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A spherical template indenter for a frozen soil long-term shear strength test
Cold Regions Science and Technology 131 (2016) 10–15
Contents lists available at ScienceDirect
Cold Regions Science and Technology journal homepage: www.elsevier.com/locate/coldregions
A spherical template indenter for a frozen soil long-term shear strength test Ze Zhang a,⁎, Hong Zhou a,b,c, Wenjie Feng a, Zhongqiong Zhang a, Donghui Xiao a a b c
State Key Laboratory of Frozen Soil Engineering, Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Science, Lanzhou 730000, China Key Laboratory of Mechanics on Disaster and Environment in Western China of Ministry of Education, Lanzhou University, Lanzhou, Gansu 730000, China College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou, Gansu 73000, China
a r t i c l e
i n f o
Article history: Received 14 April 2014 Received in revised form 21 July 2016 Accepted 30 July 2016 Available online 2 August 2016 Keywords: Spherical template indenter Frozen soil Mechanical property Long-term strength
a b s t r a c t Certain mechanical apparatus have long been considered indispensible to practical engineering design. In particular, the spherical template indenter (STI) has been widely used for permafrost soil testing in the former USSR and Russia. Over the last 60 years, experimental engineering theories and methods have been greatly improved. But the STI has gone largely unchanged, the long-term strength and total deformation modulus analyzed by the impression of STI on soil, simple as it is to use, and effective as it is at quickly measuring the properties and forecasting the long-term strength of frozen soil. This paper makes a brief introduction to the STI apparatus. The capabilities of the STI are shown through a series of test results. It is evaluated under the pretext of being a promising tool for the investigation of frozen soil strength property. Three different methods were used to yield results predicting the long-term strength of frozen loess. © 2016 Elsevier B.V. All rights reserved.
1. Introduction As more infrastructures continue to be constructed in permafrost regions, it's of great importance that builders understand the mechanical properties and long-term shear strength of frozen soil. To determine the capacity of a frozen soil structure, one must first determine the soil's long-term shear strength. Many researchers have conducted tests on the shear strength properties of frozen soil using wedge shear equipment, a direct shear device, or a triaxial apparatus (Zhu, 1988). There are limitations when using the direct shear test to measure the mechanical properties of frozen soil. For instance, the high strength of the frozen soil makes it difficult to shear. In addition, it's cost prohibitive to control the temperatures of testing sites in the field. Because of these difficulties, a triaxial apparatus is often used to study mechanical property of frozen soil. However, because this device requires a long testing period, and can be expensive to use, it has not been widely adopted in the practical applications (Zhang et al., 2012). Many researchers have undertaken studies on long-term shear strength by using the triaxial creep test (Zhu et al.,1998; Chen, 1995; Ma et al., 1994, 1997; Mi et al., 1993; Qu et al., 2011; Sheng et al., 1996; Wang et al., 1996; Wu et al., 1997; Yang, 1996; Zhang et al., 1995; Arenson and Springman, 2005; Zhang and Fu, 2011; Yin et al., 2013). These studies are primarily concerned with the changing law of deformation with regard to time, and the myriad factors that influence creep indexes (Lai et al., 2013). The triaxial creep test of frozen soil's ⁎ Corresponding author. E-mail address: [email protected] (Z. Zhang).
http://dx.doi.org/10.1016/j.coldregions.2016.07.011 0165-232X/© 2016 Elsevier B.V. All rights reserved.
long-term and shear strength requires a lengthy process to maintain the uniformity of the samples. Due to the large errors inherent to the sample preparation, the experimental results are often incomparable. In an effort to find a solution to these testing issues, this paper introduces the spherical template indenter (STI) — an instrument that can be used to quickly test and predict frozen soil's long-term strength. In 1947, Tsytovich was the first to use the instrument to study cohesive force of different soils, such as silt, coarse soils, loess, frozen and other kinds of soils (Tsytovich, 1947). In 1952, Dinnik (1952) adopted the impression of a sphere in a visco-elastic half-space as a basis question in this study, and Chertolyas (1977) used STI to determine compression modulus in thawed clayey soils, then Roman (1987) validated the possibility of determining deformation characteristics for permafrost from data on the impression of STI. In Russia, this method has long been used in the study of frozen soil mechanics long-term shear strength. In the fields of science and construction engineering it has also been highly regarded, and even written into Russia's standard testing procedures for frozen soil testing. Others have confirmed the notion that this apparatus is well-suited for testing frozen soil (Chamberlain et al., 1972; Ma, 1983; Ourvy, 1985; Zhu, 1988; Zhang et al., 2012). Due to the need of economical constructions, engineering construction in frozen soil regions rises in China, which mainly includes the Qinghai–Tibet Highway, the Xining–Yushu Highway, the Qinghai–Tibet Railway, the Qinghai–Tibet power transmission lines, the Golmud–Lhasa Oil pipe, China–Russia Oil pipe and the West Route of South-to-North Water Diversion (Lai et al., 2013). The STI apparatus has seen increased use in applied research. In fact, a series of test programs were carried out to demonstrate the effectiveness of this device.
