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A versatile triaxial apparatus for frozen soils
Cold Regions Science and Technology 92 (2013) 48–54
Contents lists available at SciVerse ScienceDirect
Cold Regions Science and Technology journal homepage: www.elsevier.com/locate/coldregions
A versatile triaxial apparatus for frozen soils Xiaoliang Yao, Jilin Qi ⁎, Fan Yu, Ling Ma State Key Laboratory of Frozen Soil Engineering, Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, Lanzhou 730000, China
a r t i c l e
i n f o
Article history: Received 23 November 2012 Accepted 30 April 2013 Keywords: Triaxial apparatus Frozen soil Temperature control Radial strain Volumetric change
a b s t r a c t Settlement and damage to infrastructures in permafrost regions depend in part on the mechanical properties of permafrost layers. In order to get a better understanding of the mechanical behavior of frozen soils, a triaxial apparatus was developed with three new features in addition to the traditional functions. The first is the accurate temperature control, which allows temperature to fluctuate within ± 0.1 °C during the loading period, and ± 0.02 °C before loading, so as to get a better understanding of the mechanical properties of frozen soils under temperatures close to thawing point. The second feature is used to measure K0 of frozen soils. A highly-sensitive radial strain measurement device was designed and the K0 state can be accurately maintained by automatically adjusting the radial pressure when radial deformation changes more than ± 10 μm. The third is the precise measurement of the volumetric strain through the displacement of axial and radial loading pistons. The capabilities of the triaxial apparatus are shown using a series of test results. It is considered to be a promising tool to investigate the mechanical properties of frozen soils. © 2013 Elsevier B.V. All rights reserved.
1. Introduction With increasing construction of infrastructures in permafrost regions, the mechanical properties of frozen soil and their dependence on ambient temperature are becoming more important. Many studies have shown that with global warming significant increases in the temperature of permafrost have occurred (Oberman and Mazhitova, 2001; Osterkamp, 2005; Smith et al., 2005; Wu and Zhang, 2008). This inevitably influences the mechanical properties of frozen soil as temperature is one of the main factors determining the mechanical properties of frozen soils (Bourbonnais and Ladanyi, 1985; Wu and Ma, 1994; Zhu and Carbee, 1984). Even small change in temperature will probably lead to serious consequences for engineering constructions, such as creep of high-temperature (MAGT ≥ − 1.5 °C) frozen layers (Ma et al., 2008; Qi et al., 2007; Zheng et al., 2010) and instability of slope in permafrost regions (Niu et al., 2004; Niu et al., 2006; Wang and French, 1995). To investigate the influence of temperature on mechanical behavior of frozen soils, triaxial apparatus is essential because of its simple stress state and clear boundary conditions. Temperature control is the first task for testing on frozen soils. There have been two main cooling methods frequently used for temperature control of triaxial apparatus. The first uses a refrigerating unit to cool the room and as a result the triaxial apparatus in the room, known as the “air-cooling method”. This method simplifies the construction of the triaxial apparatus, and avoids the influence of daily temperature fluctuations, but is associated with poor cooling efficiency and precision
⁎ Corresponding author. Tel./fax: +86 931 4967261. E-mail address: [email protected] (J. Qi). 0165-232X/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.coldregions.2013.04.001
due to the large cooling volume (the whole room) and instable air stream. In addition, with radial pressure loading/unloading, the piston does positive/negative work on the hydraulic oil, resulting in changes in the oil temperature. This cooling method cannot respond rapidly to such changes. As a result, the sample temperature will show an obvious fluctuation. Some improvements were then made on this method. For instance, a triaxial apparatus was designed with a large volume of cell fluid, which acts as a “buffer” to reduce the temperature fluctuations (Arenson et al., 2004). The temperature control precision, in the environmental chamber (the triaxial apparatus in the chamber), was increased using a small electronic fan and a heating bulb, and the temperature was controlled more uniform with an air pump to circulate the hydraulic oil in the pressure cell (Gregory et al., 2003). Nevertheless, the “air-cooling method” is still poor in the cooling efficiency and the temperature fluctuation more than ±0.1 °C. The second method uses an anti-freeze liquid, the so-called “liquid-cooling method”, where the triaxial apparatus is refrigerated by the cooled liquid circulating in the device. However, the precision of this method is influenced considerably by daily temperature fluctuations and heat emission in long-term tests. This kind of device has a higher temperature control precision than the first method. For instance, Hazirbaba et al. (2011) used two cooling baths, one for the temperature at the top and bottom plates and another for the ambient temperature of soil sample. However, the use of a single cooling device for both the top and bottom temperature may induce non-uniform temperatures throughout the soil sample caused by temperature difference between the outlet and inlet of the cooled liquid. From the above, it can be seen that the two cooling methods have their advantages and disadvantages. As far as the mechanical properties of frozen soil are concerned, two indexes still remain difficult to measure. One is the coefficient
X. Yao et al. / Cold Regions Science and Technology 92 (2013) 48–54
of lateral earth pressure (K0) at rest of frozen soils, which is a very important parameter for designing and analyzing geotechnical engineering such as tunnel, mineshafts, and retaining walls. For unfrozen soils, there are mainly three methods used: the oedometer, plane strain or triaxial test, respectively. Among these methods the triaxial apparatus might be more conventionally available. However, frozen soils are much stiffer, and less deformation occurs than in unfrozen soils under the same stress, requiring higher radial pressures to reach the zero lateral strain once a small lateral deformation occurs. Therefore, in order to precisely measure K0, the controller and loading system for frozen soil should be more sensitive. In triaxial tests on frozen soil, the measurement of K0 remains difficult and is rarely investigated. The second problem is the measurement of volumetric changes of frozen soil samples. Devices from conventional triaxial apparatus may be applied for frozen samples. However, due to the more complicated structure needed for such devices for use with frozen soils, there are some drawbacks to measure volumetric change precisely, e.g. the leakage of fluid out of pressure cell, base flexure of the cell due to the applied axial load (Gregory et al., 2003), and the relative low resolution of the measurement (Arenson et al., 2004). The above mentioned require precise temperature control, multi-functions, especially in K0-state control, as well as the precise measurement of volumetric change for triaxial tests on frozen soil. Here, a versatile triaxial apparatus is presented in which both airand liquid-cooling methods are combined to increase the precision of temperature control. A very precise radial strain measurement device is used to measure K0. The volumetric change can be precisely measured and is capable of strain (rate) and stress (rate) controlled loading, with excellent long-term stability. A series of test programs were carried out to show performance of the device.
