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Aleatory Uncertainty in Non-linear Behavior Observed in MPS Simulation

This study investigates the collapse of a slope due to gravity in MPS simulation, exploring uncertainty, non-linear behavior, and deformation, with focus on collapse ratios and response standard deviation.

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Aleatory Uncertainty in Non-linear Behavior Observed in MPS Simulation

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  1. Aleatory Uncertainty in Non-linear Behavior Observed in MPS Simulation Ikumasa Yoshida Tokyo City University

  2. Collapse of Slope due to Gravity 4 sec. 5 sec. 6 sec. 10 sec. Gravity (m/s2) 1G=9.8 Displacement in 1G 0.0 2.0 4.0 6.0 8.0 10.0 Time (sec.) 0.0m - 0.1m 0.1m - 0.5m 0.5m or more Collapse Ratio =Ratio of to all particles 2

  3. Deformation in early stage, weak nonlinear Magnification 100.0 Nonlinearity is still weak though failure progresses at the left boundary. Vertical disp. at top 1 sec. Disp. 0.00m～0.01m (1G) 0.01m～0.02m more than 0.02m 2 sec. Strong nonlinearity near the slope No magnification (1.0) 0.0m～0.1m 0.1m～0.5m 0.5m 4 sec.

  4. Uncertainty due to Property perturbation Surface 10m 30m 20m 22m 20m 2m 60m COV of Young’s Modulus (%) d : depth Material Property Young’s Modulus [E0] 50000 kPa Coefficient [CE] 500 kPa/m Poisson’s Ratio0.35 Damping Ratio0.05 Cohesion80.0 kPa Internal Friction30 (degree)

  5. Uncertainty of Response Standard deviation of the vertical displacement Vertical displacement of particle at slope top 1 sec. proportional to COV of Young’s modulus 2 sec. 4 sec. Almost same St.Dev. despite of Young’s modulus Collapse Ratio =Ratio of “>0.5m” Almost same St.Dev. =0.27 1.0 sec. 2.0 sec. 4.0 sec. Collapse ratio Case1 Case2 Case3 small medium large (uncertainty) Rosenblueth method to save computation time, MCS (size,10,20) is also performed in a specific case. Almost same result was obtained.

  6. Uncertainty of Response Standard deviation of the vertical displacement DEM • If you place the particles regularly, the regularity affect the failure phenomenon strongly. • Packing (initial placement of particles) is important. Same goes for MPS method. Several initial models are prepared and standard deviations of the response are estimated. (Particle size does not affect?) Collapse Ratio =Ratio of “>0.5m” Almost same St.Dev. =0.27 Standard Deviation Collapse Ratio Initial Case (Property) Model 1 2 3 Input uncertainty Small Large Rosenblueth method to save computation time, MCS (size,10,20) is also performed in a specific case. Almost same result was obtained. 6

  7. Computational Environment All input data, program are same except Compiler Compiler B Compiler A Collapse Ratio 0.24 Collapse Ratio 0.27 Treatment of significant digit depends on compiler, its option or PC, which leads to significant difference in nonlinear response. Displacement in early stage (linear response) is same irrespective of compliers

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