Chapter 2 grain texture

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Chapter Grain Texture Clastic sediment and sedimentary rocks are made up of discrete particles The texture of a sediment refers to the group of properties that describe the individual and bulk characteristics of the particles making up a sediment: Grain Size Individual Bulk (Grain Size Distribution) Grain Shape Grain Orientation Porosity Permeability } Secondary properties that are related to the others These properties collectively make up the texture of a sediment or sedimentary rock Each can be used to infer something of: The history of a sediment The processes that acted during transport and deposition of a sediment The behavior of a sediment This section focuses on each of these properties, including: Methods of determining the properties The terminology used to describe the properties The significance of the properties Grain Size I Grain Volume (V) a) Based on the weight of the particle: m = Vρ S Where:m is the mass of the particle V is the volume of the particle ρs is the density of the material making up the particle (ρ is the lower case Greek letter rho) Weigh the particle to determine m Determine or assume a density (density of quartz = 2650kg/m3) Solve for V m V = ρS Error due to error in assumed density; Porous material will have a smaller density and less solid volume so this method will underestimate the overall volume b) Direct measurement by displacement b) Direct measurement by displacement b) Direct measurement by displacement Accuracy depends on how accurately the displaced volume can be measured Not practical for very small grains For porous materials this method will underestimate the external volume of the particle c) Based on dimensions of the particle Where:d is the diameter of the particle And the particle is a perfect sphere Measure the diameter of the particle and solve for V Problem: natural particles are rarely spheres πd V = II Linear dimensions a) Direct Measurement Natural particles normally have irregular shapes so that it is difficult to determine what linear dimensions should be measured Most particles are not spheres so we normally assume that they can be described as triaxial ellipsoids that are described in terms of three principle axes: dL or a-axis longest dimension dI or b-axis intermediate dimension dS or c-axis shortest dimension To define the three dimensions requires a systematic method so that results by different workers will be consistent Sedimentologists normally use the Maximum Tangent Rectangle Method Step Determine the plane of maximum projection for the particle -an imaginary plane passing through the particle which is in contact with the largest surface area of the particle The maximum projection area is the area of intersection of the plane with the particle Step Calculate the magnitude (R) of the resultant vector R= v +w 2 Remember that R is some proportion of the sum of the magnitudes of all of unit vectors in the data set Its value depends on the total number of observations in the data set and the amount of dispersion A useful measure of the dispersion is to express the magnitude of the resultant vector as a percentage of the sum of the magnitudes of all of the unit vectors in the data set (L), where: R L= N × 100 L → 100% There is little dispersion of the data (all measurements point towards the same direction) L → 0% There is a great deal of dispersion of the data (measurements point in all direction) L = 26% L = 92% Step Calculate the probability that the directional data are uniformly distributed (p) ( p=e −1 L2 × N ×0.0001) ) e is the natural logarithm = 2.71828, N is the total number of measurements in the data set p = 1; an equal number of observations in each directional class p → 0; all observations fall into the same directional class Raw data: Grouped data: 184 187 191 196 198 201 204 205 207 208 210 212 214 216 222 224 Class interval Midpoint Frequency 180-189° 184.5° 190-199° 194.5° 200-209° 204.5° 210-219° 214.5° 220-229° 224.5° Note: 10° classes Total (N): 17 205 Raw data: 184 187 191 196 198 201 204 205 207 208 210 212 214 216 222 224 Treatment of ungrouped data: N w = ∑ ni sin θ i = i =1 Total: sin 184° sin 187° sin 191° sin 196° sin 198° sin 201° sin 204° sin 205° sin 205° sin 207° sin 208° sin 210° sin 212° sin 214° sin 216° sin 222° sin 224° -7.04 N v = ∑ ni cosθ i = i =1 cos 184° cos 187° cos 191° cos 196° cos 198° cos 201° cos 204° cos 205° cos 205° cos 207° cos 208° cos 210° cos 212° cos 214° cos 216° cos 222° cos 224° Total: -15.13 205 N N w = ∑ ni sin θ i = − 7.04 v = ∑ ni cosθi = − 15.13 i =1 i =1 −7.04 θ = tan = 24.95° −15.13 w θ = tan v −1 −1 ∴θ = 24.95°+180°=204.95° Apply the Case Rule: if w>0 AND v>0 θ remains unchanged if w>0 AND v0 AND v[...]... diameter of a particle (dn): dn is the diameter of the sphere with volume (V1) equal the volume (V2) of the particle with axes lengths dL, dI and dS V1 = volume of the sphere V2 = volume of a particle (a triaxial ellipsoid) π 3 V1 = d n 6 π V2 = d L d I d S 6 By the definition of nominal diameter, V1 = V2 Therefore: π 3 π dn = d L d I ds 6 6 π 3 π dn = d L d I ds 6 6 dn can be solved by rearranging... screen with holes just smaller than the grains The grains collected on each screen are weighed to determine the weight of sediment in a given range of size The later section on grain size distributions will explain the method more clearly Details of the sieving method are given in Appendix I of the course notes III Settling Velocity Another expression of the grain size of a sediment is the settling... Sieving Used to determine the grain size distribution (a bulk property of a sediment) A sample is passed through a vertically stacked set of square-holed screens (sieves) A set of screens are stacked, largest holes on top, smallest on the bottom and shaken in a sieve shaker (Rotap shakers are recommended) Grains that are larger than the holes remain on a screen and the smaller grains pass through, collecting... thin sections Thin sections are 30 micron (30/1000 mm) thick slices of rock through which light can be transmitted Click here to see how a thin section is made http://faculty.gg.uwyo.edu/heller/Sed %20 Strat %20 Class/SedStratL1/thin_section_mov.htm Axes lengths measured in thin section are “apparent dimensions” of the particle The length measured in thin section depends on where in the particle that the...Step 2 Determine the maximum tangent rectangle for the maximum projection area -a rectangle with sides having maximum tangential contact with the perimeter of the maximum projection area (the outline of the particle) maximum tangent rectangle Step 2 Determine the maximum tangent rectangle for the maximum projection area -a rectangle... from the top of a column of fluid, starting at time t1 The particle accelerates to its terminal velocity and falls over a vertical distance, L, arriving there at a later time, t2 The settling velocity can be determined: L ω= t2 − t1 A variety of settling tubes have been devised with different means of determining the rate at which particles fall Some apply to individual particles while others use bulk... particles Settling velocity (ω; the lower case Greek letter omega ): the terminal velocity at which a particles falls through a vertical column of still water Possibly a particularly meaningful expression of grain size as many sediments are deposited from water When a particle is dropped into a column of fluid it immediately accelerates to some velocity and continues falling through the fluid at that velocity
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