Deformation and transport processes in salt rocks: An ...

I

Deformation and transport processes in salt rocks:

An experimental study exploring effects of pressure and

stress relaxation

Nawaz Muhammad

Utrecht University

No. 084

II

Members of the dissertation committee:

Prof. dr. Janos L. Urai

RWTH Aachen University, Germany

Prof. dr. Hongwei Zhou

Xi'an Technological University, China

Prof. dr. Georg Dresen

GFZ German Research Centre for Geosciences, Germany

Prof. dr. M.R. Drury

Utrecht University, The Netherlands

Dr. Chloé Arson

Georgia Institute of Technology, USA

The research was carried out at:

High Pressure and Temperature Laboratory, Faculty of Geoscience, Utrecht University

(Budapestlaan 4, 3584 CD Utrecht, The Netherlands)

Printed by: Gildeprint

Copyright © Nawaz Muhammad

All right reserved. No parts of this publication may be reproduced in any form, by print or photo print, microfilm or

other means, without written permission by the publisher.

ISBN/EAN: 978-90-6266-396-5

III

Deformation and transport processes in salt rocks:

An experimental study exploring effects of pressure and

stress relaxation

Deformatie- en transportprocessen in zoutgesteentes:een experimentele studie naar de

effecten van druk en spanningsrelaxatie

(met een samenvatting in het Nederlands)

Proefschrift

ter verkrijging van de graad van doctor aan de Universiteit Utrecht op gezag van de rector

magnificus, prof. dr. G.J. van der Zwaan, ingevolge het besluit van het college voor

promoties in het openbaar te verdedigen op dinsdag 23 juni 2015

des ochtends te 10.30 uur

door

Nawaz Muhammad

geboren op 15 december 1975

te Lahore, Pakistan

IV

Promotor: Prof. dr. C.J. Spiers

Copromotoren: Dr. J.H.P. de Bresser

Dr. C.J. Peach

Dit proefschrift werd (mede) mogelijk gemaakt door een beurs toegekend door de Higher

Education Commission (HEC) van Pakistan aan Nawaz Muhammad, en door aanvullende

financiële ondersteuning onafhankelijk ter beschikking gesteld door AkzoNobel Industrial

Chemicals B.V., Nedmag Industries Mining & Manufacturing B.V., en de Nuclear Research

and Consultancy Group NRG.

V

To My Parents

VI

He created the heavens without any pillars that ye can see; He set on the

Earth Mountains standing firm, lest it should shake with you;

Surah Luqman, Chapter 31, Ayah 10

By Him in Whose Hand is my soul, the Hour (Qiyamah) will not come until

wild creatures talk to men, and a man speaks to the end of his whip and the

straps of his sandals (shoes), and his thigh will tell him about what happened

to his family after he left.

Prophet Muhammad (SAW)

Ahmad Musnad (3:84 and 85),

Hakim Mustadrak (4:467).

VII

Contents

Synopsis 1

Chapter 1: Introduction 7

1.1 Scope of the present work 8

1.2 Rocksalt 9

1.3 Bischofite and carnallite salt rocks 11

1.4 Transport properties and permeability of rocksalt 11

1.5 The main aims of this study 12

1.6 Plan of thesis 14

Chapter 2: The transition from dislocation glide to dislocation climb

controlled creep in dry rock salt in the temperature range 22-

350 oC (0.27-0.58T/Tm): using the pressure sensitivity of stress

to evaluate microphysical models

2.1 Introduction 18

2.2 Microphysical models for dislocation creep 23

2.2.1 Dislocation climb 23

2.2.2 Dislocation cross-slip 24

2.2.3 Dislocation glide 27

2.3 Method 29

2.3.1 Sample preparation 29

2.3.2 Deformation apparatus, testing and data processing 30

2.3.3 Preparation for microstructural study 33

2.4 Results 34

2.4.1 Mechanical data 34

(i) Experiments at room temperature (22 oC) 34

(ii) Experiments at 125-350 oC 34

(iii) Pressure sensitivity of normalized flow stress at different strain

values 42

(iv) General inferences from the observed pressure dependence of

creep 43

(v) n-value (stress exponent) 49

VIII

2.4.2 Microstructures 50

2.5 Discussion 55

2.5.1 Results of non-linear regression analysis 56

(i) Climb controlled creep 56

(ii) Cross-Slip controlled creep 59

(iii) Glide controlled creep 60

2.5.2 Comparison with previous studies involving tests at various

pressures 64

2.5.3 Deformation mechanism map 64

Conclusions 66

Chapter 3: Stress relaxation of synthetic and natural polycrystalline halite

3.1 Introduction 70

3.2 Method 72


3.2.2 Deformation apparatus 73

3.2.3 Experiments 76

3.2.4 Data acquisition and processing 76

3.2.5 Microstructural preparations 79

3.3 Results 80


(i) Stress vs. natural strain and time 80

(ii) n-value for the natural halite 86

(iii) Stress relaxation 86


3.4 Discussion 92

3.4.1 n-value 92

3.4.2 Composite flow law 94

Conclusions 104

IX

Chapter4: Creep behaviour of bischofite, carnallite and mixed bischofite-

carnallite-halite salt rock at in situ conditions

4.1 Introduction 107

4.2 Method 108


4.2.2 Deformation apparatus 112

4.2.3 Experiments 115

4.2.4 Data acquisition and processing 115

4.2.5 Young’s modulus measurement 118

4.2.6 Microstructures (only carnallite) 118

4.3 Results 118

4.3.1 Bischofite 119

(i) Stress vs. strain curves 119

(ii) Effect of confining pressure 123

(iii) Flow behaviour 128

(iv) Stress relaxation 131

4.3.2 Carnallite 134


(ii) Flow behaviour 134


(iv) Microstructures 144

4.3.3 Mixture samples of bischofite, carnallite and halite 146


(ii) Flow behaviour 147


4.3.4 Elemental analysis using micro X-Ray Fluoroscopy (μ-XRF) 153

4.4 Discussion 160

4.4.1 Mechanical behaviour 160

(i) Creep law for bishofite using stresses at the end of constant strain

rate steps 161

(ii) Creep law for carnallite using stresses at the end of constant strain

rate steps 163

X

(iii) Comparison of steady state values 165

(iv) Relating the relaxation behaviour to the creep at near steady

state 165

(v) Composite flow laws 176

4.4.2 Effect of composition 180

Summary and conclusions 182

Chapter 5: Permeability of interfaces in layered rock salt under different

stresses and geometries

5.1 Introduction 186

5.2 Method 187

5.2.1 Samples source, composition and preparation for experiments 187

5.2.2 Apparatus and testing conditions 190

5.2.3 Calibrations 192

5.2.4 Experimental procedure and data processing 192

5.2.5 Preparations for Microstructural study 194

5.3 Results 195


5.3.2 Permeability 200

5.3.3 Results Batch-I (20 MPa confinement) 201

(i) NP1 (vertical interface) 201

(ii) NP2 (oblique interface) 202

(iii) NP3 (mixed) 202

(iv) NP4 (oblique interface) 203

(v) NP5 (interlayer with salt) 204

5.3.4 Results Batch-II (10 MPa confinement) 207

(i) NP6 (vertical interface) 207

(ii) NP7 (horizontal interface) 207

(iii) NP8 (oblique interface) 207

(iv) NP4-Re-test (oblique interface) 208

5.4 Microstructures 217

(i) NP3 (mixed) 218

(ii) NP4 (oblique interface) 218

(iii) NP6 (vertical interface) 218

(iv) NP7 (horizontal interface) 219

XI

(v) NP8 (oblique interface) 220

5.5 Discussion 221

5.5.1 Summary of results 221

(i) Comparison of Batch-I results 221

(ii) Comparison of Batch-II results 223

5.5.2 Effect of confining pressure 223

5.5.3 Elastic response of existing cracks to the hydrostatic pressure 224

5.5.4 Compaction and dilatancy 226

5.5.5 Localised dilatancy at interface 226


5.5.7 Consequences of drilling the interfaces 229

5.5.8 Permeability: bulk and interface 231

5.5.9 Comparison with previous work and implications 232

Conclusions 233

Chapter 6: Conclusions and suggestions for further refinement 239

References 251

Samenvatting 261

Acknowledgements 269

Curriculum vitae 272

1

Synopsis

2

The presence of evaporitic formations in sedimentary basins, often

dominated by the salt mineral halite, is of great influence on the structural

style developed during tectonic events. On a somewhat smaller scale, salt

rocks often host a variety of deep solution mined caverns, which are

increasingly finding use for strategic storage of energy resources in the form

of gaseous or liquid fuels and as vessels for off-peak energy storage in

compressed gas. This is in addition to the use of conventionally mined

galleries for the long term storage of hazardous waste materials. The low

permeability of most salt rocks, with weak rheological behaviour and

tendency to self-seal, has attracted engineers to use salt formations to host

such projects. The Zechstein salt deposits in the Netherlands exist in the

form of original beds and as migrated salt domes/pillows that may reach the

kilometre scale. Some contain magnesium rich salts which are solution

mined as an economic resource. Caverns constructed within these more

soluble and weaker materials pose additional challenges for long term

storage management. Careful management of fluid filled caverns requires a

full knowledge of the rheological and transport properties of the host salt

formations for a safe operation into the future.

This thesis addresses a number of deficiencies in the current knowledge of

salt mechanical behaviour regarding the mechanical creep of halite and its

mixtures with magnesium salts. In particular the pressure sensitivity of

creep is investigated, using synthetic and natural halite rock, to identify the

constituent mechanisms which contribute to the overall deformation

process, with a view to better understand the physics of salt flow. The

rheology of the magnesium bearing salts; carnallite and bischofite, is also

investigated, with special attention to the mechanical behaviour of mixtures

of these salts with halite. In addition to rheological issues, the effects of

compositional layering on permeable transport in the excavation damage

3

zones around mined cavities are investigated, using natural layered material

from mines in China, to better understand effects of bedding orientation

relative to deformational stresses expected in cavity and gallery walls at

depth.

Chapter 1 covers the literature survey on salt rheology, main aims of this

study and planning of the thesis.

Chapter 2 is about the rate controlling mechanism in the creep of

polycrystalline dry salt. The temperature range covered in this work is from

22 to 350 oC. The deformation/strain rates used lie in the range 4×10

-7 s

-1 to

10-4

s-1

, including constant strain rate and strain rate stepping tests. The main

idea behind this part of the study is to discriminate between several

dislocation creep mechanisms, such as dislocation climb, dislocation cross-

slip and dislocation glide, using the pressure sensitivity of flow stress of dry

salt. Theory suggests that there is an atomistic activation energy and

activation volume associated with solid state flow under dislocation creep.

Following theoretical models then, the salt is expected to show higher

strength under higher confining pressures for positive activation volumes

and lower strength under lower confining pressure for negative activation

volume, depending upon the rate controlling mechanism. For this

investigation, the confining pressure was varied in the range 50-600 MPa,

which was never systematically done before for fully confined salt. The salt

was found stronger at higher confining pressures, and the rate controlling

mechanism was found to be transitional from glide to climb.

Chapter 3 is about the flow law at in situ conditions of wet halite, using

synthetic and natural salt samples. The temperature and confining pressure

applied were 125 oC and 50 MPa, respectively. The samples were tested in

multi-step experiments with constant strain rate parts (5×10-5

– 5×10-8

s-1

)

4

followed by stress relaxation after selected steps. The relaxation data

showed that the rate controlling mechanism does not remain the same, but

changes from dislocation creep (at higher stresses and faster strain rates) to

grain size dependent (likely pressure solution) creep at the end of relaxation

(i.e. at lower stress and strain rates).

Chapter 4 is a compilation of tests on bischofite, carnallite and their

mixture with halite, performed at real in situ conditions of confining

pressure 40 MPa and temperature 70 oC. These tests were conducted on

polycrystalline samples obtained from natural cores. The samples were

tested employing deliquescence conditions around the sample in the same

way as reported in Chapter 3 for halite, namely in multi-step experiments

with constant strain rate parts (10-5

– 10-8

s-1

) followed by stress relaxation

after selected steps. The results revealed that the carnallite was stronger than

bischofite and the mixture was in turn stronger than carnallite. The strength

of the mixture was found to have a direct relation to the halite weight

percentage i.e. higher halite wt. % makes the mixture stronger. The

compositions of various samples were tested using a micro XRF technique.

Stress relaxation showed a change of flow mechanism from dislocation

creep at the higher stresses and strain rates (at the start of relaxation) to

grain size dependent creep towards lower stress and strain rates (at the end

of relaxation). Composite flow laws resulted for bischofite and carnallite, as

a combination of grain size insensitive creep and grain size sensitive creep

for higher and slower stresses, respectively.

Chapter 5 is about the transport properties of layered bedded salt rocks

from salt mines in China. The samples were tested for their permeability,

under increasing differential stresses, at the interface of two layers namely

halite and glauberite, using transient step argon gas permeametry method.

5

The experiments are classified into two batches, batch-I for comparatively

higher depth (20 MPa confinements) and batch-II for shallower depths (10

MPa confinements). Various geometries, with interface orientation (vertical,

oblique and horizontal) to deformation direction were tested by adding

stress in steps of 10 MPa. The axial and volumetric strains, during

deformation, were measured, which revealed that all samples were

compacted despite the increase or decrease in permeability. The

microstructural investigation revealed that local dilatancy occurred at

interfaces, which must give a local increase in permeability but was masked

by the bulk compaction of the samples.

7

Chapter 1

Introduction

8

1.1 SCOPE OF THE PRESENT WORK

The presence of evaporitic formations in sedimentary basins, often

dominated by the salt mineral halite, is of great influence on the structural

style developed during tectonic events (e.g. Hudec & Jackson 2007). Owing

to its low viscosity, causing Halokinesis, a whole range of complex

structures may develop involving salt rock, varying from salt pillows and

diapirs to detached salt sheets and even glaciers (e.g. Talbot 1979, Jackson

& Talbot 1991, Vendeville & Jackson 1991, Rouby et al. 2002, Debois et al.

2010). These complex structures are of great interest for the oil industry,

since many hydrocarbon findings are associated with salt structures (e.g.

