Chapter 2 grain texture

Grain Volume V a Based on the weight of the particle: Where:m is the mass of the particle.. Axes lengths measured in thin section are “apparent dimensions” of the particle.The length mea

Chapter 2 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 SizeGrain ShapeGrain Orientation

PorosityPermeability} Secondary properties

that are related to theothers

Individual Bulk (Grain Size Distribution)

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

Grain Size

I Grain Volume (V)

a) Based on the weight of the particle:

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).

ρ

=

1 Weigh the particle to determine m.

2 Determine or assume a density

(density of quartz = 2650kg/m3)

3 Solve for V.

Error due to error in assumed density;

Porous material will have a smaller density and less solid volume so

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.

6

3

d

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.

II Linear dimensions.

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

a) Direct Measurement

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 1 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 2 Determine the maximum tangent rectangle for the maximum

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)

dL is the length of the rectangle

dI is the width of the rectangle

Step 3 Rotate the particle so that you view the surface that is at right angles to the plane of maximum projection.

dS is the longest distance through the particle in the direction normal to

the plane of maximum projection

V = π

6 d L x d I x d S

The volume of a triaxial ellipsoid is given by:

For fine particles only dL and dI can be measured in 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%20Strat%20Class/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 plane of the thin

section passes

The length measured in thin

section depends on where in the

particle that the plane of the thin

section passes

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 plane of the thin

section passes

For a spherical particle its true

diameter is only seen in thin section

when the plane of the thin section

passes through the centre of the

particle

Axes lengths measured in thin section are “apparent dimensions” of the particle

The three axes lengths that are commonly measured are often

expressed as a single dimension known as the nominal diameter of a

particle (dn):

d n is the diameter of the sphere with volume (V 1 ) equal the volume (V 2 )

of the particle with axes lengths d L , d I and d S

V1 = volume of the sphere 1 3

b) 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 bottomand 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 on

the 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

III Settling Velocity

Another expression of the grain size of a sediment is the settling velocity

of the 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 (often termed the terminal settling velocity).

The speed of the terminal settling velocity of a particle depends on properties of both the fluid and the particle:

Properties of the particle include:

The size if the particle (d)

The shape of the particle

The density of the material making up the particle (ρs)

Settling velocity can be measured using settling tubes: a

transparent tube filled with still water

In a very simple settling tube:

A particle is allowed to fall 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

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 samples.

Important considerations for settling tube design include:

i) Tube length: the tube must be long enough so

that the length over which the particle initially

accelerates is small compared to the total length

over which the terminal velocity is measured

Otherwise, settling velocity will be underestimated

ii) Tube diameter: the diameter of the tube must be at least 5 times the diameter of the largest particle that will be passed through the tube.

If the tube is too narrow the particle will be slowed as it settles by the walls of the tube (due to viscous resistance along the wall)

iii) In the case of tubes designed to measure bulk samples, sample size must be small enough so that the sample doesn’t settle as a mass of sediment rather than as discrete particles

Large samples also cause the risk of developing turbulence in the

column of fluid which will affect the measured settling velocity

b) Estimating settling velocity based on particle dimensions.

Settling velocity can be calculated using a wide variety of formulae

that have been developed theoretically and/or experimentally

Stoke’s Law of Settling is a very simple formula to calculate the settling

velocity of a sphere of known density, passing through a still fluid

Stoke’s Law is based on a simple balance of forces that act on a particle

as it falls through a fluid

FG, the force of gravity acting to make the

particle settle downward through the fluid

FB, the buoyant force which opposes the

gravity force, acting upwards

FD, the “drag force” or “viscous force”, the

fluid’s resistance to the particles passage

through the fluid; also acting upwards

FG depends on the volume and density (ρs) of the particle and is given by:

FB is equal to the weight of fluid that is displaced by the particle:

FD is known experimentally to vary with the size of the particle, the

viscosity of the fluid and the speed at which the particle is traveling

through the fluid

Viscosity is a measure of the fluid’s “resistance” to deformation as the particle passes through it

U d

FD = 3 π µ

Where µ (the lower case Greek letter mu) is the fluid’s dynamic

viscosity and U is the velocity of the particle; 3πd is proportional to the

3 3

6

FB = π × ρ × = π ρ

FG and FB are commonly combined to form the expression for the

“submerged weight” ( ) of the particle; the gravity force less the

We now have two forces acting on the falling particle.

Acting upward, retarding the settling of the particle

They are equal: F D = FG'

Stoke’s Law is based on this balance of forces.

FD = 3 π µ and Where

Stoke’s Law has several limitations:

i) It applies well only to perfect spheres (in deriving Stoke’s Law the

volume of spheres was used)

The drag force (3πdµω) is derived experimentally only for spheres

Non-spherical particles will experience a different distribution of viscous drag

ii) It applies only to still water

Settling through turbulent waters will alter the rate at which a particle

settles; upward-directed turbulence will decrease ω whereas directed turbulence will increase ω

downward-iii) It applies to particles 0.1 mm or finer.

Coarser particles, with larger settling velocities, experience different forms of drag forces.

iii) It applies to particles 0.1 mm or finer

Stoke’s Law overestimates

the settling velocity of quartz

density particles larger than

0.1 mm

When settling velocity is low

(d<0.1mm) flow around the

particle as it falls smoothly

follows the form of the sphere

Drag forces (FD) are only due to the

viscosity of the fluid

When settling velocity is high (d>0.1mm) flow separates from the sphere and a wake of eddies develops in its lee

Pressure forces acting on the sphere vary

Negative pressure in the lee retards the passage

of the particle, adding a new resisting force

Stoke’s Law neglects resistance due to

pressure

iv) Settling velocity is temperature dependant because fluid viscosity and density vary with temperature.

