Electrical Resistivity of Compacted Kaolin and its ... · Electrical Resistivity of Compacted Kaolin and its Relation with Suction Dias, ... order to propose relationships between

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Electrical Resistivity of Compacted Kaolin and its Relation with Suction

Dias, Ana Sofia – [email protected]

Summary The electrical characteristics of compacted kaolin were studied and related with their water content in

order to propose relationships between suction and electrical resistivity. Knowledge in such

relationships is important for the interpretation of electrical resistivity measurements considering the

degree of saturation of the soils in geophysical prospection tests, or to develop resistive sensors for

soil suction measurement. Samples studied were prepared with different void ratios. The presence of

salt with known concentration was also investigated. Water retention curves were measured using

vapour equilibrium technique and equipment WP4, in parallel to measurements of electrical resistivity

for each case. Experimental data was interpreted considering the continuity of the liquid phase.

1 Introduction The electrical resistivity of soils is a property

which can be used in geophysical prospection

tests as depends on the type of soil. However

it is affected by their degree of saturation,

because the electrical conductivity of water is

much larger than that of the solids.

The electrical properties of a compacted kaolin

were studied in parallel with suction

measurement for a better understanding of the

coupling between electrical current flow and

the degree of saturation, and also between

suction and electrical resistivity. Besides the

improvement on the interpretation of ins situ

tests, the interest on knowing these

relationships may also contribute to developing

resistive sensors, which measure the

electrical resistivity in soil and convert the

value into total suction after calibration.

Samples of compacted kaolin were prepared

with different void ratios for the same water

content. Suction was applied using vapour

equilibrium and electrical resistivity was

measured for each case.

2 Background fundaments 2.1 Water retention curve The water retention curve (WRC) (Figure 1)

relates water content, or degree of saturation,

with total suction (matric and osmotic). This

curve can be given by Equation 1 (van

Genuchten 1980):

𝜔 =

𝑒𝐺!

1 +𝑠𝑃

!!!!

!!

(1)

where w is water content, e is voids ratio, Gs is

the density of the solid particles, s is suction

and P and λ are constants.

Figure 1 – Typical water retention curve (adapted

from Vanapalli et al. 1999).

2

WRC present particular features that reflects

the partial fill of the soil pores with water, as

illustrated in Figure 1 (Vanapalli et al. 1999).

2.2 Soil electrical resistivity Flow of electrical current in soils occurs along

soil's three phases (solid, liquid and gaseous).

However the contribution of the gaseous

phase is neglected due to the high resistivity of

air. In case of granular materials, the

conductivity of solid phase can also be

neglected due to the same reason. In this

context, Archie (1942) proposed Equations 2

and 3 to explain the dependency of electrical

resistivity on porosity, electrolyte resistivity and

pores tortuosity. This would consider current

path through the liquid phase in the porous

material.

𝐹 =𝜌!"#𝜌!"

(2)

𝐹 = 𝑎 ∙ 𝑛!! (3)

Parameter F is named formation factor,

defined considering the electrical conductivity

of the saturated porous medium, 𝜌!"# , and that

of the electrolyte, 𝜌!". Parameter n is porosity

and a and m are constants.

Abu-Hassanein et al. (1996) introduced

Equation 4 to explain the dependency of the

soil electrical resistivity 𝜌 on the degree of

saturation, Sr. In this equation, B is a constant.

𝜌 = 𝜌!"#𝑆!!! (4)

Therefore, soil’s electrical resistivity is mainly

influenced by the degree of saturation,

resistivity of the liquid phase and pores size

and tortuosity, as documented by Archie

(1942), Abu-Hassanein et al. (1996) and Gunn

et al. (2014). The previous relations can be

joined into Equation 5.

𝜌 = 𝑎 ∙ 𝜌!" ∙ 𝑛!! ∙ 𝑆!!! (5)

It is important to note that the continuity of the

liquid phase in soil pores strongly affects

resistivity. Indeed, for natural and remoulded

clays Fukue et al. (1999) observed an abrupt

increase in the resistivity once the liquid phase

become discontinuous. This occurs when

water contents equals the critical water content

identified in Figure 2.

Figure 2 – Relationship between electrical resistivity

and water content of a clay (Fukue et al. 1999).

