An experimental determination of the diffusion constant for high in-situ salt concentrations in the Norwegian marina clays

NORGES GEOTEKNIS KE INSTITUTT

Norwegian G e o t e c h n i c a l I n s t i t u t e

In ter nal R epor t

An experilTIental determination of the diffusion constant for hig}: in- situ salt concentrations in Nc!"wegian marine clays.

50703-2 June, 1973

FORSKNINGSVEIEN I, OSLO 3 - TLF. 695880

GES GEOTEKNISKE INSTITUTI

List of Cont e nt -

I. Introduction . ll. The clays studied

Ill. The experimental set-up

IV. The influence of the procedure of salt extraction on determined salt concentrations

V. The diffusion constants VI. Conclusions

Refer ences

Drawings 001 through 013 Appendix

Tables of experimental results

( i)

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'GES GEOTEK 'lSKE INSTlTUTT

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Drawing 001 The soil profile at Danneviks gate 16, Drarnrnen 002 The determination of a + concentrations by

differ ent methods of salt extraction

003 The determination of K+ concentrations by different methods of salt extraction

( ii)

004 The determination of Mg ++ concentrations by different methods of salt extraction

005 The determination of relative Ca ++ concentrations by different methods of salt extraction

006 The determination of pH in the water extracted from the clays by differ ent methods

007 Schematic drawing of the diffusion experiment equipment

008 Natural water content distribution in the test cylinders 009 Normalized a + concentrations ; measured and computed

values; and normalized electrical conductivities

010 Normalized K+ concentrations. Measured and computed values

all Nor malized Mg++ concentrations. Measur ed and computed values

012 Normalized Cat t

concentrations. Measured values.

013 t t

Extracted Ca by diffusion as a function of the squar e root cf time

GES GEOTEKNlSKE INSTlTUTT 1.

1. INTRODUCTION

An earlier internal report has reviewed a number of field observations of salt concentration profiles in Scandinavian marine clays (Heiberg, 1972). The development of the observed salt concentration pr ofiles were modeled by applying elementary concepts of salt diffusion superimposed on por e water flow. For a given elapsed time since the surfacer s) became fr esh, an observed salt concentration profile was consistent with only one value of each of the two physical parameters involved, namely the pore water velocity and the diffusion constant. The time elapsed since the top surface became fr esh could be estimated from the data on isostatic uplift of the region. This allowed numerical values of pore water velocities and diffusion constants to be estimated from the salt concentration profiles. The esti- mates of the diffusion constants indicated that it varied within very narrow limits. It was found necessary to confirm this indication by me·asuring the diffusion constant under controled conditions in the laboratory. One reason for this was that the times used in computing diffusion constants from field data could be in error if a considerable amount of clay compression had occurred after the surface first rose above sea level.

This report will present the results of the laboratory experiments. The experiments included:

( 1 ) A study of the influence of method of

the measured concentrations of Na

+,

C_a ++ _lons. .

salt extraction on

+ ++

K ,Mg ,and

(2) A study of the soil profile at the site wher e the clay for the experiment was sampled.

(3) A study of the diffusion process in the two types of clays sampled as a function of temperature. Diffusion was allowed towards a fr esh water reservoir in one end of

+

+ ++ ++

the cylinder. The amount of Na , K ,Mg , and Ca in the reservoir was r ecorded as a function of time.

After completing the experiment, the concentration of Na +, K+, Mg ++, and Ca

++

was r ecorded in the clay at

GES GEOTEKNISKE I 'STlTUTT 2.

different distances from the fresh surface. These

sets of measurements allowed independent computations of the diffusion constant to be made.

II. THE CLA YS STUDIED

It was decided to determine the diffusion constants in two clays which embraced the types of clays encounter ed in southern Norway. It was therefore natural to collect samples fr om a site in Drammen where NGI pr eviously have taken numerous samples for a multitude of labor atory studies. The soil profile is given by Bjerrum (1967), Fig. 19. The determinations carried out in this investigation on natural water content, Atterberg limits, and salt concentrations are given in Drawing 001. The

soil profile consists of 4 m sand, underlain by plastic Drammen clay, a post-glacial clay with high clay content and a natural water content of 50%. This cl.5J.y layer extends to a depth of 11 m . Below is a lean glacial clay with lower clay content and lower water content, 25-40'70. This clay contains occasional layers of sand and silt. The salt concentrations increase with depth to about 9 meter below gr ound level. They r emain practically constant below this depth. (The different methods used to extract the salt has a distinct influence on the value determined. So does the time of

storage on the magnesium concentrations. This will be discussed separa- tely later in the report). The porosities of the post-glacial plastic clay and of the glacial lean clay embrace those of the clays most fr equently encounter ed in southern Norway.

