effect of compactness and initial moisture content of the...

Effect of compactness and initial moisture content of the soil on the process of capillary rise


I. Ijjas Department of Water Resources Development, Technical University of Building and Transport Engineering,

Budapest, Hungary

A B S T R A C T : T h e effect of compactness and initial (natural) moisture content of the soil on the process of capillary rise and on capillary transmissivity is discussed in the paper. T h e analogy between deviations of capillary characteristics in soils of identical grain size distribution, but with different compactness and initial moisture content, and those in soils of different grading is examined. A comparison is m a d e between capillary processes taking place in soils compacted in strata and those in soils composed of two layers. Characteristics of capillary flow directed upwards and enclosing an angle 0 < a < 9 0 ° with the horizontal are also studied.

R É S U M É : L'étude traite l'effet de la compacité et de l'humidité initiale (naturelle) du sol sur le processus d'ascension capillaire ainsi que sur la conductivité capillaire. L'analogie entre les différences des caractéristiques capillaires des sols de granulométrie identique mais de compacité et d'humidité initiale différentes, et celles des sols à granulométrie différente est examinée. U n e comparaison est faite entre les processus capillaires dans des sols compactés par couches et dans ceux composés de deux couches, et les caractéristiques des mouvements d'eau ascendants (d'une direction enfermant un angle de 0 < a < 9 0 ° avec l'horizontale) sont étudiées.

I. INTRODUCTION

T h e laboratory investigations, serving as a basis of this paper, w e r e directed to study a n d to determine, in a concrete w a y , capillary rise a n d capillary conductivity in sand soils. Results of these studies have t h r o w n light u p o n a n u m b e r of n e w aspects regarding water balance p r o b l e m s of soils.

T h e following will be discussed: a) relationships b e t w e e n soil compactness a n d natural moisture content a n d capillary rise, as well as capillary transmissivity, a n d b ) u p w a r d capillary flows enclosing a n angle of inclination of 0 < a < 90° with the horizontal.

II. EFFECT OF COMPACTNESS A N D NATURAL MOISTURE CONTENT O N THE PROCESS OF CAPILLARY RISE

In the literature m a n y references can b e found concerning the fact that the process of capillary rise m a y be considerably influenced b y the natural moisture content a n d compac tnes s of soils. It is, for e x a m p l e , a generally accepted statement today that the height a n d velocity of capillary rise are smaller in a dry soil than in a we t o n e , since a significant a m o u n t o f energy is required for hydration. Z u n k e r (1924) points out further that, f r o m the aspect of capillary p h e n o m e n a , a n important role is to b e attributed to the lack of contact water.

A. MATHEMATICAL FORM OF THE RELATIONSHIP BETWEEN COMPACTNESS AND CAPILLARY RISE

CAPACITY, AS WELL AS PERMEABILITY COEFFICIENT OF THE SOIL

S o m e authors already try to take into consideration the effect of soil compactness in their approx imate formulae developed for c o m p u t i n g the height of capillary rise (hc).

547

/. Ijjas

A s it has been found by R o d e (1952), in a med ium composed of grains with identical diameter D capillary rise shows a m i n i m u m in the loosest state and with wetting from below upwards, whereas a m a x i m u m is attained in the most compact state and when draining. According to a theoretical relationship the quotient of the extreme values of the capillary rise m a y reach even a numerical value 5.

Zunker (1924), and Terzaghi and Peck (1948) present relationships for soils with different grain-size distributions. According to them, in soils of identical grading the ratio of capillary rises (hcl and hc2) corresponding to void ratios e¡ and e is expressed by the following relationship:

lhl = <il. (!)

The natural moisture content of soils (ic) is not included in the relationship given by Zunker, and Terzaghi and Peck, which shows that these formulae are likely to relate to dry soils (w0 (& 0).

Theories serving for mathematical formulation of the relation between the permeability coefficient (k) and void ratio (e) or porosity (n) of soils, respectively, do not express the effect of compactness in such a simple way . For example by using the concrete form k = AeB (Kezdi, 1960) to relationship can be obtained:

*I = d (2) I B K '

Both theoretical considerations and practical experiments, however, point to the fact that the soil mechanical-hydraulic approach involved in eqs. (1) and (2) should be developed. It is desirable to determine a relationship of more general character between the individual factors influencing capillary phenomena. O n the present level of development it is indisputable that, in characterizing natural capillary phenomena, there is an indispensable need to take into account the initial moisture content of soils. After all, it is only possible on the basis of such investigations to reveal in a more exact way , what kind of effect the geohydrologic, hydraulic and other factors have on groundwater balance and within this on capillary phenomena.

