Recent progress in research on the dynamic response of frozen soil

Transcription

1 Recent progress in research on the dynamic response of frozen soil Permafrost, Phillips, Springman & Arenson (eds) 2003 Swets & Zeitlinger, Lisse, ISBN S.P. Zhao, Y.L. Zhu & P. He State Key Laboratory of Frozen Soil Engineering, CAREERI, CAS, Lanzhou, Gansu, China ABSTRACT: Determining the dynamic response of frozen soil is important for the study of the deformation, strength and stability of frozen soil under dynamic loading conditions for engineering design in cold regions. This paper discusses the recent progress in research on the dynamic response of frozen soil from the following three aspects: (1) influence of various testing conditions (confining pressure, temperature, water content, frequency, strain amplitude and maximum load) on dynamic properties (dynamic elastic modulus, dynamic shear modulus and damping ratio), (2) dynamic stress-strain properties and the influence of various testing conditions on dynamic strength, (3) effect of testing conditions on dynamic creep factors (time to failure, failure strain and minimum strain rate) and the dynamic creep models. 1 INTRODUCTION Frozen soil dynamics links the subjects of dynamics and frozen soil mechanics, to study mainly the deformation, strength and stability of frozen soil under dynamic loading condition for engineering design in cold regions (Zhu et al. 1995a, 1996). There are a series of developments in research on the dynamic properties of frozen soil as well as in engineering practice in recent years. In this paper, the main progress and achievements in frozen soil dynamics are reviewed, including investigations into dynamic parameters of frozen soil, dynamic stress-strain properties and dynamic strength and creep characteristics. 2 DYNAMIC PARAMETERS 2.1 Measurement technique The dynamic parameters of frozen soil consist of dynamic elastic modulus, dynamic shear modulus and damping ratio. They can be measured or evaluated in the laboratory through the cyclic triaxial test, the resonant-column test and ultrasonic testing. The cyclic triaxial method is associated with low frequencies and high strain amplitudes, which can simulate earthquake loading conditions. This test method is favored by many researchers. When confining pressure equals zero, it is called a uniaxial test. The loading methods include application of a constant amplitude stress and a constant amplitude strainrate, which are named creep tests and strength tests, respectively. The former method is to apply a cyclic axial load varying as sine wave, furthermore, the load amplitude will be kept constant: Pmin 0, Pmax constant, Pmax (1) Pd 1 sin 2 p 2 T where P min and P max represent the minimum and maximum value of applied load respectively, P d represents the variational load and T represents time. The latter method is to make the maximum and minimum strain increase at the same rate, and keep the amplitude of strain stable. The resonant-column test is a non-destructive test method, which is associated with relatively high frequencies and low strain amplitudes of loading. One should apply longitudinal or torsional vibratory load to a cylindrical frozen soil specimen and then increase the vibratory frequency to the resonant frequency of the sample. As a result, the dynamic elastic modulus E d and shear modulus G d can be calculated on the basis of resonant frequency, sample size and boundary condition: E d (2) where f n is the resonant frequency, H is the height of the sample, b L and b S are roots of equations: b L tan b L W/W 0 and b s tan b s I/I 0 in which W and W 0 are the weight of the sample and the mass block, while I and I 0 are the inertia moment of the sample and the mass block. The damping ratio can be obtained by the free vibratory method. When an initial angle displacement is applied, then liberated abruptly, the sample appears to be under a free vibratory condition. The calculation formula of the damping ratio 1 is: h 2pfH n 2pfH n r Gd r b, b L 1 A ln 2pm A N N m 2 2 where A N and A N m represent the amplitudes of the Nth and (N m)th loading cycles, respectively, if we s 1301

