Litteraturförteckning

Arbetsmaterial från IV A Pålkommissionens Arbetsgrupp för kohesionspålgrundläggningar.

Beigler, S-E, 1976: Soil-Structure Interaction Under Static Loading, Doktorsavhandling, Chalmers Tekniska Högskola, Department of Geotechnical Engineering.

BFS 1988: 18, Boverkets Nybyggnadsregler (Föreskrifter och Allmänna råd), Allmänna Förlaget, Stockholm, ISBN 91-38-09758-3.

Bolteus, L, 1979: Soil-Structure lnteraction - 1. Introductory review, Chalmers Tekniska Högskola, Division of Structural Design, Publikation 1979:9.

Bolteus, L, 1984: Soil-Structure Interaction - A Study Based on Numerical Methods, Doktorsavhandling, Chalmers Tekniska Högskola, Publikation Nr. 84:3, Division of Structural Design.

Boulon, M, 1989: Basic Features oj Soil Structure Inteiface Behaviour, Computers and Geotechnics, Vol. 7, pp. 115-131.

Boulon, M, 1990: Modelling of Soil-Structure Inteiface Behaviour -A Comparison between Elastoplastic and Rate Type Laws, Computers and Geotechnics, Vol 9, pp. 21-46.

Boussinesq, J, 1885: Application des Potentiels a l'Etude de l'Equilibre et du Moumvement des Solides Elastique, Gauthier-Villars, Paris.

Carol,. A G I et al., 1988: An Inteiface Element Formulationfor the Analysis of Soil­

Reiriforcement Interaction, Computers and Geotechnics, Vol. 7, pp. 133-151.

Chamecki, S, 1956: Structural Rigidity in Calculating Settlements, Proc. Am. Soc. Civil Eng., J. Soil Mech. Found. Div., Vol. 82, No. SMl, pp. 1-19.

Cooke, R W, 1986: Piled Raft Foundations on Stijf Clays - A Contribution to Design Philosophy, Geotechnique, Vol. 36, No. 2, pp. 169-203.

Desai, C S och Sargand, S, 1984: Hybrid FE Procedurefor Soil-Structure lnteraction, ASCE Journal of Geotechnical Engineering, Vol. 110, No. 4, pp. 473-486.

Filonenko-Borodich, MM, 1940: Some Approximate Theories of the Elastic Foundation, Uch. Zap. Mosk. Gos. Univ. Mekh., 46:3-18 (på ryska).

Filonenko-Borodich, MM, 1945: A Very Simple Model of an Elastic Foundation Capable of Spreading the Load, Sb. Tr. Mosk. Elektro. Inst. Inzh. Trans. No: 53 Transzheldorizdat (på ryska).

Griffiths, D V, 1987: Numerical Studies of Soil-Structure Interaction Using a Simple lnteiface Mode!, Canadian Geotechnical Journal, Vol. 25, pp. 158-162.

Hetenyi, M, 1946: Beams on Elastic Fondations, University of Michigan Press, Ann Arbor, Michigan.

Hird, C C och Russell, D, 1990: A Benchmarkfor Soil-Structure Interaction Elements, Computers and Geotechnics, Vol. 10, pp. 139-147.

Information från FEM-TECH AB i Västerås (ABAQUS).

Information från University of Cambridge (PIGLET) Information från Imperial Colleget (ICFEP)

Information från Nippon Institute of Technology (PI GRAF) Information från Danmarks Geotekniska Institut (PLAS3D)

The Institution of Structural Engineers, 1989: Soil-Structure Interaction - The Real Behaviour oj Structures, London.

Kerr, AD, 1964: Elastic and Viscoelastic Foundation Modets, J Appl. Mech. (Trans.

A.S.M.F.E.), 31, pp. 491-498.

Kolar, V och Nemec, I, 1989: Modelling oj Soil-Structure Interaction, Developments in Geotechnical Engineering Vol. 58, Elsevier, ISBN 0-444-98859-9.

Larnach, W J, 1970: Computation oj Settlements in Building Frames, Civ. Eng. Pub. Wks.

Rev., 65, p. 1040.

Martin, T C och Hoadley, P J, 1979: Non-Linear Finite Element Analysis ojDiaphragm Wall Behaviour, Proc. 3d Int. Conf. in Australia on Finite Element Methods, July, 1979, University of New South Wales.

