1. Introduction to soil water relationships

3. NS 2 Dec 1982, p 564

5. Particle density (rs)
Definitions
Mass of soil particle divided by volume of soil particle
Specific gravity, SG = ratio of mass of soil particle to
mass of equal volume of water of water at 4°C
Particle density in cgs or tonnes m-3
numerically equal to SG
mean particle density depends on:
ratio of OM to mineral matter
constitution of soil minerals
constitution of OM

6. Determination
SG bottle
boiled water to remove dissolved air
de-aerate for several hours with vacuum pump to remove
air trapped between particles
problem of floating OM
Typical values
organic matter = 1.3 g cm-3
quartz = 2.66 g cm-3
average for clay = 2.65 g cm-3
orthoclase = 2.5 to 2.6 g cm-3
mica = 2.8 to 3.2 g cm-3
limonite = 3.4 to 4.0 cm-3
Fe (OH)3 = 3.75 cm-3
normally taken as 2.65 cm-3

7. Bulk density (rb) and related parameters
rb = mass of solids
total volume
Value is effected by particle density, degree of compaction,
organic matter content

8. Typical values:
0.9 for organic soil (peaty) to 1.8 for compacted sand
Sand generally has a higher density than clay - why?
What do we mean by heavy & light soils?
Determination:
soil coring devices
problems of compaction
oven drying at 105°C
gamma ray transmission

9. Gamma ray transmission
measures density –
2 probes - transmitter & detector

10. Wet v dry bulk density
Ms + Mw Vt

11. Coefficient of linear extensibility (COLE)
Bulk density changes in swelling - shrinking soils.
COLE is a measure of this
Compares dry with saturated soil after it comes to equilibrium.
Cracks complicate the problem of determining BD of
swelling soils.
Even allowing for cracks the overall density may be higher
on shrinking as the surface becomes lower.

13. Total pore space (T)
= volume of (air + water)
vol. of (air + soil + water)

14. Volume of (air + water)
= total volume (air + soil + water) - volume of soil
where Vt and Vs are the volumes of the total sample and
the soil particles respectively
Vs = Ms /rs and Vt = Ms /rb
where Ms is the mass of oven dry soil and rs and rb are the
particle density and bulk density respectively. So:

15. rb = (1-T)/rs and so: and :
Used in agricultural (soils) research especially for
compaction studies.
Typical values 0.3 to 0.6. Often expressed as a %.

16. Packing density
measure of compaction of particular texture class
Void ratio (e)
Used mainly in engineering applications
e = volume of (air + water)
volume of soil
e = T/(1-T) [void ratio]
Typically 0.3 to 2.0
Air filled porosity
= volume of air
volume of total

17. Moisture content and related parameters
(a) Volumetric basis:
volume of water
volume of total
qv = Vw/Vt
(b) Gravimetric basis:
mass of water
mass of soil
qm = Mw/Ms

18. As Vw = Mw/rw and Vt = Ms/rb then
and so qv = qmrb/rw
= qmrb/1 (not dimensionally correct)
in metric measurements - density of water is 1
Often expressed as depth/depth for example mm/m

19. Degree of saturation (s)
degree of saturation = volume of water
volume of (water + air)
s = qV/T
Liquid ratio
Liquid ratio = volume of water
volume of solid

20. An example to try
A hole 30 cm X 30 cm x 30 cm is dug in a field. The wet
soil weighs kg. The soil is taken back to the
laboratory and oven dried. The final weight is kg.
(a) What is the bulk density
(b) What was the moisture content in the field
(i) by volume
(ii) by weight
(c) If the mean particle density is 2.64, what is the total
pore space

21. Graphical representation ....
Q. Why is the moisture content less at depth?)

22. Measurement of soil moisture
Laboratory
definitive
weigh, oven dry at 105°C for 24 hours, reweigh
if volume of hole from which sample was taken is known, bulk density can be calculated and hence volumentric moisture content
Field methods
Include:
neutron scattering
gamma ray transmission
time domain reflectometry
all need calibration against laboratory method

