General

FOUNDATIONS OF SOIL PHYSICS RESEARCH1

WlLLARD GARDNER2

THE nature of the stress distribution'transmittedto the soil by the shearing and rolling effect of the

plow would be difficult to describe. Even more com-plicated is the nature of the resultant heterogeneousdeformation and heterogeneous rupture that results.The manner in which it appears to roll and crumbleindicates to the farmer that it is either a good, poor,or medium soil, or that it is too wet or too dry orideally moist. He distinguishes between soils by meansof the qualitative impressions that come to him as theresult of visual observation.

If he irrigates his land he observes that the waterseeps laterally and vertically and disappears leavinga modified color and a modified physical characterthat is not a simple linear combination of the respec-tive characters of the water and the dry soil. He mayhave a simple terminology like mellow, cloddy, rough,vuct, -moist, and dry. He has no time nor inclinationto make measurements and computations.

Terms like wilting coefficient, moisture equivalent,exchange capacity, dispersion, flocculation, thixo-tropy, structure viscosity, pH, pF, electrokineticpotential, zwitterion, electrovalence, co-valence, hetero-polar, homopolar, etc. convey nothing to him. X-raypatterns on a photographic plate determined by themineralogical composition of the soil would to himaccount for nothing.

The specialist does not desire to divorce himselffrom these concepts of the man who toils. They arein fact his own concepts. He does not desire to be-come a pedant or a snob, but his vocation if not hiscuriosity demands that he should inquire somewhatmore deeply.

Sensible objectives for the soil physicist would beto develop, a rational analytical formulation of prin-ciples and laws and to provide appropriate instru-

ments and devices for measuring the significant andimportant soil characteristics, with the practical endin view of aiding the engineers and the farmers topreserve and improve their soils.

This is obviously an ambitious program, the seri-ous pursuit of which necessarily leads him to a studyof the mechanics of the soil, the dynamics of themoisture it contains, .the behavior of the colloidalparticles and colloidal continua and their influence onthe microscopic and macroscopic properties of thesoil, and thus ultimately to fundamental physicaltheory. By this time it may seem that he has wanderedfar from the elemental concepts having to do withthe soil.

The problems of the soil physicist are essentiallydifficult. Ingenious and indirect experimental methodsbecome necessary. Much of his experimental infor-mation is the result of deductive inference concerningthe numerical data he obtains. His heritage is thefar-reaching consequence of centuries of research andin particular a quarter century or more of unparal-leled progress. He should be in position to attack andsolve many of the problems that confront him. Heinherits the laws of conservation of mass and ofenergy, the law of gravitation, Newton's laws ofmotion, the kinetic theory, the theory of probability,Coulomb's law, Ampere's law, Faraday's law, Joule'slaw, the law of the dynamo, the electron theory, andeven the theory of relativity and the quantum theory.

In this category of laws and theories there are per-haps none that can be deduced from the others. Theyare independent and, properly construed, are accepteduniversally. Some of them seem profoundly simpleand obvious, whereas others have actually shockedscientific men because of their seeming transcendentalcharacter and implication.

We infer that the physical properties of soils and

"Presented on the general program of the Soil Science Society of America, New Orleans, La., November 23, 1939. Contributionfrom the Utah Agricultural Experiment Station, Logan, Utah.

2Physicist. In the preparation of this paper the author has consulted various texts and original papers. He has been influencedin particular by Page's Theoretical Physics, Lewis and Randall's Thermodynamics, Lamb's Hydrodynamics, Briscow's Structureof Matter, Sidgwick's the Covalent Link in Chemistry, Houwink's Elasticity and Plasticity and Structure of Matter, Rouse'sFluid Mechanics for Hydraulic Engineers, Doherty and Seller's Mathematics of Modern Engineering, Fowler's StatisticalMechanics, Abramson's Electrokinetic Phenomena, Muskat's Movement of Fluids Through Porous Media, and other importanttexts. He has been particularly stimulated by the various papers by Kelley, Bodman, Jenny, Mattson, Keen, Haynes, Blair,Schofield, Childs, Weaver, Slichter, King, Hilgard, Bradfield and Jamison, Baver, Edlefsen, L. A. and Sterling Richards, R.Gardner, Affleck, Linfprd, Alexander, Middleton, Olmstead, Nichols, Smith, Lutz, Bennett, Allison, and many others whosenames should be mentioned.