Mindlin, R D, 1936: Force at a Point in the Interior oja Semi-lnfinite Solid, J. Appl.

Phys., Vol. 7, No. 5, pp. 195-202.

Pasternak, P L, 1954: On a New Method ojAnalysis oj an Elastic Foundation by means oj Two Foundation Constants, Gosudarstvennoe Izdatelstro Liberaturi po Stroitelstvui

Arkhitekture, Moskva (på ryska).

Poulos, H G och Davis, E H: Elastic Solutions for Sot! and Rock Mechanics, John Wiley &

Sons.

Reissner, E, 1958: Deflection oj Plates on Viscoelastic Foundation, J. Appl. Mech. (Trans A.S.M.E.), 80, pp. 144-145.

Selvadurai, AP S, 1979: Elastic Analysis oj Soil-Foundation Interaction, Developments in Geotechnical Engineering, Vol. 17, Elsevier, ISBN 0-444-41663-3.

Smith, I M, 1970: A Finite Element Approach to Elastic Soil-Structure Interaction, Canadian Geotechnical Engineering, Vol. 7, No. 2, pp. 95-105.

SBN 80, Svensk Byggnorm, Statens Planverks Författningssamling, 1980: 1, LiberFörlag, Stockholm, ISBN 91-38-05209-1.

Trochanis, A M et al., 1991: Three-Dimensional Nonlinear Study ojPiles, ASCE Journal of Geotechnical Engineering, Vol. 117, No. 3, pp. 429-447.

Vlazov, V Z och Leontiev, U N, 1966: Beams, Plates and Shells on Elastic Foundations, Israel Program for Scientific Translations, Jerusalem (översatt från ryska).

Winkler, E, 1867: Die Lehre von der Elastizitat und Festigkeit, Dominicus, Prague.

Zaman, MM och Mahmood, I U, 1988: Analysis of Cylindrical Storage Tank-Foundation Interaction Using Finite Element Method, Indian Geotechnical Journal, Vol. 18, No. 4, pp. 356-384.

Zbirohowski-Koscia, K F och Gunasekera, D A, 1970: Foundation Settlement and Ground Reaction Calculations Using a Digital Computer, Civ. Eng. Publ. Wks. Rev., 65, p. 152.

Zienkiewicz, 0 C, 1977: The Finite Element Method in Engineering Science, McGraw­

Hill, London.

Yao, Yu, 1993: Testin and Modelling of Silty and Sulphide-Rich Soils, Doktorsavhandling 1993: 121D, Luleå Tekniska Högskola, Institutionen för Anläggningsteknik, Avdelningen för Geoteknik, ISSN 0348-8373.

A description on the FE calculations oj settlements oj the pile group

Three-dimensional elastic finite element analyses are carried out for two cases of pile­

group-plate-soil system, i.e. pillar loading case and wall loading case.

Due to the symmetry of the system, only one fourth of the system is considered. The sym­

metric lines are restricted by certain proper boundary conditions. 8-node cubic elements are used for all the system. For the P-case a total number of elements is 1857 with 2394 nodes and for the W-case 2143 with 2670 nodes. Outside the system elements with larger lengths and/or thicknesses are used for simulating the far field.

The concrete plate is set on the bottom surface of excavation and the piles are pinned into it. No interaction between the plate side and the soil is considered. Both the bottom of the plate and the pile shaft are assumed to be perfectly bonded to the soil, i.e. no slippage is allowed at these interfaces. The distributed loads on the surface of the plate are 41 kPa and 37 kPa for the P-case and W-case, respectively.

· The plate and piles are modelled as elastic materials with E = 5.E6 kPa and v = 0.2.

The ground soils are also modelled as elastic materials but with different Young's moduli in c;lifferent layers. However, the Poisson 's ratio is assumed as v

=

0.3 for all the ground soil layers, see Table 1. Since the system is only considered in the serviceability state, the following calculations for the Young's moduli with a partial safety factor r₀

=

1.2 are adopted.

(1 +v') (l -2v') E'o

=

rn (1-v') Mo

(1 + v') (1 - 2v')

=

rn ( 1 - v') 5001:fu

(1 + v') ( 1 - 2v')

=

rn(l-v') 500(12+z)

=

309(12+z)

Table 1: Elastic parameters used in the FE calculations Layer Averaged Depth z

(thickness, m) ^(m)

Table 2: Calculated results for the pillar loading case

X y

s

Stressat node Load

Pile no.

