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Numerical analysis of a piled foundation in Numerical analysis of a piled foundation in granular material using slip elementgranular material using slip element

Yongjoo Lee

Soil Mechanics Group

Department of Civil and Environmental Engineering

University College London

Gower Street, London WC1E 6BT

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IntroductionIntroduction

• Reasonable mesh type in association with CPU time

• Number of increments for displacement norm convergence in connection with MNR (Modified Newton-Raphson)

• Values of dilation angle () for displacement norm convergence under New Mohr-Coulomb soil model (Non-associated flow rule applied)

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2D model pile-load test2D model pile-load test P-S curve

0 5 10 15 20 25P ile h ea d se ttlem en t (m m )

0

5

10

15

20

25

30

Loa

d (

Kg)

0

0 .0 8

0 .6 8

2 .3 4

4 .2 9

11 .8 3

2 0 .3 9

Laboratory test using ideal material (Aluminium rods)

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Mesh AMesh A

Total 639 nodes

Total 1160 elements:

1132 LSTs + 28 LSQs

Plane Strain Mesh

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Mesh BMesh B

Total 195 nodes

Total 176 elements:

4 LSTs + 172 LSQs

Plane Strain Mesh

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Parameters (drained condition)Parameters (drained condition)

Granular material: Hypothetical elastoplastic material based on New Mohr-Coulomb model – Linear elastic perfectly plastic model

C = 0.1Kpa, = 30°, = 20°, = 0.35, E0 = 1600Kpa, mE = 40000Kpa, bulk = 24KN/m3 , Y0 = 0.72m

Slip model: C = 0.005Kpa, = 5°, Kn =

16000Kpa, Ks=8000Kpa, Ksres = 0.8Kpa, t = 0.1m

Concrete pile: Isotropic elastic model

E = 1.55e7Kpa, = 0.2, bulk = 23KN/m3

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Analysis conditions:Analysis conditions:

1. Simulation of pile loading Pile head settlements from the pile load test applied to the centre node of the pile head (i.e. DCM)

2. Iterative solution scheme MNR (Modified Newton-Raphson) Tolerance: 0.05, Max. iteration: 40

3. In-situ stress condition K0 = 0.5

4. Number of increments 320 increments

DCM 

Soil element

Slip element

Pile element

applied y

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Increment Block ParametersIncrement Block Parameters

Increment Block No.

Increment Block List

Pile head settlement (mm)

Time-Step (sec)

Number of Increments

Case 1 Case 2 Case 3 Case 4

1 Install pile 0 1 5 5 5 5

2 y1 = 0.08mm 0+0.08=0.08 1 5 10 20 5

3 y2 = 0.6mm 0.08+0.6=0.68 1 5 10 20 20

4 y3 = 0.32mm 0.68+0.32=1 1 5 10 20 40

5 y4 = 1.34mm 1+1.34=2.34 1 5 10 20 50

6 y5 = 1.95mm 2.34+1.95=4.29 1 5 10 20 50

7 y6 = 3.71mm 4.29+3.71=8 1 5 10 20 50

8 y7 = 3.83mm 8+3.83=11.83 1 5 10 20 50

9 y8 = 8.56mm 11.83+8.56=20.39 1 5 10 20 50

Total 20.39 9 45 85 165 320

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Displacement norm convergenceDisplacement norm convergencecheck for the Mesh Bcheck for the Mesh B

Increment size effect (based on = 20°)

Dilation angle effect (based on total 320 increments)

Number of increments

convergence

45 No

85 No

165 Yes

320 Yes

Dilation angle (degrees)

convergence

0 No

5 No

10 No

15 No

20 Yes

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Comparison of CPU timesComparison of CPU times

More than 1hr

Less than 12min

0

500

1000

1500

2000

2500

3000

3500

4000

Mesh A Mesh B

Types of mesh

CP

U t

ime

(s

ec

)

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Comparison of Comparison of Modified Newton-Raphson methodsModified Newton-Raphson methods

ICFEP (by Potts et al, 1999) The MNR results are insensitive to

increment size e.g. Pile problem:

SAGE CRISP The MNR results are dependent on

increment size

The MNR solution was not fully implemented in connection with relationship between load and displacement norms, being based only on the displacement norm convergence checking system at the moment

There is no detailed information of the MNR iterative solution in the Crisp technical manual

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ConclusionsConclusions

CPU time can be improved through the reasonable mesh type using the Linear strain quadrilateral elements (i.e. LSQs).

