Pore Behavior in Water-Saturated Soil: NJ Geological Survey, Lecture notes of Acting

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PR O C EEDINGS O F

U N IVERS I TY S E M IN A R ON

P O L L U TI O N A N D WA TER RE SO UR CES

COLUMBIA UNIVERSITY

Volume VI 1972-

P R O C EED I NGS O F

UN I VE R SIT Y SEMINAR ON

POLLUTION AND WATER RES O UR C E S

Vol u me VI 1972-

by

George J. H alasi-Kun , Editor in Chief an d George W. Whetstone, Assistant Editor

COL UMB I A UN I VERS IT Y

in c oo p erati o n with

U. S. DEPAR T MENT O F TH E I NTER IO R GEOLOGICAL SURVEY

The New Jersey Department of Environmental Pr o tection Bureau of Geology & Topography

BULLETIN 72 - E

INTRODUCTION

Wa t er pr o blems are centuries o ld , and pr o blems o f industrial polluti o n date back to the beginning o f the in du strial revolution. Expanding popula- tion and industry, together with increasing abuse of water reso u rces, only accentuated the serio u sness of the problems.

T he sixth vol u me of the Proceedings is concerned abo u t the impact of the water quality on the environment and the availability of water reso u rces to the increasing needs. The "Ann u al December Meeting in Washington, D.C." with the World B a nk as host became a traditional review of the world sit u ation in water reso u rces d istribution in the past t hree academic years.

On December 4-8, 1972 in Mexico City the Interna t ional Symposium on Water Resources Planning was held and four papers were delivered by our Seminar members.

In June 1973 in Madrid the Sy m posium on the Design of Water Resources P rojects wi t h Inadequate Data was organized by UNESCO, WMO and IA H S. The Seminar participated with two papers. Similarly, on March 4-8, 1974 one paper represented the Seminar in the UNESCO sponsored International Symposi u m on Hy d rology of Volcanic Rocks, Canary Islands.

On July 30-August 2, 1974 I FIP Conference on Modeling and Simulation of Water Resources at Ghent University, Belgium, a rep o rt on the water resources data bank (LORDS) of New Jersey was presented by the Seminar.

The editors of the Proceedings wish to express their gra t itude to all members contrib u ting articles and lect u res to foster the Seminar. The publi- cation was made possible only by the generous help and cooperation of the U.S. Department of t he Interior, Geological Survey and the State o f New Jersey, Department of Environmental Protection in the series o f U.S. Geological S u rvey--Water Resources Investigation.

George J. H alasi-Kun Chairman of the Univesity S e m in a r o n P olluti o n and W a ter Resources Col u mbia University

v

H YD ROLOGI C AL I N VE ST I GA TIO N

O F THE UN S A T U R A TED ZONE

b y

D r. G. KO VA C S

D eputy Dire cto r, Resear c h I ns t itute o f Water

Resour c es Develop m ent

Se c retary General, Internati o nal Associati o n

of H ydrological Sciences

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applied in t he in co rrect f o rm ment i oned. It is necessary, therefore, to raise the acc u racy of the observations and to develop special measuring equipment (lysimeters c ombined with soil moisture measurements). Theoretical investigations concerning storage capacity of and water movement thro u gh the unsaturated zone can also decrease the uncertainties in the hydrological

description of layers above the water table.

According to aspects explained in the previ ou s paragraph, the summariza- tion of hydrological investigations concerning the unsaturated z o ne can be divided into three parts. The first chapter includes the detailed descrip- tion of hydrological phenomena and their interactions together with the evaluation of data collected with lysimeters. The second part deals with the theoretical analysis of the pF curve, which is an important aid for the char- acterization of storage capacity in the unsaturated zone. Finally, the investigations of hydraulic resistivity of porous media can be extended to cases in which pores are only partly filled with water, containing also air. The physical relationships used in description of vertical water movement in the unsaturated layer can give important information for the analysis of the process o f infiltration as it is summarized in Chapter 3.

i. HYDROLOGICAL PROCESSES OCCURRING IN THE UNSATURATED ZONE

The investigation of these processes is a boundary field of surface water hydrology, gro u nd water hydrology (hydrogeology), and pedology (soil science and agronomy). Because of this interdisciplinary character and partly beca u se of the very many infl u encing phenomena and factors, the c o llected data and the results of basic research concerning the u nsaturated zone are not yet sufficient to describe correctly and completely these processes, although the solution of many practical problems requires the synthesis of a well founded mathematical model.

