GM V [txéETREC {aw-aims CELL Et¥\§&$TLGATE©IN Q35 HYWEQESES ARE? H‘fEZiMU‘L—[C CQNDUETEW-Wig ZN $3ng Thesis. EM fEm Daqmo 0‘3 M. S. } maxim: mm umwm i Emem Ufot Nwa : 1987 | I h I E I f ‘ _ A - .._.. . ”rd..-‘ u ‘LI LIBRARY ‘3' at: Michigan State University ABSTRACT GRAVIMETRIC PRESSURE CELL INVESTIGATION OF HYSTERESIS AND HYDRAULIC CONDUCTIVITIES IN SOILS by Emem Ufot Nwa Irrigation, drainage, and infiltration are processes important to crop production. These processes involve the complex problem of flow through unsaturated porous materials. The complexity of water flow through unsaturated porous media has often forced engineers, who manipulate the above processes in an effort to optimize crop production, to make the unrealistic assumption that the soil is either completely saturated or completely dry. The need to better understand this complex problem led to this investigation of hysteresis and hydraulic conductivities of two Michigan soils. In this study the Tempe pressure cells were used to investigate the reproducibility of the moisture-tension curves for Hillsdale sandy loam and Sim's loam soils. The moisture content of the five soil samples, made up of three layers of the first soil type and two of the second, were determined at each preset pressure point by weighing the pressure cells. The initial pressures were 0, 27.1, 54.2 cm of water and thereafter increased by 54.2 cm increments up to and included 455.6 cm of water. Three hysteresis loops Emem Ufot Nwa were run for each sample and the turn-around points were 453.6, 271.0 and 108.4 cm of water, respectively. The experiment was carried out in a constant temperature-humidity chamber with a temperature of 25.0.: 0.060C and 97% relative humidity. The investigation showed that the moisture-tension curves were not reproducible for the two soils. The scanning curves also fell outside the primary boundary curves at the higher suction range contrary to the requirements of the independent domain theory of hysteresis. The above two con- ditions are attributed to the swelling and consolidation of the samples. Using the method of Millington and Quirk with a matching factor, unsaturated hydraulic conductivities were computed and plotted against the moisture content and pressure. The hysteresis in the (K,9) relationship was small in comparison to that of (K,P) relationship but it was far from being negligible. A system for predicting the absorption scanning curves from one major desorption curve was tested and it predicted one experimental scanning curve fairly accurately but failed to predict the second. This calls for a refinement of the system. % Approved y ski/1&4 Major Prbfessor Approved oufl epartment Chairman Date /‘/ gagg/qé? GRAVIMETRIC PRESSURE CELL INVESTIGATION OF HYSTERESIS AND HYDRAULIC CONDUCTIVITIES IN SOILS BY Emem Ufot Nwa A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Engineering 1967 ACKNOWLEDGEMENTS As a major professor E. H. Kidder has been of immense help throughout my study program and was most encouraging throughout this investigation. Sincere appreciation is expressed to him. I am deeply indebted to Dr. J. R. Kunze (Department of Soil Science) who supervised this research and whose inspi- ration made the completion of this work possible. Gratitude is expressed to Dr. E. J. Monke (Department of Agricultural Engineering, Purdue University) who generated my initial interest in this topic. Equipment used in this research was purchased in part by funds provided by the United States Department of Interior as authorized under the Resources Research Act of 1964, Public Law 88-379. Thanks are also due the United States Agency for Inter- national Development (AID) who sponsored my training program. ii TABLE OF CONTENTS ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . LIST OF TABLES LIST OF FIGURES . . . . . . . . . . . . . . . . . . NOMENCLATURE I. INTRODUCTION. . . . . . . . . . . . . . . . . . 1.1. Objectives . . . . . . . . . . . . . . II. REVIEW OF LITERATURE . . . . . . . . . . . . . 2.1. 2.2. 2.5. 2.4. 2.5. 2.6. 2.7. III. SCANNING Flow Through Saturated Media . . . . . Flow Through Unsaturated Media . . . . Laboratory Measurement of Saturated Hydraulic Conductivity . . . . . . . . Measurement of Unsaturated Conductivi- ties . . . . . . . . . . . . . . . . . Hysteresis in Soil Moisture and Hy- draulic Conductivity Characteristics . The Independent Domain Theory of Hysteresis . . . . . . . . . . . . . . Theory of Infiltration . . . . . . . . CURVE GENERATING SYSTEM. . . . . . . . IV. EXPERIMENTAL PROCEDURE. . . . . . . . . . . . . 4.1. 4.2. 4.5. 4.4. 4.5. Description of Equipment . . . . . . . Equipment Set-up . . . . . . . . . . . Description of Soil Samples Investi- gated. . . . . . . . . . . . . . . . . Sample Preparation . . . . . . . . . . Pressure Steps and Turn-Around Points. iii Page ii vi vii m e- +> (DO) 15 18 25 29 50 50 52 55 55 57 TABLE OF CONTENTS - Continued Page V. RESULTS AND DISCUSSION. . . . . . . . . . . . . 59 5.1. Moisture-Tension Curves. . . . . . . . 59 5.2. Hydraulic Conductivity . . . . . . . . 49 5.5. Experimental Test of Scanning Curve Generating System. . . . . . . . . . . 62 VI. SUMMARY . . . . . . . . . . . . . . . . . . . . 64 VII. CONCLUSIONS . . . . . . . . . . . . . . . . . . 66 SUGGESTIONS FOR FUTURE STUDIES . . . . . . . . . . . 67 REFERENCES . . . . . . . . . . . . . . . . . . . . . 68 APPENDIX . . . . . . . . . . . . . . . . . . . . . . 74 iv LIST OF TABLES TABLE Page 1. Description of soils and soil fractions studied. 56 2. Particle size distribution of samples. . . . . . 56 5. Saturation and run time for the soil samples . . 40 4. Dates of moisture equilibrium and total number of weighings for run 2 of Hillsdale sandy loam soil . . . . . . . . . . . . . . . . . . . . . . 41 5. Pore classes and matching factors for samples. . 50 FIGURE 1. 8. 9. 10. 11. 12. 15. 14. 15. 16. 17. 18. 19. 20. LIST OF FIGURES The Tempe pressure cells and water well on cell holder. . . . . . . . . . . . . . . . . Components of the pressure cell. . . . . . . Diagramatic plan of the experimental set—up. Equipment inside the constant temperature humidity chamber . . . . . . . . . . . . . . e vs P, sample 1 . . . . . . . . . . . . . e vs P, sample 2 . . . . . . . . . . . . . . e vs P, sample 5 . . . . . . . . . . . . . . 9 vs P, sample 4 . . . . . . . . . . . . . . e vs P, sample 5 . . . . . . . . . . . . . . K vs 9, sample 1 . . . . . . . . . . . . . . K vs 9, sample 2 . . . . . . . . . . . . . . K vs 9, sample 5 . . . . . . . . . . . . . . K vs 9, sample 4 . . . . . . . . . . . . . . K vs 9, sample 5 . . . . . . . . . . . . . . K vs P, sample 1 . . . . . . . . . . . . . . K vs P, sample 2 . . . . . . . . . . . . . . K vs P, sample 5 . . . . . . . . . . . . . . K vs P, sample 4 . . . . . . . . . . . . . . K vs P, sample 5 . . . . . . . . . . . . . . Testing the generating system. . . . . . . . vi Page 51 51 55 54 45 44 45 46 47 51 52 55 54 55 57 58 59 60 61 65 90 sat BOD. *6: < O NOMENCLATURE volumetric moisture content (cc/cc) initial moisture content saturated moisture content bulk density (gm/cc) particle density (gm/cc) pressure (cm of water) pressure, suction or head (cm of water) hydraulic conductivity (= f(e), cm/min) intrinsic permeability (= K €3’, cm2) density of water (gm/cc) absolute water viscosity (poise = gm/cm sec) capillary pressure potential (cme/sece) - -. = .p_5_‘¥_ diffu51v1ty ( K W 56 , cmg/sec) moisture flux (cm/min) hydraulic gradient (cm/cm) porosity (cm3/cm3) total number of pore classes number of pore classes up to water content of interest radius of conducting pore (cm) surface tension (dynes/cm = gm/sece) acceleration due to gravity (cm/sece) vii NOMENCLATURE — Continued S sorptivity [f(eo)] t time x vertical ordinate, positive downwards- Z vertical ordinate, positive upwards (x.= —Z) Q,Y,w parameters [f(e)] WC water capacity (Be/SH) viii I . INTRODUCTION The relation of soil moisture to plant growth is obvious to all concerned with crop production. Irrigation and drainage are processes by which engineers manipulate soil moisture in an effort to optimize crop production. These processes of getting water into and out of the soil involve the flow through unsaturated porous media. In spite of this fact, most engineers, in the design of irrigation and drainage systems, have often made the unrealistic assumptions that the soil is either completely saturated with water or is completely dry. This is mostly due to the complexity of the problem of water flow through unsaturated porous materials. The complexity of the problem notwith- standing, there is a great need to better understand soil parameters and factors that affect soil water storage and movement that in turn affect efficient crop production. Hydraulic conductivity and diffusivity are two of the soil prOperties basic to soil water phenomenon. Infiltration, the entry of water into the soil from the soil surface, is a process important to conservation farming. After a heavy rainfall or irrigation, the rate of infiltration depends upon the developing moisture profile therefore a knowledge of the rate of profile development will aid in the determination of the infiltration rate. It is necessary to know "whether a given soil profile can admit the required application of water in the time during which irrigation water is made available to the farmer, and it is important to know (in the case of conservation) what proportion of rainfall of known intensity can be absorbed by soil and what proportion must remain at the surface to produce surface run-off with its concomitant erosion danger."l In the study of infiltration, moisture profile development, or moisture redistribution after infiltration, diffusivity and hydraulic conductivity must be known over the range of moisture change. Also the conductivity—suction, moisture content-suction, and water-capacity—suction relationships must be established. Unfortunately it is not easy to de- termine these parameters and establish these relationships. Matters are further complicated by the existence of hy- steresis, the non—single—valued nature of the conductivity- suction and moisture content-suction relationships. The methodology for determining hydraulic conductivity and diffusivity can be divided up into three general classes: 1. Steady-state method 2. Transient outflow method 5. Pore-size distribution method. 