The influence of pore distribution on the hydraulic conductivity of some Swedish tills

Journal of Hydrology, 112 (1989) 41-53

41

Elsevier Science Publishers B.V., Amsterdam m Printed in The Netherlands [1]

THE INFLUENCE OF PORE DISTRIBUTION ON THE HYDRAULIC CONDUCTIVITY OF SOME SWEDISH TILLS

BOB. LIND

Department of Geology, Chalmers University of Technology and University of Gothenburg, S-412 96 GSteborg (Sweden) (Received October 28, 1988; accepted after revision February 27, 1989)

ABSTRACT Lind, B.B., 1989. The influence of pore distribution on the hydraulic conductivity of some Swedish tills. J. HydroL, 112: 41-53. The relationship between pore-size distribution and hydraulic conductivity was studied on 42 undisturbed till samples. The results show a random pattern in the relationship between the total porosity and the hydraulic conductivity. A significant positive correlation was obtained between the hydraulic conductivity and the porosity in the interval 95-30/an, whereas no such relationship could be established between the hydraulic conductivity and coarser pores. This could be explained by the fissility structure in the till matrix which forms continuous micro-fissures, about 50-100/an in width, whereas the coarser pores are more or less isolated.

INTRODUCTION Till is the most predominant quaternary sediment in Sweden, covering three-quarters of the land area. The typical Swedish tills are formed from crystsIJlineand coarse sedimentary bedrocks. The thickness varies from one to a few metres, up to 40-50 m in big morain accumulations. The texture is usually siltyto sandy, often with a clay content of about 5%. The tillis commonly built up with interbedded lenses and bands of sorted material (sand-clay) in the diamicton matrix. Fissility (a property of splitting up along closely spaced planes, often subparallel to the deposition surface) iscommonly observed in the field whereas prominent fractures are rare. Knowledge about the hydraulic conductivity properties and the saturated groundwater flow pattern in tillis very sparse. The hydraulic conductivity is governed by the sediment structure as well as the texture. The importance of macropores (root channels, fractures, etc) for the groundwater recharge through the upper, unsaturated zone has been described by Hendry (1983), S c h j 6 n n i n g (1986), J o h a n s s o n (1987) a n d E s p e b y (1988). D e e p e r d o w n i n t h e C - h o r i z o n o f t h e soil p r o f i l e t h e p o r o s i t y v a l u e s a r e l o w e r (see e.g. L u n d i n , 1982; J o h a n s s o n , 1987; E s p e b y , 1988) a n d t h e m a c r o p o r e s t r u c t u r e w i t h o p e n

0022-1694/89/$03.50

© 1989 Elsevier Science Publishers B.V.

42

channels is less developed. In this part of sandy and silty tillsthe primary sediment structure determines the hydraulic properties. This investigation was undertaken to study the pore-sizedistributionand its ini|uence on the saturated hydraulic conductivity in the C-horizon of homogene,ous till. SAMPLING A N D A N A L Y S E S

Pore-size distribution,texture and hydraulic conductivity were studied on 42 undisturbed tillsamples, varying from sandy to clayey. Lumps of tillwere ca:refully excavated from the C-horizon, from shaft walls 2-3m below the ground surface.The samples were taken horizontally with known geographical orJientation and trimmed to cylinders of about 300cm 3 and placed in 9 5 m m PVC-cylinders. The magnitude of the representative element volume, REV, co~rresponds to the hydraulic properties such as fractures and coarse layers. Hydraulic conductivity measurements in the laboratory cannot be extr~Lpolv.tedto the macro fieldscale. All measured values relate to the specific sample itself.Interest must therefore be focused not on the sample sitesbut on each single sample and the relationship between texture, structure and hy,draul~c conductivity that can be established. Nipple permeameters were made, as in Fig. 1, by pouring epoxy resin over the tillsamples in the PVC-cylinders. The natural moisture content of about 5-10% was kept in the samples, which effectively prevented the resin from penetratftng the till. The hydraulic conductivity was measured with steady upward flow in a constant head permeameter. To prevent air becoming trapped in the samples, the saturation process was accomplished gradually, which facilitatescapillary rise in the finer part of the pore system. The inflow water was de-aired by heating and during the tests it was warmed up to 25°C, which is about 5°C warmer than the tillsample. The pore pressure nipples had an inner diameter of 3 m m to prevent capillary effects.The tests were carried out at a relatively low pressure head, with the gradient 2. The hydraulic conductivity varies with the water temperature and the K-value is specifiedfor 15.6°C (60°F),according to the definition given by Wenzel (1942). HYDRAULIC CONDUCTIVITY

The hydraulic conductivity was calculated in two ways (Fig. 2). K-nipple is calculated from the observed flow rate and the pressure drop observed from the two pore pressure valves. K-pipe is calculated from the flow rate and the gradient over the sample height. There is a fairlygood correlation between the two methods of calculation but it is evident that the K-nipple values are systematically somewhat higher. The K-values lie within the range of the hydraulic conductivity measurements in Swedish and Norwegian tills (Lindblad~ 1981; Jensen and K~hler, 1986).