Davison et al. 2000, Tang et al. 2004, Huvaz et al. 2007, see also Hudec &

Jackson 2007). On a somewhat smaller scale, salt rocks host a variety of

deep caverns and mined galleries which are increasingly finding use for

strategic storage of energy resources in the form gaseous or liquid fuels and

also as off peak buffered storage in the form of compressed air (Stormont

1997, Istavan et al. 1997) This type of strategic storage comes in addition to

the long term storage of hazardous waste materials (Hunsche & Hampel

1999, Tsang et al. 2005). The low permeability of most salt rocks, with

weak rheological behaviour and tendency to self-seal has attracted engineers

to use salt formations to contain such projects. Management of caverns

requires a full knowledge of the rheological and transport properties of the

host salt formations for a safe operation into the future. Note that in addition

to halite, this also concerns salt rocks consisting of minerals such as

bischofite and carnallite. Expanding our understanding of the rheological

and transport properties of halite, bischofite and carnallite forms the broad

aim of this study. Most importantly, such enhanced understanding will help

reliable extrapolation of laboratory results to in situ conditions, and is of

9

importance for modelling the flow of salt in settings varying from salt

diapirs to solution–mined cavities and the stability and integrity of bore

holes through sediment packages containing salt horizons.

1.2 ROCKSALT

Despite the large body of data that already exists on the mechanical

behaviour of rocksalt and resulting empirical flow laws (Heard 1972, Heard

& Ryerson 1986, Wawersik & Zeuch 1986, Carter 1993, Ter Heege et al.

2005a), the underlying question regarding what microphysical mechanisms

govern plastic flow of natural dense halite rock at in situ conditions has not

yet been answered to full satisfaction. In particular, the exact mechanism

controlling dislocation motion at relatively low temperature is still

insufficiently understood. As a result, uncertainties exist regarding the

appropriate mechanism-based flow-law for low temperature, hampering

reliable extrapolation of lab creep data to in situ strain rates. Several

dislocation models have been proposed to control plastic flow of rocksalt at

in situ conditions, such as dislocation climb (Senseny et al. 1992, Carter et

al. 1993, Franssen 1994), and dislocation cross-slip or glide (Auten et al.

1973, Skrotzki et al. 1981, Wawersik & Zeuch 1986, Conrad & Yang 1999).

Since the various dislocation mechanisms are characterized by quite

different constitutive equations, the results of extrapolation of laboratory

data may vary substantially depending on the inferred mechanism, thus

hampering reliable modelling. Many of the flow laws presented in the

literature for rocksalt are based on short term experiments with little or no

basis regarding the exact microphysical mechanism controlling creep. One

way to test which model is appropriate is by investigating the pressure

dependence of strength of rocksalt, which works against the atomistic scale

activation volume associated with the different mechanisms governing the

10

rate of dislocation creep. Dislocation glide is expected to be hardly affected

by pressure, notably at low temperature, dislocation cross slip, in which

dislocations overcome obstacles by temporary gliding onto a plane oriented

oblique to the initial glide plane, may either become easier with increasing

pressure or more difficult, depending on the details of the cross slip process,

and dislocation climb is expected to become more difficult with pressure. In

this study, new data on the rheology of rocksalt, under dry conditions, have

been tested against various models taking the effect of confining pressure

into account. The rock salt was taken dry to avoid water-involved processes

like solution-precipitation to play a role.

Salt rocks in nature are wet rather than dry (Urai et al. 1986, Spiers et al.

1990). The creep of these salt rocks usually occurs at strain rates in the

range of 10-8

to 10-15

s-1

(Heard 1972, Van Eekelen et al. 1981, Jackson &

Talbot 1986, Carter et al. 1993). In order to fully understand the creep

behaviour of halite under natural conditions, it thus is of importance to not

only know, in general, which mechanisms may control dislocation creep of

halite, i.e. dislocation glide, cross slip or climb, but also to establish to what

extent solution-precipitation mechanisms play a role and at what conditions

a given mechanism prevails. The strain rates relevant for in situ

deformation, 10-8

to 10-15

s-1

, are difficult to achieve in laboratory

experiments. However, stress-relaxation experiments (Rutter & Mainprice,

1978) allow strain rates as slow as 10-9

s-1

to be achieved, by allowing the

stress on a sample to relax through plastic deformation. In the current study,

such experiments have been carried out on a limited number of synthetic

and natural wet polycrystalline halite samples.

11

1.3 BISCHOFITE AND CARNALLITE SALT ROCKS

Many salt deposits are mainly composed of halite, but substantial amounts

of the evaporites bischofite and carnallite may be present. In order to give

practical answers to questions asked regarding salt rock behaviour during

solution mining, it is important to know the rheology of the different salts at

real in situ conditions, so that the rate of inflow into the caverns as well as

surface subsidence can be predicted. Not many studies have been performed

on these materials (Van Eekelen et al. 1981, Urai 1983, 1985), hence, the

creep behaviour of bischofite, carnallite and their mixtures, is still relatively

poorly known. As was indicated above, the slow strain rates that are

relevant, in the range of 10-8

to 10-15

s-1

, may be approached in laboratory

scale experiments by applying the stress relaxation technique. In this case

study, the mechanical properties of bischofite, carnallite and their mixtures

are studied on the basis of standard constant strain rate deformation

experiments as well as stress relaxation tests. Main aim is to produce

constitutive flow laws than can be applied at real in situ conditions.

1.4 TRANSPORT PROPERTIES AND PERMEABILITY OF

ROCKSALT

Solution mined salt caverns are of great interest for fluid storage e.g.

compressed air, natural gas etc., and are expected to show excellent healing

and sealing capacity. However, it is of utmost importance to be able to

reliably quantify the permeability of salt cavern walls, so that potential loss

of the stored asset may be assessed. In contrast to recrystallized, relatively

homogeneous domal salt, bedded salt is characterized by original

sedimentary/compositional layering which forms interfaces between various

evaporitic minerals (halite, glauberite, dolomite, clays etc.). In order to

12

reliably use caverns in layered salt for gas storage, it is essential to have

insight into the sealing capacity at interfaces between such layers. Data for

the dilatancy, permeability and damage for pure salt are readily available

(Peach & Spiers 1996, Hatzor & Heyman 1997, Stormont 1997, Popp et al.

2012), but very little is known about the permeability of layered salt under

various differential stresses. In particular, little is known regarding the effect

of differential stress on the permeability through the interfaces between salt

layers (Liang et al. 2007 and 2012). These interfaces can have different

orientations with respect to the direction of maximum differential stress, so

their response to differential stress can be expected to differ between

geometries. Consequently, the permeability can change depending on

various factors, such as bonding strength at the interface, flexure due to

different strength at the two sides of the interface, the anisotropic ductility

of the various layers under shear and orientations of bedding (vertical,

horizontal and oblique) to the axial loading direction. Management of

caverns in such layered salt, is a problem for engineers in the Hubei

province of China and this prompted experiments on layered salt from that

region within the framework of this thesis

1.5 THE MAIN AIMS OF THIS STUDY

The extrapolation of laboratory data obtained from different studies to real

in situ conditions gives a broad band of uncertainty in predicted creep rate.

Rigorous experimentation is needed to ascertain the rate controlling

mechanism in salt rock. One problem in this is the difficulty to reach in the

laboratory the slow strain rates relevant for the natural systems, from

geotechnical settings such as caverns and bore holes, to the geological

development of salt pillows and diapirs. This study has the following main

aims:

13

1. To determine the microphysical mechanism controlling dislocation

creep of halite at 20-350 C, and to develop a mechanism-based

flow law providing a solid basis for extrapolation of lab data to

long time scales. Current debate regarding which dislocation

mechanism explains the rheology of halite best, under relatively

low temperature conditions, is entered by systematically

investigating the pressure dependence of creep across a range of

pressures not attempted before (50-600 MPa). Focus is on dry,

synthetic polycrystalline halite.

2. To establish if a transition can be observed from creep behaviour

governed by dislocation mechanisms to creep behaviour controlled

by a solution-precipitation mechanism, in wet polycrystalline

halite, and if so, what the conditions of this transition are in terms

of strain rate. As an important criterion, we will the stress exponent

n of a conventional power law creep equation, expected to be above

3 in case of dislocation creep, and being ~1 for solution-

precipitation creep.

3. A new and improved flow law for bischofite and carnallite to be

used at real in situ conditions by achieving the deformation rates as

low as ~10-9

s-1

by means of stress relaxation technique.

4. To test the permeability of layered rocksalt (from mines in Hubei

province China) as response to differential stress using various

geometries/orientation to deformation direction. By studying the

bulk and local compaction/dilation (at the interface) with the help

of dilatometry in conjunction with the deformation apparatus and

microstructural studies of interface of pre tested samples.

Permeability is determined using argon gas transient step

permeametry, throughout the deformation.

14

1.6 PLAN OF THESIS

The current study is based upon experimental work.

Chapter 2 reports on constant and strain-rate stepping experiments at fixed

pressures, also constant and pressure-stepping experiments at fixed strain

rates, and focuses on the pressure sensitivity of flow stress of dry salt at

temperatures 22 to 350 oC and confining pressures 50 to 600 MPa. The

results are evaluated against various microphysical models for dislocation

creep.

Chapter 3 reports on the results of multi-step experiments on wet synthetic

and natural rock salt. The experiments involved steps of constant strain rate

in the range 5×10-5

to 5×10-8

s-1

, and relaxation steps. The experiments were

carried out at a temperature of 125 oC and a confining pressure of 50 MPa

and. The strain rates achieved during stress relaxation were as low as 10-9

s-

1.

Chapter 4 is about the study of flow behaviour of wet salt rocks containing

bischofite, carnallite and their mixtures of these two salt minerals and halite.

Multi- step strain rate stepping experiments of the same type as applied to

the wet synthetic and natural halite (chapter 3) were performed and the

results obtained are discussed with respect to the role of grain size

insensitive (dislocation) mechanism and grain size sensitive mechanism

such as solution-precipitation. A first-order impression was obtained of the

effect on the strength of the salts of the wt. % of the various salts in the

mixture.

Chapter 5 is about the transport properties of layered rocksalt with special

emphasis on the response of interface permeability to differential stress

using different geometries. Permeability change and compaction/dilation of

15

bulk and interface is discussed. An important finding about the local

dilatancy vs. bulk compaction and change of permeability revealed by

microstructural analysis is special feature of this work.

Chapter 6 contains the main conclusions of this work and gives suggestions

for future directions.

17

Chapter 2

The transition from dislocation glide to

dislocation climb controlled creep in

dry rock salt in the temperature range

22-350 oC (0.27-0.58T/Tm): using the

pressure sensitivity of stress to

evaluate microphysical models

Muhammad, N., C.J. Spiers, C.J. Peach & J.H.P. de Bresser, 2012

Mechanical behaviour of salt VII.

18

2.1 INTRODUCTION

It has been a long standing dispute as to what dislocation mechanism

controls the creep of dry rock salt in the temperature range of 25-350 oC.

Solving this dispute is of importance in order to come to a reliable

extrapolation of laboratory derived creep data to the in situ strain rates

relevant for the long term geomechanical behaviour of salt, for example

around solution-mined caverns. Several authors suggest that dislocation

creep at these temperatures is climb controlled (Senseny et al. 1992, Carter

et al. 1993, Franssen 1994), while others conclude control by dislocation

cross-slip or glide (Auten et al. 1973, Skrotzki et al. 1981, Wawersik &

Zeuch 1986, Conrad & Yang 1999). Since the various dislocation

mechanisms are characterized by quite different constitutive equations, the

results of extrapolation of laboratory data may vary substantially depending

on the inferred mechanism, hampering reliable modelling.

Previous experimental studies on the rheology of rock salt have explored

a wide range of temperature, strain rate and confining pressure. Aladag et al.

(1970) and Auten et al. (1973) deformed polycrystalline salt at room

temperature (RT), a strain rate of 10-4

s-1

and at various pressures ranging

0.1 to 1000 MPa. They reported a decrease in the plastic flow strength with

increasing confining pressure, via cross-slip of screw dislocations. The tests

were performed on unjacketed samples, i.e. the samples were not sealed but

open to penetration by the confining medium (n-pentane), along grain

boundaries, helping the progressive opening of fractures through lowering

of effective stress.

Heard (1972) conducted a series of confined tests on salt using a constant

confining pressure of 200 MPa, temperatures ranging from RT to 400 oC

and strain rates 10-4

to 10-7

s-1

. He concluded that at low temperature and

19

relatively fast strain rate, the rate controlling mechanism is stress-assisted

glide, whereas for slower strain rates and higher temperatures, the results

can best be explained by Weertman’s dislocation climb model (Weertman,

1955) of the type 𝜀̇ ∝ 𝜎𝑛, with stress exponent n = 5.5. The samples used

were jacketed and the water content in the samples was in the range of 20 to

45 ppm.

Carter et al. (1993) reported rheological behaviour of natural aggregates

with water content of < 100 ppm (considering it dry) while experiments

were conducted in the temperatures ranging from 50 to 200 oC. The rate

controlling mechanism was reported as transitional cross-slip, at faster strain

rates and high stresses, to dislocation climb at slower strain rates and low

stresses, as far as the power law equation 𝜀̇ ∝ 𝜎𝑛 was devised. The two

regimes, dislocation cross-slip and dislocation climb were differentiated

with n-values given as 5.3 and 3.4 respectively, along with the other

parameters obtained using best fit.

Franssen (1994) presented the results of uniaxial deformation tests on

synthetic rocksalt in the temperature range of 250-780 oC, performing

constant and strain rate stepping tests in the range of 10-3

to 10-7

s-1

. The

samples were considered dry at such high temperature conditions. The flow

law reported was given by a power law of the form 𝜀̇ ∝ 𝜎𝑛, whereas two

regimes were defined. In the temperature range of 250 to 450 oC, dislocation

climb with an n-value of 5.7, and in the temperature range of 500-780 oC

lattice diffusion with an n-value of 4.4 were found as rate controlling creep

mechanisms. The tests were conducted in unconfined state, and the

mechanical data were supported by extensive microstructural analyses.

Conrad & Yang (1999) reported unconfined creep behaviour of rock salt

(unknown water content) consistent with cross slip control, up to a

20

temperature of 264 oC, and a transition to dislocation climb above 264

oC.

However, unconfined samples are highly susceptible to ductile -brittle

transitional behaviour, due to expected micro-fracture and dilatancy of

samples under stress. This casts doubt on the reliability of the conclusions of

Conrad and Yang (1999) regarding the controlling dislocation mechanism.

Later studies have shown that salt can only be considered dry if its water

content is below ~ 5ppm (Watanabe & Peach 2002, Ter Heege et al. 2005b).

For higher water content, pressure solution mechanisms are likely to play a

role during creep (also see Urai et al. 1986, Spiers et al. 1990) complicating

the description of the mechanical behaviour in terms of a flow equation.