For clarification of hydrological phenomena occurring in the unsaturated zone and their interaction, a physical model of this zone was established to indicate all acting effects. As sh o wn schematically in fig. I, the physical model d o es not incl u de only the unsaturated zone but also the zone of plants covering it, as well as a part of the gravitational ground water space, which is the lower boundary of the z o ne of aeration. The path of water within or through the unsat u rated zone can be easily followed in this model.

The physical model can be regarded also as the vertical section of a lysimeter. It can be used, theref o re, for detailed analysis of the reliabil- ity of this very important measuring instrument and for evaluation of d ata collected by lysimeters (Kov_cs and P_czely, 1973).

i. Analysis of relevant hydrological processes

Regarding the model as a closed system, the water amounts moving through the boundaries of the selected column are the inputs and the o utputs of the system, and are indicated by arrows in fig. i. The investigated prism is divided int o three subsystems: zone of plants, zone of aeration, and zone of saturation. The water exchange between the subsystems can also be represent- ed by arrows. The surface has a special role in the system, being the border between the zone of plants and the unsaturated zone, although the roots are

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c r o ssing it. t the same time , a part of precipitation reaching the surface is turned back Jut< the zone of plants by evaporation. The sur- face could be regarded, tnere'_re, as a fourth subsystem, the special effect of which is indicated by d otted arrows.

Apart from input s and outputs a system is characterized by the operations within the system itself. Storage within the zone of plants and aeration as well as the fluctuation o f the water table (which represents the storage in the zone of saturation) is indicated in the figure as such internal opera- tions. Some characteristic val u es governing the operation of the system are als o mentioned (such as: pF c u rve, m o isture distribution).

For better u nderstanding of the hydrological phenomena and their inter- actions, it is useful to group and classify the various processes influencing water movement through and within the unsaturated zone. For this grouping the physical model sketched in fig. I. can be used.

The investigated column is in c onnection at its upper b o undary with the atmosphere. The input through this surface is precipitation, either liquid or solid, while the outputs are combined under the term of actual evapo- transpiration.

Along the vertical faces the model is bordered by the same zones as are in the prism, i.e., zone of plants a bove the surface, unsaturated zone between the s u rface and the water table, and finally gravitational ground water space below the water table. The lower horizontal boundary of the column is similar to the lower part of the vertical face; it is in contact with the saturated zone. By separating the model from its surroundings, a discontinuity is caused along the listed bo u ndaries, which has to be replaced by inputs and outp u ts acting on and originating from the system respec- tively. Such replacing factors are:

• Horizontal vapor movement in the zone of plants; Horizontal moisture movement in the unsaturated zone;
• S u rface r u noff into and out of the prism; and ground water flow.

The listed types of water movement may be either inputs or outputs of the system depending on the direction of the flow (whether it is directed into or out of the investigated prism).

Further groupings of actingprocesses can be distinguished according t o the s u bsystems mentioned previously. Storage in the zone of plants and the evaporation of the water stored here may be combined into the investigation of interception. Storage on the surface a nd the direct evap o ration from here are closely related to the former gro u p, although these processes already belong to the next subsystem (i.e., the surface itself), which is character- ized by surface runoff as one of its inputs (inflow on the surface to the investigated space), and also as the outp u t of this subsystem (o u tflow on the surface). The water exchange between the zones of plants and aeration is the resultant of infiltration through the s u rface as well as the evaporation and transpiration from soil moisture. The two draining processes mentioned (evaporation and transpiration) are only a part of the actual evapo- transpiration, because the latter in c lu d es the direct evaporation from the surfa c e of both plants and earth. The next subsystem is the unsaturated

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moisture. This type of data can assist also with the better explanation of

the special problems mentioned previously.

This is the reason why the remaining objective of the first chapter of

the paper is to classify the types of lysimeters and methods of measure-

ments. This is to make the collected data comparable and has the long range

aim of standardization of equipment.

1.2 Classification of lysimeters

According to the most simple and very general definition, lysimeters are

soil columns separated from thei_ s u rroundings in which some of the compo-

nents of water balance in the unsaturated layer are m_asurable. There are

many possible solutions for construction of such a closed space in the soil.

Lysimeters may differ not only in their size (depth, surface area) but also

in their constr u ction and operation. Variable aspects include: type of sur-

face (bare or covered with vegetation); type of soil (homogeneo u s or layered,

cohesive or cohesionless material), position of the water table; recharge of

water (natural, or artificial, in the second case recharged thro u gh the sur-

face, or by ensuring water supply in the gravitational ground water space);

measuring techniques of various components of the water balance; etc.

