Deformation Analysis of Ground Foundation Usage and theory of DACSAR

Transcription

1 Deformation Analysis of Ground Foundation Usage and theory of DACSAR Visiting scholar in RCUSS of Kobe university Zhang Xiangxia 8-3-4

2

3 DACSARs: DACSAR (DACSAR-original) Oen to the ublic DACSAR-MC (DACSAR-udated) * EC/LC model is incororated; * Subloading surface; * Macro element is incororated; Oen to the ublic DACSAR-3D (3-Dimensional version of DACSAR) Not oen to the ublic DACSAR-F (finite deformation version of DACSAR) Soil/water couled elasto-lastic FE based on incremental finite deformation theory Not oen to the ublic DACSAR-U Unsaturated soil/water couled elasto-lastic FE Not oen to the ublic DACSAR-D Dynamic soil/water couled elasto-lastic FE Not oen to the ublic

4 CONTENTS Preface -Descrition of DACSAR -Details of theories used in DACSAR 3-Practical use 4-References Aendix A- Inut manual Aendix B- Examles

5 CONTENTS Preface -Descrition of DACSAR -Details of theories used in DACSAR 3-Practical use 4-References Aendix A- Inut manual Aendix B- Examles

6 CONTENTS Preface -Descrition of DACSAR -Details of theories used in DACSAR 3-Practical use 4-References Aendix A- Inut manual Aendix B- Examles

7 -DESCRIPTION of DACSAR Introduction Origination of reort Program overview

8 INMAT INNOD INELM INCOND INDRN INLOAD INDSK MAIN READ MAKE UP D MATRIX CALALPG MAKE UP TOTAL STIFFNESS NODISP CALJP CALJE CALNAE JDGNO CALGXY CALJPP DMAT Program overview SOLVER STRAIN CGAMM FCONSL for DACSAR-MC STRESS FEXCA FELM FNODL STIGLO NODISP FRSIG JUDGE NODFOC INFILE OUTPUT OUTDSK

9 CONTENTS Preface -Descrition of DACSAR -Details of theories used in DACSAR 3-Practical use 4-References Aendix A- Inut manual Aendix B- Examles

10 -Details of theories used in DACSAR. Constitutive models emloyed in DACSAR. Singular oint on the yielding surface (SO) 3. Yielding Judgment 4. Metastability (SO-EP) 5. Functions 6. Macro element roosed by Sekiguchi et al. 7. Bar, Beam, Joint, Shell element etc.

11 .Constitutive models emloyed in DACSAR. Theoretical exlanation. Demonstration

12 . Theoretical exlanation MT Element tye Elasto-(visco)lastic lane element Linearly elastic lain element Linearly elastic Beam element 3 Linearly elastic Bar element 4 Elastic erfectly lastic Joint element 5 Linearly lastic Shell element 6 Drucker-Prager lane element 7 Hyerbolic lane element Constitutive models are discussed here 8 Modified Cam-Clay model 9 EC model element LC model element

13 . Theoretical exlanation Constitutive models used in DACSAR MT MT= MT= MT=6 MT=7 MT=8 MT=9 MT= Model tye Sekiguchi-Ohta model, includs () SO-EP model () SO-EVP model; (3) SO-EP with subloading surface model(soss model) Linear elastic materials Drucker-Prager model Hyerbolic materials Modified Cam-Clay model EC model (Exonential contractancy model), includs () EC-EP model () EC-EVP model (3) EC-EP with subloading surface model(soss model) LC model (Logarithmic contractancy model), includs () LC-EP model () LC-EVP model (3) LC-EP with subloading surface model(soss model)

14 . Theoretical exlanation MT=, Sekiguchi-Ohta model Deviator stress, q SO-EP model yielding surface c K - line Deviator stress, q yielding surface subloading surface y c K - line Effective mean stress, ' Effective mean stress, ' (a) Yield surface of SO-E(V)P model (b) Sketch of subloading surface Fig. Yield surface of SO model

15 . Theoretical exlanation MT=6, Drucker-Prager model MT=8, Modified Cam-Clay model D-P Modified Cam-Clay model Yielding surface q line 3 stress, q Deviator Effective mean stress, ' Fig. Yield surface of DP model in rincial stress sace Fig.3 Yield surface of Modified Cam-Clay model

