Constitutive Modelling of Unsaturated Soils: Discussion of Fundamental Principles

Transcription

1 Contitutive Modelling of Unaturated Soil: Dicuion of Fundamental Principle Daichao SHENG The Univerity of Newcatle, Autralia General Report 5 th International Conference on Unaturated Soil 6-8 Sept, 2010, Barcelona, Spain 1/66

2 Outline 1. Introduction 2. Volume change behaviour of unaturated oil 3. Yield tre veru uction relationhip 4. Shear trength of unaturated oil 5. Hydro-mechanical coupling for unaturated oil 6. Implementation of unaturated oil model into FEM 7. Concluding remark 2

3 1. Introduction: Fundamental Iue Volume change caued by uction change (Li, 2010) (Gen, 2007 Viggiani) 3

4 1. Introduction: Fundamental Iue Shear trength change caued by uction change Thredbo Landlide ( , NSW, Autralia) Zhou-Qu Landlide ( , Ganu, China) 4

5 1. Introduction: Fundamental Iue Hydraulic propertie of unaturated oil UNSATURATED SOIL LAYERS Flow of moiture, oxygen, heat, MINE WASTE 5

6 1. Introduction: Fundamental Iue Volume change behaviour aociated with uction change. Shear trength behaviour aociated with uction change. Flow characteritic (hydraulic behaviour) of unaturated oil. + Saturated Soil Model Complete Soil Model (aturated & unaturated) 6

7 1. Introduction: BBM (Alono, Gen & Joa, 1990) Modified Cam Clay model (aturated oil) + hear trength v uction + volume change v uction q Zero hear trength line Loading-collape urface volume p = p u a 7

8 1. Introduction: BBM (Alono, Gen & Joa, 1990) BBM (Alono et al, 1990): 1. It i the very firt complete model that accommodate the key fundamental iue of unaturated oil. 2. BBM eminal contribution: treating uction a an additional variable in the tre pace and uing the Loading-Collape (LC) yield urface to model wetting-induced volume collape. 3. It ha inpired many reearcher to unaturated oil mechanic. Numerou other model have ince been developed. 8

9 1. Introduction: State-of-Art Report State-of-the-art review on contitutive modelling of unaturated oil: 1. Gen (1 t Int. Conf. Unat. Soil, Pari, 1995) 2. Wheeler & Karube (1 t Int. Conf. Unat. Soil, Pari, 1995) 3. Alono (2 nd Int. Conf. Unat. Soil, Beijing, 1998, expanive oil) 4. Fredlund (3 rd Int. Conf. Unat. Soil, Recife, 2002, hydraulic) 5. Vaunat (1 t MUSE School, Barcelona, 2005) 6. Wheeler (4 th Int. Conf. Unat. Soil, Arizona, 2006) 7. Gen (1 t European Conf. Unat. Soil, Durham, 2008) 8. Gen (4 th Aian-Pacific Conf. Unat. Soil, Newcatle, 2009) 9. Gen (47 th Rankine Lecture, Geotechnique, 2010) Thi report focue on a elected number of fundamental iue. 9

10 Outline 1. Introduction 2. Volume change behaviour of unaturated oil 3. Yield tre veru uction relationhip 4. Shear trength of unaturated oil Alternative method 5. Hydro-mechanical coupling for unaturated oil 6. Implementation of unaturated oil model into FEM 7. Concluding remark 10

11 2. Volume Change Behaviour: Saturated Soil 3.0 Saturated, normally conolidated oil: ( ) v= N λln p = N λln p u dv dp d( uw ) = λ λ p u p u w w w u w =0 N=3, λ=0.2, v 2.5 u w =-10 kpa ae >100kPa Normally conolidated 2.0 u w =-100 kpa lnp 11

12 2. Volume Change Behaviour: Unaturated Soil Saturated NC oil: dv dp d( uw ) = λ λ p u p u w ( ) v= N λln p = N λln p u w w Unaturated oil? Approach A. Separate tre and uction approach (net tre and uction approach: Alono et al. 1990; Wheeler & Sivakumar 1995; Cui & Delage 1996;.) Approach B. Combined tre-uction approach (effective tre approach: Kohgo et al 1993; Bolzen et al 1996; Loret & Khalili 2002; Sheng et al 2003, 2004; Sun et al. 2006; ) Approach C. A more recent approach (SFG approach: Sheng, Fredlund & Gen, 2008) 12