Z. Zhang et al. / Cold Regions Science and Technology 131 (2016) 10–15
2. Apparatus description and theoretical basis As shown in Fig. 1, the device has three primary parts: the pressure system, support member, and displacement meter. The pressure system is used for loading the samples and includes spherical indenter (4), samples with fresh-keeping film (5), screw cap (6) and horizontal scaffold (7). The support member binds the instrument together and includes bearing plate (3), weight (8) and guide bar (10). The displacement meter (1, 2) measures the depth pressed into a sample by the spherical indenter (4). The experimental principle of the STI is similar to the Brinnel hardness meter (Tsytovich, 2010). This principle, first proposed by Ishlinskiy, was based on the plasticity theory of ideal viscosity and non-strengthening body (Ishlinskiy, 1945). Tsytovich and Vyalov used the apparatus to determine soil mechanics, and established a theory on frozen soil strength, experimentation, calculation and prediction methods. More recently, Roman expanded upon the application of the apparatus, building a method for calculating the modulus and improving the process for predicting long-term strength. The shear strength of frozen soil is influenced by the soil skeleton, mineral composition, and structure, as well as the permafrost temperature (θ), water content (W), and the time of loading (t). Just like with thawed soil, the shear strength of frozen soil is made of cohesive force
11
and internal friction angle, while also qualifying for the MohrCoulomb criterion under certain conditions. The shear strength can be calculated with the following procedure (Ma, 1983): τ ¼ C ðθ; W; t Þ þ σ tanφðθ; W; t Þ
ð1Þ
Frozen clayed-soil is often an ideal viscoplastic body; its internal friction angle φ (θ, W, t) is close to zero, then the above formula (1) can be simplified as: τ ¼ C ðθ; W; t Þ
ð2Þ
In other words, the shear strength will in fact equal the cohesive force. The value of the cohesive force deduced from the theory of plasticity is expressed as (GOST, 1991; Ershov and Roman, 1995): Ct ¼ K
P πdSt
ð3Þ
where Ct is the cohesion of the per unit area, which changes with time, kg/cm2; P is the vertical load on the ball presser, kg; the proportion coefficient (K) is 0.18; d is the diameter of the pressing plate, cm; St is the depth pressed into a sample, cm.
Fig. 1. Device of spherical template indenter.
12
Z. Zhang et al. / Cold Regions Science and Technology 131 (2016) 10–15
In Eq. (1), Ct can be calculated using the St testing records, which are shown in Fig. 2. Because of the influence of internal friction, Ct can be considered as an equivalent cohesion (Cequ) that is the comprehensive characteristic index for the cohesive force of plastic soil. The representation is Cequ = Ct (Zhang et al., 2012). Cohesion is an essential characteristic of soil strength, and correlates with the intensity indexes under external loading (Zhang et al., 2012). An advantage of using the STI is that it can be used for outdoor or indoor testing within a short test period. Its measuring head is also controllable. However, there's a higher demand for sample homogeneity when using the STI. More specifically, STI experiments require larger samples and the STI cannot determine pore water pressure (Ershov and Roman, 1995). The equivalent cohesion is calculated by determining the depth the spherical template sinks into the soil (St, deformation recorded in test). This calculation is then used to determine the deformation index and the total deformation modulus E0. The equation for the total deformation modulus (Eθ,t) can be expressed as (Ershov and Roman, 1995): Eθ;t ¼
3 1−μ 20 P 3=2
1=2
4St ðd−St Þ
ð4Þ
where, μ0 is the Poisson coefficient; P is the vertical load on the ball presser, Pa; d is the diameter of the pressing plate, cm; St is depth that the spherical indenter presses into a sample, cm. The long-term strength can be predicted on the basis of the different prediction methods. First, the logarithmic equation is based on the longterm damage conditions and creep equation (Vyalov, 1959): σt ¼
β t þ t ln B
ð5Þ
The test data can be arranged into a diagram of 1/σ − ln t(s). In Eq. (5), the value of β (MPa) is the cotangent of the straight line (Fig. 3). The parameter B is closely related to the intercept (α), and the relational expression is B = e− αβ. t⁎ is the unit time which has a same unit with t. Then, assuming the thermal fluctuation characteristics of the failure process, the power equation for the long-term strength includes the following dynamic parameters (Roman, 2002): σt ¼
σ0
ð6Þ
ðt=t 0 Þβθ
Fig. 3. The schematic diagram (Vyalov) of test data arranging of frozen soil (Vyalov, 1959).
