Creep of frozen soils

Transcription

1 Merger No Creep of frozen soils Prof. Jilin Qi State Key Lab of Frozen Soil Engineering Cold & Arid Regions Env. & Eng. Res. Institute Chinese Academy of Sciences

2 Vienna: For the extension of the underground line U2 from the first to the second district of Vienna, the underground station Schottenring is constructed with low overburden right beneath the Danube channel. Because of the low overburden, artificial ground freezing was employed as temporary support and sealing device. ( Copenhagen: A pedestrian passage from a new metro station to an existing railway station was constructed underground. Since the existing rail traffic had to continue, the ground was frozen to avoid the risk of collapse due to excavation of the transfer tunnel. Artificial Ground Freezing Widely used in Europe Berlin: unter den Linden Metro Station (2006) The Netherlands: Artificial Ground Freezing at Sophiaspoortunnel Soft clay: supporting during excavation; diaphragm wall

3 Permafrost distribution Climate Temperature Precipitation Wind speed etc. Environment Vegetation Geography Water supply etc. Svalbard Altitude Delft Latitude Geographical Conditions

4 Permafrost table and Active layer Active layer: depth ranging from tens cm to several metres Active layer Permafrost table Colder regions Warmer regions From Andersland and Ladanyi (1999)

5 AGENDA Factors influencing creep of frozen soils Creep of Warm Frozen Soils: Field Observations State of The Art: Creep Models for Frozen Soils Our attempts on constitutive modeling Concluding Remarks

6 AGENDA Factors influencing creep of frozen soils Creep of Warm Frozen Soils State of The Art: Creep Models for Frozen Soils Our attempts on constitutive modeling Concluding Remarks

7 CREEP CURVES FOR FROZEN SOILS TYPICAL creep curves for frozen soil (Ting 1983) d m Strain rate vs. time t f Strain vs. time Frozen soil displays features very similar to that of unfrozen soil

8 STRESS DEPENDENCE From Wu and Ma =0.5 MPa Temperature MPa 2.5 MPa 4.5 MPa -5 o C Time/min Uniaxial compression Frozen Lanzhou sand Triaxial compression Frozen ISO Standard sand Both very much stress dependent.

9 STRAIN RATE DEPENDENCE Under the same temperature, stress increases with strain rate. -2 o C From Zhu and Carbee (1984)

10 THERMAL DEPENDENCE d m vs. stress Creep strain /% From Wu and Ma o C -5 o C MPa -10 o C t f vs. stress Time / h Temperature plays a role similar to load Minimal strain rate and time to failure all dependent on temperature

11 DEPENDENT ON TOTAL WATER CONTENT* d m /mm.h -1 Water content / % o C, 1.4 MPa; o C, 2.2 MPa; o C, 3.4 MPa From Wu and Ma Generally, different water content range, different minimal strain rate development for frozen silty clay (samples from Lanzhou, China) * Total water content: ice is counted as water together with unfrozen water

12 SOLUTE DEPENDENCE Solute (Nixon and Lem 1984): The higher solute content, the larger axial strain under a certain stress level. 3-4

13 TEMPERATURE & SOLUTE CHANGE UNFROZEN WATER CONTENT Unfrozen water content plays important roles in mechanical properties of frozen soils Warm Frozen Soils T m

14 AGENDA Factors influencing creep of frozen soils Creep of Warm Frozen Soils State of The Art: Creep Models for Frozen Soils Our attempts on constitutive modeling Concluding Remarks

15 DEFINE WARM FROZEN SOIL (Qi and Zhang, 2008) Shields et al. (1985): -2.5 and -3.0 C. Foster et al. (1991): -1 C Tsytovich(1975): different temperature boundaries for different soils Temperature boundary: Detecting unfrozen water content is rather difficult (NMR) Tend to use mechanical properties Constant load and stepped temperature Material: silty clay (CL) Qinghai-Tibet Plateau Different water content: 40%, 80%, 120% Constant Loads: 0.1, 0.2 and 0.3 MPa, respectively Temperature steps: -1.5, -1.0, -0.6, -0.5 and -0.3 C

