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Triaxial compression deformation for artificial frozen clay with thermal gradient
Cold Regions Science and Technology 67 (2011) 171–177
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Cold Regions Science and Technology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / c o l d r e g i o n s
Triaxial compression deformation for artificial frozen clay with thermal gradient Xiaodong Zhao, Guoqing Zhou ⁎, Guozhou Chen, Xiangyu Shang, Guangsi Zhao State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, Jiangsu, 221008, China
a r t i c l e
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Article history: Received 11 September 2010 Accepted 21 February 2011 Keywords: Artificial frozen clay K0DCGF test GFC test Thermal gradient Stress–strain relationship
a b s t r a c t In order to study the deformation characteristics of artificial frozen soil with thermal gradient, such as the stress–strain relationship, a series of triaxial compression tests for frozen clay had been conducted by K0DCGF (K0 consolidation, freezing with non-uniform temperature under loading) method and GFC (freezing with non-uniform temperature, isotropic consolidation) method at various consolidation pressures and thermal gradients. Stress–strain curves in K0DCGF test present strain softening during shearing process and the elastic strain is approximately 0.001;but which present the strain hardening characteristics in GFC tests and the elastic strain is approximately 0.01. The elastic modulus and peak stress for frozen clay decrease as the thermal gradient increased at different consolidation pressure both in K0DCGF test and GFC test. The peak stress and elastic modulus in K0DCGF test are significant independent on the pressure melting and crushing phenomena occurring in GFC test. To describe the shear deformation characteristics for frozen clay with thermal gradient, the exponent and power equations considering the correction equation on thermal gradient and model parameters from frozen clay with uniform temperature are developed .The results indicated that the proposed equations can reproduce the shear deformation well both in K0DCGF test and GFC test. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Large amounts of deep coal need to be explored to meet the energy consummation in China, but that was always covered by thick and deep stiff clay formations (the current greatest alluvium depth nearly approached to 700 m). The artificial freezing shaft was usually adopted to supply the temporary supporting structure for excavation at home and abroad. With the increasing of freezing depth for alluvium, the deformation and strength characteristics with nonuniform temperature at higher consolidation pressures for artificial frozen soil in freezing shaft became more complex. Following Tsytovich (1985) fundamental work, which represented the first comprehensive study of the subject of deformation and strength for frozen soil, major contributions were made to this topic through the experiment in laboratory (Ladanyi and Johnston, 1973; Lai et al., 2009, 2010; Ma et al., 1999; Yang et al., 2010a,b; Youssef, 1988; Zhang et al., 2007). Over the following decades mechanics properties for frozen soil at various confining pressure, temperature, and test methods continued to be the subject of extensive research (Bragg and Andersland, 1988; Li et al., 1993; Ma, 2000; Parameswaran and Jones, 1981). Furthermore, researches on deep artificial frozen soil by different institutions, such as State Key Laboratory of Frozen Soil Engineering, China University of Mining & Technology, China Coal Research Institute, and Anhui University of Science & Technology,
⁎ Corresponding author. Tel.: +86 516 83995178; fax: +86 51683590136. E-mail address: [email protected] (G. Zhou). 0165-232X/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.coldregions.2011.02.009
began to develop rapidly (Chang et al., 2007; Li et al., 1993; Yang, 1995; Zhang, 2006). However, the findings by different researchers have not been entirely consistent for the differences between test methods (Li et al., 1993; Ma, 2000), stress release or soil structure destruction during sampling (Li et al., 1993; Yang, 1995; Zhang, 2006). Cui (1998) proposed the concept of “deep frozen soil mechanics” to distinguish traditional “shallow frozen soil mechanics” through the construction practice on freezing shafts and the simulation tests in laboratory for the first time. The corresponding research method on artificial frozen soil in freezing shaft consisted of three stages: consolidation at higher pressure, freezing the soil under loading, and unloading the consolidation pressure at one dimensional or two dimensional directions. Ma and Chang (2002) first used the K0DCF (K0 consolidation-freezing soil under loading) method to conduct triaxial tests. The observations showed that the frozen soil presented greatest compression strength and lowest failure deformation in K0DCF test, but the frozen soil presented the lowest compression strength and greatest failure deformation in FC test. This supported the importance of consolidation before freezing once time. Wang (2006) and Wang et al. (2004, 2008) established strength criterion by combining of uniaxial compression strength for frozen loss with internal friction angle for unfrozen loss. In addition, the author found that the elastic modulus for frozen loss was greater than that for unfrozen loss, and the effects of confining pressure to elastic modulus of frozen loss were more obviously than that to elastic modulus of unfrozen loss. The deformation and strength in K0DCF tests involved with nonuniform temperature were investigated gradually because of the recognition of the physical mechanics differences between frozen soil
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with uniform temperature and with non-uniform temperature (Chen et al., 2000). Sheng et al. (1995) performed creep test at un-constant load and un-constant temperature, and his results showed that the frozen soil behaved like ageing geotechnical materials during decaying creep stage and the flowing rules were inapplicable for reproducing the creep process, however, the ageing theory (or hardening theory, or inheritance theory) could be developed to capture the creep characteristics. For stable and accelerating creep stage, creep deformation was controlled by flowing rules. Moreover, the ageing theory and Boltsmann's superposition theory were inapplicable either. Sheng et al. (1996) showed that creep deformation of frozen soil with Sine variation temperature was controlled by high temperature deformation and low temperature deformation comprehensively, and the creep deformation could be replaced by test results under uniform temperature. Chen et al. (2000) pointed out that the strength of artificial frozen soil in freezing shaft in non-uniform temperature field was quite different from that in uniform temperature field. Yang and Zhang (2003) adopted the non-uniform temperature to simulate the deformation of freezing wall by FEM (Finite Element Method), and found the deformation was 0.8 times more than the results with uniform temperature. The studies mentioned above are the latest developments in strength and deformation properties for frozen soil, especially for the deep artificial frozen soil, and represent a great advance in the investigation on this domain. In fact, the deformation and strength behavior of artificial frozen soil with non-uniform temperature are the results of thermo-mechanical response. Liu and Peng (2009) studied the strength weakening characteristics of thawing soil adopting the modified triaxial apparatus and obtained the effects of initial water amounts, cooling temperature and thawing temperature to stress– strain and strength. Zhou et al. (2010) conducted the deformation and strength research on frozen sand at different thermal gradient and different stress paths. Test results indicated that the stress–strain curves in unloading path was similar to that in loading path, and relationship of stress–strain curve could be described by modified Duncan–Chang equation. The soils tested with non-uniform temperature in K0DCF test in recent research work were always focusing on the cohesionless soil (Liu and Peng, 2009; Zhou et al., 2010). The broad objective of this project is to study experimentally the deformation of artificial frozen saturated clay at different thermal gradient in K0DCGF (K0 consolidation, freezing with non-uniform temperature under loading) and GFC (freezing with non-uniform temperature, isotropic consolidation) triaxial compression tests.
