Large deformation modelling in geomechanics
MPM, LBM-DEM and LEM
Krishna Kumar, kks32@cam.ac.uk
University of Cambridge
The University of Cambridge
14th November 2018
Scales in modelling soil
Cambridge-Berkeley Computational Geomechanics
- Material Point Method
- Lattice-Boltzmann + Discrete Element Method
- Finite Element Method - Thermo-Hydro Mechanical Coupling
- Lattice Element Method
Global landslide hazard
Oso landslide (2014)
Mesh-based vs Mesh-free techniques
Material Point Method
Material Point Method
Granular column collapse
Experimental results (Lube et al 2005)
MPM column collapse
Discrete Element Method
- Particle level interaction based on Newton's equation of motion
- The contact force is computed as:
- The Newton's equation of motion
$F_n=\left\{ \begin{matrix} \text{ }0\text{ },\text{ }{{\delta }_{n}}>0 \\
-{{k}_{n}}{{\delta }_{n}}-{{\gamma }_{n}}\frac{d{{\delta }_{n}}}{dt},\text{ }{{\delta }_{n}}<0 \\
\end{matrix} \right.$
$F_n =m \times a $
MPM v DEM column collapse
MPM v DEM column collapse
DEM column collapse
MPM v DEM column collapse
Collisional dissipation mechanism is missing in the continuum approach.
MPM slope failure
Horizontal velocity (m/s)
MPM v DEM runout slope v collapse
MPM 2-phase formulation
MPM slope failure: pore pressure changes
Selborne case study of a 9 m high cut-slope slope (Soga et al., 2016)
Slump cone MPM simulation
Wilkes et al (2018)
HPC MPM code
- Generic Templatised C++14
- 2D/3D MPM Code
- Generalise Interpolation Material Point
- Distributed MPI
- Intel TBB parallelisation
- Isoparametric elements
- HDF5 data stores
- Jupyter Notebooks integration
- Material models:
- Linear elastic
- Mohr coulomb
- Bingham fluid
- Newtonian
Disney's Frozen: Snow simulation
Photo-realistic rendering
- HDF5 + VTK
- Disney Partio: Houdini / Maya / Pixar's RenderMan
Possible boundary conditions of submarine run‐out
- Presence of ambient water (larger drag force & less gravity).
- Water entrainment.
- Pore pressure does not dissipate.
MPM submarine landslide
Depth-averaged Material Point Method (Taka et al., 2012)
Mechanism of submarine landslides
Modelling Test at 1g Condition
- Material type influences the mode of the flow.
- Target: Clay‐rich flow (Less diffusive, Hydroplaning).
Mechanism of submarine runout
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.
LBM-DEM fluid-solid coupling
$$\Delta t_{s}=\frac{\Delta t}{\mathit{n}_{s}} \qquad (\mathit{n}_{s}=[\Delta t/ \Delta t_{D}]+1) $$
- At every fluid iteration, $\mathit{n}_{s}$ sub-steps of DEM iterations are performed using the time step $\Delta t_{s}$.
- The hydrodynamic force is unchanged during the sub-cycling.
LBM laminar & turbulent flows
Smagorinsky model (LES):
Karman Vortex Street
Collapse in a fluid
Granular collapse in a fluid: Effect of aspect ratio
aspect ratio 'a' of 0.4
aspect ratio 'a' of 4
Runout: dry vs fluid
Dry collapse flowed further than the underwater collapse
Collapse on an inclined plane
aspect ratio 'a' of 6 on a slope of 5*
Collapse of a dense column on an inclined plane
Collapse of a dense column on an inclined plane
Collapse of a dense column on slopes: runout
Collapse of a loose column on slopes: runout
Loose v dense: Initiation phase
Loose v dense: Initiation phase
Pore-pressure distribution along the failure plane during initiation.
Loose v dense: Runout phase
Loose v dense: Runout phase
Water entrainment front (~15d length) at a slope of 5*
Loose v dense: Runout phase
Collapse on slopes: loose v dense
Kinetic energy evolution
Loose v dense: Settlement phase
Collapse on slopes: loose v dense
CPU v GPU
LBM-DEM Multi-GPU implementation
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
2D to 3D
LBM multi-component multi-phase
Lattice Element Method
LEM: Tension test (uniform)
LEM: Tension test (Log-Normal 1.0)
LEM Tension test
LEM Tension test
Lattice Element Method - Fluid coupling
- First assume injection pressure $P_{in}$ and injection rate $Q_{in}$ at injection point
- Solve fluid pressure at each fluid node
- Convert pressure to node force and solve LEM to update fracture aperture
- Repeat the above process until convergence
LEM fracturing
Wong et al., (2016)
Agent Based Modelling of cities
Soga et al., (2017)
Super computing
Scaling ABM: Time
Scaling ABM: Speed-up
Pavement condition
Agent Based Modelling of Tokyo
Bingyu et al., (2018)
Network analysis of Herpes Simplex Virus (HSV2)
Paranthropus boisei is the intermediary species that gave humans herpes!
(Underdown et al., 2017)
(Underdown et al., 2017)
The usual suspects
Cellular Automata modelling of disease
Top 5% of all research outputs scored by Altmetric
#3. We found out who gave us herpes