Fig 1.
Schematic illustration of sphericity, roundness and roughness of a particle.
Fig 2.
An example of particle shape evaluation: (a) microscope photograph of an Ottawa sand grain; (b) particle boundary, maximum inscribed circle and index of sphericity; (c) internal rolling by a given covering disc; (d) normalised covered area against normalised disc area; (e) roundness characteristic curve and index of roundness; (f) sphericity-roundness diagram.
Fig 3.
Calibration of particle shape evaluation: (a) constructed geometries: Particles a~i; (b) RCCs for Particles a~i; (c) S-R diagram for Particles a~i; (d) typical sands: Particles j~r; (e) RCCs for Particles j~r; (f) S-R diagram for Particles j~r.
Fig 4.
Indices of sphericity and roundness for particles from Krumbein [5].
Fig 5.
Validation of particle shape evaluation: (a) comparisons between IS and SA; (b) comparisons between IS and SC; (c) comparisons between IS and AR; (d) RCCs; (e) comparisons between IR and RK1941; (f) particles in S-R diagram.
Fig 6.
Statistical evaluation of particle shape: (a) a patch of microscope photograph for Ottawa sand; (b) PDC of IR; (c) PDC of IS; (d) PDS in S-R diagram.
Fig 7.
Particle shape reconstruction for Ottawa sand: (a) target value and estimated RCC with 8 balls; (b) ball areas and their contributions; (c) reconstructed particle with random ball positions; (d) reconstructed particle shape indices and RCC; (e) particle shape reconstruction with a given PDS from Fig 6D; (f) PDS for 100 reconstructed particles.
Fig 8.
Effects of on particle shape indices: (a) error of IS; (b) error of IR.
Fig 9.
Evaluation of roughness: (a) illustration of covering discs inside and outside of particle boundary; (b) IRough of an Ottawa sand grain against .