43 OUTLET NIPPLE

OUTFLOW

FILTER PVC- CAP

pone PRESSURe VALVE

~

I I:-'~'Z)~-~I~~'.'.~|

I t"~-~~'~l~-~.~;-~'~'['-:~.-Z.t

I I

jSAUPLE

PVC -TUBE

"80JMM PORE PRESSURE VALVE

AIR VENT PVC-CAP

FILTER

INLET NIPPLE

I N FLOW

Fig. 1. Nipple permeameter, with sample size about 300 c m 3. The air vent ventilates the filter during the initial phase of saturation. The height of the outer PVC.tube is 90 nun.

K is expressed as the mean of 3-8 measurements, with generally lower variance of the K-pipe measurements. The accuracy of the two methods seems to be equal in this investigation and, because of the lower variance and the large effective volume measured in the K-pipe calculations, it is warranted to use these values in the further discussion. The results and conclusions are, however, essentially the same using the K-nipple values. The hydraulic conductivity of proctor packed disturbed till samples from the same sites is considerably lower, 1 0 - s - 1 0 - 9 m $ -1. This corresponds to findings by Knutsson (1971), Dahl et al. (1981) and Haldorsen et al. (1983), who conclude that the sediment structure is of great importance for saturated water transport in Scandinavian tills.

44

10 -4,

I 0 -s

"~EIO -="

"O e

e eo

e

•

•

°m • °

I

v

•

10 -7, •

m

10 -a.

10 - t 10 "=

!

10 -o

10 -7

10 -e

10 -s

10 4

K-nipple, m/s

Fig. 2. Hydraulic conductivity calculated from the gradient over the sample-height, K-pipe, and from the gradient between the pore pressure valves, K-nipple.

PORE-SIZE DISTRIBUTION

After the hydraulic conductivity tests, the top and bottom of the permeameters were removed and the pore-size distributions obtained from standard suction moisture content measurements. To prevent structural disturbance of the samples, the maximum pressure (suction) applied was 2.1 m water head (pF 2.3), which comprises pores down to about 15~um. However, the relationship between applied pressure and pore-size is not strict (Hall et al., 1977; Bullock a ~]Thomasson, 1979), and the pore d'~tribution obtained from water retention measurements should be considered as minimum values. Examples of representative moisture release curves are presented in Fig. 3. The total porosity varies from 18 to 48%. However, more than 80% of the samples have a total porosity between 20 and 35%. This corresponds well with other findings in Swedish and Norwegian tills (Nordberg and Modig, 1974; Lundin, 1982; Haldorsen et al., 1983; Johansson, 1986; Espeby, 1988). Most of the samples had a uniform pore distribution within the measured range but some curves deflect at about pF 1-2 and form either concave curves with large numbers of coarse pores, about 100-2000/~m, or cGnvex curves with correspondingly smaller numbers of coarse pores. Of interest concerning the hydraulic condl, ctivitv i~ the effective porosity, ne. Usually, n e is defined as: "the ratio expressed as a percentage of the volume of material which after being saturated can be drained by gravity to its own volume" (Todd, 1959). Drainable water is usually defined as the amount of water that, after saturation, can be drained by a pressure (suction) of pF 2.0. The effective porosity values varied between 2.5 and 32%, but approximately

45

2.5

2.0

1.5 E :3

I

[~1.0

0.5

0.0

, , , , , , , , , i , , , , , , , , ,

S

10

i,,,

, , , , i , , , , , , , ,

15

20

, , , , , , , i ,

25

30

,,

,

,,,

35

J

40

,

.

45

Water content, vol~ Fig. 3. Representative water retention characteristics.

50•

•

I

40,

o

00

0

-'o 30: o

: o

•

:

0

c o o

I

o

~20:

*i

10

o .........

iS . . . . . . . . .

2'0. . . . . . . . .

3b . . . . . . . .