13 2. Volume Change Behaviour: Approach A Separate tre and uction (net tre and uction) approach: v N λ ( ) ln p λ ln + u at = vp v uat Advantage: the compreibilitie due to tre and uction change are handled eparately. Toll (1990) Toll & Ong (2003) λ vp λ(s r =1) λ v 13

14 2. Volume Change Behaviour: Approach A The normal compreion line (NCL) i a traight line in the v N λ ( ) ln p λ ln + u at = vp v uat v ln p pace: v >0, d=0 Thi ha implication on yield urface. =0 ln ( ) p = ln p u a 14

15 2. Volume Change Behaviour: Approach A The volume change i not well defined at the tranition uction. For a tre change from to : Δv Δv ae ae p 0 + = λ = λ vp vp p ln ln p p 0 p+ p + ae 0 ae in unaturated zone in aturated zone Implication on the zero hear trength (apparent tenile trength) urface. 15

16 2. Volume Change Behaviour: Approach B Combined tre-uction (effective tre) approach: ( ) v= N λln p = N λ( )ln p+ f( ) v =0 >0, d=0 Advantage: 1. NCL i curved in pace. v ln p 2. It recover the aturated oil model. lnpp 16

17 2. Volume Change Behaviour: Approach B Difficult to handle the different compreibilitie due to tre and uction change λ vp Toll (1990) Toll & Ong (2003) λ(s r =1) λ v 17

18 2. Volume Change Behaviour: Approach B Alternative form of Approach B ( ) v= N λln p = N λ( ) ln p+ f( ) N v A Drying path B λ() λ(0) < 1 >0 =0 1 ln p 18

19 2. Volume Change Behaviour: Approach C SFG Approach: A middle ground between Approach A and B: Approach A: Approach B: dv dp d = λvp λv p+ f() p+ f() ( ) v= N λ ln p λ ln ( + u ) / u vp v at at ( ) v= N λ ln p+ f( ) Simplet form: f() = Sheng, Fredlund & Gen (2008) 19

20 2. Volume Change Behaviour: Approach C Normal compreion line under contant uction dv dp d = λvp λv p + f () p+ f () N=3.0, λ vp =0.2, a =10kPa NCL: =0 kpa All curve are NCL e NCL: =10 kpa NCL: =1000 kpa Potentially collapible volume p : kpa

21 2. Volume Change Behaviour: Approach C Volume change caued by uction change: d= v λ vp dp d λv p + f() p+ f() E1 NC 25 kpa E2 NC 50 kpa e p=1 kpa p=10 kpa p=100 kpa VOID RATIO E7 NC 200 kpa E11 NC 400 kpa E5 OC 200 kpa E6 OC 800 kpa p=1000 kpa SUCTION (kpa) (kpa) Vicol. (1990) 21

22 2. Volume Change Behaviour: Approach C Air-dry ilt: Data from Jenning and Burland (1962) λ v λ = λ vp vp a > a a e 0.81 Prediction of SFG model (kpa) 22

23 2. Volume Change Behaviour: Approach C Compacted expanive clay: Sivakuma and Wheeler (2000) Unloading-reloading line Yield tre NCL by Approach A NCL by SFG model v = 0 = 300 kpa p (kpa) 23

24 2. Volume Change Behaviour Comment on volume change modelling: Exiting model all have advantage and diadvantage. There i no model that ue one ingle tre variable to decribe the volume change of unaturated oil. The volume change model alo underpin the yield tre uction relation. Dicuion: In the combined tre-uction approach (Approach B), it i perhap worthwhile to explore: ( ) v= N λ( S )ln p+ f( ) = N λ ( S )ln p r r In thi cae, S r (intead of ) i ued a an additional axi in the tre pace. 24

25 Outline 1. Introduction 2. Volume change behaviour of unaturated oil 3. Yield tre veru uction relationhip 4. Shear trength of unaturated oil 5. Hydro-mechanical coupling for unaturated oil 6. Implementation of unaturated oil model into FEM 7. Concluding remark 25

26 3. Yield Stre v Suction: Approach A v=1+e Iotropic Compreion Curve =0 0< 1 < 2 < 3 p c1 < p c2 < p c pc1 pc2 pc3 ln p 26

