A Model for Rockfall Test ●Artificial rock model for rockfall test Five iron balls (diameter 11mm, weight 5.48g) are connected by adhesive. x y 2 1 3 4 z 5 Plane Side Opposite side The model is easily simulated by DEM

Experiment Condition Slope (Wood) Magnetic switch rock Height 30cm ↑ 4 5 1 2 100cm ← front 50cm 30 degree ＜side view＞ Initial Direction Set the rock model to same direction, then drop it by magnet switch in order to drop the rock model in same condition From slope foot, Y From center, X drop ＜plane view＞

Distribution of distance We repeat the experiment 300 times (drop of the rock model) X-direction (from center) 　Mean μx =0.4cm 　St.Dev. =19.2cm Y-direction (from foot) 　Mean μY ＝68.0cm 　St.Dev.σY＝24.2cm X Center line Y slope foot From slope foot, Y (cm) slope drop slope top ＜plane view＞ From center, X (cm)

Numerical Simulation by DEM ●Input parameter ●DEM model ↑up ・Spring constant (normal, shear) 　　2.40×105 N/m ・Damping constant (normal) 　　4.54×101 N・s/m ・Damping constant (shear) 　　5.80×101 N・s/m ・Friction angle between slope and particles 　　24.7 degree They are determined from simple test (rebound height), and material property. ←front All conditions, such as initial position, height of drop, etc., are same as the experiment

Perturbation of initial position in DEM Rotate the model around axis X, Y, Z with uniform random number Case 1 : -1 to 1, Case 2 : -3 to 3, Case 3 : -5 to 5 (degree) An example of DEM result Trajectory of the rock model Magnetic switch ↑ 4 5 1 2 X in plane view From center, X (cm) Side view Height (cm) ← front x z y Horizontal location (cm)

Comparison of Experiment and DEM Rotate the model around axis X, Y, Z, with uniform random number Case 1 : -1 to 1 degree Experiment DEM From slope foot, Y (cm) From center, X (cm)

Comparison of Experiment and DEM Rotate the model around axis with uniform random number Case 1 : -1 to 1, Case 2 : -3 to 3, Case 3 : -5 to 5 (degree) Cumulative curves are almost same irrespective of case 1-3 (uncertainty of position) Output uncertainty does not depends on input uncertainty From center, X From slope foot, Y Cumulative Distribution DEM, Case 1 DEM, Case 2 DEM, Case 3 Experiment 　From center, X (cm) or From slope foot, Y (cm)

DEM result by Compiler A and B Highly nonlinear simulation is sensitive to small change of any condition. What happens when the compiler is changed? All conditions are same except the COMPILER! Case 1 : -1 to 1 (degree) Compiler A Compiler B Plane View Side view From center, X (cm) Height (cm) From slope foot, Y (cm) Compiler A Compiler B Horizontal location (cm) From center, X (cm) Treatment of last digit of significant figures depends on compiler, option.

DEM result by Compiler A and B Rotate the model around axis X, Y, Z, with uniform random number Case 1 : -1 to 1 (degree) From center, X From slope foot, Y Cumulative Distribution Compiler A Compiler B Experiment From center, X (cm) or From slope foot, Y (cm)

Concluding Remarks Rockfall test The places where the rock model stop have large uncertainty Simulations of the rockfall test by DEM Good agreement in terms of distributions of the place where the model stop Uncertainty level of initial condition does not affect the distribution A compiler of DEM program affect each simulation, but does not affect the distribution 10 10