2. Apparatus description Fig. 1 shows a schematic of the triaxial apparatus that was designed and completed in 2010. It consists of two major systems: loading system (stress (rate) and strain (rate) control) and temperature controlling system. Details of all the setups and sensors used in the triaxial apparatus are shown in Table 1.
49
2.1. Loading system In the system, a steel airtight pressure cell is designed to withstand a confining pressure of about 30 MPa. Aircraft hydraulic oil in the cell is used to reduce viscosity at low temperatures. Another advantage of the oil is that it can avoid corroding the rubber membrane used to seal the spacemen during testing. It also offers the benefit of being nonconductive, which is essential when locating electronic devices such as the temperature sensors and radial strain measurement device within the pressure cell. Radial pressure is applied to the specimen (D = 6.18 cm × H = 12.5 cm) through a piston pressing the hydraulic oil into the cylinder. The sample is axially loaded through a hardened steel piston, with a maximum pressure of 100 kN. The piston enters the top of the pressure cell through two O-ring seals. Two O-rings seal the joint between the bottom plate and the pressure cell. The displacement of both the axial and radial loading pistons is recorded by the revolution of servo-motors in terms of angle, which is transformed into distance by an EDC (External digital controller). A load cell is used to monitor the axial pressure, while two pressure sensors to monitor the radial and pore water (for unfrozen soil) pressure. Automated control is carried out by the EDCs (which is manufactured by DOLI Elektronik GmbH in Germany with four control loops and can control the stress and strain on axial and radial directions separately) for data acquisition and closed loop control of testing instruments. A computer with specially developed software allows for simultaneous control of stress (rate) and strain (rate) in both axial and radial directions. The working principles are shown in Fig. 2(a, b, and c). With this system, it is possible to perform conventional triaxial tests, stress path tests, K0 consolidation, etc. 2.2. Temperature controlling system To prevent the influence of laboratory temperature fluctuations on the temperature control precision, a high-power air-conditioner is used to maintain the laboratory temperature at around 22 °C, which is also comfortable for laboratory technicians to work in. Three refrigeration circulators are used to control the temperature at the top, bottom and side of the soil sample. Taking into account the cooling loss due to the heat effect of room temperature and pipe lines, the temperature of cooling bath is set lower than the target temperature.
Fig. 1. Schematic of the triaxial apparatus.
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Table 1 The setups and sensors used in the triaxial apparatus. Setup or sensor
Range
Refrigeration circulator for ambient environment (°C) Refrigeration circulators for top and bottom (°C) Radial strain measurement device (mm) Axial loading equipment containing servo-motors, ball screws, etc. (mm) Radial loading equipment containing servo-motor, ball screw, etc. (mm) Load cell (kN) Pressure sensor for radial pressure (MPa) Pressure sensor for pore water pressure (MPa) Temperature sensors (°C)
−40–90 −30–90 0–15 0–80 0–250 0–100 0–30 0–1 −50–260
Every target temperature is associated to a corresponding actual cooling bath temperature determined on the basis of experience at a room temperature of 22 °C. Prior to loading, the target temperature is applied for 4 h to stabilize the temperature of the soil sample. Three thermal sensors (a kind of special thermistor, which is developed by the State Key Laboratory of Frozen Soil Engineering for frozen soil tests) are mounted respectively on the top cap, bottom plate and at the middle point of the sample height. They monitor the temperature at corresponding positions and send measurements to the temperature controllers. Each temperature controller has a single loop and manufactured by Xuezhongtan Ltd. in China. The controllers can automatically control the magnetic valves and adjusts the flow of cooling liquid so as to control the temperature at individual position. In addition, the large volume of aircraft hydraulic oil in the pressure cell also has a buffering effect on temperature fluctuations. As a result, the temperature fluctuation in pressure cell will be less than in refrigeration circulators without load. The working principle of temperature control is shown in Fig. 2(d). Fig. 3 shows the temperature at the top, bottom and side of the soil sample prior to and during radial loading at two different speeds. It is seen that temperatures at the three above-mentioned surfaces fluctuate within ± 0.02 °C prior to loading, within ±0.05 °C during relatively slow loading (0.1 MPa/s) and within ± 0.1 °C during relatively fast loading (0.6 MPa/s). The higher temperature fluctuation during loading is caused by the oil compression. This fluctuation can be reduced by adjusting the opening frequency of the magnetic
Accuracy
Fluctuation ±0.05 ±0.05
0.001 0.001 0.001 0.05 0.05 0.05 0.03
valve and buffering of large volume of cell fluid. In addition the rubber membrane enclosing the soil sample acts as thermal insulation when fast loading is applied, so that the actual temperature fluctuation of soil sample is likely to be less than the measured. 2.3. K0 coefficient The strain in the middle section of the soil sample is measured using a radial strain measurement device (a kind of electrical resistance displacement transducer and manufactured by Chaoyang Instrumentation Ltd. in Changchun City, China) contacting the soil sample at four points (small nuts), each separated by 90°, as shown in Fig. 4. The device has four steel levers transferring the deformation at the four points to strain transducers. The final strain is determined as the average of individual deformation at the four points. With this device, the radial deformation will fluctuate within ±10 μm, corresponding to a radial strain of less than 3.2 × 10 −4. 2.4. Volumetric strain Volume change of a soil sample is an important parameter for analyzing compressibility, shear dilation (contraction), etc. For frozen soils, it can be calculated as follow: ΔV ¼ −V1 −V2 þV3 þV4
Fig. 2. Working principle in (a) axial and radial stress (rate) control, (b) axial strain (rate) control, (c) radial strain (rate) control and (d) temperature control.