B. RELATIONSHIP BETWEEN COMPACTNESS, NATURAL (INITIAL) MOISTURE CONTENT AND HEIGHT OF CAPILLARY RISE

In order to solve the functional relationship given above in a concrete manner, the process of capillary rise was investigated in a soil prism of 20 x 20 c m cross-section. Compactness and natural (initial) moisture content of the soil selected for this purpose was varied. In order to be able to observe the time-dependent rise of the wetting front, even in a soil with natural moisture content, an electrical detector equipped with a series of measuring heads along the vertical (fig. 1) was built in the soil.

The curves expressing the time dependence of capillary rise (hc) in soils with various initial moisture content (ÍÍ'0) and compactness («), determined by this method are represented in fig. 2.

A s regards the capillary phenomena connected with fig. 2, according to the present approach reflected in the special literature, the beginning and end sections of the curve of capillary rise are approximately characterized by hc = a • tb.

O u r investigations showed that, in the initial and final phase of the capillary rise process, the curve of capillary rise relating to the same soil but with different moisture content and compactness conditions, i.e. also the function hc = fit, n, w0) can be written in the

548


general form:

where:

accordingly:

hr = a • f

a = / i ( w 0 , n ) , b = f2(w0, n),

he=Mw0,n)'^"^

(3)

(4)

'i rfje o / rrrecJauring heap No 5

272 mm

U.-Í.3Z ¡D-W/.

ground-water-—^ 1

/

.300

<0

Si

too •

Q.

J O

0 t Z 3 U

Time elapsed since ¿he beginning

of investigation, t [hour]

F I G U R E 1. Curve of capillary rise determined by the aid of an electric measuring head s eries Initial moisture content of the soil w0 = 4 . 3 % ; porosity n = 42.0% (Dio = 0.13 m m ; U = 2.3)

For the sandy soils examined in our experiments, the dependence of the value b on the factors ^ Q and n m a y be considered as negligible for the final section of the curves.

For example, for a soil with medium-fine grain size ( D 1 0 = 0.13 m m , U = 2.3), for eq. (3) referring to the final section of the curve the following functional relationship was obtained:

/i„ = 58 n -[0.003(6 - m o ) 2 - 7 + 0.72] ^ . 1 3 (5)

valid only when w0 = 0 to 6 per cent. In soils with greater moisture content than that w e made no measurements. The relationship (5) is of approximate character from a theoretical point of view, and

can be considered as valid only for the soil investigated. For its more accurate determination far-reaching and statistically évaluable measurement would be necessary.

For dry soils (i.e. if w0 ~ 0 ) , eq. (5) takes the form

hc = 58n -1.08 jO.13 (6)

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/. Ijjas

and thus in soils of different compactness (nx and n2, respectively) the values of capillary

rise (Jici and hc2) show at a certain point of time after beginning the examination the

following ratio:

h n 1 " 0 8

U „1.08 V

hc2 «i

30

1

CO

c

Q

Co

20

10

0 3 6 3 12

Time elapsed since the beginning of investigation,

t [hour]

F I G U R E 2 . Curves of capillary rise in a medium grained sand soil at varying initial moisture content {wo) and porosity («) (£>io = 0.13 m m ; U- 2.3)

Thus the relationship between capillary rise and porosity in a dry soil (w0 ~ 0) can be written similar to the general equation expressing the relation between the coefficient of permeability and porosity, in the following general form:

h2

(8)

W h e n investigating the process of capillary rise in soils of identical grain-size distribution, but of different compactness and initial moisture content, the question arises, whether the curves indicating the capillary rise intersect each other, similarly to those relating to soils with different grading (clay, sand).

In our studies, w e found that there are cases w h e n they intersect one another, but the point of intersection falls often to the initial section of the curve of capillary rise to such

550


an extent, that they are hardly perceptible (fig. 3). The probable explanation of this phenomenon is that the water, raised under the effect of capillary forces, comes up initially against a greater resistance in a soil of higher compactness and higher moisture content (e.g. in a soil of considerable moisture content, air permeability is smaller), and it is also presumable that, in a more compact soil, even the distance to be m o v e d by water particles is longer than in less compact soils. In the saturated capillary zone the velocity of capillary rise is proportional to the permeability coefficient of the soil and to the capillary lifting force. In a loose soil the coefficient of permeability is greater but the capillary force is smaller, than in a compact soil. The existence and location of the intersection point is therefore influenced by the coefficients of permeability, as well as by the magnitudes of the capillary lifting forces.