Ter Heege et al. (2005a) performed triaxial experiments on dense

synthetic wet rocksalt in the temperature range of 75 to 240 oC at fixed

confining pressure of 50 MPa, using constant deformation strain rates in the

range of 5×10-7

to 10-4

s-1

. The authors confirmed that the salt can be

considered dry if its water content is ≤ 5 ppm, whereas for higher water

content, 9-46 ppm, the strength of salt was found to decrease to half of the

value tested otherwise at same conditions. This higher water content was

inferred to assist pressure solution creep and recrystallization by grain

boundary migration, both enhanced by fluid assisted diffusional transport in

the wet grain boundaries. The steady state flow law reported was a

conventional power law with an n-value of 5.6.

It is clear from the above that uncertainties still exist regarding the creep

mechanism controlling rock salt, notably at relatively low temperature. In

this study, considering the important points mentioned above, jacketed and

dry polycrystalline samples were tested in the temperature range of 25 to

350 oC. The rate controlling mechanism was evaluated applying non-linear

regression to the data. The best fitting parameters thus obtained revealed

21

that the mechanism is transitional, from glide (Peierls resistance controlled),

for the temperature range of 25-125 oC, to dislocation climb with an n-value

of 4.7 in the temperature range of 250 to 350 oC.

While deforming a crystalline material, several intra-crystalline defects

are usually produced, mostly in the form of edge and screw dislocations.

These dislocations glide under stress, unless affected by some obstacle on

the glide plane. At such obstacles, piling up of dislocations may cause strain

hardening of the material, except if the obstacles can be overcome by some

recovery process. The rate of motion of the dislocations is then determined

by the rate of the recovery process. One common process for overcoming

obstacles is dislocation climb, in which edge dislocations can climb out of

their glide plane due to vacancy-ion diffusion at the obstacle.

In dislocation cross-slip, a screw dislocation temporarily changes its

glide motion by moving onto a glide plane oblique to the primary glide

plane, in order to surmount the obstacle, after which it continues to glide on

the primary glide plane.

When these recovery processes are not rate controlling, for example

because they are too slow to be effective, the dislocations are constrained on

their glide plane. The rate of dislocation motion is then limited by the rate of

overcoming barriers in the glide plane, which itself is determined by the

nature of the barriers and of the dislocation core scale mechanisms by which

they are overcome (Frost and Ashby 1982, Cannon & Langdon 1983).

Glide-controlled models are usually not capable of recovering complex

dislocation substructures, hampering steady state creep. However, plastic

deformation prevails due to the movement of atomic layers overcoming

lattice friction often referred as Peierls resistance, and it depends upon size

and nature of dislocations.

22

During thermally activated dislocation processes like climb and cross

slip, there will be a small volume difference between the initial and final

state of the activated process, expressed by the activation volume (ΔV)

(Stocker & Ashby 1973, Poirier 1976, Karato 2008, De Bresser 2002). The

activation volume determines the pressure dependence of the strain rate

(Karato 2008). For dislocation climb, ΔV is related to vacancy diffusion

(Poirier 1976). The volume change associated to cross-slip is related to the

modification of stacking faults by the activity of dislocation partials, as

explained by different models (Escaig 1968a, Escaig 1968b, Skrotzki & Liu

1982). The dislocation partials need to be constricted before cross-slip, and

subsequently get dissociated again after cross slipping. The activation

volume ΔV for the constriction part is negative, whereas for the subsequent

serial step of dissociation, it is positive. Dislocation glide does not usually

involve vacancy diffusion or cross-slip as dominant mechanisms, but it can

be expected to show a minor activation volume while overcoming the

energy barriers to glide (Peierls mechanism, Karato 2008).

Confining pressure works against the activation volume and can promote

or hinder the activated processes depending upon whether it is negative or

positive. In other words, in case of a process in which the activation volume

ΔV is positive, the confining pressure will suppress the dilation and creep

will slow down, but the process with negative ΔV, the creep will speed up

by assistance of confinement.

Following the suggestion that the effect of pressure on the mechanical

behaviour of rock salt can be used to evaluate which microphysical model

best explains creep; tests have been conducted on dry polycrystalline salt

with average grain size of 300 μm under a wide range of confining

pressures. We have used jacketed dry synthetic polycrystalline salt samples

23

in axi-symmetric testing using argon gas as confining medium at pressure

values in the range from 50 to 600 MPa. At these pressures, micro-crack

dilatancy is strongly suppressed (Peach and Spiers 1996). The temperature

range studied is from room temperature (22oC) to 350

oC (i.e. T/Tm of 0.27-

0.58), i.e. outside the field of bulk diffusional flow. In general, the

polycrystalline salt was found to be stronger at higher confining pressures,

(in particular) at the higher temperatures 125-350 oC. This is in contrast to

what was found by Aladag et al. (1970) and Auten et al. (1973)

2.2 MICROPHYSICAL MODELS FOR DISLOCATION CREEP

2.2.1 Dislocation climb

Dislocation climb is a mode of recovery in which the edge dislocations of

opposite signs annihilate one another by solid state diffusion at an obstacle,

because the obstacle is too large to be overcome by natural thermal

vibrations alone. It is a process in which strain hardening may be balanced

by recovery, and steady state creep can occur. Favourable conditions for this

process to occur are slow strain rates and high temperatures (Heard 1972). A

generalized form of Weertman’s dislocation climb model (Weertman 1955)

is given as (after Frost & Ashby 1982)

𝜀̇ =𝐴𝜇

𝑇(

𝜎

𝜇)

𝑛𝑒𝑥𝑝 [−

𝛥𝑈+𝑃𝛥𝑉

𝑘𝑇] (2.1)

where A and n are constants, μ is the shear modulus, T is temperature, σ is

the differential stress, ΔU is the activation energy for self-diffusion of

slowest ion and vacancy, P is the hydrostatic pressure, k is the Boltzmann’s

constant and ΔV is the activation volume which represents the atomistic

24

scale expansion at the lattice site when an ion jumps into a vacancy and the

crystal restores its bond lengths. Notably, the activation energy ΔU for such

diffusion process is independent of applied stress. Depending upon the

diffusion mode, i.e. bulk diffusion or through the dislocation cores, the n-

value has the range from 3 to 6.5 (Poirier 1985). The PΔV term indicates

that creep will be slower or the material will be stronger at higher

hydrostatic pressures, provided that the activation volume ΔV is positive.

2.2.2 Dislocation cross-slip

De Bresser (2002) explains in detail the general flow law for cross-slip and

the details for the models controlled by constriction or dissociation. The

most important elements will be repeated below.

In dislocation cross slip, screw dislocations may surmount an obstacle by

temporarily gliding onto a plane oblique to the primary glide plane. Screw

dislocations of opposite sign cross slip towards each other and mutually

annihilate. Cross slip is a thermally activated process in which the activation

barrier is reduced by stress. Its general creep equation is given as (after

Poirier 1976)

𝜀̇ = 𝐾 (𝜎

𝜇)

2𝑒𝑥𝑝 [−

𝛥𝑈𝑐𝑠(𝜎,𝑃)

𝑘𝑇] (2.2)

where K is a constant and ΔUcs is the activation energy which is dependent

on stress and the hydrostatic pressure.

Screw dislocations often get dissociated into partials to form stacking

faults (e.g. Skrotzki & Liu 1982). These partials need to be constricted to be

able to move onto the oblique glide plane, in order to overcome obstacles.

25

Re-dissociation on the cross slip plane follows as start of further glide, and

the same process of constriction and dissociation takes place if the partials

move back to the primary glide plane. The width of a stacking fault is

dependent on the stacking fault energy γ (Hull and Bacon 1983) which

determines the force required to constrict two partials together

𝛾 = 𝛾𝑜 + [𝜀𝑜𝑏

2] 𝑃 (2.3)

where b is the Burgers vector length, γo is the stacking fault energy at

atmospheric pressure and εo is the maximum relative dilatation for a fault

with Burgers vector b/2. So the stacking fault energy will be higher for high

confining pressures, assisting the dislocation partials to constrict before

cross-slip and also resisting the dissociation after cross-slip. Depending

upon the slower of these serial processes, constriction or dissociation

controls cross-slip.

Considering constriction of partials as rate controlling mechanism, Wolf

(1960) and Skrotzki & Liu (1982) expressed the activation energy as

follows

𝛥𝑈𝑐𝑠(𝜎, 𝑃) = 𝛥𝑈𝑐𝑠 [𝑙𝑛𝜎𝑜

𝜇𝑜− 𝑙𝑛

𝜎

𝜇] (2.4)

where (σo/μo) is the normalized shear stress at 0 K, and ΔUcs is a constant

related to the stacking fault energy. This equation shows that if the applied

stress σ is zero, then the activation energy ΔUcs(σ,P) approaches infinity,

means that in the absence of applied stress, recovery is not possible. Or in

26

other words, this is a stress assisted recovery phenomenon. For FCC

materials, ΔUcs for large γ is described by Wolf (1960) as

𝛥𝑈𝑐𝑠 = [𝜇𝑏3

157(𝛾/𝜇𝑏)] (𝛽 − (𝛾/𝜇𝑏))

0.5 (2.5)

where β depends on the elastic constants (anisotropy) of the material. As

described by Seeger (1956), β = α/2π√3 with α = 2C44/(C11-C12), where Cij

are the values of elastic constants of the material.

Now considering dissociation as the rate controlling mechanism in cross

slip, Escaig (1968a) (see also Poirier 1976) approximates the activation

energy as

𝛥𝑈𝑐𝑠(𝜎, 𝑃) = 𝛥𝑈𝑐𝑠 [1 −𝛼𝑏𝜎

𝛾] (2.6)

where α is a geometrical constant of the order of 3, ΔUcs is constant and

represents the activation energy at zero applied stress, which means that

dissociation can occur without applying stress. For FCC materials, Escaig

(1968a) estimated the value for ΔUcs as

𝛥𝑈𝑐𝑠 = [𝜇𝑏3

1859 (𝛾/𝜇𝑏)] (𝑙𝑛

2√3

16𝜋(𝛾/𝜇𝑏))

0.5

(2.7)

The pressure dependence of stacking fault energy (Eq. 2.3) shows that,

its value increases with pressure. Using this value in Equation 2.5, will

make the ΔUcs term of Equation 2.4 decrease and consequently, the flow

rate given by Equation 2.2 will go up after using Equation 2.4 in Equation

27

2.2. In other words the material will be weaker for higher confining

pressure. On the other hand, for the dissociation control, using the pressure

dependent stacking fault energy in Equation 2.7 will decrease the constant

term ΔUcs of Equation 2.6. The 𝛥𝑈𝑐𝑠(𝜎, 𝑃) term depends on relative values

of α, σ and γ, where γ is relatively lower than α and σ. The increase in

𝛥𝑈𝑐𝑠(𝜎, 𝑃) will decrease the flow rate given by Equation 2.2, which means

that the material will be stronger at higher confining pressure.

2.2.3 Dislocation glide

Dislocations are forced to stay into their glide plane under the conditions

that climb and cross slip are unlikely to be of importance, usually at

relatively low temperature (Frost and Ashby 1982). While gliding, the

dislocations face resistance due to several factors which can determine the

deformation rate. These resistances are usually classified into two categories

(Verrall et al. 1977, Poirier 1985, De Bresser 1991, Karato 2008) namely;

discrete obstacles and intrinsic lattice friction (Peierls) resistance. Discrete

obstacles are, for example, point defects like foreign atom or dislocations

oriented oblique to the glide plane. These objects impede the dislocation

movement and consequently dislocations start piling up around the

obstacles. These obstacles can be surmounted by dislocations with the help

of external stress. The second type of resistance is offered by lattice friction.

For a comparatively pure material, the existing bonds need to be broken and

reformed in order to allow a dislocation to pass. The energy required to

overcome this periodic rise and fall in the energy of barrier, often referred as

Peierls potential hill, can be overcome by external stress or temperature.

This lattice friction phenomenon may involve a serial recovery process like

dislocation climb, but rate controlling mechanism is still Peierls stress being

slower (see for more details, Weertman 1957, De Bresser 1991). The

28

respective model equations after (Verrall et al. 1977, De Bresser 1991 and

Haseeb 2006) are given as:

Barrier controlled

𝜀̇ = 𝐾𝑒𝑥𝑝 [−(𝛥𝑈+𝑃𝛥𝑉)

𝑘𝑇(1 − (

𝜎

𝜎𝑜)

𝑝)

𝑞

] (2.8)

𝜀̇ = 𝐾 (𝜎

𝜇)

2𝑒𝑥𝑝 [−

(𝛥𝑈+𝑃𝛥𝑉)

𝑘𝑇(1 − (

𝜎

𝜎𝑜)

3/4)

4/3

] (2.9)

Peierls stress controlled

𝜀̇ = 𝐾 (𝜎

𝜇)

2.5𝑒𝑥𝑝 [−

(𝛥𝑈+𝑃𝛥𝑉)

𝑘𝑇(1 −

𝜎

𝜎𝑜

𝜋

2)] (2.10)

where 𝜀̇ is the strain rate of deformation, K is mechanism constant, P is the

confining pressure, ΔU and ΔV are the activation energy and activation

volume for a certain process to occur, k is the Boltzmann constant, T is

temperature, σ is applied stress, σo is the stress at 0 K and p and q are

parameters depending upon the nature of obstacle. For regularly arranged

obstacles (Eq. 2.8) and for Peierls resistance controlled glide (Eq. 2.10)

these are taken as 1, and for lattice resistance controlled glide these have got

the best values as 3/4 and 4/3 respectively (Verrall et al. 1977).The 0 K term

σo is in fact a pressure dependent term (Karato 2008), but since this value

can be expected to be high compared with the differential stress values

applied, this effect of pressure is neglected here.

29

These Equations (2.8-2.10) suggest that for positive activation volume,

the pressure will reduce the strain rate, in other words, the material will be

stronger at higher confining pressure. According to Karato (2008), the

pressure dependence of glide can be expected to be less than that of

conventional power law (Eq. 2.1).

In order to actually use the effect of pressure on flow stress to evaluate

the creep controlling mechanism, the pressure (and temperature)

dependence of the shear modulus has to be taken into account. The

following relationship is applied (based on Clark 1966, Simmons & Wang

1971, Frost & Ashby 1982):

𝜇 = 18199 + 1.342𝑃 − 9.94𝑇 (2.11)

where μ is the shear modulus in MPa, P is the confining pressure in MPa

and T is the temperature in Kelvin.