(m) (m) (mm) (kPa) (kN)

1 0.0 1.0 44.8 7462 564

2 0.0 6.0 40.0 6513 492

3 6.0 6.0 39.5 6642 502

4 12.0 6.0 36.0 6253 473

5 18.0 6.0 26.3 3904 295

6 6.0 1.0 44.3 7605 547

7 12.0 1.0 40.8 7281 574

8 18.0 0.0 32.2 6100 461

Table 3: Calculated results for the wall loading case

X y

s

Stress at node Load

Pile no.

(m) (m) (mm) (kPa) (kN)

1 3.0 3.0 41.2 7133 540

2 6.0 3.0 39.4 6574 497

3 10.0 3.0 37.1 6264 473

4 14.0 3.0 33.4 5822 440

5 18.0 0.0 28.7 5219 394

6 _- 8.0 6.0 33.5 5121 387

7 18.0 6.0 23.3 3315 250

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0

--- PILLAR CASE

---X y U3 (M)

PILE

8 18.0 0. -7.7825E-02

1 0.0 1. -8.9615E-02

6 6.0 1. -8.9169E-02

7 12.0 1. -8.5843E-02

2 0.0 6. -8.4943E-02

3 6.0 6. -8.4529E-02

4 12.0 6. -8.1344E-02

5 18.0 6. -7.2377E-02

PILE LOAD (KN)

1 535

2 461

3 471

4 445

5 275

6 547

7 525

8 437

--- WALL CASE

---X y 03 (M)

PILE

5 18. 0. -6.9971E-02

1 3. 3. -8.1471E-02

2 6. 3. -7.9852E-02

3 10. 3. -7.7811E-02

4 14. 3. -7.4340E-02

6 8. 6. -7.4342E-02

7 18. 6. -6.4957E-02

PILE LOAD (KN)

1 508

2 470

3 450

4 419

5 374

6 361

7 234

-Y

CALCULATION EXAMPLE: SOIL-STRUCTURE INTERACTION

by

Fumio KUWABARA and

Minoru TANAKA

Nippon Institute of Technology

We conducted our calculation on Two cases of lirnit state.

a) Ultimate Limit State, and b) Serviceability state

Two kinds of structure.

a) Case "P", and b) Case "W"

Two cases of treatment for the stiffness of the raft.

a) The raft is assumed perfectly rigid, and b) "Umbrella" model is used.

Therefore, eight cases of calculation were performed.

Our program PGRAFT can treat the raft stiffness in three

representative rnodels, i.e., a) perfectly rigid, b) perfectly

:~ fl~xible, and c) urnbrella model.

Perfectly rigid model: raft is perfectly rigid, thus the settlernent of any place of the raft and that of pile heads are equal. The contact pressure on the raft and the pile head load distribution will be uneven.

Perfectly flexible model: The rigidity of raft can be negli­

gible. Applied load distribution should be known. The settle­

ments of the raft and the piles will be not equal.

Umbrella model: An unit consisting of a raft element anda nurnber of piles is considered. The raft in an unit is assumed

2

rigid, however, the stress can not be transmitted at the interface between the rafts of neighboring sets. This model is considered in between the perfect rigid model and perfect flexible model.

BASIC ASSUMPTION FOR PGRAFT

1) Interaction between piles, raft and soil are considered by Mindlin's equations in an elastic mass.

2) Both pile and soil are assumed as elastic materials expressed by Young's modulus and Poisson's ratio.

3) Slip between pile shaft and-surrounding soil, and failure of soil under the raft or pile tip can be taken inta account.

4) Soil non homogeneity is considered by approximate manner.

PARAMETER USED IN THE ANALYSIS

1) pile diameter, Young's modulus of pile

As our analysis can be made only for circular cross section piles, the pile diameter and Young's modulus should be modi­

fied to equalize the circumference of the pile and compress­

ibility of the pile between the prototype and the analytical model.

