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On the uniaxial compression strength of frozen gravelly soils
Cold Regions Science and Technology 171 (2020) 102965
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On the uniaxial compression strength of frozen gravelly soils Junlin Zhao, Pei Zhang, Xiao Yang, Jilin Qi
⁎
T
School of Civil and Transportation Engineering, Beijing University of Architecture and Civil Engineering, China
ARTICLE INFO
ABSTRACT
Keywords: Frozen gravelly soil Uniaxial compression strength Temperature Strain rate Gravel content
Frozen gravelly soils are often encountered in both cold regions engineering and urban underground constructions by artificial freezing method. This work takes a gravelly sand in Beijing as the basic material. Gravel grains of 10–20 mm in size are obtained and mixed with sand grains at certain ratios and then saturated frozen samples are prepared. Uniaxial compression test is used to study the uniaxial compression strength (UCS) of the material under 3 temperatures and 3 strain rates. Together with 4 gravel contents, 36 combinations are investigated. Test results show that stress-strain curves generally demonstrate strain-softening manner, with different strain energy dependent upon temperature and strain rate on the one hand, and on gravel content upon the other hand. An inclination of approximately 55° to 58° is found for the failure surface. UCS is obtained from all tests for analysis. It is found that the UCS of frozen gravelly soil increases with the decrease of temperature and the increase of strain rate. Generally accepted empirical relationships for fined-grained frozen soils are still applicable with the correlation coefficient of very close to 1. Gravel content plays another important role in the UCS of frozen gravel soil. UCS is found to decrease significantly with the increase of gravel content at high strain rate. At relatively low strain rates however, influence of gravel content on UCS turns out to be complicated. Mechanism of the mechanical performance of the sand-gravel-ice system is proposed in terms of gravel contents, ice contents as well as strain rate.
1. Introduction Strength of frozen soils is an important parameter to be considered in the construction of infrastructures when frozen soils are involved, which is one of the most widely studied topics in the field of frozen soil mechanics. Frozen gravelly soils are often encountered not only in the subgrade, pipelines and coal mines in cold regions (Zhu et al., 2010; Yue et al., 2013), but also in artificial freezing applied underground constructions in urban development (Esmaeili-Falak et al., 2018). Therefore, the mechanical properties, especially strength of frozen gravelly soils must be well understood. The routine method to investigate strength of frozen soils is the element test where the maximum soil grain size cannot exceed certain limitation dependent on the sample configuration. For instance, the Chinese standard for soil test method (Standard for geotechnical testing method GB/T 50123–2019, 2019) defines that the maximum grain size of soil grains in the cylindrical sample should not exceed 1/5 of the sample diameter for the sample has a diameter of 101 mm; while 1/10 for sample with a diameter of 39.1 or 61.8 mm. It is not explicitly defined in standards for frozen soil testing, and the regulations for nonfrozen soils are generally adopted in practice without strong evidence though. According to such requirements, in order to carry out ⁎
mechanical tests on frozen gravelly soils, fairly large test apparatuses are required, which is unaffordable for most research institutions in terms of capital and space. Thus, the investigation of mechanical properties of frozen gravelly soils has not yet been extensively carried out. The strength of frozen soil is influenced by various factors, which makes it rather complicated in mechanism. Qi et al. (2016) made a detailed summarization from both micro and macro aspects. The strength of frozen soil is composed of molecular bonding, structure coupling and ice bonding. The strength of frozen soil is mainly originated from the strength of ice, the strength of soil skeleton and the interaction between the ice-unfrozen water-soil particles. It is generally recognized that ice plays a dominant role in the strength of frozen soils, while for a coarse-grained soil, the fraction of soil skeleton defines the relative contents of soil grains and ice, and therefore is important to strength of the frozen soil sample. Uniaxial compressive strength (UCS) of frozen soils is easy to be obtained and therefore has been investigated by a large number of experimental studies. Given a certain soil classification, it has been found that temperature and strain rate are the most important factors influencing UCS of saturated frozen soils. In comparison with the strength of unfrozen soils, it is easy to understand that temperature is the first substantial influencing factor for
Corresponding author. E-mail address: [email protected] (J. Qi).
https://doi.org/10.1016/j.coldregions.2019.102965 Received 8 September 2019; Received in revised form 20 November 2019; Accepted 11 December 2019 Available online 12 December 2019 0165-232X/ © 2019 Elsevier B.V. All rights reserved.
Cold Regions Science and Technology 171 (2020) 102965
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Fig. 1. Frozen soil uniaxial compression testing apparatus.
2. Testing methodology
strength of frozen soils to be considered by scholars. Tsytovich (1975), Haynes and Karalius (1977) and Bourbonnais and Ladanyi (1985) revealed that UCS of frozen clay, silt and sand all increases with the decrease of temperature in a power function. The parameter m of the power function is related to the material and test conditions, within a range roughly between 0.5 and 1.0. When m = 1.0, a linear relationship is then obtained between UCS and temperature, which sometimes performs fairly well (Sayles and Epanchin, 1966; Wu and Ma, 1994). On the other hand, the presence of ice makes frozen soils an obvious rheological material. The strain rate therefore has a great influence on the strength of frozen soils. Sayles and Epanchin (1966), Baker (1979), and Parameswaran (1980) have studied the effect of strain rate on saturated frozen sand. It was generally recognized that UCS of frozen soils increases with the increase of strain rate in an exponential form. Richard and Andersland (1981) considered temperature, strain rate as well as sample size in frozen sand tests. Zhu and Carbee (1984) also considered the effects of temperature and strain rate on saturated Fairbanks frozen silt. Both Zhu and Carbee (1984) and Li et al. (2004) consider the effect of temperature and strain rate on strength. The study objects in the above-mentioned work are frozen sand, silt or clay, relatively fine-grained soils. Few studies have been carried out on gravelly soils. With the extensive development of cold regions and urban underground development, the research needs for the mechanical properties of frozen gravelly soils have been recognized. In recent years, Zhang et al. (2017) conducted triaxial compression on frozen sandy gravels collected from Beijing, and analyzed the characteristics of stress-strain curve and the variation of strength with temperature and confining pressures. Feng et al. (2018) and Liu et al. (2019) studied the mechanical properties of frozen mixed soils with different gravel content. The basic mechanical properties including strength of the materials generally agree with that for relatively frozen fine-grained soils, while the maximum size of gravel particles included in their study objects were 2–4 mm, only a little larger than sand grains. The authors of this paper wonder how the material would behave if the grain size of gravels further increases on the one hand, and gravel content changes on the other hand. Considering the complexity of strength of frozen gravelly soils, this paper starts from simple and controllable conditions, i.e., to carry out uniaxial compression tests on a series of man-made frozen gravelly soils with different gravel content, with the size of gravel grains of up to 20 mm. The variation of UCS of frozen gravelly soils under different combinations of temperature, strain rate and gravel content will be studied.
