lect 03 grain size

7/30/2019 Lect 03 Grain Size

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S= SIZE, SORTING

indicate:

- length of transport

-selective sorting

-mode of transport

-flow velocity, competence



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.



Sedimentologists often express grain size in units call Phi Units (φ;

the lower case Greek letter phi).

phi was originally defined as: )(log2 mmd −=φ

To make phi dimensionless it waslater defined as:

phi units assign whole numbers to the boundaries between size classes.

Od mmd )(log 2−=φ

Where d O = 1 mm.



Detrital Sediments & Sedimentary Rocks

gravelgravel

& &

conglomerateconglomerate

sandsand& &

sandstonesandstone

clay, siltclay, silt

& &

mudstonemudstone



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 theminimum size for each

size class.



Note that when grain size is plotted as phi units grain size becomes

smaller towards the right.



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.



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.



Describing Grain Size Distributions.Folk and Ward (1957) introduced the Graphic Method to estimate the

various statistical parameters describing a grain size distribution usingonly percentiles taken from cumulative frequency curves.

50 Md φ =Median

16 50 84

3 M

φ φ φ + +=Mean

6.64

5951684 φ φ φ φ σ

−+

−=Standard deviation

( ) ( )595

50595

1684

501684

22

22

φ φ φ φ φ

φ φ φ φ φ

−−++

−−+=Sk Skewness

2575

595

(44.2 φ φ

φ φ

−

−=K Kurtosis )



Standard Deviation (σ; lower case Greek letter sigma)

Also referred to as the sorting coefficient or dispersion coefficient of asediment.

It is a measure of how much variation in grain size is present within a

sample.

68% of the total weight of

sediment in a sample falls within

+/- 1 standard deviation of the

mean.

The units of sorting are phi units.



Sedimentologists use a specific terminology to describe the sorting

of a sediment:

Very well sorted 0 < σ

< 0.35φ

Well sorted 0.35 < σ

< 0.50φ

Moderately well sorted 0.5 < σ

< 0.71φ

Moderately sorted 0.71 < σ

< 1.00φ

Poorly sorted 1.00 < σ

< 2.00φ

Very poorly sorted 2.00 < σ

< 4.00φ

Extremely poorly sorted σ > 4.00φ



Sorting - visual estimate



Skewness (Sk)

A measure of the symmetry of the distribution.

Values range from –1.0 to +1.0.

Sk = 0

Perfectly symmetrical.

Md = M

Sk 0



Sk > 0

The distribution has more fine particles than a symmetrical distribution

would have.

The distribution is said to be fine tailed .

M is finer than Md

Sk 0



Sk < 0

The distribution has more coarse particles than a symmetrical

distribution would have.

The distribution is said to be coarse tailed .

M is coarser than Md

T i l Sk 0 3 t l fi k d



Terminology: Sk > 0.3 strongly fine skewed

0.1 < Sk < 0.3 fine skewed

-0.1 < Sk < 0.1 near symmetrical

-0.3 < Sk < -0.1 coarse skewed

Sk < -0.3 strongly coarse skewed

K t i (K)



Kurtosis (K)

A measure of the peakedness of the distribution (related to sorting).

K > 1 sharp peaked (Leptokurtic)

K = 1 normal (Mesokurtic)

K < 1 flat peaked (Platykurtic)



I t t ti



Sediment transport & sorting

Interpretation



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lect 03 grain size

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