Table 2 Mineral composition. Composition
Value
Montmorillonite quartz (%) Quartz (%) Illite (%) Kaolinite (%) Calcite (%) Illite smectite mixed layer (%) Chlorite (%) Feldspar (%) Gypsum (%)
45.0 20.0 6.5 8.3 6.1 8.8 2.5 1.3 0.3
were then saturated with distilled water under a vacuum of 73 mm Hg for 24 h to achieve a Skempon's B value of at least 0.98. Tests were conducted on apparatus of TATW-500 .The TATW-500 shown in Fig.1 consisted of an axial loading system, confining loading system, freezing system, and auto controlling system. K0DCGF tests were carried out by the four steps: (1) Sample installation. Firstly, the saturated specimens were put on the pedestal of TATW-500, and then the membrane and thermal resistors (Fig. 2) were installed on the surface of samples; (2) K0 consolidation. In this step, drainage valve was opened and the samples were consolidated without radial deformation until the axial strain rate was less than 0.05%/h; (3) Freezing. Firstly, closing the drainage valve and the entry valves of triaxial cell, and specimens freezing with non-uniform temperature then were conducted under loading. The required thermal gradient was formed along the vertical direction, but the temperature was remained uniform along the radial direction at different specimen height. Comparison between the measured temperature distribution in test and designed temperature distribution is presented in Fig. 3(a); (4) Shearing. The triaxial piston was controlled to load on the samples at a displacement rate of 0.2 mm min− 1. Both the temperature distribution and the consolidation stress (or confining stress in GFC test) on samples were remained constant during shearing. The GFC method consisted of three stages: freezing stage, isotropic consolidation stage, and shearing stage. The thermal gradient can be calculated by the following expression: gradT =
2. Experimental method The soils used in test were taken from a mine shaft at a depth about 510 m ~ 530 m and the physical parameters were listed in Table 1. Mineral composition of tested clay was detailed introduced by Shang (2009), and that was listed in Table 2 again. The specimens were prepared as follows: Firstly, distilled water was added to air dried soil to make initial water content of 20%. Then the soil was put into a cylindrical rigid mold with 100 mm in diameter and 200 mm in height and compacted to the desired dry density. The average dry density of specimens was 1.42 g cm− 3. These specimens
Table 1 Physical parameters of clay. Plastic limit (%)
Liquid limit (%)
Specific gravity
Particle size (μm) content (%) b5
5–75
75–250
23.67
51.88
2.715
47.6
42.3
10.1
Tb −Tt H0
Where gradT stands for the thermal gradient; Tt represents the top temperature in specimen; Tb represents the bottom temperature in specimen, and H0 is the height of frozen clay before the application of consolidation. The average temperature for frozen clay is calculated by the following equation: Tθ =
Tt + Tb 2
Where Tθ stands for the average temperature for the specimen. The average temperature was −20 °C and the thermal gradients were 0.00 °C cm− 1, 0.25 °C cm− 1, and 0.50 °C cm− 1 respectively. On the other hand, the thermal resistors were placed at 2 cm, 6 cm, 10 cm, 14 cm, and 18 cm heights of the samples (Fig. 2). Temperature at different specimen height was kept constant in shearing, however, the specimen's height reduced gradually during consolidation and shearing, which made the actual thermal gradient increasing gradually. Hence, the thermal gradient in present research
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Fig. 1. Test apparatus.
was referred to as the initial thermal gradient before consolidation and shearing. Fig. 3 shows the temperature distribution in K0DCGF test (gradT = 0.25 °C cm− 1).It can be seen from Fig. 3(a) that temperature at different specimen's height is almost stable during shearing (The test period was approximately 4 h when the axial deformation reached 20%). The temperature fluctuation amounts lie between 0.1 °C and 0.3 °C as shown in Fig. 3(b), which agrees with the designed temperature distribution well. It also can be observed from Fig. 3(b) that maximum difference between internal and external temperature at different specimen's height is less than 0.3 °C. When the freezing period is long enough, the temperature distribution tends to be stable and the maximum difference between internal (at the center of the sample) and external temperature is less than 0.1 °C.
experiences three stages; the initial linear elastic stage, the plastic stage and the softening stage. In the initial linear elastic stage, stress increases linearly with the increasing axial strain, and there is little plastic strain in this stage. With further increase of axial strain, the slope of the stress–strain curves gradually decreases. The plastic deformation is dominating, and the elastic deformation is relatively subordinate in plastic stage. In softening stage, the slope of stress– strain curves is negative, which indicated that the stress decreases
3. Stress–strain characteristics 3.1. Thermal gradient versus stress–strain From Fig. 4(a), it can be noticed that the stress–strain behavior of frozen clay with thermal gradient in K0DCGF test approximately
Fig. 2. Fixation of thermal resistors.
Fig. 3. Temperature distribution. (a) Designed and measured temperature distribution. (b) Temperature difference along the radial direction during shearing.
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Fig. 4. Stress–strain curves for frozen clay with different thermal gradient.
