A Numerical Investigation on Scaling Rolling Friction Effects in Shaking Table Model Tests

Table 2

Scale parameters with scaling density.

Physical parameter	Units	Equation	Scale
			1 : 1	1 : 4	1 : 7	1 : 10	1 : 13	1 : 16	1 : 19
Length	m	1/L	1	1/4	1/7	1/10	1/13	1/16	1/19
Friction increment ratio (friction coefficient increment per meter)	1/m	L	1	4	7	10	13	16	19
Elastic modulus	kN/m^2	1	1	1	1	1	1	1	1
Stress	kN/m^2	1	1	1	1	1	1	1	1
Density	t/m^3	D	1	0.522	2.800	8.163	17.934	33.436	55.990
Mass	t	D/L^3	1	0.00816	0.00816	0.00816	0.00816	0.00816	0.00816
Force	kN	1/L^2	1	0.0625	0.0204	0.01	0.00592	0.00391	0.00277
Damping constant	kN·s/m	D^0.5/L^2	1	0.0452	0.0341	0.0286	0.0251	0.0226	0.0207
Time	s	D^0.5/L	1	0.181	0.239	0.286	0.326	0.361	0.394
Velocity	m/s	1/D^0.5	1	1.384	0.598	0.350	0.236	0.173	0.134
Acceleration	m/s^2	L/D	1	7.656	2.5	1.225	0.725	0.479	0.339
Gravity acceleration 1	m/s^2	L/D	1	7.656	2.5	1.225	0.725	0.479	0.339
Gravity acceleration 2	m/s^2	1	1	1	1	1	1	1	1