Using AC Conductivity Measurements to Study the Influence of Mechanical Stress on the Strength of Geomaterials

doi:10.4236/ojapps.2012.22007

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Open Journal of Applied Sciences, 2012, 2, 61-65

doi:10.4236/ojapps.2012.22007 Published Online June 2012 (http://www.SciRP.org/journal/ojapps)

Using AC Conductivity Measurements to Study the

Influence of Mechanical Stress on the Strength of

Geomaterials

Ilias Stavrakas1, Kostantinos Moutzouris1, Kostantinos Ninos1, Nikos Mitritsakis2,

Zacharias Agioutantis2, Dimos Triantis1

1Department of Electronics, Technological Educational Institute of Athens, Athens, Greece

2Department of Mineral Resources Engineering, Technical University of Crete, Chania, Greece

Email: [email protected]

Received March 6, 2012; revised April 10, 2012; accepted April 20, 2012

ABSTRACT

The Dielectric Spectroscopy technique is a tool that can be used to provide information regarding the physical and

chemical properties of materials. In this work Dielectric Spectroscopy (DS) measurements were conducted on marble

specimens that were previously subjected to uniaxial compressive stress up to fracture in order to investigate the influ-

ence of the mechanical stress on the dielectric properties of the specimens. Specifically, the ac conductivity (σac) was

measured when an ac electric field in the frequency range 1 kHz - 1 MHz was applied upon dry and saturated specimens

which were subjected successively to higher levels of mechanical stress. The experimental results indicate that there are

systematic variations in the values of the ac conductivity after each stress application at a higher stress level. Such

variations become more intense at higher stress values and can be used to indicate the upcoming fracture since signifi-

cant increase of conductivity is recorded when microcracks formations appear and propagate in the sample bulk.

Keywords: AC Conductivity Measurements; Marble; Mechanical Load

1. Introduction

Mechanical stress applied on rocks creates microscopic

and macroscopic discontinuities resulting in changes in

their mechanical behaviour [1-3]. Marble is a metamor-

phic rock with imperfections in its structure due to either

internal or external factors such as mechanical strain,

chemical or physical processing which play an important

role in the behaviour of the material.

Various laboratory experiments on marble samples

have been recently conducted in order to determine the

impact of the mechanical stress and the consequent me-

chanical damage on the electrical properties of geomate-

rials. Such experiments include Dielectric Spectroscopy

in the frequency domain [4,5] and Isothermal Depolari-

zation Currents [6].

Dielectric properties are related to the capability of a

material to be polarised under the influence of an exter-

nally applied electrical field. The polarisability of a ma-

terial depends on its structure and molecular properties

and therefore dielectric measurements can provide in-

formation in this respect. Dielectric Spectroscopy (DS) is

an electrical technique that has been used to characterize

the rock microstructure and to provide useful information

about the relationships governing microstructure, elec-

trical properties, and chemical processes during hydra-

tion [7-9]. The complex relative permittivity *



(here-

after, referred to as complex permittivity for convenience)

is defined as:











  (1)

where





and





 are the real and imaginary parts of





respectively,



is the electrical conductivity, 0



is the vacuum permittivity and



is the angular fre-

quency (2π





). It is widely observed that the ac con-

ductivity with respect to frequency obeys a power law

[10,11]. Jonscher [10] suggested that this law constitutes

a “universal” property of the materials. In general, ac con-

ductivity







is found to vary with frequency f as:













 (2)

at frequencies well below the lattice vibrational fre-

quency [10]. In Equation (2), is the dc limit of

conductivity, A is a parameter depending on temperature

and pressure and the exponent n takes values between 0

and 1. In the high frequency range since













Equation (2) can be written as follows:









 (3)

I. STAVRAKAS ET AL.

In this work, marble specimens were subjected to uni-

axial compressive stress in order to cause damage to their

bulk. After each stress application and while the speci-

men remained unstressed two sets of ac conductivity

measurements were conducted in the frequency range

between 1 kHz and 1 MHz. During the first set of meas-

urements the specimen included its natural moisture

while during the second set the natural moisture of the

specimen was removed after heating. Initially, pilot ac

conductivity measurements were conducted for all the

specimens used.

2. Materials and Experimental Techniques

2.1. Materials

Marble belongs to the class of metamorphic rocks. Its

structural inhomogeneities are due to either natural or

man-made causes like the application of mechanical or

chemical processing. The marble specimens used were

prepared from samples collected from Mt. Penteli, Attica,

Greece. Marble from this area is mainly composed of

calcite (98%) and other minerals, such as muscovite,

sericite and chlorite. Its content in quartz is very low

(0.2%), while its density is 2.7 g/cm3 and its porosity is

approximately 0.4%. Matrix rocks of the above origin

were intentionally selected to be quasi single grained.

The dimensions of the prismatic specimens subjected to

compression were 38 mm × 20 mm × 9 mm. The me-

chanical stress was applied in parallel to the long edge of

the specimens.