The constructional and operational aspects infl u ence not only the relia-

bility and corre c tness of meas u rements but they determine at the same time

what combination of the phenomena or which group of components are included

in the data measured by the lysimeter. This is the reason data obtained

u sing different equipment are not comparable.

It is n o t possible, however, to give preference to one type of construc-

tion or operation over the others because there is no way to measure all

components separately. Only a combined or summarized effect of a group of

phenomena can be observed. The purposes served by the lysimeter determine,

therefore, which gro u p should be measured and thus which type of construction

sho u ld be ch o sen. In other cases the comparison of data of two different

lysimeters allows characterization of a special component, which is included

in one group only while other components measured with the two lysimeters are

identical. Thus the difference of the observed data describes the phenomenon

in question.

Considering the facts explained previously, there is no possibility for

complete standardization of lysimeters. Nevertheless the data can be made

comparable by classification of the equipment used and by determination of

which components are measured with a given type of lysimeter. The proposed

steps of this indirect standardization are as follows:

• To classify the types of lysimeters;

To determine the components measured either separately or in groups by

the various types (q u alification);

To investigate which type of lysimeter can measure a given component

or group of components (eval u ation);

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T o pr o p o se standardization o f a set o f e q uipmen t s u i table to provide research-workers with reliable information on all acting phenomena;

• To collect standard sets of compared data measured with the vario u s types of lysimeter proposed to be included into the u nified system of equip- ment.

The proposed classification is based on 21 members divided among 7 gro u ps each comp o se d of 3 members. Each group describes a special character of the lysimeter using three figures which can be a ny integer between 1 and 9. Thus the character in question is given by three data each classified at most into nine categories. Indicating the members of the basic fig u re of classifica- tion by letters it has the following form:

abc def ghi klm nop rst u vz.

The meaning of the groups and the special characteristics indicated by each of the letters are listed below, while the categories belonging to the various letters are given in Table i.

A(abc) description of the container a - surface area b - depth c - material of the container B(def) composition of the soil column investigated d - soil layers e - effective diameter of the basic layer f - porosity of the basic layer C (ghi) location of the lysimeter g - related to the surface of the surroundings h - related to the vegetation of the surroundings i - related to the surrounding layers D(klm) composition (formation) of the lysimeter surface k - slope of surface 1 - type of vegetation m - depth of the root-zone E(nop) water balance of the lysimeter n - s u rface runoff o - water table p - recharge of the soil column F(rst) methods of basic measurements r - method of measuring the stored amount of water s - methods of soil moist u re m easurements t - period of basic meas u rements G(uvz) supplementary measurements u - meteorol o gical meas u rements v - a gronomic a l measurements z - other measurements

Some of the features listed do not influence the character of the meas- ured data but others determine basically the type of data obtained by a given lysimeter. A detailed investigation can be carried out to select those parameters influencing the character of the meas u red data and the lysimeters can be classified into four main gro u ps.

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o nl y as a g ro u p by l y sime t ers. It is al w ays advisable to apply this observa- tion in lysimeters.

• Hydrological phenomena in lysimeters covered by vegetation are always strongly influenced by the type and the grade of development of the plants used. Detailed agronomical observations are necessary, therefore, for the evaluation of dat a in this case. It is advisable to inclu d e the measurement of the total dry material of plants in this gro u p of observations as well.

C onsidering the aspects listed previously some c o nstructions can be selected from each main gro u p which might be proposed for general use in the future and probably for standardization. (The symbols used there are identi- cal with those in Table 2.)

LA bare lysimeter without @roundwater

The most complete information can be collected by lysimeters which weigh as well as measure the drained water and soil moisture (LA4). It is not reasonable to construct a lysimeter capable of weighing and neglect the measure m ent of drained water. LA 1 and LA 2 types should be e x cluded from the possible variations (this remark refers to all types with index i. and 2. and, therefore, they will not be mentioned again). Data provide d by LA 5 are insufficient. The components measured by LA 6 are the same as by LA 4. The advantage of LA 4 is the greater accuracy of data and the con- trol of storage in the u nsaturated zone. At the same time the construction of LA 6 is considerably cheaper than that of LA4, especially in the case of a thick soil col u mn. It has to be considered, however, that the applica- tion of lysimeters with o ut groundwater is basically a rough approximation acceptable only when water table is very deep. In this case the depth of the lysimeter is not determined by any factor to be simulated in the lysimeter. The thickness of the layer investigated can be chosen, therefore, according to the requirements of weighing (the error of meas u rements should be s m aller than the components observed). Thus the final recommendations is to acce_)t type LA 4 as the generally used bare l_simeter witho ut @roundwater and to apply type LA6 only as members of larger networks when cheaper constructi o n allows a greater number o f lysimeters.