1E. C. Childs, “Recent advances in the study of water movement in unsaturated soil," Trans. 6th Intern. Congr. Soil Sci. B, p. 265. The steady-state method applies to systems in which the water content, tension, and flux do not change with time. But irrigation and drainage of soils are dynamic processes hence steady-state methods are not directly applicable. The extreme variability in the capillary conductivity values obtained by the transient outflow method, the inherent con- stant diffusivity assumption, and the poor reproducibility of the diffusivity measurement, cast a serious doubt on the data obtained by the outflow method. Also this method does not apply at the higher moisture range and is not easily adaptable to field experimentation. The pore-size distribu- tion method depends on the analysis of the moisture tension curves. This method is best for soils having a narrow pore size distribution, and near the saturation range where the other two methods fail. Because of the difficulties and inaccuracies involved in the direct methods of determining conductivity and diffusivity, the indirect method of moisture tension curve analysis is becoming more popular. Recently several numerical techniques have been developed for solving the unsaturated flow equation and most of them used the indirect method of conductivity determination. The moisture tension technique of the moisture profile and redistribution analysis is made particularly attractive by the development of the gamma-ray attenuation method of measuring soil water. This method of measuring soil water is easily adapted to field measurements and moisture changes with time can be followed rapidly and accurately without destroying the soil- water system. In every case the accuracy of the soil parameters is imperative for a realistic solution of the unsaturated flow equation. This calls for a closer examination of hysteresis inherent in the moisture-tension, and hydraulic conductivity— tension relationships. It is also necessary to check the reproducibility of the moisture-tension curves since the present methods of analyses make this assumption. Soil scientists who have worked in this area are aware of the prohibitive amount of time involved in the determination of the primary moisture-tension curves and the intermediate scanning loops. Any system that can predict the complete moisture-tension curves and their scanning loops from only one major branch—-desorption or absorption-will be an in- valuable contribution to the study of unsaturated flow in porous materials. A preliminary test of such a system is one of the objectives of this thesis. 1.1. Objectives 1. To characterize the moisture-tension relationship for Hillsdale sandy loam and Sim's loam soils. 2. To characterize the moisture-conductivity relationship for the above two soils. To investigate the reproducibility of the moisture content-tension curves. To observe the effect of hysteresis on soil hydraulic conductivities. To test a system for generating scanning curves. II. REVIEW OF LITERATURE 2.1. Flow Through Saturated Media In 1856 (Baver, 1965) Darcy opened the way to the scientific study of fluid flow through porous materials when he noted that the velocity of flow of water through saturated sand beds was directly proportional to the hydraulic gradient. Using the Poiseullian law Slichter (1899) derived an equa- tion of flow through the soil from which he calculated an approximate value of Darcy's proportionality constant. Slichter further combined Darcy's law and continuity equation and derived a saturated flow equation analogous to that for steady flow of heat or electricity. Most subsequent work in saturated flow have been based on Slichter's differential equation. 2.2 Flow Through Unsaturated Media Since the electrical and thermal potential theories were well developed Buckingham (1907) and Gardner (1920) felt that this knowledge could be applied to the phenomenon of soil moisture. Buckingham's 'capillary potential' and 'capillary conductivity' concept became the two major steps in the development of the conceptual basis for the study of soil moisture movement. Bearing BuckinghamFS capillary flow theory in mind Richards (1951) proposed that Slichter's equation be extended to cover unsaturated flow. With con— venient symbolism Richards' equation in the vertical direction may be written __ _ §_ __ §_ 29 where e is volumetric moisture content, K is hydraulic con- ductivity assumed to be a function of moisture content, p is fluid density, n is fluid viscosity, and Y is pressure potential. Richards' equation has dominated the work in unsaturated flow through porous materials ever since. The concept of diffusion was first proposed explicitly by Childs (1956a,b) but Childs and Collis—George (1948,1950) first derived the concentration-dependent diffusivity equa- tion while Klute (1952a,b) explicitly deduced and stated that equation. Klute's equation can be derived from equation (1) by writing _8_9_=_8__ g?— +33% at 32 ‘9 az ) n 52 (2’ - -- =2 .fl where difquiVity D n K 89 .. . ,= 11. and permeability K K pg (5) In equations (1) and (2) Darcy‘s law is assumed to be valid but Swartzendruber (1962,1965) has shown that Darcy's law is not valid at the lower moisture content. In spite of this the above two equations and the assumption that Darcy's law is valid have remained basic in studies of the moisture movement through unsaturated porous materials. 2.5. Laboratory Measurement of Saturated Hydraulic Conductivity Permeability and hydraulic conductivity both measure the ability of the soil to transmit water. Permeability is the property of the porous medium alone and has the dimen- sions of the square of a length while conductivity is the property of both the porous medium and of the fluid flowing in the medium. It has the dimensions of a velocity. Both permeability and conductivity are related by equation (5) above. Darcy's law which can'be written as v = —Ki (4) where v is the flux of water and i is the hydraulic gradient, has long been the basis for measuring saturated hydraulic conductivities in soils. The constant—head, and the falling- head methods are the two most common techniques of making laboratory measurements of saturated hydraulic conductivi- ties. Klute (1965) has given the details of these techniques. The fact that it is possible to come fairly close to complete saturation where the hydraulic conductivity can be assumed to be constant, makes the measurement of saturated hydraulic conductivity quite simple and straight forward. This is not the case for unsaturated hydraulic conductivity measurement. 2.4. Measurement of Unsaturated Hydraulic Conductivities Methods for measuring the unsaturated hydraulic con- ductivities can be grouped into three general classes, namely (1) steady state, (2) transient outflow, and (5) pore size distribution methods. Richards (1951) developed a pressure- type apparatus for making a steady state measurement of unsaturated hydraulic conductivities of soils. Richards and Moore (1952) made an improvement on Richard's method and presented conductivity data for six soils using the new pressure—type apparatus. Relative permeabilities in unsatur- ated porous rocks and in soils were measured by Geffen et al. (1951), Osoba et al. (1951), and Corey (1957) using variations of the steady-state method. Nielsen and Biggar (1961) pre— sented a simple apparatus constructed from stock materials while Elrick and Bowman (1964) used the apparatus improved by Richards and Moore for measuring capillary conductivities by the steady state method. Elrick and Bowman measured conductivities for Guelph loam soil and noted that their ap— paratus was well adapted for making measurements in the high moisture content range. They expressed their preference for this method because of the problems associated with the transient outflow method. 10 Gardner (1956) proposed the pressure plate outflow method of calculating capillary conductivity, and Miller and Elrick (1958) refined Gardners method by accounting for non-negligible membrane impedance. They developed a method that employs all of the experimental data rather than just the exponential tail and they noted that neglect- ing membrane impedance would have made the calculated con- ductivity 5.5 times too small. Rijtema (1959) varied Miller and Elrick's method to obviate separate measurement of contact impedance, while Kunze and Kirkham (1962) simplified it experimentally and computationally. Kunze and Kirkham used only the initial outflow data for their computations. Elrick (1965) measured conductivities under both transient and steady state conditions and found that the experimental outflow does not fit the predicted theory close to saturation. He attributed the descrepancy to basic assumptions of the diffusion theory namely that (1) Darcy's law is valid in a general form for unsaturated systems and (2) the capillary pressure is a unique function of moisture content. Using different methods Jackson et al. (1965) tested the reproducibility of the results and com- pared the different theories of the outflow method. They concluded that the constant diffusivity assumption is a serious limitation of the method, that reproducibility of diffusivity measurements by the method is close to nill, and so they cast serious doubt on any data obtained by this method in its present state of development. 