*0

30

S

£20

•2 t!

! «

o

o 50 /OO ISO

Time elapsed since the beginning of

investigation, t [min]

F I G U R E 3. Initial sections of capillary rise curves in a fine grained sand soil at different porosity

(n\ = 4 6 % ; «-3 = 51 % ) but identical initial moisture content (wo = 4 % ) (Dio = 0.08 m m ; U = 2.7)

The considerable effect of compaction on capillary rise is also verified by the curve of capillary rise shown in fig. 4 . The soil was intentionally stratified and the effect of this compaction was examined. A s can be seen, when the moistening contour arrived at a more compact layer from a looser one, the velocity of rise increased, which shows an agreement with the process occurring at the boundary of two soil layers with different grading, observed by Rétháti (1953). This phenomenon m a y be attributed to the fact that the capillary potential suddenly increases, when the moistening contour comes from a looser layer to a more compact one.

O n the basis of our investigations it m a y be established that the process of capillary rise is considerably influenced by the degree of compactness and natural moisture content of soils. With regard to the fact that the effect of natural moisture content m a y increase

551

/ . Ijjas

the capillary raising capacity of soils even by 25 to 50 per cent, it would be expedient to introduce in general the capillary investigation of soils with natural moisture content in laboratories concerned with pedology and soil mechanics.

30 ^^

Q D O

•too

Time elapsed since the beginning

of investigation, t [mm J

F I G U R E 4 . Curve of capillary rise in a medium grained sand soil compacted in strata (Dio = 0.13 m m ; C / = 2.3)

T o sum up, our studies unambiguously point to the fact that allowance for the initial moisture content is of great importance. In the future, however, research work must be extended to greater values than those included in the range of moisture contents examined by us. The effect on capillary rise is probably less important in the range of greater moisture content than in that of lesser moisture content, it would be, however, of basic importance to clear up the question of orders of magnitude.

III. EFFECT OF COMPACTNESS A N D NATURAL MOISTURE CONTENT OF SOILS ON CAPILLARY TRANSMISSIVITY

In a soil being compacted the diameters of capillaries decrease, capillary potential increases and the moistening contour rises farther and more rapidly. It is a more difficult problem to decide h o w the quantity of water raised under the effect of capillary forces will change.

With increasing compactness the velocity and height of capillary rise (hc) tend to increase, while the effective porosity («) and the cross-section dz, through which water percolates in an upward direction, decrease.

For determining capillary transmissivity in the literature concerned with this question the relationship

q = vn-r (9)

is suggested, where r represents the relative humidity of the soil.

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The water quantity percolating vertically upwards at a given height above a groundwater table was computed using this relationship. T h e calculations related to soil samples in different compactness and moisture states. At a certain height, already in the case of a porosity change of some per cent, a considerable difference in capillary transmissivity could be obtained.

Our calculations have shown that there is a height h, in m a n y cases somewhat above the groundwater table, above which the water quantity raised upwards in a vertical direction by capillary force through a unit area—i.e. capillary transmissivity—is greater on the top in a compact and wet soil, than in a loose and dry one. In the case of soils with various compactness this is due to the fact that above the given limit height h the following laws are valid:

— The velocity of capillary rise (vt), as well as the relative humidity formed during this rise (rt) is greater in a compact soil, than in a loose one (v, and r,);

— Effective porosity is smaller (nt) in a compact state, than in a loose one («,);

— The ratio of the products of velocities and relative humidities is greater, than that of effective porosities, i.e.:

V-lHl>n-i (10) v, • r, n,

and thus the capillary transmissivity (q,) is greater in a compact soil, than in a loose one (q():

qt = v,-rt-nt > vl-rl-nl = q, (11)

It is evident even without computations, that there exists a height h above which the water quantity raised upwards in a vertical direction under the effect of capillary forces is greater in a compact soil, than in a soil of the same grain-size distribution but in a loose state.

In a soil of greater compactness water rises higher (hcl) than in a loose soil (fic¡). Accordingly, there exists a range (hcl — hcl) where a soil of loose state has no capillary transmissivity at all. Thus, there is a height h smaller than the capillary raising capacity of the loose soil (hcl) above which, when passed by the wetting front, a compact soil shows a greater capillary transmissivity, than a loose soil. In a loose soil, near the height hc¡ the velocity of capillary rise is m u c h lower than in a soil of greater compactness, but the value of relative humidity is smaller—both being functions of the capillary potential.