LB bare iysimeter with 9ro undwater

As before the lysimeter capable of weighing as well as measuring recharge, drainage and soil-moisture (LB4) provides the largest am o unt of information. Equipment capable only of weighing (LB 1 an d LB2) or unable to measure soil moisture (LB 3, LB 4 and LBs) may be excluded from the advisable constr u ctions. A special problem is to determine how to control the water table. There are two possible ways:

To drain and recharge the groundwater with a given amount of water (which can be constant or changing according to a seasonal program) and leave the water table to develop freely as a result of natural and artificial effe c ts, or

T o keep the water table at a determined level (which can be c onstant or fl u ctuating according to seasons) and to ensure the recharge or drainage ne c ess a ry for maintenance of this level.

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The most perfect solution would be to keep the water table within the

lysimeter at the same level as in the surroundings and to measure recharge or

drainage necessary for this operation. The techhical solution of this con-

struction raises difficulties, and therefore, either the maintenance of

constant waterlevel (LB4 and LB62 ) or the application of constant

recharge or drainage (LB61) are the generally accepted measuring methods.

The latter type (constant drainage or recharge) can hardly be constructed

with capability of weighing, because the fluctuation of the water table

requires a deep lysimeter and in this case the accuracy of weighing is gener-

ally lower than the amounts to be measured. This is also the reason why

weighing cannot be used for investigation of a thi c k unsaturated zone. It is

necessary to note, that the maintenance of a constant water table or

recharging (draining) a constant amount of water creates unnatural conditions

(conditions different fro m the ground water regime in the surrounding areas)

and, therefore, a group of such lysimeters has to be constructed. In this

way a suitable model of the s u rro u ndings can be selected from the group in

all periods of the year. As a final summary of the evaluation of this group

it can be stated, that the construction of LB 4 t_ rpe is advisable only in

the case of a shallow water table. In other cases type LB 6 is the suitable

construction. This gives almost the same amo u nt of information (except

interception). Within the latter type LB61 operates with a fluctuating

water table and constant recharge or drainage, while in LB62 the level of

ground water is constant. The complete investigation of the unsaturated zone

requires the construction of a group of such lysimeters in the same area (in

the case of LB61 with different constant discharges and LB62 with differ-

ent constant levels).

LC lysimeter covered by ve getation without 9roundwater

Following the same reasoning as in the case of type LA, the lysimeter

capable of weighing and measuring discharge as well as soil moisture can be

bro u ght into the limelight as the best construction. It can be stated,

therefore, that type LB 4 should be the @enerally used lysimeter and type

LB 6 can be applied only as a member of lar ge networks.

LD lysimeter covered by ve@etation, with groundwater

As in the case of LC lysimeters, it is not necessary to repeat the rea-

soning given in connection with the bare lysimeters. The final conclusions

can be applied for lysimeters covered by vegetati o n as well. Thus the con-

struction of LD 4 type is advisable only in the case of shallow water

table. If the unsaturated zone is thick or the purpose is the modeling of

groundwater fluctuation, type LD 6 is the proposed construction either with

constant recharge-drainage (LD61) , or with constant level (LD62).

2. THEORETICAL ANALYSIS OF THE pF CURVE

It was already mentioned in C hapter i, that some theoretical investiga-

tions could help the evaluation of the measured data and the clarification of

the influence o f some hydrological processes on the water balance in the

unsaturated zone. Storage in this layer was mentioned as an example.

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D is c ussi o n o f me t hods f o r measuring soil m o ist u re would lead, however,