27 3. Yield Stre v Suction: Approach A Suction Increae (SI) p Loading-collape yield urface (LC) 3 Zero hear trength (Apparent tenile trength, ATS) 2 1 pc1 pc2 pc3 p 27

28 3. Yield Stre v Suction: Soil recontituted from lurry Variation of yield tre with uction B' D Stre path B D i elatoplatic, not purely elatic. B Initial elatic zone yield urface evolution A 45 o E F G p 28

29 3. Yield Stre v Suction: Approach A NCL for >0 are curved! v=1+e A =0 B' B' B' All normal compreion line? D D D ln p 29

30 3. Yield v Suction: Approach C (SFG) Evolution of yield urface during drying and compreion p0 pcb B D ATS SI B D p cd A p Initial elatic zone LC o A p (kpa) 30

31 3. Yield Stre v Suction: Approach B (Effective Stre) Evolution of yield urface in effective tre pace SI LC zero hear trength line: p = 0 ATS B' D B'D: elatoplatic v= N() λ ()ln p? B ABB' : Drying under p = 0 A 45 o p 31

32 3. Yield Stre v Suction Comment on yield tre uction relationhip: The yield tre uction relationhip i embedded in the volume change model. The zero hear trength (ATS) urface, the uction-increae (SI) urface and the loading-collape (LC) urface are related to each other. In effective tre model and in the SFG model, the SI and LC urface are all evolved from the zero hear trength urface. 32

33 Outline 1. Introduction 2. Volume change behaviour of unaturated oil 3. Yield tre veru uction relationhip 4. Shear trength of unaturated oil 5. Hydro-mechanical coupling for unaturated oil 6. Implementation of unaturated oil model into FEM 7. Concluding remark 33

34 4. Shear Strength of Unaturated Soil In a critical tate contitutive model, the hear trength of the oil i fully defined by: - The lope of the critical tate line M() (or the friction angle φ) and - The zero hear trength function, p 0 () q p () 0 M() CSL M() CSL 45 o p 34

35 4. Shear Strength of Unaturated Soil Bihop & Blight (1963): ( ) τ = c+ σn + χ tanφ = c+ σ tanφ Fredlund et al (1978): p 0 () τ = c+ σ φ+ tanφ b n tan Volume change 35

36 4. Shear Strength of Unaturated Soil Deviator tre (kpa) Variou hear trength equation ued to define χ or φ b Tet data (after Cunningham et al, 2003) Prediction Suction (kpa) To capture the peak value: 3 4 χ = χ φ or b = φ χ = χ ( S r ) b( ) S r ( e S ) Pereira & Alono (2009) r 36

37 4. Shear Strength of Unaturated Soil The lope of CSL (M) or the friction angle (φ): Some experimental data upport that M or φ doe not depend on uction (Ng & Chiu, 2004; Thu et al 2007; Nuth & Laloui 2008) Nuth & Laloui (2008) Deviator tre (kpa) Thu et al (2007) Suction (kpa) Mean net tre (kpa) 37

38 4. Shear Strength of Unaturated Soil Some data upport that the friction angle (φ) depend on uction or degree of aturation (Toll, 1990; Merchán et al 2008) Merchán et al (2008) Toll & Ong (2003) 38

39 4. Shear Strength of Unaturated Soil Comment on hear trength of unaturated oil: If the friction angle (φ) i independent of uction, all exiting hear trength equation can be formulated in term of a ingle effective tre. The real challenge i to find an effective tre when φ depend on uction. 39

40 Outline 1. Introduction 2. Volume change behaviour of unaturated oil 3. Yield tre veru uction relationhip 4. Shear trength of unaturated oil 5. Hydro-mechanical coupling for unaturated oil 6. Implementation of unaturated oil model into FEM 7. Concluding remark 40

41 5. Hydro-Mechanical Coupling: SWCC & It Hyterei Soil water characteritic (or retention) curve, SWCC or SWRC ln Main drying curve I 0 D C D B A Scanning curve D B C Main wetting curve 1 S r 41

42 5. Hydro-mechanical Coupling: VRJ Model Vaunat, Romero & Jommi Model (2000) ln SI Surface: Drying ELASTIC ZONE LC Surface: Loading SD Surface: Wetting ln p 42

