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 kbriggs@nrlssc.navy.mil

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.

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)

Measuring Grain Roughness Primary Profile

Linearized Roughness Profile Measuring Grain Roughness Linearized Roughness Profile

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

Measuring Grain Roughness Quartz Grain Profile

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

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

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

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

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

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

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: 2.00 x 107 mm3 Surface area: 4.35 x 105 mm2 Aspect ratio: 1.88 (major axis: minor axis) Number of contacts: 14 (large value; upper end of spectrum)

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

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

Measuring Grain Roughness