2.3 METHOD

2.3.1 Sample preparation

The salt samples were prepared artificially in the laboratory. Analytical

quality sodium chloride, powder salt was obtained from Merck salt

company, with an average grain size in the range 200-400 m. An amount

of 50 gram was weighed and placed in vacuum chamber with a ~ 1.5 gm of

water for 12 hours, in order to moisturize it to less than 1.0 wt. % water

content. The moisturized powder was sealed in rubber sleeves after

evacuation, followed by cold pressing at 100 MPa confining pressure for

one hour. The cold pressed rough cylindrical shaped salt samples were

30

machined down to the required dimension of 25 mm length and 10 mm

diameter. The cylindrical samples were subsequently sealed in FEP

(Fluorinated Ethylene Propylene) sleeves, enclosed by two specially

designed steel end pieces provided with a valve which allowed evacuation

of the sleeve. The evacuated and sealed assembly was placed inside a high

pressure vessel at 100 MPa confining pressure and 150 oC for annealing for

one week, to allow ‘Hot Isostatic Pressing’ (HIPing). After annealing, the

samples were measured for their volume and mass, to calculate density and

porosity. This procedure of sample preparation resulted in dense samples

(99.3 % of the theoretical density. The annealed samples were then dried in

a continuous, dry argon gas flow atmosphere, at 520 oC for 12 hours,

applying a very slow heating and cooling rate of 0.1 oC min

-1. The samples

obtained were ultra-dry with a water content varying between 1 to 10 ppm

(measured using FTIR spectroscopy). Each dried sample was finally

encapsulated between hard steel end pieces in soft metal jackets (Indium for

temperature ≤ 125 oC, Lead for temperature up to 250

oC and zinc for 350

oC) to avoid contamination and penetration of the confining medium into the

sample during the triaxial testing.

2.3.2 Deformation apparatus, testing and data processing

The experimental testing of the salt samples was done using an axial

symmetric, horizontally mounted Instron 1362 frame loading samples

confined within a 1.0 GPa capacity argon gas medium, volume

compensated, vessel (so called Gas Apparatus). It is equipped with two load

cells with 100 kN capacity; one external for control purposes and the other

internal to allow sample load to be measured without the uncertainty of seal

friction. Both cells had 20 N resolutions and are accurate to within ± 0.1%.

The internal load cell is pressure sensitive, and its signal was carefully

31

calibrated at various pressures, so that it could be corrected for the small gas

leakage if found. The dynamically sealed deformation piston was driven by

servo controlled electromechanical actuator of the Instron loading frame,

using software to set the deformation speed according to the desired

equivalent strain rate value for a particular experiment. The pressure is

measured using a strain gauge type pressure transducer with a resolution of

.01 MPa. The deformation/shortening of the sample was measured using an

externally mounted standard linear variable differential transformer

(LVDT), +/- 50 mm range, 0.1% linearity and 0.05 m resolution (also used

by the Instron position controller). The Gas Apparatus is equipped with an

internal three zone furnace placed around the sample and the temperature on

the sample was controlled with a three term (PID) controller using a type-S

thermocouple close to the furnace kanthal windings. Measurement of

sample temperatures and gradient was done by using three type-S

thermocouples around the sample jackets. Maximum gradient along the

sample was recorded as to be within maximum of 3 oC. The cooling of the

pressure vessel was done using continuous flow of cooling water maintained

at 21 oC. For more detailed description of the deformation apparatus, see

McDonnell et al. (1999) and De Bresser (2002).

The tests were performed in the temperature range of 22-350 oC (0.27 -

0.58 T/Tm), using argon gas as a confining medium in the pressure range of

50-600 MPa. Strain rates ranged 5×10-7

to 10-4

s-1

). Maximum natural strain

achieved during deformation was in the order of 0.25. For all individual

tests, the temperature was kept constant. The main focus of this study was to

investigate the pressure sensitivity of the strength of salt. For that, three

types of experiments were carried out:

32

a) Constant displacement rate approaching constant strain rate tests at

different but constant confining pressures (50, 300 and 600 MPa).

b) Strain rate stepping tests using (4×10-7

- 4×10-6

- 4×10-5

- 4×10-6

-

4×10-7

s-1

) at different but constant confining pressures (50, 300 and

600 MPa). In these tests, the strain rate was first instantaneously

increased from 4×10-7

to 4×10-6

to 4×10-7

and then decreased again

to 4×10-7

and 4×10-7

. The subsequent strain rate was employed by

stopping the piston and switching to the new strain rate (by adjusting

the equivalent speed of deformation piston). This was done quickly

(~ 5 s) to avoid the relaxation of the stress already given to the

sample from the last step.

c) Pressure stepping test (stepping down) at fixed strain rate. For each

confining pressure step, the sample was deformed through natural

strain of 0.02 - 0.03, subsequently the piston was pulled back and

pressure was reduced to next lower value and deformation was

started once again, after stability of the signals were achieved.

The data during the test, including confining pressure, load on the

sample, temperature and position of deforming piston were logged every 10

seconds at 16-bit precision. At the end of test, the sample was unloaded

immediately to avoid relaxation of the sample under load. The data were

processed to calculate the stress, strain and strain rate of the sample, taking

into account the change of area during shortening of sample (assuming

homogeneous deformation at constant volume). For the jacket correction,

the cylinders of the same metals as that of jackets, i.e. indium (In) for the

temperature range of 25-125 oC, lead (Pb) for the temperatures of 250

oC

and zinc (Zn) for 350 oC were deformed at similar conditions of

temperatures and strain rates. The stress data were used to calculate the

33

equivalent force on jacket according to its thickness, and subsequently the

force on jacket was removed to get the real force on the sample.

The experimental data on salt samples were corrected for the stiffness of

the machine, the pressure dependence of the load cell signal (in case of

pressure stepping), the jacket strength, the effect on the load cell output

signal in case of occasional small gas leaks, and drift in the internal load

signal if observed by correcting its base signal using slope from calibration

tests. From the reduced data and application of all the corrections, the errors

in the final calculated stress are about 2.5 % (De Bresser 2002).

2.3.3 Preparation for microstructural study

The deformed samples were carefully removed from their jackets and

selected samples were prepared for microstructural study. These samples

were cut along their length using a diamond tipped saw and using so-called

’evaporating oil’ (Shell light oil (organic), S4919) as lubricant. The sample

halves thus obtained were bonded onto glass slides and were polished, first

by SiC papers and then finalized to an optical finish of 1.0 micron using

diamond-oil suspension (Metadi, Buehler). To reveal the microstructure,

samples were treated with a chemical etchant (95% saturated NaCl solution

+ 5% de-ionized water + 8.0 gm FeCl3 per litre) followed by rinsing with n-

hexane spray and drying using hot air. The images were made using a Leica

optical polarization microscope equipped with high resolution digital image

capturing and analysis system.

34

2.4 RESULTS

2.4.1 Mechanical data

The results of all experiments performed on the dry salt samples are given in

Table 2.1. Below, the results obtained for the tests at different temperatures,

pressures and strain rates are presented in detail.

(i) Experiments at room temperature (22 oC)

Two experiments (N108 and N119) were performed to determine the

strength of the material at room temperature, at 50 and 600 MPa confining

pressures and constant strain rate (10-4

s-1

). The differential stresses thus

obtained are plotted against natural strain in Figure 2.1. The Figure shows

that the samples behaved elastically at start, at natural strains up to 0.01,

followed by plastic deformation pre-dominated by strain hardening until the

end of the test at a natural strain of about 0.17. Overall, the sample

deformed at a confining pressure of 600 MPa is slightly stronger than the

one at 50 MPa, but the difference decreases towards higher strain.

(ii) Experiments at 125-350 oC

At 125 oC, 12 experiments were performed (see Table 2.1). The pressure

sensitivity of the flow stress was tested using two sets of constant strain rate

tests (1×10-6

and 10-4

s-1

) at constant pressures (50 to 600 MPa), and one

pressure stepping test (stepping down: 600 – 450 – 300 – 150 – 50 MPa) at

constant strain rate 1×10-6

s-1

(Figure 2.2a & 2.2b). All stress-strain curves

show strain hardening, though the hardening rate appears to decrease

towards higher strain (up to 0.17), in particular at the slower strain rate. The

salt samples were consistently found stronger at higher confining pressures.

35

Figure 2.1. Stress strain graph of room temperature (22 oC) experiments, showing

very little difference in strength of salt as a function of pressure

For the deformation at 1×10-6

s-1

, the increase in the maximum flow stress

was observed to be 63% (i.e. from an average of 19 to 31 MPa) for

confining pressures of 50 and 600 MPa respectively. In the pressure

stepping test at constant strain rate 10-6

s-1

(Fig. 2.2b), the flow stress of salt,

measured at the end of each step, was found to decrease from ~ 24.2 MPa to

20.9 MPa for a stepwise pressure drop from 600 to 50 MPa. In other words,

the results of the pressure stepping tests are consistent with those of the tests

at constant pressure (Fig. 2.2a), namely a higher strength at higher confining

pressure.

At faster strain rate of (10-4

s-1

), samples were tested using 50, 300 and

600 MPa confining pressures, and the salt presented positive pressure

sensitivity, i.e. salt appeared stronger at higher

0

10

20

30

40

50

60

70

0.00 0.05 0.10 0.15 0.20 0.25

Dif

fere

nti

al S

tres

s [M

Pa]

Natural strain

Room temperature

𝜀̇ = 10-4 s-1

N108_50 MPa

N119_600 MPa

36

(a)

(b)

0

5

10

15

20

25

30

35

0.00 0.05 0.10 0.15 0.20 0.25

Dif

fere

nti

al S

tres

s [M

Pa]

Natural strain

N74_600 MPa

N81_600 MPa

N78_300MPa

N98_150 MPa

N80_50 MPa

N75_50 MPa

Temp = 125 oC

𝜀̇ = 10-6 s-1

0

5

10

15

20

25

30

35

0.00 0.05 0.10 0.15 0.20 0.25

Dif

fere

nti

al S

tres

s [M

Pa]

Natural strain

N83_Pressure stepping

Temp = 125 oC

𝜀̇ = 10-6 s-1

600 MPa 450 300 150 50

37

(c)

(d)

Figure 2.2. Differential stress vs. natural strain at temperature 125 oC, a) pressure

sensitivity at strain rate 10-6

s-1

, b) pressure stepping test at 10-6

s-1

, c) pressure

sensitivity at strain rate 10-4

s-1

, d) strain rate stepping tests (step up followed by

step down) at fixed confining pressures of 50, 300 and 600 MPa.

0

5

10

15

20

25

30

35

40

0.00 0.05 0.10 0.15 0.20 0.25

Dif

fere

nti

al S

tres

s [M

Pa]

Natural strain

N104_600 MPa

N106_300 MPa

N101_50 MPa

N102_50 MPaTemp = 125 oC

𝜀̇ = 10-4 s-1

0

5

10

15

20

25

30

35

40

0.00 0.05 0.10 0.15

Dif

fere

nti

al S

tres

s [M

Pa]

Natural strain

N109_600 MPa

N105_300 MPa

N103_50 MPaTemp = 125 oC

4×10-7

4×10-7 4×10-6

4×10-6 4×10-5

38

confining pressure (Fig. 2.2c). For the two extreme pressures of 50 and 600

MPa, the flow stress appeared to be 30.2 and 37.9 MPa respectively, i.e. salt

was found 27% stronger at 600 MPa than at 50 MPa.

At similar temperature of 125 oC, three strain rate stepping experiments

(4×10-7

- 4×10-6

- 4×10-5

- 4×10-6

- 4×10-7

s-1

) were performed at confining

pressures of 50, 300 and 600 MPa (Fig. 2.2d). The samples showed positive

strain rate sensitivity, i.e., were stronger at higher strain rates.

Within each step, the samples showed limited strain hardening and

appeared stronger at repeat strain rate steps at higher strains (compare stress

strain segments of same strain rate at low and higher natural strain, Fig.

2.2d).

At 250 oC, three samples were tested at constant confining pressures of

50, 300 and 600 MPa, at constant strain rate of 10-6

s-1

(Table 2.1). All

stress-strain curves show near steady state flow behaviour. As was found at

125 oC, the strength of the samples was higher at higher confining pressures

(Fig. 2.3a). Maximum natural strain imparted to individual sample was

~0.16. The final value of the flow stress at 50, 300 and 600 MPa

confinement was found to be 8, 12 and 15 MPa, respectively (Table 2.1), i.e.

a total of 88% increase in strength of the salt samples if pressure is increased

from 50 to 600 MPa, at strain rate of 10-6

s-1

. The strain rate sensitivity was

tested at a constant pressure of 50 MPa by performing a 5-steps (4×10-7

-

4×10-6

- 4×10-5

- 4×10-6

- 4×10-7

s-1

) strain rate stepping test. The sample

was deformed through 0.02-0.03 natural strain for each step (Fig. 2.3b).

Figure 2.3b shows that the strength of the salt was higher for faster

deformation steps. The slow deformation at 4×10-7

s-1

shows behaviour

approaching steady state, at the faster deformations steady state could not be

reached within the limited strain imposed.

39

At 350 oC, one pressure stepping experiment (600 – 300 – 50 MPa) was

performed at a constant strain rate of 4×10-5

s-1

(Fig. 2.4a). For each step,

the sample was deformed through a natural strain of 0.06-0.07. The

maximum strength of the salt at 600 MPa was found to be 10 MPa, whereas

the strength at both 300 and 50 MPa was found to be 8 MPa, i.e. in this

experiment, no significant difference in strength was resolved for 300 and

50 MPa confinements. Three strain rate stepping tests were performed at

confining pressures of 50, 300 and 600 MPa. Each test consisted of five

strain rate-steps (4×10-7

- 4×10-6

- 4×10-5

- 4×10-6

- 4×10-7

s-1

) (Fig. 2.4b).

The sample showed positive strain rate dependence, i.e. higher strength at

faster deformation steps. Whereas no distinct difference could be resolved

for the tests performed at 50 and 300

(a)

0

2

4

6

8

10

12

14

16

18

0.00 0.05 0.10 0.15 0.20

Dif

fere

nti

al S

tres

s [M

Pa]

Natural strain

N145_600 MPa

N146_300 MPa

N142_50 MPa

Temp = 250 oC

𝜀̇ = 10-6 s-1

40

(b)

Figure 2.3. Differential stress vs. natural strain at temperature 250 oC, a) strain rate

10-6

s-1

, b) strain rate stepping at confining pressure of 50 MPa.