Temp µ ρ ω

°C Ns/m2 Kg/m3 mm/s

0 1.792 × 10-3 999.9 5

100 2.84 × 10-4 958.4 30

Grain size is sometimes described as a linear dimension based on Stoke’s Law:

Stoke’s Diameter (dS): the diameter of a sphere with a Stoke’s settling velocity equal to that of the particle.

µ

ρ

ρ ω

IV Grade Scales

Grade scales define limits to a range of grain sizes for a given class (grade) of grain size

They provide a basis for

a terminology that

describes grain size

Sedimentologists use the Udden-Wentworth Grade Scale.

Sets most boundaries to

vary by a factor of 2

e.g., medium sand falls

between 0.25 and 0.5 mm

Sedmentologists often express grain size in units call Phi Units (φ; the lower case Greek letter phi).

Phi was originally defined as: φ = − log2 d ( mm )

To make Phi dimensionless it was

later defined as:

Phi units assign whole numbers to the boundaries between size classes

O d

mm

d( )log2

−

=

φ

Where dO = 1 mm

Phi is the negative of the power to which 2 is raised such that it

equals the dimension in millimetres

) (

(mm

d

You can convert Phi to millimetres:

Note that when grain size is plotted as phi units grain size becomes smaller towards the right.

V Describing Grain Size Distributions

Data on grain size distributions are normally collected by sieving

1 Grain Size

Class ( φ )

2 Weight (grams)

3 Weight (%)

1 Grain Size Class

( φ )

2 Weight (grams)

3 Weight (%)

4 Cumulative Weight (%) -0.5 0.40 1.3 1.3

0 1.42 4.6 5.9 0.5 2.76 8.9 14.8 1.0 4.92 15.9 30.7 1.5 5.96 19.3 50 2.0 5.96 19.3 69.3 2.5 4.92 15.9 85.2 3.0 2.76 8.9 94.1 3.5 1.42 4.6 98.7

1 Grain size class: the size of holes on which the weighed sediment

was trapped in a stack of sieves

2 Weight (grams): the weight, in grams, of sediment trapped on the

sieve denoted by the grain size class

3 Weight (%): the weight

1 Grain Size Class

( φ )

2 Weight (grams)

3 Weight (%)

4 Cumulative Weight (%) -0.5 0.40 1.3 1.3

0 1.42 4.6 5.9 0.5 2.76 8.9 14.8 1.0 4.92 15.9 30.7 1.5 5.96 19.3 50 2.0 5.96 19.3 69.3 2.5 4.92 15.9 85.2 3.0 2.76 8.9 94.1 3.5 1.42 4.6 98.7 4.0 0.40 1.3 100

Each value in column 4 is the percentage of the sample that is coarser than the screen on which the sediment was trapped

1 Grain Size Class

( φ )

2 Weight (grams)

3 Weight (%)

4 Cumulative Weight (%) -0.5 0.40 1.3 1.3

0 1.42 4.6 5.9 0.5 2.76 8.9 14.8

1.5 5.96 19.3 50 2.0 5.96 19.3 69.3 2.5 4.92 15.9 85.2 3.0 2.76 8.9 94.1 3.5 1.42 4.6 98.7

Each value in column 4 is the percentage of the sample that is coarser than the screen on which the sediment was trapped

30.7% of the total sample is

coarser than 1.0 φ

1 Grain Size Class

( φ )

2 Weight (grams)

3 Weight (%)

4 Cumulative Weight (%) -0.5 0.40 1.3 1.3

0 1.42 4.6 5.9 0.5 2.76 8.9 14.8 1.0 4.92 15.9 30.7 1.5 5.96 19.3 50 2.0 5.96 19.3 69.3

3.0 2.76 8.9 94.1 3.5 1.42 4.6 98.7 4.0 0.40 1.3 100

Each value in column 4 is the percentage of the sample that is coarser than the screen on which the sediment was trapped

30.7% of the total sample is

coarser than 1.0 φ

85.2% of the total sample is

coarser than 2.5 φ

b) Displaying Grain Size Data

i) Histograms

Readily shows the relative amount of sediment in each size class

Each bar width equals

the class interval (0.5

φ intervals in this case)

Bars extend from the

maximum size to the

minimum size for each

size class

ii) Frequency Curves

A smooth curve that joins the midpoints of each bar on the histogram

iii) Cumulative Frequency Curves

A smooth curve that represents the size distribution of the sample

Several curves for different samples can be plotted together on one diagram for comparison of the samples

Sedimentologists commonly plot cumulative frequency curves on a

probability scale for the cumulative frequency.

On such plots normal, bell shaped distributions plot as a straight line

Plots of samples which are made up of normally distributed

subpopulations plot as a series of straight line segments, each segment representing a normally distributed subpopulation

Plots of samples which are made up of normally distributed

subpopulations plot as a series of straight line segments, each segment representing a normally distributed subpopulation

A benefit of cumulative frequency plots is that percentiles can be taken

direction from the graph

φn is the grain size that is finer than n% of the total sample

φn is referred to as the nth

percentile of the sample.

In the example φ20 is 0.86φ

0.86φ is that grain size that is

finer than 20% of the sample

Conversely, 0.86φ is coarser