Fig. 5. Stress–strain curves for frozen clay with a thermal gradient of 0.25 °C cm− 1.
with increasing in axial strain. The findings mentioned above are consistent with what had been established by Yang et al. (2010a,b). However, the stress–strain behavior of frozen clay with thermal gradient in GFC test as shown in Fig. 4(b) experiences two stages: the initial linear elastic stage and the linear strain hardening stage. In other words, the frozen clay with thermal gradient in K0DCGF test presents the brittle failure characteristics, and which presents the elastic-viscoplastic characteristics in GFC test. The experimental results indicated that the stress–strain curves of frozen clay with thermal gradient are significantly affected by the thermal gradient. With increasing in thermal gradient, the slopes of the initial stages of the stress–strain curves decrease in K0DCGF test and GFC test, which shows that the initial elastic modulus decrease with the increasing thermal gradient. In addition, the elastic modulus and shear strength for frozen clay in K0DCGF test are greater than that in GFC test, which verify the importance of consolidation before freezing once again.
pressure, but with a further increasing in confining pressure, the strength decreases in GFC test. Nevertheless, the peak shear stress in K0DCGF test presents a continuous increase characteristic as consolidation pressure increased. It also concluded from Figs. 4(a) and 5(a) that the increase of consolidation stress and thermal gradient both can induce the brittle characteristics increase, however, the transition from viscoplastic characteristics to brittle characteristics in GFC test appears to be less obvious than that in K0DCGF test as shown in Figs. 4(b) and 5(b). As seen from the experimental result, although the stress–strain relationship is identical for frozen clay at different thermal gradient, the elastic modulus and peak stresses in present work are affected significantly by thermal gradient. The mechanical characteristics of frozen clay is not only related to physical conditions and test method proposed by numerous researchers (Parameswaran and Jones, 1981; Yang et al., 2010a,b), but also related to thermal gradient. 4. Stress–strain equations
3.2. Consolidation pressure versus stress–strain We can conclude from Fig. 5 that the stress–strain curves of frozen clay with thermal gradient are also significantly affected by the consolidation pressure. However, the effects of consolidation pressure are less evident in GFC test than that in K0DCGF test. With increasing of consolidation pressure, the slopes of initial stages of the stress– strain curves increase in K0DCGF test, but that appears to be affected by confining pressures little in GFC tests. In other hand, the experimental results also show that the strength of frozen clay with thermal gradient increases to a peak value with increasing confining
The constitutive models are the bases of describing the mechanical behavior of materials under external load, and in formulation of such complex problems (Betten, 1988; Sung et al., 2010). The mathematical modeling has become a powerful tool (Yang et al., 2010a,b). But there is still lack of generally accepted procedures for establishment stress–strain model for frozen clay with thermal gradient. In order to describe the shear deformation of frozen clay under different test method, an approach of establishment stress–strain equations considering the thermal gradient will be presented in the following studies.
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stress, and the corresponding axial strain in Eq. (2). As a result, the functions of fE, fσp, and fε1,f in K0DCGF test are written as:
4.1. Stress–strain equations Based on the analysis for test results, the exponent equation (Zhu et al., 1992) is proposed to describe the shear deformation of frozen clay with uniform temperature in K0DCGF test as follows: ðσ1 −σ3 Þ−ðσ1 −σ3 Þ0 8 Eε > > < 1 i = h > > : ðσ1 −σ3 Þp −ε1;y E
!
ε1 −ε1;y ε1 −ε1;y exp 1− ε1;f −ε1;y ε1;f −ε1;y
!
ε1 ≤ε1; + ε1;y E ε1 N ε1;
ð1Þ Where (σ1–σ3) is the shear stress; ε1 is the axial strain; (σ1–σ3)p is the peak shear stress; ε1,f is the corresponding axial strain; (σ1–σ3)0 is the initial shear stress before application of shearing; E is the elastic modulus and ε1,y represents the yielding strain. Considering that the stress–strain curve for frozen clay with thermal gradient can be described by introducing the correction equation f. Hence, the following expression is obtained: ðσ1 −σ3 Þ−ðσ1 −σ3 Þ0 8 f Eε > > > E 1 ! ! > > < ε1 ≤ε1;y ε1 −ε1;y ε1 −ε1;y exp 1− fσp ðσ1 −σ3 Þp −ε1;y EfE = fε1;f ε1;f −ε1;y fε1;f ε1;f −ε1;y ε1 N ε1;y > > > > > : + ε Ef 1;y E
ð2Þ Where fE, fσ p, and fε1,f stand for the correction equations for frozen clay with thermal gradient in K0DCGF test. Furthermore, the stress–strain curves for frozen clay with uniform temperature in GFC test can be expressed by power equation: ( σ1 −σ3 =
Eε1 n ε1 ≤ε1;y ε1 N ε1;y ε1;y E + A ε1 −ε1;y
ð3Þ
Where A is the shear stress at the axial strain of (ε1−ε1, y) = 1%; n ( b 1) is the parameter relating to confining pressure and thermal gradient. The stress–strain curves for frozen clay with thermal gradient can be written in terms of correction equations of fE, fA, and fn: ( σ1 −σ3 =
175
fE Eε1 f n ε1 ≤ε1; n ε1 N ε1; ε1;y fE E + fA A ε1 −ε1;y
ð4Þ
fE = 1−KE gradT
ð5Þ
fσp = 1−Kσp gradT
ð6Þ
fε1;f = 1−Kε1;f gradT
ð7Þ
Where KE, Kσp, and Kε1,f are the materials parameters relating to consolidation pressure. In K0DCGF test, the parameters KE, Kσp, and Kε1,f are given by: σ1;0 KE = 0:0111 + 0:1121 10pa
ð8Þ
σ1;0 2 σ1;0 + 0:1805 −0:2167 Kσp = −0:012 10pa 10pa
ð9Þ
σ1;0 2 σ1;0 + 0:1524 + 0:4205 Kε1;f = −0:0136 10pa 10pa
Where σ1,0 represents consolidation pressure in K0DCGF test, σ1,0 is equal to initial axial stress before the application of shearing. The variations of the Kσp and Kε1,f are plotted against consolidation pressure in Fig. 6. It is found that the relationship between elastic modulus and consolidation pressure for frozen clay with uniform temperature in K0DCGF test can be described by following formulation: E = 10:727σ1;0 + 841:480
ð11Þ
The axial strain of ε1,f decreases and the peak shear stress of (σ1–σ3) p increases for frozen clay with uniform temperature in K0DCGF test as the consolidation pressure increased as shown in Fig. 5 (a). The relationships between peak shear stress, corresponding axial strain and consolidation pressure can be described as follows: ðσ1 −σ3 Þp = 0:1123σ1;0 + 5:1389
ð12Þ
σ1;0 ε1;f = −0:4454 + 12:708 10pa
ð13Þ
Where pa represents standard atmospheric pressure, p a = 0.10133 MPa. Substituting Eqs. (5)–(13) into Eq. (2), the shear deformation for frozen clay with thermal gradient in K0DCGF test can be calculated.