2.1. Testing apparatus The apparatus used in the test is a self-developed frozen soil uniaxial testing device (Fig. 1). The apparatus consists of a loading system, a temperature control system and a data acquisition system. The loading system applies loads up to 100 kN with a precision of 0.05% of the applied load. It allows several control modes including stress control, strain control and strain rate control, etc. The temperature control system provides a temperature range of - 30 °C to 60 °C, with a temperature control accuracy of ± 0.1 °C. The data is digitally collected by a computer. 2.2. Preparation of frozen soil samples The gravelly soil used for tests was taken from a site of subway station construction in Beijing. Artificial freezing method will be applied in that gravelly soil layer. The grain size distribution curve of the soil is illustrated in Fig. 2 (a). The soil was sieved to obtain sand grains with a particle size range of 0.075–2 mm and gravel grains of 10–20 mm in size. Sand and gravels were then mixed at a certain ratio for sample preparation. Taking gravel as reference, the samples were prepared in four gravel contents of 0% (pure sand), 25%, 72% and 100% (pure gravel). The grain size distribution curves of the four soils are illustrated in Fig. 2 (b). Fig. 3 shows pictures of the mixed soil materials corresponding to the four particle size distribution curves illustrated in Fig. 2 (b). A certain material is compacted layer by layer so as to ensure the uniformity. According to a desired gravel content, certain amounts of sand and gravel are homogenously mixed. A relative density of 0.8 in the whole testing program is used, based on which the sand-gravel mixture is compacted layer by layer in a cylindrical mold to a certain height, and then was slowly immersed in a water vessel and stayed in water for 48 h for saturation. The saturated sample together with the water vessel was placed in a refrigerator with a pre-set temperature of −30 °C for quick freezing and stayed in the refrigerator for 24 h. During the process, the sample was kept in the mold all the time, so that the shape and dimension remained unchanged. After demolding, the frozen sample was quickly covered with plastic film to keep water content unchanged. At last, the sample was kept in the refrigerator at a constant desired temperature for testing. In this way, a cylinder sample was prepared with a diameter of 101 mm and a height of 200 mm. The basic physical indexes for the samples are listed in Table 1. 2
Cold Regions Science and Technology 171 (2020) 102965
J. Zhao, et al.
Fig. 2. Grain size distribution curves.
Fig. 3. The pictures of four materials for sampling.
Table 1 The basic physical indexes of the test material. 100% gravel Relative density Dry unit weight/kN·m−3 Water content
0.8 γd, max 16.9 22.7%
72% gravel γd, min 14.2
25% gravel
γd, max 22.2 10.1%
γd, min 16.4
3
γd, max 18.7 16.4%
0% gravel γd, min 16.3
γd, max 17.2 19.6%
γd, min 14.3
Cold Regions Science and Technology 171 (2020) 102965
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2.3. Testing plan
Table 2 The testing scheme. Gravel contents
Temperature
Strain rate
100% gravel 72% gravel 25% gravel 0% gravel
−5 °C −10 °C −15 °C
10−3 s−1 10−4 s−1 10−5 s−1
The uniaxial compression test was used to investigate the influence of temperature, strain rate as well as especially gravel contents on the UCS of the frozen gravelly soil samples. The testing scheme is listed in Table 2. Before the test, a certain desired temperature was set for the thermostat box on the testing apparatus. A sample was taken out from the
Fig. 4. Stress-strain curves (T denotes test temperature, 4
refers to strain rate.)
Cold Regions Science and Technology 171 (2020) 102965
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Fig. 5. The failure picture of four kinds of gravel samples.
refrigerator and mounted on the device. The desired temperature was kept constant for four more hours so that a homogenous temperature can be reached in the whole sample. The test temperature was controlled at −5 °C, −10 °C, −15 °C, respectively. As can be seen in Table 2 that 3 strain rates of 10−3 s−1, 10−4 s−1, 10−5 s−1 were used. Considering that the samples have a height of 200 mm, it means that the loading speeds are 12 mm/min, 1.2 mm/min, 0.12 mm/min, respectively. UCS was taken as the stress either corresponding to a peak if available, or a strain of 15% on the stress-strain curve according to the Chinese standard for soil test method (Standard for geotechnical testing method GB/T 50123–2019, 2019).
3. Analysis of testing results 3.1. Test results Fig. 4 shows the stress-strain curves of the samples. It can be seen that the stress-strain curves are all strain-softened. Here we take the peak point of the curve as the UCS of the samples. Generally speaking, with the decrease in strain rate the curves reach the peak more gently. Under the same temperature and at the same strain rate, with the increase in gravel content, the curves tend to enclose more area within the same strain range, i.e., the increase in gravel content results in
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Fig. 6. UCS versus temperature for the frozen gravelly soils.
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decrease in the strain energy. Fig. 5 presents failure pictures of samples with four different gravel content under the strain rates of 10−3 s−1. The approximate inclination of the failure surface is in the range of 55° to 58°. It is worth mentioning that pictures with a clear failure surface is not always available. Deep analysis on the failure behaviors needs further additional work.
Table 3 Fitting parameters of two equations.