11 A theory in which permeability is related to pore size distribution was proposed by Childs and Collis-George (1948, 1950). The theory was based on the probability that pores of different radii were continuous in a material like sand. They determined permeability for slate dust, 1/2 to 1/4 mm sand fraction, and 1 to 1/2 mm sand fraction and found good agreement between experiment and theory. Childs and Collis- George needed a matching factor given by the ratio of ob- served permeability at saturation to calculated permeability at saturation for their computation. Marshall (1958) facili— tated the computation by using equal classes of porosity. He found a close agreement between his measured and calculated values. Millington and Quirk (1959,1960) eliminated the matching factor of Childs and Collis-George and the recipro- cal of suction (1/h) and replaced them with pore radii and Poiseuille's coefficient of 1/8. Their computation yielded the same results as that of Marshall. Nielsen, Kirkham, and Perrier (1960) measured capillary conductivities for two loess soils and two glacial till soils at four depths and five water suction values up to and in- cluding 100 cm. They used Marshall's and Childs and Collis- George's methods and found that Marshall's method gave cbn— ductivity values considerably higher than the measured values ‘Mhile the method of Childs and Collis-George gave satisfactory rxesults for the loess soils. Jackson, Reginator, and \nan Bavel (1965) calculated conductivity values for graded 12 sand using the methods of Childs and Collis-George, Marshall, and Millington and Quirk. They concluded that the method of Millington and Quirk with a matching factor gave the best results. Their matching factor is the ratio of measured saturated conductivity to calculated saturated conductivity. Marshall's equation can be written as K' = ——————— [ r12 + 5r22 + 5r3é + ... +(2n—1)rn2] (5) where K' (cma) is the permeability, €(cm3/cm3) is the poros— ity, n is the number of pore classes up to the water content of interest, and r is the radius of conducting pores. When a suction of h cm of water is applied to a porous material the radius of the largest pores remaining full of water is given by r = 2y/pgh (6) where y is the surface tension of water, p the density, and g the acceleration due to gravity. Substituting equation (6) in (5) gives 2 2 2 —2 Kl = ELL [h1— -2 -2 ... _ “2 zng2 + Shg + 5h3 + +(2n 1)hn ] (7) Marshall and Childs and Collis—George only considered radius interaction but Millington and Quirk considered both the radius and pore area interactions. To do this, e2 in Marshall's equation was replaced by 64/3 and n was replaced 15 by m where m is the total number of pore classes. With these changes equation (7) becomes 4/3 2 -2 . K' = ezpaggm [hfa + 5h2‘2 + 5h3’2 +---+ (2m-1)hm'2] (8) To convert K' (cma), the intrinsic permeability, to K (cm/ min), the hydraulic conductivity, multiply K' by 60pg/n; equation (8) then becomes K - pgn [hl + Shg + 5h3 +---+ (2m-1)hm ] (9) Equation (9) with matching factors is used for computing the conductivities in this thesis. 2.5. Hysteresis in Soil Moisture and Hydraulic Conductivity Characteristics If two states A and B of a thermodynamic process are related in such a way that it is impossible to trace the same path when moving from B to A as when moving from A to B, then time independent hysteresis is said to exist. Very few causes of hysteresis have been demonstrated but several causes have been proposed. Some of the proposed causes are (1) pore geometry of the porous material (2) variation in contact angle during desorption and absorption of fluid (5) shrinking and swelling of porous medium and (4) entropy changes in the system. Contact angle is said to be responsible 14 for about 6 per cent of hysteresis while the majority is caused by the geometry of the pores. Long before any causes could be suggested several work- ers were convinced of the existence of hysteresis. To dem- onstrate its existence Haines (1950) used a material called glistening dew--a tinsel consisting of uniform minute glass spheres. The mean sample radius was 0.019 cm and the pore space was between 56 and 57 per cent after packing. In his experiment Haines found that there was no unique association between particular values of pressure and moisture content. Haines postulated that desorption is governed by a higher pressure deficiency as determined by the narrower section of the pores while absorption is governed by a lower pressure deficiency as determined by the wider section of the pores. When the pressure deficiency of the controlling section of the pore is satisfied the movement of the meniscus is quite sudden. This sudden movement of the meniscus when emptying or filling a pore is known as "Haines jump," and the associ— ated pressure deficiency can be called 'jump pressure.‘ In his experiment L. A. Richards (1951) observed hysteresis in the relationship between moisture content and capillary potential but he said it was difficult to predict the reproducibility of hysteretic effect for all porous media made up of particles. He speculated that changes in packing might be sufficient to account for the observed hysteresis effect. For Preston Clay Richards thought that the hysteretic 15 effect in the capillary potential—-conductivity relationship will not be large if it existed at all. To calculate the change in the quantity of water held in soil from capillary tension records S. J. Richards (1958) assumed that the mois— ture content for a given soil is a single-valued function of the capillary tension. But he observed a measureable hysteresis in his experimental moisture-tension curves. L. A. Richards and Weaver (1945) did not worry about the effect of hysteresis when developing their moisture meter because they felt that hysteresis effects will be the same in the soil and block systems. They gave data on the hyster- esis effect for six soils. In order to solve petroleum reservoir problems Osoba et al. (1951) and Geffen et al. (1951) investigated the fac— tors affecting relative permeability measurements. They named hysteresis as one of the factors which influence the measurement of relative permeability and concluded that rela- tive permeability obtained in the laboratory must be used according to the conditions under which it was obtained (desorption or absorption). Using benzene-water and air— water interfacial tensions Collis-George (1955) obtained moisture content—suction relationship for a non-swelling system of sintered glass and for swelling clay. He used a tension plate for the sintered glass and a pressure membrane for the clay experiment. He noted the hysteretic nature of both results and concluded that at least three mechanisms 16 are required to cause hysteresis in ordinary soils. He named contact angle as the minor cause and pore geometry as the major cause of hysteresis and stated that any mechan— isms proposed as causes of hysteresis must satisfy Everret's (1952,1954,1955) independent domain model of hysteresis. Childs and Collis-George (1948), L. A. Richards and Moore (1952), Day (1955), Biggar et al. (1960), Naar et al. (1962), and Elrick and Bowman (1964) have also demonstrated experimentally the hysteretic nature of soil moisture and hydraulic conductivity characteristics. Day (1955) developed in terms of tension the theoretical conditions for the equi— librium of water in the soil and for water emergence from the soil and considered tension not merely as an applied external restraint but as an intrinsic property of the soil water system. He showed graphically the hysteresis in the water content-tension relationship for quartz sand and noted the practical implication of the moisture tension phenomenon in such areas like irrigation and drainage. He emphasized that the variation of hydraulic conductivity with tension must be taken into consideration in all capillary flow studies. Biggar and Taylor (1960) noting hysteresis in their study of the movement of water into an air-dry silt loam soil as a function of temperature, proposed contact angle, shrink- ing and swelling, and entrOpy changes in the soil system as possible causes of hysteresis. Elrick and Bowman (1964) noted hysteresis in their moisture tension curve for Guelph 17 loam soil but pointed out that they did not notice any hysteresis in the moisture content-conductivity relationship for the same soil. In their paper Brooks and Corey (1964) noted that the functional relationships among effective perme— ability, saturation, and capillary pressure are all affected by hysteresis. They avoided the problem of hysteresis by dealing only with the desorption of water from the porous material. Youngs (1958a,b,1960) pointed out that hysteresis is a serious obstacle to progress in the theory of moisture movement in unsaturated soils and in the study of moisture profile development. He also advanced that hysteresis is the cause of the breakdown of the diffusion concept of mois— ture flow in the case of redistribution of water after infil— tration. Although hysteresis is an obstacle to the study of water flow in unsaturated soils, Youngs (1960)considered it a useful phenomenon since it plays an important part in soil moisture retention. To explain its usefulness Youngs stated: The lower moisture content of the step which consti- tutes the wetting zone during the redistribution, is a direct result of the hysteresis effect in the mois- ture content-suction relationship. The lower hydraulic conductivities associated with lower moisture contents reduce the migration of water downwards. Moisture is thus retained nearer the surface for a longer period of time than if there were no hysteresis effect, and since the surface moisture is the first to be lost from the infiltration zone, the soil more easily becomes sealed off from heavy evaporation losses.l 1E. G. Youngs, "The hysteresis effect in soil moisture studies," Trans. 