In the case of clays, the surface conductivity

may also decrease soil’s electrical resistivity

for lower porosities ( Santamarina et al. 2001).

This is because clay minerals allow the

formation of a double layer of charges

favourable to the current flow. The contribution

of this term was not considered in the

calculations performed in this work due to the

lack of information necessary for its

quantification. However this contribution is

considered in the interpretation of the

experimental results presented.

3 Material and experimental setup suction and electrical resistivity were

measured in compacted samples of

commercial white kaolin classified as MH

accordingly to USCS. The main physical

properties of this material are presented in

Table 1 (Gingine & Cardoso, 2015), where wL

and wp are the liquid and plastic limits,

respectively, IP is the plasticity index, Gs is the

3

density of solid particles, and Silt and Clay are

the percentages of silt-size and clay-size

particles, respectively.

Table 1 – Kaolin properties.

wL wP IP Gs Silt Clay

52% 30% 22% 2.61 53% 40%

The samples were prepared with the same

water content of 25% and different voids ratio

(0.6, 0.9 and 1.2, named ‘6W’, ‘9W’ and ‘12W’,

respectively) aiming to provide information on

the effect of soil structure on electrical

resistivity. For this reason, a reconstituted

sample prepared with water content w=1.5wL

following the procedure suggested by Burland

(1990). Another kind of sample with voids ratio

of 0.9 and same water content was prepared,

however using a 0.5M NaCl solution in order to

provide information on the nature of the

electrolyte.

The WRC of each kind of sample wwere

measured using the water potentiometer

equipment, WP4, defining the reference curve.

small pieces were used for this measurement.

All samples were compacted in moulds with

the geometry presented in Figure 3, in which

nails were inserted to work as electrodes.

These electrodes were equally spaced and

were used to measure the electrical resistivity

using Wenner method (BS 1377-3, 1990).

Figure 3 – Scheme of the soil sample geometry.

Suction was applied by vapour equilibrium

technique (Romero, 1999), using NaCl

solutions prepared with different

concentrations. Five different solutions were

prepared, applying 1MPa, 5MPa, 15MPa and

39MPa. Figure 4 shows a photograph of the

one sample during equilibrium time.

Figure 4 – Vapour equilibrium setup.

Both wetting and drying paths were applied, as

illustrated in Figure 5: for the wetting path al

the samples were previously dried in

laboratory environment (s=107MPa) and then

partially wetted, while for drying they all were

first full saturated and then dried. The extreme

cases of dried in the laboratory and full

saturation provides extra points for the

definition of the WRC.

Figure 5 – Paths followed by the samples in vapour

equilibrium technique.

4

Electrical resistivity was measured once

vapour equilibrium was reached. . Total

suction was measured in pieces of samples

using WP4, as well as water content. Suction

applied using the solutions partially saturated

with NaCl was corrected after measuring their

electrical conductivity using a Crison probe

and suction using WP4.

The comparison between the reference curve

measured with WP4 and the curves found by

vapour equilibrium after each correction

allowed to validate the methodology adopted

when using vapour equilibrium technique for

WRC measurement.

Further details about the experimental work

can be found at Dias (2015).

4 Results and discussion 4.1 Reference water retention curves Equation 1 was used to fit the different WRC.

The calibration parameters are presented in

Table 2. This table also presents the values of

the residual state of saturation (Rss) previously

identified in Figure 1.

Table 2 – WRC parameters for the reference curve

and residual state of saturation (Rss).

Voids ratio Wetting Drying

P Λ Rss P λ Rss

0.9 0.50 0.38 3.5 1.20 0.42 3.0

0.9 (S) 0.25 0.40 3.2 2.00 0.37 4.2

1.2 0.23 0.34 4.2 0.70 0.39 3.8

0.6 1.00 0.4 2.0 3.26 0.47 1.8

1.1 (R) 0.23 0.30 5.2 0.60 0.33 4.6

As observed in Figure 6, for both branches the

curves diverge only for the higher values of

water content. This can be explained by the

different structures of the compacted samples,

differing mainly in the sizes of macropores

(largest macropores are observed for the

specimens with the largest voids ratio at

compaction).

Figure 6 – Drying and wetting branches of the

reference curves.