The specimens were cleaved from the rock using two

different directions (see Figure 1). According to the di-

rection of cleavage the specimens were named as type-1

and type-2. The dashed lines of Figure 1 correspond to

the chlorite ((Mg,Fe,Al)6(Si,Al)4O10(OH) 8) and musco-

vite (KAl2(AlSi3)O10(OH)2) layers of the material.

Figure 1. Orientation of the specimens according to the

directions of the applied stress, the dielectric measurement

probes and the conductive layers of muscovite and chlorite

(type-1 and type-2 specimens).

It must also be noted that these layers due to their

chemical compositions are considered to be more con-

ductive than calcite which is the main mineral in marble.

Both types of specimens were tested in the subsequent

experiments.In order to achieve acceptably dry material,

the specimens were heated for 24 hours in a constant

temperature chamber at 378 K. The failure load of the

samples was detected after preliminary tests to vary be-

tween 8.6 kN and 10kN for both types of specimens.

2.2. Experimental Technique

The experimental apparatus that was used to conduct the

uniaxial compression test on the specimens is shown in

Figure 2 and comprises a stiff loading frame (MTS-815).

In this apparatus, the spherical seat is incorporated in the

upper loading platen of the frame. The load force was

parallel to the longest side of the specimen. The load on

the specimens was applied continuously at a displace-

ment rate equal to 0.001 mm/s. After reaching the prede-

termined stress level, the load was removed suddenly.

The selected mechanical load levels applied on the

specimens were 3.2 kN, 3.8 kN, 4.2 kN, 6.0 kN 7.3 kN

and 8.5 kN. After each loading ac conductivity measure-

ments were conducted. The experimental arrangement for

conducting the ac conductivity measurements (see Fig-

ure 3) comprises an LCR meter (Agilent model 4284A),

accompanied by a dielectric test fixture (Agilent model

16451B) and further supported by a computer for data

recording, storage and analysis. The dielectric test fixture

that was used to hold the specimen was protected by a

cabin providing constant temperature (298 K), inert at-

mosphere and also low humidity by continuous effusion

of nitrogen.

Figure 2. Typical testing system for uniaxial compression

testing.

I. STAVRAKAS ET AL. 63

3. Results and Discussion

Pilot ac conductivity measurements in the frequency

range 1 kHz - 1 MHz were conducted for type-1 and

type-2 specimens without removing their natural mois-

ture. Figure 4 shows the behaviour of the ac conductivity

with respect to the frequency for type-1 and type-2 speci-

mens. It becomes clear that type 2 specimens exhibit

higher ac conductivity in the whole frequency range. This

behaviour can be attributed to the fact that the external

electric field applied to measure the ac conductivity was

directed in parallel to the muscovite and chlorite layers

that act as conductive paths between the two electrodes

of the dielectric measurements probe (see Figure 1).

The high frequency part of the ac conductivity meas-

urements was fitted with the universal conductivity power

law (i.e. Equation 3). The fitting provided approximate

values 0.64 and 0.80 for the exponential factor n for

type-1 and type-2 specimens respectively. These values

seem to be characteristic for the two types since the error

deviation is very low (i.e. 0.64 ± 0.03 and 0.80 ± 0.04

respectively).

Figure 5 shows two representative ac conductivity

experimental datasets with respect to frequency for type-1

specimens. Figure 5(a), shows the behaviour of the ac

conductivity when the specimen without subjecting it to

any mechanical load while b shows the corresponding

behaviour of the same specimen after applying a me-

chanical load of 7.3 kN.

As can be seen in the Figure 5 the applied load has no

impact on the ac conductivity behaviour at the high fre-

quency ranges (>250 kHz) but it severely influences the

ac conductivity values at the low frequencies. It becomes

clear that the values of the ac conductivity become higher

after applying the mechanical load on the specimen. This

can be attributed to crack formation and propagation that

create additional conductive paths at the crack edges.

Figure 3. Dielectric measurements arrangement including

the inert gas tank.

Figure 4. A typical set of experimental datasets demonstrat-

ing the behaviour of the ac conductivity with respect to fre-

quency for both (solid squar es, a) type-1 and (ope n squares,

b) type-2 specimens.

Figure 5. A typical set of experimental datasets demonstrat-

ing the behaviour of the ac conductivity with respect to fre-

quency for type-1 specimen (solid squares, a) before and

(open squares, b) after apply ing 7.3 kN me c hanic al load.

This phenomenon provides greater freedom of charge

motion and consequently higher ac conductivity in the

low frequency range. The higher the frequency of the

applied ac field the lower is the current flowing along the

microcrack and macrocrack edges. The same behaviour

is observed for the type-2 specimens (see representative

datasets in Figure 6). Figure 6 clearly shows a variation

of the values of the ac conductivity before (a) and after (b)

applying mechanical load. Specifically, this variation

becomes evident only in the frequencies below 120 kHz.