III. THE EXPERIME TAL SET-UP

The diffusion exper im ent was conducted on si" undisturbed samples. Three were taken in the plastic clay, at a depth where the salt concentrations were constant with depth. Three wer e taken in the lean clay.

Two duplicate samples from each clay wer e tested at 7⁰C which corresponds to the ground temperature. One sample fr om each clay was tested at room temperatur e (approximately 220

C) . The samples wer e taken in reinforced plastic cylinder s and br ought to the laboratory. The clay was flush with the bottom end of the cylinder . The clay at the bottom of the cylinder was capped with a thin filter paper and a sheet of gaz, Drawing 007. (This pr evented soil to fall out without obstructing the diffusion path markedly).

GES GEOTEK 'ISKE INSTlTUTT 3.

The top end was sealed with wax and a rubber cap. The open end of the cylinder was then placed in approxiJnately 700 ml of demineralized water. This water was changed regularly, and the quantity of salt removed was deter mined.

The distribution of salt concentration and of relative electrical conductivity in the cylinders was determined at the end of the experiment.

The determinations of salt concentration were made by measuring concen- trations of Na +, K+, Mg ++ and Ca ++ on a Perkin-Elmer atomic absorption spectrophotometer (model 290). The Ca ++ determinations r eported below were made using La203 as releasing agent, with the exception of the deter- minations r eported in Drawings 005 and 013. The results shown in Draw- ing 005 are not entir ely r eliable and should be considered as an indication only. The results shown in Drawing 013 ar e probably reliable due to the low salt concentrations in the solutions analysed.

The data involving determinations of salt concentrations wer e recorded and analysed as explained in repor t 50703- 1. The data sheets and the intermediate computations are on file, wher eas the final computed results ar e included in the appendix of this r epor t.

IV. THE INFLUENCE OF THE PROCEDURE OF SALT EXTRACTION

°

^{T DETERMINED SALT CONCENTRATIONS}

The influence of the pr ocedure used to extract the salts from the clay was studied on cylinder P2 after the diffusion exper iment was terminated. The methods of extraction used were :

(1 ) To press the clay and determ ine the concentrations in the water thus pr oduced.

(2) To stir approximately 25 g of clay with 25 ml of demineralized water, and to analyse the water phase after excluding the clay by centrifugation and filtration.

(3) As procedur e 2, but now using 75 ml of demineralized water.

(4) To stir appr oximately 25 g of clay with 50 ml of a 1.0 molar BaCIZ solution. The water phase is separated and the procedur e

GES GEOTEKNISKE INSTITUTT 4.

is repeated twice. The final volume of solution (approximately 150 ml) is diluted to 250 ml. The Ba ++ ions will replace the

+ + ++ ++

ions of Na , K ,Mg ,and Ca adsorbed on the clay surfaces. The solution will therefore contain both the ions which normally are in the pore water and those which normally are adsorbed on the clay. These concentrations serve as r eference concentrat_

ions for the concentrations determined by the other three methods. The first three methods are aimed at determining the salt con- centrations in the fr ee pore water only.

Samples of 6 cm length were homogenized and analysed. The natural water content of the clay varied little from 55%, as shown in Drawing 008. Diffusion had been allowed to take place for 205 days prior to the analysis. Drawings

+ + ++ ++ .

002 to 005 show the concentrations a , K ,Mg , and Ca as determmed by the different methods of extraction. Drawing 006 shows measur ed values of pH. The pH values r eported from the pr essed clay was measured in the pr esse:

por e water. The other values wer e recorded in the clay suspension after stirring. Drawing 002 gives the values of relative electrical conductivities recorded.

The experimental r esults show that the differ ent procedures of salt extraction. from the fr ee pore water influences the salt concentrations determined.

When the salt concentration in the free pore water is diluted, there occurs a change in the relative composition of the solution. The r elative concentrations of the monovalent ions Na + and K+ ar e incr eased, the relative concentrations

++ ++ .

of the divalent ions Mg and Ca are decr eased and the pH 1S changed towards the basic side.

The greatest change in milli-equivalents per litre Occurs for Na+ and Mg++

The change in percent of the total concentration is negligible for Na +, however, due to the high concentration of this ion.

These r esults may be interpr eted to r eflect an exchange of ions between the free pore water and the phase adsorbed on the minerals. This exchange accompanies an expansion of the adsor bed phase. Wnether the exchange is b a ance I d , may not b e d eterm1ne Wl . d . th certalntyas . th e C a ++ concentratlOns . ar e not determined reliably.