Exponential
= A (T /T0 )m
Linear
= A + BT
0% gravel
A = 4.39 m = 0.52 R = 0.9936 A = 3.19 m = 0.62 R = 0.9984 A = 2.36 m = 0.68 R = 0.9998 A = 1.70 m = 0.75 R = 0.9789 A = 6.40 B = 0.77 R = 0.9992 A = 4.60 B = 0.83 R = 0.9999 A = 3.25 B = 0.80 R = 0.9996 A = 1.94 B = 0.75 R = 0.9710
A = 2.23 m = 0.64 R = 0.9921 A = 2.23 m = 0.63 R = 0.9918 A = 1.59 m = 0.77 R = 0.9992 A = 2.11 m = 0.50 R = 0.9998 A = 3.20 B = 0.64 R = 0.9975 A = 3.23 B = 0.62 R = 0.9974 A = 1.95 B = 0.72 R = 0.9999 A = 3.06 B = 0.35 R = 0.9984
A = 1.79 m = 0.62 R = 0.9739 A = 1.86 m = 0.60 R = 0.9823 A = 1.16 m = 0.80 R = 0.9998 A = 1.56 m = 0.52 R = 0.9966 A = 2.63 B = 0.47 R = 0.9855 A = 2.72 B = 0.46 R = 0.9919 A = 1.31 B = 0.58 R = 0.9999 A = 2.27 B = 0.28 R = 0.9881
0% gravel 25% gravel 72% gravel 100% gravel
(1)
3.3. Influence of strain rate on UCS The test results show that UCS of the frozen gravelly soil increases with the increase of strain rate. This change tendency is also consistent with that for frozen fine-grained soils. Keeping temperature and gravel content constant, the relationship between UCS and strain rate can be analyzed in the following. A lot of studies have investigated the relationship between the strength, especially UCS of frozen soils and strain rate (Sayles, 1974; Parameswaran, 1980; Richard and Andersland, 1981;). Baker (1979) proposed the simplest but very powerful exponential. relationship as follows:
(2)
where, T is temperature (°C); T0 is a reference temperature, generally taken as −1 °C; A and B are material parameters related with the strain rate; m is a dimensionless parameter. The above two exponential functions are essentially the same, the only difference lies the parameters, especially the exponent m. As was indicated above, when m = 1, Eqs. (1) and (2) become a linear relationship, when strength and temperature can take the form of Eq. (3): m
10−5 s−1
100% gravel
where, σm is the UCS of frozen soil (MPa); A, B and m are test coefficients; T is temperature (°C). Zhu and Carbee (1984) suggested another relationship for a frozen silty clay: m
10−4 s−1
72% gravel
The test results show that UCS of frozen gravelly soil sample increases significantly with the decrease of temperature. The reason for this is that the strength of the ice is increased due to the decrease of the temperature, which enhances the strength of the sample as the consequence (Sayles and Epanchin, 1966; Li et al., 2004). The change tendency and mechanism of UCS are consistent with that for frozen fine-grained soils. In the following, the change of UCS along with temperature will be analyzed with the strain rate and the gravel content remaining constant. Many previous studies have shown that the effect of temperature on UCS of frozen soils can be expressed by an exponential relationship. After examining a large number of different frozen soils at no less than −15 °C, Tsytovich (1975) proposed the following relationship:
= A + B |T|m
10−3 s−1
25% gravel
3.2. Influence of temperature on UCS
m
Strain rate
(3)
m
where, A and B are test coefficients; T is the absolute value of the test temperature. In investigating the effect of temperature on UCS of frozen gravelly soil, we tried the exponential relationship Eq. (2) and the linear relationship of Eq. (3), respectively. The results are illustrated in Fig. 6. The parameters of curve fitting for both forms are listed in Table 3. It can be noticed from Table 3 that parameters for exponential relationship do not make too much sense in terms of strain rate. However, for the linear relationship, parameter B consistently decreases with the decrease in strain rate, which reasonably reflects the change rate of UCS with strain rate. It can be seen that the fitting correlation coefficients of the two forms are greater than 0.97 for all cases, with no significant difference. Relationship between UCS and temperature for frozen gravelly soils is therefore in consistent with that for fine-grained soils, while the linear formula can be taken.
=A
b
(4)
where, is the strain rate; A and b are material coefficients. In this work, Eq. (4) is used to fit the experimental data of UCS at certain temperatures, as shown in Fig. 7. It can be noticed from Fig. 7 that under double logarithmic coordinates, UCS increases linearly with the increase of the strain rate. Table 4 lists the fitting parameters, where it can be noticed that the curve slope b does not change obviously with temperature, while parameter A increases with the decrease of temperature. In other words, the curves are almost parallel with different intercept under different temperature. The above fitting has very high correlation efficient, which implies fairly good fitting abilities of the previously proposed relationships. However, the parameters do not have correlation with gravel contents, which will be analyzed in the following subsection.
7
Cold Regions Science and Technology 171 (2020) 102965
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Fig. 7. UCS with different temperatures vs. strain rate at various gravel content.
significantly. When the sample has a gravel content of 0%, it is in fact a frozen sand. This kind of sample has the high water content and the largest specific surface area. Both ice bonding and interaction between sand particles and ice crystals are the greatest. As a result, UCS of this sample is the greatest at any temperature and strain rate as can be noticed in Fig. 4 and Fig. 8. As the gravel content increases to 25% and 72%, water content decreases, as can be seen in Table 1. When the samples are frozen, ice content decreases correspondingly in comparison with the frozen sand sample with 0% gravel content, and the ice bonding decreases as well (Liu et al., 2019). At the same time, inclusion of gravels weakens the ice-sand system in terms of mechanical performance. At a large strain rate of 10−3 s−1, UCS decreases almost linearly with the increase in gravel contents, as is indicated in Figs. 4 (a), (d), (g) and Fig. 8 (a). However, at relatively small strain rates of 10−4 s−1and 10−5 s−1, when the sand-ice system breaks, the gravel has certain time to take over some load. Due to its greater angle of internal friction than sand, the gravel skeleton can compensate the weakness it brings into the sample to some extent. Therefore, UCS of these samples is almost the same as that of the sample with 0% gravel content, as can be noticed in Figs. 4 (e), (f), (h), (i) and Figs. 8 (b) and (c). For samples containing 100% gravel, there is no sand-ice interaction, and the gravel contacts each other to form a stable skeleton. Due to the irregular shape of the gravel and the small contact area between the gravel, the corresponding stress of the gravel increases, and the particle breakage becomes easier
Table 4 Fitting parameter of the exponential function.