same test method at different temperatures. The experimental results have only one pole, due to the many straight lines. The extrapolation on the coordinate of the pole is great, thus making the calculations difficult. Nonetheless, all the calculations tend to ordinate log t0 (s) (t0 atomic free oscillation time, the range is 10−12–10−13 s). βθ is equal to the tangent of the line at the temperature of θ. Next, during the prediction of the long-term strength, the power equation — which contains stress parameters as well as the failure time (Wu et al., 1983) — is expressed as: σt ¼
σΗ ðt=t Η Þβθ
ð7Þ
In Eq. (7), σH is the intensity value of the initial segment of the longterm curve (Fig. 5) at any time; tH is the time corresponding to σH. βθ is equal to the tangent of the straight line. 3. Some test results using the apparatus
In Fig. 4, the test data can be better arranged into a straight line of log σ (MPa)–log t (s). A set of tests make use of the same soil type and the
To verify the results, a series of test programs were carried out. The Shaanxi-Fuping loess was used as the research object. The remolded and saturated soil samples were prepared with a diameter and height of 61.8 mm and 20 mm. In order to achieve a state of freezing and melting, the temperature was controlled to −20 °C and +20 °C. In a closed state, the freeze-thaw cycles were carried out 50 times in the constant temperature box. After the freeze-thaw tests, the frozen samples were removed at −20 °C (limit ambient temperature) to experiment on the shear strength. The axial loading was 15 kg, and the strength test should be conducted for at least six times on the same soil sample. 3.1. Instantaneous strength and long-term strength
Fig. 2. Sketch of testing of spherical template indenter.
During the mechanical test, the spherical indenter is brought into contact with the surface of the soil sample. Under the vertical load, the sinking depth is calculated as the difference between zero and the long-term limit settlement. As seen in Fig. 6a, the fracture strength caused by the cohesive force is first effected by the initial relative instantaneous strength (C0) and then effected by the long-term strength (C∞). The failure occurs in the soil sample under the load, and the failure
Z. Zhang et al. / Cold Regions Science and Technology 131 (2016) 10–15
13
Fig. 4. The schematic diagram (Roman) of test data arranging of frozen soil (Roman, 2002).
strength (Cf) can be determined at this time. The change in cohesion with time is presented in Fig. 6b. The soil particles continue to rearrange; the granularity composition transforms; and the long-term strength of the soil gradually becomes smooth. The new, stable structure of the soil has then formed. As observed in the variation curve of cohesion, the essence of the shear strength is actually a representation of the rheological process for frozen soil. Since the area of contact increases, the stress is reduced, and the soil becomes more uniform and stable. Therefore, this method is more efficient in determining the long-term cohesion. 3.2. Total deformation modulus The total deformation modulus is of great significance for determining the deformation characteristics of a soil layer. The variation of the deformation modulus is similar to the long-term strength (Fig. 7). When the total deformation modulus is larger, the soil samples have a
stronger ability to resist deformation. Therefore, the deformation modulus for the frozen loess becomes smaller over time, and the ability to resist an external load becomes weaker. 3.3. Forecast of long-term strength Depending upon the soil's failure time, the strength of the frozen soils can be divided into three types: instantaneous strength, longterm strength, and long-term strength limit. The instantaneous strength is the strength against a fast failure. The long-term strength is the failure stress against a given failure time. The long-term strength limit is the stress value that, when the actual stress is lower than itself, the failure will never happen, i.e. the failure time is infinite (Wu and Ma, 1994). We forecast the long-term strength using the previously mentioned three methods. The prediction results were obtained and compared, as seen in Fig. 7. The results found with Eq. (5) are larger than the results of the other two methods. Note that the latter two results are relatively
Fig. 5. The schematic diagram (Wu) of test data arranging of frozen soil (Wu and Ma, 1994).
14
Z. Zhang et al. / Cold Regions Science and Technology 131 (2016) 10–15
Fig. 6. The change curve of the equivalent cohesion of frozen loess: a) C∞–t; b) C∞–log t.
close to each other. Thus, the latter two methods are safer than the third method for forecasting the long-term strength of soil (Fig. 8). 4. Summary
Fig. 7. The change curve of the total deformation modulus of frozen loess.
