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
14th Crisp user meeting at UCL
1
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)
14th Crisp user meeting at UCL
2
Laboratory test using ideal material
(Aluminium rods)
2D model pile-load test
14th Crisp user meeting at UCL
P-S curve
3
Plane Strain Mesh
Mesh A

Total 639 nodes

Total 1160 elements:
1132 LSTs + 28 LSQs
14th Crisp user meeting at UCL
4
Plane Strain Mesh
Mesh B

Total 195 nodes

Total 176 elements:
4 LSTs + 172 LSQs
14th Crisp user meeting at UCL
5
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
14th Crisp user meeting at UCL
6
Analysis conditions:
1. Simulation of pile loading
DCM
Pile head settlements from the pile
load test applied to the centre node
of the pile head (i.e. DCM)
applie dy
2. Iterative solution scheme
MNR (Modified Newton-Raphson)
Tolerance: 0.05, Max. iteration: 40
3. In-situ stress condition
K0 = 0.5
Pile e le m e nt
4. Number of increments
320 increments
Slip e le m e nt
Soil e le m e nt
14th Crisp user meeting at UCL
7
Increment Block Parameters
Increment
Block No.
Increment
Block List
Pile head settlement
(mm)
TimeStep (sec)
1
Install pile
0
2
y1 = 0.08mm
3
Number of Increments
Case 1
Case 2
Case 3
Case 4
1
5
5
5
5
0+0.08=0.08
1
5
10
20
5
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
14th Crisp user meeting at UCL
8
Displacement norm convergence
check for the Mesh B


Increment size effect
(based on  = 20°)
Dilation angle effect
(based on total 320 increments)
Number of
increments
convergence
Dilation angle
(degrees)
convergence
45
No
0
No
85
No
5
No
10
No
15
No
20
Yes
165
Yes
320
Yes
14th Crisp user meeting at UCL
9
Comparison of CPU times
4000
More than 1hr
3500
CPU time (sec)
3000
2500
2000
1500
1000
Less than 12min
500
0
Mesh A
Mesh B
Types of mesh
14th Crisp user meeting at UCL
10
Comparison of
Modified Newton-Raphson methods

ICFEP (by Potts et al, 1999)

The MNR results are insensitive to
increment size
SAGE CRISP
The MNR results are dependent on
increment size
e.g. Pile problem:
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
14th Crisp user meeting at UCL
11
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.
14th Crisp user meeting at UCL
12
Results of plastic stage (20 – 30Kg)
1.
2.
3.
4.
5.
6.
7.
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
14th Crisp user meeting at UCL
13
1. Vector movements
Experimental result from the
photo image processing (Scale:15)
SAGE CRISP (M.F.=10) based
on the mesh B ( = 20°)
14th Crisp user meeting at UCL
14
2. Horizontal displacements
Experimental result
SAGE CRISP
Horizontal displacement contour
(Pile loading: 200 - 300N)
700.00
6.00
5.50
5.00
4.50
4.00
3.50
3.00
2.50
2.00
1.50
1.00
0.50
0.00
-0.50
-1.00
-1.50
-2.00
-2.50
-3.00
-3.50
-4.00
-4.50
600.00
500.00
400.00
300.00
300.00
400.00
500.00
600.00
700.00
800.00
14th Crisp user meeting at UCL
15
3. Vertical displacements
Experimental result
SAGE CRISP
Vertical displacement contour
(Pile loading: 200 - 300N)
700.00
600.00
6.50
6.00
5.50
5.00
4.50
4.00
3.50
3.00
2.50
2.00
1.50
1.00
0.50
0.00
-0.50
-1.00
-1.50
-2.00
-2.50
-3.00
-3.50
500.00
400.00
300.00
300.00
400.00
500.00
600.00
700.00
800.00
14th Crisp user meeting at UCL
16
4. Dilatant volumetric strains
Experimental result
SAGE CRISP
Volumetric strain contour
(Pile loading: 200 - 300N)
700.00
0.10
0.00
600.00
-0.10
-0.20
-0.30
500.00
-0.40
-0.50
-0.60
400.00
-0.70
-0.80
300.00
300.00
400.00
500.00
600.00
700.00
800.00
14th Crisp user meeting at UCL
17
5. Max. shear strains
Experimental result
SAGE CRISP
Shear strain contour
(Pile loading: 200 - 300N)
700.00
0.80
0.70
600.00
0.60
0.50
0.40
500.00
0.30
0.20
0.10
0.00
400.00
-0.10
300.00
300.00
400.00
500.00
600.00
700.00
800.00
14th Crisp user meeting at UCL
18
6. Major principal strain directions
Experimental result
SAGE CRISP
14th Crisp user meeting at UCL
19
7. Zero extension line directions
(/or Slip line directions)
Experimental result
14th Crisp user meeting at UCL
SAGE CRISP
20
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
14th Crisp user meeting at UCL
21