23. Neutron scattering

24. H scatters and slows neutrons very effectively - elastic collisions with atomic nuclei
called “thermalisation” of fast neutrons - come to same thermal (vibrational) energy as atoms at ambient temperature
hydrogen, has nucleus of about same size & mass as neutron and so has much greater thermalising effect on fast neutrons than any other element
method detects mostly H atoms not water per se
single probe containing radioactive source of high-energy neutrons such as radium-beryllium or americium-beryllium or caesium-137
thermal neutron density easily measured
thermal neutron density may be calibrated against water concentration on volume basis of other sources of H are constant

25. Time domain reflectometry
measures dielectric constant - ability of soil to
transmit electromagnetic (radar) waves -
mostly but not entirely dependent on water

26. Theta Probe

27. Simple parameters to characterise H2O & O2 availability
Soil water potential
matric potential
gravitational potential
pressure potential

28. Note on units
Soil water potential is the energy density -
usually per unit volume
Since dimensions of energy is ML2T-2 (force x distance)
dimensions of soil water potential has dimensions of
ML-1T-2
Pressure is force per unit area so has units of
MLT-2/L2 = ML-1T-2
Soil water potential thus has same units as pressure.
It can this be expressed as bars, cm H2O, cm Hg,
atmospheres
SI unit of Pressure, and so energy density, is the Pascal
1 kPa = 10 mb, 1 bar = 100 kPa

29. Capillarity and
adsorbed water
combine to produce
matric potential

30. Permanent wilting point
Usually taken as 15 (1500 kPa) bars, but may be more,
e.g. 20 bars (2000 kPa).
Water held between 1500 and 2000 kPa negligible
in virtually all soils.
PWP strongly correlated with clay.
In reality, a dynamic property which depends on:
potential evapotranspiration,
unsaturated hydraulic conductivity of the soil,
type of plant.

31. Field capacity
the upper limit of available water;
traditionally defined as the moisture content of a soil
48 hours after saturation and subsequently being allowed
to drain;
a high proportion of irrigation water added above
field capacity is “wasted”;
FC has also been considered to be:
0.33 bars [33 kPa] in USA or
0.1 bars [10 kPa] in the UK
FC also sometimes considered as the mean soil moisture
content in winter (cold climates) when the potential
evapotranspiration is small (and so drainage is main factor
governing equilibrium moisture content.

32. The tension equivalent to FC will be at least equal to
the air entry potential - see below.
FC, PWP and AWC are strongly dependent on texture, OM and BD

33. Air capacity
Defined as the air content (%) at field capacity.
Used in poaching studies.
Low air capacity usually means poor aeration.
Available water capacity
Difference between FC and PWP (%)
often x soil depth to give mm

34. Exercise The moisture content of a soil at field capacity was
found to be 27.3% by weight. At wilting point, the
moisture content was 19.7%. After oven drying of a
volumetric sample, it was found that the bulk
density was 1.42 g cm-3.
What is the available water capactiy as a percentage
of the volume?
A crop has a rooting depth of 1.5 m. How much water
is potentially available to the crop in mm equivalent.
If irrigation is to take place when the AWC is depleted
by 40%, how much water would need to be added?

35. Effect of bulk density on air capacity, wilting point &
field capacity

37. Dependence of compaction on moisture content

39. Wet year
Any
suggestions?
Dry year

40. Dynamic nature of FC, PWP, AWC
It is important to realise that FC, PWP and AWC are
commonly conceived as static soil properties but that
in reality, the are used as proxies for characteristics of dynamic system.
They do not take into account:
field conditions such as underlying horizons;
rainfall and or irrigation frequency and amount;
hydraulic conductivity of the soil;
run-off characteristics;
roots extension;
water infiltration and redistribution;
drainage from soil profile;
some water may drain at the same time as
evapotranspiration takes place;
ground cover changes;

41. crop height changes
climate, especially evapotranspiration rate effect the
values
Beware of too simplistic a view.
Even so, FC, PWP and AWC are very useful concepts.