The following features of the STI have been demonstrated in this study: (1) It uses a simple test method with a short testing time. (2) The apparatus is suitable for determining the shear strength and long-term strength limit of cohesive soil as well as dispersive freezing and nonfreezing soil, dispersive frozen sand and ice. (3) The value of Ct can be considered as the equivalent cohesion (Cequ). Ct is a synthetic reflection of the cohesive force and the internal friction, which runs counter to the usual claim that the single cohesive force adheres to the Mohr-Coulomb criterion. Moreover, the total modulus can be determined. The device is widely used for testing the mechanics index of frozen soils, especially for in situ tests of practical engineering. To verify the accuracy of the apparatus, some test programs were performed. Three different methods were used for predicting longterm soil strength. The calculation results of the Vyalov's equation were larger, while the others results were closer to each other. Therefore, the author suggests that it is safer to use the two latter
Z. Zhang et al. / Cold Regions Science and Technology 131 (2016) 10–15
Fig. 8. The forecast curve of the long-term strength of frozen loess.
methods—the two that yielded similar results—to forecast the longterm strength of soil. Acknowledgement This work was supported in part by the Natural Science Foundation of China (41301070, 41301071), West Light Program for Talent Cultivation of Chinese Academy of Sciences and the project-sponsored by SRF ([2013]639-46) for ROCS, SEM granted to Dr. ZHANG Ze. References Arenson, L.U., Springman, S.M., 2005. Triaxial constant stress and constant strain rate tests on ice-rich permafrost samples. Can. Geotech. J. 42 (2), 412–430. Chamberlain, E., Groves, C., Perham, R., 1972. The mechanical behaviour of frozen earth materials under high pressure triaxial test conditions. Geotechnique 22, 469–483. Chen, X.S., 1995. Creep mathematic model of frozen clay and its application in China. J. China Coal Soc. 20 (4), 399–402 In Chinese. Chertolyas, N.F., 1977. Evaluation of the strength and deformation properties of cohesive soils by the impression of a spherical template indenter. Abstract of Dissertation for Candidate of Technical Sciences. Moscow State University, Moscow, pp. 1–26 in russian. Dinnik, A.I., 1952. Compression of Contacting Bodies. Izdatel'stvo Akademii Nauk UkrSSR, Kiev in russian. Ershov, E.D., Roman, L.T., 1995. Methods for Determining the Mechanical Properties of Frozen Soils. Moscow State University Press, Moscow in Russian.
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GOST 12248-96, 1991. Soils – Laboratory Methods for Determining the Strength and Strain Characteristics. Ministry of Construction of Russia Federation, Moscow in Russian. Ishlinskiy, A.Y., 1945. The equation of deformation is not completely elastic and viscoplastic bodies. Proc. USSR Acad. Sci. Sect. Tech. Sci. 1 (2), 25–30. Lai, Y., Xu, X., Dong, Y., et al., 2013. Present situation and prospect of mechanical research on frozen soils in China. Cold Reg. Sci. Technol. 87, 6–18. Ma, S.M., 1983. Experiment study on shear strength of frozen soils. Professional Papers on Permafrost Studies of Qinghai-Xizang Platent. Science Press, Beijing, pp. 106–111 In Chinese. Ma, W., Wu, Z.W., Sheng, Y., 1994. Creep and creep strength of frozen soil. J. Glaciol. Geocryol. 16 (2), 113–118 In Chinese. Ma, W., Wu, Z.W., Pu, Y.B., et al., 1997. Monitoring the change of structures in frozen soil in triaxial creep process by CT. J. Glaciol. Geocryol. 19 (1), 52–57 In Chinese. Mi, H.Z., Wu, Z.W., Ma, W., et al., 1993. Characteristic of shear creep of frozen fine sand. J. Glaciol. Geocryol. 