Outline
• More Wikipedia stuff
• Where were we?
• Kinds of models
• Mass and Volume
Soil Physics 2010
Wikipedia stuff
• 3 (out of 16) students have now
claimed topics. Don’t be left out!
Avoid the rush!
• On Monday, Jan 25, I will start
assigning topics to students who
have not yet chosen their own.
Soil Physics 2010
Quiz!
Soil Physics 2010
Quiz
1: Give one example each of a:
(a) Fibrous porous medium
wood, fibrous plant material, fungal
hyphae, plant roots
(b) Granular porous medium
sand, silt, soil solids
(c) Foam porous medium
pumice, tuff, vessiculated basalt,
Extra points if all 3 naturally occur in soils.
Soil Physics 2010
Quiz
2: A soil has porosity f = 0.33, and particle
density rs = 2700 kg m-3. What is its bulk
density (rb)?
Method 1 – just reasoning through the
problem:
Consider a cubic meter of this soil. If it
had zero porosity, it would mass 2700 kg.
But 1/3 of it is air, so it must mass
(2/3)*2700 = 1800 kg. It’s a cubic meter,
so its bulk density is rb = 1800 kg m-3.
Soil Physics 2010
Quiz
2: A soil has porosity f = 0.33, and particle
density rs = 2700 kg m-3. What is its bulk
density (rb)?
Method 2: drawing on the assigned reading
Hillel gives an example
Solving for
rb gives
r
showing f  1  b
rs
rb  1  f r s , so
rb = (2/3)*2700 kg/m3
= 1800 kg/m3
Soil Physics 2010
Where were we?
Porous implies Pores: What’s a pore?
The porespace is typically
multiply connected: each pore
connects to several others.
A complete description of the
porespace must have both
geometrical (size) and
topological (connectivity)
components.
After K.K. Mohanty, 1980
Soil Physics 2010
What are the available models for porous media?
Irwin Fatt said (Petr. Trans. AIME, 1956):
Capillary tubes are too simplistic – they’re singly connected
Glass beads are intractable, and they’re still too simple.
Soil Physics 2010
Kinds of models
What is a model?
Soil Physics 2010
What is a model?
• A representation of reality
• A simplified representation or description
• A physical, mathematical, or otherwise logical
representation of a system, real world entity,
phenomenon, or process
• A representation of a process or system that
attempts to relate the most important variables in
the system in such a way that analysis of the
model leads to insights into the system
Soil Physics 2010
Conceptual models
All models start as conceptual models:
• “Think of the soil as a sandpile”
• “Imagine that this soil is a sponge”
• “What if all the pores in this soil were
the same size?”
Soil Physics 2010
Physical models, physical analogue models
Soil Physics 2010
Mathematical models
Concept
Equation
Continuum
models
Soil Physics 2010
System(s) of equations
Agent-based
models
All models are wrong.
Some models are useful.
(George Box)
The most dangerous
models give the right
answer for the wrong
reason.
Take-home message:
be a critical model user
Soil Physics 2010
Mass & Volume relationships
Air
Vf
Ma
Water
Mw
t
Mt
Solid
Soil Physics 2010
Ms
Systems of measurement
Indigenous
Standardized
English
metric
Système Internationale (S.I.)
mks:
meter, kilogram, second
cgs:
centimeter, gram, second
LMT:
Length, Mass, Time
Soil Physics 2010
It is your… density
r
(rho) Greek letter r – widely used for density
Mass
Density 
Volume
rw ≈ 1000 kg m-3 = 1.0 g cm-3
rs ≈ 2650 kg m-3 = 2.65 g cm-3
mks
Soil Physics 2010
cgs
3 phase system as commonly used
Air:
Vf
ra ≈ 0
Water: rw
≈ 1000 kg m-3
Ma=0
Mw
t
Solid: rs
≈ 2650 kg m-3
Why 2650?
Density of Silica
Soil Physics 2010
Mt
Ms
Widely used Mass & Volume relationships:
Ms
rs 
Vs
Particle density:
Air
M L-3
Ma
Water
Mw
t
Solid
Soil Physics 2010
Mt
Ms
Widely used Mass & Volume relationships:
Ms
rb 
Vt
(Dry) Bulk density:
Air
M L-3
Ma
Water
Mw
t
Solid
Soil Physics 2010
Mt
Ms
Widely used Mass & Volume relationships:
Va  Vw
f
Vt
Porosity:
Air
Unitless
Range?
Ma
Water
Mw
t
Solid
Soil Physics 2010
Mt
Ms
Widely used Mass & Volume relationships:
Porosity again:
Air
Water
t
Solid
rb
f  1
rs
Ma
Mw
Mt
Ms
 Ms 


Vt 

1
 Ms 


 Vs 
For Volumes,
Solid fraction + Void fraction = 1
Soil Physics 2010
Unitless
Ms Vs
 1
Ms Vt
Vs
 1
Vt
Solid
fraction
Other widely used:
Vw

Vt
Volume wetness:
Volumetric water content
Units?
Water volume fraction
Air
Range?
Ma
Water
Mw
t
Solid
Soil Physics 2010
Mt
Ms
Other widely used:
Degree of saturation:
Vw

S

Va  Vw f
Unitless; range [0..1]
Air
Ma
Water
Mw
t
Solid
Soil Physics 2010
Mt
Ms
Other widely used:
Air-filled porosity:
Va
fa 
Vt
Also written fa, e
fa  f 
Air
Unitless
Ma
Water
Mw
t
Solid
Soil Physics 2010
Mt
Ms
Engineers prefer to norm to Vs or Ms
Vt changes when soil shrinks, swells,
or is compressed.
Void ratio:
Vf
e
Vs
e
f
1f
e
f
1 e
Soil Physics 2010
Unitless
Engineers prefer to norm to Vs or Ms
In agricultural & environmental soil physics,
we tend to use f and , not w and e
Mass wetness:
Mw
w
Ms
rw
w 
rb
rb
 w
rw
Soil Physics 2010
Unitless