'4'o

Effective porosity at pF 2 Fig. 4. Total and effective porosity in the till samples.

three-quarters of the samples had an he-value between 3 and 10%. Similar values have been calculated by Lundin (1982) and Nordberg and Modig (1974) on samples taken at some metres depth in Swedish tills. Figure 4 shows a positive correlation between the total and effective porosity. The relationship is linear and the total porosity is about 2-3 times the effective porosity. POROSITY

AND

HYDRAULIC

CONDUCTIVITY

Figure 5 shows that the relationship between the total porosity and the hydraulic conductivity is random. It was assumed, however, that a higher

46

50.0

40.0 •

• •

o 30.0

•

•

• • •

o

e:

•

o

~*

, •

I

•

•e

•

• e

0

8

" 20.0 0 p-

10.0

0.0

!

0 "¢

i

:||:"I

|

,

~l,,,q

I

i

,

l"|,|J,

I

i

|

|l,,:|i

,

10 4 10 -7 10 -e 10 -~ Hydroulic conductivity, m / s

,

|'|||'I

10 -4

Fig. 5. Total porosity and hydraulic conductivity.

correlation should occur between the hydraulic conductivity and the flowactive pore space, where the major part of the flow occurs. The relationship between the hydraulic conductivity and four pore intervals, defined at different pressures, was therefore calculated. This is a way of studying the influence on the hydraulic conductivity of smaller and smaller intervals of the coarsest pores, starting with the pore range from the total porosity, n, to the retained water capacity at pF 2.3. The results, which are summarised in Fig. 6, show a surprisingly weak correlation in all the intervals. It is obvious that the coarse porosity alone is not the only factor determining the hydraulic conductivity in the till and the results underline the role of the till structure. One limitation of the above method is that the samples are treated equally, without consideration of the individual pore distribution. The samples were therefore classified according to the shapes of the water retention curves between pF 2.3 and pF 1.0, defined as: (a) straight; (b) concave; and (c) convex; as described above. The results (Fig. 7) show that the hydraulic conductivity is slightly dependent on the curve shape. A concave curve, that is a greater proportion of coarse pores, leads to higher hydraulic conductivity. The relationship can be studied further by plotting the hydraulic conductivity against pore segments along the measured pore range. The correlations between the hydraulic conductivity and porosity segments between pF 1.2 and pF 2.3 are shown in Fig. 8. The porosity, as well as the log hydraulic conductivity, is normally distributed and Fig. 9 shows the correlation coefficient for linear regression analysis on plots of hydraulic conductivity versus pore s~ments. The best correlation occurred in the pore interval between pF 1.5 and pF 2.0, that is a pore-size of about 95-30/~m, with a correlation coefficient of 0.4 at a significance level of 98%. The interval 95-30/~m comprises 1-35% of the total

47 40.0

pF

Porosity at

2.3 vol~.

30.0

.~_~2 0 . 0

"

~) t....

"

•

•

o

•

g

O.

10.0

....

e•

0.0

i

i

10 -e

¢ illllj

i

s l illllj

10 -e

i

i

•

"

; illllj

10 -7

i

•

I

•

l illtl|

10 -6

Hydraulic conductivity, m/s

40.0-

i

i

i illllj

10 -s

10 -4

Porosity at pF 2.0 vol~ (effective porosity)

30.0

20.0 •O O O.

10.0 o•

•

•

• e=

•

0.0

i

|

e |,|||1

i

! t ItH=|

10 -8 10 -7 10.4 10 -s Hydraulic conductivity, m / s

0-~ 20.0

10 "*

Porosity at pF 1.5 vol~

e 0

10.0 ...:

.. •

• •

0.0 I

r

!

II , 1 | 1 1 1 |

1 0 -s

!

•

J gollnl

1 0 -s

|

I

: •• •

•

iiJ|llr

F

1 0 -7

•

• • ~

• | I

1 0 -e

~

~

1 0 -s

10

Hydroulic conductivity, m/s

20.0

"

Porosity at pF 1.2 vol~

2

O Q..

10.0 _

.

•

O0

I 10 -e

• •

l

l

!

i illl|l

10 4

! t zJiJij

10 -7

!

• • •• ,=9 •

! i iiHij

• !

•

i i liJJ~

1 0 -e

10 -s

-i

,

,~lJJ-lj

1 0 -4

Hydraulic conductivity, m/s

Fig. 6. Relationship between the hydraulic conductivity and smaller and smaller intervals of the coarsest pores.

48

so

so

I,

I

~ :

0-i.-

I\"

-i-,,

o

:m

0 ..c

-,i

O.