SOIL SCIENCE SOCIETY PROCEEDINGS 1939

their behavior must be compatible with these generalfoundation principles. Owing, however, to the greatcomplexity of such problems as confront the soilphysicist, it becomes necessary for him, as for investi-gators in other fields, to set out anew on programs ofexperimentation and programs of analysis in the vari-ous lines of research. This in fact is the inherent andcharacteristic procedure in the inductive sciences.

It becomes necessary to modify Ampere's law inorder to include variable fields in dielectrics, but fromthe fundamental basis of electricity and magnetismthus modified we obtain Gauss's law, Maxwell's equa-tions of the electromagnetic field, and an extendedmathematical theory of electrodynamics, without newappeal to experiment.

Until the advent of thermodynamics, chemistrywas essentially an experimental science. Its data arenow required to conform with the law of conservationof matter, with the atomic and molecular theories,with the law of conservation of energy and with thesecond law. The third law is coming likewise to havesignificance. The second law, taken as a fundamentalprinciple or as an inference from the theory of prob-ability and the kinetic theory, combined with the firstlaw, supplies a foundation that has been far-reachingin its consequences and has led to numerous forecastsand predictions concerning practical and importantrelations. between the properties of chemical sub-stances, and concerning the problem of chemical equi-librium in general. The Clapeyron equation for therelation of vapor pressure to temperature, the Gibbs-Helmholtz equation for the reversible cell, Gibbs'phase rule, Van't Hoff's laws for osmotic pressureand freezing point lowering, the law of mass action,the gas laws, and many other important relations arededuced from this axiomatic foundation in thermo-dynamics.

There are likewise in mechanics secondary prin-ciples and generalizations, some of which result fromanalysis alone and some from new experimental infor-mation. The law of conservation of momentum andof angular momentum, Hamilton's principle, La-grange's equations, and many specialized mechanicaland mathematical theorems are the product of analy-sis alone.

In his attempts to solve his problems, the soilphysicist relies on these fundamental principles, butrequires new information and new analytical methods.

To develop a satisfactory theory of elasticity it hasbeen necessary to introduce the concept of stress in ahypothetically continuous medium as the resultant ofmultitudes of electrostatic and electromagnetic fields.

For small deformations linear homogeneous relationsbetween the various elements of a stress dyadic and acorresponding dyadic for strain have been assumedand confirmed by experiment.

A similar analytical procedure relating these stresscomponents in a plastic medium to corresponding rateof strain components has led to a successful theoryof plastic flow, as expressed in the Navier-Stokesdifferential equations of motion. For the special caseof laminar or simple flow a velocity potential has beenshown to exist for the mean velocity, resulting in agreat simplification of flow problems. This theory hasbeen confirmed by experiment to a high degree ofprecision. The Darcy velocity law is its representationin soil physics. Newton's laws of motion are involveddirectly in the development of this system of differ-ential equations.

Classical hydrodynamics is in essence a branch ofapplied mathematics built upon the law of conser-vation of mass and Newton's laws of motion, butproblems in hydraulics and flow of moisture throughthe soil require a new analytical approach and newexperimental information. It is apparent that geo-metric boundary conditions, kinematic and dynamiccharacteristics of flow, and the fluid properties ofdensity, specific weight, viscosity, surface tension, andelasticity, are involved in problems of fluid motion,but the fundamental kinds of measured quantitiesreduce to three, usually mass, length, and time, andthe discovery of what is known in dimensional analy-sis as the II-theorem leads to an immediate simplifi-cation of empirical relationships between these basicfactors.

