allowed to stabilize at this temperature for approximately 4–8 h. To reduce sample disturbance, specimen temperature was not measured during testing. However, prior to the test program, an investigation was performed using samples instrumented with several thermocouples to determine the required time for stable sample temperature.

Data analysis One of the main purposes of this study was to compare the resilient performance in CCP and VCP testing during

p [kPa]

40

50

60

70

Fig. 4. Stress parameters in p–q space. pm, mean of mean normal stress; pmax, maximum normal stress; pr, normal stress; qm, mean of deviator stress; qr, deviator stress. 70

pr

60

pmax

50

q = (σ1-σ3)

0

CCP

40

VCP

pm

qr

30 20

qm

10 0

0

20

40

60

80

100

120

p = 1/3(σ1+2σ3)

freezing and thawing. Because of the nature of the tests, however, CCP and VCP triaxial tests are different and do not produce equal soil deformations, although equal maximum stress is applied in both tests. Moduli calculated from a CCP tests are chord values, in the sense that they are calculated relative to a consolidated state. In this case, the consolidation is due to the constant confining pressure applied prior to testing. In VCP tests, the moduli are secant values, since they are calculated relative to a generally unloaded state, and hence the measured deformations are higher, generally resulting in lower values of the resilient moduli. In this study, the CCP and VCP test results were generally compared using stress parameters defined in p–q space according to Fig. 4. The resilient modulus (Mr) for the CCP triaxial tests is defined as the ratio of repeated deviator stress (σd) to resilient axial strain (ε1,r), and Poisson’s ratio (ν) as the ratio of resil© 2001 NRC Canada

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Fig. 5. Resilient modulus at subfreezing temperatures.

Average Resilient Modulus [MPa]

10000 8000 6000 LinSa - CCP LinSa - VCP LuSi - CCP LuSi - VCP LinSub - CCP LinSub - VCP

-12

-10

4000 2000

-8

-6

-4

-2

0

0

o

Temperature [ C] ient radial strain (ε3,r) to resilient axial strain (ε1,r) according to Mr =

σd ; ε1,r

v =−

ε3,r ε1,r

This method of calculating resilient parameters is the same as would apply to an isotropic, linear–elastic material under uniaxial loading. When variable confining pressure (VCP) is applied, the generalized Hooke’s law is employed. The values of the resilient modulus and Poisson’s ratio are then derived from the following: Mr =

∆(σ1 − σ3) ∆( σ1 + 2σ3) ; ε1,r ∆( σ1 + σ3) − 2ε3,r ∆σ3 v=

∆σ1ε3,r −∆σ1ε1,r 2∆σ3 ε3,r − ε1,r ∆(σ1 + σ3)

where ∆ signifies changes in ε1,r, ε3,r, and major and minor principal stresses σ1 and σ3, respectively. A different approach, characterizing the stress–strain relationship by decomposing stress and strain into volumetric and shear components, was also employed. In this case, the resilient modulus and Poisson’s ratio are replaced by bulk modulus (K) and shear modulus (G), respectively. The bulk modulus is calculated as the ratio of mean normal stress (p) to resilient volumetric strain (εv), the shear modulus is calculated as the ratio of deviator stress (q) to three times the resilient shear strain (εs): 1 (σ1 + σ3); 3 q = σ1 − σ3 ;

p=

εv = εa + 2 εr ; 2 εs = (εa − εr ); 3

K= G =

p εv q 3εs

where εa and εr are the axial and radial strains, respectively. In this investigation, only the volumetric and shear stress/strain

components were used for the evaluation of resilient behavior. According to Brown and Hyde (1975), there are three advantages to employing a shear and volumetric approach in characterizing nonlinear materials: no assumptions of linear elastic behavior are needed in the calculations, the volumetric and shearing components of stress and strain are separated from each other, and the components have a more realistic physical meaning in a three-dimensional stress regime than resilient modulus and Poisson’s ratio.

