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 : 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/m 3 = 1800 kg/m 3

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

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

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 MtMt MsMs MwMw MaMa VfVf

cgs:centimeter, gram, second mks:meter, kilogram, second LMT:Length, Mass, Time Systems of measurement Soil Physics 2010 Indigenous Standardized English metric Système Internationale (S.I.)

It is your… density  (rho) Greek letter r – widely used for density  w ≈ 1000 kg m -3 = 1.0 g cm -3  s ≈ 2650 kg m -3 = 2.65 g cm -3 Soil Physics 2010 mks cgs

t MtMt MsMs MwMw VfVf Air :  a ≈ 0 M a =0 Water:  w ≈ 1000 kg m -3 Solid:  s ≈ 2650 kg m -3 Soil Physics phase system as commonly used Why 2650? Density of Silica

Soil Physics 2010 Widely used Mass & Volume relationships: M L -3 Particle density: Air Water Solid t MtMt MsMs MwMw MaMa

Soil Physics 2010 Widely used Mass & Volume relationships: (Dry) Bulk density: M L -3 Air Water Solid t MtMt MsMs MwMw MaMa

Soil Physics 2010 Porosity: Unitless Air Water Solid t MtMt MsMs MwMw MaMa Range? Widely used Mass & Volume relationships:

Soil Physics 2010 Widely used Mass & Volume relationships: Porosity again:Unitless Air Water Solid t MtMt MsMs MwMw MaMa Solid fraction For Volumes, Solid fraction + Void fraction = 1

Soil Physics 2010 Other widely used: Volume wetness: Air Water Solid t MtMt MsMs MwMw MaMa Volumetric water content Water volume fraction Units? Range?

Soil Physics 2010 Other widely used: Degree of saturation: Air Water Solid t MtMt MsMs MwMw MaMa Unitless; range [0..1]

Soil Physics 2010 Air-filled porosity: Unitless Other widely used: Air Water Solid t MtMt MsMs MwMw MaMa Also written  a, 

Soil Physics 2010 Engineers prefer to norm to V s or M s Void ratio: Unitless V t changes when soil shrinks, swells, or is compressed.

Soil Physics 2010 Engineers prefer to norm to V s or M s Mass wetness: Unitless In agricultural & environmental soil physics, we tend to use  and , not w and e