43 5. Hydro-mechanical Coupling: WSB Model Wheeler, Sharma & Buion Model (2003) n SI Surface: Drying Fully coupled: movement of one urface will caue the movement of other urface. ELASTIC ZONE LC Surface: Loading SD Surface: Wetting p 43

44 5. Hydro-mechanical Coupling: SSG Model Sheng, Sloan & Gen Model (2004) SI Surface: Drying The movement of SI & SD urface are not coupled with the movement of LC urface. ELASTIC ZONE LC Surface: Loading SD Surface: Wetting p 44

45 5. Hydro-mechanical Coupling: Denity Effect on SWCC The denity effect on SWCC (Sun et al, 2007b): (1) The hift of SWCC a the initial void ratio of the oil change, (2) The volume change along SWCC, or (3) The change of degree of aturation caued by loading/unloading when the uction i kept contant. 45

46 5. Hydro-mechanical Coupling: Denity Effect on SWCC In the literature, the change of degree of aturation i often attributed to the change of uction and the change of oil volume, in a form a: ( ) ( ) ds = d+ dε r v (29) Thi ha been ued in Sheng et al. (2004); Sun et al. (2007b); Nuth & Laloui (2008a); Mašín (2010); Nuth & Laloui (2008b); Khalili et al. (2008);. Note: SWCC i uually obtained under contant tre, not contant volume. Suction change (d) will alo caue volume change (dε v ). 46

47 5. Hydro-mechanical Coupling: Denity Effect on SWCC r ( ) ( ) ds = d+ dε The embedded S r relation i for contant volume and i different from the conventional SWCC. If thi difference i neglected, we may run into inconitency, a hown by Zhang & Lytton (2008): v LC yield urface SI urface Main drying curve Main drying curve SD urface A C D B p A A Scanning curve C D B Main wetting curve S r A C D B Main wetting curve S r Stre path (undrained: dw=0) Inconitent change of S r Conitent change of S r 47

48 5. Hydro-mechanical Coupling: Denity Effect on SWCC Alternative way to formulate the hydraulic equation: ( ) ( ) ( ) ( ) where de 0 i the change of void ratio purely due to tre change.? ds = SWCC d+ dp = SWCC d+ de r 0 There are contraint on the S r e relationhip: S e r = 0, when S = 1 or S = 0 S S 1 S e e e r r r S e r dsr = d e, when dw= 0 r r Sr Sr(1 Sr) = e e 0 0 Sheng & Zhou (2010) β 48

49 5. Hydro-mechanical Coupling: Denity Effect on SWCC Thi approach i comparable with Gallipoli et al (2003b) where the van Genuchten equation i modified to account for void ratio effect: S r 1 = ψ n 1+ ( φ e0 ) m Thi modified VG equation can alo be written a: 1/ m Sr Sr(1 Sr ) = mnψ e e 0 0 c.f. Sr Sr(1 Sr) = e e 0 0 = 1 Sheng & Zhou (2010) β 49

50 5. Hydro-mechanical Coupling: Denity Effect on SWCC S r 1 = n 1 + ( α ) m, Sr Sr(1 Sr) = e e 0 0 β, and SFG model for volume change e 0 =1.73 Tet data Prediction Data of Sun et al (2007a, b) 1.5 e e 0 = e 0 = e 0 = (a) Mean net tre, kpa S r Tet data Prediction (b) Mean net tre, kpa 50

51 5. Hydro-mechanical Coupling: Denity Effect on SWCC S r 1 = n 1 + ( α ) m, Sr Sr(1 Sr) = e e 0 0 β, Data of Jotiankaa (2005) 0.30 Calibration K S r L 7-10-V 7-10-U 7-10-W 0.05 Prediction 5-10-I 7-10-P e 51

52 5. Hydro-mechanical Coupling: Denity Effect on SWCC S r 1 = n 1 + ( α ) m, Sr Sr(1 Sr) = e e 0 0 β, Data of Sharma (1998) Calibration curve 0.90 S r 0.80 Prediction =100kPa =300kPa =200kPa e 52

53 5. Hydro-mechanical Coupling: Denity Effect on SWCC S r 1 = n 1 + ( α ) m, Sr Sr(1 Sr) = e e 0 0 β, Data of Vanapalli (1999) e 0 =0.444 S r 0.8 e 0 =0.474 e 0 =0.514 e 0 = Prediction (kpa) 53

