EFFECT OF TEMPERATURE AND STRAIN RATE ON THE …
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Introduction The constitutive relation of a material is the stress- strain relationship of the material considering the effects of the strain rate, or the elapsed time during loading. The constitutive relation is an element of the basic mechanical behavior of frozen soil and is very important for both the design of structural foundations on, or in, frozen ground, and theoretical investigations of frozen soil mechanics. Therefore, various researchers have carried out many experimental and theoretical investigations and have presented different forms of the constitutive relations of frozen soils (Vialov, 1962; Fish, 1980; Ting, 1981; Zhu et al., 1987; Cai et al., 1990; Zhu et al., 1991). It should be mentioned that Zhu et al. (1991), in particular, presented a constitutive relations map of frozen soil in uniaxial compression, based on many test results. This summarized the typical constitutive rela- tions for various types of frozen soils, with different water contents, and at different temperatures and strain rates. However, the effects of temperature and strain rates on the constitutive relations of frozen soil that are the focus of the present paper were not quantitatively analyzed in the earlier one. Test conditions Constant strain-rate uniaxial compression tests were conducted on frozen saturated silt (Lanzhou loess) at various temperatures and strain rates. The average water content and dry density of the tested specimens were 24.5% and 1.58 g/cm 3 , respectively. The prepara- tion of the specimens was described in detail by Zhu and Carbee (1987). Test results and discussion The test results, including the yield stress ( s y ), peak strength ( s m ) and failure strain ( e f ), together with the test temperature ( q ) and strain rate ( ), are summarized in Table 1. Several typical stress-strain curves for the tested samples are shown in Figures 1, 2, 3 and 4. It can be seen from the four figures that there is an obvious elastic yield point on all of the ( s e ) curves under the test conditions. The stress and strain corre- sponding to the yield point are defined as the yield stress ( s y ) and yield strain ( e y ), respectively. Based on regression analyses of the test data shown in Table 1, the yield stress, as a function of temperature and strain rate, can be expressed as [1] where ( s y ) is in MPa, is in s -1 , q is the negative temperature (…C) of the frozen soil, and q o = -1¡C is a reference temperature. e • e • Abstract Uniaxial constant strain-rate compression tests were conducted on frozen, saturated silt (Lanzhou loess) at various strain rates and temperatures. The average water content and dry density of the specimens were 24.5% and 1.58 g/cm 3 , respectively. It was found from the test results that the yield strain of the samples was inde- pendent of the strain rate, and that the yield stress varies with temperature and strain rates. Based on regres- sion analyses of the test data, the constitutive relation in uniaxial compression of the frozen, saturated silt is presented, and the effects of temperature and strain rates on the constitutive relation are quantitatively dis- cussed. Zhu Yuanlin, et al. 1235 EFFECT OF TEMPERATURE AND STRAIN RATE ON THE CONSTITUTIVE RELATION OF FROZEN SATURATED SILT Zhu Yuanlin, He Ping, Zhang Jiayi, Zhang Jianming State Key Laboratory of Frozen Soil Engineering, Lanzhou Institute of Glaciology and Geocryology, Chinese Academy of Sciences, Lanzhou, 730000, China e-mail: ZHUYL @ ns. lzb. ac. cn s e q q = L l 1 123 0 089 0 0 887 . ˙ . .
Transcript of EFFECT OF TEMPERATURE AND STRAIN RATE ON THE …
Introduction
The constitutive relation of a material is the stress-strain relationship of the material considering theeffects of the strain rate, or the elapsed time duringloading. The constitutive relation is an element of thebasic mechanical behavior of frozen soil and is veryimportant for both the design of structural foundationson, or in, frozen ground, and theoretical investigationsof frozen soil mechanics. Therefore, various researchershave carried out many experimental and theoreticalinvestigations and have presented different forms of theconstitutive relations of frozen soils (Vialov, 1962; Fish,1980; Ting, 1981; Zhu et al., 1987; Cai et al., 1990; Zhu etal., 1991). It should be mentioned that Zhu et al. (1991),in particular, presented a constitutive relations map offrozen soil in uniaxial compression, based on many testresults. This summarized the typical constitutive rela-tions for various types of frozen soils, with differentwater contents, and at different temperatures and strainrates. However, the effects of temperature and strainrates on the constitutive relations of frozen soil that arethe focus of the present paper were not quantitativelyanalyzed in the earlier one.
Test conditions
Constant strain-rate uniaxial compression tests wereconducted on frozen saturated silt (Lanzhou loess) atvarious temperatures and strain rates. The averagewater content and dry density of the tested specimens
were 24.5% and 1.58 g/cm3, respectively. The prepara-tion of the specimens was described in detail by Zhu and Carbee (1987).
Test results and discussion
The test results, including the yield stress ( sy ), peakstrength ( sm ) and failure strain ( ef ), together with
the test temperature ( q ) and strain rate ( ), aresummarized in Table 1. Several typical stress-straincurves for the tested samples are shown in Figures 1, 2,3 and 4.
