The Importance of Particle Size Distributions
to The Characterization of Soils
Andy Ward, Ph.D.
Caribbean Institute for Meteorology and Hydrology
October 25, 2012
Acknowledgments
The U.S. Department of Energy for funding
through the Remediation and Closure Science and
Science Focus Area Projects.
Kathryn Draper, formerly of the Pacific Northwest
National lab, who performed most of the
measurements as part of her M.Sc research
Gary Rawson, Technologies North America Inc,
perhaps the only sales person I have ever trusted
Background
Reliable prediction of multiscale transport behavior
needed to support:
Environmental remediation
Engineered waste repositories
Geologic sequestration
Oil and gas production
Water resources management
A critical need for all
application areas is reliable
estimation of model
parameters, particularly flow
and transport properties
Major Challenge
Rocks, soils and sediments are
naturally heterogeneous
Known to control near-surface
and subsurface contaminant
distributions
Knowledge of flow and
transport (energy, mass)
properties and how they vary in
space (and time) to:
Typical Stratification
Interpret current contaminant
distributions
predict future contaminant
migration
Manage soil and water resources
under changing climate
Atypical Stratification
Particle Size Distribution Transcends all Scales
Ice-Age flood deposits in the southern Pasco Basin
Effects Manifested at Multiple Scales
6
Why Measure Particle Size Distributions?
Particle size is a
fundamental property of any
sediment, soil or dust
deposit
can provide important clues to
nature and provenance
It influences a variety of
other properties
Can be defined across a
hierarchy of scales
Stratigraphic Architecture
Sedimentary Sequences
Lithofacies
Small-scale heterogeneities
Particle Size Distributions
Properties estimated from
texture cannot explain
transport behavior
Measured PSDs mostly
multi-modal
Size fractions
Gravel coatings
Rarely log normal
More realistic and unique
description using size
statistics
mean diameter
sorting coefficient
must account for gravel
Particle Size Classes
Boulders
Pebbles
Very coarse
Coarse
Medium
Fine
Very fine
Sand
Very coarse
Coarse
Medium
Fine
Very fine
Silt
Very coarse
Coarse
Medium
Fine
Very fine
Clay
Properties Dependent on Particle Size
Primary sediment properties are controlled by facies distributions, which in turn are
controlled by grain size distributions resulting from the depositional environment
Electrical Properties
Dielectric Spectroscopy
Surface conductivity
Formation Factor
Chargeability
Reactive Properties
Specific surface area
CECpor
Spor
Reaction Kinetics
Natural Isotope Abundance
40K, 238U, 232Th
Gross -ray response
Hydraulic Properties
Bulk density
Porosity
Residual water content
Water retention
Relative Permeability
Particle Size
Distribution
Transport Properties
Tortuosity
Intrinsic Permeability
Dispersivity
Formation Factor
Thermal Properties
Heat Capacity
Thermal conductivity
Characterization of Primary Particles
Traditional characterization of
size of “individual” particles by:
Sieving
Sedimentation
Soil whose mineral phase is to
be characterized is
Pretreated to remove organic
matter
Treated to disperse aggregates
Passed through series of sieves
with specified openings
(smallest is 0.05 mm)
Sizes of remaining dispersed
separates characterized
indirectly by sedimentation
(based on Stokes’ Law)
Challenges in Estimating Properties
Robust relationships
demands a higher level of
characterization
whole sediments
size fractions
coatings
4
3
2
1
0
0.01
0.1
1
10
100
1000
3000
Particle Size (µm)
C6216/2-29 39'-41' 32mm (Pre sonic) - Average, Thursday, January 08, 2009 3:19:48 PM
C6216/2-29 39'-41' 32mm (10min sonic) - Average, Thursday, January 08, 2009 3:46:33 PM