54 5. Hydro-mechanical Coupling: Denity Effect on SWCC S r 1 = n 1 + ( α ) m, Sr Sr(1 Sr) = e e 0 0 β, Data of Tarantino (2009) S r e 0 =0.62 e 0 =0.54 e 0 =0.50 Prediction (kpa) 54

55 5. Hydro-mechanical Coupling: Denity Effect on SWCC Comment on hydro-mechanical coupling: The conventional oil-water characteritic curve (or oil-water retention curve) i obtained under contant tre, not contant volume. Thi mut be conidered in the hydro-mechanical coupling. 55

56 Outline 1. Introduction 2. Volume change behaviour of unaturated oil 3. Yield tre veru uction relationhip 4. Shear trength of unaturated oil 5. Hydro-mechanical coupling for unaturated oil 6. Implementation of unaturated oil model into FEM 7. Concluding remark 56

57 6. Implementation of Contitutive Model: Non-Convexity Net tre uction pace: BBM Elatic zone p 57

58 6. Implementation of Contitutive Model: Non-Convexity Effective tre uction pace Elatic zone p 58

59 6. Implementation of Contitutive Model: Non-Convexity Challenge: An elatic trial tre path with both the tarting and ending tre tate inide the elatic zone can caue platic yielding. B p A 59

60 6. Implementation of Contitutive Model: Integration Interection between tre path and initial yield urface 1. For a given train increment, compute the elatic trial tre 2. Find if the elatic trial tre path interect the current yield urface: the number (N) of root of nonlinear function: f( α) = f( σ α, α, z k ) = 0 3. If N > 1, divide the train increment into two equal ubincrement 4. Find the number of root within each ubincrement 5. Repeat the proce until each ubincrement contain at mot one root f Pedroo et al (IJNME, 76: , 2008) 0 1 α 60

61 6. Implementation of Contitutive Model: Integration Number of Root The number (N) of root of nonlinear function f( α) = f( σ α, α, z k ) = 0 N ([ f( a) g( b) f( b) g( a) ]) b 2 γ f( α) h( α) g( α) 1 γ = dα arctan π + f( α) + γ g( α) π f( a) f( b) + γ gagb ( ) ( ) a f: yield function g: firt order derivative of f h: econd order derivative of f Kronecker Picard formula (Kavvadia et al, 1999) It i computationally expenive to etimate N 61

62 6. Implementation of Contitutive Model: Integration Numerical Example: Integration of the SFG model p Sheng et al (Comput. Mech., 42: , 2008b) 62

63 7. CONCLUDING REMARKS 1. Partial aturation i a tate of oil and any oil be unaturated with water. Model for unaturated oil hould be able to deal with arbitrary uction and tre change within poible pore preure and tre range. 2. The volume change equation i one of the mot fundamental propertie for unaturated oil. It underpin the yield tre uction and hear trength uction relationhip. 3. When coupling the hydraulic component with the mechanical component in a contitutive model, it i recommended to take into account the volume change along oil-water characteritic curve. 63

64 7. CONCLUDING REMARKS 4. The volume change of unaturated oil can not eaily be decribed by one ingle tre variable. 5. On the other hand, there i little difference in formulating hear trength equation in one ingle tre variable or in two independent tre variable, if the friction angle i aumed to be independent of uction. 6. Unaturated oil model are characteried by non-convex yield urface near the tranition between aturated and unaturated tate. Thi non-convexity, if handled rigorouly, can ignificantly complicate the implementation of thee model into finite element code. 64

65 Gen (2008, Durham) BBM SFG 65

66 ACKNOWLEDGEMENT A number of people have read the draft paper and provided valuable comment: YJ Cui, DG Fredlund, D Gallipoli, SL Houton, J Kodikara, DM Pedroo, JM Pereira, WT Solowki, DA Sun, C Yang, X Zhang, AN Zhou The work preented in the paper involve important contribution from: DG Fredlund, A Gen, DM Pedroo, DA Sun and AN Zhou Autralian Reearch Council ha provided financial upport for reearch on unaturated oil at Newcatle. THANK YOU ALL 66