16 Strain rate vs. Temperature Temperature ( C) Strain (%) % MPa Strain vs. Time Temperature vs. Time Time (S) 2E+005 4E+005 6E+005 Strainrate(h -1 ) % % % % % % % % % C Temperature ( C) 0 like we applied higher loads in oedometer test

17 Compressive Coefficient vs. Temperature Turning point around: -1 C Compressive coefficient (x10-2 kpa -1 ) Temperature ( C) Own test w=40% w=80% w=120% Compressive coefficient (10-2 kpa -1 ) Temperature ( C) Testing results by Zhu et al. (1982) -1 C is defined as the temperature boundary for warm frozen soil for the silty clay we frequently encounter on the plateau.

18 Settlement of road embankment Surcharge Load Active Layer PF Table Freeze-Thaw Thaw Settlement (Warm) Frozen SoilCreep Different layers, different physical and mechanical processes Thaw Settlement Freeze-Thaw Creep

19 FIELD OBSERVATION QINGHAI-TIBET RAILWAY Temperature ( C) Duration (Days) Settl. of Warm PF Depth (m) PF Table stable Warmer PF layer Settlements (m) PF table Ebkmt Base Ebkmt Surf Location: DK (QT Railway)

20 FIELD OBSERVATION QINGHAI-TIBET HIGHWAY Road Surface Lubr. Oil Steel Tube PVC Tube No. 1 No. 3 No. 4: Nail Original Surface No. 2 Permafrost Table Mitigate Friction Convenience; Protection Plat Keep Vertical Cap

21 Along the highway: 300 km, 10 observation sites, 4500 m a.s.l.

22 Beiluhe -0.5 o C On each site: we obtained total settlement and creep The warmer it is, the more creep occurred. Test section -1.2 o C

23 LONG-TERM LOAD TEST (by Dr. Zhang) No.06 Permafrost zone Seasonally frozen zone Working Site: Beiluhe field station 23/47 No.09

24 Natural ground, only cared about creep of frozen layer. p Natural Surface Glove PVC tube Active layer Grease PF Talbe Permafrost Load plate 24/47

25 Settlement (m) kpa 250 kpa Settlement Temperature 09-1# 09-1# Date 06-1# Temperature () -1-2 No Settlement (m) Settlement curve Temperature curve Temperature () No kpa 200 kpa 300 kpa Date

26 AGENDA Factors influencing creep of frozen soils Creep of Warm Frozen Soils State of The Art: Creep Models for Frozen Soils Our attempts on constitutive modeling Concluding Remarks

27 CREEP MODELS FOR FROZEN SOILS Model classification based on its scale of representation: Microscopic view The theory of rate process Damage creep model Phenomenological view Empirical model Time Hardening Theory Elementary element based creep model 4-1

28 CREEP MODELS FROM MICROSCOPIC VIEW_1 The theory of rate process: View deformation as a thermal activation process Statistical thermodynamics Activation energy Activation energy Activation energy Displacement Equation for rate of deformation = exp exp from Fish 1983 Related studies: Andersland (1967), Assur (1980) A reasonable physical description Difficulty: Parameters obtained qualitatively by current testing technology 4-2

29 CREEP MODELS FROM MICROSCOPIC VIEW_2 Endochronic time theory: irreversible thermodynamic process of dissipative material Thermodynamic constraints Constitutive relationship from Gopal et al Deviatoric: z = + Internal variable (Endochronic time) Volumetric:z Definition z and z = + dz d dt z d dt dz z 2 1 Parameters determined by Bazant et al Endochronic time theory 1) Strain hardening and softening law; 2) Expansion and contraction 3) Hydrostatic pressure sensibility Unnecessary to specify a yield surface Difficulty: Parameters for this theory are too many 4-3