The comparison between the WRC found for

the samples compacted with e=0.9 using

distilled water or the 0.5M NaCl solution is

presented in Figure 7. It can be seen that the

curve for the sample prepared using the salt

solution is affected by the contribution of

osmotic suction that depends on the

concentration of NaCl in the pore fluid. When

drying occurs and the fluid is saturated by salt,

maximum osmotic suction is 39 MPa, while

this concentration is minimum when the soil is

full saturated. For the void ratio adopted, and

assuming no volume changes, suction reaches

1MPa. This value corresponds to the

horizontal branch in Figure 7.

0.001

0.01

0.1

1

10

100

1000

0 10 20 30 40 50

Suct

ion

(MPa

)

Water content (%)

a. Drying branches

9W

6W

12W

Macropore

0.001

0.01

0.1

1

10

100

1000

0 10 20 30 40 50

Suct

ion

(MPa

)

Water content (%)

b. Wetting branches

9W

6W

12W

Macropore

5

Figure 7 – WRC of 0.9 void ratio samples prepared

with NaCl solution and distilled water.

4.2 Vapour equilibrium technique The electrical conductivity and suction of the

NaCl solutions prepared for suction application

using vapour equilibrium were measured after

reaching equilibrium to check if these values

are affected by water exchanges between the

soil and the solution. Equations 6 and 7 were

used to convert electrical conductivity 𝜒 into

suction s, following the work of Romero (2001),

where m is the concentration of the solution.

𝜒 = −6,9858𝑚! + 78,645𝑚 + 8,0453 (6)

𝑠 = 4,7814𝑚!,!"#$ (7)

As observed in Figure 8, suction presented

only a very small variation. Therefore, the

technique is reliable in terms of maintaining

suction constant apart from the water

exchanges during the process.

4.3 Electrical resistivity The calculation of the formation factor was

done using Equation 2 considering the

electrical resistivity of the different electrolyes

shown Table 3.

Table 3 – Electrical resistivity of the electrolytes.

Fluid ρel (kΩm)

NaCl 0.5M 2.19 x 10-4

Distilled water 1.53 x 10-3

Figure 8 – Suction and electrical conductivity of

NaCl solutions for vapour equilibrium.

The formation factor defined by Archie's law

(Equation 3) is presented in Figure 9 for the

compacted samples prepared with water. High

values were obtained for F. It can be seen in

this figure that the signal of parameter m

changes for the drying and wetting branches.

The differences can be explained by changes

in voids ratio during full saturation.

Nevertheless, the swelling potential of the

clays used was considered to be low (Dias,

2015), and for this reason such volume

changes were not expected to affect much the

results.

Figure 9–Variation of the formation factor with

porosity for the compacted samples prepared with

water.

0.001

0.01

0.1

1

10

100

1000

0 10 20 30

Suct

ion

(MPa

)

Water content (%)

9S wetting

9W wetting

0

50

100

150

200

250

0 10 20 30 40 50

Elec

tric

al c

ondu

ctiv

ity (m

S/cm

)

Suction (MPa)

calibration

measured

initial

F = 28.378e-0.925 R² = 0.81961

F = 162.4e1.3625 R² = 0.91697

20

30

40

50

60

70

80

0.4 0.45 0.5 0.55 0.6

Form

atio

n fa

ctor

Porosity

wetting

drying

6

The values found for the electrical resistivity of

the unsaturated specimens were used to

calibrate Equation 4. As expected, electrical

resistivity decreases with increasing degree of

saturation, tending to a fixed value. This shows

that the pore fluid is a preferential medium for

current flow.

For the same degree of saturation the

compacted samples present increasing

resistivity with decreasing voids ratio. This may

be explained by the fact that samples with

higher voids ratio have larger pores, which for

a fixed water content may be filled with mass

of water larger then when the pores are small.

Figure 10 also shows the results found for the

samples 9S prepared with the salt solution.

They show lower resistivity when compared

with the others because of the higher

conductivity of the electrolyte. Yet, for low

degrees of saturation this curve tends to the

electrical resistivity of the samples prepared

with distilled water, which can be explained by

the appearance of repulsive forces decreasing

ions mobility.

The destructured samples present behaviours

distinct from the others, which may prove that

soil structure has a strong influence on

electrical resistivity, even for the unsaturated

cases.