(a)

0

2

4

6

8

10

12

14

16

18

0.00 0.05 0.10 0.15 0.20

Dif

fere

nti

al S

tres

s [M

Pa]

Natural strain

𝜀̇ _stepping

Temp = 250 oC

𝑃 = 50 MPa

4×10-7

4×10-6

4×10-7

4×10-5

4×10-6

0

2

4

6

8

10

12

14

16

18

0.00 0.05 0.10 0.15 0.20

Dif

fere

nti

al S

tres

s [M

Pa]

Natural strain

N164_P_stepping

Temp = 350 oC

𝜀̇ = 4×10-5 s-1

600 MPa 300 50

41

(b)

Figure 2.4. Differential stress vs. natural strain at temperature 350 oC, a) pressure

stepping at strain rate of 4×10-5

s-1

, b) strain rate stepping tests (stepping up

followed by down stepping).

(a)

0

2

4

6

8

10

12

14

16

18

0.00 0.05 0.10 0.15 0.20

Dif

fere

nti

al S

tres

s [M

Pa]

Natural strain

N161_50 MPa

N162_300 MPa

N163_600 MPa

Temp = 350 oC

𝜀̇ stepping

-3.8

-3.6

-3.4

-3.2

-3.0

-2.8

-2.6

-2.4

-2.2

0 100 200 300 400 500 600

Lo

g(σ

/µ)

Confining Pressure P [MPa]

22 ºC, 1E-4 s^-1 125 ºC, 1E-4 s^-1

125 ºC, 1E-6 s^-1 250 ºC, 1E-6 s^-1

350 ºC, 4E-5 s^-1 350 ºC, 4E-6 s^-1

350 ºC, 4E-7 s^-1

10-4 s-1

10-6 s-1

4×10-5 s-1

4×10-7 s-1

10-4 s-1

10-6 s-1

4×10-6 s-1

42

(b)

Figure 2.5. Pressure sensitivity of flow stress, normalized to pressure and

temperature corrected shear modulus, at natural strains of, a) 0.12, b) 0.16.

MPa confinements, perhaps it was beyond the limits of the measurements.

The flow stress presented steady state behaviour for all steps.

(iii) Pressure sensitivity of normalized flow stress at different

strain values

In Figures 2.5a and 2.5b, the normalized flow stress is plotted against the

confining pressure by taking the data at two values of natural strain, i.e. 0.12

and 0.16. The Figure forms a summary of the observations described above,

namely that strength of the synthetic dry rock samples is higher at higher

confining pressure, in particular at slow strain rate and high temperature.

-3.8

-3.6

-3.4

-3.2

-3.0

-2.8

-2.6

-2.4

-2.2

0 100 200 300 400 500 600

Log(σ

/µ)

Confining Pressure P [MPa]

22 ºC, 1E-4 s^-1 125 ºC, 1E-4 s^-1

125 ºC, 1E-6 s^-1 250 ºC, 1E-6 s^-1

350 ºC, 4E-5 s^-1 350 ºC, 4E-7 s^-1

350 ºC, 4E-6 s^-1

10-4 s-1

10-6 s-1

4×10-5 s-1

4×10-7 s-1

10-4 s-1

10-6 s-1

4×10-6 s-1

43

(iv) General inferences from the observed pressure dependence

of creep

The observed pressure dependence of the flow behaviour of the dry salt is

illustrated by the stress–strain curves of Figures 2.1-2.4, for room

temperature, 125, 250 and 350 oC, respectively. The stress-strain curves

demonstrate limited pressure sensitivity at room temperature, but a distinct

effect of pressure at all higher temperatures. The effect of pressure is also

visualized in Figures 2.5a-b and 2.6a-f plotting the maximum stress values

obtained per test, normalized to the pressure and temperature corrected

shear modulus (see Eq. 2.11), against confining pressure, strain rate and

reciprocal temperature (1/T). The sensitivity of the differential stress to

strain rate clearly changes with increasing temperature, illustrated by a

change in slope in the graph, while the effect of pressure on this sensitivity

is rather limited (compare Figs. 2.6a, b & c). Figures 2.6d-f show that the

logarithmic normalized stress is not linearly dependent on the reciprocal

temperature. This non-linear dependence is visible at all pressures tested.

These observations on the sensitivity of the differential stress, as a function

of strain rate (Figs. 2.6a-c) and temperature (Figs. 2.6d-f), suggest that a

change in rate controlling mechanism occurs going from room temperature

22 oC to 350

oC. Note also in this respect that all stress-strain curves at RT-

125 o

C show strain hardening, while near steady state behaviour was

observed at 250-350 oC.

44

(a) Log-log plots of flow stress, normalized to shear modulus, vs deformation rates

at fixed pressure (50 MPa) and at: 125, 250 and 350 oC. Higher temperature tests

are more sensitive to strain rates.

(b) Log-log plots of flow stress, normalized to shear modulus, vs deformation rates

at fixed pressure (300 MPa) and at: 125 and 350 oC. Higher temperature tests are

more sensitive to strain rates. (Only one point at 250 oC for 300 MPa confining

pressure, no trend).

-3.8

-3.6

-3.4

-3.2

-3.0

-2.8

-2.6

-2.4

-2.2

3 4 5 6 7

Log (

σ/μ

)

-Log (Strain rate

125 ºC 50 MPa

250 ºC 50 MPa

350 ºC 50 MPa

[s-1])

-3.8

-3.6

-3.4

-3.2

-3.0

-2.8

-2.6

-2.4

-2.2

3 4 5 6 7

Lo

g (

σ/μ

)

-Log (strain rate [s-1])

125 ºC 300 MPa

250 ºC 300 MPa

350 ºC 300 MPa

45

(c) Log-log plots of flow stress, normalized to shear modulus, vs deformation rates

at fixed pressure (600 MPa) and at: 125 and 350 oC. Higher temperature tests are

more sensitive to strain rates. (Only one point at 250 oC for 600 MPa confining

pressure, no trend).

(d) Log of flow stress, normalized to shear modulus, vs reciprocal temperature at

fixed confining pressure 50 MPa. The slope of data varies with temperature.

-3.8

-3.6

-3.4

-3.2

-3.0

-2.8

-2.6

-2.4

-2.2

3 4 5 6 7

Log (

σ/μ

)

-Log (strain rate [s-1])

125 ºC 600 MPa

250 ºC 600 MPa

350 ºC 600 MPa

-3.8

-3.4

-3.0

-2.6

-2.2

0.0015 0.0025 0.0035

Lo

g (

σ/μ

)

1/T [K-1]

1.00E-06

1.00E-04

4.00E-07

4.00E-06

4.00E-05

10-6 s-1

10-4 s-1

4×10-7 s-1

4×10-6 s-1

4×10-5 s-1

46

(e) Log of flow stress, normalized to shear modulus, vs reciprocal temperature at

fixed confining pressure 300 MPa.

(f) Log of flow stress, normalized to shear modulus, vs reciprocal temperature at

fixed confining pressure 600 MPa. The slope of data varies with temperature

Figure 2.6. Sensitivity of differential stress (normalized by shear modulus, μ), a, b,

c) strain rate sensitivity at confining pressures of 50, 300 and 600 MPa at various

temperatures, d, e, f) 1/T plots at 50, 300 and 600 MPa confining pressures at

various strain rates.

-3.8

-3.4

-3.0

-2.6

-2.2

0.0015 0.0025 0.0035

Log (

σ/μ

)

1/T [K-1]

1.00E-06

1.00E-04

4.00E-07

4.00E-06

4.00E-05

10-6 s-1

10-4 s-1

4×10-7 s-1

4×10-6 s-1

4×10-5 s-1

-3.8

-3.4

-3.0

-2.6

-2.2

0.0015 0.0025 0.0035

Log (

σ/μ

)

1/T [K-1]

1.00E-06

1.00E-04

4.00E-07

4.00E-06

4.00E-05

10-6 s-1

10-4 s-1

4×10-7 s-1

4×10-6 s-1

4×10-5 s-1

47

Table 2.1: Mechanical data with conditions of tests

Test T

[oC]

P

[MPa] 𝜀̇

[s-1

]

σ

[MPa] ε

H2O

[ppm]

N108 25 50 10-4

64 0.18 0.9

N119 25 600 10-4

63.6 0.18 13.7

N75 125 50 10-6

18.7 0.16 20

N80 125 50 10-6

19.6 0.16 4.3

N94 125 150 10-6

24.8 0.15 2.2

N98 125 150 10-6

22.3 0.16 3.8

N78 125 300 10-6

25.9 0.17 5.3

N99 125 450 10-6

24.4 0.16 ---

N74 125 600 10-6

32.7 0.17 2

N81 125 600 10-6

31.7 0.17 21

N83* 125 600 10-6

24.2 0.05 10

N83* 125 450 10-6

22.7 0.08 10

N83* 125 300 10-6

23.6 0.11 10

N83* 125 150 10-6

21.9 0.14 10

N83* 125 50 10-6

20.9 0.17 10

N101 125 50 10-4

30.2 0.16 9

N102 125 50 10-4

28.8 0.16 18.3

N106 125 300 10-4

33.1 0.16 8.9

N104 125 600 10-4

37.9 0.16 1.1

N103** 125 50 4×10-7

18.2 0.16 8.4

N103** 125 50 4×10-6

23.5 0.16 8.4

N103** 125 50 4×10-5

29.4 0.16 8.4

N105** 125 300 4×10-7

21 0.16 8.4

N105** 125 300 4×10-6

27.5 0.16 11.1

N105** 125 300 4×10-5

34.2 0.16 11.1

N109** 125 600 4×10-7

22 0.16 13.7

N109** 125 600 4×10-6

29.4 0.16 13.7

N109** 125 600 4×10-5

35 0.16 13.7

48

Table 2.1: contd.

Test T

[oC]

P

[MPa] 𝜀̇

[s-1

]

σ

[MPa] ε

H2O

[ppm]

N147** 250 50 4×10-7

8.3 0.16 5.1

N147** 250 50 4×10-6

10.5 0.16 5.1

N147** 250 50 4×10-5

14.8 0.16 5.1

N142 250 50 10-6

7.7 0.16 8.6

N146 250 300 10-6

12 0.16 6.4

N145 250 600 10-6

14.8 0.16 6.6

N164** 350 600 4×10-5

10.9 0.16 2

N164** 350 300 4×10-5

8.2 0.16 2

N164** 350 50 4×10-5

7.8 0.16 2

N161** 350 50 4×10-7

2.8 0.16 2

N161** 350 50 4×10-6

4.7 0.16 2

N161** 350 50 4×10-5

6.8 0.16 2

N162** 350 300 4×10-7

2.8 0.16 4

N162** 350 300 4×10-6

4.2 0.16 4

N162** 350 300 4×10-5

7.9 0.16 4

N163** 350 600 4×10-7

4 0.16 5

N163** 350 600 4×10-6

5.2 0.16 5

N163** 350 600 4×10-5

11 0.16 5

T: test temperature

P: confining pressure

𝜀̇: strain rate

σ: differential stress measured at the end of individual step or test

ε: maximum value of natural strain in a test

*P-stepping experiment

**strain-rate-stepping experiment

Note: Water content was measured at the end of test

49

Figure 2.7. Differential stress vs strain rate data taken from Table 2.1. Note

the change in n-value with pressure and temperature.

(v) n-value (stress exponent)

In order to obtain a first order impression of the sensitivity of the flow stress

on strain rate, the flow stress obtained at the end of each experiment is

plotted against strain rate in log-log space in Figure 2.7. A conventional

power law of the type 𝜀̇ = 𝜎𝑛 was used to determine the stress exponent n

for the individual isotherms at confining pressures of 50, 300 and 600 MPa.

The n-value corresponds to -1/slope of the best fit lines. As only one strain

rate was applied at room temperature, no n-value could be determined at this

condition. The data of 125 oC shows that the n-value increases with

pressure, giving 7.4 (± 2.2), 11.4 (± 1.5) and 15.3 (± 7.8) for 50, 300 and

600 MPa confining pressures respectively. For 250 oC, the data were only

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

3 4 5 6 7

Log (

flow

str

ess[

MP

a])

-Log (strain rate[s-1])

125 ºC 50 MPa 250 ºC 50 MPa 350 ºC 50 MPa



7.4

7.1

4.8

11.4

15.3

t

4.3

4.4

50

available for 50 MPa confinements, and n-value came out to be 7.1 (± 1.6).

The n-value for 350 oC came out to be in 4.8 (± 0.4), 4.3 (± 0.4) and 4.4 (±

0.8) at confining pressure of 50, 300 and 600 MPa. So overall, the n-value

has a decreasing trend with temperature, and the error in the value is higher

for higher confining pressure.

2.4.2 Microstructures

The microstructures of selected deformed salt samples are shown in Figure

2.8. The undeformed (Fig. 2.8a) microstructure shows a dense aggregate of

polygonal and cubic grains with an average size of ~300 μm. The straight

grain boundaries are often intersecting at high angle ~120o, with no

evidence of intra-crystalline deformation inherited from the sample

preparation. A few holes are visible in and at boundaries of grains, probably

representing limited porosity.

The microstructures of the samples tested at different confining pressures

and otherwise similar conditions of temperature, strain and strain rates, did

not show any difference, e.g. Figure 2.8b and 2.8c are microstructures of

samples deformed at 600 and 50 MPa respectively.

Figures 2.8c-f show samples tested at 50 MPa confining pressure at

different temperature. The microstructure of the sample deformed at room

temperature (Fig. 2.8c) shows grains full of small scale elongated sub-grains

(< 10 μm) with following somewhat wavy trajectories through the grains.

No evidence has been found of grain boundary bulging or more pervasive

recrystallization.

The microstructures of the samples at tested at 125 oC are shown in

Figure 2.8d-e, deformed at 10-6

and 10-4

s-1

respectively. The microstructures

51

show flattened grains with slightly elongated sub-grains that appear to be

aligned in wavy arrays or deformation bands. In some grains, equi-axed sub-

grains are visible. No signs were found of recrystallized grains, neither at

grain boundaries nor internally in grains. A few grains do not show much

sub-grain activity (e.g. Fig 2.8b, c & e), which can be associated to

heterogeneous etching of the sections.

The micrographs of the samples deformed at 250 and 350 oC (Figs. 2.8f-

g) show a well-defined substructure of close-to-equidimensional sub-grains,

with average size of ~50 μm, in grains with straight grain boundaries. The

sub-grains appearing near the grain boundary appear to have a somewhat

smaller size (~20 μm) than the ones on the centre of the grains,

demonstrating heterogeneous straining.