far from the original topic, which is the hydrological investigation of the unsat u rated zone. It is necessary, therefore, to turn back and continue the physical interpretation of water content. The water content determined in the way explained is an instantaneous value describing the momentary state of the investigated sample, p o int or section (vertical line) without giving any information on the behaviour of the soil containing the meas u red amount of water. It is obvious that the same water content can saturate one sample, but leave considerable open pore space in another sample of greater porosity. The c oefficient of saturation, (the quotient of the volumetric water content and porosity) gives, therefore, very important supplementary information W s =-- ; 3. n showing the saturated rati o of the pores. (s=l if the sample is saturated; s = 0 in the case of c o mpletely dry sample. It may have any val u e between the two limits given). One can easily argue that the knowledge of the ratio of saturation is still insufficient information t o judge the expected behaviour of the soil because a change of saturation in sand does not involve considerable modifi- cation as may be caused in a clay soil. Measuring water content at a given state of the sample gives guidance for complete understanding the effects of the actual or instantaneous soil moisture on the investigated soil. Knowing these specific values of water content of the soil in question and comparing the actual soil moisture to them the behaviour of the soil can be estimated. When selecting the specific parameters, the most important requirement is that the state described by them should be characteristic and easily repeat- I able. From this aspect the parameters o f plasticity used in soil physics are well determined values, altho u gh they belong to arbitrarily chosen states of the sample (WL liq u id limit is a water c ontent described by Casagrande and Wp limit of plasticity is moisture content, when a string of 3 mm can be rolled from the sample). The index of consistency, which is the ratio of two differences (that between liquid limit and instantaneous water content related to the difference of WL and Wp) W L - W K = 4. l W L - Wp' is a good example o f how act u al water c o ntent is compared to selected limit values. Altho u gh the specific soil moisture values used generally in soil science as parameters belong to more natural conditions than the physical parameters of soils, their reproduction causes, however, some difficulties, beca u se the conditions described are not determined precisely enough. E.g. field capa- city (WFc) indicates the water amount retained in the sample against gravity. This is a very important parameter, but it is influenced by n u mer- ous undetermined factors (e.g. temperature, relative humidity of air, etc. Among these the position of the investigated point related to the actual A-

water table is perhaps the most important as will be demonstrated later). Therefore, field c apacity can h a rdly be reproduced or physically interpret- ed. The s a me statement c an be made of wilting point (Wwp) as well, because the suction of the roots d iffers from plant to plant.

The most stable and repeatable parameters describing specific moisture contents used in soil science are various measures of hygroscopic m oisture content (or hygroscopicity) which measure the water content retained by the sample in closed space in the presence of sulfuric acid. Thus Mitscherlich's hygroscopicity (WHy) is determined with 10% concentration of the acid while Kuron's hygroscopicity (Why) is measured with s u lphuric acid of 50% concen- tration (Mitscherlich, 1932; Kuron, 1932). Because of the high stability of these parameters it is reasonable to accept their general use in the future and to regard the others only as ro u gh approximations which can be estimated as functions of hygr o scopicity using linear relationships. There are many of s u ch equati o ns proposed in the literature (M_dos 1939; 1941; Juh_sz 1967). A few of these a re listed here:

wFC = 4 Why + 12;

WWp = 4 Why + 2 ;

w L =2,0 wHy + 12;

Wp =1,7 wHy +6,5; 5.

Why =0,45 wHy.

2.2 Interpretation of field capacity and 9ravitational porosity

As was already mentioned, the water holding capacity of a soil cube depends on the position of the investigated sample (whether it is a sample separate d from its surro u ndings or is in a soil profile and in the latter case what is its elevati o n above the water table). The reliability of this statement can be easily understood. In the case of an isolated sample the effect of gravity is e x pressed by the weight of the water contained in the pores. If the soil cube (the water holding capacity of which is investigat- ed) is part of a contin u o u s soil profile, the sample is fitted into a space of gravitational potential, the dat u m (reference level) of which is the water table where the surplus pressure is z ero (the gravitational potential is zero at this level). Everywhere in this space the effect of gravity should be expressed with respect to this datum. Thus above the reference level gravity causes a s u ction proportional to the height of the investigated point above the water table. Physically this process can be explained by imagining that the continuous chain of water films composes a closed system in which the pressure on a water particle (in this case negative pressure i.e. suction because the particle is above the water table with zero press u re) is propor- tional to the weight of a straight water col u mn between the particle and the reference level, independent of the form of the container (the form of the chain composed of the water fil m s). This is the reason field capacity will be larger near the water table, where the suction caused by gravity is smaller, than at a higher point of the profile, and why water holding

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achieved as final result describes the position of the dividing line of Fig. 2.