ð1Þ
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Fig. 3. Measured temperatures of the top, side and bottom of the soil sample (a) no loading and (b) during radial loading with the speed of 0.1 MPa/s and (c) 0.6 MPa/s.
where ΔV is the volume change of the soil sample (positive means dilation); V1 is the change in volume due to the axial loading piston entering the pressure cell, V2 is the change in volume due to radial
loading piston entering the cylinder; V3 is the change in volume due to hydraulic oil leakage; and V4 is the change in volume due to base flexure to the applied axial load (Gregory et al., 2003). In the apparatus described, A1 and A2 are the cross-section areas of the axial and radial loading pistons, and L1 and L2 are the displacements of the pistons (positive for the loading direction). In Eq. 1, V1 and V2 can be calculated based on the testing records about the movement of loading pistons, while the sum of V3 and V4 is difficult to distinguish. However, they can be obtained together from a calibration test, i.e., if the cell is only filled with oil without a soil sample inside, the volume change caused by pistons is equal to the sum of V3 and V4 under certain conditions such as temperature, cell pressure and axial loads. In the calibration test, Eq. 1 can be expressed as 0 ¼ −V1 −V2 þV3 þV4 :
ð2Þ
The sum of V3 and V4 is A L V3 þV4 ¼ V1 þ V2 ¼ A1 L1 þ A2 L2 ¼ A1 L1 1 þ 2 2 : A1 L1
ð3Þ
According to Fig. 5, the displacements of both pistons are changed linearly with time under different conditions of cell pressure of 1, 5 and 10 MPa, and the axial loading piston moves at a rate of − 1, 1, and 3 mm/min. Obviously, the ratio (K) of the speeds of the axial (U1) to radial (U2) loading pistons is equal to LL12 , which is constant under certain testing conditions (in the cases presented in Fig. 5, K = − 0.59, − 0.62 and − 0.60). From which, Eq. 3 can be further expressed as A V3 þV4 ¼ A1 L1 1 þ 2 : A1 K
ð4Þ
Substituting Eq. 4 into Eq. 1, the volume change of a soil sample can be finally calibrated as 1 ΔV ¼ A2 L1 −L2 : K
Fig. 4. Radial strain measurement device.
ð5Þ
where, K is the correction coefficient obtained from the calibrating test. Before a real test, it must be determined with the same testing conditions.
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Fig. 5. Displacement of the radial loading piston relative to that of the axial loading piston under three radial pressures: (a) U1 = −1 mm/min, P = 1 MPa; (b) U1 = 1 mm/min, P = 5 MPa;and (c) U1 = 3 mm/min, P = 10 MPa.
3. Some test results using the apparatus To verify the performances of the apparatus, a series of case test programs were carried out. Two kinds of soils were taken as study objects: standard sand and silty clay obtained from Qinghai–Tibet Plateau. All the remolded and saturated soil samples were prepared in the laboratory with the diameter and height of 61.8 mm and 125 mm. For the silty clay, liquid and plastic limits of silty clay are respectively 25.3% and 12.9%, and the grain size distribution curve is presented in Fig. 6.
1–2 mm. Three different temperatures were controlled: − 2, − 5 and − 10 °C. The radial pressure was automatically kept constant at 0.5 MPa and then an axial loading rate of 1.25 mm/min was applied. Fig. 7 shows the stress–strain and volumetric strain of the standard soil under the different temperatures. The volumetric strain is calculated according to formula (1). It can be seen that the failure strength increased with the decreasing of temperature, and the volume
3.1. Conventional triaxial test In this test, the standard sand with a dry density of 1.86 g/cm 3 was used. The fine content is 1% for particle diameter b0.076 mm, 12% for 0.076–0.15 mm, 20% for 0.15–0.5 mm, 34% for 0.5–1 mm and 33% for
Fig. 6. The grain size distribution curve of silty clay in tests.
Fig. 7. Stress–strain (a) and volumetric strain (b) of the standard sand under different temperatures.
X. Yao et al. / Cold Regions Science and Technology 92 (2013) 48–54
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Fig. 10. Changes in axial and radial pressures over time.
