14th crisp user meeting at ucl1 numerical analysis of a piled foundation in granular material using...
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14th Crisp user meeting at UCL 1
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