−5 °C −10 °C −15 °C
0% gravel
25% gravel
72% gravel
100% gravel
A = 30.46 b = 0.16 R = 0.9858 A = 40.68 b = 0.16 R = 0.9979 A = 44.13 b = 0.13 R = 0.9984
A = 19.96 b = 0.12 R = 0.9955 A = 32.76 b = 0.14 R = 0.9984 A = 39.20 b = 0.12 R = 0.9994
A = 15.89 b = 0.11 R = 0.9998 A = 22.42 b = 0.10 R = 0.9997 A = 27.85 b = 0.09 R = 0.9959
A = 8.90 b = 0.08 R = 0.9506 A = 30.94 b = 0.16 R = 0.9841 A = 37.23 b = 0.16 R = 0.9908
3.4. Influence of gravel content on UCS Keeping temperature and strain rate unchanged, the variation of UCS of samples with different gravel content is illustrated in Fig. 8. It can be seen that UCS generally decreases with the increase of gravel content. The greater the strain rate is, the more obvious is this tendency. In Fig. 8 (a) for instance where the strain rate is 10−3 s−1, UCS decreases significantly with the increase of gravel content; while in Fig. 8 (b) and (c) where strain rates are 10−4 s−1 and 10−5 s−1, respectively, UCS for samples with 0%, 25% and 72% gravel remains basically unchanged. For the samples with 100% gravel, UCS drops 8
Cold Regions Science and Technology 171 (2020) 102965
J. Zhao, et al.
Fig. 8. UCS versus gravel content at different strain rate.
during the compression process (Guo, 1987; Cai et al., 2016). Since the gravel has a small specific surface area, the interaction between the gravel particles and the ice is the weakest, further aggravating the development of the fracture. As a result, the UCS of the frozen gravel drops sharply, as can be noticed in Fig. 4 and Figs. 8 (b) and (c).
double logarithmic coordinates, UCS increases linearly with the increase in strain rate. An exponential relationship can fit the experimental results fairly well. (4) Gravel content plays another role in UCS. Test results show that UCS decrease significantly with the increase of gravel content at a high strain rate of 10−3 s−1. At relatively low strain rates however, influence of gravel content on UCS is complicatedly related to strain rate. The mechanism of influence of gravel content on UCS is proposed for the gravel-ice-sand system considering in terms of strain rate and ice content.
4. Conclusions This work investigated the UCS of frozen gravelly soils of 4 different gravel contents using uniaxial compression test under 3 different temperatures and 3 different strain rates. The following conclusions can be reached:
The findings in this work applies for frozen sand with different contents of gravel at a grain size range of 10–20 mm. Mechanical properties of frozen gravely soils with larger grains are yet to be further investigated.
(1) Stress-strain curves of all the 36 test combinations present a strain softening manner. Under the same temperature and at the same strain rate, the increase in gravel content results in decrease in the strain energy. Pictures of samples after failure approximately present an inclination of 55° to 58°. (2) Temperature plays the most important role in the UCS of the tested frozen soil. An exponential relationship and a linear relationship were tried to fit the relationship between UCS and temperature. Considering the appropriate accuracy and simplicity, it is recommended that a linear relationship can be used to describe the relationship between UCS and temperature. (3) The UCS of the tested frozen soil is affected by the strain rate under the same temperature. With the strain rate in a range of 10−5 s−1 to 10−3 s−1, UCS increases with the increase of strain rate. Under
Declaration of Competing Interest On behalf of all authors, the corresponding author states that there is no conflict of interest. Acknowledgements This work was financially supported in part by the National Natural Science Foundation of China (Nos. 41972279, 41902284 and 51908023), and the Joint Key Project of BNSFC and BMEC (No. KZ201810016020). 9
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References
Qi, J.L., Dang, B.X., Xu, G.F., Wu, W., Guo, X.L., 2016. A State of the Art for Strength of Frozen Soils. J. Beijing Univ. Civ. Eng. Arch. 32 (3), 89–95 (In Chinese with English abstract). Richard, A.B., Andersland, O.B., 1981. Strain rate, temperature, and sample size effects on compression and tensile properties of frozen sand. Eng. Geol. 18, 35–46. Sayles, F.H., 1974. Triaxial constant strain rate tests and triaxial creep tests on frozen Ottawa sand. U.S. Arm, Corps of Engineers. In: Cold Regions Research and Engineering Laboratory, NH, Technical Report No.253. Sayles, F.H., Epanchin, N.V., 1966. Rate of strain compression tests on frozen Ottawa sand and ice. U.S. Arm, Corps of Engineers. In: Cold Regions Research and Engineering Laboratory, Hanover, NH, Technical Note, 54. Standard for geotechnical testing method GB/T 50123–2019, National standards of People’s Republic of China., 2019. China Planning Press. Tsytovich, N.A., 1975. The Mechanics of Frozen Ground. Scripta Book Co., Washington, D.C. Wu, Z.W., Ma, W., 1994. Strength and Creep of Frozen Soil. Lanzhou University Press, Lanzhou (In Chinese). Yue, Z.R., Wang, T.L., Ma, C., Sun, T.C., 2013. Frost heave control of fine round gravel fillings in deep seasonal frozen regions. Cold Reg. Sci. Technol. 5 (4), 425–432. Zhang, J.X., Yang, H., Shan, R.L., Sui, S.M., Xue, D.C., 2017. Experimental research on triaxial compressive strength of frozen saturated sandy gravel. Rock Soil Mech. 39 (11), 3993–4000 (In Chinese with English abstract). Zhu, Y.L., Carbee, D., 1984. Uniaxial compressive strength of frozen silt under constant deformation rates. Cold Reg. Sci. Technol. 9 (1), 3–15. Zhu, Z.Y., Ling, Z.X., Chen, S.J., Feng, Z., Wang, L.N., Zou, Z.Y., 2010. Experimental investigation on the train-induced subsidence prediction model of Beiluhe permafrost subgrade along the Qinghai-Tibet Railway in China. Cold Reg. Sci. Technol. 62 (1), 67–75.