3.3. Triaxial creep experiments
Fig. 8. Changes in the radial deformation with the increasing of axial pressure under K0 control.
initially decreased, but significantly increased under all three temperatures. The shear contraction in the early stages may be due to pressure melting of the ice, crushing of the sand, and compaction of the sample while the shear dilation in the later stage possibly results from sand slipping and structural changes.
In this experiment, the silty clay of Qinghai–Tibet Plateau with a dry density of 1.7 g/cm3 was taken as the object. Five temperatures were used, i.e., −2, −1.5, −1.0, −0.5 and −0.2 °C. The radial and axial pressures were maintained constant at 0.2 MPa and 0.3 MPa for about 2 months. When the radial deformation remained constant, the temperatures were changed gradually from −2 to −0.2 °C. Changes in radial and axial pressures with time are shown in Fig. 10. Changes in radial strain and measured temperatures (ambient environment) with time are shown in Fig. 11. It can be seen that the axial and radial pressures and the temperature can be kept constant for a long period of time. The rather large fluctuations in radial and axial pressures are due to the temperature adjustment. The modulus of compressibility decreases significantly with the increase in temperature.
3.2. K0 experiments A series of experiments on K0 measurement have been carried out using the radial strain sensor (Fig. 4). To investigate the effect of the temperature on K0, five temperatures were used, i.e., − 0.2, − 0.5, − 1.0, − 2.0, and − 5.0 °C. The axial pressure is applied at the rate of 0.05 MPa/s. Fig. 8 shows the changes in the radial deformation with the increasing of axial pressure under K0 control. It can be seen that the radial deformation is negligible, with the fluctuation of less than ± 10 μm. Changes in K0 with the axial pressure under different temperatures for the silty clay on Qinghai–Tibet Plateau were obtained, as shown in Fig. 9. From this, it is seen that for the silty clay, K0 of frozen soil increases with increase in the temperature. During the tests it increased rapidly followed by a slower increase rate and then finally remains constant with increasing pressure.
Fig. 9. Changes in K0 with the increasing of axial pressure under different temperatures.
3.4. Stress relaxation tests In this experiment, the silty clay was taken as the object. The temperature was maintained at − 1 °C and the radial pressure was maintained at 1 MPa. Six initial strains of 3%, 4%, 6%, 8%, 10% and 12% were achieved with the axial loading piston moving at a rate of 1.25 mm/min. Fig. 12 shows the dissipation of the axial stress under the different initial axial strains (for the details, the readers are referred to Wang et al. (2011)). Two relaxation stages are observed:
Fig. 11. Changes in axial strain under different temperatures.
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Acknowledgment This work was supported in part by the National Natural Science Foundation of China (No. 41201064 and No. 41172253) and the Project for Excellent State Key Laboratory of Natural Science Foundation of China (No. 41023003). References
Fig. 12. Dissipation of the axial stress under different initial axial strains (Wang et al., 2011).
intensive and slow relaxation, the first one was completed within around 2 h. 4. Summary We have developed a versatile triaxial apparatus with two major parts: loading system and temperature controlling system. The features of the apparatus have been displayed: (1) It combines the advantages of air- and water-cooling methods, using a high-power air-condition to control the indoor temperature and three refrigeration circulators to freeze the top, side and bottom of the soil sample, which enables a temperature fluctuation within ±0.02 °C prior to loading and within ± 0.1 °C during loading; (2) it is equipped with a radial strain measurement device for the K0 experiment, by which the radial pressure can automatically change to maintain the radial deformation within ±10 μm during axial loading; and (3) it can precisely calculate the volumetric strain via the displacement of the axial and radial loading pistons and being capable of stress (rate) and strain (rate) controlled loading. To verify performances of the apparatus, a series of case testing programs were performed. These experiments proved a high temperature control precision, powerful functions and excellent stability profile. The setup of this versatile apparatus can provide some critical indexes needed by engineering design in cold regions and precise mechanical behavior for theoretical study of frozen soil.
Arenson, L.U., Johansen, M.M., Springman, S.M., 2004. Effects of volumetric ice content and strain rate on shear strength under triaxial conditions for frozen soil samples. Permafrost and Periglacial Processes 15 (3), 261–271. Bourbonnais, J., Ladanyi, B., 1985. The mechanical behavior of frozen sand down to cryogenic temperatures. Proceedings of the 4th International Symposium on Ground Freezing, Sapporo, Japan. Gregory, D.R., Germaine, J.T., Ladd, C.C., 2003. Triaxial testing of frozen sand: equipment and example results. Journal of Cold Regions Engineering 17 (3), 90–118. Hazirbaba, K., Zhang, Y., Hulsey, J.L., 2011. Evaluation of temperature and freeze–thaw effects on excess pore pressure generation of fine-grained soils. Soil Dynamics and Earthquake Engineering 31 (3), 372–384. Ma, W., Qi, J.L., Wu, Q.B., 2008. Analysis of the deformation of embankments on the Qinghai–Tibet Railway. Journal of Geotechnical and Geoenvironmental Engineering 134 (11), 1645–1654. Niu, F.J., Cheng, G.D., Lai, Y.M., Jin, D.W., 2004. Instability study on thaw slumping in permafrost regions of Qinghai–Tibet Plateau. Chinese Journal of Geotechnical engineering 26 (3), 402–406 (In Chinese). Niu, F.J., Cheng, G.D., Ni, W.K., Jin, D.E., 2006. Engineering-related slope failure in Permafrost regions of the Qinghai–Tibet Plateau. Cold Regions Science and Technology 42 (3), 215–225. Oberman, N.G., Mazhitova, G.G., 