Prototype Model

Width (Diameter) 0.275x0.273 m (square) 0.35 m (circle)

Young's modulus 5/1. 2

*

GPa 3270 MPa

Area of cross section 0.07563 m2 0.09621 m2

3

Circumference 1.1 m 1.1 m

2) Young's modulus of soil E' = (l+v' )(1-2V' )/(1-v') M M = 500,:;fu (kPa)

,:;fu = (12+z) (kPa)

V' = 0.3

Eo

=

E'/1.2

* =

310(12+z)/1000 (MPa)

3) Limiting value of shaft friction between pile and soil ,:;a = 0.8,:;fu = 0.8(12+z)/1000 (MPa)

4) Limiting value of end bearing at pile tip qb

=

9,:;fu

=

9(12+z)/1000 (MPa)

5) Limiting value of hearing pressure at raft qu ⁼ 6,:;fu ⁼ 6(12+z)/1000 (MPa)

*

The value of 1.2 is used for serviceability. This value is changed to 1.3 for ultimate limit state .

.-,

***

Only load and modulus are changed between ultimate limit state and serviceability state. The limiting values of stress described above are NOT changed between two limit states. (If partial factors should be introduced for these local yielding to analyze the settlement, please let me know the value of the partial factor)

4

1. 500 mm 6. 000 mm

"r ,sr

24. 000 mm 30,000 mm ^34.

^{'1" .,}

20 2] 22 23 24 25 26

=

llL15Jl..JruL

=

^{I I I I}

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=

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=

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₀

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I

= =

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=· =

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_-

_-

-= <.Ö

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ooo

I 6,

ooo

6. 000 6. 000 3,000

L'illiLnuL

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= =

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2 3 4 5 6 ^{7' ], 250 mm}

I c--.i

6,000 6. 000 6. 000 6,000 6. 000 6,000

36. 000

Analytical model of case P

~

~ ~ ..

N Ut

~

SERVICEABILITY STATE CASE P

BOTTOM JOISTS

(MPa)

(m)

DEPTH

(m)

MODULUS -SOIL STRESS

(m)

DEPTH

(m)

MODULUS -SOIL STRESS

2. 0 2. 0

6. 4 4. 2 5. 0

o.

^{013 6. 4 4. 2 4. 6}

o.

⁰¹³

10. 8 8. 6 6. 4

o.

^{017 10. 8 8. 6 5. 9}

o.

⁰¹⁷

15. 2 13. 0 7. 8

o.

^{020 15. 2 13. 0 7. 2}

o.

⁰²⁰

19. 6 17.

4

9. 1

o.

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o.

⁰²⁴

24. 0 21. 8 10. 5

o.

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o.

⁰²⁷

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o.

^{031 28. 4 26. 2 l 0. 9}

o.

⁰³¹

32. 8 30. 6 13. 2

o.

^{034 32. 8 30. 6 12. 2}

o.

⁰³⁴

37. 2 35. 0 14. 6

o.

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o.

⁰³⁸

41. 6 39.

4

15. 9

o.

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⁴

^{14. 7}

o.

⁰⁴¹

46. 0 43. 8 17. 3

o.

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o.

⁰⁴⁵

YOUNG'S MODULUS or SOIL SURFACE

^{·3. 72}

YOUNG' S MODULUS OF SOIL SURFACE

3. 43

YOUNG' S MODULUS OF BASE LAYER

180

YOUNG'S MODULUS OF BASE LAYER

166

YOUNG'S MODULUS OF SOIL AT PILE TIP

18. 0

YOUNG'S MODULUS OF SOIL AT PILE TIP

16. 6

LIMITING END-BEARING STRESSAT PILE TIP o.

⁵²²

LIMITING END-BEARING STRESSAT PILE TIP o.

⁵²²

LIMITING BEARING STRESSAT THE CONTACT o.

⁰⁷²

LIMIT!NG BEAR!NG STRESSAT THE CONTACT o.

072

OF SLAB AND SOIL SURFACE OF SLAB AND SO!L SURFACE

O:i

Endast värden motsvarande bruksgränstillstånd (serviceability state) har använts vid

~

jämförelsen. ₍₎

;;i:..

..

N -...l

6. 3

~

Contact pressure (case P, rigid) (unit:kPa) ~

~

Serviceabili ty ; Settlement 4. 7cm

^{00 ~}

load (kN)

0 100 200 300 400 500 600 700 800 0

10

.. ^Il ;"' ^{•D ..}.,•' :

~ 8

20~-;-~~~~~~~-i-,--i-~

'-...,/

...c

--f-)

g ^{3 0}

- - - , - y , " - - 1 ' - + - - , - - - - H

9 ^{pile No. 1}

Q

Q

pile No.4

40 • pile No. 8

11!1

I

pi le No. 1-1

I

Distribution of axial force on piles (Rigid, case P)

Serviceability

703.8 657. 7 629. 9 622. l 685. 8 605.2 554. 2 543._6

Sreviceability

_N

_..