67 2. Volume Change Behaviour: Approach B v C Approach C (SFG): dv dp d = λvp λv p+ f() p+ f() Approach B (effective tre): ( ) v= N λ ln p+ f( ) Approach C recover Approach B only if: λ v = λ vp df d Therefore, Approach B i more contraint than Approach C. 67

68 2. Volume Change Behaviour: Unaturated Soil Iotropic compreion curve for recontituted oil Jenning & Burland (1962) 68

69 2. Volume Change Behaviour: Unaturated Soil Iotropic compreion curve for compacted oil Wheeler & Sivakumar (2000) 69

70 2. Volume Change Behaviour: Gallipoli et al (2003a) Iotropic compreion curve for compacted oil Gallipoli et al(2003a), data of Sharma (1998) 70

71 2. Volume Change Behaviour: Romero & Jommi (2010) Iotropic compreion curve for compacted oil Romero & Jommi (2010) 71

72 2. Volume Change: Approach B Why can t we hift the NCL upward in the v lnp' pace? ( ) v= N() λ()ln p+ f() v N() N(0) A NCL(>0)? Drying path under contant p'? Compreion under contant (elatic) Zero hear trength line Drying under contant p': Where i the expanion of the elatic zone? NCL(=0) ln p A p 72

73 2. Volume Change: Approach B Alternative form of Approach B r ( ) v= N λ( S )ln p+ f ( ) N v A Drying path under contant p S r p = c λ (1) κ ( ) κ ( p ) λ Sr c0 B Al-Badran & Schanz (2009) >0 Zero hear trength line LC urface 1 =0 ln p p 73

74 Quetion 2. Why hould the loading-collape yield urface recover the apparent tenile trength urface when p c (=0)=0? The zero hear trength line mut be unique. The LC urface i evolved from thi lurry line. lurry (v=n) 45 o p lurry p 74

75 Quetion 3. Why do you tate that the effective tre i not effective in controlling oil volume, or why do we need uction a an additional axi in the tre pace? ( ) v = N λ()ln p = N λ()ln p+ f() LC urface p 75

76 Quetion Implication of Bi-modal v mono-modal pore ize ditribution (PSD) Unaturated oil with a bi-modal PSD are uually collapible. Therefore, wetting of uch a oil (point A) can collape the macro-pore and hence change the PSD to a mono-modal (point B). However, drying the mono-modal oil at point B to A and then compreing to C will regenerate the bi-modal PSD (oil at point C become collapible again). Bi-Modal: A p B: Mono-Modal C: Bi-Modal? That mean that the PSD can change with tre and hydraulic path. Indeed, compreing a recontituted oil (mono-modal) at unaturated tate hould alo be able to generate a collapible oil (bi-modal). 76

77 Quetion 4. In a critical tate model, hould the critical tate hear trength depend on hydraulic hyterei? In other word, two ample of the ame oil are heared under exactly the ame uction, the mean net tre and the ame void ratio, but different degree of aturation. Should it critical tate trength be different? o Implication: I it neceary to have both S r and in the hear trength and volume change equation? o o Pro: Some data eem to how uch difference in CS trength (e.g. Sun et al. 2010). Con: CS hear trength i le dependent on the initial condition of the ample (e.g. OCR, water content, void ratio, initial tructure, cementation, ) for aturated oil. An unaturated oil model can not be better than it bae model for aturated tate. 77

78 Quetion Implication of the maximum hear trength at intermediate uction (SFG) q v SFG: λ v = λ? vp a λvp > a a Zero hear trength line 45 o p ln 78

79 Stre Path Dependency in Elatic Zone (SFG Model) Arbitrary yield urface unaturated B D (p, ) dv e dp d = κvp κv p + p+ aturated A (p 0, 0 ) C p p = 11, = 10 (kpa) 0 0 p= 20, = 20, = 10 (kpa) a dv e d( p + ) dp d = κvp = κvp κvp p + p+ p+ Δv Δv e e ABD ACD = κ = κ vp vp ln(36.9) ln(38.2) 38.2 ln1.03 e e vp Δv Δv = κ ABD ACD vp ln( ) = κvp ln1.03, = = 0.8% 36.9 κ vp ln 36.9 κ 79