(a)

52

(b)

(c)

53

(d)

(e)

54

(f)

(g)

55

Figure 2.8. Microstructures of the dry salt samples. Deformation/shortening

direction is horizontal, all deformed microstructures have similar confinement

condition of 50 MPa and the scale bar is also similar 50 μm a) undeformed or

reference sample, showing annealed structure with well-defined boundaries

intersecting at high angle ~120o with average grain size of 300 μm, b-c) N108 (Pc =

50 MPa), N119 (Pc = 600 MPa), T = 22 oC, 𝜀̇ = 1×10

-4 s

-1, 𝜀𝑚𝑎𝑥 = 0.18, flattened

grains with elongate sub-grains often aligned in wavy arrays or deformation bands,

d) N75, T = 125 oC, 𝜀̇ = 1×10

-6 s

-1, 𝜀𝑚𝑎𝑥 = 0.16, flattened grains, with a few equi-

axed sub-grains, no signs of recrystallized grains, e) N101, T = 125 oC, 𝜀̇ = 1×10

-4 s

-

1, 𝜀𝑚𝑎𝑥 = 0.16, grains with different orientation as revealed by light reflection, no

sign of grain bulging or recrystallization at grain boundaries or inside the grains, f)

N142, T = 250 oC, 𝜀̇ = 1×10

-6 s

-1, 𝜀𝑚𝑎𝑥 = 0.16, polygonised with clear grain

boundaries, each bigger grain has developed sub-grain of an average size of 50 μm,

no wavy boundaries as seen in lower temperature deformed samples, the

development of a new grain formation is also obvious at the middle of

microstructure, g) N161, T = 350 oC, 𝜀̇ = 4×10

-5 s

-1, 𝜀𝑚𝑎𝑥 = 0.16, comparatively less

dense in sub-grain formation than 250 oC and inferred (Franssen 1994) to show

dislocation climb features, no signs of wavy lines.

2.5 DISCUSSION

The change in characteristic microstructures when going from room

temperature to 350 oC, as described in section 2.4.2, supports the

interpretation that the rate controlling mechanism changes. The ill-defined

sub-grain structure observed at the low temperatures appears to rule out

climb-controlled creep at those conditions, while that mechanism may

become more prominent at higher temperature. The wavy features seen at

temperature 22-125 oC may correspond to structures seen in other deformed

salts (e.g. Skrotzki et al. 1981, Skrotzki & Welch 1983, Franssen 1994)

where they have been interpreted as indicating cross slip of screw and jogs

of edge dislocations. Whereas the well-defined boundaries of polygonal

grains and the newly formed strain free sub-grains at higher temperature

(250 to 350 oC), are representative of cross slip and dislocation climb

process (Skrotzki et al. 1981, Franssen 1994).

56

In the next part of this Discussion, different models for dislocation creep

will be tested against the data in order to investigate which are the

mechanisms that most likely explain the behaviour seen at the lower and

higher temperature ranges tested. In particular, the observed effect of

pressure will be used to discriminate between different models, focussing on

dislocation glide, cross-slip and climb. The experimental data will be fit to

the model equations applying non-linear regression best fitting. The

resulting values for the various parameters of the models will be put against

constraints from the literature.

2.5.1 Results of non-linear regression analysis

(i) Climb controlled creep

Non-linear regression of the data was carried out applying Equation (2.1),

testing three temperature ranges, 125 to 350 oC, 125 to 250

oC and 250 to

350 oC. The best fitting parameters are listed in Table 2.2. The best fit for

125-350 oC gives poor result in terms of quality of fit. This was as expected,

given the gradual change in stress exponents n with temperature (Fig. 2.5)

and confirms that a single climb controlled creep mechanism cannot explain

the behaviour observed in the dry rock salt. For temperatures 125 to 250 oC,

the quality of fit is better, but the n-value obtained (8.9 ± 0.6) is too high to

be supportive of climb controlled creep, in which values of 3-4.5 are to be

expected in case of lattice diffusion control of climb, or 6.5 if dislocation

core (pipe) diffusion plays a role (Frost & Ashby 1982, Poirier 1985, De

Bresser 1991). The most reasonable result was found for the temperature

range of 250 to 350 oC, both in terms of quality of fit and considering the

fitting values for the model parameters. The stress exponent of power law

came out to be 4.7 ± 0.3, which is in agreement with the theory of climb

57

controlled creep (Weertman 1968, Sherby & Weertman 1979, Poirier 1985)

and also corresponds well to values obtained previously in other studies

(Franssen 1994, dry salt in the T-range of 250-780 oC, Ter Heege et al.

2005a on wet rock salt in the T-range of 75 to 250 oC). The value obtained

for the activation energy, 126 ± 7 kJmol-1

is also reasonably close to values

reported in literature for short circuit diffusion through dislocation cores,

pipe diffusion (Wawersik & Zeuch 1986, Franssen 1994). The n-value

obtained is slightly higher than the value fit with standard dislocation climb

flow law (i.e. 4.5). The activation energy for halite is normally associated

with diffusion of the slowest moving ionic species (Cl-), and the value

reported is 146 kJmol-1

for dislocation core diffusion (Barr et al. 1960), or in

the range of 103 to 155 kJmol-1

(Wawersik and Zeuch 1986, Franssen

1994). This energy also looks in good agreement with the predicted value

that, activation energy for core diffusion lies in the range of 0.5 to 0.7 of

activation energy of lattice diffusion of the slowest moving Cl- ion which is

Table 2.2. Power law, dislocation climb model best fit parameters

Temp.

[oC]

n LOGA

ΔV

(×10-29

)

[m3]

ΔV/Vm

ΔU

(×10-19

)

[J]

ΔU

[kJmol-1

]

R2

125-

350

5.4

(±0.5)

10.9

(±2.3)

1.3

(±0.4)

0.30

(±0.09)

1.1

(±0.1)

66.9

(±7.0) 0.55

ONLY

125

and

250

8.9

(±0.6)

22.2

(±2.7)

2.4

(±0.4)

0.54

(±0.08)

1.3

(±0.1)

76.7

(±7.7) 0.77

ONLY

250

and

350

4.7

(±0.3)

14.4

(±1.4)

2.9

(±0.4)

0.66

(±0.08)

2.1

(±0.1)

125.9

(±7.2) 0.90

n:power law stress exponent

LOGA: constant

ΔV: activation volume

ΔU: activation energy

R2: correlation coefficient

58

Table 2.3. Cross-slip dissociation control model best fit parameters

Temp.

[oC]

LOGK γo

[Jm-2

] εo α R

2

22-125- 11.4

(± 1.2 )

0.026

(± 0.002)

0.006

(±0.004)

0.58

(± 0.06) 0.80

125-350 4.8

(± 0.3)

0.040

(± 0.002)

-0.017

(± 0.010)

1.74

(± 0.09) 0.77

ONLY 125

and 250

4.2

(± 0.5)

0.050

(± 0.005)

-0.044

(± 0.020)

1.95

(± 0.20) 0.77

ONLY 125

and 350

4.8

(± 0.3)

0.040

(±0.0.003)

-0.018

(± 0.020)

1.73

(± 0.09) 0.79

LOGK: constant

γo: stacking fault energy at atmospheric pressure

εo: maximum relative dilatation for a fault with Burgers vector b/2

α: geometrical constant


Table 2.4.Dislocation glide model best fit parameters after non-linear regression

analyses

Glide

mode

Temp.

[oC]

LOG

K

ΔV

×10-29

[m3]

σo

[MPa]

ΔV/Vm

ΔU

×10-19

[J]

ΔU

[kJmol-1

]

R2

Lat

tice

resi

stan

ce

con

tro

lled

22

-12

5

14.1

(±1.5)

3.0

(±0.5) 219

(±11.4) 0.66

(±0.11)

1.5

(±0.1)

138.2

(±14.1) 0.83

Ob

stac

le

con

tro

lled

22

-12

5

13.1

(±1.8)

2.8

(±0.5)

139.0

(±4.4)

0.63

(±0.10)

2.8

(±0.3)

168.6

(±15.5) 0.81

Pei

erls

resi

stan

ce

con

tro

lled

22

-12

5

17.1

(±1.7)

2.6

(±0.4)

238.1

(±8.3)

0.58

(±0.10)

2.3

(±0.2)

138.5

(±15.1) 0.82

LOGK: constant

ΔU: activation energy

ΔV: activation volume

σo: stress at 0 K


59

205-221 kJmol-1

(Franssen 1994, Ter Heege et al. 2005a). The activation

volume ΔV parameter for halite is not well constrained in literature, but as

theory of ion-vacancy diffusion suggests that annihilation of vacancy and

ion can cause atomic scale expansion to restore the lattice, so the value

0.66Vm looks reasonable for the associated dislocation climb recovery under

discussion. This obtained activation volume value (0.66Vm) lies in close

approximation to the value reported in literature for metals (e.g. Werner &

Mehrer 1983, Mehrer 2011), where authors have reported that for fcc

metals, the activation volume may lie in the range of 0.6Ω to 1Ω (Ω is the

atomic volume of the metal).

On the basis now of the mechanical behaviour observed (near steady

state stress-strain and stress-strain rate trends), the microstructural

observations, and the best fitting analysis, it is concluded that dislocation

climb is the rate controlling mechanism in the temperature range of 250-350

oC. The flow law describing the behaviour is:

𝜀̇ = 2.51 × 1014 (𝜇

𝑇) (

𝜎

𝜇)

4.7𝑒𝑥𝑝 [−

2.1×10−19+𝑃(0.66𝑉𝑚)

𝑘𝑇] (2.12)

Please note that in Equation 2.12, pressure (P), differential stress (σ) and

shear modulus (μ), are in MPa.

(ii) Cross-Slip controlled creep

Cross-slip is a serial process of constriction and dissociation of partials

allowing dislocations to glide on planes oblique to the initial glide plane, in

order to overcome obstacle hindering glide (see section 2.2.2). Confining

pressure promotes constriction and hinders dissociation of partial

dislocations, causing faster or slower creep of the material, respectively,

60

depending on which of these two, constriction of dissociation, is the slowest

step. In the current study, the dry polycrystalline salt showed higher strength

at higher confining pressures, so the constriction part does not appear to be

rate controlling (section 2.2.2). Non-linear regression was done by using the

data with the dissociation controlled cross slip model testing four

temperature ranges, 22 to 125 oC, 125 to 350

oC, 125 to 250

oC and 250 to

350 oC. The best fit parameters are listed in Table 2.3. The values for the

stacking fault energy γo lie in the range 0.03 - 0.05 Jm-2

, which is

substantially lower than the values reported for rock salt in literature; 0.195

- 0.288 Jm-2

(Fontaine 1968, Fontaine & Haasen 1969, Mohammed &

Langdon 1974, Tasker & Bullough 1981, Skrotzki & Liu 1982). The best fit

values of the dilatation constant εo are rather small and negative, ranging -

0.044 to -0.017, whereas in previous studies the reported value of this

dilatational constant was ~0.3 (Fontaine & Haasen 1969). Given these

results, it appears unlikely that dissociation controlled cross-slip is the rate

controlling mechanism in the lower temperature range of 25-125 oC.

In conclusion, thus, neither constriction controlled cross slip, nor

dissociation controlled cross slip is likely to describe the creep behaviour of

dry rock salt at 25-350 oC.

(iii) Glide controlled creep

The best fitting results using non-linear regression for glide controlled creep

are given in Table 2.4 for the three models of glide; discrete obstacle

control, intrinsic lattice resistance including kink nucleation process, and

lattice resistance including dislocation climb (see section 2.2.3). Analysis is

confined to only one temperature range, RT-125 o

C, given that climb

controlled creep appears well established for the higher temperature range

61

250-350 oC, and cross slip is ruled out as likely controlling mechanism

overall. The quality of fit is rather good for all three models.

The fitting parameters for the obstacle controlled glide model include an

activation energy of 169 kJmol-1

and a value of 139 MPa for σo , the stress at

0 K. Verrall et al. (1977) and Frost & Ashby (1982) quote 289 kJmol-1

for

the activation energy and only 38 MPa for σo. These values deviate from the

fitting values, casting doubt on the applicability of the obstacle controlled

glide model.

The fitting parameters for the two lattice resistance models are very

much alike, with almost identical activation energies of ~138 kJmol-1

and

values of 219-238 MPa for σo. This agreement is of course related to the fact

that the model equations (section 2.2.3) are very much alike. Verrall et al.

(1977) and Frost & Ashby (1982) quote 69 kJmol-1

for the activation energy

and 272 MPa for σo. for the double kink model. No constraints are known to

the author regarding the climb-related glide model. However, the best fitting

value for the activation volume, ~0.6-0.7 of the molecular volume of halite

(Table 2.4), is of the same order of magnitude as that for climb controlled

creep described by Equation (2.1). For that reason, the glide model

involving climb is preferred above the lattice resistance kink nucleation

model. The flow law describing the behaviour of dry rocks salt in the

temperature range RT-125 oC accordingly is:

𝜀̇ = 1.26 × 1017 (𝜎

𝜇)

2.5𝑒𝑥𝑝 [−

(2.310−19+𝑃(0.58𝑉𝑚))

𝑘𝑇(1 −

𝜎

238

𝜋

2)] (2.13)

Please note that in Equation 2.12, pressure (P), differential stress (σ) and

shear modulus (μ), are in MPa.

62

The activation energy parameter fit value in the current data lies in the

range of 138-169 kJmol-1

. Verrall et al. 1977 and Frost & Ashby 1982

proposed the activation energy in the range of 69 to 289 kJmol-1

, where the

lower 69 kJmol-1

value is proposed for Peierls/lattice resistance controlled

glide and 289 kJmol-1

is for obstacle controlled dislocation glide

mechanism. The 0 K stress values obtained by the best fit of the current data

found in the range of 139 to 238 MPa. Whereas the values given by Verrall

et al. are 38 MPa for obstacle and 272 MPa for of Peierls/lattice resistance

controlled glide. So, the closest values to the published work are for Peierls

resistance with activation energy slightly higher and 0 K flow stress slightly

lower. So we propose Peierls resistance glide model with the best fitted

parameter as in this study to consider as the rate controlling mechanism for

the temperature range of 22-125 oC.

The complete data set of flow stress and strain rate is plotted in log-log

space in Figure 2.9. The obtained stress exponents n, i.e. the reciprocal

values of the slopes of the isotherms, change from rather high values at 125

oC (>7), to ~4-5 at 350

oC (Fig. 2.7). In fact, the distribution of data points at

125 oC fits better to a slightly curved isotherm, flattening off at the faster

strain rates (i.e. an exponential relation), than to a linear trend (i.e. at

constant n).

