1. 14th Crisp user meeting at UCL1 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. 14th Crisp user meeting at UCL2 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. 14th Crisp user meeting at UCL3 2D model pile-load test P-S curve Laboratory test using ideal material (Aluminium rods)

4. 14th Crisp user meeting at UCL4 Mesh A Total 639 nodes Total 1160 elements: 1132 LSTs + 28 LSQs Plane Strain Mesh

5. 14th Crisp user meeting at UCL5 Mesh B Total 195 nodes Total 176 elements: 4 LSTs + 172 LSQs Plane Strain Mesh

6. 14th Crisp user meeting at UCL6 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, E 0 = 1600Kpa, mE = 40000Kpa,  bulk = 24KN/m 3, Y 0 = 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/m 3

7. 14th Crisp user meeting at UCL7 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 K 0 = 0.5 4. Number of increments 320 increments DCM

8. 14th Crisp user meeting at UCL8 Increment Block Parameters Increment Block No. Increment Block List Pile head settlement (mm) Time- Step (sec) Number of Increments Case 1Case 2Case 3Case 4 1 Install pile015555 2  y1 = 0.08mm 0+0.08=0.081510205 3  y2 = 0.6mm 0.08+0.6=0.68151020 4  y3 = 0.32mm 0.68+0.32=115102040 5  y4 = 1.34mm 1+1.34=2.3415102050 6  y5 = 1.95mm 2.34+1.95=4.2915102050 7  y6 = 3.71mm 4.29+3.71=815102050 8  y7 = 3.83mm 8+3.83=11.8315102050 9  y8 = 8.56mm 11.83+8.56=20.3915102050 Total20.3994585165320

9. 14th Crisp user meeting at UCL9 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 45No 85No 165Yes 320Yes Dilation angle (degrees) convergence 0No 5 10No 15No 20Yes

10. 14th Crisp user meeting at UCL10 Comparison of CPU times More than 1hr Less than 12min

11. 14th Crisp user meeting at UCL11 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. 14th Crisp user meeting at UCL12 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. 14th Crisp user meeting at UCL13 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

14. 14th Crisp user meeting at UCL14 1. Vector movements Experimental result from the photo image processing (Scale:15) SAGE CRISP (M.F.=10) based on the mesh B (  = 20°)

15. 14th Crisp user meeting at UCL15 Experimental resultSAGE CRISP 2. Horizontal displacements

16. 14th Crisp user meeting at UCL16 3. Vertical displacements Experimental resultSAGE CRISP

17. 14th Crisp user meeting at UCL17 4. Dilatant volumetric strains Experimental resultSAGE CRISP

18. 14th Crisp user meeting at UCL18 5. Max. shear strains Experimental resultSAGE CRISP

19. 14th Crisp user meeting at UCL19 6. Major principal strain directions Experimental resultSAGE CRISP

20. 14th Crisp user meeting at UCL20 7. Zero extension line directions (/or Slip line directions) Experimental resultSAGE CRISP

21. 14th Crisp user meeting at UCL21 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