It is evident that a functional relation between thevelocity and these various factors should exist. Themerit of the II-theorem consists in the fact that itmakes possible their replacement by a set of dimen-sionless or II-factors and provides a rational andsuccessful guide for the planning of experimental pro-cedure. Three significant, types of factors becomeapparent, ( i) those pertaining to boundary condi-tions; (2) those characterizing the basic flow patternof classical hydrodynamics, and (3) those pertainingto the action of weight, viscosity, surface tension, andelasticity, known respectively as the Froude, Rey-nolds, Weber, and Cauchy numbers familiar to theengineers.

For the case of turbulent flow there is a priorijustification for separating the velocity into a primaryand a secondary velocity field, and, as a matter ofconvenience to rewrite the Navier-Stokes differential

GARDNER: SOIL PHYSICS RESEARCH

equations of motion in the Osborne Reynolds formin order to introduce explicitly these primary andsecondary characteristics of the motion. These prob-lems entail great difficulties but the physicists and theengineers are making satisfactory progress in theirsolution.

The mechanics of the erosion problem cannot besolved with any satisfactory degree of completionwithout taking into account in one way or another theinfluence of turbulent motion.

To develop confidence in fundamental principlesand to utilize them in any program of research in thesolution of the problems of the soil would seem to bea rational procedure holding greatest promise of suc-cess. The terms "rational" and "empirical" are ofcourse relative. The fundamental generalizations arethemselves founded on experiment and are thereforeempirical. On the other hand, the development ofempirical formulae should have a certain amount ofa priori justification. The simplest of analytical rela-tions are the linear relations and that they should betried in numerous cases is a natural consequence ofthe mounting difficulties inherent in a different choice.Problems concerned with dielectric media were re-solved by this simple procedure. The polarization wasassumed to be proportional to the electric field inten-sity. It turns out to be so and leads to a definition ofthe dielectric constant and a simple theory of dielec-trics, and the electron theory provides a physical pic-ture of what happens when electric fields are imposedlocally or generally in devious ways. The theory ofthe diffuse double layer at the interface betweenphases, the electrokinetic potential, primary and sec-ondary bonds, the stability or instability of colloids,crystal structure, and in general the structure of mat-ter all hinge definitely upon this simple linear rela-tionship.

The forty years of physics research just past hasbeen a period of unparalleled progress, but the elec-tron theory and the quantum theory, themselves theproducts of experimental physics, preceded this im-portant era and provided the stimulus for untiringresearch. Although the principles of quantum me-chanics have much of the character and quality ofempiricism, they have nevertheless had a certain de-gree of a priori background because of the fact thata wide domain of experimentation appears to becompatible with this revolutionary theory.

Colloidal phenomena present complicated difficul-ties, but Coulomb's law, the electron theory, thetheory of valence based on the electron theory, andthe fruitful methods of statistical mechanics provide

a satisfactory basis of understanding and a satisfac-tory method of solution of problems in colloidalphysics and colloidal chemistry, and great credit isdue those whose efforts through intelligently guidedexperimentation and analysis have made at least asuccessful attack on many of these problems. Resultsachieved in one domain of science react to revealnew knowledge in another. The production of charac-teristic diffraction patterns by X-rays, an achieve-ment in recent experimental research in the field ofradiation, reveals the hidden secrets concerning thestructure of crystalin colloids and leads on to a betterunderstanding of the inward behavior of physicalmatter.

Chemical bonds, cohesive and adhesive forces ofattraction, and ultimate forces of repulsion may proveto represent resultant fields due to electrostatic andelectromagnetic attraction and repulsion, subject tothe principles of quantum mechanics. However, theresultant field becomes an extremely complicatedfunction (wholly unknown) of a great many coordi-nates describing the positions and velocities of theparticles concerned, and empirical substitutes for gen-eral principles become necessary aids in summarizingexperimental facts. In dealing with particles of sizelarge compared with the size of the atom we mayspeak of neutral bodies, but the field due to equalnumbers of positive and negative charges, as in aneutral atom, does not in general vanish in themicroscopic interior.