42. Measurement of soil potential
Tensiometers
After Richards, 1965

43. Electrical resistance methods
Gypsum blocks
Granular Matrix Sensors
e.g. WATERMARK sensor from Irrometer Co, USA

44. Relationship of soil water potential to soil vapour pressure
If vapour between soil particles is in equilibrium with held
water, the vapour pressure is influenced by the “pull” of
the soil water ...
where :
Yt is the sum of matric and osmotic potential
 is the density of the water at the prevailing temperature,
R is the Universal Gas Constant
M is the molecular weight of water
T is the Temperature (°K)
e is the vapour pressure in the soil pores
e0 is the saturated vapour pressure of free water at the
particular temperature

45. The phenomenon is used as the basis of:
(a) the determination of the potential of a soil in the
laboratory (often in order to determine the moisture
release characteristics) by allowing a filter paper of
known pore size / moisture release characteristics to
come into equilibrium with the moist air over the soil
which is also in equilibrium with the soil water
potential.
(b) to determine the soil water potential in the field by
determining the humidity of the soil air using a
thermocouple psychrometer

47. Moisture release characteristics
Determination
pressure plate apparatus
sand; sand/kaolin bath apparatus
filter paper - allow to come into equilibrium and weigh
paper
solution - mixture so that vapour pressure is known and
this can be equated to soil potential, allow soil to come
into equilibrium with solution
use of pF scale

48. Filter paper method
top filter paper not in
contact - measures
sum of matric and
osmotic
potential of soil
bottom filter paper is
in pore contact so
measures matric
potential

49. Hysteresis

51. Typical curves
Near air entry
potential

52. Air entry potential (fe)
Also known as air entry value or bubbling pressure
= pressure at which largest pores begins to empty
Related to structure and field capacity.
fe corresponds to the largest pore size
where
and

53. f es is the air entry potential when the bulk density is f is in J/kg
1.3 g cm-3
f is in J/kg
dg the geometric mean particle diameter, is in mm, and
sg is the geometric standard deviation of the particle sizes
in mm (ranges from 1 to 30).

54. Example calculation of dg and sg (based on Campbell, p.9)
It is assumed that
clay has d < mm
silt has < d < 0.05 mm
sand has 0.05 < d < 2 mm
The predictor equations assumes that particle size
distribution is log normal
Logarithm of geometrical mean is given by:
ln dg = S mi ln di
where the di are the textural class sizes and mi are the
amounts in each class
The di for the size classes are calculated from
(lower limit + upper limit)/2

55. dclay = 0.001 mm; ln(dclay) = - 6.91
thus:
dclay = mm; ln(dclay) =
dsilt = mm; ln(dsilt) =
dsand = mm; ln(dsand) =
If a soil is 0.6 clay, 0.25 silt and 0.15 sand, then
ln dg = (0.6 x ) + (0.25 x ) + (0.15 x 0.025)
= =
= mm

56. (ln sg )2 = f1(ln d1)2 + f2 (ln d2)2 + f3 (ln d3)2 - (ln dg)2
Substituting this in the above equation,
the standard air entry potential is - 12 J kg-1
To make allowances for bulk density,
we need first to calculate sg.
The normal standard deviation is given by:
In a similar way, the logarithmic standard deviation is given
by:
(ln sg )2 = f1(ln d1)2 + f2 (ln d2)2 + f3 (ln d3)2 - (ln dg)2
The geometric SD is the antilog of the SD of the log
transformed values.
Thus: ln sg = 2.42 and so sg = e2.42 = 11.24
and b = 2 x x = = 26.25

57. Thus for this soil,
For bulk densities of 1.1, 1.3 and 1.5, the air entry potentials
would be:
- 0.84,
- 12
J kg -1
respectively

58. Sand tension table (0 to 100 cm potential)

59. Kaolin table (100 cm to 400 cm potential)
H should be added to difference between atmospheric pressure and
pressure in aspirator bottle

60. Pressure plate method
for potentials from
1 bar to 15 bars

61. Prediction of matric potential
Not reliable but some workers use equations of the form:
where qs = saturation % (vol) and Fe, the air entry potential
is calculated as before from:

62. Clays
Treated here because flocculation in the field is an essential
part of reclamation of sodic soils.
Flocculation occurs when clay particles “stick” together
because of electrical forces to form larger particles and
hence improves the hydraulic properties of the clay
Flocculation changes the hydraulic conductivities and the
moisture holding properties of clay soils.
Clay = 0.2 m -2m ; Colloidal clay: =< 0.2m ; m = 10-6 m
Adsorption: concentration of one material at surface
of another
Absorption: uptake of one material into another

63. Colloidal material is surrounded by thin layer of solution
which is different in composition from the solution
(relatively) far away from the particles.
Layer moves with the particle.
Micelle: colloidal particle + hydration shell
Intermicellar fluid : solution between micelles

65. Micelles usually negatively charged because of:
isomorphic substitution:
Si++++ in the clay may be substituted by Fe+++ or Al+++
which makes the clay short of + charge and so
negatively charged - smectite or illite type materials
Fe++ or Mg++ may replace Fe+++ or Al+++ in alumina or
gibbsite sheets
ionisation at the surface:
e.g. appearance of OH - at the surface and edges of
micelle
H2O adsorption and subsequent ionisation & diffusion
of H+ leaving a net negative charge because of the OH –
preferential adsorption of anions from solution for
example the adsorption of CO3- onto calcium carbonate
leaving an associated ion in solution

66. Some mutual attraction occurs between particles because of edge effects

67. Double layer
Double layer is name given to accumulation of positively charged ions around negatively charged micelles – some attached, some in solution
controls flocculation and dispersion
dependent on
cation type
cation concentration pH
the thicker the double layer, the greater the net repulsion and the more dispersed a soil becomes
important in structure and aggregation and reclamation of saline and sodic soils

68. Negative ion concentration in solution increases with distance & positive ion concentration decreases
negatively charged
soil particle +
a layer of cations directly
satisfies some of the
negative charge +
diffuse second layer eventually
reaches same
concentration as surrounding
bulk solution

69. Helmholtz model - assumes the charge concentration
Different models:
Helmholtz model - assumes the charge concentration
decreases linearly with distance
Gouy-Chapman model - assumes charge concentration
decreases exponentially with distance
Stern model - assumes linear decrease in the Stern
layer near the surface and then an exponential
decrease - thickness of Stern layer normally
taken as equal to the ionic radius of the adsorbed
species.
Taylor & Ashcroft, Fig. 5.7

70. The double layer is depressed by increasing the
valency of the ions in the intermicellar solution and hence the
packing of the charge near the micelle surface.
This is known as the depression of the double layer.

71. smaller cations, like Mg2+, will decrease double layer thickness
Effect of cation type + +
smaller cations, like Mg2+, will
decrease double layer thickness
larger cations, like Na+, will
increase double layer thickness

72. If concentration of intermicellar solution is increased,
concentration of ions in double layer reaches concentration of
intermicellar concentration nearer the micelle
surface

73. Effect of Cation Concentration+ +
high ionic concentrations will
decrease double layer thickness
low ionic concentrations will
increase double layer thickness

74. pH Kaolinite edge OH O Si Si Si OH Al Al Al OH neutral pH lower pH
(+1/2) OH Si Al
(+1/2)
(-1/2)
lower pH
higher pH OH O Si Al
(-1/2)
(-1)

75. London - van der Vaals forces
In addition to repulsive forces caused by accumulated
positive charges, there is also an attractive force between
clay particles caused by London - van der Vaals forces.
These forces, which occur even between electrically neutral
atoms, are due to the fact that, although the average
electrical field of a neutral spherical atom is zero,
the instantaneous field is not zero but fluctuates with the
movements of the electrons in the atom (or ion).
When 2 atoms (or ions) approach, they can synchronise their
electronic motions so that the electrical charge in one surges
towards the other when the fluctuations in this second atom
happen to leave its nuclear field somewhat exposed in this
particular direction.

77. Depending on relative strength of forces of attraction and
forces of repulsion, attractive van der Waals forces may
predominate in which case flocculation takes place.