16 . Theoretical exlanation MT=9, EC model (Exonential contractancy model) MT=, LC model (Logarithmic contractancy model) Deviato or stress, q EC M..5 n E n E n E n E Deviator stress, q LC model M..5 n L n L n L n L n L Effective mean stress, ' Fig.4 Yield surface of EC model Effective mean stress, ' Fig.5 Yield surface of LC model

17 . Demonstration Case for D consolidation for OCR= D consolidation Linear model SO model DP model EC model LC model for OCR= case Value of arameters Lame s constant Permeability ~ kg / cm ~ kg / cm kcm/ min * -6 Fig.6 Boundary condition for Case

18 . Demonstration Degree of consolidation U..5 Plane strain LE model DP model SO model EC model LC model Theoretical Degree of consolidation U..5 Axi-symmetric LE model DP model SO model EC model LC model Theoretical Time factor T Time factor T v v Fig.7(a) Relationshi between degree of consolidation and time factor

19 . Demonstration P w /P w...5. P w /P w..5.. Z/H.5 Z/H.5. T v =. T v =. T v =.4 T v =.8. T v =. T v =. T v =.4 T v =.8 Fig.7(b) Consolidation Isochrone for Case by using linear elastic model

20 . Demonstration Case (-)~(3-9) for the alication of different constitutive models with different value of OCR and different drainage condition OCR Drainage SO- model EC-model LC-model condition EP EVP SS EP EVP SS EP EVP SS Undrained (-) (-) (-3) (-4) (-5) (-6) (-7) (-8) (-9) Fully draind (-) (-) (-3) (-4) (-5) (-6) (-7) (-8) (-9) Undrained (-) (-) (-3) (-4) (-5) (-6) (-7) (-8) (-9) Fully draind (-) (-) (-3) (-4) (-5) (-6) (-7) (-8) (-9) Undrained (3-) (3-) (3-3) (3-4) (3-5) (3-6) (3-7) (3-8) (3-9) Fully draind (3-) (3-) (3-3) (3-4) (3-5) (3-6) (3-7) (3-8) (3-9)

21 Three tyes of tests including lane strain shear, axisymmetric shear and direct shear. Demonstration Constitutive model Undrained condition v Drained condition Boundary condition Plane strain shear Axisymmetric shear Direct shear CIU, CK U, CPD CIU, CK U, CPD z a z x r r x Fig.8 Three tyes of tests

22 . Demonstration Effect of corresonding arameter to some model is considered SO model Elasto-lastic Elasto-viscolastic Subloading surface EC model LC model n E. (SO model) n.5.% min E n E n L n L..5. z a.% min z a m m m n L.5

23 . Demonstration Inut arameters D.76 (kg/cm )..549 (kg/cm ). M.96 v (/min).% v K.65 i v vi K e Fig..9 One element F.E. mesh and boundary condition

24 . Demonstration Case- SO-EP model for undrained condition with OCR= (Same with Case-3 SO-SS model) PS AS DS z a xz s z x a r xz s/' Plane Strain(PS) Axi-Sym. (AS) Direct Shear(DS) -3 3 (AS) (PS) s/' (PS) C.S.L. (AS) K - line (DS) (AS) C.S.L. (PS) /' - - Fig. Stress-strain relation and effective stress ath

25 . Demonstration Case- SO-EVP model for undrained condition with OCR= PS AS DS z a xz z x a r xz s/' Plane Strain(PS) Axi-Sym. (AS) Direct Shear(DS) -3 3 (AS) (PS) s s/' C.S.L. (AS) (DS) (PS) (AS) (PS) /' K - line.% min z a - - Fig. Stress-strain relation and effective stress ath

26 . Demonstration Case-4 EC-EP model for undrained condition with OCR= (Same with Case-6 EC-SS model) n E z a xz z x a r xz s/' Plane Strain(PS) Axi-Sym. (AS) Direct Shear(DS) PS AS DS (AS) (PS) s - s/' C.S.L. (AS) (PS) (DS) (AS) - C.S.L. (PS) K - line /' Fig. Stress-strain relation and effective stress ath

