Ikumasa Yoshida Tokyo City University ETH, 2014.11.14, 10:00-11:00 Slope failure analysis by MPS method (Moving Particle Simulation) and its aleatory uncertainty Ikumasa Yoshida Tokyo City University

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

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

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

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

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

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 iyoshida@tcu.ac.jp 7