Lecture 1: A teaser on soils, porous media, and physical properties generally

Soil is a particular sub-class of the broader group of materials called porous media.  Immediately we have two questions: what are the properties of porous media generally? and, in what way are soils distinct from other porous media?  We start with the first question first, and hope to rejoin the second question in the next few lectures.

A porous medium is a composite of solid and fluid. In general, the solid is interconnected (such that, for example, it is at least partially load-bearing), and the fluid may or may not be:

Strictly speaking, non-porous solids are rare.  Rock, glass, and steel, for example, generally have non-zero porosity.  In rock and hence soil particles, the porosity can occur along the interface between differently-oriented crystals, and in the form of stress-induced fracture networks - not to mention the inter-granular porosity in clastic sedimentary rock.

If a medium is permeable, it is likely bicontinuous – fluid and solid phases are both continuous – and the mathematicians assure us that within each phase there will be constrictions and junctions.  Visualize a random pack of marbles, and you’ll notice that each marble touches many others and so is a junction; and the points of contact are constrictions.  Likewise, the pore space between marbles also has junctions and constrictions.  The fluid and solid phases in a bicontinuous medium therefore form complementary networks.  We will use some elementary concepts about networks (which mathematicians call graphs) as we proceed.

A porous medium has definable and measurable properties, such as porosity, permeability, and surface area.  Notice that these are all macroscopic properties.  Properties of a medium are necessarily defined at a larger scale, and the language we use - “this soil has a porosity of 0.47" - conveniently implies that the property applies to the whole thing.  But at a specific point, porosity is either 0 or 1 - the point is either in a solid or a fluid - and permeability and surface area aren’t defined.  Furthermore, the porosity we speak of, and the porosity we measure, are strongly affected by smaller-scale properties such as connectivity.  An extruded polystyrene, for example, has fluid bubbles separated by a solid matrix.  It is porous but not permeable, which is why it’s such a good insulator.  This kind of medium is sometimes called “Swiss cheese rock”!  Clearly, measurement methods that ignore fluid inclusions will give different values than methods that take them into account.  How would you measure the porosity of a medium with fluid inclusions?

The above discussion illustrates why the mean value of a property is a blunt instrument for characterizing a medium.   What range or distribution of values does the mean represent?  Is the value different, or does it have a different distribution, at larger or smaller scales?  A mean value gives no insight into how internally variable the property is.  And even a mean and statistical distribution are insufficient: what is the spatial distribution of the property?  How does it correlate with other properties?  How do these further details contribute to the mean value which represents the whole?  How do these details affect other properties?  Hydraulic conductivity, for example, varies from point to point and this variability contributes to other properties such as dispersivity.  In soil physics (as in other sciences), it is well to maintain some skepticism regarding the degree to which a parameter value truly characterizes the property.