27 . Demonstration Case-5 EC-EVP model for undrained condition with OCR= s s/' Plane Strain(PS) Axi-Sym. (AS) PS z z x a a r AS Direct Shear(DS) DS xz xz -3 3 (AS) (PS) s/' (PS) (AS) C.S.L. K - line (DS) (AS) C.S.L. (PS) /' n E % min z a Fig.3 Stress-strain relation and effective stress ath

28 . Demonstration Case-7 LC-EP model for undrained condition with OCR= (Same with Case-9 LC-SS model) s/' Plane Strain(PS) s Axi-Sym. (AS) PS z z x a a r AS Direct Shear(DS) DS xz xz -3 3 (AS) (PS) - s/' (PS) C.S.L. (AS) K - line (DS) - (AS) C.S.L. (PS) /' n L Fig.4 Stress-strain relation and effective stress ath

29 . Demonstration Case-8 LC-EVP model for undrained condition with OCR= s/' Plane Strain(PS) Axi-Sym. (AS) PS z z x a a r AS Direct Shear(DS) DS xz xz -3 3 (AS) (PS) s s/' C.S.L. (AS) (DS) (PS) C.S.L. (AS) (PS) K - line /' n L.5.% min z a - - Fig.5 Stress-strain relation and effective stress ath

30 . Demonstration Case- SO-EP model for undrained condition with OCR= s Plane Strain(PS) PS z z x Axi-Sym. (AS) a a r AS Direct Shear(DS) DS xz xz -3 3 (AS) (PS) s/' s/' (PS) C.S.L. (AS) K - line (DS) (AS) C.S.L. (PS) /' - - Fig.6 Stress-strain relation and effective stress ath

31 . Demonstration Case3- SO-EP model for undrained condition with OCR=.3 s Plane Strain(PS) Axi-Sym. (AS) PS z z x a a r AS DS xz xz Direct Shear(DS) (AS) (PS) s/'.3 s/' (PS) (AS) C.S.L. (DS) K - line...3 (AS) (PS) C.S.L. /' Fig.7 Stress-strain relation and effective stress ath

32 . Demonstration Case3-3 SO-SS model for undrained condition with OCR=.3 s Plane Axi-Sym. (AS) PS z z x a a r AS Direct DS xz xz (AS) (PS) s/'.3 s/' (PS) (AS) C.S.L. (DS) K - line...3 (AS) (PS) C.S.L. /' m Fig.8 Stress-strain relation and effective stress ath

33 . Demonstration Case3-3 SO-SS model for undrained condition with OCR=.3 Plane Strain(PS) s Axi-Sym. (AS) PS z z x a a r AS DS xz xz (AS) (PS) s/'.3 s/' (PS) (AS) C.S.L. (DS) K - line...3 (PS) (AS) C.S.L. /' m Fig.9 Stress-strain relation and effective stress ath

34 . Demonstration Case3-3 SO-SS model for undrained condition with OCR=.3 Plane Strain(PS) s Axi-Sym. (AS) PS z z x a a r AS Direct Shear(DS) DS xz xz (AS) (PS) s/'.3 s/' (PS) (AS) C.S.L. (DS) K - line...3 (AS) (PS) C.S.L. /' m Fig. Stress-strain relation and effective stress ath

35 -Details of theories used in DACSAR. Constitutive models emloyed in DACSAR. Singular oint on the yielding surface (SO) 3. Yielding Judgment 4. Metastability (SO-EP) 5. Functions 6. Macro element roosed by Sekiguchi et al. 7. Bar, Beam, shell element etc.