7th Intern. Congress of Soil Sci. Vol. 1, p. 109. 18 2.6. The Independent Domain Theory of Hysteresis Although there had been theories of hysteresis in the fields of magnetism, adsorption, and solid transitions however Everett and Whitton (1952) were the first to attempt a broad approach stressing the generality of the ideas and their thermodynamic implications. Everett and Whitton (1952) postulated that hysteresis is to be attributed to the exist- ence of a very large number of independent domains in a system. The pores in a porous material are the domains in Everett's theory. The states through which the hysteretic systems pass are treated as thermodynamically stable. The existence of scanning loops is a characteristic of hysteresis phenomena and the scanning loops are also supposed to be stable and reproducible. Everett and Smith (1954) developed further the treat- ment of Everett and Whitton (1952) to take a more general distribution of domain properties into consideration. They also outline an approximate graphical method of calculating the behavior of a system with given domain properties and further enunciate general theorems which govern the behavior of a hysteresis system. A formal mathematical treatment of the independent domain model and vigorous proofs of the in- dependent domain theorems of hysteresis were presented by Everett (1954). He defined a function by means of which the thermodynamic state of a system and its future behavior can 19 be specified and derived a method for deducing the character— istic distribution functions from experimental data. He also discussed the limitations of the model and briefly mentioned its possible application to some phenomena in cHemistry, biology, and economics. In his last paper in the series Everett (1955) compared several methods of formal representation of the domain theory of hysteresis and de- velOped a symmetrical treatment with which the equations of scanning curves within a hysteresis 100p can be written down. Enderby (1955) described a new theoretical approach to the independent domain model of hysteresis and amended some of Everett's theorems to make them more generally applicable. He derived relations between the various scanning curves that would permit the theory to be tested experimentally. Realizing the limitations of an assumption that the character— istics of a given domain are independent of the state of its neighbors, Enderby (1956) extended the theory to include the case of interaction from the neighboring domains and showed the method of calculating the hysteresis curves from the properties of the individual domains. In order to test the independent domain theory of hysteresis Poulovassilis (1962) prepared a porous body of constant pore geometry from sintered glass beads. He used a tension plate apparatus for the experiment. At each pres- sure step the system was allowed to come to equilibrium be— fore measuring the volume of water lost or gained by the 20 porous body. Poulovassilis (1962) assumed that the total volume of water, V that drains out over a given range of t' suction also re-enters when the suction is relaxed and that this volume can be subdivided into small elements of volume each of which retains its identity and is completely speci- fied by small ranges of suction over which the small element drains out or re-enters the porous body. These small ele— ments are equivalent to the domains of the independent domain theory. He divided the whole suction range into intervals of 4 cm of water and drew primary wetting curves from the points of the drying boundary curve corresponding to the end of each suction interval. A comparison of the theoretical and experimental scanning curves showed a good agreement. Philip (1964) formulated the similarity hypothesis which depends on a bivariate distribution density function and used it to test the data of Poulovassilis. He found a good agreement between the data and theory. The similarity hypothesis is equivalent to the independent domain theory of Poulovassilis. The most interesting thing about the similarity hypothesis is the claim by Philip that he can use this hypothesis to estimate hysteresis properties from a single boundary curve. He was able to account for over 60 per cent of the total variance in the distribution density function when the hypothesis was applied to boundary curves alone. He concluded by emphasiz- ing the need for further experimental studies in this respect. Topp (1964) greatly simplified Poulovassilis' method of determining the distribution function used for predicting 21 the scanning loops. The two states A and B of Everett's hysteresis system were described by Topp (1964) as states 1 (filled) and 2 (emptied). The transition from state 1, where the pores are filled to state 2 where the pores are emptied, takes place at different value of the pressure change p, than does the reverse transition from 2 to 1. The volume of water desorbed or absorbed at each pressure step was noted and the moisture content at the end of each step was expressed as per cent saturation, S, of the whole sample. The saturation per cent was plotted against the pressure and the determination of the distribution function became a matter of finding the saturation difference between two points using this plot. In order to test the independent domain theory of hysteresis Topp (1964)carried out an experiment for two samples of glass-bead media made up of 95% spheres and soft glass with a density of 2.47 gm cm‘3. The first sample had a bulk density of 1.67 grams per cubic centimeter and porosity of 0.526 while the bulk density and porosity of the second sample were 0.97 grams per cubic centimeter and 0.609 respectively. Gamma-ray detection equipment and a dynamic flow system were used for the hysteresis measurements. The data of Topp (1964) did not agree with the independent domain theory of hysteresis. This failure was attributed to the two basic assumptions of the theory namely that the volume of water leaving or entering a pore when it empties or fills 22 are the same and that there is no interaction between the pores. Even if the experimental data agreed with theory there seems to be no advantage in using the independent domain theory for predicting the hysteresis lOOpS. This lack of advantage was expressed by TOpp when he stated: It is clear that only one point on each predicted dry- ing curve can be obtained from a single wetting scanning loop.l In other words it would be much faster and easier to run a drying curve directly rather than try to predict it from a wetting curve and vise versa. This failure of the theory and the lack of advantage call for another theory or method for predicting the hysteresis scanning loops. Although Rubin's method does not deal with the inde- pendent domain theory the fact that it is one of the systems that attempt a prediction of the moisture-tension curves and their scanning loops makes it necessary to review it at this point. In his study of the Rehovot sand Rubin (1967) used three empirical equations with about nine empirical constants to represent the hysteretic family of curves. One equation "describes the main wetting—retention curve," the second describes "a limiting curve of all drying retention curves," and the third equation represents both the main drying reten— tion curve and all the primary drying scanning curves. A fair agreement was reported between the empirical equations 1C. G. Topp, Hysteretic moisture characteristics and hydraulic conductivities for glass-bead media. Ph. D. Thesis, Univ. of Wisconsin, Mad. Wis. Univ. Microfilms Ann Arbor, Mich. p. 65. 25 and experimental data. No test has yet been reported in literature whether this method is only applicable to Rehovot sand or whether it can be generalized to include other soil types. 