Where fE, fA, and fn stand for the correction equations for frozen clay with thermal gradient in GFC test. The present investigation for frozen clay with different thermal gradient indicated that the yielding strain is a constant, which is independent on thermal gradient and consolidation stress both in K0DCGF test (ε1, y = 0.1%) and in GFC test (ε1, y = 1%). In addition, the other parameters in Eqs. (1) and (3) are can be directly determined by using conventional triaxial compression test for frozen clay with uniform temperature. Accordingly, the shearing deformation for frozen soil with non-uniform temperature can be described by the correction equations and the parameters obtained from triaxial test for frozen soil with uniform temperature. 4.2. Correction equation We propose a linear correction equation here to describe the weakening effects of thermal gradient to elastic modulus, peak shear
ð10Þ
Fig. 6. Parameter of Kσp and Kε1,f in K0DCGF test.
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In GFC test, the linear correction equations to describe the weakening effects of thermal gradient to A and n can be defined as: fA ⋅A = ð1−KA gradT Þð−0:0138σ3 + 0:6208Þ
ð16Þ
σ3 + 0:1661 fn ⋅n = ð1−Kn gradT Þ 0:0409 10pa
ð17Þ
Where KA and Kn are the materials parameters relating to confining pressure. Fig. 7 shows the comparison for parameters of KA and Kn in GFC test at various confining pressures. As it can be observed in Fig. 7, the parameters of KA and Kn increase and then decrease as the confining pressure increased, this phenomena is identical with that in K0DCGF test. So the parameters KA and Kn are given by:
Fig. 7. Parameter of KA and Kn in GFC test.
KA = −0:0156
In other hand, the relationships between elastic modulus and thermal gradient in GFC test can be obtained as: fE ⋅E = 261:3ð1−KE gradT Þ
ð14Þ
Parameter of KE in GFC test is given by: KE = −0:0582
σ3 10pa
Where σ3 stands for the confining pressure in GFC test.
2 + 0:2246
σ3 −0:3270 10pa
σ3 2 σ3 + 0:3944 −1:1231 Kn = −0:0205 10pa 10pa
ð18Þ
ð19Þ
Substituting Eqs. (14)–(19) into Eq. (4), the shear deformation for frozen clay with thermal gradient in GFC test can be calculated. 4.3. Verification and analysis
+ 0:9983
σ3 10pa
ð15Þ
The proposed exponent equation and power equation are now used to describe some laboratory tests to check their validity. The calculations of triaxial compressive tests on frozen clay with thermal gradient have been performed by K0DCGF method and GFC method. Some representative results are shown in Fig. 8.
Fig. 8. Comparisons of shear strain between measured results and predicted results under consolidation pressure of 12.0 MPa.
X. Zhao et al. / Cold Regions Science and Technology 67 (2011) 171–177
Fig. 8 show the stress–strain curves obtained by both computation and experiment in K0DCGF test and GFC test From Fig. 8, it can be seen that there is a good agreement between the calculated results and experimental data. The influence of thermal gradient on the deformation behavior of frozen clay is correctly reproduced by the proposed method. Furthermore, the proposed equations considering the parameters for frozen clay with uniform temperature and the correction equations relating thermal gradient can reflect the increase of brittle characteristics in K0DCGF test and elastic-viscoplastic deformation characteristics in GFC test. 5. Summaries and conclusions A series of triaxial compressive tests of frozen clay at various thermal gradient and consolidation pressures have been conducted. The following results can be drawn based on this study: (1) Stress–strain curves present strain softening characteristics in K0DCGF test, and the elastic deformation is approximately 0.001. However, stress–strain curves present strain hardening characteristics in GFC test and the elastic deformation is approximately 0.01. (2) The elastic modulus for frozen clay with thermal gradient increases with the increasing of consolidation pressure in K0DCGF test, but that is independent on the confining pressure in GFC test. The elastic modulus decreases as the thermal gradient increased both in K0 DCGF test and GFC test. Furthermore, the elastic modulus in K0DCGF test is usually greater than that in GFC test. (3) The peak stress of frozen clay with thermal gradient increases with the increasing of consolidation pressure in K0DCGF test, but that decreases with the increasing of confining pressure for the pressure melting and crushing phenomena. However, the peak stress is affected significantly by thermal gradient both in K0DCGF test and GFC test. (4) To describe the shear deformation of frozen clay with thermal gradient by different test method, the exponent equation and power equations considering the correction equation on thermal gradient have been developed respectively. The results show that the deformation behavior of frozen clay can be represented by exponent equation in K0DCGF test (power equation in GFC test), and the proposed equations can describe the thermal gradient effects to the shear deformation well. Acknowledgements We would like to thank very much the two anonymous reviewers whose constructive comments are helpful for the paper revision. This research was supported by the National Natural Science Foundation of China (Grant nos. 50534040 and 50974117). Special thanks to the National Natural Science Foundations of China. References Betten, J., 1988. Applications of tensor functions to the formulation of yield criteria for anisotropic material. International Journal of Plasticity 4, 29–46. Bragg, R.A., Andersland, O.B., 1988. Strain rate, temperature, and sample size effects on compression and tensile properties of frozen sand. Engineering Geology 18, 35–46. Chang, X.X., Ma, W., Wang, D.Y., 2007. Study on the strength of frozen clay at high confining pressure. Journal of Glaciology and Geocryology 29 (4), 636–638 (In Chinese).