C6216/2-29 39'-41' 32mm (Post sonic) - Average, Thursday, January 08, 2009 3:50:32 PM
Particle Size of Coatings on 32 mm Gravel
C5213 3-30 6.5'-8'
C6216 2-29 39'-41'
C6213 2.5'-5'
C6212 2-28 47'-49'
C6216 2-29 30-33
clay
silt
100%
90%
80%
70%
60%
50%
40%
30%
20%
2 µm
Size (mm)
50 µm
10%
0%
Percent Passing
PSDs typically multi-modal
Fractions NOT log normal
Coatings that affect
sorption
Particle Size Distribution
5
Volume (%)
Properties estimated from
traditional PSDs often do
not explain transport
behavior
Paradigm Shift
Heterogeneous
Sediment
Grain
Subclasses
Identifying such
relationships requires a
higher level of sediment
characterization
Whole sediments
Size fractions
Characterize mineralogy
x1,1
x1,2
x1,3
x1,4
x2,1
x2,2
x2,3
x2,4
x3,1
x3,2
x3,3
x3,4
x4,1
x4,2
x4,3
x4,4
x5,1
x5,2
x5,3
x5,4
Lithocomponents
Grain Size Classes
CEC, SA, etc
Mass Fraction of
Lithocomponents
Sieving
Measure particle size
distributions
Measure Physico-chemical
properties
Mass Fraction, xij, of
Size class and Lithocomponents
Conceptual Model for Polydiserse Materials
Soils are linear systems that
obey the additivity principle
For all linear systems F(x) = y,
where x is a stimulus and y is
a response, the superposition
of stimuli yields a
superposition of the
respective responses:
F ( x1  x2  )  F ( x1 )  F ( x 2 )  
PSD of whole sample is
then calculated from the
distributions of, e.g., 2
components as:
f  p1 f1  (1  p1 ) f 2
Challenges to Approach
Particle Shape:
Assumption of spherical shape
Controls arrangement and
packing thus mass-volume
relationships
Individual property as
fundamental as size
Sample Size
Need PSD of very small samples
Requires
precise determination
using a rapid and reliable
method with a high degree of
precision
Mineralogy
Affect geochemical properties
Transported aggregates are
often polymineralic
Accounting for Mineralogy
Figure 1.5: Mineralogy of Yukon River Sediment as a function of grain size for
(a) fine material, and (b) coarse material (after Matthews, 2007).
Solution to Most of My Problems
Horiba LA 950 Particle Size
Analyzer
Widest Range Available: 0.013000μm
Fastest sample analysis
available
60 seconds sample-to-sample
Rapid change from wet to dry
analysis
Fully automated, modular
sampling systems
Easy and cheap to repair even
when no technician available
provided Home Depot is open
Materials
Coarse and fine fractions
Silt loam
Accusand (.84-.54 mm)
Silica beads (4.95 mm)
Pebbles (4-5.6 mm)
Binary mixtures
Triplicate samples
10% increasing fines
Solution-Solid ratio 2:1
Synthetic Groundwater
pH = 8.0
[CO3] = 1.05 × 10-3 mol L-1
100 ppb U(VI)
Uranium Sorption Experiments
Design
Contact times: 0.083, 0.167,
0.33, 0.5, 1, 2, 4, 8, 16, 32, 64,
128, 256 hrs
Supernatant separation using
15 minute centrifugation
Supernatant filtered (0.25 μm)
and analyzed for U and pH
Orbital shaker (116 rpm)
Binary Mixture
Fine End Member
Kinetics
9% Silt + 91% Marbles
51% Silt + 49% Marbles
Pebble and Silt end members
Coarse End Member
Sorption on Binary Mixtures
Accusand, Marbles, Silt, Pebbles
Contact times: 24 hrs, 5 days
Pebble End Member
Analytical Methods
Solid Phase
Continuous particle size
distribution by laser
diffraction
Surface area measured
by N2 gas adsorption
Surface area calculated
by geometric method:
Quantachrome
Autosorb 6B
Surface Area and
Pore Size Analyzer
n
 i pi
p
SAGEO  
  i i
i 1  i  i d i
i ns 1  i  i li
ns
Surface topography and
chemical composition by
optical and scanning
electron microscopy
Horiba LA-950
laser diffraction
analyzer
Laboratory Studies with Model Mixtures
Figure 2. Post-sonication Laser Particle Size Distribution of Textures Based on
USDA Classification
How Do we Use these Data?