The concentrations determined by extr acting the salts by pressing the clay, and by washing approximately 25 g of clay with 75 g of water, may be COm-

• ~ES GEOTEKNISKE INSTlTUTI 5 .

- \

pared for the entir e soil profile in Drawing 001. The discrepancies in the concentrations are negligible for Na + and quite marked for K+ and Mg

++

Compar ative determinations of Ca

++

are not available. The Mg

++

concen- trations obtained by pressing after the end of the diffusion experiments show that a mar ked change has occurred upon storage of the samples.

The salt concentrations determined by pressing the clay ar e less scattered than those obtained by washing. The r eason may well be that the amount of dilution was not the same in each sample washed. (The amount of clay to be washed was not the same in each sample, nOr was the natural water content of the clay).

The diffusion process will lead to a dilution of the salt concentrations in the

!lore water of the samples. It may therefore be expected that the exchange of ions repor ted on above will interfere as a SOurce of a + and K+ ions and

++ ++ .

a sink of Mg and Ca ,ons. As such SOUI' ces and sinks ar e disregarded in the theory used to analyse the diffusion process, they may be expected to appear as "abnormal" behaviour, when the amount of salt which has left the cylinders is to be compared with the difference between the initial and final amounts.in the sample. It will be seen that the exchange processes may

be neglected when analysing the diffusion of bulk salt at the concentrations studied in this work. The r eason is that the salt consists pr edominantly of

TaCl, and only a very small fraction of a

+

takes part in the exchange process. The exchange processes may complicate the diffusion consider- ably at low salt concentrations, however .

V. THE DIFFUSIO CONSTANTS

The diffusion constants are computed from the rate of outflow of ions from the cylinders. The salt concentration profiles ^In the cylinders at the end of the experiment (after about 190 days of diffusion) are computed from the diffusion constants, and compared with the measured concentrations for Na

+

+ ++ . ++ . . . '

K , and Mg ,ons. The Ca ,on d,d not conform w,th the behaviour expected for simple diffusion. The behaviour of this ion is discussed separately.

The results of significance in this study ar e the diffusion constants for Na

+.

The computed value of this constant is O. 0122 ~ 0.0003 m 2 /year at 7⁰C.

The corresponding value at room temperature (approximately 22⁰C) is 0.0217

~

0.0003. These values are applicable to both the lean and the

. GES GEOTEKNlSKE 1 'STlTUTT 6.

plastic clays. This proves that diffusion at high salt concentrations is a pr e- dictable process, and that very detailed knowledge of the clay properties is not a prerequisite for predicting it.

The concentration profiles in the cylinders may be computed from knowledge of the diffusion constant by the equation:

C

z

Co ' e rf ("N"D"'t:-) where

C is the concentration

Co is the initial concentration

z is the distance from the fresh surface D is the diffusion constant

t is the elapsed time

A comparison between the computed and the measured concentration profile is pr esented in Drawing 009. The measur ed values confirm the computed ones. The measurements were performed by pressing slices of the test cylinder. Each slice was 2 cm thick.

The apparent diffusion constant for K+ ions, computed from the amounts removed from the sample, were not in agr eement with the concentration profiles measur ed at the end of the experiment.

The computed values of the diffusion cons tans wer e as shown below:

Clay Sample D ₁₀ . m 2/ year D In . rn 2/ year No. at 7⁰

c

^{at 220C}

Plastic PI .023 "]

-

Plastic P2 .028 ^r

Lean P4 .034 ^~->

Lean PS .034

Plastic P3 .061

Lean P6 .068 :l 2 ^I

-,

The concentration pr ofiles computed from diffusion constants of 0.02.7 m2

/year and 0.060 m2

/year are compared with the measur ed values in Drawing 010. The computea concentrations are much too low. The measured concentrations indicate that the diffusion constant for K+ is nearly identical with the constant for Na

+.

. GES GEOTEKNISKE INSTlTUTT 7 .

The observation that more K+ has left the sample than what is removed from the pore water is consistent with the observation in the above paragraph, that K+ is brought out in solution in the pore water when the salt concentrat- ion in it is decreased.

The computed apparent diffusion constants for Mg ++ are also in disagree- ment with the measured salt concentration pr ofiles. The computed diffusion cons tan ts ar e :

Clay Sample D in . m 2/ year D . _In m 2/ year No. at 7⁰C at 22⁰C

Plastic P I 0.0061 /1

Plastic P2 0.0059 c

Lean P 4 0.0068 ") .I.

Lean P S 0.0060

"

Plastic P 3 0.0083 ^{,.