80 Stre Path Dependency in Elatic Zone (Model A) Arbitrary yield urface unaturated B D (p, ) dv dv e e dp = κvp κ p v d dp d = κvp κv p + u at aturated A (p 0, 0 ) C p p = 11, = 10 (kpa) 0 0 p= 20, = 20, = 10 (kpa) a dv e d( p + ) dp d = κvp = κvp κvp p + p+ p+ Δv Δv e e ABD ACD = κ = κ vp vp ln(76.4) ln(60) 76.4 ln1.27 e e vp Δv Δv = κ ABD ACD vp ln( ) = κvp ln1.27, = 0.06 = 6% 60 κ vp ln 60 κ 80

81 Stre Path Dependency in Elatic Zone (Model B) Arbitrary yield urface unaturated B D (p, ) p aturated A (p 0, 0 ) C B D D Stre path in net tre pace p A C Correponding path in effective tre pace 81

82 Work-Conjugate Stre and Strain Variable Work Input (Houlby, 1997): ( ) a W = σij Srδij uw (1 Sr) δij ua εij + ns r + n(1 Sr) u ρ a ρ a W = σ δ u ε S u u δ ε + ns + n(1 S) u ( ) ( ) ij ij a ij r w a ij ij r r a = σ δ u ε + S ε + ns + n(1 S) u ( ) ij ij a ij r v r r a = σ δ u ε + θ+ n(1 S) u ( ) ij ij a ij r a ρ a ρ a ρ a ρ a ρ a ρ a 82

83 Work-Conjugate Stre and Strain Variable Work Input (Couy, Pereira & Vaunat, 2010) With two non-connected aturating fluid: ( ) dw= p u dε + S dε + qdε nds With connected fluid: a v r v q r ( ) ( ) dw= p u dϕ + p u dϕ + qdε n ds a a w w q 0 r 83

84 SFG Modelling Approach Volumetric Model Hardening Law Yield Stre Shear Strength SFG model (Sheng, Fredlund and Gen, Canadian Geotechnical Journal, 45(4), , 2008) 84

85 SFG MODEL: Hardening Law and Yield Surface dp dλ d εv = λvp( ) κ + ln p d p d p vp Volumetric model (BBM): ( ) Loading-Collape YS: p p c r λ0 κ p λ () κ c0 = pr Volumetric model (SFG): p d d d ε p v = ( λ vp κ vp) + ( v v) p f() λ + κ p+ f() Yield urface:? 85

86 SFG MODEL: Hardening Law and Yield Surface Initial yield urface and it evolution during compaction p 0 p cb B D 800 ATS SI p cd 700 B D A p Initial elatic zone LC 400 p 86 c pc0 < = p ln a c0 a a a a pcn0 < pcn = pcn0 p + ln pc a p c0 p cn0 0 a c0 a a a a p (kpa)

87 SFG MODEL: Hardening Law and Yield Surface Yield urface for oil recontituted from lurry 2 2 ( )( ) f = q M p p p p 0 c 0 q p 87

88 SFG MODEL: Hardening Law and Yield Surface Yield urface for a compacted oil 2 2 ( )( ) f = q M p p p p 0 c 0 q p 88

89 5. Hydro-mechanical Coupling: SFG Model Sheng, Gen & Fredlund (2008) p 0 S I : Drying p c ELASTIC ZONE S D : Wetting p (kpa) 89

90 2. Volume Change Behaviour: Approach C 1.54 Recontituted ilty clay: Data from Cunningham et el. (2003) Prediction of SFG model v λ v λ = λ vp vp a > a a (kpa) 90

91 2. Volume Change Behaviour: Approach C Recontituted ilty clay: Data from Cunningham et el. (2003) Meaured Predicted by SFG = 0 kpa = 400 kpa = 650 kpa =1000 kpa 1.48 v Data from Cunningham et al. (2003) p kpa 91

92 (σ 1 σ 3 ) (kpa) (σ 1 σ 3 ) (kpa) SFG MODEL: Shear Strength Shear trength of recontituted ilty clay: Data from Cunningham et al. (2003) Meaured SFG (a) Unconfined (kpa) 2000 Meaured SFG (c) Confining preure 100kPa (kpa) (σ 1 σ 3 ) (kpa) (σ 1 σ 3 ) (kpa) Meaured SFG (b) Confining preure 50kPa (kpa) Meaured SFG (d) Confining preure 200kPa (kpa)