15 (3), 492–497 In Chinese. Ourvy, F., 1985. Results of triaxial compression tests and triaxial creep tests on an artificially frozen stiff clay. Proc. of 4th Inter. Symp. on Ground Freezing, pp. 207–212. Qu, G.Z., Zhang, J.M., Cheng, X.D., 2011. Experimental study of direct shear creep properties of frozen silty clay on Qinghai-Tibetan Plateau. Rock Soil Mech. 32 (1), 95–98 In Chinese. Roman, L.T., 1987. Frozen Peat Soil Is Used as the Building Foundation. RAS press Novosibirsk In Russian. Roman, L.T., 2002. Mechanics of Frozen Soil. MAIK bbNAUKA/INTERPERIODIKANN, Moscow. Sheng, Y., Wu, Z.W., Miao, L.N., et al., 1996. The unified creep model of frozen soil under uniaxial compressive condition. Prog. Nat. Sci. 6 (3), 357–360. Tsytovich, N.A., 1947. Determination of the cohesive forces of frozen soils by the method of ball probe. Funds Permafrost Institute USSR Academy of Sciences. Tsytovich, N.A., 2010. Mechanics of Frozen Soil, Book House "LIBROKOM" Moscow (in Russian). Vyalov, S.S., 1959. The Rheological Properties and the Frozen Soil Bearing Capacity. RAS press, Moscow In Russian. Wang, Z.G., Ma, W., Sheng, Y., et al., 1996. A progressive yield criteria on creep of frozen soil. J. Glaciol. Geocryol. 18 (2), 155–161 In Chinese. Wu, Z.W., Ma, W., 1994. Strength and Creep of Frozen Soil. Lanzhou University Press, Lanzhou, China In Chinese. Wu, Z., Zhang, J., Zhu, Y., 1983. Field experiments creep of ground ice on Qianghai-xizang plateau. Professional Papers on Permafrost Studies of Qianghai-Xizang Plateau. Academia Sinica. Chine, Lanzhou, pp. 120–123. Wu, Z.W., Ma, W., Pu, Y.B., et al., 1997. Submicroscopic analysis on deformation characteristics in creep process of frozen soil. Chin. J. Geotech. Eng. 19 (3), 1–6 In Chinese. Yang, P., 1996. Determination of time coefficient in simulation tests of frozen soil structure. J. Xi'an Mining Inst. 16 (4), 315–319 In Chinese. Yin, X.W., Fu, Q., Ma, K.L., 2013. Study of the nonlinear mathematical model for triaxial creep of frozen soil. J. Glaciol. Geocryol. 35 (1), 171–176 in Chinese. Zhang, X.D., Fu, Q., 2011. Experimental study of triaxial creep properties of frozen soil and thickness determination of flat frozen soil wall. Rock Soil Mech. 32 (8), 2261–2266 in Chinese. Zhang, C.Q., Wei, X.X., Miao, T.D., 1995. Microstructure damage behavior and change characteristic in the frozen soil creep process. J. Glaciol. Geocryol. 17 (S), 60–65 In Chinese. Zhang, Z., Ma, W., Zhang, Z.Q., Li, B., Yao, X.L., 2012. Application of spherical template indenter to long-term strength tests for frozen soil. Rock Soil Mech. 33 (11), 3516–3520 in Chinese. Zhu, Y.L., 1988. Studies on strength and creep behaviour of frozen soils in China. J. Glaciol. Geocryol. 10 (3), 332–337 In Chinese. Zhu, Y.L., He, P., Zhang, J.Y., et al., 1998. The triaxial creep model for frozen soil under vibration loading. Prog. Nat. Sci. 8 (1), 60–62 In Chinese.
Contents lists available at ScienceDirect
Cold Regions Science and Technology journal homepage: www.elsevier.com/locate/coldregions
A spherical template indenter for a frozen soil long-term shear strength test Ze Zhang a,⁎, Hong Zhou a,b,c, Wenjie Feng a, Zhongqiong Zhang a, Donghui Xiao a a b c
State Key Laboratory of Frozen Soil Engineering, Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Science, Lanzhou 730000, China Key Laboratory of Mechanics on Disaster and Environment in Western China of Ministry of Education, Lanzhou University, Lanzhou, Gansu 730000, China College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou, Gansu 73000, China
a r t i c l e
i n f o
Article history: Received 14 April 2014 Received in revised form 21 July 2016 Accepted 30 July 2016 Available online 2 August 2016 Keywords: Spherical template indenter Frozen soil Mechanical property Long-term strength
a b s t r a c t Certain mechanical apparatus have long been considered indispensible to practical engineering design. In particular, the spherical template indenter (STI) has been widely used for permafrost soil testing in the former USSR and Russia. Over the last 60 years, experimental engineering theories and methods have been greatly improved. But the STI has gone largely unchanged, the long-term strength and total deformation modulus analyzed by the impression of STI on soil, simple as it is to use, and effective as it is at quickly measuring the properties and forecasting the long-term strength of frozen soil. This paper makes a brief introduction to the STI apparatus. The capabilities of the STI are shown through a series of test results. It is evaluated under the pretext of being a promising tool for the investigation of frozen soil strength property. Three different methods were used to yield results predicting the long-term strength of frozen loess. © 2016 Elsevier B.V. All rights reserved.
