Measurement of the mechanical properties of granular packs by wavelength-scanning interferometry by Yanzhou Zhou, Ricky D. Wildman, and Jonathan M. Huntley Proceedings A Volume 466(2115): March 8, 2010 ©2010 by The Royal Society

System configuration: (a) schematic diagram and (b) photo of the experimental system for measurement of the contact forces at the bottom of a granular pack. Yanzhou Zhou et al. Proc. R. Soc. A 2010;466: ©2010 by The Royal Society

Deformation map following the application of a two-bead load to the substrate surface: (a) raw data deformation map, (b) model form of the deformation map obtained by fitting equation (2.1) to the data shown in (a) and (c) difference between raw data and mo... Yanzhou Zhou et al. Proc. R. Soc. A 2010;466: ©2010 by The Royal Society

Calibration curve for substrate deformation versus normalized contact force; l3 is the peak of the substrate deformation (nm) (equation (2.1)), F is the contact force (mN) and mg is the weight of an 8 mm steel bead, mN. Yanzhou Zhou et al. Proc. R. Soc. A 2010;466: ©2010 by The Royal Society

Contact-force distribution in the whole field of view of the optical wedge, showing: (a) contact forces (normalized by the weight mg of one bead) in one of trial C (see table 1) and (b) map of contact points. Yanzhou Zhou et al. Proc. R. Soc. A 2010;466: ©2010 by The Royal Society

Contact-force correlations before and after the local disturbing forces have been applied to the top surface: (a) L1=4.99 N and (b) L3= N. fA, fB, fD and fE are the normalized contact forces f=F/ 〈 F 〉 for experiments A, B, D and E, respectively. Yanzhou Zhou et al. Proc. R. Soc. A 2010;466: ©2010 by The Royal Society

Probability distributions of the normalized contact forces. Yanzhou Zhou et al. Proc. R. Soc. A 2010;466: ©2010 by The Royal Society

Combined normalized contact-force fraction Φ (equation (3.2)). Yanzhou Zhou et al. Proc. R. Soc. A 2010;466: ©2010 by The Royal Society

Coarse-grained mean response forces and lateral displacements as a function of the radial position. Yanzhou Zhou et al. Proc. R. Soc. A 2010;466: ©2010 by The Royal Society

Probability distributions for the response forces, normalized by the applied loads L1, L2 and L3, shown (a) separately (filled square, L1; filled circle, L2; asterisk, L3) and (b) combined (filled square, experiment; dotted line, exponential law). Yanzhou Zhou et al. Proc. R. Soc. A 2010;466: ©2010 by The Royal Society

Probability distributions for the lateral displacements, normalized by the applied loads L1, L2 and L3, shown (a) separately (filled square, L1; filled triangle, L2; asterisk, L3) and (b) combined (filled square, experiment; dotted line, power law). Yanzhou Zhou et al. Proc. R. Soc. A 2010;466: ©2010 by The Royal Society

Comparison between the response forces and lateral displacements as a function of applied load. Yanzhou Zhou et al. Proc. R. Soc. A 2010;466: ©2010 by The Royal Society