Baker, T.H.W., 1979. Strain rate effect on the compressive strength of frozen sand. Eng. Geol. 13, 223–231. Bourbonnais, J., Ladanyi, B., 1985. The mechanical behavior of frozen sand down to cryogenic temperatures. In: Proceeding, 4th International Symposium on Ground Freezing, Sapporo, Japan. Vol 1. pp. 235–244. Cai, Z.Y., Li, X.M., Guan, Y.F., Huang, Y.H., 2016. Particle breakage rules of rockfill materials. Chin. J. Geotech. Eng. 38 (5), 924–928. Esmaeili-Falak, M., Katebi, H., Akbar, J., 2018. Experimental Study of the Mechanical Behavior of Frozen Soils - a Case Study of Tabriz Subway. Period. Polytech. Civ. 62 (1), 117–125. Feng, H., Lai, Y.M., Liu, E.L., Luo, H.W., Liu, X.Y., 2018. A creep constitutive model for frozen soils with different contents of coarse grains. Cold Reg. Sci. Technol. 145, 119–126. Guo, Q.G., 1987. Experimental study on shearing strength characteristics of coarse-grained soil. J. Hydraul. Eng. 5, 59–65. Haynes, F.D., Karalius, J.A., 1977. Effect of temperature on the strength of frozen silt. CRREL Report 3–77. Li, H.P., Zhu, Y.L., Zhang, J.B., Lin, C.N., 2004. Effects of temperature, strain rate and dry density on compressive strength of saturated frozen clay. Cold Reg. Sci. Technol. 39 (1), 39–45. Liu, X.Y., Liu, E.L., Zhang, D., Zhang, G., Yin, X., Song, B.T., 2019. Study on effect of coarsegrained content on the mechanical properties of frozen mixed soils. Cold Reg. Sci. Technol. 158, 237–251. Parameswaran, V.R., 1980. Deformation behavior and strength of frozen sand. Can. Geotech. J. 17 (1), 74–88.
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On the uniaxial compression strength of frozen gravelly soils Junlin Zhao, Pei Zhang, Xiao Yang, Jilin Qi
⁎
T
School of Civil and Transportation Engineering, Beijing University of Architecture and Civil Engineering, China
ARTICLE INFO
ABSTRACT
Keywords: Frozen gravelly soil Uniaxial compression strength Temperature Strain rate Gravel content
Frozen gravelly soils are often encountered in both cold regions engineering and urban underground constructions by artificial freezing method. This work takes a gravelly sand in Beijing as the basic material. Gravel grains of 10–20 mm in size are obtained and mixed with sand grains at certain ratios and then saturated frozen samples are prepared. Uniaxial compression test is used to study the uniaxial compression strength (UCS) of the material under 3 temperatures and 3 strain rates. Together with 4 gravel contents, 36 combinations are investigated. Test results show that stress-strain curves generally demonstrate strain-softening manner, with different strain energy dependent upon temperature and strain rate on the one hand, and on gravel content upon the other hand. An inclination of approximately 55° to 58° is found for the failure surface. UCS is obtained from all tests for analysis. It is found that the UCS of frozen gravelly soil increases with the decrease of temperature and the increase of strain rate. Generally accepted empirical relationships for fined-grained frozen soils are still applicable with the correlation coefficient of very close to 1. Gravel content plays another important role in the UCS of frozen gravel soil. UCS is found to decrease significantly with the increase of gravel content at high strain rate. At relatively low strain rates however, influence of gravel content on UCS turns out to be complicated. Mechanism of the mechanical performance of the sand-gravel-ice system is proposed in terms of gravel contents, ice contents as well as strain rate.
1. Introduction Strength of frozen soils is an important parameter to be considered in the construction of infrastructures when frozen soils are involved, which is one of the most widely studied topics in the field of frozen soil mechanics. Frozen gravelly soils are often encountered not only in the subgrade, pipelines and coal mines in cold regions (Zhu et al., 2010; Yue et al., 2013), but also in artificial freezing applied underground constructions in urban development (Esmaeili-Falak et al., 2018). Therefore, the mechanical properties, especially strength of frozen gravelly soils must be well understood. The routine method to investigate strength of frozen soils is the element test where the maximum soil grain size cannot exceed certain limitation dependent on the sample configuration. For instance, the Chinese standard for soil test method (Standard for geotechnical testing method GB/T 50123–2019, 2019) defines that the maximum grain size of soil grains in the cylindrical sample should not exceed 1/5 of the sample diameter for the sample has a diameter of 101 mm; while 1/10 for sample with a diameter of 39.1 or 61.8 mm. It is not explicitly defined in standards for frozen soil testing, and the regulations for nonfrozen soils are generally adopted in practice without strong evidence though. According to such requirements, in order to carry out ⁎
mechanical tests on frozen gravelly soils, fairly large test apparatuses are required, which is unaffordable for most research institutions in terms of capital and space. Thus, the investigation of mechanical properties of frozen gravelly soils has not yet been extensively carried out. The strength of frozen soil is influenced by various factors, which makes it rather complicated in mechanism. Qi et al. (2016) made a detailed summarization from both micro and macro aspects. The strength of frozen soil is composed of molecular bonding, structure coupling and ice bonding. The strength of frozen soil is mainly originated from the strength of ice, the strength of soil skeleton and the interaction between the ice-unfrozen water-soil particles. It is generally recognized that ice plays a dominant role in the strength of frozen soils, while for a coarse-grained soil, the fraction of soil skeleton defines the relative contents of soil grains and ice, and therefore is important to strength of the frozen soil sample. Uniaxial compressive strength (UCS) of frozen soils is easy to be obtained and therefore has been investigated by a large number of experimental studies. Given a certain soil classification, it has been found that temperature and strain rate are the most important factors influencing UCS of saturated frozen soils. In comparison with the strength of unfrozen soils, it is easy to understand that temperature is the first substantial influencing factor for
Corresponding author. E-mail address: [email protected] (J. Qi).
https://doi.org/10.1016/j.coldregions.2019.102965 Received 8 September 2019; Received in revised form 20 November 2019; Accepted 11 December 2019 Available online 12 December 2019 0165-232X/ © 2019 Elsevier B.V. All rights reserved.