1. Introduction As more infrastructures continue to be constructed in permafrost regions, it's of great importance that builders understand the mechanical properties and long-term shear strength of frozen soil. To determine the capacity of a frozen soil structure, one must first determine the soil's long-term shear strength. Many researchers have conducted tests on the shear strength properties of frozen soil using wedge shear equipment, a direct shear device, or a triaxial apparatus (Zhu, 1988). There are limitations when using the direct shear test to measure the mechanical properties of frozen soil. For instance, the high strength of the frozen soil makes it difficult to shear. In addition, it's cost prohibitive to control the temperatures of testing sites in the field. Because of these difficulties, a triaxial apparatus is often used to study mechanical property of frozen soil. However, because this device requires a long testing period, and can be expensive to use, it has not been widely adopted in the practical applications (Zhang et al., 2012). Many researchers have undertaken studies on long-term shear strength by using the triaxial creep test (Zhu et al.,1998; Chen, 1995; Ma et al., 1994, 1997; Mi et al., 1993; Qu et al., 2011; Sheng et al., 1996; Wang et al., 1996; Wu et al., 1997; Yang, 1996; Zhang et al., 1995; Arenson and Springman, 2005; Zhang and Fu, 2011; Yin et al., 2013). These studies are primarily concerned with the changing law of deformation with regard to time, and the myriad factors that influence creep indexes (Lai et al., 2013). The triaxial creep test of frozen soil's ⁎ Corresponding author. E-mail address: [email protected] (Z. Zhang).
http://dx.doi.org/10.1016/j.coldregions.2016.07.011 0165-232X/© 2016 Elsevier B.V. All rights reserved.
long-term and shear strength requires a lengthy process to maintain the uniformity of the samples. Due to the large errors inherent to the sample preparation, the experimental results are often incomparable. In an effort to find a solution to these testing issues, this paper introduces the spherical template indenter (STI) — an instrument that can be used to quickly test and predict frozen soil's long-term strength. In 1947, Tsytovich was the first to use the instrument to study cohesive force of different soils, such as silt, coarse soils, loess, frozen and other kinds of soils (Tsytovich, 1947). In 1952, Dinnik (1952) adopted the impression of a sphere in a visco-elastic half-space as a basis question in this study, and Chertolyas (1977) used STI to determine compression modulus in thawed clayey soils, then Roman (1987) validated the possibility of determining deformation characteristics for permafrost from data on the impression of STI. In Russia, this method has long been used in the study of frozen soil mechanics long-term shear strength. In the fields of science and construction engineering it has also been highly regarded, and even written into Russia's standard testing procedures for frozen soil testing. Others have confirmed the notion that this apparatus is well-suited for testing frozen soil (Chamberlain et al., 1972; Ma, 1983; Ourvy, 1985; Zhu, 1988; Zhang et al., 2012). Due to the need of economical constructions, engineering construction in frozen soil regions rises in China, which mainly includes the Qinghai–Tibet Highway, the Xining–Yushu Highway, the Qinghai–Tibet Railway, the Qinghai–Tibet power transmission lines, the Golmud–Lhasa Oil pipe, China–Russia Oil pipe and the West Route of South-to-North Water Diversion (Lai et al., 2013). The STI apparatus has seen increased use in applied research. In fact, a series of test programs were carried out to demonstrate the effectiveness of this device.
Z. Zhang et al. / Cold Regions Science and Technology 131 (2016) 10–15
2. Apparatus description and theoretical basis As shown in Fig. 1, the device has three primary parts: the pressure system, support member, and displacement meter. The pressure system is used for loading the samples and includes spherical indenter (4), samples with fresh-keeping film (5), screw cap (6) and horizontal scaffold (7). The support member binds the instrument together and includes bearing plate (3), weight (8) and guide bar (10). The displacement meter (1, 2) measures the depth pressed into a sample by the spherical indenter (4). The experimental principle of the STI is similar to the Brinnel hardness meter (Tsytovich, 2010). This principle, first proposed by Ishlinskiy, was based on the plasticity theory of ideal viscosity and non-strengthening body (Ishlinskiy, 1945). Tsytovich and Vyalov used the apparatus to determine soil mechanics, and established a theory on frozen soil strength, experimentation, calculation and prediction methods. More recently, Roman expanded upon the application of the apparatus, building a method for calculating the modulus and improving the process for predicting long-term strength. The shear strength of frozen soil is influenced by the soil skeleton, mineral composition, and structure, as well as the permafrost temperature (θ), water content (W), and the time of loading (t). Just like with thawed soil, the shear strength of frozen soil is made of cohesive force
11
and internal friction angle, while also qualifying for the MohrCoulomb criterion under certain conditions. The shear strength can be calculated with the following procedure (Ma, 1983): τ ¼ C ðθ; W; t Þ þ σ tanφðθ; W; t Þ
ð1Þ
Frozen clayed-soil is often an ideal viscoplastic body; its internal friction angle φ (θ, W, t) is close to zero, then the above formula (1) can be simplified as: τ ¼ C ðθ; W; t Þ
ð2Þ
In other words, the shear strength will in fact equal the cohesive force. The value of the cohesive force deduced from the theory of plasticity is expressed as (GOST, 1991; Ershov and Roman, 1995): Ct ¼ K
P πdSt
ð3Þ
where Ct is the cohesion of the per unit area, which changes with time, kg/cm2; P is the vertical load on the ball presser, kg; the proportion coefficient (K) is 0.18; d is the diameter of the pressing plate, cm; St is the depth pressed into a sample, cm.