To Describe Particle Size Statistics
Folk and Ward (1957) introduced the Graphic Method to
estimate the various statistical parameters describing a grain
size distribution using only percentiles taken from cumulative
frequency
Median
Md  50
Mean
M
Standard deviation

16  50  84
3
84  16
4

95  5
6.6
84  16  250 95  5  250

284  16 
295  5 
Skewness
Sk 
Kurtosis
95  5
K
2.44(75   25 )
Example Calculation of the Mean
Mean
M
16  50  84
3
1. Determine 16, 50and 84
16 = -0.59
50 = 0.35
84 = 1.27
0.59  0.35  1.27
M
3
= 0.34
Texture and Mean Diameter
0.6
0.8
0.5
Silt M ass Fraction
Sand M ass Fraction
1.0
0.9
0.7
0.6
0.4
0.3
0.5
0.4
0.3
0.2
0.2
0.1
0.1
0.0
0
0
0.5
1
1.5
2
0
0.5
dg (mm)
1.5
2
1.5
2
dg (mm)
0.6
0.08
0.07
0.5
M ud M ass Fraction
Clay Mass Fraction
1
0.06
0.4
0.05
0.04
0.3
0.03
0.2
0.02
0.1
0.01
0
0.0
0
0.5
1
dg (mm)
1.5
2
0
0.5
1
dg (mm)
To Understand Depositional Environments
Samples collected from
rivers and beaches (lake
and ocean)
Skewness plotted against
Sorting Coefficient
Beach sands better sorted
and with more common
coarse tail skewness than
river sands
Reflects difference in
processes acting on rivers
and beaches
Rivers carry wider range
of sizes: large particles
move in contact with bed;
large volume of fine
particles in suspension
Poorly sorted; rich in fine
particles (+ve skewness).
Particle Size and Water-Storage in Alluvium
Particle Size and Porosity
Typical sediment made up of
Spheres of different sizes
Small spheres can fill in pore
throats formed by larger spheres
Result is a lower porosity
•
n  0.255(1  0.83C )
d
C  60
d10
The porosity, b, of a
multicomponent mixture may
then be calculated as:
b  f ( X 1 , X 2 ,, X n ; d p , d p ,, d p ;1 , 2 ,n )
1
2
n
where Xi is the fractional solid volume of the ith
component.
Porosity Predicted from Particle Size Distributions
3
-3
Predeicted Porosity (m m )
0.50
0.45
0.40
0.35
0.30
0.3
0.35
0.4
0.45
3
-3
Measured Porosity (m m )
0.5
Particle Size and Permeability
Hydraulic Properties From Particle Size Distributions
Microstructure Characterization
grain parameters controlling particle
arrangement and packing
Incomplete Mixing Concept
Gravel Supported
Matrix Supported
Pore Structure
Identify individual particles and
arrangement
Simulate packing
Extend binary fractional packing
concept to the n fractions of the
Udden-Wentworth particle-size scale
Robust approach for upscaling basic
parameters derived from grain size
distributions
Allows correction for sizes > 2000
micron
Porosity
c
Dispersed mixture
0
min
100
Fines Content by Volume (%)
Water Rentention Curve with Unimodal PSD
100000
Measured Data
Fitted Params
10000
Pressure Head(cm )
Feasibility established with simple
case of binary mixture (coarse +
fine)
f
Linear mixture
1000
100
10
1
0
0.1
0.2
0.3
Theta
0.4
0.5
0.6
0.4
Fi = 29.5618 k
R 2 = 0.96
0.55
0.4805
s(m3 m-3)
Fredle Index
Hydraulic Properties and Texture
0.2
0.0
0
5e-005
0.0001
0.00015
 s = 0.2766 FI -0.0892
0.45
R 2 = 0.67
0.35
0.25
2
0.0
Permeability (mm )
1.0
0.4
0.6
150
ae (cm)
BC
0.2
Fredle Index
 ae = 7.0550 FI
100
0.5
 BC = 0.9015 FI
0.3863
R 2 = 0.96
0.0
0.0
0.2
R 2 = 0.94
50
0
0.4
0.6
0.0
Fredle Index
CEC (meq/100g)
b (g cm-3)
1.8
1.6
 b = 1.9401+0.0871 Ln(FI)
1.4
R 2 = 0.74
0.2
Fredle Index
0.2
0.4
0.6
Fredle Index
2.0
0.0
-0.4897
0.4
0.6
20
CEC = 2.3521 FI
-0.3542
R 2 = 0.94
10
0
0.0
0.2
Fredle Index
0.4
0.6
Facies Identifcation Particle Size Distributions
Identification of Lithofacies
Clay %
Th/K expresses relative K enrichment as indicator of clay