2 rank the loading cycles as one, two, three,..., N,..., (N+m),... The ultrasonic test is also a non-destructive test method, which is associated with relatively high frequencies and low strain amplitudes of loading. One should simulate the earthquake wave propagation in soil, then record the longitude and shear wave velocity, and calculate the dynamic elastic and shear modulus. E d rvs ( 3Vl 4Vs ) G 2 2, d V V (4) where V l is the longitudinal wave velocity, V s is the shear wave velocity, r is the density of sample. 2.2 Dynamic modulus l s rv Various test results show that the dynamic properties of frozen soil are influenced by confining pressure, temperature, frequency, strain amplitude and water content. The conclusions that have been accepted by almost all researchers can be stated as follows: (1) Variation of dynamic elastic modulus and shear modulus complies with a similar law. (2) The values of dynamic elastic modulus vary with the state of frozen soil. The dynamic elastic modulus of frozen soil is approximately two orders of magnitude, or more, greater than that of unfrozen soil. (3) The dynamic modulus of coarse-grained soil is higher than that of fine-grained soil (Vinson 1978, Wang et al. 2002). (4) The dynamic modulus of frozen soil increases with decreasing temperature and increasing frequency, and descends with ascending strain amplitude (Vinson 1978, Vinson et al. 1983, He et al. 1993, 1994, Shen & Zhang 1995, Xu & Zhong 1998, Wang et al. 2002). There are some other conclusions obtained from a particular type of test method or soil. (1) The influence of frequency and strain amplitude on E d in the high frequency range associated with the resonant column test is more obvious than that in the low frequency range associated with triaxial test (Vinson 1978). (2) Vinson et al. (1983) drew the following conclusions based on cyclic dynamic triaxial results. At 4 C and 10 C, the dynamic modulus appears to decrease with increasing water content, while the dynamic modulus may increase slightly with increasing water content at 1 C. In other words, the influence of water content at warmer temperature within the frozen range is negligible. Wang et al. (2002) reach the following conclusions based 2 s on ultrasonic test results. Both dynamic elastic modulus and shear modulus of frozen silt increase with increasing water content in the lower water content range. However, the dynamic modulus of frozen clay decreases with increasing water content at a higher water content range. The values of E d of frozen soil are influenced by temperature, soil type and water content range. A perfect water content may exist, with which the dynamic modulus of frozen soil reaches the maximum value. (3) Vinson (1978) concluded that for some finegrained soil, such as Alaska silt, Hanover silt and Ontonagon clay, there is no significant change in dynamic modulus over the range of confining pressure from 0 to 1.4 MPa, while there is a significant increase in modulus with increasing confining pressure for the coarse-grained soil, such as Ottawa sand. Subsequently, in 1983, he found that the E d of frozen silt slightly decreases with increasing confining pressure from 0 to 0.5 MPa. According to the information obtained from triaxial tests on frozen silt, Shen & Zhang (1997b) concluded that when confining pressure s 3 changes from 0 to 10 MPa, there is a critical confining pressure s 3c corresponding to the maximum elastic modulus. That is, the dynamic elastic modulus increases with increasing confining pressure, as s 3 s 3c, whereas E d decreases with increasing confining pressure, as s 3 s 3c. The reason for the difference between Vinson s and Shen s conclusions may be that the range of confining pressure used by Vinson is much lower than that of Shen. More tests should be conducted on frozen soil by all of the methods described herein to examine the influence of confining pressure on dynamic modulus. 2.3 Damping ratio l Since the factors that affect E d often influence damping ratio, too, when the value of E d is higher, the value of l is higher as well (Vinson 1978). The damping ratio of frozen soil decreases with decreasing temperature and increasing frequency (Vinson 1978, Xu & Zhong 1998). The decrease in damping ratio with reducing temperature may be a function of both the increase in the strength of ice and the decrease in unfrozen water content with reducing temperature. Under the dynamic loading condition, the sliding between ice and soil particles causes creep effect, which can decrease the damping ratio. When frequency becomes higher, the creep effects will be more obvious, so damping ratio decreases. The value of l vary, but not follow certain law, when water content and confining pressure change. Damping ratio appears to increase slightly with increasing water content and confining pressure (Vinson et al. 1302