In numerical analysis using the slip element, the MNR iterative solution result is very sensitive to the number of increments (or increment size) in contrast to the comment by Potts et al. (1999).

In the New Mohr-Coulomb soil model (i.e. linear elastic perfectly plastic model), the value of dilation angle () is a key factor in order to satisfy the displacement norm convergence.

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Results of plastic stage (20 – 30Kg)Results of plastic stage (20 – 30Kg)

1. Vector movements

2. Horizontal displacement contours

3. Vertical displacement contours

4. Volumetric strain contours

5. Max. shear strain contours

6. Major principal strain directions

7. Zero extension line directions

Note that these displacements are associated with

strain fields in soil mechanics problems

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1. Vector movements1. Vector movements

Experimental result from the

photo image processing (Scale:15)

SAGE CRISP (M.F.=10) based

on the mesh B ( = 20°)

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Experimental result SAGE CRISP

3 0 0 .0 0 4 0 0 .0 0 5 0 0 .0 0 6 0 0 .0 0 7 0 0 .0 0 8 0 0 .0 0

H o rizo n ta l d isp la cem en t co n to u r(P ile lo a d in g : 2 0 0 - 3 00 N )

3 0 0 .0 0

4 0 0 .0 0

5 0 0 .0 0

6 0 0 .0 0

7 0 0 .0 0

-4 .5 0-4 .0 0-3 .5 0-3 .0 0-2 .5 0-2 .0 0-1 .5 0-1 .0 0-0 .5 00 .0 00 .5 01 .0 01 .5 02 .0 02 .5 03 .0 03 .5 04 .0 04 .5 05 .0 05 .5 06 .0 0

2. Horizontal displacements2. Horizontal displacements

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3 0 0 .0 0 4 0 0 .0 0 5 0 0 .0 0 6 0 0 .0 0 7 0 0 .0 0 8 0 0 .0 0

V ertica l d isp la cem en t co n tou r(P ile lo ad in g : 2 0 0 - 3 0 0 N )

3 0 0 .0 0

4 0 0 .0 0

5 0 0 .0 0

6 0 0 .0 0

7 0 0 .0 0

-3 .5 0-3 .0 0-2 .5 0-2 .0 0-1 .5 0-1 .0 0-0 .5 00 .0 00 .5 01 .0 01 .5 02 .0 02 .5 03 .0 03 .5 04 .0 04 .5 05 .0 05 .5 06 .0 06 .5 0

3. Vertical displacements3. Vertical displacements

Experimental result SAGE CRISP

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3 0 0 .0 0 4 0 0 .0 0 5 0 0 .0 0 6 0 0 .0 0 7 0 0 .0 0 8 0 0 .0 0

V o lu m etr ic stra in co n to u r(P ile lo a d in g : 2 0 0 - 3 0 0N )

3 0 0 .0 0

4 0 0 .0 0

5 0 0 .0 0

6 0 0 .0 0

7 0 0 .0 0

-0 .8 0

-0 .7 0

-0 .6 0

-0 .5 0

-0 .4 0

-0 .3 0

-0 .2 0

-0 .1 0

0 .0 0

0 .1 0

4. Dilatant volumetric strains4. Dilatant volumetric strains

Experimental result SAGE CRISP

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3 0 0 .0 0 4 0 0 .0 0 5 0 0 .0 0 6 0 0 .0 0 7 0 0 .0 0 8 0 0 .0 0

S h ear stra in co n tou r(P ile lo ad in g : 2 0 0 - 3 0 0N )

3 0 0 .0 0

4 0 0 .0 0

5 0 0 .0 0

6 0 0 .0 0

7 0 0 .0 0

-0 .1 0

0 .0 0

0 .1 0

0 .2 0

0 .3 0

0 .4 0

0 .5 0

0 .6 0

0 .7 0

0 .8 0

5. Max. shear strains5. Max. shear strains

Experimental result SAGE CRISP

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6. Major principal strain directions6. Major principal strain directions

Experimental result SAGE CRISP

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7. Zero extension line directions7. Zero extension line directions(/or Slip line directions)(/or Slip line directions)

Experimental result SAGE CRISP

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Numerical analysis of a piled foundation in Numerical analysis of a piled foundation in granular material using the slip modelgranular material using the slip model

Yongjoo Lee

Soil Mechanics Group

Department of Civil and Environmental Engineering

University College London

Gower Street, London WC1E 6BT