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Triaxial compression deformation for artificial frozen clay with thermal gradient Xiaodong Zhao, Guoqing Zhou ⁎, Guozhou Chen, Xiangyu Shang, Guangsi Zhao State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, Jiangsu, 221008, China
a r t i c l e
i n f o
Article history: Received 11 September 2010 Accepted 21 February 2011 Keywords: Artificial frozen clay K0DCGF test GFC test Thermal gradient Stress–strain relationship
a b s t r a c t In order to study the deformation characteristics of artificial frozen soil with thermal gradient, such as the stress–strain relationship, a series of triaxial compression tests for frozen clay had been conducted by K0DCGF (K0 consolidation, freezing with non-uniform temperature under loading) method and GFC (freezing with non-uniform temperature, isotropic consolidation) method at various consolidation pressures and thermal gradients. Stress–strain curves in K0DCGF test present strain softening during shearing process and the elastic strain is approximately 0.001;but which present the strain hardening characteristics in GFC tests and the elastic strain is approximately 0.01. The elastic modulus and peak stress for frozen clay decrease as the thermal gradient increased at different consolidation pressure both in K0DCGF test and GFC test. The peak stress and elastic modulus in K0DCGF test are significant independent on the pressure melting and crushing phenomena occurring in GFC test. To describe the shear deformation characteristics for frozen clay with thermal gradient, the exponent and power equations considering the correction equation on thermal gradient and model parameters from frozen clay with uniform temperature are developed .The results indicated that the proposed equations can reproduce the shear deformation well both in K0DCGF test and GFC test. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Large amounts of deep coal need to be explored to meet the energy consummation in China, but that was always covered by thick and deep stiff clay formations (the current greatest alluvium depth nearly approached to 700 m). The artificial freezing shaft was usually adopted to supply the temporary supporting structure for excavation at home and abroad. With the increasing of freezing depth for alluvium, the deformation and strength characteristics with nonuniform temperature at higher consolidation pressures for artificial frozen soil in freezing shaft became more complex. Following Tsytovich (1985) fundamental work, which represented the first comprehensive study of the subject of deformation and strength for frozen soil, major contributions were made to this topic through the experiment in laboratory (Ladanyi and Johnston, 1973; Lai et al., 2009, 2010; Ma et al., 1999; Yang et al., 2010a,b; Youssef, 1988; Zhang et al., 2007). Over the following decades mechanics properties for frozen soil at various confining pressure, temperature, and test methods continued to be the subject of extensive research (Bragg and Andersland, 1988; Li et al., 1993; Ma, 2000; Parameswaran and Jones, 1981). Furthermore, researches on deep artificial frozen soil by different institutions, such as State Key Laboratory of Frozen Soil Engineering, China University of Mining & Technology, China Coal Research Institute, and Anhui University of Science & Technology,
⁎ Corresponding author. Tel.: +86 516 83995178; fax: +86 51683590136. E-mail address: [email protected] (G. Zhou). 0165-232X/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.coldregions.2011.02.009
began to develop rapidly (Chang et al., 2007; Li et al., 1993; Yang, 1995; Zhang, 2006). However, the findings by different researchers have not been entirely consistent for the differences between test methods (Li et al., 1993; Ma, 2000), stress release or soil structure destruction during sampling (Li et al., 1993; Yang, 1995; Zhang, 2006). Cui (1998) proposed the concept of “deep frozen soil mechanics” to distinguish traditional “shallow frozen soil mechanics” through the construction practice on freezing shafts and the simulation tests in laboratory for the first time. The corresponding research method on artificial frozen soil in freezing shaft consisted of three stages: consolidation at higher pressure, freezing the soil under loading, and unloading the consolidation pressure at one dimensional or two dimensional directions. Ma and Chang (2002) first used the K0DCF (K0 consolidation-freezing soil under loading) method to conduct triaxial tests. The observations showed that the frozen soil presented greatest compression strength and lowest failure deformation in K0DCF test, but the frozen soil presented the lowest compression strength and greatest failure deformation in FC test. This supported the importance of consolidation before freezing once time. Wang (2006) and Wang et al. (2004, 2008) established strength criterion by combining of uniaxial compression strength for frozen loss with internal friction angle for unfrozen loss. In addition, the author found that the elastic modulus for frozen loss was greater than that for unfrozen loss, and the effects of confining pressure to elastic modulus of frozen loss were more obviously than that to elastic modulus of unfrozen loss. The deformation and strength in K0DCF tests involved with nonuniform temperature were investigated gradually because of the recognition of the physical mechanics differences between frozen soil
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with uniform temperature and with non-uniform temperature (Chen et al., 2000). Sheng et al. (1995) performed creep test at un-constant load and un-constant temperature, and his results showed that the frozen soil behaved like ageing geotechnical materials during decaying creep stage and the flowing rules were inapplicable for reproducing the creep process, however, the ageing theory (or hardening theory, or inheritance theory) could be developed to capture the creep characteristics. For stable and accelerating creep stage, creep deformation was controlled by flowing rules. Moreover, the ageing theory and Boltsmann's superposition theory were inapplicable either. Sheng et al. (1996) showed that creep deformation of frozen soil with Sine variation temperature was controlled by high temperature deformation and low temperature deformation comprehensively, and the creep deformation could be replaced by test results under uniform temperature. Chen et al. (2000) pointed out that the strength of artificial frozen soil in freezing shaft in non-uniform temperature field was quite different from that in uniform temperature field. Yang and Zhang (2003) adopted the non-uniform temperature to simulate the deformation of freezing wall by FEM (Finite Element Method), and found the deformation was 0.8 times more than the results with uniform temperature. The studies mentioned above are the latest developments in strength and deformation properties for frozen soil, especially for the deep artificial frozen soil, and represent a great advance in the investigation on this domain. In fact, the deformation and strength behavior of artificial frozen soil with non-uniform temperature are the results of thermo-mechanical response. Liu and Peng (2009) studied the strength weakening characteristics of thawing soil adopting the modified triaxial apparatus and obtained the effects of initial water amounts, cooling temperature and thawing temperature to stress– strain and strength. Zhou et al. (2010) conducted the deformation and strength research on frozen sand at different thermal gradient and different stress paths. Test results indicated that the stress–strain curves in unloading path was similar to that in loading path, and relationship of stress–strain curve could be described by modified Duncan–Chang equation. The soils tested with non-uniform temperature in K0DCF test in recent research work were always focusing on the cohesionless soil (Liu and Peng, 2009; Zhou et al., 2010). The broad objective of this project is to study experimentally the deformation of artificial frozen saturated clay at different thermal gradient in K0DCGF (K0 consolidation, freezing with non-uniform temperature under loading) and GFC (freezing with non-uniform temperature, isotropic consolidation) triaxial compression tests.