A further consequence m u st be deduced from the c o nditions explained. It was already mentioned that the water content does not give sufficient infor- mation on the behaviour of the soil. It is necessary to c o mpare these data to parameters belonging to spe c ial conditions o f the sample. This restric- ti o n should be enlarged. Point meas u rements, even compared to such specific characteristics as hygroscopic moisture c ontent, liquid limit or limit of plasticity are ins u fficient to describe field c o nditions. The complete ver- tical d istribution of moisture content must always be determined in a profile and the result m u st be compared to soil moist u re distribution belonging to the dynamic eq u ilibri um. Only the differences between the actual distribu- tion and the matching curve shows where water deficit or surpl u s exists in the profile. This indicates also the possible vertical water movement either upwards or d o wnwards. The total hydraulic gradient can be calculated from the curves and the existence of a gradient not eq u al to zero is the precondi- tion of m o vement.

The only remaining problem is the determination of the equation of the line dividing field capacity and gravitational porosity, which describes the state of equilibrium of soil moist u re in a pr o file, as was pr o ved earlier. It was also shown that in hom o geneo u s media this pr o blem can be reduce d to the investigation of the relationship between tension and water c ontent. This con d ition immedi a tely suggests that the pF curve could be used for d etermin a - tion of or can be identical with the d esired matching curve, since, according to its definition, the pF curve represents the relationship mentioned, being the tension in the height of the water column pl o tting on a logarithmic scale. This is the reas o n the physical interpretation of the pF curve is dealt with in detail in the next section.

2.3 Construction and calculation of pF curves

The usually accepted way for the determination of a pF curve is to apply various suctions on the investigated sample and to meas u re retained soil moisture. After plotting the points with suction - which is supposed to be equal with the tension on the surfa c e of water films - as the logarithm of t he height of t he equ i valent wat er co lumn and w at er c o n t e nt a s an a ri t hmetic val u e, the pF curve can be easily construc t ed (Fig. 3.). Various methods are use d to create suction on the sample. The choi c e of method depends m ostly on the range of suctions to be applied.

Most commonly pF curves are composed of three clearly recognizable sections (Fig. 4-a) (Kov_cs, 1968). The u pper part of the c u rve is almost vertical and is foll o wed by a nearly horiz o ntal secti o n. The c u rves are com- ple t ed by a vertical line at a moisture content eq u al to the por o sity (W n; s i). There a re only a few exceptions, always in the case of very fine materials, when the firs t two stretches are replaced by a c u rved line of moronicall y decreasing slope as water - conten t increases (Fig. 4-b).

This chara c ter of the pF curve can be easily explained considering that in t he u nsaturated z one gravity is balanced by two different intermolecular for c es, i.e.: adhesion and capillari t y.

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At the upper part of the pF curve, far from the water table, the water

covers grains in the f o rm of a thin film. The force keeping the water here

against gravity is adhesion. Without investigating the character of this

f o r c e i n detail, its ex i stence can be explained as t he a t tra c ti o n be t ween

s o lids and water molecules created by the elec t rostatic charges of grains and

the orientation of dipolar water molec u les (Van der Waals force). This type

of force is generally approxima t ed in theoretical physics by relating the

tension at the surface of the water film (W) to the thickness of the film (_)

in the form of a hyperbola of sixth order

It is quite evident, that the thickness of the water film is closely cor-

related with the water content of the sample. U sing some approximations this

relationship can be determined:

W : 4n _-- (i - ); s : --

where _o is the average diameter of the pores, or that of a model pipe

hydraulically equivalent to the network of channels compose d of the pores.

The correctness o f Eqs. 8 and 9 was proved by comparing calculated and

measured parameters of numerous samples (Kov_cs, 1972. Fig. 5.).

As was already mentioned, in the state of dynamic equilibrium the tension

on the surfa c e of the water film balances the effect of gravity which is pro-

portional to the elevation of the point investigated above water table:

Substituting this value together with Eq.9 into Eq.8 the vertical distribu-

tion of soil moisture at equilibrium (WB or SB) can be determined

A 4n |i - 1 A |

W B

- (h q) i / 6 d o [ To (h )i / ] ;G

A 4 1 1 A SB = 1 do d 1

(h / 6. o (h , '() /G

(It is necessary to note, that accepting Eq. i0. as a basic principle, any

kind of _ = f (W) function will obviously satisfy the condition given in Eq.

6. This equation c annot serve, therefore , as a control, and the reliability

of the proposed relationship between tension and water content m u st be

checke d by measurements as was already referred in connection with Eq.9).

Continuing the theoretical analysis, the constant of Eq. 8 can be

expressed as the f u nction of the soil physical parameters Dh (effective

diameter), _(shape coeffi c ient of grains) and n (porosity). This theoretic a l

relationship is in a good accordance with the empirical result gained from

measurements (Fig. 5) except the power of Dh / _ , which is 1 in theory.

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