Cold Regions Science and Technology 171 (2020) 102965
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Fig. 1. Frozen soil uniaxial compression testing apparatus.
2. Testing methodology
strength of frozen soils to be considered by scholars. Tsytovich (1975), Haynes and Karalius (1977) and Bourbonnais and Ladanyi (1985) revealed that UCS of frozen clay, silt and sand all increases with the decrease of temperature in a power function. The parameter m of the power function is related to the material and test conditions, within a range roughly between 0.5 and 1.0. When m = 1.0, a linear relationship is then obtained between UCS and temperature, which sometimes performs fairly well (Sayles and Epanchin, 1966; Wu and Ma, 1994). On the other hand, the presence of ice makes frozen soils an obvious rheological material. The strain rate therefore has a great influence on the strength of frozen soils. Sayles and Epanchin (1966), Baker (1979), and Parameswaran (1980) have studied the effect of strain rate on saturated frozen sand. It was generally recognized that UCS of frozen soils increases with the increase of strain rate in an exponential form. Richard and Andersland (1981) considered temperature, strain rate as well as sample size in frozen sand tests. Zhu and Carbee (1984) also considered the effects of temperature and strain rate on saturated Fairbanks frozen silt. Both Zhu and Carbee (1984) and Li et al. (2004) consider the effect of temperature and strain rate on strength. The study objects in the above-mentioned work are frozen sand, silt or clay, relatively fine-grained soils. Few studies have been carried out on gravelly soils. With the extensive development of cold regions and urban underground development, the research needs for the mechanical properties of frozen gravelly soils have been recognized. In recent years, Zhang et al. (2017) conducted triaxial compression on frozen sandy gravels collected from Beijing, and analyzed the characteristics of stress-strain curve and the variation of strength with temperature and confining pressures. Feng et al. (2018) and Liu et al. (2019) studied the mechanical properties of frozen mixed soils with different gravel content. The basic mechanical properties including strength of the materials generally agree with that for relatively frozen fine-grained soils, while the maximum size of gravel particles included in their study objects were 2–4 mm, only a little larger than sand grains. The authors of this paper wonder how the material would behave if the grain size of gravels further increases on the one hand, and gravel content changes on the other hand. Considering the complexity of strength of frozen gravelly soils, this paper starts from simple and controllable conditions, i.e., to carry out uniaxial compression tests on a series of man-made frozen gravelly soils with different gravel content, with the size of gravel grains of up to 20 mm. The variation of UCS of frozen gravelly soils under different combinations of temperature, strain rate and gravel content will be studied.
2.1. Testing apparatus The apparatus used in the test is a self-developed frozen soil uniaxial testing device (Fig. 1). The apparatus consists of a loading system, a temperature control system and a data acquisition system. The loading system applies loads up to 100 kN with a precision of 0.05% of the applied load. It allows several control modes including stress control, strain control and strain rate control, etc. The temperature control system provides a temperature range of - 30 °C to 60 °C, with a temperature control accuracy of ± 0.1 °C. The data is digitally collected by a computer. 2.2. Preparation of frozen soil samples The gravelly soil used for tests was taken from a site of subway station construction in Beijing. Artificial freezing method will be applied in that gravelly soil layer. The grain size distribution curve of the soil is illustrated in Fig. 2 (a). The soil was sieved to obtain sand grains with a particle size range of 0.075–2 mm and gravel grains of 10–20 mm in size. Sand and gravels were then mixed at a certain ratio for sample preparation. Taking gravel as reference, the samples were prepared in four gravel contents of 0% (pure sand), 25%, 72% and 100% (pure gravel). The grain size distribution curves of the four soils are illustrated in Fig. 2 (b). Fig. 3 shows pictures of the mixed soil materials corresponding to the four particle size distribution curves illustrated in Fig. 2 (b). A certain material is compacted layer by layer so as to ensure the uniformity. According to a desired gravel content, certain amounts of sand and gravel are homogenously mixed. A relative density of 0.8 in the whole testing program is used, based on which the sand-gravel mixture is compacted layer by layer in a cylindrical mold to a certain height, and then was slowly immersed in a water vessel and stayed in water for 48 h for saturation. The saturated sample together with the water vessel was placed in a refrigerator with a pre-set temperature of −30 °C for quick freezing and stayed in the refrigerator for 24 h. During the process, the sample was kept in the mold all the time, so that the shape and dimension remained unchanged. After demolding, the frozen sample was quickly covered with plastic film to keep water content unchanged. At last, the sample was kept in the refrigerator at a constant desired temperature for testing. In this way, a cylinder sample was prepared with a diameter of 101 mm and a height of 200 mm. The basic physical indexes for the samples are listed in Table 1. 2
Cold Regions Science and Technology 171 (2020) 102965
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Fig. 2. Grain size distribution curves.
Fig. 3. The pictures of four materials for sampling.
Table 1 The basic physical indexes of the test material. 100% gravel Relative density Dry unit weight/kN·m−3 Water content
0.8 γd, max 16.9 22.7%
72% gravel γd, min 14.2
25% gravel
γd, max 22.2 10.1%
γd, min 16.4
3
γd, max 18.7 16.4%
0% gravel γd, min 16.3
γd, max 17.2 19.6%
γd, min 14.3
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2.3. Testing plan
Table 2 The testing scheme. Gravel contents
Temperature
Strain rate
100% gravel 72% gravel 25% gravel 0% gravel
−5 °C −10 °C −15 °C
10−3 s−1 10−4 s−1 10−5 s−1
The uniaxial compression test was used to investigate the influence of temperature, strain rate as well as especially gravel contents on the UCS of the frozen gravelly soil samples. The testing scheme is listed in Table 2. Before the test, a certain desired temperature was set for the thermostat box on the testing apparatus. A sample was taken out from the
Fig. 4. Stress-strain curves (T denotes test temperature, 4
refers to strain rate.)