36 . Singular oint on the yielding surface (Takeyama,7, Doctoral dissertation). Exlanation of theoretical treatment. Demonstration

37 . Theoretical exlanation Associated flow rule : ε f σ C.S.L. f σ? Deviator stress, q -line K Singular oint C.S.L Effective mean stress, ' Fig. Singular oint on the yield surface of SO model

38 . Theoretical exlanation Governing function for the singular oint Koiter s associated flow rule: f f Consistency condition: f, f Yield function: n : s 3 ln ), ( v v v D MD f n : s 3 ln ), ( v v v D MD f Plastic roortional coefficient: L X X det L L X X X X X where, det X X X X X 3 D G K D X, 3 D G K D X 3 D G K D X, 3 D G K D X - n v : η 3 M, - n v : η 3 M, d v d v v G K G K η η n

39 . Demonstration C.S.L.. Deviatoric stress, (' a -' r ) (kpa) K -Line C.S.L. - Effective mean stress, ' (kpa) v.% s.% v.% s.7% v.% s.58% v.% s.% v.% s.67% v.58% s.% v.7% s.%.%.% v (a) Effective stress ath s Void ratio, e.9.8 Theoretical line Effective mean stress, ' (kpa) (b) e-ln' relation Fig.3 Simulation result of effective stress ath and e-ln' relation near to singular oint on the yielding surface of SO model before coing the singular oint

40 . Demonstration C.S.L.. Deviatoric stress, (' a -' r ) (kpa) K -Line C.S.L. - Effective mean stress, ' (kpa) v.% s.% v.% s.7% v.% s.58% v.% s.% v.% s.67% v.58% s.% v.7% s.%.%.% v s Void ratio, e.9.8 Theoretical line Effective mean stress, ' (kpa) (a) Effective stress ath (b) e-ln' relation Fig.4 Simulation result of effective stress ath and e-ln' relation near to singular oint on the yielding surface of SO model after coing the singular oint

41 -Details of theories used in DACSAR. Constitutive models emloyed in DACSAR. Singular oint on the yielding surface (SO) 3. Yielding Judgment 4. Metastability (SO-EP) 5. Functions 6. Macro element roosed by Sekiguchi et al. 7. Bar, Beam, shell element etc.

42 3. Yielding Judgment (Takeyama,7, Doctoral dissertation) 3. Imroved Yielding judgment criterion for SO-EVP, EC-EVP, LC-EVP model 3. Corrected Akai & Tamura s method for satially discretization of ore water dissiation 3.3 D consolidation (couled) for Linearly elastic body by using two tyes of mesh generations

43 3. Imroved Yielding judgment criterion for SO-EVP, EC-EVP, LC-EVP model Imroved judgment criterion () For elastic state g g σ, h f σ, h f h h : : elastic elasto - visco - lastic () For elasto-visco-lastic state : : elastic elasto - visco - lastic

44 3. Imroved Yielding judgment criterion for SO-EVP, EC-EVP, LC-EVP model For SO-EVP D MD f ln, For EC-EVP n E n E M MD MD f ln For LC-EVP n L n L M MD MD f ln ln, h f h g ex ln, v v v t v t h F F F F t F F v v e e σ : C : σ : C : σ, is lastic coefficient, F v v

45 3. Imroved Yielding judgment criterion for SO-EVP, EC-EVP, LC-EVP model Yielding judgment criterion for SO model at the singular oint () The stress roceeds on the singular oint(figure (a)) f f () The stress gets away from the singular oint(figure (b)) f f f q C.S.L. q C.S.L. σ n σn K -Line σ n () σn K -Line (a) Stress roceeds on the singular oint (b) Stress gets away from the singular oint Fig.3.

46 3. Imroved Yielding judgment criterion for SO-EVP, EC-EVP, LC-EVP model det L L X X X X X where, det X X X X X 3 D G K D X, 3 D G K D X D, D 3 D G K D X, 3 D G K D X - n v : η 3 M, - n v : η 3 M, d v d v v G K G K η η n

47 3. Corrected Akai & Tamura s method V Nodal oint Element Quadrangular divided Fig 3. satial discretization x S ei x i E mi G, y, y i E mi G y x h m ei h m e x h G x i S, y, y G i S (a) original method y h m e8 h n e4 h n e x h 6 h h m e3 h n e7 h h 5 h h n e5 h h n e3 h n e h m e7 7 4 h m h m e h m e4 h n e6 h n e8 8 3 h h m h e5 6 h m e h m e (b) corrected method Fig3.3 Method for Satially discretization of ore water dissiation (consolidation) be corrected