2.7. Theory of Infiltration Infiltration is used to describe the entry of water into the soil from the soil surface. It is a physical phenomenon encountered in everyday life and it is a major process of the hydrologic cycle. Many scientists have shown interest in infiltration and other hydrologic phenomena but it was not until recently that Philip (1954a) felt the need to fit the various hydrologic concepts that have developed into a coherent theoretical structure. This was the begin— ning of the physical studies that became the basis of Philip's theory of infiltration. In a more general form Philip (1954b) expressed Klute's vertical flow equation as _5_ ._ 2 .5? §_ 2 . where m is the liquid content. and the other symbols remain as defined earlier. Substituting equation (5), (10) becomes '37: (Pm) = 33‘ 4;) + 3-i- (K) (11) 24 59 .. _5_ 9.9. .5_K ae_§_ a9. “5.5 with the conditions e=eo,t=o, x>o} e=esat,x=o,t_>_o (14) where x is the vertical ordinate, positive downward, e is the volumetric moisture content, 90 is the initial moisture content, and esat is the saturated moisture content of the soil. From his new numerical method Philip (1957a) expressed the solution of (15) subject to (14) in the form of a power fil: series in t m x‘—‘Qt% +xt+ w€3+wt2 +°°°+ fm(e)tE+-°- (15) where the coefficients Q, x, Y, m --- fm(e) are functions of 9. Since the series (equation 15) converges for finite t, Philip (1957b) developed another approach for dealing with infiltration problems as t -—+-oo. This approach excluded the case in which there could be hysteresis in Y(9) relation. The conditions under which hysteresis cannot emerge were clearly defined. In his third paper on the theory of infil- tration Philip (1957c) critically examined the basic assump— tions of his mathematical analysis and found any errors due 25 to these assumptions reasonably small. In order to study the available, mostly empirical, algebraic infiltration equations Philip(1957d) introduced a new physical property of porous media. The new physical property was called 'sorptivity,' S, and was defined as a measure of the capil- lary uptake or removal of water. Sorptivity is comparable to permeability or conductivity and is a function of the initial moisture content of the material. The other algebraic infiltration equations tested either failed completely or fitted moderately but Philip's infiltration equation was simple and gave good results. The initial moisture content and the depth of water over the soil had been known to affect infiltration.but most previ— ous studies of these questions have been empirical. In his fifth and sixth papers of the infiltration theory series Philip (1957e,1958a) examined the effect of initial moisture content and water depth on the infiltration rate, the cumu— lative infiltration, the moisture profile, and the advance of the wet front. Increasing the initial moisture content, at small times after infiltration begins, is found to reduce the infiltration rate but increase the velocity of the advance of wetting front. The influence of the initial moisture content diminishes as time increases and ultimately becomes negligible while its influence on the wet front persists. Also for small values of water depth h, on the soil surface, infiltration rate and cumulative infiltration increase with h 26 on the outset but as time increases the effect of h on infil- tration rate diminishes and ultimately becomes negligible. The depth of saturated zone increases with h and this effect persists with time. In all the infiltration analysis the key functions are w(e) and K(e). Philip (1958b) confirmed the importance of these functions as a means of characteriz— ing soils hydrologically, and emphasized (1957f) the need for accurate methods of measuring Y and K functions. Youngs (1957) tested Philips theory in the laboratory for slate dust and glass bead product and found good agree- ment between theory and experiment. The field test for the same theory was carried out by Nielsen et al. (1961) for two silt loam textured soils, Monona and Ida silt loams, of western Iowa. The theory adequately predicted the shape of the wetting front and the depth of penetration for Monona soil and the profile of the Ida soil but failed to predict the depth of penetration for the Ida soil. The descrepancy between theory and experiment was said to be due to the variation of the physical properties of the entire profile from those of the first 50 cm and to the plot size. Using Philip's procedure and the finite difference method Gupta and Staple (1964) solved the equation for the case of infil- tration into vertical columns of air—dry Greenville silt loam soil under a small positive head. Philip's method satisfactorily predicted the drier moisture profile but the predicted profile at zero tension was less than experimental. 27 When the higher conductivities in the saturated and transi- tion zone near the surface were taken into account, the finite difference method predicted the entire profile satis- factorily. Hanks and Bowers (1962) estimated the solution of the moisture flow equation for vertical infiltration into layered soils. They found that infiltration is governed by the least permeable soil layer. Their method agreed excel— lently with Philip's. Hanks and Bowers (1965) also investi- gated the influence of variation in the diffusivity-water content relation on infiltration and found a marked change in infiltration when diffusivity was increased or decreased by a factor of 2 at saturation. However at drier moisture range a factor change of 100 had no effect on infiltration. This implies the great effect on infiltration by soil proper- ties at saturation and the little influence these properties have at drier moisture range. Green et al. (1964) used the procedure of Hanks and Bowers (1962) to solve the mois- ture flow equation for infiltration into field soil. Calcu— lated infiltration rates generally agreed with field rates measured with a sprinkling infiltrometer. Rubin and Steinhardt (1965) made a mathematical analy- sis for moisture changes in soils and for rates of water entry during rain infiltration. They assumed the validity of Darcy's and continuity equations, a unique relationship be- tween diffusivity, conductivity, and moisture content, and the rainfall entering the soil to be a continuous body of water. 28 Experimental results did not support their model. Whisler and Klute (1965) undertook a numerical analysis of infiltra- tion, considering hysteresis, into a vertical soil column at equilibrium under gravity. For their numerical solution they needed graphical representation of conductivity (K) vs pressure or suction (p), moisture content (9) and water capacity (C) vs p. They found out that if only the absorption curve was used in the computation, the advance of the wetting front was underestimated and if only the desorption curve was used the advance of the wetting front was over-estimated. Hanks (1965) stressed that hysteresis must be considered since infiltration is an absorption process. Nielsen (1965) carried out a field experiment to measure the soil water move— ment during infiltration and redistribution for four irriga- tion treatments on Panoche clay loam. He emphasized the need for the accurate determination of K vs 6 relationship and other soil parameters in order to solve infiltration prob- lems. Biswas et al. (1966) used gamma radiation absorption technique to investigate soil water redistribution after infiltration. They also stressed the importance of accurate determination of e vs p, K vs 9 relationships in order to solve this problem. III. SCANNING CURVE GENERATING SYSTEM The following is a preliminary equation developed by Kunze for generating scanning curves. The equation can be expressed as WC = ch + k x ch (16) where WC is the water capacity of the absorption scanning curve to be generated, PWC is the water capacity generated from the previous calculation, and k is a function of the moisture content and head (k = f(e,h). 29 IV. EXPERIMENTAL PROCEDURE 4.1. Description of Equipment 4.1.1. The Tempe pressure cell The Tempe pressure cell (Cat. No. 1400) was recently developed at the U. S. Water Conservation Laboratory at Tempe, Arizona (see figs. 1 and 2). It is constructed of plexiglass which permits an unrestricted View of the internal parts. It is pressure sealed with "0" rings. The porous ceramic plate inside the cell has a bubbling pressure in excess of 1 bar. The pressure cell was designed for accurate work in the 0-1 bar range. The soil sample is contained in a brass cylinder 5.4 cm in diameter and 5.0 cm long. A special soil core sampler is available if one desires to work with undisturbed samples. The moisture change in the soil sample is determined by weighing the whole pressure cell. The moisture content is determined at moisture equilibrium points—-the points at which the soil ceases to gain or lose water. The small size of the light pressure cell makes it possible to experiment with many samples or replications at one time. 50 51 '= v . . ' - ,- f , . w. ' h. ‘1’ ‘ y“? Q _ i J '9‘ ['j 1. \ q.‘ ‘ g ‘4 x. - (‘K 1 l‘ C J , *‘ —‘, -'— ‘ — \~'I’—L—»— —— ._____——4-IIIIII-‘lIl---—————’ . , ~“——-~_.—— __ ~‘ .. ‘u I Figure 1.--The Tempe pressure cells and water well on cell holder. Figure 2.—-Components of the pressure cell. 52 4.1.2. The manifold The function of the manifold is to distribute pressure equally to the samples in the different pressure cells. Its dimensions are determined principally by the total number of pressure cells operated at one time. The only critical and important factor about the manifold is that it must be pressure tight. For this experiment it was constructed of plexiglass with dimensions of 2 in. x 2 in. x 5 1/4 in. and with ten outlets to supply pressure to ten pressure cells. 4.2. Equipment Set-up The apparatus was set up as shown in figure 5. Air pressure from the main pressure line A was regulated by the regulator B and the regulated pressure was registered on the gauge C. The gauge C was used to make sure the limit of 50 psi was not exceeded. Valve D was used to cut off pressure from the system when no longer needed. The air from the pressure line was filtered through the air filter E before passing through the coarse and fine regulators F and G respectively. These two regulators can regulate a maximum operating pressure of 500 cm of water. The mercury manometer J served to indicate the pressure step applied to the soil samples. The rest of the system--the manifold H, the ten pressure cells, and the water well I--were all in the constant temperature and humidity chamber K (figs. 5 and 4). 55 .Q: How HaucmEHHOQXm mnu mo swam UHumEmumMAQII.n musmflm «=8 9539.1 CI .5an5 3.6.8:: ESPEQEE E2280 . x 3.62652 . s. =63 .633 .. I 29:52 . I 68:62 as... .. 