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Methods for Slope Failure Induced by EQ

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

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Methods for Slope Failure Induced by EQ

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  1. 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 1

  2. 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 2

  3. Most important features in formulation of MPS Shear and Normal strain Volumetric 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 μλ Lame’s Constant Formulation with difference not differentiation 3

  4. Viscous Condition and Response Vs =100m/s m=1.5 Viscous Vs =150m/s m=2.0 2E+input Visous Small amount of reflection is observed, but generally good result 4

  5. 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 5

  6. Boundary Condition and Material Properties Boundary Condition Base : Viscous Boundary, Side : Free Input Motion : Ricker Wavelet Material Property Input Motion Ricker Wavelet Rayleigh Damping ：Characteristic frequency 1Hz, 15Hz 6

  7. Response Acceleration horizontal direction Time=0.74 sec. Red <-0.2m/s2, Blue> 0.2m/s2 FEM MPS: r=1.0m Response at Top Slope Horizontal Direction Vertical Direction Acc. Acc. 7 Time, (sec.) Time, (sec.)

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