The separation between the continuity and

discontinuity of the liquid phase (residual state

of saturation) occurs for values of degree of

saturation ranging between 7.8% and 12.3%.

Resistivity presents a significant increase for

water contents larger than this value, as

observed by Fukue et al. (1999).

An interpolation to obtain the evolution of the

parameter ‘B’ with void ratio was done and is

presented in Figure 11Figure . These

equations, with those presented in Figures 9

and 11, were used to define electrical

resistivity as function of the degree of

saturation and void ratios.

Figure 10 - Electrical resistivity variation with degree

of saturation of (a) drying and (b) wetting paths.

These curves are in Figure 12. For constant

voids ratio the highest resistivity occurs for low

degrees of saturation, as expected. The

graphs are divided in two zones (A and B) to

consider different trends of behaviour. They

may be explained considering some

hypothesis about the contribution of the clay

minerals surface for electrical conductivity.

(a)

(b)

7

Figure 11– Variation of ‘B’ with void ratio.

Figure 12– Electrical resistivity variation with degree

of saturation and void ratio.

In Zone A, for the lowest voids ratio, electrical

resistivity decreases with increasing voids

ratio. It appears that in Zone A the surface

electrical conductivity may be favourable

enough to allow the increase of current flow, in

opposition to the expected increase of

resistivity caused by the reduction of the pores

size reducing the amount of water through

which water can flow.

in Zone B, for the largest voids ratio, electrical

resistivity decreases with decreasing voids

ratio for the same degree of saturation. Such

behaviour was predicted by Equations 3 and 4.

In this case surface conductivity would

decrease soil resistivity because the number of

contacts between the particles would increase

This may also explain the decreasing

formation factor (F), proportional to the

electrical resistivity, with porosity in the case of

the drying branch (Figure 6).

4.4 Electrical resistivity and suction A final expression that relates total suction and

electrical resistivity was deduced from joining

Equations 1 and 4, resulting into Equation 8.

The calibration parameters are in Table 2 and

Figure 11Figure .

𝜌 = 𝜌!"# 1 +

𝑠𝑃

!!!!

!"

(8)

The comparison between the experimental

data and the curves defined by this equation,

presented in Figure 13, appears to provide a

good adjustment, except for higher values of

electrical resistivity. The hysteresis of the WRC

and changes in structure caused by the drying

or saturation process are well visible when

comparing Figures 13Figure .a and 13.b.

Though, the curves for the destructured

samples appear to be the least dependent

from the branch (Figure 13.d).

B = -2.3947e2 + 3.9772e - 0.1154 R² = 1

B = -6.4294e2 + 8.9774e - 0.1828 R² = 1

0.5

1

1.5

2

2.5

3

3.5

0.5 0.7 0.9 1.1 1.3

B

Void ratio e wetting drying Salt

0.01

0.1

1

10

100

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3

Elec

tric

al re

sist

ivity

(kΩ

m)

Void ratio

a. Drying

0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

Degree of saturation

Zone A Zone B

0.01

0.1

1

10

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3

Elec

tric

al re

sist

ivity

(kΩ

m)

Void ratio

b. Wetting

0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

Degree of saturation

Zone A Zone B

8

The electrical resistivity of the samples for e=0-

9 (9s) prepared with NaCl is lower than the

values found fo the samples prepared with

water (9W) in all the suction range (Figure

14Figure .c). This may be consequence of the

presence of ions in the solution responsible for

increasing osmotic suction and for decreasing

the electrical resistivity.

For the same suction, the highest void ratio

sample presents low resistivity because it has

the bigger voids with more water. The sample

with voids ratio of 0.6 has the smallest voids

and the least content of water, therefore higher

resistivity. However, the relative position of the

curves in Figure 13.b. is not clear considering

the voids ratio at preparation, because the

sample with a void ratio of 0.9 appears to have

the highest resistivity followed by the samples

prepared with the voids ratio of 0.6 and the

1.2. This may be explained by the contribution

of the surface electrical conductivity.

Figure 13–Comparison of experimental data with Equation 8 deduced curves.