The number of data points at 250 oC is too limited to conclude with

confidence whether these data correlate better with the non-linear stress-

strain rate relation of 125 oC or with the linear trends at 250

oC. However,

the near steady state behaviour observed at 250 oC (Fig. 2.3a) matches the

350 oC data rather than the 125

oC and RT data (compare Fig. 2.3a with Fig

2.1, 2.2 and 2.4).

63

Figure 2.9. Complete data with best fit lines in log space. Shows the changing trend/slope for 22- 125 oC and constant trend at 350

oC

in log-space. The data of previous study by Franssen 1994 on dry salt is also plotted along, which shows slightly higher strength at

350 oC as compared with current study, Colour lines are the glide model predictions at room temperature and 125

oC, at 50, 300 and

600 MPa, pointing higher strength at higher confining pressures. The green (double arrow line at 1.2 (=LOG (16 [MPa])) presents the

transition between glide and climb control creep.

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

-7.0-6.0-5.0-4.0-3.0

Log (

stre

ss [

MP

a])

Log (strain rate [s-1] )

22 ºC 50 MPa

22 ºC 600 MPa

125 ºC 50 MPa

125 ºC 300 MPa

125 ºC 600 MPa

250 ºC 50 MPa

250 ºC 300 MPa

250 ºC 600 MPa

350 50 MPa

350 ºC 300 MPa

350 ºC 600 MPa

Franssen 1994 350 ºC

Unconfined

Peierls

resistance

glide

models at

50, 300 and

600 MPa.

Dislocation

s climb

models at

50, 300 and

600 MPa.

64

On the basis of the above, it is inferred that within the range of

conditions tested, the dislocation mechanism controlling creep of dry rock

salt changes when going from low to high temperature. The transition is

likely to occur in between 125 and 250 oC.

2.5.2 Comparison with previous studies involving tests at various

pressures

Limited previous studies have been performed exploring effects of pressure

on the creep of halite. Aladag et al. (1970) and Auten et al. (1973) reported

that salt (single and polycrystalline) got weaker at higher confining pressure

while tested at room temperature. This is inconsistent with the results of the

current study. In the studies of Aladag et al. (1970) and Auten et al. (1973),

the samples were not jacketed to protect them from infiltration of the

confining fluid. In addition, the sample preparation was done using abrasive

papers followed by polishing with water and rinsing with methanol and

ether. So the water content, as well as, the impurity content of the samples

was not known. In current work, the salt samples were prepared from

reagent grade pure salt powder and special care was taken to dry and jacket

the samples. The testing of the samples, deformed at similar conditions to

(Aladag et al. 1970, Auten et al. 1973), i.e. room temperature and using

strain rate of 10-4

s-1

, did not show decrease in strength, but increase with

confining pressure. It is thought that, given the special care in sample

preparation and testing procedure, these current results are more reliable and

should form the basis for extrapolation to in situ conditions.

2.5.3 Deformation mechanism map

Figure 2.9 can be regarded as a deformation mechanism map show for dry

rock salt, in logarithmic stress-strain rate space, with the predictions of the

65

lattice resistance glide model (Eq. 2.13) and of the climb controlled model

(Eq. 2.12). These predications can of course be extrapolated to strain rates

10-11

– 10-15

s-1

, representing realistic strain rates in salt mines (maximum)

and salt domes (minimum) according to Carter et al. (1982). The question

now is where exactly the boundary between the two creep mechanisms is

located. In the experiments presented in the current Chapter, the transition

from glide control to climb control occurs in between 125 and 250 oC. The

character of the creep Equations, exponential vs. power law for glide and

climb control, respectively, is illustrated in Figure 2.9 by the straight and

curved lines in log-log space of stress and strain rate. The location of the

boundary is very sensitive to the values for the fitting parameters (Equations

2.12 and 2.13) and in fact, the current data set is not sufficient to define this

boundary with full confidence. We thus, for now, follow the approach by

Frost & Ashby (1982) in which the boundary between glide and other

mechanisms is at a stress value independent of strain rate or temperature.

For the transition from glide to climb for the dry polycrystalline halite

investigated here, the corresponding stress value is 16 MPa. For common in

situ conditions, for both geotechnical applications like at caverns and mines,

and at natural salt halokinetic settings such as at salt domes, the climb-

controlled creep Equation (Eq. 2.12) thus appears a meaningful description

of flow behaviour of (dry) rock salt.

It is noted that from the analysis given above, it was concluded that the

rate controlling mechanism for creep of dry rock salt is dislocation glide or

climb, depending on extrinsic conditions, rather than cross-slip. However, it

cannot be ruled out that cross slip does play some role, as microstructures

suggested that there exists waviness at sub-grain level, pointing towards the

cross-slip. However, the mechanism is not rate controlling at tested

66

conditions and accordingly, no cross slip regime is included in the

deformation mechanism map of Figure 2.9.

CONCLUSIONS

In this chapter, the results are presented of new experiments on jacketed

samples of dry synthetic rock salt. Aim was to determine the microphysical

mechanism controlling dislocation creep of halite at 20-350 C, and to

present a mechanism-based flow law providing a solid basis for

extrapolation of lab data to long time scales. One way of distinguishing

between the various dislocation mechanisms that may control creep in dry

rock salt is by the effect of confining pressure. For that reason, systematic

pressure stepping tests were carried out across a range of pressures not

attempted before (50-600 MPa). The following was concluded:

In the temperature range of 22 to 350 oC, the rate controlling

dislocation mechanism changes from Peierls resistance controlled

glide at room temperature to climb controlled creep governed by

dislocation diffusion at 350 oC. At all conditions tested, the dry

rock salt is stronger if the confining pressure is higher. The

activation volume for creep was found to be about 0.58Vm for the

Peierls resistance controlled glide, and about 0.66Vm for climb

controlled creep, where Vm is the molecular volume of halite.

The data allowed to obtain values for the fitting parameters for the

Peierls resistance controlled glide model and for the climb

controlled creep model, compiled in two creep laws (equations 2.12

and 2.13 above).

The temperature at which the transition from glide to climb control

takes place was found to lie in between 125 and 250 oC, at a stress

67

of about 16 MPa. Given the slow strain rates and low stresses

normally relevant for in situ conditions, dislocation creep of

rocksalt in nature will likely be controlled by dislocation climb.

69

Chapter 3

Stress relaxation of synthetic and

natural polycrystalline halite

70

3.1 INTRODUCTION

The mechanical behaviour of halite has been studied extensively before in

the laboratory; both for dry and wet conditions, at different temperatures and

pressures (see e.g. Heard 1972, Heard & Ryerson 1986, Wawersik & Zeuch

1986, Spiers et al. 1990, Senseny et al. 1992, Peach et al. 2001, Ter Heege

et al. 2005a). For dry conditions, Carter & Hansen (1982) suggested

dislocation climb process as rate controlling mechanism, Franssen (1994)

concluded that at laboratory strain rates and relatively low temperatures,

250-450 oC, the behaviour is best explained by climb-controlled dislocation

creep with climb itself being governed by diffusion through dislocation

cores, while at higher temperatures, 500-780 oC, lattice diffusion controlled

creep is dominant. In chapter 2 of this thesis, pressure stepping tests have

been used to investigate the creep behaviour of dry halite in the temperature

range 22-350 oC, where a transition was observed from glide to dislocation

climb. For wet conditions, several authors have suggested that under

laboratory conditions of temperature 23 to 500 oC, dislocation creep is the

main mechanism controlling creep (Heard 1972, Heard & Ryerson 1986,

Carter et al. 1993), while other authors concluded that if grain size is small

and temperature is low, solution-precipitation creep plays an important role

(Urai et al. 1986, Spiers et al. 1990). Ter Heege et al. 2005b) argued on the

basis of an experimental study that in wet polycrystalline halite, both

dislocation and solution-precipitation mechanisms might contribute to the

overall deformation, provided that microstructural modification processes

such as dynamic recrystallization and grain growth can take place freely.

Salt rocks in nature are wet rather than dry (Roeder & Bassett 1981, Urai

1983). The creep of these salt rocks usually occurs at strain rates in the

range of 10-8

to 10-15

s-1

(Heard 1972, Van Eekelen et al. 1981, Jackson &

71

Talbot 1986). In order to fully understand the creep behaviour of halite

under natural conditions, it thus is of importance to not only know, in

general, which mechanisms may control creep of halite, i.e. dislocation vs.

solution-precipitation mechanisms, but also to be able to constrain the strain

rates under which a given mechanism prevails. The strain rates relevant for

in situ deformation, 10-8

to 10-15

s-1

, are difficult to achieve in laboratory

experiments. However, one way of approaching such slow strain rates is to

perform stress-relaxation experiments (Rutter & Mainprice, 1978). In this

technique, strain rates as slow as 10-9

s-1

can be achieved by allowing the

stress on a sample to relax through plastic deformation. The experiments are

time consuming, but result in valuable data regarding creep behaviour at low

stresses and slow strain rate.

In the current study we have used both synthetic and natural wet

polycrystalline halite samples to investigate what controls the rate of

deformation at real in situ conditions, by applying the stress relaxation

technique. The main research question to be answered was if a transition can

be observed, from creep behaviour governed by dislocation mechanisms to

creep behaviour controlled by a solution-precipitation mechanism, and if so,

what the conditions of this transition are in terms of strain rate. As an

important criterion, we used the stress exponent n of a conventional power

law creep equation, expected to be above 3 in case of dislocation creep, and

being ~1 for solution-precipitation creep.

The experiments were performed as multi-step strain rate stepping while

keeping the temperature and confining pressure as constant, at 125 oC and

50 MPa, respectively. Indeed, for higher stresses and strain rates, we found a

high stress exponent n of the standard power law, in the range 10 to 13,

while towards lower stress and slower strain rate, the n-value showed a

72

decreasing trend and reduced to ~1 at the end of the relaxation step. This

transition took place over the strain rate interval 10-8

to 10-9

s-1

, at stresses 10

to 3 MPa, at 125 oC.

3.2 METHOD


In this study, synthetic as well as natural salt samples were used. All

samples were manufactured such that they became cylindrical samples with

length in the range of 80-85 mm and diameter 35-36 mm.

The synthetic rock salt sample (halite1) was prepared in the laboratory

starting from analytical grade NaCl powder from Merck, with an average

particle size of 200-400 μm. The powder salt was cold pressed in a hardened

steel, piston-cylinder assembly. The pistons used on both sides of the

cylinder were perforated at the centre to provide evacuation of air molecules

from the powder prior to cold pressing, using a vacuum pump. The cylinder

was polished and lubricated with Teflon spray before pouring the salt

powder in. The powder was axially pressed at 200 MPa for 20 minutes The

resulting cylindrical sample was sealed in a Viton rubber sleeve and was put

in a silicone oil pressure vessel for annealing under 100 MPa confining

pressure and a temperature of 150 oC for one week. The sample thus

obtained had a theoretical density (mass to volume ratio) of 99.5%. For

more details about the sample preparation technique, see Peach (1991).

Two natural halite samples (halite2 and 3) were prepared from

‘Speisesalz’ cores. These cores come from the Asse mine, Germany, and

were taken from the ~800m gallery level and from a depth of >3m inside the

horizontal gallery wall (Spiers et al. 1986, Urai et al. 1987, Peach 1991).

73

The samples had a grain size in the range of 3-10 mm. The constituents of

the cores were mainly halite (> 98%), a small amount of poly-halite

(K2SO4.MgSO4.2CaSO4.2H2O; ~1%), and some minor quantity of

anhydrite. The microstructure shows high angle ~120o boundaries, with a

few cracks and very little internal dislocation structure and corresponding

low dislocation densities.

In order to create a deliquescence condition in our samples, comparable

to that at in-situ, these were moisturized with water < 0.5 wt. % using

atomizer in a chamber and carefully measured for its mass increase. This

was followed by wrapping up the samples in a double layer of perforated

glass fibre sheet (0.3 mm starting thickness) creating an equilibrated humid

environment around the sample. These wrapped samples were further sealed

in 1.0 mm thick polymer “ethylene propylene diene monomer (EPDM)”

jackets to avoid contamination of the samples by the confining medium

(silicone oil) used in the deformation apparatus. The deformation pistons

were inserted in the open ends of the jacket. To seal the ends, stainless steel

wires were tightly wound in grooves of steel pistons from over the jacket.

3.2.2 Deformation apparatus

The apparatus used for this study was the so-called “Shuttle Vessel” (Fig.

3.1) of the experimental rock deformation (HPT) laboratory at the

department of Earth Sciences at Utrecht University. The Shuttle Vessel

machine is an internally heated 100 MPa confining pressure vessel mounted

on a standard 100kN Instron 1362 loading frame with an electro-mechanical

servo controlled positioning system. This machine can be used to deform the

sample at a constant piston speed, approaching constant strain rate if total

strains are kept relatively low. The machine is provided with a (Instron

standard, +/- 50 mm) linear variable differential transformer (LVDT), but to

74

Figure 3.1. Shuttle vessel triaxial deformation apparatus

come to an accurate measurement of the sample deformation, another

(LVDT_2, 0- 25 mm range, H.F. Jensen, Denmark) was installed at the top

of the vessel and near the sample, to reduce the effect of the elastic

distortion of the apparatus and measure accurately the shortening of the

sample, especially during stress relaxation, where very limited natural strain

in the order of 0.001 is to be monitored. The temperature was measured by

thermocouples at two locations inside the vessel; one was positioned close

to the middle of sample and, the other was at the top of the sample. K-type

thermocouples were used, which are accurate within ± 1 oC. The axial load

on the sample was measured using a 100 kN load cell accurate within 0.1 %

of the full scale. The confining pressure was created by using silicone oil

which is kept at constant pressure within ± 0.1 MPa using a servo pump.

Measurement of the pressure was done using a diaphragm pressure

LVDT_2

Deformation piston

Thermocouples

connections

Pressure vessel

containing sample

assembly

75

Figure 3.2. Sample with piston assembly and steel discs

transducer (Teledyne 2403, 100 MPa range). To avoid rusting of the

deformation pistons and related contamination of the samples, two grooved

stainless steel discs having 2.0 mm thickness and 35.0 mm diameter were

used as separators, along with 50 μm thin teflon sheets to reduce the friction

between sample and the deforming pistons (Fig. 3.2). The triaxial apparatus

used is very sensitive to the environmental conditions. For example, a little

variation in laboratory temperature not only causes a drift in the load cell

signal, but also may cause a small change in the pressure, which would

influence the load cell signal. Such (small) change in pressure will result in

some elastic expansion/contraction of the pressure vessel, hampering

straightforward processing of the data from the LVDT_2. Therefore the

apparatus was carefully calibrated for the effect of pressure and temperature

on the load cell. The elastic distortion of machine was corrected on the basis

of tests using a steel dummy of known Young’s modulus. This was done by

applying gradually increasing axial load to the dummy and measuring the

LVDT_2 reading in parallel, then using a 10 order polynomial to relate the

LVDT_2 value to the internal load.