Results and discussion Resilient moduli and Poisson’s ratio As previously discussed, one of the major concerns regarding the frequently used CCP triaxial tests is the observed deviations of resilient moduli and Poisson’s ratio compared with those from the VCP tests. Figure 5 illustrates the average resilient moduli for the tested soils at subfreezing temperatures. For all soils, the CCP moduli exceed the corresponding VCP moduli. At nonfreezing temperatures, the VCP moduli are approximately 45–55% lower than the corresponding CCP moduli. However, at subfreezing temperatures this difference decreased to approximately 20% for the three soils studied. The fine sand (LinSa) freezes rapidly, and practically no change in modulus occurs below –5°C. Both the sandy silt (LuSi) and the gravel (LinSub) display a considerably slower increase in resilient modulus. Figures 6 and 7 show the maximum normal stress (pmax) versus resilient modulus at +20 and –10°C for the gravel and fine sand, respectively. At nonfreezing temperatures the materials display increasing modulus with increasing deviator stress and mean normal stress. This behavior is to be expected for coarser materials. The dependence is similar in the CCP and VCP tests for both soils. At –10°C, the influence of mean stress remains highly significant for the gravel. However, for the sand the significance of mean stress is © 2001 NRC Canada

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Fig. 6. Resilient modulus versus maximum mean normal stress at selected temperatures for gravel.

Resilient Modulus [MPa]

10000 -10 oC 1000 LinSub CCP LinSub VCP +20 oC

100

10 0

50

100 pmax [kPa]

150

200

Fig. 7. Resilient modulus versus maximum mean normal stress at selected temperatures for fine sand.

100000

Resilient Modulus [MPa]

-10 oC 10000 1000 LinSa CCP LinSa VCP

100

+ 20 oC

10 1 0

50

reduced. For both soils, the CCP modulus is overestimated compared with the VCP modulus (by approximately 50%) over the range of applied stress. Generally, fine-grained soils display different behavior compared to coarse granular material during repeated loading. In the CCP tests, fine-grained soils generally display a decreasing resilient modulus with increasing deviator stress, whereas granular materials display the opposite behavior. Figure 8 shows the maximum deviator stress (qmax) versus computed resilient modulus from CCP and VCP tests. In the CCP test, the silt behaved as expected: increasing modulus with increasing confining pressure and decreasing modulus with increasing deviator stress. Beyond approximately 40 kPa, the influence of deviator stress diminishes and the resilient modulus remains fairly constant. However, the re-

100 pmax [kPa]

150

200

sults from the VCP tests display contradictory behavior. In this case, the influence of confining pressure is limited and the resilient modulus increases with increasing levels of deviator stress. This contradictory behavior must be explained by the inherent difference between the CCP and VCP tests. In the VCP test, the axial strains are considerably higher than those obtained in the CCP test. This, in turn, results in notably higher volumetric strain and slightly higher shear strain in the VCP test compared with the CCP test. The shear strains also increase with increasing levels of deviator stress in both tests. In contrast, the volumetric strain increases in the CCP test but decreases in the VCP tests with increased deviator stress. This is explained by the influence of dynamic confining pressure successively being balanced by the increasing deviator stress. © 2001 NRC Canada

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Fig. 8. Resilient modulus versus maximum deviator stress for sandy silt in the CCP and VCP tests.

Resilient modulus [MPa]

120

σ3 = 28 kPa σ3 = 42 kPa

100

o

+20 C

CCP

80 60 40

VCP

20 0 0

20

Currently, great efforts are being spent on modeling granular materials. As a result, several models capable of describing the nonlinear resilient behavior of unbound materials have appeared (e.g., Hoff et al. 1998; Hornych et al. 1998). However, there is generally a link between the model and the test procedure under which it was developed. This, in turn, reduces the applicability of these models to stress paths differing from those used for their development. However, one recently developed model has shown good performance irrespective of the test conditions under which the model parameters have been obtained (Correia et al. 1999). These findings may have considerable implications in the future, mainly by providing a simple CCP test to establish the nonlinear resilient behavior of unbound granular material in pavement layers. In our tests, however, the finegrained silt displayed contradictory influence of deviator stress in the CCP and VCP tests. This suggests that the potential of fully describing nonlinear behavior solely on the basis of CCP tests cannot be extrapolated without caution to include fine-grained subgrade soils. Figures 5–8 have shown that the magnitudes of the resilient moduli computed from CCP or VCP tests are not in agreement. In turn, this demonstrates that the resilient behavior depends not only on the maximum values of deviator and mean normal stress, but also on the stress path. It has previously been suggested that compatible values of resilient modulus from CCP and VCP tests could be obtained, provided that an equal mean value of the mean normal stress is applied. However, our test procedure was not specifically designed to meet this condition. Furthermore, fine-grained soils generally display a significant dependence on deviator stress. For this reason, it is suggested that compatible values of resilient modulus are obtained, provided that the product of mean deviator stress (qm) and mean of mean normal stress (pm) is equal in both tests. Theoretically, qm is not needed, since this investigation was designed with equal qmax in both the CCP and the VCP tests. In practice, qmax will deviate slightly between CCP and VCP tests due to the different