0 «Mil. .5639: 3600 - u asks<-m o 23> . Q 325 - o 65:69. we... Seaweed - m we... 95363 to £22 . < 54 .HwQEmno >uflcflfisn onsumummEmu usmumsou msu mcflmsfl usmEmHSUMII.w mnemflm 55 The temperature was maintained at 25.0.i 0.060 C and the humidity was 97%. The end of the inflow-outflow tube of the pressure cell was placed under water for both the absorption and desorption runs so as to minimize the chance of air entering the tube and becoming entrapped in the system. It is important to maintain a constant level of water in the well so as to maintain a constant hydraulic head. 4.5 Description of Soil Samples Investigated Two Michigan soils, Hillsdale sandy loam, and Sim's loam, were used for the experiment. Mokma (1966) has given the detailed description of the Hillsdale sandy loam soil and the history of its location. The mimeographed detailed properties of the Sim's loam can be found in the Department of Soil Science at Michigan State University. The soil types, horizon, depth, and the porosities of the soil frac- tion investigated are given in Table 1. The particle size distribution of the soil samples are shown in Table 2. 4.4. Sample Preparation A mechanical analysis of each layer of the two soil types was made and the particle sizes passing through No. 25 (710 micron, opening), No. 45 (550 u), and No. 140 (105 u) Table 1.--Description of soils and soil fractions studied. Porosity of Depth soil fraction Soil type Horizon (inches) investigateda Hillsdale sandy loam Ap 0-9 55.50 Hillsdale sandy loam A2 9—15 55.25 Hillsdale sandy loam B1 15-175' 25.00 Sim's loam Ap 0-7 48.07 Sim's loam BlG 7-22 50.20 aPorosity = (1- given. Table 2.--Particle size distributiona Per cent by weightb of samples. ) x 100%; average of two replications is Depth Soil type (inches) Sand Silt Clay Hillsdale sandy loam 0—9 66.5 25.5 10.2 Hillsdale sandy loam 9—15 70.0 21.0 9.0 Hillsdale sandy loam 15-17%' 72.2 16.5 11.5 Sim's loam 0-7 47.0 55.6 19.4 Sim's loam 7-22 59.6 27.8 52.6 aAverage of two replications. Based on the method of Bouyoucos. 57 sieves were mixed together to form the final sample particle size (oz m meme .NH .>oz meme .5 .uoo m some .5 .uoo meme .es .ummm a meme .es .ummm some .e .ummm smog macaw easemaagm any sun cam GOAHMHSDMm coauMHSDMm mmwu aflom so cam so uumum Hmfluflce fineness MO was mo unaum .mmHmEMm HHOm map How mEHu CUM cam COHDMHSummII.m manme 41 Table 4.--Dates of moisture equilibrium and total number of weighings for run 2 of Hillsdale sandy loam soil. Dates of Pressure Number Number of Total moisture points of weighings number of equilibrium cm of H20 samples per sample weighings Oct. 7, 1966 0.0 9 8 72 27.1 9 5 27 11 54.2 9 7 65 15 108.4 9 5 45 14 162.6 9 2 18 15 216.8 9 2 18 16 217.0 9 2 18 17 525.2 9 2 18 18 579.4 9 2 18 19 455.6 9 2 18 20 579.4 9 5 27 21 525.2 9 2 18 22 271.0 9 2 18 24 216.8 9 5 27 25 162.6 9 5 27 26 108.4 9 2 18 28 54.2 9 4 56 Nov. 5, 1966 27.1 9 8 72 12 0.0 9 10 90 42 That of samples two and four was obtained from an average of two replications each because of a leak in the third replication. The variation between the replicates was within the limits of experimental error. The moisture-tension relationship of the five samples are represented graphically in figures 5, 6, 7, 8 and 9. In order to test the reproducibility of the hysteresis loops the same pressure steps were utilized for each run. In each sample the total volume of moisture expelled during desorption was greater than the total volume taken in during absorption for the first run. This was expected (Poulovassilis, 1962). This difference is due to the volume of air entrapped during the initial sample saturation. Except for samples one and four, subsequent runs, within the limits of experimental: error, returned to the same moisture content at zero suction. This means that the volume of air entrapped remained constant. On the other hand more and more water was absorbed by samples one and four. This discrepancy may be due to the fact that samples one and four are surface layer samples with higher organic matter and larger pores and subsequently the volume of air entrapped was becoming less and less. There is a striking similarity in the moisture char- acteristics of the two soil types (see figs. 5-9). The sur- face layers, samples one and four, exhibited much larger hysteresis than the subsurface layers. The mechanical analy- sis indicated that these surface samples contain more sand 45 (G) JUOJUOQ OJDJSIOW OIJIOWMOA 8 .Ammnocfl mlo .EMOH >©nmm waMCmHHflmv mso meEmmII.m musmam .203 .6 Eu E. 0539.1 o ow. 8- on... 3... cow. 9...... can. can. own- co..- 0..“ b n P p b p n n n n .. .p . \IHIUIIII 9.0” I. )+ I5.) - cud... u i .203 .0 So ov.mo.- .u ......oa 3.0. 2:96-52 5...: e3. 055.03 2.8% a .1. .20.... ..o .60 RN. .o .58 .. 5596-5... 5...: doc. 9.5.03 3...... 4 5.... 9.80m .. doc. 6.82 O. 5.... .9...» .. doc. .652 + ..QZMGMJ nnxv 44 (9) JUGJUOQ SIMSIOW oIJIGwnloA ..mmeua. ms-m .EmoH mpcmm mamcmaaflmv m mHmEmmll.m mudmflm .20.... .6 Eu an: 533k. on. - DON p OVN OmN ON» 00» 00v . .h . p p , .29... .0 Eu ov.mo.- .o ......oq 2:50-52 5...: doc. 055.com 28mm 8 .29: .0 Eu Km. .0 .....oq 3:96-52 5...: moo. 9:568 3...“. fl :5 become .30. 3.33. 0 :5 .2: - doc. 8.32 + ..szom 4 45 (9) wawoo 91n4316w omowmoA .Ammnosfi hfifilmfi .EmoH mcsmm wampmaaflm. m mHmEmmll.> gunmen .203 6 Eu an: 5:0»er CI 0'! 8| g I 8.... SN! O'Nl OQNI ONnI 0%”! 00V! 20° I P b D L b b b D F l ‘IIIIIIII-I -).. ..Hul.‘ . I \‘lll. -|.)|I.‘|I.III|.III - IIII‘IH .IIIIIIII‘III‘. j ; L nfiOI .... I. O “I O 1 .203 e0 .60 Coupe.- 6 6.6.. 0:66-52 5...: Q00. 00.60000 neocom n. 6.0.: .0 .60 Km- .0 E.6q 00:06-52 5...: Q00. 055000 6...". d :5 0.603 - Q00. 6.62 0 0:. 3...... - 000. .663. + ”ozmwm... 46 (9) wawoo SJMSIOW amawnloA .Ammcosfl slo .EmoH m.Eflm. 0 mHQEmmII.m gunman .66... .0 E0 3. 0.0005,“. o O..- OO- ON.- 00.- OON- OVN- omw- ONn- con- 00..- 8.0 h b P p b p r p b b was: . . 0 .n.ILquIIIl, ens. . I n '2 O 3, o 1] ljllLllJ LllJLiiiLinn 6.03 .0 .80 000.- 6 6.60 00:06-52 5...... 000. 0:..::000 080mm 9 6.03 .0 ...:0 Km- .0 .:..00 0:66.53 .....3 000. 055.600 6...... Q :5 .00... -000. 6.6.). + 00.0 . nozmomq OED. 47 .Ammnosd Nuns .EmoH n.5flm. m mamfimmll.m musmam 0.0.03 .0 :6 «n. . 50000.... O'- 8? 8.- 00M.- OVN- Ocu- ON». on».- On..- ON-O b p n r F n P b F - W h III-“II. u q .IILrII I nNAu S, o (e) wawoo ammow omawngoA 3 0 0nd 6.03 .0 :6 ¢.mo.- .0 6.60 0:36-53 5...: 000. 0:..::00m 060% a 6.03 .0 .80 RN. .0 .:.6n. 00:06-50. 5...: 000. 056000 6...... 4 :0. .5... - 000. 6.63. + ”Ozmwmq 48 than the other samples. The larger hysteresis is explained by the higher sand content. Even though the pressure steps were the same and there was agreement between the equilibrium time of equivalent pressure steps of each run, it was not possible to reproduce the moisture—tension curves in this experiment. An exception can be seen in fig. 5 where a portion of the absorption curve of run one was reproduced during run two and in fig. 9 where the desorption curve of run two was reproduced during run three between 0 and -108.4 cm of water pressure. At the higher suction range (figs. 5-8) each subsequent desorption and absorption run left a higher moisture content in the sample between each pressure step. The same phenomenon is true at the lower suction range with the exception that the first desorption curve remained as the upper limit. In addition to indicating the lack of reproducibility of the moisture-tension curves, figs. 5, 6, 7, 8 and 9 also Show that the higher suction end of the scanning curves fell outside the primary boundary curves. These two situations contradict the requirements of the independent domain theory of hysteresis. The requirements are that the scanning loops be stable and reproducible and that they should remain within the major desorption-absorption loop. This lack of repro- ducibility and the fact that part of the scanning curves fell outside the primary boundary curves can be explained in terms of consolidation and swelling. As the sample consoli— dates the size of the pores is decreased thus making the 49 sample retain more water. Also when the pressure is relaxed and the sample takes in water it begins to swell and admit more water. The swelling rate and the amount of consoli— dation are not the same from run to run and so the moisture- tension curves could not be reproduced. Poulovassilis (1962) obtained reproducible curves probably because he used a porous material of constant pore geometry. If this lack of reproducibility is not perculiar to this experiment it means that a given set of soil parameters can only be valid for the particular set of conditions under which the parameters were determined and it also means that the past history of the soil must be specified. This would mean, for example, that we cannot simply state the hydraulic conductivity of Hillsdale sandy loam soil at a given moisture content but we must specify its history either with a mean— ingful parameter or by other means and with this information properly interpret the conductivity data. 5.2. Hydraulic Conductivity The equation of Millington and Quirk (1959,1960) shown as equation (9) of this thesis together with a matching factor explained by Jackson et al. (1965) was used to calcu— late the unsaturated hydraulic conductivity in this experi— ment. The matching factor is the ratio of measured saturated conductivity to calculated saturated conductivity. The sur- face tension, density, viscosity, and gravity used in 50 equation (9) were 71.97 dynes/cm, 1.00 gm/cc, 0.008957 poise and 980.0 cm/seca, respectively. The moisture content—conductivity relationship is represented graphically in figs. 10, 11, 12, 15 and 14. The conductivity is represented on a logarithmic scale. The total number of pore classes used for computing the hydraulic conductivities and the respective matching factors are presented in table 5. Table 5.