I L

I

I0

-9

........ IO' -0........ IO' -~ ..... i'{~-6 ........ I O' -s Hydroulic conductivity, m / s

i

i

,,,,'~ I

10

-'

Fig. 7. Relationship between the shapes of the pF-curves and the hydraulic conductivity. (a) straight; (b) concave; (c) convex curves. Range, arithmetic m e a n and standard deviation.

pore space, with an average of 7%. With the applied regression model, the variance of hydraulic conductivity attributable to porosity is 16%. The goodness-of-fit of the model is presented in Fig. 10. DISCUSSION

It could be concluded from this investigation that there is a great variance of the hydraulic conductivity within the tillmatrix. Samples from the same locality varied within three decades (10-s-10-s m s- i).Till includes many interrelated sediment structure elements and their relationships to the hydraulic conductivity are very complex. One important structure element is the porosity but the hydraulic conductivity in the C-horizon cannot be explained from the total and effective porosity alone. The results indicate that the hydraulic conductivity in the samples was dependent, in the first place, not on the coarsest pores but on the pores between 95 and 30/~m. Although the goodnessof-fitof the regression line is rather weak, there is nevertheless a significant positive correlation between the porosity and the hydraulic conductivity in this interval. This could be seen as the limiting pore space for the hydraulic conductivity. A decrease in porosity in this interval causes a lower hydraulic conductivity. W h y is the porosity between 95 and 30/~m so important for the hydraulic conductivity? Discussion of this question should start from the fact that this interval represents a minor part of the total pore space only and the importance for the saturated flow must be due to the pore pattern. This can be looked upon

49 40-

Porosity between n - t o t ond pF 2.3 vo~

30. 8

20-" g

>,

."

-~lOP o

el•

•

•

•

e

•

•

0

i

i ,iilil I

,

, =,,,,=I

•

•

%

•

•

•

•

=

•

= =,=,,,I

,

, ''IHll

'

' ''''"I

10 -8 10 -7 10 -e 10 -s Hydraulic conductivity, m / s

O-i 20-

10 -4

Porosity between n - t o t and pF 1.2 vol~

:•'g_10 •

•

IQ

• •

0

'

10

'''

,,,,I

'

,,,,!

'''

• =

•

•

• •

f~l,,,I •

''

,

, ,,,,,i~

1 0 -7 10 " 10 Hydroulic conductivity, m / s

-o

1 0 -a

:~10 t

,

,,,,,,i

I

10

-s

-"

Porosity between pF 1.5 and pF 2.3 vol~

ol ,

• • ~

t

|wllH

10 "

I

I

i

f

_

•

•

•

•

•

~

0 e

i gllll~

~

le

e

ee

•

~

•

j 5 , ii~l

• ~

•

•

i

i illll

i

10 " 10 "' 10 "= 10 Hydraulic conductivity, m / s

,

i 11111 e

10 "

-s

Porosity between pF 1.2 and pF 2.0 vol~

20

10 e Q.

•

;--r

0 10

,

...... ,

,

•

1 0 -7

, ~,"

1,|, I

10 ~

,

, ,,,,,!

1 0 -s

10 ~

Hydraulic conductivity, m / s Porosity between pF 1.5 and pF 2.0 vol~ i •

. . . . . . .

~

;

10

"~

Porosity

'

1 0 -7

~

1 0 -e

•

•

0

e.

10

pF

,,,,,I

1 0 -7

,

2.0

-s

1 0 -4

m/s

and

,';,:~'~i

*,........... " 10

-e

conductivity,

between

' ,,,,,~I

•

r , ~ , : , " ~ -,~ ,',,~," " ~ ""......

Hydraulic

10 -'

,',,~

,,~,,,

10 ~

1

O, I0 - I

,

•

ee

pF

,

1 0 -e

2.3

vol~

,,,,q

1 0 -s

,

, ,,,,,,i

10

-'

Hydraulic conductivity, m / s

Fig. 8. Relationship between different pore-size segments and the hydraulic conductivity.

50 1 .oo

-6 E 0

U

0.50 >, I

E .~_

8

r~

o.oo

E 0

0

-0.50

i

l

,

,

,|iii

10

,

t0

,

,

,

i,,,

=

I

,

l

i

,

,

10~

, , i I

104

Pore-size, pm

Fig. 9. Correlation coefficients for linear regression analysis on the plots of hydraulic conductivity versus pore-size segments in Fig. 8. Predioted with

~5~

and

Observed

interval8

for

Values

Fitted

predictions

Oh=erred

-3.2 m

-4.2

-5.2

I III

-6.2

-7.2

-e.2 -e.7

-6.

5

-6.

3

-6.

1

-5.

9

-5.

7

__r-,. 5

Predioted

Fig. 10. Predicted and observed values, with 95% intervals for predictions, for the linear regression model between log hydraulic conductivity and the porosity in the interval 95--30pm.