It is similarly evident that at a capillary rise hcw in a wet soil and at hcd in a dry one only the soil of greater moisture content has a capillary transmissivity within the range hcw — hcd. Thus, there exists for certain a range hcw — h > hcw — hci (where h < hcd), within which the water quantity raised owing to capillary forces is more considerable in a wet soil than in a dry one.

The effect of soil compactness on capillary transmissivity has also been verified by model tests. The sketch of the seepage system serving for the purpose of investigations is shown in fig. 5a. (The model test was performed to determine the seepage quantity leaking through the soil layer protecting the insulation of irrigation canals, above the insulation, owing to the effect of capillary forces (Ijjas, 1965).

Soils of identical grading but of different compactness (n1 = 43 per cent and n2 = 37.6 per cent) were built into the model and the quantity of seepage water in the capillary fringe above the sloping cover layer was measured at different values s. Fig. 5b shows that in the looser soil (n1 = 4 3 . 0 per cent), at s = 0 , a capillary discharge one and a half-fold greater is obtained, than that measured in a compact soil (n2 = 37.6 per cent). This is quite understandable, since in this case the permeability coefficient of the soil still

553

/ . Ijjas

played a considerable rôle in the whole process and this has a higher value in a loose soil than in a compact one. (The permeability coefficient of the soil investigated was k = 2.7 x 10" 2 cm/s at n = 37.6 per cent and k = 9.0 x 10" 2 cm/s at n = 43.0 per cent). A s against this, at s — 10 c m it was the compact soil where a double discharge was obtained as compared to the loose soil.

n the distance mode by water

percolating under the effect

of capillary forces

3

o-

I .8 "D

w

20

—

| 1

n2'37,6V. " i i

^nt-^3M — -

0 4 8 12 ft 20

Lfcvotion difference betueen

headwater level and upper edge

of the Impervious layer ts CcrrJ

F I G U R E 5a. Theoretical sketch of the seepage system applied to determine approximately the value

of capillary transmissivity. 5b. Capillary transmissivity in a medium-grained soil (£>io = 0.13 m m ;

U = 2.3) at varying porosity (m = 4 3 . 0 % and n% = 37 .6%)

The same situation ensued, when first a sand soil of medium grain fineness (Z>10 = 0.13 m m , U = 2.3, soil denoted by A), and later a fine sand soil (Dl0 = 0.08 m m , U = 2.7, soil denoted by B) were built in and capillary discharge was measured at various values 5 (fig. 6). The coefficient of permeability is of higher value in a medium-grained sand soil, than in a fine-grained one. Capillary transmissivity, however, was smaller even at a quite slight height above the groundwater table in the medium-grained sand soil, than in the soil of finer grain size.

IV. CAPILLARY FLOW OF DIFFERENT DIRECTION

In the first part of this paper the simplest case of capillary flow, i.e. the capillary rise vertically upwards and the water quantity raised up in vertical direction under the effect

554


of capillary forces, respectively, were discussed. (It was only in the seepage system represented in fig. 5a, that a m o r e complex capillary flow occurred).

•Si

•3

I I

40 <\

20

n

. /

i

.soil of Type A \

" > - - < • — o

-soil of Type B

2T -5 0 10 20 30

Devotion difference between head

water level and upper edge of the

impervious layer, s fern]

F I G U R E 6. Capillary transmissivity of soils with different grain-size distribution Soil denoted by A ; medium-grained sand (Dio = 0.13 m m ; U — 2.3) Soil denoted by B ; fine-grained sand (Dio =0.08 m m ; U = 2.1)

Capillary flow occurring in nature are in general movements of different direction. Moreover, in a great n u m b e r of cases they are curvilinear movements. A t several capillary movements , boundary conditions of seepage are of such nature, that e.g. the streamlines show a fan-like spreading. This situation holds for the case indicated in fig. 7 where the water particles get across the obstacle (i.e. the impervious layer). (The streamlines were dyed and, photographs were taken at different times, and projected to a figure. The object of this experiment in a large-scale model was to determine the capillary water loss in insulated irrigation canals).