The ac conductivity measurements of type-1 specimens

that had previously been loaded at 7.3 kN was also fitted

I. STAVRAKAS ET AL.

by the conductivity universal power law and factor n

found to be approximately equal to 0.63. This reduction

of the factor n indicates that the specimen has been sub-

jected to compressive stress [12]. Similar results were

extracted for type 2 specimens (see Figure 6).

When the natural moisture of the specimens is re-

moved by heating, the ac conductivity becomes lower.

This is evident in Figure 7 which shows the behaviour of

the ac conductivity with respect to frequency for a typical

type-1 specimen before and after the application of me-

chanical load.

Figure 6. A typical set of experimental datasets demon-

strating the behaviour of the ac conduc tivity with respect to

frequency for type-2 specimen (solid squares, a) before and

(open squares, b) after apply ing 8.5 kN me c hanic al load.

Figure 7. Representative experimental datasets of the ac

conductivity in the frequency range between 1 k Hz - 1 MHz

for type-1 specimen. (a) and (b) correspond to the specimens

that maintained their natural moisture before and after ap-

plying mechanical loa d (7.3 kN) respectively. (c) and ( d) cor-

respond to the specimens after removing their natural

moisture before and after applying mechanical load respec-

tively.

As it was expected when removing the natural mois-

ture of the specimens, their conductivity decreased due to

lack of free charges provided by water in the specimen

system. The variation breadth of the ac conductivity due

to the applied mechanical load is more intense for the

specimens containing their natural moisture compared to

the variation breadth for the dried specimens.

For the dried specimens a low frequency limit was set

to the measurements due to conductivity values that be-

come too low to comply with the measuring system

specifications and the corresponding conductivity values

exhibit error factor of 5%. This limit is obvious in Figure

7 where the ac conductivity measurements for the dehy-

drated specimen are conducted in the frequency range

between 10 kHz and 1 MHz.

The ac conductivity behaviour at the frequency of 10

kHz was selected to be studied with respect to the ap-

plied mechanical load. This frequency was selected since

the phenomena of ac conductivity variation due to stress

and due to water content become more intense in the low

frequency range. Additionally, this frequency is high

enough to avoid hardware limitations due to low conduc-

tivity effects, thus, ensuring that the total measurement

factor will not exceed 1%.

Figure 8 shows the relative ac conductivity for the

frequency of 10 kHz with respect to the applied uniaxial

load for both dehydrated (a) and hydrated (b) type-1

specimens. The value measured before any load applica-

tion was considered as reference conductivity. The verti-

cal axis corresponds to the relative conductivity (σ/σ0)

where σ0 is the reference conductivity and σ is the 10

kHz conductivity value. The horizontal axis corresponds

to the applied load.

The Figure 8 also contains the ac conductivity devia-

tion limits in order to include the results from all meas-

ured specimens. The circles in the figure correspond to

the mean value of ac conductivity for each value of the

applied load.

Figure 8. Representative plot of the behaviour of ac con-

ductivity for all type-1 specimens in both before (b) and af-

ter (a) removing their natural moisture.

I. STAVRAKAS ET AL.

Figure 9. Representative plot of the behaviour of ac con-

Observing Figure 8 it can be stressed that for type-1

ductivity of the specimens that were s

4. Conclusions

rimental results manifest that uniaxial

crack

e marble specimens that were subjected to uni-

ductivity for all type-2 specimens in both before (b) and

after (a) removing their natural moisture.

ecimens that was subjected to load up to approximately

3 kN, the ac conductivity decreases while the applied

load increases. This can be attributed to the pore-closing

process that takes place in this load range and the conse-

quent limitation of the conductive paths in the bulk of the

specimen.

The ac conub-

cted to load in the range between 3 kN and 7.5 kN,

increases significantly with increasing load. This increase

can be attributed to the crack propagation mechanisms

that create additional conductive paths at the crack edges.

The behaviour of the dehydrated specimens was simi-

r but exhibited lower conductivity magnitudes. The

lower magnitude of the changes of the ac conductivity

can be attributed to the absence of water in the bulk of

the specimen. It can be concluded that ac conductivity

measurements can provide information regarding the

mechanical status of marble specimens that have suffered

stress enough to create damages in their bulk. The same

behaviour holds for type 2 specimens and it is shown in

Figure 9 with slightly smaller variations.

The presented expe

compressional loading, causes significant variations to

the ac conductivity spectrum of marble specimens.

The applied uniaxial load when leading to micro

neration in the bulk of the specimens makes conduc-

tivity to increase due to hydration within the micro-

cracks.

For th

ial compressional load the ac conductivity was meas-

ured in the frequency range 1 kHz up to 1 MHz. The re-

sults presented here correspond to the frequency of 10

kHz since it is the most sensitive to show up ac conduc-

tivity variations for changes of load.

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