1. Ikumasa Yoshida Tokyo City University
ETH, , 10:00-11:00
Slope failure analysis by MPS method (Moving Particle Simulation) and its aleatory uncertainty
Ikumasa Yoshida
Tokyo City University

2. Motivation
Safety Assessment of slope against Earthquake is one of the important issue in Japan
2011 great Tohoku EQ killed tens of people by slope failure
Collapse (Strong nonlinear problem) involves aleatory uncertainties.
numerical studies, DEM, MPS method
experimental stduies
Uncertainty involved in strong nonlinear phenomenon is not known widely. 2

3. Contents of Presentation
Self-Introduction, motivation
Uncertainty in rock fall experiment and its simulation by DEM
Uncertainty in slope failure simulation by MPS method
What is MPS method?
Randomness of particle placement
Gravity
Seismic motion
Concluding remarks
P2-DEM
P3-MPS
P4-MPS
P5-MPS
P6-MPS
P7-MPS 3

4. Nonlinear Behavior
Very sensitive to small change of condition such as initial particle position, property, computational environment
Image of uncertainty propagation from input to output
In weak nonlinear or linear behavior
the output uncertainty is proportional to input uncertainty.
In strong nonlinear behavior
the output uncertainty is constant irrespective of uncertainty level of input data when the input uncertainty is less than certain level.
The range of the constant uncertainty depends on nonlinearity in the phenomenon.
Strong
Nonlinear
Output
Uncertainty
Nonlinear
Aleatory Uncertainty
Related to Bifurcation?
Linear
Input Uncertainty 4 4

5. Aleatory and Epistemic Uncertainties
in Reliability Estimation of Existing structures
Aleatory : Inherent natural variability
Epistemic : Lack of knowledge (Model and statistical uncertainties)
By observation data, epistemic uncertainty can be reduced, but aleatory uncertainty should not for prediction.
The clear line that separates aleatory and epistemic uncertainties does not exist. The line depends on the (simulation) model we adopt.
Strong nonlinearity uncertainty is classified into Aleatory even if you use most advanced method. E E E E E A E E A A A
Strong nonlinear uncertainty A 5

6. That happens in real world!
Credibility of Advanced Numerical Method
Some people says “numerical method for collapse behavior is not credible (reliable)”
Very small changes affect the result.
Even compiler affects.
That happens in real world!
It is difficult to reproduce perfectly same collapse in experiment.
Advanced Numerical Method for collapse
recognize the uncertainty involved in collapse behavior.
interpret the result based on not single value (result) but
distribution (or band, interval). 6 6

7. Thank you for your kind attention
御清聴ありがとうございました
Welcome any question and discussion 7