3 1983). For fine-grained soils, such as silt and clay, there is an increase in l with increasing axial strain amplitude. The damping ratio decreases with increasing axial strain amplitude for the coarse-grained soils, such as frozen sand (Vinson 1978). 3 DYNAMIC STRESS-STRAIN PROPERTIES AND DYNAMIC STRENGTH OF FROZEN SOIL 3.1. Dynamic stress-strain properties The dynamic stress-strain relationship represents the dynamic characteristics of frozen soil, which is the significant foundation for studying dynamic stability of frozen ground. Because of the rheology of frozen soil, even under static loading condition, a unified equation, such as s A n, cannot be used to express the relationship between strain and stress. Zhu et al. (1992) developed nine types of stress-strain equation associated with various soil types, water content, strain rate and temperature. According to the creep test result, Cai & Zhu (1990) presented viscoelastic and viscoplastic constitutive model, which can describe damping creep and non-damping creep respectively of frozen soil. He et al. (1999) developed a viscoelastic and plastic damage constitutive model of frozen soil based on theoretical analysis. When the dynamic stress-strain behavior of frozen soil was described, usually elastic relationships were employed. Using linear viscoelastic theory, Stevens (1973) computed the mechanical parameters of frozen soil based on the result of subjecting a cylindrical sample to steady-state vibration. However, until now, there has been no systematic research on the dynamic constitutive model of frozen soil. Only some empirical models have been proposed based on statistical analysis of test data, such as the following strength and creep models. 3.2 Dynamic strength In constant strain rate dynamic triaxial or uniaxial tests, the peak value of stress is defined as the dynamic strength. Shen (1996) and Shen & Zhang (1996, 1997a, 1998) have done a lot of research in this field and have drawn the following conclusions. (1) The dynamic strength of frozen soil under triaxial loading condition is greater than that under uniaxial loading condition. (2) The frequency has little influence on dynamic strength. (3) The dynamic load results in rate-effects and cyclicaleffects. The former is caused by applying load on sample at very high speed over short durations. Because frozen soil can resist transient deformation better, rate-effects will improve the strength of frozen soil. The latter is caused by applying cyclic load repeatedly for a long period of time. These cyclic-effects will weaken the strength of frozen soil because of the creep characteristics. Information from triaxial tests as well as uniaxial tests indicates that there is a critical strain rate. c. When.. c, the dynamic strength is equal to the static strength. Failure strain under dynamic loading is similar to that under static loading. Frequency nearly has no influence on dynamic strength. If.. c, the rate-effect is predominant, so that the strength and failure strain under dynamic load conditions is greater than that under static load conditions. Dynamic strength decreases slightly with increasing frequency. On the contrary, as.. c, the cyclic-effect is predominant, so that the strength and failure strain under dynamic conditions is less than that under static conditions. Dynamic strength increases slightly with increasing frequency. (4) There is a critical confining pressure s 3c. When s 3 s 3c, the dynamic strength increases with increasing confining pressure, and the tendency is inverse as s 3 > s 3c. The confining pressure influences the dynamic response in two ways. On the one hand, the confining pressure tends to reduce the porosity and to close micro-cracks, which causes the strength of the frozen soil to increase. This is called the strengthening-effect. On the other hand, confining pressure makes the freezing temperature of frozen soil lower. Under the same experimental temperature conditions, the higher the confining pressure, the more difficult it will be for the soil to remain frozen because the bonds become weaker. Furthermore, the increased confining pressure encourages the unfrozen water in the frozen soil to flow easier. The flowing of unfrozen water leads to connections between the pore channels and an increase in local pore pressure, which reduces the effective stress and weakens the frictional resistance between soil particles, so that the strength of the frozen soil will decrease. This is called the weakening effect. When s 3 s 3c, the strengthening effect is predominant, and dynamic strength increases with increasing confining pressure. Whereas, when s 3 s 3c, the weakening effect is predominant, and dynamic strength decreases with increasing confining pressure. (5) A dynamic uniaxial strength model is proposed as follows: s dp n & 0 k f C (5) 1303

4 where s dp is the dynamic strength,. 0 is the critical strain rate, f is the frequency of the load, and k, n and C are experimental parameters. (6) A failure criterion for the dynamic shear strength s is recommended. t C 0 s s tan w e (6) where w e is equivalent internal angle of friction, which is a dynamic variable value varying with temperature, strain rate, frequency, etc. and C 0 is the cohesion. The dynamic strength tests were only conducted on frozen silt, and it is necessary to conduct the dynamic strength tests on other types of soil. 4 DYNAMIC CREEP PROPERTIES OF FROZEN SOIL 4.1 Dynamic creep model The static creep models usually adopted by researchers are the primary creep model (Vyalov & Gorodetsky 1965): A 0 s m t l (7) the engineering creep model (Ladanyi 1972): i & f( s) t and a tertiary creep model (Ting 1983): & (8) (9) Gardner et al. (1984) developed a new creep equation for frozen soil and ice, which gives a better estimate of both creep strain and strain rate for the whole of the creep curve than before: C m m At 0 exp(b t) 0 t c c t tm 1 t exp ( 1/2 )( / ) (10) Where C is the creep strain, 0 is the initial strain and m is the failure strain, t m is the time to failure, and c is a dimensionless parameter describing the shape of the creep curve. Benefiting from these static creep models and considering the specialties of dynamic load, He (1992) presented a dynamic creep equation that expressed the first and second creep stages: A Bs 13 / C Dln smin max m ee ( t t) E ln s F ln f m max C (11) where max is the maximum applied stress, m is the strain corresponding to max, min is the minimum applied stress, f is the frequency, t is the loading time, and A, B, C, D, E and F are parameters. Analyzing the triaxial creep test results of frozen silt under cyclic loading, Zhu et al. (1998) presented the corresponding creep model: A 1 A 2 t A 3 t 1/3 (12) where t is the elapsed time, A 1, A 2, and A 3 are parameters dependent upon confining pressure and temperature. This model can describe the creep process of frozen silt under axial cyclic loading and a confining pressure accurately before failure. 4.2 Creep failure characteristic and dynamic creep strength Because of the rheology of frozen soil, it will undergo damage after some time under constant amplitude dynamic loading. The turning point on the creep curves, where the strain rate reaches its minimum value and strain changes from a steady creep stage to a gradually flowing creep stage, indicates the beginning of the destruction of the frozen soil matrix. The corresponding strain, elapsed time and strain rate to this point are called failure strain, time to failure and minimum creep rate, respectively, representing three creep factors. The characteristics of creep failure are usually described by the three creep factors. The test results show that maximum applied stress, temperature and frequency all have an influence on the three creep factors (He et al. 1995, Zhu et al. 1995b, Zhao et al. 2002). (1) The lower the temperature, the smaller the failure strain, the longer the time to failure and the slower the minimum creep rate will be. (2) Frequency has little influence on failure strain, time to failure and minimum creep rate. (3) When the applied stress increases, failure strain increases as well, time to failure shorten and minimum creep rate will be greater. (4) The failure strain of frozen silt is independent of confining pressure, and the average value is about half of that under static loading under similar test conditions. Time to failure and minimum creep rate depend on confining pressure. There is a critical confining pressure s 3 s 3c, for which the time to failure is longest and the minimum creep rate is lowest. The trends for time to failure and minimum creep rate are inverted when s 3 s 3c changes to s 3 s 3c. Similar to the creep strength under static loading conditions, the dynamic creep strength of frozen soil is also influenced by temperature and time to failure. For the same time to failure, dynamic creep strength will 1304

