Modelling transient dynamics of granular slopes

MPM, DEM and CD


Krishna Kumar, kks32@cam.ac.uk
University of Cambridge.

Patrick Mutabaruka, Kenichi Soga, Jean-Yves Delenne and Farhang Radjai




1st International Conference on MPM
Delft, January 2017.

Global landslide hazard

Fatalities due to landslides, 2007 - 2013 (Source: Nasa, 2015).

Aerial landslides

Afghanistan landslide - 2014 (Source: Boston Globe, 2014).

Granular column collapse

Experimental results (Lube et al 2005)

Multiscale modelling in geomechanics

Material Point Method

Discrete Element Method

  • Particle level interaction based on Newton's equation of motion

  • The contact force is computed as:

    • $F_n=\left\{ \begin{matrix} \text{ }0\text{ },\text{ }{{\delta }_{n}}>0 \\ -{{k}_{n}}{{\delta }_{n}}-{{\gamma }_{n}}\frac{d{{\delta }_{n}}}{dt},\text{ }{{\delta }_{n}}<0 \\ \end{matrix} \right.$

  • The Newton's equation of motion

    • $F_n =m \times a $

Micro to Macro

Simple shear test
Critical state friction angle

MPM v DEM column collapse

a = 0.4
a = 6

Column collapse runout

Run-out v aspect ratio

DEM column collapse

MPM v DEM column collapse

a = 0.4
a = 6

Granular slope subjected to impact

DEM slope with gradient and uniform impact energy

Granular slope subjected to impact

MPM simulation

MPM v DEM uniform impact (200 J)

MPM
DEM

Runout slope subjected to impact

Duration of runout subjected to impact

MPM v DEM energy dissipation

MPM
DEM

Energy dissipation

Normalised kinetic energy
Normalised vertical kinetic energy

Energy dissipation

MPM v CD gradient impact (200 J)

MPM
Contact Dynamics

Gradient v uniform energy subjected to impact

Granular collapse v slope subjected to impact

Effect of friction

Runout evolution
Time evolution

Summary

  • A power-law dependence of the run-out distance and time as a function of aspect ratio (column) and input energy (slope)
  • Two regimes with different values of the exponents are observed: a low-energy and a high-energy regime.
  • Column collapse: MPM captures frictional regime, however does not capture collisional regime
  • Slope - Low input energies: the distribution of kinetic energy in the system is found have a significant effect on the run-out, as the energy is mostly consumed in the destabilisation process.
  • MPM captures the “saturation effect” of dissipation due to friction, where the dilation of granular materials and rolling of the grains change in response to increase in friction coefficient
  • Slope: MPM is successfully able to simulate the transient run-out evolution with a single input parameter

Thank you!!


Krishna Kumar, kks32@cam.ac.uk