It can be seen from the four figures that there is anobvious elastic yield point on all of the ( s Ñ e ) curvesunder the test conditions. The stress and strain corre-sponding to the yield point are defined as the yieldstress ( sy ) and yield strain ( ey ), respectively. Basedon regression analyses of the test data shown in Table 1,the yield stress, as a function of temperature and strainrate, can be expressed as
[1]
where ( sy ) is in MPa, is in s-1, q is the negativetemperature (¼C) of the frozen soil, and qo = -1¡C is areference temperature.
e·
e·
Abstract
Uniaxial constant strain-rate compression tests were conducted on frozen, saturated silt (Lanzhou loess) atvarious strain rates and temperatures. The average water content and dry density of the specimens were 24.5%and 1.58 g/cm3, respectively. It was found from the test results that the yield strain of the samples was inde-pendent of the strain rate, and that the yield stress varies with temperature and strain rates. Based on regres-sion analyses of the test data, the constitutive relation in uniaxial compression of the frozen, saturated silt ispresented, and the effects of temperature and strain rates on the constitutive relation are quantitatively dis-cussed.
Zhu Yuanlin, et al. 1235
EFFECT OF TEMPERATURE AND STRAIN RATE ON THE CONSTITUTIVERELATION OF FROZEN SATURATED SILT
Zhu Yuanlin, He Ping, Zhang Jiayi, Zhang Jianming
State Key Laboratory of Frozen Soil Engineering, Lanzhou Institute of Glaciology and Geocryology, Chinese Academy of Sciences, Lanzhou, 730000, China
e-mail: ZHUYL @ ns. lzb. ac. cn
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Figure 1. Stress-strain curves of frozen silt in uniaxial compression at Ð2¡C.
Figure 2. Stress-strain curves of frozen silt in uniaxial compression at Ð5¡C.
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Figure 3. Stress-strain curves of frozen silt in uniaxial compression at Ð10¡C.
Figure 4. Stress-strain curves of frozen silt in uniaxial compression at Ð15¡C.
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Table 1. Test results of uniaxial compression on frozen Lanzhou silt
Based on the pattern of the curves shown in Figures 1-4, the s Ñ e relationship for the saturated frozen siltcan be described by
[2]
where ey is the yield strain, which is independent ofthe strain rate and has an average value of 1.2% whenq>-5¼C, and 1.6% when q<-5¡C and m is the hardeningcoefficient. Obviously, m = 1 when e£ey and m<1 when
e>ey according to the shape of the s Ñ e curves shown.
The values of m, calculated from the test data for eachspecimen, also are listed in Table 1. The variation of m,with temperature and strain rate, can be described bythe following equation based on regression analyses:
[3]
Substituting equation (1) into equation (2), we obtainthe following constitutive relation of the frozen satura-ted silt under the test conditions:
where [4]
This equation can accurately predict the stress-strainrelationship of the frozen, saturated silt in uniaxial com-pression under the ranges of test temperatures andstrain rates. The s Ñ e curves predicted by equation (4)also are shown in Figures 1, 2, 3, and 4, and agree wellwith the test results.
Conclusions
It can be concluded from the test results that:
(1) There exists an obvious elastic yield point on thestress-strain curves of the frozen, saturated silt under acertain range of temperatures and strain rates. The yieldstrain is independent of the strain rate and has a valueof 1.2% when q>-5¼C, and 1.6% when q<-5¼C, while theyield stress varies with the temperature and strainrates.
(2) The constitutive relation of frozen saturated silt inuniaxial compression can be well described by equation (4).
Acknowledgments
The authors would like to express their thanks to Dr.Max C. Brewer for his preliminary review of this paper.Thanks also are given to Shen Zhongyan, PengWanwei, Chang Xiaoxiao, Pan Fengzhen and the staffmembers of the Instrumentation and RefrigerationGroup of our Laboratory for their support. This projectwas supported by the Natural National ScienceFoundation of China.
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References
Cai Zhongmin, Zhu Yuanlin and Zhang Changqing (1990).Viscoelastic-plastic constitutive model of frozen soil anddetermination of its parameters. Journal of Glaciology andGeocryology, 12, 31-40.
Fish, A.M. (1980). Kinetic nature of the long-term strength offrozen soil. In Proceedings of the 2nd International Symposiumon Ground Freezing. Trondheim, Norwegian Institute ofTechnology, pp. 95-108.
Ting, J.M. (1981). The creep of frozen sands: qualitative andquantitative models (Final Report Part ). USA CRRELResearch Report, R81-5.
Vialov, S.S. (1962). Strength and creep behaviour of frozensoils and calculations in ice-rich retaining structures. USACRREL Translation, 76, AD 484093.
Zhu Yuanlin and Carbee, D. (1987). Creep and strengthbehaviour of frozen silt in uniaxial compression. USACRREL Report, 87-10.
Zhu Yuanlin, Zhang Jiayi, Peng Wanwei, Sheng Zhongyanand Miao Lina (1991). Constitutive relations of frozen soilin uniaxial compression. In Proceeding of the 6thInternational Symposium on Ground Freezing, Beijing, China,pp. 211-216.
