By Michael A Hicks
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RANDOM-XFEM The approach a deterministic XFEM implementation and executes multiple realisations, with material properties randomised spatially in each realisation using the random field technique. A Monte Carlo analysis is then carried out to establish the range of behaviour. 2 (3) ⎞⎤ ⎛ K ⎞ 1 K ⎥ θc = 2 tan−1 ⎢⎢ ⎜ I − sign i ( K II ) ⎜ I ⎟ + 8 ⎟ ⎥ ⎟ 4 ⎜ K II ⎝ K II ⎠ ⎢⎣ ⎝ ⎠ ⎥⎦ (2) where KI and KII are stress intensity factors. 3 Random field realisations A random field generator is used following the approach of Hicks & Spencer (2010) utilising Figure 1.
Specht, B. 1988. Modified shape functions for the threenode plate bending element passing the patch test. International Journal for Numerical Methods in Engineering, 26: 705–715. S. 1978. Lumped mass matrices with non-zero inertia for general shell and axisymmetric shell elements. International Journal for Numerical Methods in Engineering, 12: 1635–1650. J. W. 1975. Principles of pavement design (2nd Edition). John Wiley & Sons. ACKNOWLEDGEMENT This research is funded by the CSC (China Scholarship Council), TU Delft and Deltares.
A very fine layer of mesh was predefined on the predicted soil and pile contact region to increase the contact accuracy. The Mohr-Coulomb failure criterion was used as the constitutive model of the soil. 50 kN/m2 and N 1 N N p Kij = ∑ ∑ ∑ ... VmVn m =1 n =1 p × MODELLING OF PILE PENETRATION SIMULATION COUPLING OF MPM WITH FEM The analysis of MPM requires more computation effort than FEM. To couple the calculation process between MPM and FEM, a mesh relaxation technique is introduced. In this technique, both MPM and FEM are sharing the same computation mesh.
Installation effects in geotechnical engineering by Michael A Hicks