Table 2 Mineral composition. Composition
Value
Montmorillonite quartz (%) Quartz (%) Illite (%) Kaolinite (%) Calcite (%) Illite smectite mixed layer (%) Chlorite (%) Feldspar (%) Gypsum (%)
45.0 20.0 6.5 8.3 6.1 8.8 2.5 1.3 0.3
were then saturated with distilled water under a vacuum of 73 mm Hg for 24 h to achieve a Skempon's B value of at least 0.98. Tests were conducted on apparatus of TATW-500 .The TATW-500 shown in Fig.1 consisted of an axial loading system, confining loading system, freezing system, and auto controlling system. K0DCGF tests were carried out by the four steps: (1) Sample installation. Firstly, the saturated specimens were put on the pedestal of TATW-500, and then the membrane and thermal resistors (Fig. 2) were installed on the surface of samples; (2) K0 consolidation. In this step, drainage valve was opened and the samples were consolidated without radial deformation until the axial strain rate was less than 0.05%/h; (3) Freezing. Firstly, closing the drainage valve and the entry valves of triaxial cell, and specimens freezing with non-uniform temperature then were conducted under loading. The required thermal gradient was formed along the vertical direction, but the temperature was remained uniform along the radial direction at different specimen height. Comparison between the measured temperature distribution in test and designed temperature distribution is presented in Fig. 3(a); (4) Shearing. The triaxial piston was controlled to load on the samples at a displacement rate of 0.2 mm min− 1. Both the temperature distribution and the consolidation stress (or confining stress in GFC test) on samples were remained constant during shearing. The GFC method consisted of three stages: freezing stage, isotropic consolidation stage, and shearing stage. The thermal gradient can be calculated by the following expression: gradT =
2. Experimental method The soils used in test were taken from a mine shaft at a depth about 510 m ~ 530 m and the physical parameters were listed in Table 1. Mineral composition of tested clay was detailed introduced by Shang (2009), and that was listed in Table 2 again. The specimens were prepared as follows: Firstly, distilled water was added to air dried soil to make initial water content of 20%. Then the soil was put into a cylindrical rigid mold with 100 mm in diameter and 200 mm in height and compacted to the desired dry density. The average dry density of specimens was 1.42 g cm− 3. These specimens
Table 1 Physical parameters of clay. Plastic limit (%)
Liquid limit (%)
Specific gravity
Particle size (μm) content (%) b5
5–75
75–250
23.67
51.88
2.715
47.6
42.3
10.1
Tb −Tt H0
Where gradT stands for the thermal gradient; Tt represents the top temperature in specimen; Tb represents the bottom temperature in specimen, and H0 is the height of frozen clay before the application of consolidation. The average temperature for frozen clay is calculated by the following equation: Tθ =
Tt + Tb 2
Where Tθ stands for the average temperature for the specimen. The average temperature was −20 °C and the thermal gradients were 0.00 °C cm− 1, 0.25 °C cm− 1, and 0.50 °C cm− 1 respectively. On the other hand, the thermal resistors were placed at 2 cm, 6 cm, 10 cm, 14 cm, and 18 cm heights of the samples (Fig. 2). Temperature at different specimen height was kept constant in shearing, however, the specimen's height reduced gradually during consolidation and shearing, which made the actual thermal gradient increasing gradually. Hence, the thermal gradient in present research
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Fig. 1. Test apparatus.
was referred to as the initial thermal gradient before consolidation and shearing. Fig. 3 shows the temperature distribution in K0DCGF test (gradT = 0.25 °C cm− 1).It can be seen from Fig. 3(a) that temperature at different specimen's height is almost stable during shearing (The test period was approximately 4 h when the axial deformation reached 20%). The temperature fluctuation amounts lie between 0.1 °C and 0.3 °C as shown in Fig. 3(b), which agrees with the designed temperature distribution well. It also can be observed from Fig. 3(b) that maximum difference between internal and external temperature at different specimen's height is less than 0.3 °C. When the freezing period is long enough, the temperature distribution tends to be stable and the maximum difference between internal (at the center of the sample) and external temperature is less than 0.1 °C.
experiences three stages; the initial linear elastic stage, the plastic stage and the softening stage. In the initial linear elastic stage, stress increases linearly with the increasing axial strain, and there is little plastic strain in this stage. With further increase of axial strain, the slope of the stress–strain curves gradually decreases. The plastic deformation is dominating, and the elastic deformation is relatively subordinate in plastic stage. In softening stage, the slope of stress– strain curves is negative, which indicated that the stress decreases
3. Stress–strain characteristics 3.1. Thermal gradient versus stress–strain From Fig. 4(a), it can be noticed that the stress–strain behavior of frozen clay with thermal gradient in K0DCGF test approximately
Fig. 2. Fixation of thermal resistors.
Fig. 3. Temperature distribution. (a) Designed and measured temperature distribution. (b) Temperature difference along the radial direction during shearing.
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Fig. 4. Stress–strain curves for frozen clay with different thermal gradient.