mineral species and useful for distinguishing architectural
elements (e.g. Coarse vs. fine) grain parameters controlling
particle arrangement and packing
45%
40%
35%
30%
25%
20%
15%
10%
5%
0%
y = 0.0368x ‐ 0.0661
R² = 0.9432
0
5
10
Th (ppm)
15
Multi-scale Heterogeneity
Identification of Lithofacies
34
Transect A-A’ Clay Content
Sorption of Marbles – Accusand
Low but non-zero sorption
with standard high SE
no change for fines < 40%
Nonlinear after 40%
Higher sorption in accusand
due to:
rough surfaces
metal-oxide coatings
organic matter
0.018
0.016
0.014
U sorbed ug/g
Accusand and marbles are
primarily silica
No sorption expected
0.020
0.012
0.010
0.008
0.006
0.004
0.002
0.000
0.0
0.2
0.4
0.6
Mass Fraction of Fines
0.8
1.0
Sorption of Pebbles - Silt Loam
0.20
Initial decrease in sorption on
the addition of silt loam
Likely blocks access to
fractures on pebbles
0.16
0.14
U sorbed ug/g
Large amount of U(VI) sorbed
by pebbles
0.18
0.12
0.10
0.08
0.06
0.04
0.02
0.00
0.0
Classic v-shaped curve
indicative of incomplete mixing
0.4
0.6
Mass Fraction of Fines
0.8
1.0
0.020
0.018
0.016
0.014
U sorbed ug/g
Pebbles sorption inconsistent
with current conceptual models
negligible surface area
no contribution to sorption
gravel correction based on
linear dilution (zero mixing)
0.2
0.012
0.010
0.008
0.006
0.004
Marbles and Silt Loam
0.002
0.000
0.0
0.2
0.4
0.6
Mass Fraction of Fines
0.8
1.0
Partial Mixing Model
Sorbed Species
Gravel Supported
Matrix Supported
Cf
Zero Mixing
Cc
Incomplete Mixing
Cmin
0
Ideal Mixing
Fines Content by Volume (%)
100
Surface Area vs. Size Statistics
Surface area measurements in
mixtures show:
25
(a)
SABET (m2/g)
20
nonmonotonic decrease with
increasing D50
decrease with geometric mean
diameter, dg
Well-behaved decrease as D10
(measure of fines) increases
Increase with sorting coefficient
15
10
5
0
1
100
1000
25
(a)
SABET (m2/g)
20
Geometric method assumes
smooth spherical particles and
not applicable to natural
materials
15
10
5
0
1
10
100
1000
Mean Diameter, dg (m)
25
25
(a)
(a)
20
SABET (m2/g)
20
SABET (m2/g)
10
Median Diameter, D50 (m)
15
10
15
10
5
5
0
0
1
10
Sorting Coefficient, g
100
0.1
1
10
D10 (m)
100
1000
Effects of Surface Roughness
intercept = internal SA,
SAint
Slope dependent on
roughness, i.e., exta/
(a)
20
SABET (m2/g)
A plot of SA(dg-1) should be
linear
Measured
25
15
10
5
0
0
0.05
0.1
0.15
dg ‐1 (m‐1)
Geometric Method
25
(b)
Nonlinear relationship
Suggest that SAint and ext
both dependent on dg
SAGEXT (m2/g)
indicates SAint > 0
inconsistent with the
smooth, nonporous
spherical particle
assumption
20
15
10
5
0
0
0.05
0.1
0.15
dg ‐1(m‐1)
Component Additivity
25
(d)
20
SACA (m2/g)
Non-zero Intercept
15
10
5
0
0
0.05
0.1
dg‐1(m‐1)
0.15
Comparison of PSD-based SA Methods
Geometric Method
Component Additivity Method
25
25
(a)
(d)
R² = 0.5466
20
SACA (m2/g)
SAGEXT (m2/g)
20
R² = 0.9112
15
10
5
15
10
1:1 Line
5
1:1 Line
0
0
0
5
10
15
SABET (m2/g)
20
25
0
5
10
15
SABET (m2/g)
20
25
Conclusions
Primary properties of sedimentary structures are
largely controlled by the distribution of facies,
which is in turn controlled by the depositional
environment and grain size distributions
Particle size is a fundamental property of any
sediment, soil or dust deposit
Shape and mineralogy can be assumed fixed for a
depositional environment
High resolution particle size distributions of <
3000 micron sediments and application of the
principle of superposition allows accurate
estimation of critical properties
Data most easily obtained with the Horiba LA-950