T h e question m a y be raised, h o w the process of capillary rise develops in time, if the inclination of the capillary tube, having a position a = 90° as compared to the water level (that is a vertical position), is changed within the range 0 < a < 90°.

headwater feue/

aground-voter level txfare slartng of capilary xepago

F I G U R E 7. Observation of capillary seepage by using colouring agent (numbers written on moistening contours indicate the time passed since the application of the colouring agent)

555

/. Ijjas

For the velocity of capillary flow with oblique direction (according to a) the following relationship is given by Rétháti (1960):

h.—z • sin a k (12)

where: z represents the height from water level p0 ; and hc the capillary raising capacity of the soil. This equation includes the idea, that the force of gravity is prevailing only along the vertical projection of the streamline with inclination angle a. T h e application of this equation is hindered by the circumstance, that the value kjn depends on the moisture distribution during the capillary rise process, i.e. on the difference hc — z • sin a.

Rétháti (1960) presents a figure in his paper as a result of a numerical example, which shows, h o w the wetting front is formed—with the above relationship taken as a basis—at the m o m e n t of the spreading of water entering the soil space horizontally. H e establishes that at the beginning—when gravity m a y be neglected in comparison to capillary forces— the velocity of capillary rise is the same in different directions, which means that the wetting front forms a circle. Later a deformation of the wetting front is caused by gravity force. The smaller is the inclination angle of flow direction, the slighter is the effect of the force of gravity, and thus, the wetting front moves further during the same period from the point entrance.

Fig. 8 shows h o w the curve of capillary rise was formed in glass tubes with different angles of inclination during investigations performed in fine-grained sand soils (£>10 = 0 . 0 8 m m , U = 2.1).

50 100 00 Time elapsed since the beginning of

investigation, t [hour]

F I G U R E 8. Curves of capillary rise in glass tubes of different inclination angle, in afine grained sand soil (Dio = 0.08 m m ; U = 2.7) (the tangents of curves characterize the trend of velocities and of their vertical components at a given height above ground water level and at a given point of time after the investigation has started

556


Fig. 9 shows the formation of wetting front, plotted on the basis of examinations concerned with capillary rise in glass tubes of different inclination. It should be noted that the results of capillary rise studies made with glass tubes of different inclination angle can only be compared exactly, if investigations are carried out under identical conditions.

hç-zsinx

F I G U R E 9. Shape of the moistening contours in fine grained sand soils (Dio = 0.08 m m ; U = 2.7)

at a time 0.5-500 hours after beginning of the investigation, based on capillary studies made in glass

tubes of different inclination angle

Based on our investigations into the process of capillary rise, made with glass tubes of oblique direction in sand and silt soils, the relationship between direction, velocity and magnitude of capillary rise was analysed.

If the velocity of capillary flow is vf in the tube of vertical direction, while va in that of oblique direction, and the vertical component of velocity in the tube of oblique direction is vaj (figs. 8 and 9), the essential conclusions to be drawn for velocity conditions of the flow with oblique direction are as follows:

a) At the same elevation above ground-water table

ur > v. and thus, naturally (13)

At the same height in the oblique tube the value of relative humidity nearly attains that in the vertical tube, that is:

na nf

Consequently, in this case the ratio of velocities m a y approximately be computed on the basis of Rétháti's (1960) theoretical relationship (eq. 12). Thus, w e obtain:

1

sin a and — 2:

1

sin2 a (14)

b) At a given point of time after the investigation has starded:

vf < K

c) At the same distance z from ground-water level:

vf< v*

(15)

(16)

Thus, the relative humidity at a distance z in an oblique tube is identical with or greater

557

/ . Ijjas

than that formed at a height z in a vertical tube, which means that:

k k — < — that is na < nf (17)

and thus, on the basis of eq. (12), this yields:

Er̂ -Azf—o (i8) vx nf h — z-siri a

In the course of our investigations concerned with capillary flows of oblique direction, it could thus be established that the characteristics of capillary flow of oblique direction depend on the angle of inclination. Therefore, w h e n investigating processes occurring in nature, the characteristics of oblique flow deviating from those of vertical flow should not in general be left out of consideration.

V. CONCLUSIONS

The paper deals with the effect of compactness and natural (initial) moisture content of the soil on the process of capillary rise, as well as on capillary transmissivity. U p w a r d capillary flows enclosing an angle 0 < a < 90° with the horizontal are also discussed.