40 qmax [kPa]

60

80

conditions imposed by the test equipment. Recognizing that many soils display a high dependence on deviator stress, this effect may in turn influence the computed resilient modulus. Figure 9 shows the resilient modulus computed from CCP and VCP tests normalized with respect to the product of qm and pm. At lower values of the normalized modulus (below approximately 150 kPa–1) the agreement between the CCP and CCP test results is very good. However, at higher values the scatter increases substantially. In this case, higher values of the normalized resilient modulus are identified by combinations of low deviator stress (less than 28 kPa) and low confining stress (less than 15 kPa). However, it has previously been shown that granular materials exhibit higher degrees of anisotropy at low stress levels (Karashin 1993). This in turn may limit the compatibility of the CCP and VCP tests to higher stress levels. Figure 10 shows the resilient modulus at subfreezing temperatures computed from CCP and VCP tests normalized with respect to the product of qm and pm. For the sand and silt, the results display considerably more scatter compared to moduli computed for nonfreezing temperatures, whereas for the gravel the results are more comparable. As previously, the agreement between the CCP and VCP tests increases with decreasing ratios of normalized resilient moduli (deviator stress less than 130 kPa and lateral stress less than 20 kPa). The more compatible values of resilient moduli computed from the gravel subbase are explained by the higher axial stresses used for this material. Poisson’s ratio has previously been observed to be significantly overestimated in the CCP tests compared with the VCP tests (Allen and Thomson 1974; Brown and Hyde 1975). Also in this investigation, Poisson’s ratio was generally overestimated in the CCP tests. However, this behavior was not observed for the silt. In this case, the Poisson’s ratio computed from the CCP tests was generally lower than the corresponding VCP value. However, the main differences in the values of Poisson’s ratio can be explained by considering the behavior in terms of volumetric and shear strain relation© 2001 NRC Canada

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Fig. 9. Normalized resilient moduli in the CCP and VCP tests at nonfreezing temperatures.

500

Mr /(qmxpm) VCP

400

LinSub LinSa LuSi

300 200 100 0 0

100

200

300

400

500

Mr /(q mxpm) CCP

Fig. 10. Normalized resilient moduli in the CCP and VCP tests at subfreezing temperatures.

1000

LinSa subfreezing LuSi subfreezing

Mr /(qmxpm) VCP

800

LinSub subfreezing

600 400 200 0 0

200

400

600

800

1000

Mr /(q mxpm) CCP ships. It follows from the basic definitions that Poisson’s ratio, obtained in the CCP tests, can be expressed as a single function of the ratio of volumetric strain to shear strain. This is the effect of assuming the CCP test as a uniaxial stress condition, albeit with a constant confining pressure boundary condition. In the VCP tests, the Poisson’s ratio is derived directly from the generalized Hooke’s law and the effect of confining pressure is included in the calculations. In this case, Poisson’s ratio can be expressed as a function of the ratio of volumetric strain to shear strain and the ratio of minor to major principal stress (R). Figure 11 shows experimental results of Poisson’s ratios obtained in the VCP tests. The reference line indicates the CCP relationship of Poisson’s ratio to the ratio of volumetric strain to shear strain. All values of Poisson’s ratio obtained in the CCP tests and derived from the simplified uniaxial

stress condition must fall on this curve. Values of Poisson’s ratio between 0.5 and 0 limit the strain ratio to between 0 and 1.5. For values of Poisson’s ratio in excess of 0.5, the strain ratio is negative and dilatation takes place. Values of Poisson’s ratio obtained in compressive VCP tests must fall between the boundaries for hydrostatic and uniaxial conditions implied by R = 1 and R = 0, respectively. At R = 0, the generalized case transforms to the simplified uniaxial stress conditions, and CCP and VCP values of Poisson’s ratio fall on the same line. Figure 11 clearly demonstrates that the strain ratio range in the VCP test is much larger. Furthermore, the main difference between CCP and VCP tests is in the volumetric strains imposed on the soil. Although the shear strains are approximately of the same magnitude, the volumetric strains are much greater in the VCP test. In these tests, different values of R were applied to the specimen and, © 2001 NRC Canada

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Fig. 11. Poisson’s ratio versus the ratio of volumetric strain to shear strain.

Fig. 12. Poisson’s ratio versus the ratio of deviator stress to confining pressure.