5 be greater as the temperature reduces. When the temperature is constant, time to failure decreases with increasing creep stress. From the triaxial and uniaxial test results, He (1992) presented a dynamic uniaxial creep strength model: s f (13) where f is the frequency of loading, t f is the time to failure, B 1, B 2, B 3 and B 4 are parameters dependent upon temperature. Li et al. (2000) developed a dynamic triaxial creep strength model: s f 2 B B f B f B ln(1 t M log( t ) N (14) where t f represents the time to failure, M and N are the parameters concerning the test conditions such as temperature, confining pressure and frequency. They also found that a critical confining pressure s 3c exists, where the dynamic creep strength reaches its maximum value. 5 OTHER ASPECTS f 12 / f In recent years, extensive research on model tests and in-situ tests have been carried out. Dufour et al. (1983) reveal the dominant mechanism for model piles vibrated into permafrost, and study the factors that influence the pile penetration rate. Zhang et al. (1996, 1998) conducted many tests on model piles in frozen soil under dynamic loading. From the tests results, they found that: (1) If the temperature decreases, settlement rate of the piles decreases as well and adfreeze strength increases. (2) Under the same experimental conditions in terms of temperature and frequency, when the initial water content of a frozen soil increases, unfrozen water content changes a little, and the ice content increases accordingly, which leads to an increase in the ice cementation between pile and frozen soil, so that the adfreeze strength increases and the settlement rate of the piles decreases. In a saturated frozen soil, the adfreeze strength reaches its maximum value and the settlement rate of the piles reaches its minimum value. (3) The greater the roughness of the model pile surface, the lower the settlement rate and the higher the adfreeze strength will be. (4) For the range of frequency tested ( f 1 9 Hz), the settlement rate of the model piles does not vary with the frequency of the dynamic loads, but 4 ) the adfreeze strength decreases with increasing frequency. The in-situ sonic wave test results (Zhang et al. 2000) indicate that the wave velocities in frozen soils are greater than those in unfrozen soil, because of the cementation caused by the ice in a frozen soil. The wave velocity increases with decreasing temperature, which may be due to the increase in ice and the decrease in unfrozen water content with lower temperatures. The wave velocity also increases with increasing density. Yang & Li (1997) studied the relationship between mechanical properties of frozen soil and sonic parameters, and concluded that the dynamic strength and dynamic modulus of frozen soils change in the positive sense with longitudinal and shear wave velocity, which indicates that using sonic tests to obtain strength and modulus of frozen soil is feasible. 6 CONCLUSIONS The laboratory dynamic test techniques seem to be improving, and many test results have been published, concerning dynamic parameters, dynamic strength and dynamic creep. However, because of the complexity of frozen soil structure and dynamic loading, it is difficult to determine the dynamic constitutive properties of frozen soil. More research should be carried out in the following fields by studying the structural changes in frozen soil under dynamic loading, to link this to a dynamic constitutive model. More in-situ tests should be conducted, so that the benefits of research into the dynamic response of frozen soil can be transferred to engineering practice. For example, Ladanyi & Paquin (1978) study the creep behavior of frozen sand under a deep circular load through the results of triaxial compression tests and in-situ stage-loaded penetration tests, as well as through a comparison between the test results and theoretical predictions. Model tests have the advantage of linking laboratory test results with engineering needs. We should combine laboratory tests, in-situ tests and model tests with engineering tests, then develop theories for dynamic response of frozen soil and improve the ability of building construction in cold regions. REFERENCES Cai, Z.M. & Zhu, Y.L Viscoelastic and plastic constitute model of frozen soil and determination of material parameters. Journal of Glaciology and Geocryology 12(1): Dufour, S., Sego, D.C. & Morgenstern, N.R Vibratory model pile driving in frozen sand. In Proceedings of Fourth International Conference on 1305

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