As an empirical procedure it proves convenient toclassify the interatomic energies under five headings,as follows : ( i ) Electrostatic energy between atoms(or ions) with net charges; (2) ele'ctrostatic energybetween permanent dipoles; (3) energy of primarypolarization; (4) energy due to secondary polariza-tion (Van der Waals energy) ; and (5) energy ofrepulsion (or overlap energy).

Elementary theory suffices as a basis for evaluatingthe mutual interaction energy concerned with a pairof dipoles. By combining this with other energy termsand substituting in the Schrodinger equation of quan-tum mechanics we are led to an estimate of the Vander Waals energy term. The methods of statisticalmechanics lead to a differential equation for the ionicpotential in the case of strong electrolytes. Themethod of Debeye and Hiickel lead to an approximatesolution of this differential equation and this in turnto an estimate of the thermodynamic potential whichdetermines the equilibrium properties of these electro-lytes. The quantum theory leads to an estimate of theoverlap or repulsion energy at great distances, but

SOIL SCIENCE SOCIETY PROCEEDINGS 1939

here again the complications in the theory for smalldistances leads to a necessity for empirical procedurefor the overlap energy. The electrostatic energy be-tween atoms (or ions) with net charges, the electro-static energy between permanent dipoles and theenergy of primary polarization, may be computed byelementary methods, and we are thus led to a pre-liminary estimate of the various types of energy ofinteraction between ultimate particles, and the im-provement and perfection of these methods constituteproblems for the soil physicists who are concernedwith the behavior of soil colloids.

The breaking down of mineral particles by randomforces is influenced by the nature of the interatomicforces but this problem is likewise a statistical oneand the theory of probability again comes to the aidof the physicist and he develops a rational size dis-tribution function involving parameters identifyingthe various mineral types.

As implied above, the air phase itself is composedof pores of varied size. The soil physicist, on the basisof Stoke's law of settling of heavy particles, hasdeveloped various sedimentation methods of deter-mining the solid particle size distribution, and hasrecently attacked the somewhat more difficult prob-lem of determining the frequency distribution of thesoil pores.

The deformation of plastic substances causes thereaction of the interatomic forces. For the case ofsimple flow with so-called simple or Newtonianliquids a simple linear relation between the stress andthe velocity gradient exists, but for the case of thixo-tropic substances this relation is more involved andunsolved problems remain in this important field.

The methods of classical statistical mechanics pro-vide an estimate of the average thermal energy of adiscrete particle or degree of freedom and the variousmethods of approach provide various potential fieldssurrounding the particle, with one or more potential

troughs, accounting for primary and secondary bonds,repulsive and attractive forces varying with variousinverse powers of distance. These attempts provideexplanation of laminar structure of such substancesas muscovite and the peptization of colloidal clay.

As stated, the kinetic theory leads to the law ofmass action and it has been successfully applied tochemical equilibrium problems, and in various waysin recent times attempts have been made to apply themass action law to base exchange phenomena withmore or less success. To take account, however, of thediffuse double layer at the boundary of colloidal par-ticles, and making use of the classical principles ofstatistical mechanics gives promise of a more satis-factory attack of this problem.

The problem of erosion of soils by wind and waterinvolves inherent difficulties. The mechanical actionof running water on soil particles involves in the firstinstance the stability of soil aggregates and secondlythe character of flow. Irregularities in the stream bedcontribute to the development of turbulence and tur-bulent flow depends upon a large number of localfactors. It is apparent, however, that the nature of thefluid, its dielectric character and ionic concentration,the velocity distribution and the orientation of thesurface in the gravitation field will be involved andthe .methods of dimensional analysis will doubtlesscontribute to the solution of these problems.

In the light of the obvious conclusion that theprocesses of nature seem to conform to a relativelyfew basic fundamental laws and that the details aresusceptible of indirect observation by means of in-genious devices and in view of the fact that hand inhand with attacks on physical problems goes equallyeffective attacks on the problems of mathematics andanalysis, it is safe to conclude that, although the hori-zon marches constantly ahead, we shall neverthelessmaster one by one the obstacles besetting our paths,and that we are even now on the road to a betterunderstanding of our problems.