51

mainly in two ways: (1) The pore system can be homogeneous, with a regular network between all pores, in which case the hydraulic conductivity can be strongly influenced by pores in a special interval if these are an integral part of a system of coarse pores where a great part of the flow occurs. The pore interval 95-30/~m can form limith~g sections in this coarse channel system. There are, however, good reasons to assume that the pore system is not spatially homogeneous and this leads to the other interpretation model (2). The hydraulic conductivity of a porous medium has the dimension distance divided by time [L/T], that is velocity. Besides the fluid itself, the flow velocity is dependent on the flow route and the inner friction at the borderline between the fluid and the pore walls. If the pore interval consists to a great extent of long elongated pores, which shortens the flow route, this will lead to a greater influence on the hydraulic conductivity. What is the spatial distribution of the pores in the interval 95-30/~m? To answer this question, two features are of great interest: sorted sediment layers and fissility. A pore-size between 95 and 30/~m is characteristic of well sorted fine sand (Odin, 1957; Andersson and Wiklert, 1972). Although sorted sediment zones are not always clearly visible, it is often assumed that such zones may occur in Scandinavian tills and may have an important influence on the hydraulic conductivity (Haldorsen et al., 1983). Sediment layers of fine sand should have great numbers of pores between 95 and 30/~m and should also have an important impact on the hydraulic conductivity. The till investigated had a visible fissility structure that is commonly observed in Sweden and has been described already by Lundqvist (1932, 1933, 1940). Fissility has been known as planes for preferred fissuring, often with more or less developed slickensides (Dreimanis, 1976; Boulton and Paul, 1976; Adrielsson, 1984; Ostmark, 1988). The planes can be caused by alternating layers of coarser and finer particles (Lundqvist, 1940) but have also been shown to occur independent of differences in grain-size or in the arrangement of particles (Van der Meer, 1987). The fissure planes often diverge around cobbles and the lens thickness between the planes is determined by the diameter of the enclosed cobbles, often between 20 and 100ram (Adrielsson, 1984). Accumulation of migrated grains on the fissility planes has also been reported (Ostmark, 1988). The microstructure studies by Van der Meer (1987) have shown that the fissility planes can consist of a number of elongated voids. The confined sections of the voids seem to be of the order of about 50-100/~m in width. Elongated pores and pore-zones of the same size have been observed in thin sections from the permeameter samples in this investigation. However this work has just begun and future studies will concentrate on micromorphological analysis of thin sections and polished till-blocks. The results from this project lead to a model with preferential saturated flow in pores of about 95-30 ~m at the fissility planes and in thin fine sand layers. This concept harmonises with the difference in hydraulic conductivity between undisturbed and packed till and it also explains the differences between the

52

h o r i z o n t a l a n d v e r t i c a l c o n d u c t i v i t y ( H a l d o r s e n et al., 1983; Lind a n d N y b o r g , 1988). The samples studied c a n be c h a r a c t e r i s e d as h o m o g e n e o u s till. T h e h y d r a u l i c c o n d u c t i v i t y , with a n a v e r a g e of 5 x 1 0 - 7 m s -1, c o r r e s p o n d s to h y d r a u l i c c o n d u c t i v i t y v a l u e s m e a s u r e d in situ in S c a n d i n a v i a n tills. T h e r e s u l t s indicate t h a t t h e m i c r o s t r u c t u r e in the till m a t r i x c a n n o t be n e g l e c t e d as a factor of i m p o r t a n c e for the h y d r a u l i c c o n d u c t i v i t y . D e t e r m i n a t i o n of t h e p a t t e r n of very small fissures is of g r e a t i m p o r t a n c e for u n d e r s t a n d i n g of t h e s a t u r a t e d w a t e r flow in the C-horizon of d i a m i c t o n sediments. ACKNOWLEDGEMENTS The r e s e a r c h h a s been s u p p o r t e d financially b y t h e S w e d i s h C o u n c i l for B u i l d i n g Research. S t i m u l a t i n g d i s c u s s i o n s w i t h M a t s N y b o r g a n d o t h e r members of the U r b a n Geo~,ydrology R e s e a r c h G r o u p in G o t h e n b u r g r e s u l t e d in v a l u a b l e c o n t r i b u t i o n s to t h e project. I t e n d e r m y sincere t h a n k s to my colleagues at t h e u n i v e r s i t y a n d for t h e financial s u p p o r t . Special t h a n k s go to J a n Hartlen, S w e d i s h G e o t e c h n i c a l I n s t i t u t e , a n d L a r s N o r d b e r g , S w e d i s h N a t i o n a l E n v i r o n m e n t a l P r o t e c t i o n Board, for t h e i r a c t i v e s u p p o r t for t h e research.

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