2001. Permafrost dynamics in the northeast of European Russia at the end of the 20th century. Norwengian Journal of Geology 55, 241–244. Osterkamp, T.E., 2005. The recent warming of permafrost in Alaska. (3)-(4)Global and Planetary Change 49, 187–202. Qi, J.L., Sheng, Y., Zhang, J.M., Wen, Z., 2007. Settlement of embankments in permafrost regions in the Qinghai–Tibet Plateau. Norwegian Journal of Geography 61 (2), 49–55. Smith, S.L., Burgess, M.M., Riseborough, D., Mark, N.F., 2005. Recent trends from Canadian permafrost thermal monitoring network sites. Permafrost and Periglacial Processes 16 (1), 19–30. Wang, B.L., French, H.M., 1995. In situ creep of frozen soil, Tibet Plateau, China. Canadian Geotechnical Journal 32 (3), 545–552. Wang, S.L., Qi, J.L., Yao, X.L., 2011. Stress relaxation characteristics of warm frozen clay under triaxial conditions. Cold Regions Science and Technology 69 (1), 112–117. Wu, Z.W., Ma, W., 1994. Strength and Creep of Frozen Soil. Lanzhou University Press, Lanzhou, China (In Chinese). Wu, Q.B., Zhang, T.J., 2008. Recent permafrost warming on the Qinghai-Tibetan Plateau. Journal of Geophysical Research 113 (D13108). http://dx.doi.org/10.1029/ 2007JD009539. Zheng, B., Zhang, J.M., Qin, Y.H., 2010. Investigation for the deformation of embankment underlain by warm and ice-rich permafrost. Cold Regions Science and Technology 60 (2), 161–168. Zhu, Y.L., Carbee, D.L., 1984. Uniaxial compressive strength of frozen silt under constant deformation rates. Cold Regions Science and Technology 9 (1), 3–15.
Contents lists available at SciVerse ScienceDirect
Cold Regions Science and Technology journal homepage: www.elsevier.com/locate/coldregions
A versatile triaxial apparatus for frozen soils Xiaoliang Yao, Jilin Qi ⁎, Fan Yu, Ling Ma State Key Laboratory of Frozen Soil Engineering, Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, Lanzhou 730000, China
a r t i c l e
i n f o
Article history: Received 23 November 2012 Accepted 30 April 2013 Keywords: Triaxial apparatus Frozen soil Temperature control Radial strain Volumetric change
a b s t r a c t Settlement and damage to infrastructures in permafrost regions depend in part on the mechanical properties of permafrost layers. In order to get a better understanding of the mechanical behavior of frozen soils, a triaxial apparatus was developed with three new features in addition to the traditional functions. The first is the accurate temperature control, which allows temperature to fluctuate within ± 0.1 °C during the loading period, and ± 0.02 °C before loading, so as to get a better understanding of the mechanical properties of frozen soils under temperatures close to thawing point. The second feature is used to measure K0 of frozen soils. A highly-sensitive radial strain measurement device was designed and the K0 state can be accurately maintained by automatically adjusting the radial pressure when radial deformation changes more than ± 10 μm. The third is the precise measurement of the volumetric strain through the displacement of axial and radial loading pistons. The capabilities of the triaxial apparatus are shown using a series of test results. It is considered to be a promising tool to investigate the mechanical properties of frozen soils. © 2013 Elsevier B.V. All rights reserved.
1. Introduction With increasing construction of infrastructures in permafrost regions, the mechanical properties of frozen soil and their dependence on ambient temperature are becoming more important. Many studies have shown that with global warming significant increases in the temperature of permafrost have occurred (Oberman and Mazhitova, 2001; Osterkamp, 2005; Smith et al., 2005; Wu and Zhang, 2008). This inevitably influences the mechanical properties of frozen soil as temperature is one of the main factors determining the mechanical properties of frozen soils (Bourbonnais and Ladanyi, 1985; Wu and Ma, 1994; Zhu and Carbee, 1984). Even small change in temperature will probably lead to serious consequences for engineering constructions, such as creep of high-temperature (MAGT ≥ − 1.5 °C) frozen layers (Ma et al., 2008; Qi et al., 2007; Zheng et al., 2010) and instability of slope in permafrost regions (Niu et al., 2004; Niu et al., 2006; Wang and French, 1995). To investigate the influence of temperature on mechanical behavior of frozen soils, triaxial apparatus is essential because of its simple stress state and clear boundary conditions. Temperature control is the first task for testing on frozen soils. There have been two main cooling methods frequently used for temperature control of triaxial apparatus. The first uses a refrigerating unit to cool the room and as a result the triaxial apparatus in the room, known as the “air-cooling method”. This method simplifies the construction of the triaxial apparatus, and avoids the influence of daily temperature fluctuations, but is associated with poor cooling efficiency and precision
⁎ Corresponding author. Tel./fax: +86 931 4967261. E-mail address: [email protected] (J. Qi). 0165-232X/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.coldregions.2013.04.001