93 SFG MODEL: Volume - Suction Behaviour Compacted Brown London Clay: Data from Marinho et el. (1995) Serie Meaured Predicted (a) (b) (c) e (kpa) 93

94 SFG MODEL: Volume - Stre Behaviour Compacted Kaolin: Thu et al. (2007) v 2.10 v (a) =0kPa 2.00 (b) =50kPa p (kpa) p (kpa) 2.10 v v (c) =100kPa 2.00 (e) =200kPa p (kpa) p (kpa)

95 SFG MODEL: Shear Strength (σ 1 σ 3 ) / 2 (kpa) Shear trength of air-dry andy oil: Data from Röhm and Vilar (1995). Meaured SFG 100 (a) Suction 20 kpa (σ 1 +σ 3 ) / 2 u a (kpa) (σ 1 σ 3 ) / 2 (kpa) Meaured SFG (b) Suction 50 kpa (σ 1 +σ 3 ) / 2 u a (kpa) 95 (σ 1 σ 3 ) / 2 (kpa) Meaured SFG (c) Suction 200 kpa (σ 1 +σ 3 ) / 2 u a (kpa) (σ 1 σ 3 ) / 2 (kpa) Meaured SFG (d) Suction 400 kpa (σ 1 +σ 3 ) / 2 u a (kpa)

96 SFG MODEL: Shear Strength Shear trength of compacted glacial till: Data from Vanapilli (1996) τ (kpa) Meaured Predicted σ n = 200 kpa σ n = 100 kpa σ n = 25 kpa (kpa) 96

97 SFG MODEL: Shear Strength Shear trength of compacted kaolin: Data from Wheeler & Sivakuma (2000) Meaured Predicted = 300 kpa = 100 kpa = 0 kpa (σ 1 σ 3 ) (kpa) (kpa) p

98 SFG MODEL PREDICTION Example 1: Soil with low air-entry value yield urface evolution a =10 kpa 300 B B' D' D A C p E 98

99 SFG MODEL PREDICTION Example 1: Soil with low air-entry value volume change 0.70 A 0.65 URL, =0 NCL, =0 e B B' D p E 99

100 SFG MODEL PREDICTION Example 2: Soil with high air-entry value yield urface evolution 2000 ae =500 kpa 1500 (kpa) 1000 B D 500 A p kpa C 100

101 SFG MODEL PREDICTION Example 2: Soil with high air-entry value volume change =0 kpa =10 kpa e =100 kpa =500 kpa =1000 kpa =2000 kpa p (kpa) 101

102 SFG MODEL PREDICTION Example 3: Compacted oil: yield urface after compaction 200 Elatic zone after compaction 150 B D E F G H (kpa) A Meaured uction level where collape tart 0 D' E' F' G' H' p (kpa)

103 SFG MODEL PREDICTION Example 3: Compacted oil: volume collape caued by wetting 1.4 NCL (=0) 1.3 e 1.2 A B D E F D' E' G H I 1.1 Meaured void ratio before and after collape F' G' 1.0 H' I' p (kpa)

104 5. Hydro-mechanical Coupling: Stre-Strain Relation Hydro-mechanically coupled model (Sheng, Gen & Sloan, 2004) dσ d Dep Wep dε = R G ds r ( 7 1) ( 7 7) ( 7 1) dσ Dep Wep dε = ds R G d r Unknown Known 104

105 Field Tet Site 100 m 2 polythene cover 300 mm wide and 500 mm deep trench Foundation movement were meaured at 5 point urface movement probe referred to in Figure 4 Data for more than 8 year 10 m trench at edge 105

106 Field Tet Site flexible cover (impermeable) wetting/drying boundary impermeable impermeable 6 m contant head (6.0m) 10 m 106

107 Field Tet Site Predicted and meaured heave under the cover 50 Diplacement (mm) FEM prediction (x=0) meaured Time (day) 107

108 Field Tet Site Predicted and meaured heave outide the cover Diplacement (mm) meaured FEM prediction (x=10m) Time (day) 108

109 Mound Shape during Dry and Wet Seaon Dry Cover Cyclic Wetting and Drying Diplacement (m) Wet eaon Dry eaon Ditance from the cover centre (m) 109