30 CREEP MODELS FROM MICROSCOPIC VIEW_2 The damage creep model: damage or recovery of soil structure Damage mechanics for continuum medium CT Damage mechanism grain orientation; damaged area Ice content Damage variable Yield criterion Dissipation potential Creep damage equation = From Miao et al Following thermodynamics; Unique internal variable in frozen soil: ice content Difficulty: Calibration of Parameters for thermodynamics and damage mechanics 4-4

31 CREEP MODELS FROM PHENOMENOLOGICAL VIEW_1 Empirical methodsa mathematical description of creep curve Basic form: Classified by creep stages: 1 2 Stress-strain-time Stress-strain rate-time I. Primary creep model (Vyalov, 1966) II. Secondary creep model (Ladanyi,1972) III. Tertiary creep model (?) Simple structure; conveniently applied in simple engineering analysis (first estimation) 1) Poor versatility; 2) do not reflect internal mechanism

32 CREEP MODELS FROM PHENOMENOLOGICAL VIEW_2 Time hardening model Stress-strain-time: Klein and Jessberger (1979) : cr f(, ) ( t) ( ) i 0 m / E A t b c Herzog and Hofer (1981): t a b dt Simple; direct Only available for constant temperature

33 CREEP MODELS FROM PHENOMENOLOGICAL VIEW_3 Elementary creep model: combination of mechanical elements Basic elements: Elastic Viscous Plastic Typical Combination: Maxwell body Kelvin body Standard Viscoelastic body Generalized Bingham body Reasonable mechanical basis; simple structure; convenient in engineering design 4-6

34 SUMMARIZATION Some are too complicated in form, too many parameters, even impossible to be obtained from conventional tests Some are lacking mechanism, just mathematical description Some are difficult to accommodate different thermal or load conditions We need something new.

35 AGENDA Factors influencing creep of frozen soils Creep of Warm Frozen Soils State of The Art: Creep Models for Frozen Soils Our attempts on constitutive modeling Concluding Remarks

36 BORROW THEORIES FROM UNFROZEN SOILS Ladanyi (1999): creep of frozen soils is not very much different from that of unfrozen soils Warm frozen soil is between frozen and unfrozen soils, most likely closer to unfrozen soils

37 Creep of unfrozen soils based on p c Yin, et al. (1989): k/ V / V ep V z ' z z ' exp z z0 z ' t 0 p ' c / Vermeer and Neher(1999): e c ' C ' A ' p B C p c p exp c B After Bjerrum, 1973

38 Questions Is there an index in frozen soils similar to p c? If so What is its relationship with creep? How is it possible to apply creep model of unfrozen soils to frozen soils?

39 Methodology Unfrozen Soil Frozen Soil Looking for such an index Relationship with creep K 0 Compression Establish a creep model for frozen soils based on this index Settlement of embankments

40 Testing Phases Purpose Conditions Samples 1 Prove the existence of an index similar to Pc Same T Different d 4 Same d Different T 4 2 Influence of creep on this index d, T, preload 30 3 Comprehensive analysis Relationship: Creep vs. Pc Orthogonal design: d, T, preload, creep time creep tests so far

41 K 0 Test Pseudo preconsolidation pressure PPC for frozen soils 1,05 MPa Strain / % Time / Hours Stress / kpa In ln(1+e)lnp coordinates, there is clearly such an index

42 PPC: Mechanical behavior of frozen soils PPC / kpa PPC / kpa d / kn/m 3 Temperature / C PPC increases with the increase in d, then does not change obviously PPC increases linearly with the decrease in temperature Well reflects the bonding in frozen soils

43 Preload MPa Preload 1.63 MPa When preload is less than original PPC, PPC increases with time When preload is larger than original PPC, PPC decreases with time We are not ready to get a relationship between PPC and temperature, creep time; but we successfully proved the existence of such an index.