due to the large cooling volume (the whole room) and instable air stream. In addition, with radial pressure loading/unloading, the piston does positive/negative work on the hydraulic oil, resulting in changes in the oil temperature. This cooling method cannot respond rapidly to such changes. As a result, the sample temperature will show an obvious fluctuation. Some improvements were then made on this method. For instance, a triaxial apparatus was designed with a large volume of cell fluid, which acts as a “buffer” to reduce the temperature fluctuations (Arenson et al., 2004). The temperature control precision, in the environmental chamber (the triaxial apparatus in the chamber), was increased using a small electronic fan and a heating bulb, and the temperature was controlled more uniform with an air pump to circulate the hydraulic oil in the pressure cell (Gregory et al., 2003). Nevertheless, the “air-cooling method” is still poor in the cooling efficiency and the temperature fluctuation more than ±0.1 °C. The second method uses an anti-freeze liquid, the so-called “liquid-cooling method”, where the triaxial apparatus is refrigerated by the cooled liquid circulating in the device. However, the precision of this method is influenced considerably by daily temperature fluctuations and heat emission in long-term tests. This kind of device has a higher temperature control precision than the first method. For instance, Hazirbaba et al. (2011) used two cooling baths, one for the temperature at the top and bottom plates and another for the ambient temperature of soil sample. However, the use of a single cooling device for both the top and bottom temperature may induce non-uniform temperatures throughout the soil sample caused by temperature difference between the outlet and inlet of the cooled liquid. From the above, it can be seen that the two cooling methods have their advantages and disadvantages. As far as the mechanical properties of frozen soil are concerned, two indexes still remain difficult to measure. One is the coefficient
X. Yao et al. / Cold Regions Science and Technology 92 (2013) 48–54
of lateral earth pressure (K0) at rest of frozen soils, which is a very important parameter for designing and analyzing geotechnical engineering such as tunnel, mineshafts, and retaining walls. For unfrozen soils, there are mainly three methods used: the oedometer, plane strain or triaxial test, respectively. Among these methods the triaxial apparatus might be more conventionally available. However, frozen soils are much stiffer, and less deformation occurs than in unfrozen soils under the same stress, requiring higher radial pressures to reach the zero lateral strain once a small lateral deformation occurs. Therefore, in order to precisely measure K0, the controller and loading system for frozen soil should be more sensitive. In triaxial tests on frozen soil, the measurement of K0 remains difficult and is rarely investigated. The second problem is the measurement of volumetric changes of frozen soil samples. Devices from conventional triaxial apparatus may be applied for frozen samples. However, due to the more complicated structure needed for such devices for use with frozen soils, there are some drawbacks to measure volumetric change precisely, e.g. the leakage of fluid out of pressure cell, base flexure of the cell due to the applied axial load (Gregory et al., 2003), and the relative low resolution of the measurement (Arenson et al., 2004). The above mentioned require precise temperature control, multi-functions, especially in K0-state control, as well as the precise measurement of volumetric change for triaxial tests on frozen soil. Here, a versatile triaxial apparatus is presented in which both airand liquid-cooling methods are combined to increase the precision of temperature control. A very precise radial strain measurement device is used to measure K0. The volumetric change can be precisely measured and is capable of strain (rate) and stress (rate) controlled loading, with excellent long-term stability. A series of test programs were carried out to show performance of the device.
2. Apparatus description Fig. 1 shows a schematic of the triaxial apparatus that was designed and completed in 2010. It consists of two major systems: loading system (stress (rate) and strain (rate) control) and temperature controlling system. Details of all the setups and sensors used in the triaxial apparatus are shown in Table 1.
49
2.1. Loading system In the system, a steel airtight pressure cell is designed to withstand a confining pressure of about 30 MPa. Aircraft hydraulic oil in the cell is used to reduce viscosity at low temperatures. Another advantage of the oil is that it can avoid corroding the rubber membrane used to seal the spacemen during testing. It also offers the benefit of being nonconductive, which is essential when locating electronic devices such as the temperature sensors and radial strain measurement device within the pressure cell. Radial pressure is applied to the specimen (D = 6.18 cm × H = 12.5 cm) through a piston pressing the hydraulic oil into the cylinder. The sample is axially loaded through a hardened steel piston, with a maximum pressure of 100 kN. The piston enters the top of the pressure cell through two O-ring seals. Two O-rings seal the joint between the bottom plate and the pressure cell. The displacement of both the axial and radial loading pistons is recorded by the revolution of servo-motors in terms of angle, which is transformed into distance by an EDC (External digital controller). A load cell is used to monitor the axial pressure, while two pressure sensors to monitor the radial and pore water (for unfrozen soil) pressure. Automated control is carried out by the EDCs (which is manufactured by DOLI Elektronik GmbH in Germany with four control loops and can control the stress and strain on axial and radial directions separately) for data acquisition and closed loop control of testing instruments. A computer with specially developed software allows for simultaneous control of stress (rate) and strain (rate) in both axial and radial directions. The working principles are shown in Fig. 2(a, b, and c). With this system, it is possible to perform conventional triaxial tests, stress path tests, K0 consolidation, etc. 2.2. Temperature controlling system To prevent the influence of laboratory temperature fluctuations on the temperature control precision, a high-power air-conditioner is used to maintain the laboratory temperature at around 22 °C, which is also comfortable for laboratory technicians to work in. Three refrigeration circulators are used to control the temperature at the top, bottom and side of the soil sample. Taking into account the cooling loss due to the heat effect of room temperature and pipe lines, the temperature of cooling bath is set lower than the target temperature.
Fig. 1. Schematic of the triaxial apparatus.