0.7

+20 oC

Poisson's ratio

0.6 0.5 0.4 0.3

LinSub VCP LinSub CCP LinSa VCP LinSa CCP

0.2 0.1 0 0

1

2

3

4

5

qr/σ3 theoretically, values of Poisson’s ratio should fall on distinct curves. In practice, the exact value of R will differ between tests due to constantly changing conditions imposed on the test equipment. At subfreezing temperatures, a significant scatter in the data can be observed. In this case, however, the range of strain ratios is much smaller, and values of Poisson’s ratio are generally closer to the CCP reference line. This is due to the considerably decreased R ratio. The stress-dependent nature of the resilient Poisson’s ratio obtained from the CCP and VCP data is shown in Fig. 12. Except for the silt, the best fit to the laboratory data was obtained by plotting the Poisson’s ratio versus the ratio of deviator stress to confining pressure. The silt displayed practically no influence on this stress ratio. As shown in Fig. 12, both the VCP and the CCP data display downward concave behavior and increasing Poisson’s ratio with increasing stress ratio. This result is in contrast with the re-

sults of Allen and Thomson (1974) and Brown and Hyde (1975). The authors observed similar stress dependence of the Poisson’s ratio obtained from the CCP data, whereas the Poisson’s ratio obtained from the VCP data displayed distinct upward concave behavior. The authors considered this behavior to be due to the CCP conditions causing the specimens to undergo greater volume change than did the VCP test. However, in this study the VCP test generally resulted in a greater volume change than the CCP test. At subfreezing temperatures, inconclusive results were obtained when plotting Poisson’s ratio versus the ratio of deviator stress to confining stress. For example, the gravel displayed upward concave behavior with increasing stress ratio, whereas the sand and silt displayed the opposite response. However, due to the relatively large scatter in the values of Poisson’s ratio at subfreezing temperatures, no significant relationship could be established. © 2001 NRC Canada

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Fig. 13. Shear strain versus the ratio of deviator stress to mean level of mean normal stress for gravel at selected temperatures. 0.0016

LinSub CCP LinSub VCP

0.0014

Shear Strain

0.0012 0.001

+20 oC

-1 oC

0.0008 0.0006 0.0004

-5 / -10 oC

0.0002 0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

qr/pm Fig. 14. Shear strain versus the ratio of deviator stress to mean level of mean normal stress for sand at selected temperatures. 0.0012

LinSa CCP LinSa VCP

Shear Strain

0.001

0.0008

+20 oC

0.0006

0.0004

-1 oC -10 oC

0.0002

0 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

qr/pm

Shear and volumetric properties The characterization of nonlinear behavior in terms of shear and volumetric properties is generally preferred to the resilient modulus and Poisson’s ratio, since this avoids the assumption of linear elasticity. Figures 13–15 show the shear strain versus ratio of deviator stress to mean level of mean normal stress at selected temperatures for the soils tested and illustrate that the shear strains obtained in the CCP and

VCP tests are comparable when interpreted in terms of mean level of mean normal stress. The scatter in VCP data is generally somewhat larger compared with that for data obtained from the CCP tests. At decreasing temperatures, the slope of the strain–stress curve decreases successively. At –10°C, the influence of the applied stress on strain development is limited. For the two coarser soils, the slope of the strain– stress curve is almost identical at all temperatures. At © 2001 NRC Canada

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Fig. 15. Shear strain versus the ratio of deviator stress to mean level of mean normal stress for sand at selected temperatures. 0.0018

LuSi CCP LuSi VCP

0.0016

Shear Strain

0.0014 0.0012

+20 oC

0.001 0.0008

-1 oC

0.0006 0.0004

-5 / -10 oC

0.0002 0 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

qr/pm Fig. 16. Volumetric strain versus stress ratio qm/pm and confining pressure for gravel. 0.0016

+20 oC

0.0014

Volumetric strain

0.0012

σ3 = 42 kPa

VCP

0.001

σ3 = 28 kPa

0.0008

σ3 = 14 kPa

0.0006 0.0004

CCP

0.0002 0 -0.0002 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

qm/pm subfreezing temperatures, the slope of the stress–strain curve for silt is similar to those obtained for the two other soils, whereas at nonfreezing temperatures the slope is higher. No comparable values of volumetric strains obtained from CCP and VCP tests could be found. Figure 16 shows an example of volumetric strain versus the stress ratio qm/pm for gravel and clearly displays the differences in volumetric strain obtained in the CCP and VCP tests. In the VCP test, the volumetric strain increases with increasing confining pressure and mean normal stress. On the other hand, the volumetric strain decreases with increasing stress ratio qm/pm. Compared with the VCP tests, the volumetric strains obtained in the CCP tests are almost unaffected by changes in