Cold Regions Science and Technology 171 (2020) 102965
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Fig. 5. The failure picture of four kinds of gravel samples.
refrigerator and mounted on the device. The desired temperature was kept constant for four more hours so that a homogenous temperature can be reached in the whole sample. The test temperature was controlled at −5 °C, −10 °C, −15 °C, respectively. As can be seen in Table 2 that 3 strain rates of 10−3 s−1, 10−4 s−1, 10−5 s−1 were used. Considering that the samples have a height of 200 mm, it means that the loading speeds are 12 mm/min, 1.2 mm/min, 0.12 mm/min, respectively. UCS was taken as the stress either corresponding to a peak if available, or a strain of 15% on the stress-strain curve according to the Chinese standard for soil test method (Standard for geotechnical testing method GB/T 50123–2019, 2019).
3. Analysis of testing results 3.1. Test results Fig. 4 shows the stress-strain curves of the samples. It can be seen that the stress-strain curves are all strain-softened. Here we take the peak point of the curve as the UCS of the samples. Generally speaking, with the decrease in strain rate the curves reach the peak more gently. Under the same temperature and at the same strain rate, with the increase in gravel content, the curves tend to enclose more area within the same strain range, i.e., the increase in gravel content results in
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Fig. 6. UCS versus temperature for the frozen gravelly soils.
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decrease in the strain energy. Fig. 5 presents failure pictures of samples with four different gravel content under the strain rates of 10−3 s−1. The approximate inclination of the failure surface is in the range of 55° to 58°. It is worth mentioning that pictures with a clear failure surface is not always available. Deep analysis on the failure behaviors needs further additional work.
Table 3 Fitting parameters of two equations.
Exponential
= A (T /T0 )m
Linear
= A + BT
0% gravel
A = 4.39 m = 0.52 R = 0.9936 A = 3.19 m = 0.62 R = 0.9984 A = 2.36 m = 0.68 R = 0.9998 A = 1.70 m = 0.75 R = 0.9789 A = 6.40 B = 0.77 R = 0.9992 A = 4.60 B = 0.83 R = 0.9999 A = 3.25 B = 0.80 R = 0.9996 A = 1.94 B = 0.75 R = 0.9710
A = 2.23 m = 0.64 R = 0.9921 A = 2.23 m = 0.63 R = 0.9918 A = 1.59 m = 0.77 R = 0.9992 A = 2.11 m = 0.50 R = 0.9998 A = 3.20 B = 0.64 R = 0.9975 A = 3.23 B = 0.62 R = 0.9974 A = 1.95 B = 0.72 R = 0.9999 A = 3.06 B = 0.35 R = 0.9984
A = 1.79 m = 0.62 R = 0.9739 A = 1.86 m = 0.60 R = 0.9823 A = 1.16 m = 0.80 R = 0.9998 A = 1.56 m = 0.52 R = 0.9966 A = 2.63 B = 0.47 R = 0.9855 A = 2.72 B = 0.46 R = 0.9919 A = 1.31 B = 0.58 R = 0.9999 A = 2.27 B = 0.28 R = 0.9881
0% gravel 25% gravel 72% gravel 100% gravel
(1)
3.3. Influence of strain rate on UCS The test results show that UCS of the frozen gravelly soil increases with the increase of strain rate. This change tendency is also consistent with that for frozen fine-grained soils. Keeping temperature and gravel content constant, the relationship between UCS and strain rate can be analyzed in the following. A lot of studies have investigated the relationship between the strength, especially UCS of frozen soils and strain rate (Sayles, 1974; Parameswaran, 1980; Richard and Andersland, 1981;). Baker (1979) proposed the simplest but very powerful exponential. relationship as follows:
(2)
where, T is temperature (°C); T0 is a reference temperature, generally taken as −1 °C; A and B are material parameters related with the strain rate; m is a dimensionless parameter. The above two exponential functions are essentially the same, the only difference lies the parameters, especially the exponent m. As was indicated above, when m = 1, Eqs. (1) and (2) become a linear relationship, when strength and temperature can take the form of Eq. (3): m
10−5 s−1
100% gravel
where, σm is the UCS of frozen soil (MPa); A, B and m are test coefficients; T is temperature (°C). Zhu and Carbee (1984) suggested another relationship for a frozen silty clay: m
10−4 s−1
72% gravel
The test results show that UCS of frozen gravelly soil sample increases significantly with the decrease of temperature. The reason for this is that the strength of the ice is increased due to the decrease of the temperature, which enhances the strength of the sample as the consequence (Sayles and Epanchin, 1966; Li et al., 2004). The change tendency and mechanism of UCS are consistent with that for frozen fine-grained soils. In the following, the change of UCS along with temperature will be analyzed with the strain rate and the gravel content remaining constant. Many previous studies have shown that the effect of temperature on UCS of frozen soils can be expressed by an exponential relationship. After examining a large number of different frozen soils at no less than −15 °C, Tsytovich (1975) proposed the following relationship:
= A + B |T|m
10−3 s−1
25% gravel
3.2. Influence of temperature on UCS
m
Strain rate
(3)
m
where, A and B are test coefficients; T is the absolute value of the test temperature. In investigating the effect of temperature on UCS of frozen gravelly soil, we tried the exponential relationship Eq. (2) and the linear relationship of Eq. (3), respectively. The results are illustrated in Fig. 6. The parameters of curve fitting for both forms are listed in Table 3. It can be noticed from Table 3 that parameters for exponential relationship do not make too much sense in terms of strain rate. However, for the linear relationship, parameter B consistently decreases with the decrease in strain rate, which reasonably reflects the change rate of UCS with strain rate. It can be seen that the fitting correlation coefficients of the two forms are greater than 0.97 for all cases, with no significant difference. Relationship between UCS and temperature for frozen gravelly soils is therefore in consistent with that for fine-grained soils, while the linear formula can be taken.
