Methods for Slope Failure Induced by EQ

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Methods for Slope Failure Induced by EQ

There is no analytical solution for wave equation
in general boundary condition.

• FEM (Finite Element Method) , SPH, MPM, Meshfree,
  etc.,
• Most widely used in many problems
• Difficulty to simulate slope failure
• a lot of cracks, i.e., small discontinuity, which
  are developed to a slip line, i.e., large
  discontinuity
• DEM (Distinct/Discrete Element method)
• The most successful method for slope failure.
• Does not satisfy the equation of wave motion
  theoretically.
• Difficulty in simulation of wave propagation

DEM
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MPS, DEM for Slope Stability Analysis

• DEM (Discrete/Distinct Element Method, Cundall
  1971)
• Good at collapse, failure problem with many
  cracks
• Difficulty in Elastic wave propagation (not
  satisfy wave equation)
• MPS (Moving Particle Semi-implicit/Simulation,
  Koshizuka et.al)
• MPS for fluid material (1995), MPS for solid
  material (2000?)
• MPS is mathematically derived from governing
  equation.
• Its formulation is close to that of DEM
• (We can use the knowledge through the experience
  of DEM)
• Few applications to geotechnical problem

DEM
Wave Propagation Collapse, failure
with many
crack
Computation Time Small Large
FEM
MPS ?
DEM
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Most important features in formulation of MPS

Volumetric strain
Shear and Normal strain
DEM can not express wave propagation precisely,
because DEM does not have the 3rd term. MPS can
be interpreted as extended DEM.
Same as DEM New Term Normal
Shear Volumetric
µ µ ? Lames Constant
Formulation with difference not differentiation
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Viscous Condition and Response
Vs 100m/s m1.5
Viscous
Vs 150m/s m2.0
2Einput Visous
Small amount of reflection is observed, but
generally good result
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Elastic Body Wave PropagationComprehensive Check
with 2-D FEM
transmission and reflection, coupling

• 3 layers slope model
• Particle(Element)-wise Rayleigh Damping
• 7, 3, 3
• Viscous boundary
• condition for input
• Ricker Wavelet

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Boundary Condition and Material Properties
Boundary Condition Base Viscous Boundary,
Side Free Input Motion Ricker
Wavelet Material Property
Input Motion Ricker Wavelet
Property Unit A B C
Unit Weight kN/m3 20 25 26
Shear Modulus MPa 720 4200 11000
Poissons Ratio - 0.40 0.37 0.35
Damping Ratio 7.0 3.0 3.0
Rayleigh Damping Characteristic frequency 1Hz,
15Hz
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Response Acceleration
horizontal direction Time0.74 sec. Red
lt-0.2m/s2, Bluegt 0.2m/s2
FEM
MPS r1.0m
Response at Top Slope
Horizontal Direction
Vertical Direction
Acc.
Acc.
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Time, (sec.)
Time, (sec.)