48 Degree of Consolidation U Degree of Consolidation U Theoretical solution Simulation Time factor T v Theoretical solution Simulation Time factor T v 3.3 D consolidation by using two tyes of mesh y/h y/h T.8 v T.4 v T. v T Normarized excess ore water ressure w / w T.8 v T.4 T. v H y w x Orthogonal mesh Fig3.4 Simulation of -D consolidation by using two tyes of mesh v v T Normarized excess ore water ressure w / w v H y w x Diagonal mesh

49 -Details of theories used in DACSAR. Constitutive models emloyed in DACSAR. Singular oint on the yielding surface (SO) 3. Yielding Judgment 4. Metastability (SO-EP) 5. Functions 6. Macro element roosed by Sekiguchi et al. 7. Bar, Beam, shell element etc.

50 4. Metastability (SO-EP) (Takeyama,7, Doctoral dissertation) 4. Theoretical exlanation 4. Demonstration

51 4. Theoretical exlanation For the isotroic consolidated clay, the infinitesimal increment of stress ratio can induce a raid lastic shear deformation, which is called Metastability characteristic (Roscoe et.al. 963), this stress state can be called Metastable state. Deviatoric stress, ss, (' a -' r ) (kpa) 5-5 C.S.L. C.S.L. 5 5 Effective mean stress, ' (kpa) K..3.. M.4 D Metastable area in π lane (.%) v a r a Metastable area in axi-symmetric lane r Fig4. Metastable area

52 4. Demontration Deviatoric strain, ( a - r )/3 (%) K -Consol Volumetric strain, v (%) Deviatoric stress, (' a -' r ) (kpa) C.S.L. K -Line C.S.L. - Effective mean stress, ' (kpa) v.% s.% v.% s.7% v.% s.58% v.% s.% v.% s.67% v.58% s.% v.7% s.%.%.% v s Void ratio, e Fig4. Simulation results of effective stress ath according to given strain ath for the metastable area of SO model after coing the singular oint

53 -Details of theories used in DACSAR. Constitutive models emloyed in DACSAR. Singular oint on the yielding surface (SO) 3. Yielding Judgment 4. Metastability (SO-EP) 5. Functions 6. Macro element roosed by Sekiguchi et al. 7. Bar, Beam, shell element etc.

54 5. Functions In DACSAR rogram, the numerical solution of initial boundary-value roblem relies on the finite element method (FEM) based on satial and time discretization. For the numerical integration rocedures, the integration of constitutive equation over a time ste to calculate the stress and strain changes corresonding to the change of the dislacement is accomlished by using the algorithm to solve the systems of linear equations. Systems of linear equations on the relation between nodal force and nodal disalacement ΔF K δd T e where, K B C B d e e e e e, is total stiffness matrix, B LN e, is strain matrix, L is differential oerator for lain roblem, N is shae function

55 5. Functions The integration technique adoted can be classified into exlicit method: Gaussian method imlicit method: Biconjugate gradient stabilized method and 5. Simle exlicit method 5. Imlicit (iterative) calculation method

56 5. Simle exlicit method F δd K Total stiffness equations K K L L L L n n- - n- F F L L L L n n- - n- n n n n F δd Forward elimination rocess Fig5. Calculation rocess of Gaussian method n nn n K δd n ii n i j j n ij n i i K d K F d Backward substitution rocess

57 5. Imlicit (iterative) calculation method Algorithm rocedure Allocate temorary vectors, ˆ, s, ŝ, t, v, r ~ Allocate temorary reals r, r,,, d K F r : r r ~ For i:= ste until max_itr do r r r ~ If i = then r : else r r v r Imlicit (iterative) calculation method (BiCGSTAB) End if Solve ( M ˆ ) K v ˆ v r r ~ v r s Solve ( s s M ˆ ) s K t ˆ t t s t s x x ˆ ˆ t s r r r End (i-loo) Deal locate all tem memory Return TRUE

58 -Details of theories used in DACSAR. Constitutive models emloyed in DACSAR. Singular oint on the yielding surface (SO) 3. Yielding Judgment 4. Metastability (SO-EP) 5. Functions 6. Macro element roosed by Sekiguchi et al. 7. Bar, Beam, shell element etc.