Fig. 5. Stress–strain curves for frozen clay with a thermal gradient of 0.25 °C cm− 1.
with increasing in axial strain. The findings mentioned above are consistent with what had been established by Yang et al. (2010a,b). However, the stress–strain behavior of frozen clay with thermal gradient in GFC test as shown in Fig. 4(b) experiences two stages: the initial linear elastic stage and the linear strain hardening stage. In other words, the frozen clay with thermal gradient in K0DCGF test presents the brittle failure characteristics, and which presents the elastic-viscoplastic characteristics in GFC test. The experimental results indicated that the stress–strain curves of frozen clay with thermal gradient are significantly affected by the thermal gradient. With increasing in thermal gradient, the slopes of the initial stages of the stress–strain curves decrease in K0DCGF test and GFC test, which shows that the initial elastic modulus decrease with the increasing thermal gradient. In addition, the elastic modulus and shear strength for frozen clay in K0DCGF test are greater than that in GFC test, which verify the importance of consolidation before freezing once again.
pressure, but with a further increasing in confining pressure, the strength decreases in GFC test. Nevertheless, the peak shear stress in K0DCGF test presents a continuous increase characteristic as consolidation pressure increased. It also concluded from Figs. 4(a) and 5(a) that the increase of consolidation stress and thermal gradient both can induce the brittle characteristics increase, however, the transition from viscoplastic characteristics to brittle characteristics in GFC test appears to be less obvious than that in K0DCGF test as shown in Figs. 4(b) and 5(b). As seen from the experimental result, although the stress–strain relationship is identical for frozen clay at different thermal gradient, the elastic modulus and peak stresses in present work are affected significantly by thermal gradient. The mechanical characteristics of frozen clay is not only related to physical conditions and test method proposed by numerous researchers (Parameswaran and Jones, 1981; Yang et al., 2010a,b), but also related to thermal gradient. 4. Stress–strain equations
3.2. Consolidation pressure versus stress–strain We can conclude from Fig. 5 that the stress–strain curves of frozen clay with thermal gradient are also significantly affected by the consolidation pressure. However, the effects of consolidation pressure are less evident in GFC test than that in K0DCGF test. With increasing of consolidation pressure, the slopes of initial stages of the stress– strain curves increase in K0DCGF test, but that appears to be affected by confining pressures little in GFC tests. In other hand, the experimental results also show that the strength of frozen clay with thermal gradient increases to a peak value with increasing confining
The constitutive models are the bases of describing the mechanical behavior of materials under external load, and in formulation of such complex problems (Betten, 1988; Sung et al., 2010). The mathematical modeling has become a powerful tool (Yang et al., 2010a,b). But there is still lack of generally accepted procedures for establishment stress–strain model for frozen clay with thermal gradient. In order to describe the shear deformation of frozen clay under different test method, an approach of establishment stress–strain equations considering the thermal gradient will be presented in the following studies.
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stress, and the corresponding axial strain in Eq. (2). As a result, the functions of fE, fσp, and fε1,f in K0DCGF test are written as:
4.1. Stress–strain equations Based on the analysis for test results, the exponent equation (Zhu et al., 1992) is proposed to describe the shear deformation of frozen clay with uniform temperature in K0DCGF test as follows: ðσ1 −σ3 Þ−ðσ1 −σ3 Þ0 8 Eε > > < 1 i = h > > : ðσ1 −σ3 Þp −ε1;y E
!
ε1 −ε1;y ε1 −ε1;y exp 1− ε1;f −ε1;y ε1;f −ε1;y
!
ε1 ≤ε1; + ε1;y E ε1 N ε1;
ð1Þ Where (σ1–σ3) is the shear stress; ε1 is the axial strain; (σ1–σ3)p is the peak shear stress; ε1,f is the corresponding axial strain; (σ1–σ3)0 is the initial shear stress before application of shearing; E is the elastic modulus and ε1,y represents the yielding strain. Considering that the stress–strain curve for frozen clay with thermal gradient can be described by introducing the correction equation f. Hence, the following expression is obtained: ðσ1 −σ3 Þ−ðσ1 −σ3 Þ0 8 f Eε > > > E 1 ! ! > > < ε1 ≤ε1;y ε1 −ε1;y ε1 −ε1;y exp 1− fσp ðσ1 −σ3 Þp −ε1;y EfE = fε1;f ε1;f −ε1;y fε1;f ε1;f −ε1;y ε1 N ε1;y > > > > > : + ε Ef 1;y E
ð2Þ Where fE, fσ p, and fε1,f stand for the correction equations for frozen clay with thermal gradient in K0DCGF test. Furthermore, the stress–strain curves for frozen clay with uniform temperature in GFC test can be expressed by power equation: ( σ1 −σ3 =
Eε1 n ε1 ≤ε1;y ε1 N ε1;y ε1;y E + A ε1 −ε1;y
ð3Þ
Where A is the shear stress at the axial strain of (ε1−ε1, y) = 1%; n ( b 1) is the parameter relating to confining pressure and thermal gradient. The stress–strain curves for frozen clay with thermal gradient can be written in terms of correction equations of fE, fA, and fn: ( σ1 −σ3 =
175
fE Eε1 f n ε1 ≤ε1; n ε1 N ε1; ε1;y fE E + fA A ε1 −ε1;y
ð4Þ
fE = 1−KE gradT
ð5Þ
fσp = 1−Kσp gradT
ð6Þ
fε1;f = 1−Kε1;f gradT
ð7Þ
Where KE, Kσp, and Kε1,f are the materials parameters relating to consolidation pressure. In K0DCGF test, the parameters KE, Kσp, and Kε1,f are given by: σ1;0 KE = 0:0111 + 0:1121 10pa
ð8Þ
σ1;0 2 σ1;0 + 0:1805 −0:2167 Kσp = −0:012 10pa 10pa
ð9Þ
σ1;0 2 σ1;0 + 0:1524 + 0:4205 Kε1;f = −0:0136 10pa 10pa
Where σ1,0 represents consolidation pressure in K0DCGF test, σ1,0 is equal to initial axial stress before the application of shearing. The variations of the Kσp and Kε1,f are plotted against consolidation pressure in Fig. 6. It is found that the relationship between elastic modulus and consolidation pressure for frozen clay with uniform temperature in K0DCGF test can be described by following formulation: E = 10:727σ1;0 + 841:480
ð11Þ
The axial strain of ε1,f decreases and the peak shear stress of (σ1–σ3) p increases for frozen clay with uniform temperature in K0DCGF test as the consolidation pressure increased as shown in Fig. 5 (a). The relationships between peak shear stress, corresponding axial strain and consolidation pressure can be described as follows: ðσ1 −σ3 Þp = 0:1123σ1;0 + 5:1389
ð12Þ
σ1;0 ε1;f = −0:4454 + 12:708 10pa
ð13Þ
Where pa represents standard atmospheric pressure, p a = 0.10133 MPa. Substituting Eqs. (5)–(13) into Eq. (2), the shear deformation for frozen clay with thermal gradient in K0DCGF test can be calculated.