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Table 1 The setups and sensors used in the triaxial apparatus. Setup or sensor
Range
Refrigeration circulator for ambient environment (°C) Refrigeration circulators for top and bottom (°C) Radial strain measurement device (mm) Axial loading equipment containing servo-motors, ball screws, etc. (mm) Radial loading equipment containing servo-motor, ball screw, etc. (mm) Load cell (kN) Pressure sensor for radial pressure (MPa) Pressure sensor for pore water pressure (MPa) Temperature sensors (°C)
−40–90 −30–90 0–15 0–80 0–250 0–100 0–30 0–1 −50–260
Every target temperature is associated to a corresponding actual cooling bath temperature determined on the basis of experience at a room temperature of 22 °C. Prior to loading, the target temperature is applied for 4 h to stabilize the temperature of the soil sample. Three thermal sensors (a kind of special thermistor, which is developed by the State Key Laboratory of Frozen Soil Engineering for frozen soil tests) are mounted respectively on the top cap, bottom plate and at the middle point of the sample height. They monitor the temperature at corresponding positions and send measurements to the temperature controllers. Each temperature controller has a single loop and manufactured by Xuezhongtan Ltd. in China. The controllers can automatically control the magnetic valves and adjusts the flow of cooling liquid so as to control the temperature at individual position. In addition, the large volume of aircraft hydraulic oil in the pressure cell also has a buffering effect on temperature fluctuations. As a result, the temperature fluctuation in pressure cell will be less than in refrigeration circulators without load. The working principle of temperature control is shown in Fig. 2(d). Fig. 3 shows the temperature at the top, bottom and side of the soil sample prior to and during radial loading at two different speeds. It is seen that temperatures at the three above-mentioned surfaces fluctuate within ± 0.02 °C prior to loading, within ±0.05 °C during relatively slow loading (0.1 MPa/s) and within ± 0.1 °C during relatively fast loading (0.6 MPa/s). The higher temperature fluctuation during loading is caused by the oil compression. This fluctuation can be reduced by adjusting the opening frequency of the magnetic
Accuracy
Fluctuation ±0.05 ±0.05
0.001 0.001 0.001 0.05 0.05 0.05 0.03
valve and buffering of large volume of cell fluid. In addition the rubber membrane enclosing the soil sample acts as thermal insulation when fast loading is applied, so that the actual temperature fluctuation of soil sample is likely to be less than the measured. 2.3. K0 coefficient The strain in the middle section of the soil sample is measured using a radial strain measurement device (a kind of electrical resistance displacement transducer and manufactured by Chaoyang Instrumentation Ltd. in Changchun City, China) contacting the soil sample at four points (small nuts), each separated by 90°, as shown in Fig. 4. The device has four steel levers transferring the deformation at the four points to strain transducers. The final strain is determined as the average of individual deformation at the four points. With this device, the radial deformation will fluctuate within ±10 μm, corresponding to a radial strain of less than 3.2 × 10 −4. 2.4. Volumetric strain Volume change of a soil sample is an important parameter for analyzing compressibility, shear dilation (contraction), etc. For frozen soils, it can be calculated as follow: ΔV ¼ −V1 −V2 þV3 þV4
Fig. 2. Working principle in (a) axial and radial stress (rate) control, (b) axial strain (rate) control, (c) radial strain (rate) control and (d) temperature control.
ð1Þ
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Fig. 3. Measured temperatures of the top, side and bottom of the soil sample (a) no loading and (b) during radial loading with the speed of 0.1 MPa/s and (c) 0.6 MPa/s.
where ΔV is the volume change of the soil sample (positive means dilation); V1 is the change in volume due to the axial loading piston entering the pressure cell, V2 is the change in volume due to radial
loading piston entering the cylinder; V3 is the change in volume due to hydraulic oil leakage; and V4 is the change in volume due to base flexure to the applied axial load (Gregory et al., 2003). In the apparatus described, A1 and A2 are the cross-section areas of the axial and radial loading pistons, and L1 and L2 are the displacements of the pistons (positive for the loading direction). In Eq. 1, V1 and V2 can be calculated based on the testing records about the movement of loading pistons, while the sum of V3 and V4 is difficult to distinguish. However, they can be obtained together from a calibration test, i.e., if the cell is only filled with oil without a soil sample inside, the volume change caused by pistons is equal to the sum of V3 and V4 under certain conditions such as temperature, cell pressure and axial loads. In the calibration test, Eq. 1 can be expressed as 0 ¼ −V1 −V2 þV3 þV4 :
ð2Þ
The sum of V3 and V4 is A L V3 þV4 ¼ V1 þ V2 ¼ A1 L1 þ A2 L2 ¼ A1 L1 1 þ 2 2 : A1 L1
ð3Þ
According to Fig. 5, the displacements of both pistons are changed linearly with time under different conditions of cell pressure of 1, 5 and 10 MPa, and the axial loading piston moves at a rate of − 1, 1, and 3 mm/min. Obviously, the ratio (K) of the speeds of the axial (U1) to radial (U2) loading pistons is equal to LL12 , which is constant under certain testing conditions (in the cases presented in Fig. 5, K = − 0.59, − 0.62 and − 0.60). From which, Eq. 3 can be further expressed as A V3 þV4 ¼ A1 L1 1 þ 2 : A1 K
ð4Þ
Substituting Eq. 4 into Eq. 1, the volume change of a soil sample can be finally calibrated as 1 ΔV ¼ A2 L1 −L2 : K
Fig. 4. Radial strain measurement device.
ð5Þ
where, K is the correction coefficient obtained from the calibrating test. Before a real test, it must be determined with the same testing conditions.
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Fig. 5. Displacement of the radial loading piston relative to that of the axial loading piston under three radial pressures: (a) U1 = −1 mm/min, P = 1 MPa; (b) U1 = 1 mm/min, P = 5 MPa;and (c) U1 = 3 mm/min, P = 10 MPa.