Lean P6 0.0010 ^;.

The salt concentration profiles computed from diffusion constants of 0.006, 0.008, and 0.010 m 2 / year ar e compared with the measured values in Draw-

ing Oil. The computed concentrations are distinctly higher than the measur ed ones. This is again in agr eement with the results presented In the above

paragraph. There it was found that the amount of Mg ++ ions in the pore water was decreased when the salt concentration was decr eased.

d 1 f M ++ . . b . th

sure va ues 0 g concentratlOn are ln etter agreement \Vl of diffusion constants for Na + than with those given above.

The mea- the values

The exper iments showed thatCa++ deviates significantly from the pattern expected from simple dIffusion. The cumulative amount of Ca ++ leaving a cylinder would be pr opor tional to the squar e root of time if simple diffusion occurred. The curves shown in Drawing 013 are linear only in the initial phase. Midway thr ough the experiment the curve steepens before it reaches a quasi-constant slope in the final stage. This slope is lower than the initial for the plastic clay and higher for the lean clay.

The pr esence of slightly soluble salts may well have an influence on this behaviour. If Ca ++ in the reservoir is

i~

equilibrium with for instance CaC0

3, the outflow curve would coincide roughly with what is descr ibed above as the ini tial range.

lGES GEOTEKNISKE INSTlTUTI 8.

The measured Ca ++ concentrations in the clay at the end of the exper iment are shown in Drawing 012. At first Sight the distribution of Ca ++ is roughly equivalent to that of a

+

A closer examination will reveal that the curves

for all the samples are concave towards the concentration axes (not towards the distance axes as expected), and that this range of the curve culminates in an" abnormal" maximum value. The reason for, or the significance of the Ca ++ behaviour cannot be assessed on the basis of the data collected in thi··s investigation.

C ++ . .

a concentrahon is

It does not affect the process of bulk diffusion, as the only a small fraction of the total salt concentration.

VI. CO CLUSIONS

The diffusion experiments described in this report have shown that the diffusion constant of a+ is 0.0122

:!"

0.0003 at 7⁰C and 0.01217

:!"

0.0003 at r oom temperature (approximately 22⁰C). The value of the diffusion con-

stant was determined on marine clays from Drammen. The diffusion constant did not var y with the natural water content of the clay. Sarr::ples of natural water content ranging from 28 to 58 percent were tested. This cover s the range encountered most frequently in southern Norway. The de terminations wer e made at salt concentrations of the order of those encounter ed in sea water (30 g/l NaCI or 10, 000 mg/l Na +). The results pr ove that the diffusion of salt at these concentrations is a predictable pr ocess, and that ver y detailed knowledge of the clay proper ties is not r equired to pr edict it.

The diffusion exper iments, and a series of dilution exper iments showed that there is an increase of the monovalent ions and a decrease of divalent ions in solution in the fr ee pore water when the salt concentration in the por e water is reduced. This exchange will influence the process of bulk diffusion at concentrations of the order of a few grams per litre NaCl. At higher con-

+ ++ ++ .

centrations, the process of diffusion of K , Mg , and Ca is affected, but not in a way which invalidates the diffusion constants quoted above. The amount of salt r emoved from the

s tants for K+, Mg ++ which differ

clays by diffusion indicates diffusion con- fr om the

bution of salt concentration determined by

values given, wher eas the distri- pr essing the clay in the test

cylinders after the exper iments confirm the values given. The behaviour of Ca ++ is not as expected from simple diffusion.

The pr ocesses which complicate t..'te elementar y process of salt diffusion is without practical significance at high concentrations. a+ behaves

GES GEOTEKNlSKE INSTlTUTT 9.

according to the elementary process. The concentrations of the other ions are minor in comparison with the Na

+

concentration.

for the

NORWEGIA GEOTECH rCAL I STITUTE

'6\ci!.v ~

Toralv Berre

~~v--rcl. ~

Sigurd Heiberg

,~GES GEOTEK 'ISKE INSTITUTT 10.

L i t e r a t u r e

Bjerrwn, L. (1967)

Engineering geology of orwegian normally-consolidated marine clays as related to settlements of buildings.

7th Rankine Lecture.

Geotechnique, Vol. 17, No.2, p.81- ll8.

Also published as : Norwegian Geotechnical Institute. Publication, 71.

Heiberg, S. and J. Mourn (1972)

Interpretation of salt concentrations in the Scandinavian mar ine clays as a tool in geotechnical engineering.

Oslo. 19p.

orwegian Geotechnical Institute. Internal r eport, 50700-3. Unpublished.

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