The most important statements concerning this problem are as follows:

A . A s regards the effect of variations in porosity («) and in natural (initial) moisture content (w0) on the process of capillary rise:

1. In soils of identical grain-size distribution, with increasing compactness and increasing initial moisture content up to the limit of the range investigated (fig. 2) the height of capillary rise (hc) also shows a considerable increase.

2. In the case of soils with identical grading but with different compactness and initial moisture content, respectively, the curves indicating capillary rise—similarly to those pertaining to soils of different grading (clay, sand)—intersect each other in certain cases, on the initial section of rise (fig. 3).

3. A soil compacted in strata behaves from the aspect of capillary rise in a similar w a y , as experienced in the case of soil layers with different grading (fig. 4).

4 . In comparison to soils in dry state even a very small initial moisture content (w0 = 1.0 per cent) causes a considerable change in the process of capillary rise. Soils occurring in nature have generally some moisture content, it is therefore expedient to m a k e allowance for the effect of w0 when investigating the phenomenon of capillary rise.

B . A s regards the effect of porosity and initial moisture content on capillary transmissivity:

1. There exists a limit height—in a number of cases scarcely somewhat above the level of groundwater table—above which capillary transmissivity is greater in a soil of the same grading but with greater compactness and higher moisture content, respectively, than in a soil with looser and drier state as compared to the former (fig. 5).

2. A s shown by our examinations, capillary transmissivity is greater even at a small height above groundwater table in a fine-grained sand soil, than in a coarse-grained one (fig. 6).

3. It depends upon the height above groundwater table, which of the soils with different grading and state (degree of compactness and initial moisture content) shows a m a x i m u m capillary transmissivity.

558

The dynamics of capillary rise

C . Features of a capillary flow tending upwards and enclosing an angle 0 < a < 90°

with the horizontal are as follows:

1. T h e angle of inclination enclosed with the horizontal plays an important rôle, the characteristics of capillary flow of different direction being considerably dependent on it (figs. 7, 8 and 9). Features of capillary flow with oblique and vertical direction m a y show great deviations, which must be taken into account by all means w h e n investigating the individual processes.

2. In the case of capillary flows with different direction the effect of compactness and initial moisture content appears similarly to the case of capillary rise with vertical direction.

REFERENCES

IJJAS, I. 1965. Capillary losses in irrigation canals. Hidrológiai Kozlony, 7. (In Hungarian, with summaries in English and Russian).

J A K Y , J. 1944. Talajmechanika. Egyetemi Nyomda, Budapest. K E Z D I , A . 1964. Bodenmechanik I-II. Akadémiai Kiadó, Budapest. K O Z E N Y , J. 1924. Über den kapillaren Aufstieg des Wassers im Boden. Der Kulturtechniker, 27. L I P T Á K , F. and G . O L L Ô S . 1964. Seepage from lined and insulated irrigation canals. (In Hungarian,

with summaries in English, French and German) Vizügyi Kozlemények, 4. N É M E T H , E . 1963. Hidromechanika. Tankonyvkiadó, Budapest. O L L Ô S , G . 1961. Effect of the capillary fringe on free surface seepage processes. Vizügyi

Kozlemények, 2. (In Hungarian, with summaries in Russian, English and French).

R É T H Á T I , L . 1953. Kapilláris emelkedés tórvényszerüségei kétrétegü talajban. Melyépitéstudo-mányi Szemle, 8-9.

— 1960. Engineering relations of capillarity in soils. Vizügyi Kozlemények, 1. (In Hungarian with summaries in French and German).

R O D E , A . A . 1952. Pochvennaia vlaga. Izdatelstvo Akademii Nauk SSSR, Moscow. T E R Z A G H I , K . and R . B . P E C K . 1948. Soil Mechanics in Engineering Practice. S. Wiley, N e w York. Z U N K E R , F . 1924. Z u m kapillaren Aufstieg des Wassers im Boden. Der Kulturtechniker, 27.

The dynamics of capillary rise

J . R . Philip, C . S . I . R . O . , Division of Plant Industry,

Canberra, Australia

A B S T R A C T : The problem of the dynamics of capillary rise associated with the sudden immersion of the bottom of a soil column in free water (and of the corresponding sub-irrigation problem) is examined. A n 'exact' method developed for analysing the dynamics of one-dimensional infiltration is appropriate at small times, but problems of convergence set limits to its applicability. The equilibrium situation approached at large times is, of course, readily found; but the 'exact' bridging of the gap between the 'small-time' solution and the final equilibrium appears to require the use of high-speed computers.

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effect of compactness and initial moisture content of the...

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