Large deformation modeling in geomechanics
MPM, LBM-DEM and LEM
Krishna Kumar, krishnak@utexas.edu
University of Texas at Austin
Hildebrand Department of Petroleum and Geosystems Engineering
23rd September 2019
Scales in modeling soil
CB-Geo 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)
Granular column collapse
Mesh-based vs Mesh-free techniques
Material Point Method
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 $
Experimental results (Lube et al 2005)
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 simulation of Oso landslide
MPM slope failure: pore pressure changes
Selborne case study of a 9 m high cut-slope slope (Soga et al., 2016)
MPM seepage failure of slopes
Credit: Mario Martinelli, Deltares. 2964 Elements, with 4 solid and 4 fluid MPs / cell
MPM rainfall-induced slope failure
Yerro et al., 2017
Photo-realistic simulations
Prof J Teran, UCLA
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)
Submarine run-out
Credit: Amanda Murphy (2016)
Mechanism of submarine landslides
Modeling 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
Loose v dense: Settlement phase
Collapse on slopes: loose v dense
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
Level-Set DEM
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)