=A
b
(4)
where, is the strain rate; A and b are material coefficients. In this work, Eq. (4) is used to fit the experimental data of UCS at certain temperatures, as shown in Fig. 7. It can be noticed from Fig. 7 that under double logarithmic coordinates, UCS increases linearly with the increase of the strain rate. Table 4 lists the fitting parameters, where it can be noticed that the curve slope b does not change obviously with temperature, while parameter A increases with the decrease of temperature. In other words, the curves are almost parallel with different intercept under different temperature. The above fitting has very high correlation efficient, which implies fairly good fitting abilities of the previously proposed relationships. However, the parameters do not have correlation with gravel contents, which will be analyzed in the following subsection.
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Fig. 7. UCS with different temperatures vs. strain rate at various gravel content.
significantly. When the sample has a gravel content of 0%, it is in fact a frozen sand. This kind of sample has the high water content and the largest specific surface area. Both ice bonding and interaction between sand particles and ice crystals are the greatest. As a result, UCS of this sample is the greatest at any temperature and strain rate as can be noticed in Fig. 4 and Fig. 8. As the gravel content increases to 25% and 72%, water content decreases, as can be seen in Table 1. When the samples are frozen, ice content decreases correspondingly in comparison with the frozen sand sample with 0% gravel content, and the ice bonding decreases as well (Liu et al., 2019). At the same time, inclusion of gravels weakens the ice-sand system in terms of mechanical performance. At a large strain rate of 10−3 s−1, UCS decreases almost linearly with the increase in gravel contents, as is indicated in Figs. 4 (a), (d), (g) and Fig. 8 (a). However, at relatively small strain rates of 10−4 s−1and 10−5 s−1, when the sand-ice system breaks, the gravel has certain time to take over some load. Due to its greater angle of internal friction than sand, the gravel skeleton can compensate the weakness it brings into the sample to some extent. Therefore, UCS of these samples is almost the same as that of the sample with 0% gravel content, as can be noticed in Figs. 4 (e), (f), (h), (i) and Figs. 8 (b) and (c). For samples containing 100% gravel, there is no sand-ice interaction, and the gravel contacts each other to form a stable skeleton. Due to the irregular shape of the gravel and the small contact area between the gravel, the corresponding stress of the gravel increases, and the particle breakage becomes easier
Table 4 Fitting parameter of the exponential function.
−5 °C −10 °C −15 °C
0% gravel
25% gravel
72% gravel
100% gravel
A = 30.46 b = 0.16 R = 0.9858 A = 40.68 b = 0.16 R = 0.9979 A = 44.13 b = 0.13 R = 0.9984
A = 19.96 b = 0.12 R = 0.9955 A = 32.76 b = 0.14 R = 0.9984 A = 39.20 b = 0.12 R = 0.9994
A = 15.89 b = 0.11 R = 0.9998 A = 22.42 b = 0.10 R = 0.9997 A = 27.85 b = 0.09 R = 0.9959
A = 8.90 b = 0.08 R = 0.9506 A = 30.94 b = 0.16 R = 0.9841 A = 37.23 b = 0.16 R = 0.9908
3.4. Influence of gravel content on UCS Keeping temperature and strain rate unchanged, the variation of UCS of samples with different gravel content is illustrated in Fig. 8. It can be seen that UCS generally decreases with the increase of gravel content. The greater the strain rate is, the more obvious is this tendency. In Fig. 8 (a) for instance where the strain rate is 10−3 s−1, UCS decreases significantly with the increase of gravel content; while in Fig. 8 (b) and (c) where strain rates are 10−4 s−1 and 10−5 s−1, respectively, UCS for samples with 0%, 25% and 72% gravel remains basically unchanged. For the samples with 100% gravel, UCS drops 8
Cold Regions Science and Technology 171 (2020) 102965
J. Zhao, et al.
Fig. 8. UCS versus gravel content at different strain rate.
during the compression process (Guo, 1987; Cai et al., 2016). Since the gravel has a small specific surface area, the interaction between the gravel particles and the ice is the weakest, further aggravating the development of the fracture. As a result, the UCS of the frozen gravel drops sharply, as can be noticed in Fig. 4 and Figs. 8 (b) and (c).
double logarithmic coordinates, UCS increases linearly with the increase in strain rate. An exponential relationship can fit the experimental results fairly well. (4) Gravel content plays another role in UCS. Test results show that UCS decrease significantly with the increase of gravel content at a high strain rate of 10−3 s−1. At relatively low strain rates however, influence of gravel content on UCS is complicatedly related to strain rate. The mechanism of influence of gravel content on UCS is proposed for the gravel-ice-sand system considering in terms of strain rate and ice content.
4. Conclusions This work investigated the UCS of frozen gravelly soils of 4 different gravel contents using uniaxial compression test under 3 different temperatures and 3 different strain rates. The following conclusions can be reached:
The findings in this work applies for frozen sand with different contents of gravel at a grain size range of 10–20 mm. Mechanical properties of frozen gravely soils with larger grains are yet to be further investigated.
(1) Stress-strain curves of all the 36 test combinations present a strain softening manner. Under the same temperature and at the same strain rate, the increase in gravel content results in decrease in the strain energy. Pictures of samples after failure approximately present an inclination of 55° to 58°. (2) Temperature plays the most important role in the UCS of the tested frozen soil. An exponential relationship and a linear relationship were tried to fit the relationship between UCS and temperature. Considering the appropriate accuracy and simplicity, it is recommended that a linear relationship can be used to describe the relationship between UCS and temperature. (3) The UCS of the tested frozen soil is affected by the strain rate under the same temperature. With the strain rate in a range of 10−5 s−1 to 10−3 s−1, UCS increases with the increase of strain rate. Under
Declaration of Competing Interest On behalf of all authors, the corresponding author states that there is no conflict of interest. Acknowledgements This work was financially supported in part by the National Natural Science Foundation of China (Nos. 41972279, 41902284 and 51908023), and the Joint Key Project of BNSFC and BMEC (No. KZ201810016020). 9
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