Where fE, fA, and fn stand for the correction equations for frozen clay with thermal gradient in GFC test. The present investigation for frozen clay with different thermal gradient indicated that the yielding strain is a constant, which is independent on thermal gradient and consolidation stress both in K0DCGF test (ε1, y = 0.1%) and in GFC test (ε1, y = 1%). In addition, the other parameters in Eqs. (1) and (3) are can be directly determined by using conventional triaxial compression test for frozen clay with uniform temperature. Accordingly, the shearing deformation for frozen soil with non-uniform temperature can be described by the correction equations and the parameters obtained from triaxial test for frozen soil with uniform temperature. 4.2. Correction equation We propose a linear correction equation here to describe the weakening effects of thermal gradient to elastic modulus, peak shear
ð10Þ
Fig. 6. Parameter of Kσp and Kε1,f in K0DCGF test.
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In GFC test, the linear correction equations to describe the weakening effects of thermal gradient to A and n can be defined as: fA ⋅A = ð1−KA gradT Þð−0:0138σ3 + 0:6208Þ
ð16Þ
σ3 + 0:1661 fn ⋅n = ð1−Kn gradT Þ 0:0409 10pa
ð17Þ
Where KA and Kn are the materials parameters relating to confining pressure. Fig. 7 shows the comparison for parameters of KA and Kn in GFC test at various confining pressures. As it can be observed in Fig. 7, the parameters of KA and Kn increase and then decrease as the confining pressure increased, this phenomena is identical with that in K0DCGF test. So the parameters KA and Kn are given by:
Fig. 7. Parameter of KA and Kn in GFC test.
KA = −0:0156
In other hand, the relationships between elastic modulus and thermal gradient in GFC test can be obtained as: fE ⋅E = 261:3ð1−KE gradT Þ
ð14Þ
Parameter of KE in GFC test is given by: KE = −0:0582
σ3 10pa
Where σ3 stands for the confining pressure in GFC test.
2 + 0:2246
σ3 −0:3270 10pa
σ3 2 σ3 + 0:3944 −1:1231 Kn = −0:0205 10pa 10pa
ð18Þ
ð19Þ
Substituting Eqs. (14)–(19) into Eq. (4), the shear deformation for frozen clay with thermal gradient in GFC test can be calculated. 4.3. Verification and analysis
+ 0:9983
σ3 10pa
ð15Þ
The proposed exponent equation and power equation are now used to describe some laboratory tests to check their validity. The calculations of triaxial compressive tests on frozen clay with thermal gradient have been performed by K0DCGF method and GFC method. Some representative results are shown in Fig. 8.
Fig. 8. Comparisons of shear strain between measured results and predicted results under consolidation pressure of 12.0 MPa.
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Fig. 8 show the stress–strain curves obtained by both computation and experiment in K0DCGF test and GFC test From Fig. 8, it can be seen that there is a good agreement between the calculated results and experimental data. The influence of thermal gradient on the deformation behavior of frozen clay is correctly reproduced by the proposed method. Furthermore, the proposed equations considering the parameters for frozen clay with uniform temperature and the correction equations relating thermal gradient can reflect the increase of brittle characteristics in K0DCGF test and elastic-viscoplastic deformation characteristics in GFC test. 5. Summaries and conclusions A series of triaxial compressive tests of frozen clay at various thermal gradient and consolidation pressures have been conducted. The following results can be drawn based on this study: (1) Stress–strain curves present strain softening characteristics in K0DCGF test, and the elastic deformation is approximately 0.001. However, stress–strain curves present strain hardening characteristics in GFC test and the elastic deformation is approximately 0.01. (2) The elastic modulus for frozen clay with thermal gradient increases with the increasing of consolidation pressure in K0DCGF test, but that is independent on the confining pressure in GFC test. The elastic modulus decreases as the thermal gradient increased both in K0 DCGF test and GFC test. Furthermore, the elastic modulus in K0DCGF test is usually greater than that in GFC test. (3) The peak stress of frozen clay with thermal gradient increases with the increasing of consolidation pressure in K0DCGF test, but that decreases with the increasing of confining pressure for the pressure melting and crushing phenomena. However, the peak stress is affected significantly by thermal gradient both in K0DCGF test and GFC test. (4) To describe the shear deformation of frozen clay with thermal gradient by different test method, the exponent equation and power equations considering the correction equation on thermal gradient have been developed respectively. The results show that the deformation behavior of frozen clay can be represented by exponent equation in K0DCGF test (power equation in GFC test), and the proposed equations can describe the thermal gradient effects to the shear deformation well. Acknowledgements We would like to thank very much the two anonymous reviewers whose constructive comments are helpful for the paper revision. This research was supported by the National Natural Science Foundation of China (Grant nos. 50534040 and 50974117). Special thanks to the National Natural Science Foundations of China. References Betten, J., 1988. Applications of tensor functions to the formulation of yield criteria for anisotropic material. International Journal of Plasticity 4, 29–46. Bragg, R.A., Andersland, O.B., 1988. Strain rate, temperature, and sample size effects on compression and tensile properties of frozen sand. Engineering Geology 18, 35–46. Chang, X.X., Ma, W., Wang, D.Y., 2007. Study on the strength of frozen clay at high confining pressure. Journal of Glaciology and Geocryology 29 (4), 636–638 (In Chinese).
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