^)l>-c;')

I-<

I-<

j

l

Contact pressure (case P, umbrella) (unit:kPa)

~

~

Sreviceability .. _,....

^;> N

N

0

load (kN)

0 100 200 300 400 500 600 700 800

0

; /

; /

/

, / · ;/

•••

~

320

....c::

+->

g ^{3 0}

- t - - - , - - + - - _ t , _ _ _ _ _ _ , _ - - + <

9 pile No. 1

Q

y pile No.4

40 • pile No. 8

11!1

I

pile No. 11

I

50

Distribution of axial force

on piles (Umbrella, case P)

Serviceability

632.0

Case P, Sreviceability state (umbrella)

slip zone

= =

^{N )}

= =

SERVICEABILITY STATE

BOTTOM JOISTS (MPa)

ULTIMATE STATE

ELEMENT WALL ELEMENT LOAD OF UNIT OWN WEIGHT OF REDUCTION WALL LOAD BOTTOM JOISTS TOTAL LOAD

BOTTOM JOISTS

(MPa)

SERVICEABILITY STATE CASE W ULTIMATE STATE CASE W

DEPTH.

^AVERAGE

OF YOUNG' S LIM ITING PI LE DEPTH AYERAGE OF YOUNG' S LIMITING PILE

(m) DEPTH (m) MODULUS -SOIL STRESS (m) DEPTH (m) MODULUS -SOIL STRESS

2. 0 2. 0

6.4 4. 2 5. 0 o. 013 6.4 4. 2 4. 6 o. 013

10.8 8.6 6. 4 o. 017 10.8 8. 6 5. 9 o. 017

15.2 13. 0 7.8 o. 020 15.2 13. 0 7.2 o. 020

19. 6 17. 4 9. 1 o. 024 19. 6 17.4 8.4 o. 024

24. 0 21. 8 10. 5 o. 027 24. 0, 21. 8 9. 7 o. 027

28.4 26. 2 11. 8 o. 031 28.4 26. 2 1 o. 9 o. 031

32. 8 30. 6 13. 2 o. 034 32.8 30. 6 12. 2 o. 034

37.2 35. 0 14. 6 o. 038 37. 2 35. 0 13.4 o. 038

41. 6 39. 4 15. 9 o. 041 41. ⁶ 39.4 14. 7 o. 041

46. 0 43. 8 17. 3 o. 045 46. 0 43. 8 16. 0 o. 045·

YOUNG' S MODULUS OF SOIL SURFACE YOUNG' S MODULUS OF SOIL SURFACE

3. 72 3.43

YOUNG' S MODULUS OF BASE LAYRE YOUNG' S MODULUS OF BASE LAYRE

180 166

YOUNG' S MODULUS OF SOIL AT PILE TIP YOUNG' S MODULUS OF SOIL AT PILE TIP

18. 0 16. 6

LIMITING END-BEARING STRESSAT PILE TIP LIMITING END-BEARING STRESSAT PILE TIP

^O:J

o. 522 o. 522

~ _►

LIMITING BEARING STRESSAT THE CONTACT LIMITING BEARING STRESSAT THE CONTACT

()_►

OF SLAB AND SOIL SURFACE OF SLAB AND SOIL SURFACE ,... ..

^N

o. ⁰⁷² o.

^{072 ---l}

,,,. ,,.. '"" ...

1 (])

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_{~ 6} ---@

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5

C ont a ct press.ur e (ca se W, rigid) ( u ni t : k P a)

Sreviceability ; Setllement 4. 3cm

^t:o

_p

;i;..

;i;.. 0

..

N

J--1.