confining pressure and stress ratio. At higher levels of qm/pm, the gravel displays dilatant behavior in the CCP tests. At subfreezing temperatures, all soils generally indicated dilatant behavior (εv < 0) in the CCP tests. Decreasing dilatant behavior is commonly associated with increasing levels of qm/pm. In contrast, volumetric strains obtained in the VCP test generally displayed contractant behavior at subfreezing temperatures. In this case, the volumetric strains decreased with increasing levels of qm/pm. Freeze–thaw effects In a previous paper, Simonsen et al. (2000) investigated the resilient properties of various fine- and coarse-grained © 2001 NRC Canada

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874

Can. Geotech. J. Vol. 38, 2001 Table 3. Statistical inference concerning freeze–thaw effects on resilient modulus. Soil

Specimen

Degree of compaction (%)

Difference in Mr after freeze–thaw (%)

Significant at α = 0.05

Sandy silt

1 2 1 2 1 2

93 100 102 105 100 102

–15 –1 –7 –1 –1 –4

Yes No Yes No No Yes

Sand Gravel

soils using CCP triaxial tests. Simonsen et al. observed a substantial decrease in resilient modulus after one freeze– thaw cycle and attributed this reduction to a net volume increase and thus a looser soil structure after freeze–thaw. Viklander (1998) also observed this phenomenon when investigating permeability changes due to freeze–thaw and found that, independent of initial porosity, the porosity after one to three freeze–thaw cycles stabilized at a residual value (i.e., densely compacted specimens increased in porosity and loosely compacted specimens decreased in porosity after freeze–thaw). The tests presented in this paper were designed to validate the observations of previous researchers, i.e., to investigate changes in resilient properties, particularly resilient modulus, due to freeze–thaw, and the effect of initial density. To determine freeze–thaw effects over the stress range applied, statistical significance tests were utilized. In practice, the actual stress applications will deviate slightly between different sets of resilient modulus tests, which in turn will affect the magnitude of the resilient modulus. To circumvent the variations in stress condition, the t tests were performed on the values of resilient modulus normalized with respect to bulk and deviator stress. However, it has previously been shown that freezing and thawing can influence the individual significance of bulk and deviator stress (Simonsen et al. 2000). To minimize this effect, the data were fitted to the commonly used universal model (Uzan 1985) using linear regression analysis. The resilient modulus was then normalized with respect to bulk and deviator stress raised to their exponents obtained in the regression analysis. Table 3 shows the results obtained in the statistical analysis. Table 3 clearly demonstrates that the results obtained in this investigation are not consistent with findings by Simonsen et al. (2000) and Viklander (1998). Simonsen et al. observed a substantial reduction (20–60%) in resilient modulus for all investigated soils. In the present investigation, however, only a minor reduction in resilient modulus was generally observed. Furthermore, based on the observations of Viklander, the reduction in resilient modulus should be affected by initial specimen density. In this investigation, no conclusive effect of initial density was observed. Despite a clear discrepancy in the results, the authors do not suggest that the conclusions drawn by Simonsen et al. (2000) and Viklander (1998) should be disregarded. There are several differences in test conditions between this and the previous investigations which can explain the inconsistency in the results obtained. In particular, there are concerns as to cooling rate and specimen rest time at the target temperatures. In the present study, liquid nitrogen was used to

lower the confining fluid temperature. Liquid nitrogen is highly effective as a cooling medium, producing a maximum cooling rate of approximately 20°C/h. This resulted in a cooling rate substantially higher than that in the investigation by Simonsen et al. Zhu and Ogawa (1997) investigated the effects of cooling rate on freezing in a closed system and found substantially reduced frost heave and frost heave pressure with increased cooling rate. In our case, the elevated cooling rate may have affected the moisture-migration potential and thus affected ice crystallization by restricting the formation of large ice crystals. Consequently, this could have reduced the volume expansion during freezing and limited the structural changes in the soil fabric, which in turn is the main factor affecting changes in resilient modulus after freeze–thaw. In this study, the samples were allowed to stabilize at the target temperature for approximately 4–8 h, which was considerably shorter than the corresponding rest time used by Simonsen et al. (2000). This time lapse is sufficient to ensure isothermal conditions for the soil tested. However, a stable sample temperature does not necessarily indicate water–ice equilibrium. In turn, this may have affected the potential of expansion due to ice crystallization and thus reduced the impact on resilient modulus after thawing.