78. Figure . In addition to attractive van der Waals forces, there are forces of repulsion between particles in suspension. The potential energy of attraction and also that of repulsion varies with distance from the particle surface. Curve 1 is an example of repulsion, and curve 6 is an example of attraction. These two curves vary with the colloid and the kinds and amounts of electrolytes. Thus, when curves 1 and 6 are summed for different conditions, they produce curves similar to 2 to 5. Curve 2 represents a stable suspension because the energy of repulsion predominates. Addition of more electrolyte will suppress the double layer and produce a curve similar to 3, 4 or 5 depending on the amount added. With curve 3, there is still an energy barrier to flocculation, but when the particles surmount the energy barrier and approach closer than point C, the forces of attraction predominate and the particles stick together. A suspension represented by curve 5 flocculates spontaneously and cannot be redispersed unless the curve is shifted back toward curve 2. This shift may be accomplished through expanding the double layer by changing the kinds and/or amounts of the electrolyte.
Fig in Taylor & Ashcroft

79. The thickness of the double layer is altered by both the
concentration and the ratio of divalent to monovalent ions
(and the ratio of tri-valent ions to mono-valent ions).
If the constitution and concentration of the soil solution
is changed, the constitution of the ions in the double layer
will change.
Replacement of monovalent ions by divalent ions in the double
layer makes it thinner and so more easy for Van der Waals
forces to take over and make the particles stick together
Langmuir equation
Relates the amount of adsorption onto clay particles to the concentration of the solution.
Look it up.

80. Specific surface
Important effect on:
cation exchange
retention and release of various chemicals
(nutrients and pollutants)
swelling of clays
retention of water
engineering properties
(e.g. plasticity, cohesion, strength )

81. am = As/Ms
av = As/Vs
ab = As/Vt
where a is the specific surface,
As is the total surface area in the sample,
Ms is the mass of solids,
Vs is the volume of the solids,
Vt is the total volume of the sample.
Suffixes m, v and b refer to whether specific surface is
on a mass basis, volume of solids basis or volume of
total soil basis.

82. Measured from amount of gas absorbed at certain T and P.
Can also be estimated from particle size distribution &
distribution of minerals
NB. surface area/volume for sphere = 6/d = av
Typical values

83. Texture and particle size distribution
Definitions of sand, silt, clay
1  = 10-6 m = 10-3 mm
sand: 
silt: 
clay : < 2

84. Texture triangles (using above definitions)

86. Mechanical analysis
Separation of particles
OM removed by H2O2
sometimes CaCO3 cementing agent removed by HCl
deflocculation by adding Calgon
(sodium hexametaphosphate)
mechanical agitation (shaking, stirring, ultrasound)
Sieving
Use sieves down to 0.05 mm (very fine sand)

87. Fd = 6phru Sedimentation Theory
Falling particle in a fluid experiences a downward force
and resistance force (drag) in opposite direction.
Stokes (1851) found that the drag was given by:
Fd = 6phru
u is terminal velocity,
h is the viscosity,
r is the radius of the sphere

88. 6phru = 4/3 p r3 g(rs - rf) When the two forces are in equilibrium,
particle reaches a “terminal velocity”. In that condition,
downward force on the particle
= gravity - upthrust due to fluid density
Upthrust = weight of particle - weight of fluid displaced
weight of particle = 4/3 p r3 rs g
where rs is the particle density
weight of water displaced = 4/3 p r3 rf g
where rw is the density of fluid
So upthrust is 4/3 p r3 (rs - rf) g
At terminal velocity,
6phru = 4/3 p r3 g(rs - rf)

89. which can be rearranged as:
where d is the diameter of the particle.
Since u = h/t where
h is height dropped and
t is the time elapsed
t = h/u
and so
and

90. Pipette method
All particles > d(h, t) will have settled out by time t
Proportion of original can be determined by taking a sample
After 8 hours only clay is left in suspension
Hydrometer
Measures density of remaining soil suspension instead of
taking a sample
X-ray transmission methods
Transmission related to density.
Gives continuous distribution

91. Soil structure
see handout