Fig. 1. Device of spherical template indenter.
12
Z. Zhang et al. / Cold Regions Science and Technology 131 (2016) 10–15
In Eq. (1), Ct can be calculated using the St testing records, which are shown in Fig. 2. Because of the influence of internal friction, Ct can be considered as an equivalent cohesion (Cequ) that is the comprehensive characteristic index for the cohesive force of plastic soil. The representation is Cequ = Ct (Zhang et al., 2012). Cohesion is an essential characteristic of soil strength, and correlates with the intensity indexes under external loading (Zhang et al., 2012). An advantage of using the STI is that it can be used for outdoor or indoor testing within a short test period. Its measuring head is also controllable. However, there's a higher demand for sample homogeneity when using the STI. More specifically, STI experiments require larger samples and the STI cannot determine pore water pressure (Ershov and Roman, 1995). The equivalent cohesion is calculated by determining the depth the spherical template sinks into the soil (St, deformation recorded in test). This calculation is then used to determine the deformation index and the total deformation modulus E0. The equation for the total deformation modulus (Eθ,t) can be expressed as (Ershov and Roman, 1995): Eθ;t ¼
3 1−μ 20 P 3=2
1=2
4St ðd−St Þ
ð4Þ
where, μ0 is the Poisson coefficient; P is the vertical load on the ball presser, Pa; d is the diameter of the pressing plate, cm; St is depth that the spherical indenter presses into a sample, cm. The long-term strength can be predicted on the basis of the different prediction methods. First, the logarithmic equation is based on the longterm damage conditions and creep equation (Vyalov, 1959): σt ¼
β t þ t ln B
ð5Þ
The test data can be arranged into a diagram of 1/σ − ln t(s). In Eq. (5), the value of β (MPa) is the cotangent of the straight line (Fig. 3). The parameter B is closely related to the intercept (α), and the relational expression is B = e− αβ. t⁎ is the unit time which has a same unit with t. Then, assuming the thermal fluctuation characteristics of the failure process, the power equation for the long-term strength includes the following dynamic parameters (Roman, 2002): σt ¼
σ0
ð6Þ
ðt=t 0 Þβθ
Fig. 3. The schematic diagram (Vyalov) of test data arranging of frozen soil (Vyalov, 1959).
same test method at different temperatures. The experimental results have only one pole, due to the many straight lines. The extrapolation on the coordinate of the pole is great, thus making the calculations difficult. Nonetheless, all the calculations tend to ordinate log t0 (s) (t0 atomic free oscillation time, the range is 10−12–10−13 s). βθ is equal to the tangent of the line at the temperature of θ. Next, during the prediction of the long-term strength, the power equation — which contains stress parameters as well as the failure time (Wu et al., 1983) — is expressed as: σt ¼
σΗ ðt=t Η Þβθ
ð7Þ
In Eq. (7), σH is the intensity value of the initial segment of the longterm curve (Fig. 5) at any time; tH is the time corresponding to σH. βθ is equal to the tangent of the straight line. 3. Some test results using the apparatus
In Fig. 4, the test data can be better arranged into a straight line of log σ (MPa)–log t (s). A set of tests make use of the same soil type and the
To verify the results, a series of test programs were carried out. The Shaanxi-Fuping loess was used as the research object. The remolded and saturated soil samples were prepared with a diameter and height of 61.8 mm and 20 mm. In order to achieve a state of freezing and melting, the temperature was controlled to −20 °C and +20 °C. In a closed state, the freeze-thaw cycles were carried out 50 times in the constant temperature box. After the freeze-thaw tests, the frozen samples were removed at −20 °C (limit ambient temperature) to experiment on the shear strength. The axial loading was 15 kg, and the strength test should be conducted for at least six times on the same soil sample. 3.1. Instantaneous strength and long-term strength
Fig. 2. Sketch of testing of spherical template indenter.