44 AN ELEMENT MODEL FOR CREEP OF FROZEN SOIL Establishing the model (Dr. Songhe Wang) Instantaneous elastic Viscous(strain rate approaches zero) viscous (strain rate increases with stress) Viscoplastic with a yield surface The creep model is Yield criterion(ma, et al. 1994) Sij Sij Sij G K eij t 1exp t ( F) 0 2GM 2HM 2GK HK Sij Sij Sij G K 1 Q eij t 1exp t F t ( F) 0 2GM 2HM 2GK HK 2HN tan F 3J2 cmtan 2p m 2 m

45 Long-term load test Field load test Loading pile Numerical model 100 kpa Only creep of underlying permafrost was considered

46 Numerical simulation After implementation of this model, Thermal state analysis Deformation analysis A simple model for creep of frozen soil might provide a way in engineering analysis.

47 A VISCO-HYPOPLASTIC CONSTITUTIVE MODEL FOR FROZEN SOIL (Dr. Guofang Xu, Prof. Wei Wu) Static part tr[( - ) ] c[tr( - )] c ( - c) f f c ( - c) c ( - c) tr( -) tr( -) c s 2 2 s 1 s 2 s cd 3 s 4 s d s c f 2 exp( l) s s is static stress, d is dynamic stress. in which c is the cohesion of frozen soil, f is a scalar function of deformation, f cd is a factor of creep damage. and are parameters, l is the accumulation of deformation. t l d t 0 d s

48 is a parameter, f 2 1 d cd t1 is Macaulay brackets. t Dynamic part 2 2 d 1 2 tr( ) 1 and 2 are parameters, is strain acceleration. Complete constitutive model - Rate dependent tr[( -)] c1[tr( - )] c2 ( c - ) f fcdc3( - ) c4( - ) d 1 2 tr( ) tr( - ) c c c tr( c - )

49 CALIBRATION OF THE CONSTITUTIVE MODEL Parameters in the static part When the two linear and nonlinear terms in the static part of the model are abbreviated as L 1, L 2, N 1 and N 2, this part can be rewritten as: cl ( ): + c L ( ): c N ( ) c N ( ) s 1 1 s 2 2 s 3 1 s 4 2 s In a conventional triaxial test, owing to can be divided into two scalar equations as follows: 2 3 0,the above equation cl cl cn 2 cn cl cl cn 2 cn

50 Owing to the radial stiffness E A3 = E B3 = 0, we have The parameters c i (i = 1,, 4) can be obtained by solving the above equation system with respect to the variables c i.

51 Parameters and Parameters and can be obtained from the following expressions: 1 ( T T ) n ref 1 ( T T ) n ref 2 in which T ref is a reference temperature and can be regarded as -1 C (Zhu and Carbee, 1984). Parameters 1 and 2 in the dynamical part can only be obtained by fitting the experimental data, as done by Hanes and Inman (1985).

52 VERIFICATION OF THE CONSTITUTIVE MODEL Uniaxial compression tests at different loading rates Compressive stress (kpa) Stress-strain relationship at different strain rates (Data from Zhu and Carbee, 1984)

53 Uniaxial creep tests at different stress levels Numerical Experimental Time (min) kpa 9000 kpa Numerical Experimental Time (min) kpa 9000 kpa kpa 7000 kpa kpa 7000 kpa kpa 3000 kpa kpa 3000 kpa E Creep strain vs. time (Test data from Orth (1986)) Creep strain rate vs. time (Test data from Orth (1986))

54 CONCLUDING REMARKS General features in stress-strain-time curves for frozen are similar to that of unfrozen soils. Warm frozen soil is closer to unfrozen soils. A warm frozen soil is defined according to mechanical properties. Its creep was successfully observed in situ. No generally recognized constitutive models are found for creep of frozen soils. We have tried in different ways.

55 ACKNOWLEDGEMENTS National Natural Science Foundation of China (Nos and ) The European Community through the program People as part of the Industry Academia Pathways and Partnerships project CREEP (PIAPP-GA ). Chinese Academy of Sciences (100-Young Talents Program granted to Dr. Jilin Qi) Prof. Wei Wu; Dr. Xiaoliang Yao; Dr. Guofang Xu; Dr. Fan Yu; Dr. Songhe Wang; Mr. Wei Hu; Ms. Ling Ma Prof. Hans Pette Jostad and all the CREEP colleagues.

56 Thanks for your attention!