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

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

1
Numerical analysis of a piled foundation in
granular material using slip element
• Yongjoo Lee
• Soil Mechanics Group
• Department of Civil and Environmental Engineering
• University College London
• Gower Street, London WC1E 6BT

2
Introduction
• 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)

3
Laboratory test using ideal material (Aluminium
rods)
P-S curve
4
Mesh A
Plane Strain Mesh
• Total 639 nodes
• Total 1160 elements
• 1132 LSTs 28 LSQs

5
Mesh B
Plane Strain Mesh
• Total 195 nodes
• Total 176 elements
• 4 LSTs 172 LSQs

6
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,
Ks8000Kpa, Ksres 0.8Kpa, t 0.1m
• Concrete pile Isotropic elastic model
• E 1.55e7Kpa, ? 0.2, ?bulk 23KN/m3

7
Analysis conditions
• 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

8
Increment Block Parameters
Increment Block No. Increment Block List Pile head settlement (mm) Time-Step (sec) Number of Increments Number of Increments Number of Increments Number of Increments
Increment Block No. Increment Block List Pile head settlement (mm) Time-Step (sec) Case 1 Case 2 Case 3 Case 4
1 Install pile 0 1 5 5 5 5
2 ?y1 0.08mm 00.080.08 1 5 10 20 5
3 ?y2 0.6mm 0.080.60.68 1 5 10 20 20
4 ?y3 0.32mm 0.680.321 1 5 10 20 40
5 ?y4 1.34mm 11.342.34 1 5 10 20 50
6 ?y5 1.95mm 2.341.954.29 1 5 10 20 50
7 ?y6 3.71mm 4.293.718 1 5 10 20 50
8 ?y7 3.83mm 83.8311.83 1 5 10 20 50
9 ?y8 8.56mm 11.838.5620.39 1 5 10 20 50
Total 20.39 9 45 85 165 320
9
Displacement norm convergencecheck 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
10
Comparison of CPU times
More than 1hr
Less than 12min
11
Comparison of Modified 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

12
Conclusions
• 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.

13
Results of plastic stage (20 30Kg)
• Vector movements
• Horizontal displacement contours
• Vertical displacement contours
• Volumetric strain contours
• Max. shear strain contours
• Major principal strain directions
• Zero extension line directions

Note that these displacements are associated
with strain fields in soil mechanics problems
14
1. Vector movements
• Experimental result from the
• photo image processing (Scale15)
• SAGE CRISP (M.F.10) based
• on the mesh B (? 20)

15
2. Horizontal displacements
Experimental result
SAGE CRISP
16
3. Vertical displacements
Experimental result
SAGE CRISP
17
4. Dilatant volumetric strains
Experimental result
SAGE CRISP
18
5. Max. shear strains
Experimental result
SAGE CRISP
19
6. Major principal strain directions
Experimental result
SAGE CRISP
20
7. Zero extension line directions(/or Slip line
directions)
Experimental result
SAGE CRISP
21
Numerical analysis of a piled foundation in
granular material using the slip model
Yongjoo Lee Soil Mechanics Group Department of
Civil and Environmental Engineering University
College London Gower Street, London WC1E 6BT