59 6. Macro element roosed by Sekiguchi, Shibata,Mimura,Sumikura(988) 6. Exlanation of the macro element 6. Exlanation of inut arameters for the macro element 6.3 Demonstration

60 6. Exlanation of the macro element Macro element is a big hysical domain which includes foundation area and vertical drain in this area. Macro element method is used to redict the ostconstruction stress changing and deformation, esecially for the lane strain roblem of vertical drain casting by using the construction method such as SCP / SD/CVC The constitutive model of SO, linear elastic, modified cam-clay, EC and LC can be used.

61 6. Exlanation of the macro element x HORIZONTAL CO-ORDINATE S x Node w3 w Node w Node Node 3 w4 S z VERTICAL CO-ORD DINATE PLANE VIEW: CONTOURS OF Pw w S x w S x w S x V.D. V.D. V.D. S z Fig6. Sketch showing the freedom of excess ore water of a centered macro element and those of the adjoining four elements z ELEVATION VIEW: PROFILE OF Pw Fig6. Sketch illustrating the distribution of excess ore water ressures around equally saced vertical drains

62 6. Exlanation of the macro element VERTICALDRAIN w3 w 3 4 c l3 d 3 d 3 Fig6.3 Sketch illustrating the roosed way of considering water flow across the boundary between the treated and untreated regions

63 6. Exlanation of inut arameters for the macro element Model arameters Radius of drain Effective collector radius Boundary condition

64 6.3 Demonstration Material arameters for macro element ~ (kn/m ) ~ (kn/m ) vi (kpa) Ki k (m/day) * -5 Three kinds of cases Case S x ( S y )(m) S z (m) a (m) b (m) a Vertical drain S z Fig6.4 Macro element model with a vertical drain S x

65 6.3 Demonstration. Degree of consolidation U.5 Case Case Case Time factor T v Fig6.5 Relation between degree of consolidation and time factor for macro element

66 -Details of theories used in DACSAR. Constitutive models emloyed in DACSAR. Singular oint on the yielding surface (SO) 3. Yielding Judgment 4. Metastability (SO-EP) 5. Functions 6. Macro element roosed by Sekiguchi et al. 7. Bar, Beam, Joint, Shell element

67 7. Bar, Beam, shell element etc. MT Element tye Alication element is used to reresent Linearly elastic Beam element 3 Linearly elastic Bar element 4 Elastic erfectly lastic Joint element 5 Linearly lastic Shell element 7 Hyerbolic lane element. Flexural members in a building frame. Columns in a building frame 3. Sheet ile walls. Reinforcement in reinforced earth structures. Tie backs for anchor walls 3. Srings 4. Structural Braces/Struts. Interface between soil and rock. Interface between fill and concrete retaining wall 3. Interface between soil and reinforcement in reinforced earth structures 4. Rock joints/fractures Suorting structure in the ground. Saturated soil inducing fills and foundation. Mass concrete structure 3. Rock

68 CONTENTS Preface -Descrition of DACSAR -Details of theories used in DACSAR 3-Practical use 4-References Aendix A- Inut manual Aendix B- Examles

69 3-Practical use Site Fukuoka N Nagasaki Oita Fig.3- Embankment as cycle way in north of Takeo I.C

70 3-Practical use x: Free y: Free Drained 5 Filling soil x: Fix y: Free Undrained +. m Ac Ac Clay Ac3 Undrained Ac4-5 x: Fix y: Free Ac5 Ac6 Ag Ag Ag3 Ag4 Gravel with - silt and sand 5 st layer x: Fix y: Fix Drained 5 Drained Fig.3- Sketch for one tyical art of the embankment with its foundation and the boundary conditions

71 settlement ore water ressure lateral movement monitored comuted (not coing with the singular oint) comuted (coing with the singular oint) G.L.-.45m 5 5 G.L.-4.85m 4 time (day) 6 deth (m) ore water ressure (kn/m ) settlement (m) fill height (m) 3-Practical use th day lateral movement (m) Fig.3-3 Monitored and Simulation results

72 THANKS FOR YOUR ATTENTION