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Soil Physics 2010 Outline More Wikipedia stuff Where were we? Kinds of models Mass and Volume

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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.

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Soil Physics 2010 Quiz!

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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

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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.

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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

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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?

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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.

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Kinds of models What is a model? Soil Physics 2010

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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

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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?”

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Physical models, physical analogue models Soil Physics 2010

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Mathematical models Concept Equation System(s) of equations Agent-based models Continuum models

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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

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Mass & Volume relationships Soil Physics 2010 Air Water Solid t MtMt MsMs MwMw MaMa VfVf

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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.)

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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

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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 2010 3 phase system as commonly used Why 2650? Density of Silica

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

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

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

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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

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

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

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

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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.

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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

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