--Pore classes and matching factors for samples. Number of Matching factor Sample pore classes Desorption Absorption 1 18 5.892 0.142 2 16 0.559 0.077 5 18 0.557 ' 0.046 4 14 0.150 0.005 5 15 0.559 0.027 The data of the second run of each sample was used to calculate the hydraulic conductivities for the sample. The data from the first run could not be used because the total volume of water expelled during desorption was different from the total volume absorbed due to the initial air entrap— ment. The volume of air entrapped during subsequent runs remained the same. Runs three and four gave higher hydraulic conductivities than two since their moisture content was slightly higher. 51 2:00'2 10'21 X Desorption 0 Absorption IO’3 -I K (cm/min) :0" .- 10'5 .- MO" 4: M , , 0.15 0.20 0.30 Volumetric Moisture Content (9) Figure 10.—-Sample 1. (135 52 4 300" 3 i0‘3q IO" j K (cm/min) 10". to" . x Desorption 0 Absorption 2 - :0" OJO fi 1 0.20 Volumetric Moisture Content (9) Figure 11.-—Sample 2. (130 55 4 “0'3 X Desorption 0 Absorption 10‘34 lO'I. K (cm/min ) 10' 5- iO‘Qfi 3x074 r 0. i0 0. 20 0.30 Volumetric Moisture Content (9) Figure 12.--Sample 5. 54 5 ath':5 X Desorption 0 Absorption to" l0".+ A .E E \. E 0 \o k: to". to" 0 ”0.7 I fl 0.30 0.40 0.45 Volumetric Moisture Content (9) Figure 15.—-Sample 4. 55 lo' X Desorption 'O-zj 0 Absorption id's-(- K (cm/min ) lo' ‘4 to" 4ul0' j , 0.20 0.30 0.40 0.45 Volumetric Moisture Content (9) Figure 14.--Sample 5. 56 The hydraulic conductivities between the samples of each soil type and between the soil types were very similar. All the unmatched calculated conductivities, except the desorption conductivities of sample one, were higher than the matched conductivities. The matched conductivities calculated from both the desorption and absorption curves were brought together near saturation and zero pressure by the matching factor (see K vs 9 and K vs P curves). The conductivity-suction graphs are represented on a semi—log scale in figures 15, 16, 17, 18 and 19. Like the K vs 9 curves, the K vs P curves were very consistent for all five samples. Large hysteresis is exhibited in the (K,P) relationship. Like the moisture-tension curves, the K vs P curves for the surface layer samples show much larger hysteresis than the subsurface layer samples. This was previously explained to be due to the greater amount of sand present in the surface layer samples as compared to the subsurface layer samples. The hysteresis in the (K,e) relationship is far from being negligible. It is small in comparison to that of (K,P) relationship. In the light of this data any general assumption of a unique relationship between unsaturated hydraulic conductivity and moisture content is bound to be in considerable error. 2x10‘2 57 i0“ 3.. K (cm/min ) Io“ 4. IO-s-i «to-5 X Desorption 0 Absorption -300 I V T I -240 -i80 -i20 -60 P (cm of water) Figure 15.--Sample 1. arm's-tr iO's-i K ( cm/min.) 10' i0"6 X Desorption 0 Absorption 58 -l 50 400 -50 P (cm of water) Figure 16.--Sample 2. 59 P ( cm of water) Figure 17.-—Sample 5. -3 GxKJ .1 I x Desorption 0 Absorption 10'3- iO'4q .E E p \ E 0 ,, v x i0”5 - io's-i 3 Xi0‘7 r I I ' -150 -i20 -90 .00 -30 -0 -3 7 7xio ’2‘“ I X Desorption 0 Absorption i0'3- A .5 5 . E 10’ - 0 \v k: iO's-i i0"- exio” T . j -200 400 420 .80 -40 60 P (cm of water) Figure 18.--Samp1e 4. 61 «:03 I I I x Desorption 0 Absorption 1634 “fa E E E 0 V M: 10.41 Mfg! -6 58K) - ' _T, 1 1 -200 400 420 -00 -40 0 P (cm of water) Figure 19.--Sample 5. 62 5.5. Experimental Test of Scanning Curve Generating System An equation was previously described for generating scanning curves from the primary desorption curve. The method was applied to the data of sample one of this experi- ment and the results are shown in fig. 20. The solid line represents experimental result while the dotted line repre- sents theory. The prediction was quite close for the absorp- tion scanning curve that started at -271 cm of water pressure. It failed to accurately predict the second absorption scanning curve beginning at -108.4 cm. The computation used for this prediction was done by the computer. Obviously this prediction system needs further refine- ment. 65 (9) iueiuoo emisgow omewmoA 0nd , .Emumhm mcfiumumcmm oSu mo ummu HmucmfifiummeIl.ON musmflm :99: :0 :8 an: 9539.1 00 ON. 0&- OON OVN 8N ON» 00» 00? - p p p - . - p *9 9:3 39:23.2. 9:3 5.5.53qu ..I. 9:3 05::on 33.630 .383 a 9:3 052:8» c2333... .95. 4 9B mEEom B E: 6:83 .. moo. 3.62 o ”02.3.”... VI . SUMMARY The Tempe pressure cell was used to investigate the moisture characteristics of five samples of two Michigan soil types--Hillsdale sandy loam and Sim's loam soils. The moisture-tension equilibrium conditions were established when water loss from the sample became negligible. The water loss or gain was determined between successive equi— librium states. Because of the increasing use of the moisture tension curves to compute unsaturated hydraulic conductivity it was necessary to test whether these curves are reproducible for real soils. It was also necessary to investigate whether the hysteresis in the (K, 9) relationship is small enough to be neglected while developing theories or conducting experi- ments° The time involved in determining the (K vs 9) primary curves and the intermediate scanning loops calls for a system for generating the scanning loops from one desorp- tion or absorption curve. Millington and Quirk's method with a matching factor was used to calculate the unsaturated hydraulic conductivi- ties for the samples and the results were shown in the form of (K vs 9) and K vs P) curves. 64 65 The results of this experiment indicated that the mois- ture-tension curves are not reproducible for the two soil types investigated. The higher suction end of the inter— mediate scanning curves fell outside the primary boundary curves contrary to the demands of the independent domain theory of hysteresis. The above two conditions were attrib- uted to the swelling and the consolidation of the samples. The hysteresis in the (K,e) relationship was small in com- parison to that of the (K,P) relationship but it was far from being negligible. The experimental data was used to test an equation for predicting scanning loops from the main desorption curve. The equation failed to accurately predict all the scanning curves tested. It predicted one scanning curve fairly well while the prediction for the second curve was poor. VI I . CONCLUS IONS Because of the lack of reproducibility of moisture- tension curves for the two soil types investigated and because of the large hysteresis exhibited in the (K,e) relationship it is concluded that: (1) The history of the soils and the experimental conditions must be specified when reporting the characteristic parameters for the soils. (2) Any general assumption of a unique relationship between unsaturated hydraulic conductivity and moisture content is bound to cause a consider— able error. Also the failure of the generating equation to accurately predict all the scanning curves tested call for a refinement of the equation. 66 SUGGESTIONS FOR FUTURE STUDIES The results of this study have further emphasized the need for more investigation in the area of unsaturated flow through porous materials. In particular there should be further investigation in the following areas: 1. It should be further investigated whether the lack of reproducibility in the moisture-tension rela— tionship is perculiar to the Hillsdale sandy loam and the Sim's loam soils or whether it can be extended to include other soils. Research should continue to either improve the very few published equations for generating scanning loops or to develop new theories and equations for this purpose. There is an indication that the number of pore classes used in the computation of hydraulic conductivity affects the values of conductivity obtained particularly at the dry moisture range. An optimum number of pore classes or a range of pore class number for accurate computation should be determined. 67 REFERENCES Baver, L. D. (1965). Soil Physics. 5rd Ed. John Wiley & Sons, Inc., New York. 489. Biggar, J. W. and S. A. Taylor (1960). Some aspects of the kinetics of moisture flow into unsaturated soils. Soil Sci. Soc. Amer. Proc. 24:81-85. Biswas, T. D., D. R. Nielsen, and J. W. Biggar (1966). Redistribution of soil water after infiltration. Water Resources Res. 2(5):515-524. Brooks, R. H., and A. T. Corey (1964). Hydraulic properties of porous media. Hydrology Paper No. 5, Colorado State Univ., Ft. Collins. Buckingham, E. (1907). Studies on the movement of soil moisture. USDA Bur. of Soils Bul. 58:28. Childs, E. C. (1956a,b). The transport of water through heavy clay soils. I and III. Jour. Agric. Sci. 26:114-127 and 527-545. Childs, E. C., and N. Collis-George (1948). Soil geometry and soil water equilibria. Discussions Faraday Soc. 5:78-85. Childs, E. C., and N. Collie-George (1950). The permeability of porous materials. Proc. Roy. Soc., London, A, 201:392-405. Childs, E. C., and N. Collis-George (1950). Movement of moisture in unsaturated soil. Trans. 4th Intern. Congress of Soil Sci. 1:60-63. Collis-George, N. (1955). Hysteresis in moisture content- suction relationships in soils. Proc. Nat. Acad. Sciences (India) 24A:80—85. Corey, A. T. (1957). Measurement of water and air permeability in unsaturated soil. Soil Sci. Soc. Amer. Proc. 21:7-10. 68 69 Day, P. R. (1955). Soil moisture tension measurement: Theoretical interpretation and practical application. Proc. 5rd. Nat. Conf. on Clays and Clay Minerals. 