Conclusions Based on findings presented in this paper, the following conclusions are drawn: (1) At nonfreezing temperatures, the VCP moduli are approximately 45–55% lower than the corresponding CCP moduli. At subfreezing temperatures, however, this difference decreases to approximately 20% for all soils. (2) In the CCP test of silt, there was a highly significant relationship between confining pressure and decreasing modulus with increasing deviator stress. In contrast, the influence of confining pressure in the VCP test is small and the resilient modulus increases with increasing levels of deviator stress. (3) The values of the resilient modulus computed from the CCP and VCP tests are compatible, provided that the product of qm and pm is similar in both tests. At low axial and radial stresses, the compatibility diminishes. (4) Shear strains obtained in CCP and VCP at nonfreezing and subfreezing temperature tests are comparable when interpreted in terms of the ratio of deviator stress to mean level of mean normal stress. (5) No comparable values of volumetric strain obtained in the CCP and VCP tests could be established. In the VCP © 2001 NRC Canada

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Simonsen and Isacsson

test, the volumetric strains increase with increasing confining pressure and mean normal stress and decrease with increasing stress ratio (qm/pm). In the CCP tests, however, the volumetric strains increase with increasing stress ratio. (6) No conclusive effect of freeze–thaw on resilient behavior could be established. Some samples showed a significant reduction in resilient modulus after freeze–thaw, whereas other samples remained unaffected. This inconsistency with previous research is probably a consequence of the test conditions applied.

Acknowledgements The financial support provided by the Swedish Road Administration and administered by the Centre for Research and Education in Operation and Maintenance of Infrastructure (CDU), Royal Institute of Technology, Stockholm, Sweden, is gratefully acknowledged.

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875 the Workshop on Modelling and Advanced Testing for Unbound Materials 21–22 January 1999. Instituto Superior Tecnico, Departamento de Engenharia Civil, Lisbon, Portugal, pp. 3–16. Fredlund, D.G., Bergan, A.T., and Sauer, E.K. 1975. Deformation characterization of subgrade soils for highways in northern environments. Canadian Geotechnical Journal, 12: 213–223. Hoff, I., Nordal, S., and Nordal, R.S. 1998. Permanent deformations in unbound layers predicted from triaxial tests using a new model for calculating stresses in pavement structures. In Proceedings of the International Conference on Bearing Capacity of Roads and Airfields, 6–8 July 1998. Edited by S. Nordal and G. Refsdal. Norwegian University of Science and Technology, Trondheim, Norway, Vol. 3, pp. 1315–1324. Hornych, P., Kazai, A., and Piau, J.M. 1998. Study of resilient behaviour of unbound granular materials. In Proceedings of the International Conference on Bearing Capacity of Roads and Airfields, 6–8 July 1998. Edited by S. Nordal and G. Refsdal. Norwegian University of Science and Technology, Trondheim, Norway, Vol. 3, pp. 1277–1287. Johnson, T.C., Cole, D.M., and Chamberlain, E.J. 1978. Influence of freezing and thawing on the resilient properties of a silt beneath an asphalt concrete pavement. U.S. Cold Regions Research and Engineering Laboratory, CRREL Report 78-23. Karashin, M. 1993. Resilient behaviour of granular materials for analysis of highway pavements. Ph.D. thesis, Department of Civil Engineering, University of Nottingham, Loughborough, U.K. Lee, W., Bohra, N.C., Altschaeffl, A.G., and White, T.D. 1995. Resilient modulus of cohesive soils and the effect of freeze–thaw. Canadian Geotechnical Journal, 32: 559–568. Simonsen, E., Janoo, V.C., and Isacsson, U. 2001. Resilient properties of unbound road materials during seasonal frost conditions. Journal of Cold Regions Engineering, ASCE. In press. Uzan, J. 1985. Characterization of granular materials. Transportation Research Record 1022, pp. 55–59. Viklander, P. 1998. Permeability and volume changes in till due to cyclic freeze–thaw. Canadian Geotechnical Journal, 35: 471– 477. Zhu, Q., and Ogawa, S. 1997. Effects of cooling rate on frost action in closed systems. In Proceedings of the International Symposium on Ground Freezing and Frost Action in Soils, Luleå, Sweden, 15–17 April 1997. Edited by S. Knutsson. A.A. Balkema, Rotterdam, pp. 217–224.

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