Soil Physics 2010

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

1: Give one example each of a:(a) Fibrous porous medium

(b) Granular porous medium

(c) Foam porous medium

Extra points if all 3 naturally occur in soils.

wood, fibrous plant material, fungal hyphae, plant roots

sand, silt, soil solids

pumice, tuff, vessiculated basalt,

Quiz

Soil Physics 2010

Quiz

2: A soil has porosity = 0.33, and particle density s = 2700 kg m-3. What is its bulk density (b)?

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 b = 1800 kg m-3.

Soil Physics 2010

Quiz

2: A soil has porosity = 0.33, and particle density s = 2700 kg m-3. What is its bulk density (b)?

Method 2: drawing on the assigned

reading

Hillel gives an example showing

Solving for b gives ,

so

b = (2/3)*2700

kg/m3

= 1800 kg/m3

s

b

1

sb 1

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.

Soil Physics 2010

After K.K. Mohanty, 1980

Where were we?

Irwin Fatt said (Petr. Trans. AIME, 1956):

What are the available models for porous media?

Soil Physics 2010

Capillary tubes are too simplistic – they’re singly connected

Glass beads are intractable, and they’re still too simple.

Kinds of models

What is a model?

Soil Physics 2010

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?”

Physical models, physical analogue models

Soil Physics 2010

Soil Physics 2010

Mathematical models

Concept

Equation System(s) of equations

Agent-based models

Continuum models

All models are wrong. Some models are useful.

(George Box)

The most dangerous models give the right answer for the wrong reason.

Soil Physics 2010

Take-home message:be a critical model user

Mass & Volume relationships

Soil Physics 2010

Air

Water

Solid

t Mt

Ms

Mw

Ma

Vf

cgs: centimeter, gram, second

mks: meter, kilogram, second

LMT: Length, Mass, Time

Systems of measurement

Soil Physics 2010

IndigenousStandardized

English

metric

Système Internationale (S.I.)

It is your… density

(rho) Greek letter r – widely used for density

Volume

MassDensity

w ≈ 1000 kg m-3 = 1.0 g cm-3

s ≈ 2650 kg m-3 = 2.65 g cm-3

Soil Physics 2010mks cgs

t Mt

Ms

Mw

Vf

Air: a ≈ 0 Ma=0

Water: w ≈ 1000 kg m-3

Solid: s ≈ 2650 kg m-3

Soil Physics 2010

3 phase system as commonly used

Why 2650? Density of Silica

Soil Physics 2010

Widely used Mass & Volume relationships:

M L-3

s

s

V

MsParticle density:

Air

Water

Solid

t Mt

Ms

Mw

Ma

Soil Physics 2010

Widely used Mass & Volume relationships:

(Dry) Bulk density:t

s

V

Mb M L-3

Air

Water

Solid

t Mt

Ms

Mw

Ma

Soil Physics 2010

Porosity:t

wa

V

VV Unitless

Air

Water

Solid

t Mt

Ms

Mw

Ma

Range?

Widely used Mass & Volume relationships:

Soil Physics 2010

Widely used Mass & Volume relationships:

s

b1 Porosity again: Unitless

AirWater

Solidt MtMs

Mw

Ma

s

s

t

s

VM

VM

1ts

ss

VM

VM1

t

s

V

V1 Solid

fraction

For Volumes,Solid fraction + Void fraction = 1

Soil Physics 2010

Other widely used:

t

w

V

VVolume wetness:

Air

Water

Solid

t Mt

Ms

Mw

Ma

Volumetric water content

Water volume fraction Units? Range?

Soil Physics 2010

Other widely used:

wa

w

VV

VSDegree of saturation:

Air

Water

Solidt Mt

Ms

Mw

Ma

Unitless; range [0..1]

Soil Physics 2010Soil Physics 2010

t

a

V

VafAir-filled porosity: Unitless

Other widely used:

Air

Water

Solidt Mt

Ms

Mw

Ma

Also written a, af

Soil Physics 2010Soil Physics 2010

Engineers prefer to norm to Vs or Ms

s

f

V

VeVoid ratio: Unitless

1

e

e

e

1

Vt changes when soil shrinks, swells, or is compressed.

Soil Physics 2010Soil Physics 2010

Engineers prefer to norm to Vs or Ms

Mass wetness:s

w

M

Mw Unitless

b

ww

w

bw

In agricultural & environmental soil physics, we tend to use and , not w and e