The experimental data was adjusted to

Equation 9 in order to obtain an alternative

way of relate electrical resistivity and suction:

Data is presented in Figure 14Figure

𝜌 = 𝛼 ∙ 𝑒!∙! (9)

In this case, the relative position of the drying

branch curves is according with the expected,

i.e. for the same suction, the highest void ratio

0.01

0.1

1

10

100

1 10 100

Elec

tric

al re

sist

ivity

(kΩ

m)

Total suction (MPa)

a. Wetting

12W 6W 9W 9W 12W 6W

0.01

0.1

1

10

100

1000

1 10 100

Elec

tric

al re

sist

ivity

(kΩ

m)

Total suction (MPa)

b. Drying

12W 6W 9W 9W 12W 6W

0.001

0.01

0.1

1

10

100

1000

0.01 0.1 1 10 100

Elec

tric

al re

sist

ivity

(kΩ

m)

Total suction (MPa)

c. 9S - 9W

9W wetting 9W drying 9S wetting 9S drying 9W wetting 9S wetting 9W drying 9S drying

0.01

0.1

1

10

1 10 100

Elec

tric

al re

sist

ivity

(kΩ

m)

Total suction (MPa)

d. 1R

1R wetting 1R drying 1R drying 1R wetting

9

sample presents low resistivity and the

opposite happens with lowest void ratio.

Parameter α is responsible for the vertical

translation of the curve, as the 9S curves have

the lowest value of α. This indicates that this

parameter depends on the nature of pore fluid.

Parameter β controls the slope of the curves

and depends on the void ratio because the

curves are parallel in Figure 14.c. Such is not

verified in Figures 14Figure .a and 14.b. A

Their detailed comparison can be found in

Dias (2015).

The results provided by both methods are very

similar. Therefore, Equation 9 can be

considered an alternative to Equation 8, having

the advantage requiring less calibration

parameters and not requiring the definition of a

WRC for the material that is being used.

Figure 14– Adjustment of the experimental data with Equation 9.

5 Conclusions The major conclusions from this work are

presented in the following points:

1. The WRC of soil prepared with NaCl

reflect the contribution of osmotic suction.

2. Suction applied using vapour equilibrium

technique is almost constant, therefore this

technique can be considered reliable.

3. The continuity of liquid phase affects

electrical resistivity because significant

increase in electrical resistivity were

y = 0.1364e0.0589x R² = 0.91285

y = 0.2208e0.0382x R² = 0.76091

y = 0.1722e0.0409x R² = 0.86813

0.1

1

10

100

1 10 100

Elec

tric

al re

sist

ivity

(kΩ

m)

Total suction (MPa)

a. Wetting

9W 12W 6W

y = 0.1927e0.1043x R² = 0.96783

y = 0.4794e0.0353x R² = 0.66237

y = 0.2668e0.2014x R² = 0.92093

0.1

1

10

100

1000

10000

1 10 100

Elec

tric

al re

sist

ivity

(kΩ

m)

Total suction (MPa)

b. Drying

9W 12W 6W

y = 0.1364e0.0589x R² = 0.91284

y = 0.0148e0.0421x R² = 0.71548

y = 0.1927e0.1043x R² = 0.96782

y = 0.019e0.0668x R² = 0.48312

0.001

0.01

0.1

1

10

100

1000

0.01 0.1 1 10 100

Elec

tric

al re

sist

ivity

(kΩ

m)

Total suction (MPa)

c. 9S - 9W

9W wetting 9S wetting 9W drying 9S drying

y = 0.0816e0.0454x R² = 0.97048

y = 0.1104e0.0406x R² = 0.90081

0.01

0.1

1

10

1 10 100

Elec

tric

al re

sist

ivity

(kΩ

m)

Total suction (MPa)

d. 1R

1R drying 1R wetting

10

observed after drying the soil above its

residual state of saturation RSS.

4. Soils compacted with water and with the

larger voids ratio are expected to have

lower electrical resistivity than those

compacted with smaller voids ratio as the

amount of electrolyte increases.

5. For the soils compacted with the lower

values of void ratio, electrical resistivity is

more probable to be affected by the

surface electrical because the number of

particle contacts increases,

Finally, the relationship between total suction

with electrical resistivity was found, which can

be used in the calibration of resistive sensors

for soil suction measurements.

Acknowledgements The author acknowledges Professor Rafaela

Cardoso for supervising the research

performed and to INESC-MN for lending the

setup to measure electrical resistivity.

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