3. Some test results using the apparatus To verify the performances of the apparatus, a series of case test programs were carried out. Two kinds of soils were taken as study objects: standard sand and silty clay obtained from Qinghai–Tibet Plateau. All the remolded and saturated soil samples were prepared in the laboratory with the diameter and height of 61.8 mm and 125 mm. For the silty clay, liquid and plastic limits of silty clay are respectively 25.3% and 12.9%, and the grain size distribution curve is presented in Fig. 6.
1–2 mm. Three different temperatures were controlled: − 2, − 5 and − 10 °C. The radial pressure was automatically kept constant at 0.5 MPa and then an axial loading rate of 1.25 mm/min was applied. Fig. 7 shows the stress–strain and volumetric strain of the standard soil under the different temperatures. The volumetric strain is calculated according to formula (1). It can be seen that the failure strength increased with the decreasing of temperature, and the volume
3.1. Conventional triaxial test In this test, the standard sand with a dry density of 1.86 g/cm 3 was used. The fine content is 1% for particle diameter b0.076 mm, 12% for 0.076–0.15 mm, 20% for 0.15–0.5 mm, 34% for 0.5–1 mm and 33% for
Fig. 6. The grain size distribution curve of silty clay in tests.
Fig. 7. Stress–strain (a) and volumetric strain (b) of the standard sand under different temperatures.
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Fig. 10. Changes in axial and radial pressures over time.
3.3. Triaxial creep experiments
Fig. 8. Changes in the radial deformation with the increasing of axial pressure under K0 control.
initially decreased, but significantly increased under all three temperatures. The shear contraction in the early stages may be due to pressure melting of the ice, crushing of the sand, and compaction of the sample while the shear dilation in the later stage possibly results from sand slipping and structural changes.
In this experiment, the silty clay of Qinghai–Tibet Plateau with a dry density of 1.7 g/cm3 was taken as the object. Five temperatures were used, i.e., −2, −1.5, −1.0, −0.5 and −0.2 °C. The radial and axial pressures were maintained constant at 0.2 MPa and 0.3 MPa for about 2 months. When the radial deformation remained constant, the temperatures were changed gradually from −2 to −0.2 °C. Changes in radial and axial pressures with time are shown in Fig. 10. Changes in radial strain and measured temperatures (ambient environment) with time are shown in Fig. 11. It can be seen that the axial and radial pressures and the temperature can be kept constant for a long period of time. The rather large fluctuations in radial and axial pressures are due to the temperature adjustment. The modulus of compressibility decreases significantly with the increase in temperature.
3.2. K0 experiments A series of experiments on K0 measurement have been carried out using the radial strain sensor (Fig. 4). To investigate the effect of the temperature on K0, five temperatures were used, i.e., − 0.2, − 0.5, − 1.0, − 2.0, and − 5.0 °C. The axial pressure is applied at the rate of 0.05 MPa/s. Fig. 8 shows the changes in the radial deformation with the increasing of axial pressure under K0 control. It can be seen that the radial deformation is negligible, with the fluctuation of less than ± 10 μm. Changes in K0 with the axial pressure under different temperatures for the silty clay on Qinghai–Tibet Plateau were obtained, as shown in Fig. 9. From this, it is seen that for the silty clay, K0 of frozen soil increases with increase in the temperature. During the tests it increased rapidly followed by a slower increase rate and then finally remains constant with increasing pressure.
Fig. 9. Changes in K0 with the increasing of axial pressure under different temperatures.
3.4. Stress relaxation tests In this experiment, the silty clay was taken as the object. The temperature was maintained at − 1 °C and the radial pressure was maintained at 1 MPa. Six initial strains of 3%, 4%, 6%, 8%, 10% and 12% were achieved with the axial loading piston moving at a rate of 1.25 mm/min. Fig. 12 shows the dissipation of the axial stress under the different initial axial strains (for the details, the readers are referred to Wang et al. (2011)). Two relaxation stages are observed:
Fig. 11. Changes in axial strain under different temperatures.
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Acknowledgment This work was supported in part by the National Natural Science Foundation of China (No. 41201064 and No. 41172253) and the Project for Excellent State Key Laboratory of Natural Science Foundation of China (No. 41023003). References
Fig. 12. Dissipation of the axial stress under different initial axial strains (Wang et al., 2011).
intensive and slow relaxation, the first one was completed within around 2 h. 4. Summary We have developed a versatile triaxial apparatus with two major parts: loading system and temperature controlling system. The features of the apparatus have been displayed: (1) It combines the advantages of air- and water-cooling methods, using a high-power air-condition to control the indoor temperature and three refrigeration circulators to freeze the top, side and bottom of the soil sample, which enables a temperature fluctuation within ±0.02 °C prior to loading and within ± 0.1 °C during loading; (2) it is equipped with a radial strain measurement device for the K0 experiment, by which the radial pressure can automatically change to maintain the radial deformation within ±10 μm during axial loading; and (3) it can precisely calculate the volumetric strain via the displacement of the axial and radial loading pistons and being capable of stress (rate) and strain (rate) controlled loading. To verify performances of the apparatus, a series of case testing programs were performed. These experiments proved a high temperature control precision, powerful functions and excellent stability profile. The setup of this versatile apparatus can provide some critical indexes needed by engineering design in cold regions and precise mechanical behavior for theoretical study of frozen soil.
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