Numerical modelling in geomechanics
MPM, LBM-DEM, LEM
Krishna Kumar
Giovanna Biscontin
Shell - Cambridge - PUC Collaboration
7th June 2018
Cambridge-Berkeley Computational Geomechanics
- Material Point Method
- Lattice-Boltzmann + Discrete Element Method
- Finite Element Method - Thermo-Hydro Mechanical Coupling
- Lattice Element Method
Multiscale modelling in geomechanics
Mesh-based vs Mesh-free techniques
Material Point Method
Material Point Method
MPM slope failure
Horizontal velocity (m/s)
MPM slope failure: pore pressure changes
Selborne case study of a 9 m high cut-slope slope (Soga et al., 2016)
MPM submarine landslide
Depth-averaged Material Point Method (Taka et al., 2012)
MPM submarine landslide: Water entrainment
Run-out for different water entrainment (Taka et al., 2012)
Concrete gravity flow
Wilkes et al (2018)
Concrete gravity flow with obstacle
Wilkes et al (2018)
Slump cone MPM simulation
Wilkes et al (2018)
Mechanism of submarine landslides
Modelling Test at 1g Condition
- Material type influences the mode of the flow.
- Target: Clay‐rich flow (Less diffusive, Hydroplaning).
LBM - DEM simulation of granular collapse in a fluid
aspect ratio 'a' of 6
Lattice Boltzmann - MRT
- $S_{\alpha i}$ 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
- 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
Collapse in a fluid: Effect of permeability
Dirichlet boundary conditions constrain the pressure/density at the boundaries (Zou and He, 1997)
$\rho_0=\sum_{a}f_{a} \mbox{ and } \textbf{u}=\frac{1}{\rho_0}\sum_{a}f_{a}$
Reduction in radius
Collapse in a fluid: Effect of permeability
Reduction ‘r’=0.7R (High permeability)
Reduction ‘r’=0.9R (Low permeability)
Effect of permeability: runout
Collapse in a fluid: Effect of permeability
Hydrodynamic force (x-dir)
250 - particle at the bottom of the flow;
872 - particle at middle of the flow; 1007 - particle at the surface of the flow
Effect of permeability: stress
Effect of permeability: pore-water pressure
Effect of permeability: drag vs hydroplaning
High permeable flow front experiences drag, while low permeable flow experiences hydroplaning.
Collapse on an inclined plane
aspect ratio 'a' of 6 on a slope of 5*
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
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
LEM: Tension test (uniform)
LEM: Tension test (Log-Normal 1.0)
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 hydraulic fracturing
John Wong, University of Cambridge