During the mechanical test, the spherical indenter is brought into contact with the surface of the soil sample. Under the vertical load, the sinking depth is calculated as the difference between zero and the long-term limit settlement. As seen in Fig. 6a, the fracture strength caused by the cohesive force is first effected by the initial relative instantaneous strength (C0) and then effected by the long-term strength (C∞). The failure occurs in the soil sample under the load, and the failure
Z. Zhang et al. / Cold Regions Science and Technology 131 (2016) 10–15
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Fig. 4. The schematic diagram (Roman) of test data arranging of frozen soil (Roman, 2002).
strength (Cf) can be determined at this time. The change in cohesion with time is presented in Fig. 6b. The soil particles continue to rearrange; the granularity composition transforms; and the long-term strength of the soil gradually becomes smooth. The new, stable structure of the soil has then formed. As observed in the variation curve of cohesion, the essence of the shear strength is actually a representation of the rheological process for frozen soil. Since the area of contact increases, the stress is reduced, and the soil becomes more uniform and stable. Therefore, this method is more efficient in determining the long-term cohesion. 3.2. Total deformation modulus The total deformation modulus is of great significance for determining the deformation characteristics of a soil layer. The variation of the deformation modulus is similar to the long-term strength (Fig. 7). When the total deformation modulus is larger, the soil samples have a
stronger ability to resist deformation. Therefore, the deformation modulus for the frozen loess becomes smaller over time, and the ability to resist an external load becomes weaker. 3.3. Forecast of long-term strength Depending upon the soil's failure time, the strength of the frozen soils can be divided into three types: instantaneous strength, longterm strength, and long-term strength limit. The instantaneous strength is the strength against a fast failure. The long-term strength is the failure stress against a given failure time. The long-term strength limit is the stress value that, when the actual stress is lower than itself, the failure will never happen, i.e. the failure time is infinite (Wu and Ma, 1994). We forecast the long-term strength using the previously mentioned three methods. The prediction results were obtained and compared, as seen in Fig. 7. The results found with Eq. (5) are larger than the results of the other two methods. Note that the latter two results are relatively
Fig. 5. The schematic diagram (Wu) of test data arranging of frozen soil (Wu and Ma, 1994).
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Z. Zhang et al. / Cold Regions Science and Technology 131 (2016) 10–15
Fig. 6. The change curve of the equivalent cohesion of frozen loess: a) C∞–t; b) C∞–log t.
close to each other. Thus, the latter two methods are safer than the third method for forecasting the long-term strength of soil (Fig. 8). 4. Summary
Fig. 7. The change curve of the total deformation modulus of frozen loess.
The following features of the STI have been demonstrated in this study: (1) It uses a simple test method with a short testing time. (2) The apparatus is suitable for determining the shear strength and long-term strength limit of cohesive soil as well as dispersive freezing and nonfreezing soil, dispersive frozen sand and ice. (3) The value of Ct can be considered as the equivalent cohesion (Cequ). Ct is a synthetic reflection of the cohesive force and the internal friction, which runs counter to the usual claim that the single cohesive force adheres to the Mohr-Coulomb criterion. Moreover, the total modulus can be determined. The device is widely used for testing the mechanics index of frozen soils, especially for in situ tests of practical engineering. To verify the accuracy of the apparatus, some test programs were performed. Three different methods were used for predicting longterm soil strength. The calculation results of the Vyalov's equation were larger, while the others results were closer to each other. Therefore, the author suggests that it is safer to use the two latter
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Fig. 8. The forecast curve of the long-term strength of frozen loess.
methods—the two that yielded similar results—to forecast the longterm strength of soil. Acknowledgement This work was supported in part by the Natural Science Foundation of China (41301070, 41301071), West Light Program for Talent Cultivation of Chinese Academy of Sciences and the project-sponsored by SRF ([2013]639-46) for ROCS, SEM granted to Dr. ZHANG Ze. References Arenson, L.U., Springman, S.M., 2005. Triaxial constant stress and constant strain rate tests on ice-rich permafrost samples. Can. Geotech. J. 42 (2), 412–430. Chamberlain, E., Groves, C., Perham, R., 1972. The mechanical behaviour of frozen earth materials under high pressure triaxial test conditions. Geotechnique 22, 469–483. Chen, X.S., 1995. Creep mathematic model of frozen clay and its application in China. J. China Coal Soc. 20 (4), 399–402 In Chinese. Chertolyas, N.F., 1977. Evaluation of the strength and deformation properties of cohesive soils by the impression of a spherical template indenter. Abstract of Dissertation for Candidate of Technical Sciences. Moscow State University, Moscow, pp. 1–26 in russian. Dinnik, A.I., 1952. Compression of Contacting Bodies. Izdatel'stvo Akademii Nauk UkrSSR, Kiev in russian. Ershov, E.D., Roman, L.T., 1995. Methods for Determining the Mechanical Properties of Frozen Soils. Moscow State University Press, Moscow in Russian.
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