00

load (kN)

0 100 200 300 400 500 600 700 0

10

~

8

20-t--~-~~-~-,--~-i-~

'-._/

9 pile No. 1

Q

pile No. 2

40 • ^{pile No. 6}

l!I

I

pile No. 8

I

50

Distribution of axial force on piles (rigid, case W)

Serviceability

611. 0 594. 0 60U 555. l 532. 6 537. I 638. 9

E

r----...

load (kN)

0 100 200 300 400 500 600 700

0

_{.• ,D .11!1}

/

•• ✓ /

••••

^,

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.· " ^/

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,n .•··

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,. /

~- : ✓•

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s20--r---t--,---t--~~r---j----t---i

'---../

~ pile No. 1

Q

:~

pile No. 2

40 • pile No. 6

11!1

I

pile No. 8

I

50

Distribution of axial force

on piles (umbrella, case W)

Serviceability

64 I. 2 571.0 573. I 532. 1 481. 3 671. 7 6J6. 3

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Program (företag/ Beräkning av till- Sättningsberäkning Jordmodell Samverkan med

institution) skottsspännirumr bn:1:maden

Kompensations- Beräkning enligt FEM -beräkning Varje element kan Stommen beskrivs med grundläggning med elasticitetsteori Elastisk-viska- ges specifika värden ram-, skiv-, balk- eller kohesionspålar FE-metod med yt- elastisk modell beträffande E, u och platt-element. Jordfjäd-Göteborgs förorter och punktlaster baserad på CRS- viskositetskonstant rama korrigeras med

resultat (M om- hänsyn till uppnådd

räknas till E) deformation vid olika

tidssteg

ICFEP Elasticitetsteori FEM -beräkning Olika elasto-plastiska Konstruktionselement

Imperial College Elastisk- modeller inklu- beskrivs med elastiska

viskoelastisk derande MIT:s och parametrar.

(plastisk) modell Lades modeller

Platta på mark Ytlaster enligt Kompressions-area- Jorden indelas i ett Platta/väggar FEM-SS/-konsult Boussinesq-Fröhlich metoden baserad på antal rutor i x/y- beräknas. Samverkan

Pållaster enligt parametrar från systemet. Inom varje genom att överens-Mindlin CRS-ödometer- ruta består jorden av stämmelse skapas

försök Även ett antal horisontella mellan sättning och elasticitetsteori kan skikt plattans deformation.

utnyttjas.

SAMVERKAN Ytlaster enligt Kompressions-area- Jorden indelas i ett Platta/väggar FEM-ADG GrundteJ.cnik Boussinesq-Fröhlich metoden baserad på antal rutor i x/y- beräknas. Samverkan J&W Pållaster enligt parametrar från systemet. Inom varje genom att

överens-Mindlin CRS-ödometer- ruta består jorden av stämmelse skapas försök ett antal horisontella mellan sättning och

skikt plattans deformation.

ABAQUS Elasticitetsteori FEM-beräkning Varje element kan Konstruktikonsel ement

rem-Tech AB Elastisk- beskrivas med beskrivs med elastiska

viskoelastisk elastiska-viska- parametrar (dvs ges sin (plastisk) modell elastiska ( elasto- riktiga styvhet).

plastiska/viska-elastiska-plastiska) parametrar

PIGRAF Ytlaster enligt Elastici tetsteori Elasticitetsteori Oändligt styv eller Nippon Jnstitute oj Boussinesq Gränsspänningar kan oändligt vek platta.

Technology, Japan Pållaster enligt anges i kontaktytan Dessutom "U mbrella

Mindlin mellan jord och påle method" där plattan

för att möjliggöra delas upp i delar med glidning ett antal pålar till varje (plasticering) del. Detta ger resultat

mellan oändligt styv och oändligt vek platta.

PIGLET Förenklad Förenklad Linjär-elastisk jord. Oändligt styv eller

Cambridge University elasticitetsteori elasticitetsteori E ökar ned till oändligt vek

Ytlaster kan ej pålspets och är överbyggnad. Pålarnas

simuleras därunder konstant styvhet beaktas.

SPLICE Elasticitetsteori Elasticitetsteori I varje nod ansätts Samverkan beskrivs Norges geotehiiska (kopplad Winkler- (kopplad Winkler- värden på fjädermot- med tre kopplade institut teori) teori). I varje ståndet (p-y- och t-z- fjädrar i varje

nod-iteration antas kurvor ansätts) punkt (modifierad linjära förhållanden. Winkler-idealisering) PLAS3D Elasticitetsteori FEM-beräkning Olika elastiska Konstruktionselement Danmarks geotekniska Elastisk-viska- modeller och en beskrivs med elastiska

institut elastisk modell elasto-plastisk parametrar ( dvs ges sin

modell med töjnings- riktiga styvhet).

hårdnande

In document beräkningar 419 (Page 34-93)