1. Acoustical Society of America Meeting
Miami, FL November 2008
Measuring Grain Roughness for the Purpose of High-Frequency Acoustic Modeling
Kevin B. Briggs
Allen H. Reed, Richard I. Ray
and Michael D. Richardson
Seafloor Sciences Branch, Naval Research Laboratory Stennis Space Center, MS 39529

2. Measuring Grain Roughness
Presentation Outline
Scanning Electron Stereomicroscopic imagery of natural sand grains
Micro-roughness power spectrum
X-ray micro-focus Computed Tomography (CT) of natural sands: tool for in situ measurements
Importance of grain contacts
presence of microasperities
understanding contact mechanics
number and type of contacts
Grain contact information is an essential starting point for developing and evaluating acoustic models that address acoustic losses at high frequencies. This information provides the basis to understand contact mechanics, such as grain slip and frame dilation, during insonification. Media frame stiffness depends, at the grain scale, on the number and type of grain-to-grain contacts, ultimately we would like to characterize sand sediments with CT imagery that identifies grain contacts.

3. 3D Surface Analysis Using SEM Imagery
Measuring Grain Roughness
3D Surface Analysis Using SEM Imagery
MeX—software from Alicona Imaging for 3D reconstruction and analysis of surfaces from stereoscopic SEM images
digital image processing algorithms compute 3D dataset in x, y, and z
2 images from different viewpoints are captured by eucentric tilting
extract 2D profiles
calculate roughness values
evaluate fractal dimension (exponent in power law)

4. Measuring Grain Roughness
Primary Profile

5. Linearized Roughness Profile
Measuring Grain Roughness
Linearized Roughness Profile

6. Estimate Power Spectra
Measuring Grain Roughness
Estimate Power Spectra
Slope: -5.18
RMS: 3.52 mm
Slope: -4.59
RMS: 4.90 mm

7. Measuring Grain Roughness
Quartz Grain Profile

8. Quartz Grain Roughness Spectra
Measuring Grain Roughness
Quartz Grain Roughness Spectra
Slope: -4.51
RMS: 1.15 mm
Slope: -4.50
RMS: 0.40 mm

9. Utilization of Roughness Parameters in Acoustic Modeling
Measuring Grain Roughness
Utilization of Roughness Parameters in Acoustic Modeling
RMS value used in Viscous Grain-Shearing model of Buckingham (1997)
affects Maxwell Element in grain contact theoretical model
Power law exponent (slope):
same spectral behavior regardless of grain type?
different slopes could indicate different provenance, minerals, weathering history?
Friction coefficient

10. Grain Contacts Probability of contact with surrounding grains:
Measuring Grain Roughness
Grain Contacts
Probability of contact with surrounding grains:
grain shape
presence of microasperities
grain packing
These aspects, especially packing, create non-ideal point contacts
necessary to observe grains in situ
X-ray Micro-focus Computed Tomography captures volumetric images of grains
Images by Loes Modderman and sandgrains.com

11. Measuring Grain Roughness
Grain Shape and Packing Effects Biot Parameters Similar for Different Shapes
rounded
subrounded
subangular
In Situ Porosity: h = 0.37
In Situ Porosity: h = 0.38
Maximum Porosity h = 0.43
h = 0.45
h = 0.46
Minimum Porosity h = 0.34
h = 0.34
h = 0.33

12. Measuring Grain Roughness
Grain Shape and Packing Effects Grain Angularity Affects Contact Variability Packing Increases Contact Number
Grain Shape Complexity Increases
Contact Variability (area & type) increases
Contact Number Increases
h = 0.43
h = 0.45
h = 0.46
h = 0.34
h = 0.34
h = 0.33
rounded
subrounded
subangular

13. Grain-Scale/Pore-Scale Evaluations
Measuring Grain Roughness
Grain-Scale/Pore-Scale Evaluations
3 mm
Pore Properties of Quartz Sand Sample (left)
Porosity
Permeability (m2)
Tortuosity (Le/L)2
0.41
1.55 x 10-10
1.33 ± 0.004
Throat Radius (mm)
Throat Length
(mm)
Body Radius
0.026 ± 0.027
0.330 ± 0.306
0.115 ± 0.032
Pore Properties of Quartz Sand Sample (left)
Porosity
Permeability (m2)
Tortuosity (Le/L)2
0.41
1.55 x 10-10
1.33 ± 0.004
Throat Radius (mm)
Throat Length
(mm)
Body Radius
0.026 ± 0.027
0.330 ± 0.306
0.115 ± 0.032
Grain Properties of Quartz Sand Sample
Grain size
Volume
Surface Area
Aspect Ratio
Coordination Number
Location in the sample
Grain Properties of Quartz Sand Sample
Grain size
Volume
Surface Area
Aspect Ratio
Coordination Number
Location in the sample

14. Individual Grain Data Grain Interaction Data Discrete Grain Data
Measuring Grain Roughness
Individual Grain Data
Grain Interaction Data
Types of Contacts: point, multiple point, face
point microasperity face
Discrete Grain Data
Inscribed radius: 115 mm
Volume: x 107 mm3
Surface area: 4.35 x 105 mm2
Aspect ratio: 1.88 (major axis: minor axis)
Number of contacts: (large value; upper end of spectrum)

15. Measuring Grain Roughness
Grain Contact Statistics Subangular Sands from Sediment Acoustic EXperiment 2004 (SAX04)
Coordination Number per Grain Statistics:
Mean 6.8
Median 6
Mode 5
Distribution of Contact Area per Grain
Frequency
Contact area– first point is the resolution limit of the CT
Coordination Number ranges more than it does for monosized spheres due to irregularity of grain shapes and to packing heterogeneity
Frequency
Contact Area (mm2)
Coordination Number/Grain
Most Contact Areas no larger than 50 mm2

16. Summary Latest acoustic models require grain information
Measuring Grain Roughness
Summary
Latest acoustic models require grain information
grain roughness: RMS roughness and spectrum
grain interactions: point, microasperity, face
Grain shape and packing affect porometric properties
porosity
permeability
tortuosity
Number and type of grain contacts determine:
contact mechanics
grain slip
frame dilation
frame stiffness
CT can give 3D imagery
required for grain/pore
information

17. Measuring Grain Roughness