Large deformation modelling in geomechanics
MPM and LBM-DEM
Krishna Kumar, kks32@cam.ac.uk
University of Cambridge
University of Nottingham, UK
8th March 2018
Cambridge-Berkeley Computational Geomechanics
- Material Point Method
- Lattice-Boltzmann + Discrete Element Method
- Finite Element Method - Thermo-Hydro Mechanical Coupling
- Lattice Element Method
Agent Based Modelling of cities
Soga et al., (2017)
Network analysis of Herpes Simplex Virus (HSV2)
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Multiscale modelling in geomechanics
Granular column collapse
Material Point Method
MPM v DEM column collapse
MPM v DEM column collapse
DEM column collapse
MPM slope failure: pore pressure changes
Selborne case study of a 9 m high cut-slope slope (Soga et al., 2016)
LBM - DEM simulation of granular collapse in a fluid
aspect ratio 'a' of 6
Lattice Boltzmann - MRT
\[f_{i}(x + dx, t +\Delta t) - f_{i}(x, t) = -S_{\alpha i}(
f_{i}(x, t) - f_{i} ^ {eq}(x, t))\]
- $S_{\alpha i}$ is the collisional matrix.
- Probability density of finding a particle : $f(x,\varepsilon, t) $, where, x is position, $\varepsilon$ is velocity, and t is time.
Granular collapse in a fluid: Effect of aspect ratio
aspect ratio 'a' of 0.4
aspect ratio 'a' of 4
Collapse in a fluid: Effect of permeability
Reduction ‘r’=0.7R (High permeability)
Reduction ‘r’=0.9R (Low permeability)
Effect of permeability: stress
Effect of permeability: pore-water pressure
Effect of permeability: runout
Collapse on an inclined plane
aspect ratio 'a' of 6 on a slope of 5*
LBM - DEM a = 0.8 & 10,000 particles
- LBM Nodes = 50 Million : DEM grains = 10000 discs
- Run-time = 4 hours
- Speedup = 125x on a Pascal P100