395:557-566. Elrick, D. E. (1965). Unsaturated flow properties of soils. Australian Jour. Soil Res. 1:1-8. Elrick, D. E., and D. H. Bowman (1964). Note on an improved apparatus for soil moisture flow measurements. Soil Sci. Soc. Amer. Proc. 28:450-452. Enderby, J. A. (1955). The domain model of hysteresis. Part 1: Independent domains. Faraday Soc. Trans. 51:855-848. Enderby, J. A. (1956). The domain model of hysteresis. Part 1. Interacting domains. Trans. Faraday Soc. 52:106-120. Everett, D. H. and W. I. Whitton (1952). A general approach to hysteresis. Part 1. Faraday Soc. Trans. 48:749-757. Everett, D. H. and F. W. Smith (1954). A general approach to hysteresis. Part 2: Development of the domain theory. Faraday Soc. Trans. 50:187-197. Everett, D. H. (1954). A general approach to hysteresis. Part 5: A formal treatment of the independent domain model of hysteresis. Faraday Soc. Trans. 50:1077-1096. Everett, D. H. (1955). A general approach to hysteresis. Part 4: An alternative formulation of the domain model. Faraday Soc. Trans. 51:1551-1557. Gardner, W. (1920). A capillary transmission constant and methods of determining it experimentally. Soil Sci. 10:105-126. Gardner, W. R. (1956). Calculation of capillary conductivity from pressure-plate outflow data. Soil Sci. Soc. Amer. Proc. 20:317-320. Geffen, T. M., W. W. Owens, D. R. Parrish, and R. A. Morse (1951). Experimental investigation of factors affect- ing laboratory relative permeability measurements. Amer. Inst. Min. and Met. Engr. Trans. 192:99-110. Green, R. E., R. J. Hanks, and W. E. Larson (1964). Estimates of field infiltration by numerical solution of the mois- ture flow equation. Soil Sci. Soc. Amer. Proc. 28: 15-19. 7O Gupta, R. P., and W. J. Staple (1964). Infiltration into vertical columns of soil under a small positive head. Soil Sci. Soc. Amer. Proc. 28:729-752. Haines, W. B. (1930). Studies in the physical properties of soil: V. The hysteresis effect in capillary properties, and the modes of moisture distribution associated therewith. Jour. Agric. Sci. 20:97—116. Hanks, R. J. (1965). Estimating infiltration from soil moisture properties. Jour. of Soil and Water Cons. 20(2):49-51. Hanks, R. J., and S. A. Bowers (1962). Numerical solution of the moisture flow equation for infiltration into layered soils. Soil Sci. Soc. Amer. Proc. 26:550-534. Hanks, R. J., and S. A. Bowers (1965). Influence of vari- ation in the diffusivity—water content relation on infiltration. Soil Sci. Soc. Amer. Proc. 27:265-265. Jackson, R. D., D. R. Nielson, and F. S. Nakayama (1965). On diffusion laws applied to porous materials. ARS USDA 41-86 Jackson, R. D., R. J. Reginato, and c. H. M. Van Bavel (1965). Comparison of measured and calculated hydraulic con- ductivities of unsaturated soils. Water Resources Research 1:375—580. Klute, A. (1952). Some theoretical aspects of the flow of water in unsaturated soils. Soil Sci. Soc. Amer. Proc° 16:144-148. Klute, A. (1952). A numerical method for solving the flow equation for water in unsaturated materials. Soil Sci. 75:105-116. Klute, A. (1965). Laboratory measurement of hydraulic con- ductivity of saturated soil. Chap. 15, pp. 210-221, in C. A. Black, ed. Methods of Soil Analysis. Amer. Soc. Agron., Inc., Wis. 770 pp. Kunze, R. J. and D. Kirkham (1962). Simplified accounting for membrane impedance in capillary conductivity determinations. Soil Sci. Soc. Amer. Proc. 26:421-426. Marshall, T. J. (1958). A relation between permeability and size distribution of pores. Jour. Soil Sci. 9:1-8. 71 Miller, E. E. and D. E. Elrick (1958). Dynamic determina- tion of capillary conductivity extended for non- negligible membrane impedance. Soil Sci. Soc. Amer. Proc. 22:485-486. Millington, R. J. and J. P. Quirk (1959). Permeability of porous media. Nature 185:587-588. Millington, R. J. and J. P. Quirk (1960). Transport in porous media. Trans. 7th Intern. Congr. Soil Sci. 1:97-106. Mokma, D. L. (1966). Correlation of soil properties, percolation tests, and soil surveys in design of septic tank disposal fields in Eaton, Genesee, Ingham, and Macomb counties, Michigan. M. S. Thesis, Mich. State Univ., East Lansing (unpublished). Naar, J., R. J. Wygal and J. H. Henderson (1962). Inhibition relative permeability in unconsolidated porour media. Amer. Inst. Min. and Met. Engr. Trans. (Petroleum Division Part II) 225:15-17. Nielsen, D. R. (1965). Field observation of infiltration and soil water redistribution. Amer. Soc. Agric. Engr. Paper 752. Nielsen, D. R., and J. W. Biggar (1961). Measuring capillary conductivity. Soil Sci. 92:192-195. Nielsen, D. R., D. Kirkham, and E. R. Perrier (1960). Soil capillary conductivity: comparison of measured and calculated values. Soil Sci. Soc. Amer. Proc. 24:157-160. Osoba, J. S., J. G. Richardson, J. K. Kerver, J. A. Hafford and P. M. Blair (1951). Laboratory measurements of relative permeability. Amer. Inst. Min. and Met. Engr. Trans. 192:47—56. Philip, J. R. (1954a). Some recent advances in hydrologic physics. Jour. Inst. Engr. Aust. 26:255-259. Philip, J. R. (1954b). An infiltration equation with physical significance. Soil Sci. 77:155-157. Philip, J. R. (1956). The theory of infiltration: 1. The infiltration equation and its solution. Soil Sci. 85:545—557. 72 Philip, J. R. (1957a). Numerical solution of equations of the diffusion type with diffusivity concentration dependent. II. Australian Jour. Phys. 10:29-42. Philip, J. R. (1957b). The physical principles of soil water movement during the irrigation cycle. Proc. 5rd. Intern. Congr. Irrig. Drainage. 127-154. Philip, J. R. (1957c). The theory of infiltration: 2. The profile of infinity. Scoil Sci. 85:455-448. Philip, J. R. (1957d). The theory of infiltration: 5. Moisture profiles and relation to experiment. Soil Sci. 84:165-178. Philip, J. R. (1957e). The theory of infiltration: 4. Sorptivity and Algebraic infiltration equation. Soil Sci. 84:257-264. Philip, J. R. (1957f). The theory of infiltration: 5. The influence of the initial moisture content. Soil Sci. 84:529-559. Philip, J. R. (1958a). The theory of infiltration: 6. Effect of water depth over soil. Soil Sci. 85:278-286. Philip, J. R. (1958b). The theory of infiltration: 7. Soil Sci. 85:555—557. Philip, J. R. (1964). Similarity hypothesis for capillary hysteresis in porous materials. Jour. Geoph. Res. 69:1555-1562. Poulovassilis, A. (1962). Hysteresis of pore water, an application of the concept of independent domains. Soil Sci. 95:405-412. Richards, L. A. (1951). Capillary conduction of liquids through porous mediums. Physics 1:518-555. Richards, S. J. (1958). Soil moisture content calculations from capillary tension records. Soil Sci. Soc. Amer. Proc. 5:57-64. Richards, L. A. and D. C. Moore (1952). Influence of capil— lary conductivity and depth of wetting on moisture retention in soil. Trans. Amer. Geoph. Union 55:551-. 540. Richards, L. A. and L. R. Weaver (1945). The sorption—block soil moisture meter and hysteresis effects related to its operation. Jour. Amer. Soc. Agron. 55:1002-1011. 75 Rijtema, P. E. (1959). Calculation of capillary conductivity from pressure plate outflow data with non—negligible membrane impedance. Netherlands Jour. Agric. Sci. 7: 209-215. Rubin, J. (1967). Numerical method for analyzing hysteresis- affected, post—infiltration redistribution of soil mois- ture. Soil Sci. Soc. Amer. Proc. 51:15-20. Rubin, J., and R. Steinhardt (1965). Soil water relations during rain infiltration: 1. Theory. Soil Sci. Soc. Amer. Proc. 27:246-251. Slichter, C. S. (1899). Theoretical investigation of the motion of ground waters. Nineteenth Ann. Report U. S. Geol. Survey 2:295. Swartzendruber, D. (1962). Modification of Darcy's law for the flow of water in soils. Soil Sci. 95:22-29. Swartzendruber, D. (1965). Non-Darcy behavior and the flow of water in unsaturated soils. Soil Sci. Soc. Amer. Proc. 27:491-495. Topp, G. C. (1964). Hysteretic moisture characteristics and hydraulic conductivities for glass bead media. Ph. D. Thesis. Univ. of Wisconsin. Univ. Microfilms, Ann Arbor, Mich. (pub. by Topp and Miller (1966), Soil Sci. Soc. Amer. Proc. 50:156-162). Whisler, F. D. and A. Klute (1965). The numerical analysis of infiltration, considering hysteresis, into a verti- cal soil column at equilibrium under gravity. Soil Sci. Soc. Amer. Proc. 29:4895494. Youngs,IL.G. (1957). Moisture profiles during vertical infiltration. Soil Sci. 84:285-290. Youngs, E. G. (1958a). Redistribution of moisture in porous materials after infiltration: 1. Soil Sci. 86:117-125. Youngs, E. G. (1958b). Redistribution of moisture in porous materials after infiltration: 2. Soil Sci. 86:202-207. Youngs, E. G. (1960). The hysteresis effect in soil moisture studies. Trans. 7th Intern. Congress of Soil Sci. 1:107-115. APPENDIX Notes on Hydraulic Conductivity Computation The equation used for computing the unsaturated hydraulic conductivity is reproduced below 2 K = 58%33'64/3 [h1_2 + 5h2’2 + 5h3'2 +---o+(2m-1)hm’2] (9) where all the parameters remain as defined previously ( m = total number of pore classes). Equation (9) can be written as K = Ae4/3 [h1'2 + 5h2’2 + 5h3‘2 +---+_(2m-1)hm'2]o-- (17) In the above expression the pressure (h) used is the average 3 is the head between two consecutive class-heads and e4/ corresponding moisture content. Suppose, for example, that we have 15 pore classes, the respective hydraulic conductivi— ties will be given by the following expressions: Kl = A€14/3[h1-2 + She-2 + 5h3-2 + "' + 27h14—2 + 29h15'2] (18) ..2 -2 ... K2 = Ae24/3[h2‘2 + 5h3'2 + 5h4 + ... + 25hl4 + 27h15 2] (19) 74 75 Ae144/3 [h14‘2 + 5h15‘21 (51) K14 and Ae154/3 [hls-g] (52) K15