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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!
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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: • Fibrous porous medium • Granular porous medium • 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, 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 showing Solving for rb gives , so rb = (2/3)*2700 kg/m3 = 1800 kg/m3 Soil Physics 2010
Where were we? After K.K. Mohanty, 1980 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
What are the available models for porous media? Capillary tubes are too simplistic – they’re singly connected Glass beads are intractable, and they’re still too simple. Irwin Fatt said (Petr. Trans. AIME, 1956): 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 Equation System(s) of equations Continuum models Agent-based models Concept Soil Physics 2010
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 Ma Vf Water Mw t Mt Solid Ms Soil Physics 2010
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 mks cgs r (rho) Greek letter r – widely used for density rw ≈ 1000 kg m-3 = 1.0 g cm-3 rs ≈ 2650 kg m-3 = 2.65 g cm-3 Soil Physics 2010
3 phase system as commonly used Air: ra≈ 0 Ma=0 Vf Water: rw≈ 1000kg m-3 Mw t Mt Solid: rs≈ 2650 kg m-3 Ms Why 2650? Density of Silica Soil Physics 2010
Widely used Mass & Volume relationships: M L-3 Particle density: Air Ma Water Mw t Mt Solid Ms Soil Physics 2010
Widely used Mass & Volume relationships: M L-3 (Dry) Bulk density: Air Ma Water Mw t Mt Solid Ms Soil Physics 2010
Widely used Mass & Volume relationships: Porosity: Unitless Air Ma Range? Water Mw t Mt Solid Ms Soil Physics 2010
Widely used Mass & Volume relationships: Solid fraction Porosity again: Unitless Air Ma Water Mw t Mt Solid Ms For Volumes, Solid fraction + Void fraction = 1 Soil Physics 2010
Other widely used: Volume wetness: Air Ma Volumetric water content Water volume fraction Units? Range? Water Mw t Mt Solid Ms Soil Physics 2010
Other widely used: Degree of saturation: Air Ma Water Mw Unitless; range [0..1] t Mt Solid Ms Soil Physics 2010
Other widely used: Unitless Air-filled porosity: Air Ma Also written fa, e Water Mw t Mt Solid Ms Soil Physics 2010 Soil Physics 2010
Engineers prefer to norm to Vs or Ms Vt changes when soil shrinks, swells, or is compressed. Void ratio: Unitless Soil Physics 2010 Soil Physics 2010
Engineers prefer to norm to Vs or Ms In agricultural & environmental soil physics, we tend to use f and q, not w and e Mass wetness: Unitless Soil Physics 2010 Soil Physics 2010