35 mm

76

3.2.3 Experiments

In this study, total three multistep experiments were performed; one on

synthetic (halite1) and two on natural (halite2 and 3). A typical experiment

consisted of a few steps at constant strain rate, in the range 5×10-5

to 5×10-8

s-1

. During the constant strain rate part of the test, the sample was deformed

until a steady (or near steady) state of stress was reached. Then the piston

was arrested and the stress on the sample was allowed to relax until the

diminishing force on the sample reached the limits of the load cell

resolution. The duration of each relaxation step was a few days.

The synthetic sample, halite1, was deformed by a 3-step repetitive strain

rate of 5×10-7

s-1

, for a natural strain of 0.01-0.03 per step and each step was

followed by stress relaxation. The natural samples, halite2 and 3, were

tested in a seven strain rate steps (5×10-5

, 5×10-6

, 5×10-7

, 5×10-8

, 5×10-7

,

5×10-6

, 5×10-5

s-1

), and the relaxation was followed after the constant strain

rate parts of 5×10-6

, 5×10-8

and 5×10-6

s-1

. The experiments were performed

at 125 oC sample temperature and 50 MPa confining pressure.

3.2.4 Data acquisition and processing

The data, containing pressure, temperature, load and position (LVDT_1 and

2) were logged throughout the test. The stress on the sample was calculated

from the load values by assuming constant volume deformation, correcting

the instantaneous area value for progressive change in length of the sample.

The cumulative strain (shortening) of the sample was calculated as the

natural strain, i.e. the natural logarithm of the ratio of the final length and

the initial length. The zero of the internal load signal was tested before the

deformation piston touched the sample and after unloading at the end of

experiment. If found necessary, correction was applied for zero-level shift.

77

The data acquired during stress relaxation was analysed with a dedicated

code to produce the plastic strain rate of the sample.

The stress relaxation technique is based on the following. During

deformation at constant rate (imposed by a moving piston), some energy

gets stored inside the material as elastically stored energy. During

relaxation, when the loading piston is arrested, this energy is dissipated

through plastic deformation of the sample. Ideally, this requires an infinitely

stiff machine which does not participate by means of the elastically stored

energy in its own frame. In practice, such a machine does not exist without

exceptional servo control to keep constant sample length, so the elastic

modulus of machine should be taken into account. In other words, the

elastically stored energy inside the active part (under force) of the machine

also dissipates through the plastic strain of the sample, so the data also need

to be corrected for the stiffness of machine. In order to calculate the sample

straining, we take the simple assumption that the stress is proportional to

strain, provided that other physical conditions (confining pressure,

temperature, microstructure) are constant (Rutter & Mainprice, 1978). The

strain rate at any instant will then be proportional to the stress relaxation

rate, with the elastic (Young’s) modulus of sample as a constant of

proportionality.

The measured total displacement” xtotal” (from LVDT_2) can be written

as the sum of the sample deformation (elastic + plastic) and elastic distortion

of apparatus

𝑥𝑡𝑜𝑡𝑎𝑙 = 𝑥𝑠𝑎𝑚𝑝𝑙𝑒 + 𝑥𝑎𝑝𝑝𝑎𝑟𝑎𝑡𝑢𝑠 (3.1)

78

After differentiating w.r.t. time and normalizing this equation using the

instantaneous length of the sample, the following relation of plastic strain

rate of the sample is obtained:

𝜀�̇�𝑙𝑎𝑠𝑡𝑖𝑐 = 𝜀�̇�𝑜𝑡𝑎𝑙 −1

𝐸𝑠𝑎𝑚𝑝𝑙𝑒(�̇�𝑠𝑎𝑚𝑝𝑙𝑒) −

1

𝐿𝑡𝑆 (

𝜕𝐹

𝜕𝑡) (3.2)

where,

𝜀�̇�𝑙𝑎𝑠𝑡𝑖𝑐 = plastic strain rate of sample [s-1

]

𝜀�̇�𝑜𝑡𝑎𝑙 = total strain rate measured by LVDT_2 [s-1

]

𝐸𝑠𝑎𝑚𝑝𝑙𝑒 = Young’s modulus of sample [MPa]

�̇�𝑠𝑎𝑚𝑝𝑙𝑒 = sample stress relaxation rate [MPas-1

]

𝐿𝑡 = instantaneous length of sample [m]

𝑆 = machine stiffness correction constant [mN-1

]

(𝜕𝐹

𝜕𝑡) = rate of change of force [Ns

-1]

We then have to determine the total strain rate, stress relaxation rate and

the rate of change of force, as on right hand side of Equation (3.2), to

calculate the plastic strain rate of the sample. The first term, the total strain

rate (𝜀�̇�𝑜𝑡𝑎𝑙), was directly measured using the external LVDT_2 attached at

the top of the vessel. The second and third terms contain the calculation of

the change of the force and stress on the sample as a function of the time,

which was done by defining a variable window size on each data point with

minimum 10 % of its value on high and low side of the data series of force

and stress.

79

During the experiments on halite reported here, at 50 MPa confining

pressure, the friction between the deformation piston and seal was rather

high, and comparatively, it was more pronounced during relaxation than

during deformation at constant strain rate (compare Figs. 3.3 and 3.5). As a

result, the irregularity in the relaxation curves was found to be substantial,

which obscured the actual trend/path of stress and strain rate during

relaxation by giving a number of different strain rate data points for a single

stress value (see high scatter in log strain rate axis). In order to resolve the

true value of strain rate during stress relaxation, a statistical analysis was

performed, in which the moving average value of strain rate at particular

(decreasing) stress values, during relaxation, was calculated (using a

variable time window to ensure a fixed level of error in the derivative of the

noisy displacement/time curve). The obtained average values of strain rates

gave a better picture of data and to understand the trend. These average

values were used for all relaxation steps (see comparison of real relaxation

data and its mode in Fig. 3.5a).

3.2.5 Microstructural preparations

After deformation, the samples were prepared for microstructural study. The

samples were cut along their length using a diamond tipped saw lubricated

by so-called ’evaporating oil’ (Shell light oil (organic), S4919). The sample

halves were bonded onto glass slides and were polished, first by using SiC

papers and then finalized to an optical finish of 1.0 micron using diamond-

oil suspension (Metadi, Buehler). To reveal the microstructure, samples

were undergone chemical etching (95% saturated NaCl solution + 5% de-

ionized water + 8.0 gm FeCl3 per litre) followed by rinsing with n-hexane

spray and drying using hot air. Photographic images were made in reflected

80

light using a Leica optical polarization microscope equipped with a high

resolution digital image capturing and analysis system.

3.3 RESULTS


The results of the experiments performed on the synthetic and natural halite

poly-crystals are given in Table 3.1. The stress vs.; strain and time curves

are shown in Figures 3.3a-f.

(i) Stress vs. natural strain and time

The synthetic salt sample, halite1, was deformed in three steps using a

similar strain rate of 5×10-7

s-1

. In each step, the sample was deformed

through a very limited amount of strain of 0.015-0.02. The stress-strain

curve of Figure 3.3a shows that steady state was not reached in any of the

three steps, but the strain hardening rate appears to decrease with increasing

strain.

The natural salt samples, halite2 and 3 were deformed in 7-steps (see

Table 3.1 for details), adding 0.025-0.03 strain at each step. The strength of

the natural halite samples is almost twice that of the synthetic salt, at strain

rate 5×10-7

s-1

. Steady state was not reached in any of the strain rate steps.

The rate of strain hardening differed depending on the strain rate and

appeared higher at the higher rates. For the slowest deformation step, 5×10-7

s-1

, a few stick slip events, due to

81

(a)

(b)

0

5

10

15

20

25

0.00 0.05 0.10 0.15 0.20 0.25

Dif

fere

nti

al s

tres

s [M

Pa]

Natural strain

Halite1

Temp = 125 oC

Pc = 50 MPa

𝜀̇ = 5×10-7 s-1

0

5

10

15

20

25

0 10 20 30

Dif

fere

nti

al s

tres

s [M

Pa]

Time [Days]

Halite1

Temp = 125 oC

Pc = 50 MPa

𝜀̇ = 5×10-7 s-1

82

(c)

(d)

0

5

10

15

20

25

30

35

0.00 0.05 0.10 0.15 0.20 0.25

Dif

fere

nti

al s

tres

s [M

Pa]

Natural strain

Halite2

Temp = 125 oC

Pc = 50 MPa

5×10-5 5×10-6

5×10-7

5×10-7

5×10-8

5×10-6 5×10-5

0

5

10

15

20

25

30

35

0 10 20 30 40

Dif

fere

nti

al s

tres

s [M

Pa]

Time [Days]

Halite2

Temp = 125 oC

Pc = 50 MPa

5×10-5

5×10-6

5×10-7

5×10-7

5×10-8

5×10-6

5×10-5

83

(e)

(f)

Figure 3.3. Differential stress curves against natural strain and time, a-b) halite1, c-

d) halite2, e-f) halite3

0

5

10

15

20

25

0.00 0.05 0.10 0.15 0.20 0.25

Dif

fere

nti

al s

tres

s [M

Pa]

Natural strain

Halite3

Temp = 125 oC

Pc = 50 MPa

5×10-5

5×10-6

5×10-7

5×10-7

5×10-8

5×10-6

5×10-5

0

5

10

15

20

25

0 5 10 15 20 25

Dif

fere

nti

al s

tres

s [M

Pa]

Time [Days]

Halite3

Temp = 125 oC

Pc = 50 MPa 5×10-5

5×10-6

5×10-5

5×10-7

5×10-8

5×10-7

5×10-6

84

Table 3.1. Mechanical data

Sample 𝜀̇

[s-1

] εa

σ

[MPa]

Halite1

5×10-7

0.01 7.7

5×10-7

0.03 8.7

5×10-7

0.05 9.2

Halite2

5×10-5

0.04 22.6

5×10-6

0.07 21.9

5×10-7

0.11 16.0

5×10-8

0.13 13.1

5×10-7

0.15 15.7

5×10-6

0.17 20.3

5×10-5

0.21 21.1

Halite3

5×10-5

0.04 21.8

5×10-6

0.07 20.9

5×10-7

0.10 15.3

5×10-8

0.13 11.9

5×10-7

0.16 15.2

5×10-6

0.18 19.5

5×10-5

0.22 21.9

𝜀̇ is the strain rate

εa is the natural axial strain at the end of the particular step

σ is the differential stress value at the end of the deformation step

high friction between deformation piston and seal, were also observed, as

seen by the irregular nature of the stress-strain curve.

Although the hardening rate per individual step in strain rate could be

established, for both the synthetic and the natural samples, the data as a

whole were insufficient to uncover a robust trend in changing hardening rate

when going from one strain rate to the other. This hampered reliable

extrapolation to higher strain, preventing a comparison of differential stress

85

(a)

(b)

Figure 3.4. Log-log plot of strain rate vs. differential stress using the maximum

differential stress values at the end of each step. Best fit lines to the data of halite2

and 3 represent power law fits, with corresponding n-values indicated.

-8.0

-7.5

-7.0

-6.5

-6.0

-5.5

-5.0

-4.5

-4.0

1.0 1.1 1.2 1.3 1.4

Log (

stra

in r

ate

[s-1

])

Log (stress [MPa])

step1 to step4

step4 to step7

Halite2

Temp = 125 oC

Pc = 50 MPa

11.8 ± 2.4

10.8 ± 2.1

-8.0

-7.5

-7.0

-6.5

-6.0

-5.5

-5.0

-4.5

-4.0

1.0 1.1 1.2 1.3 1.4

Lo

g (

stra

in r

ate[

s-1])

Log (stress [MPa])

step1 to step4

step4 to step7

11.1 ± 1.2

13.6 ± 2.6

Halite 3

Temp = 125 oC

Pc = 50 MPa

86

as a function of strain rate at the same strain. Thus, in Table 3.1, only the

values of the differential stress at the end of each step are given.

(ii) n-value for the natural halite

The dependence of the differential stress on the strain rate for the natural

halite samples (Fig. 3.4) was tested by applying a conventional power law

creep of the type 𝜀̇ = 𝐴𝜎𝑛, where 𝜀̇ is the strain rate, σ is the flow stress, and

A and n are constants. Since both halite2 and 3 presented substantial strain

hardening, any estimate of the constants A and n can only give a first-order

impression of the creep behaviour of the material the data were divided into

two parts, for both halite2 and 3; step1 to step4 (decreasing strain rate) and

step4 to step7 (increasing strain rate). Linear regression analysis in log-log

space resulted in high n-values, ranging 10.8 to 13.6 (Figs. 3.4a-b). Note

that the strain rate is the independent variable, but it is shown as dependent

in the Figure 3.4 (i.e. on Y-axis) to compare with the stress relaxation curves

(Figs. 3.5a-d).

(iii) Stress relaxation

The stress relaxation behaviour of the tested halite samples are plotted in

Figures 3.5a-d. The steady state/maximum stress values obtained at the end

of each strain rate deformation step are marked in the graphs along with the

projected slopes representing the stress exponent n-values (n = 1, 5 and 10)

according to scale. As explained earlier, the stick slip events between

deformation piston and seal were more conspicuous during stress relaxation

than during deformation. Such events caused great noise in the signal of the

measured displacement and, hence, resulted in substantial scatter in

calculated strain rate, so the mode values were used instead (see section

3.2.4).

87

Generally, the graphs show that the calculated plastic strain rate at the

start of each relaxation period fits to a trend with high n-value (>10, i.e. a

steep slope), implying that the stress is not very sensitive to strain rate.

Progressively, the sensitivity increases and the corresponding n-value

appears to approach n = 1 for lower stress and strain rate values near end of

each relaxation step. A free hand dashed-line drawing, showing trend of

relaxation is also plotted along to show the expected trend during relaxation.

(a) Noise in strain rate data and the corresponding mode values

-10.0

-9.5

-9.0

-8.5

-8.0

-7.5

-7.0

-6.5

-6.0

-5.5

-5.0

0.0 0.5 1.0 1.5

Log (

stra

in r

ate

[s-1

])

Log (stress [MPa])

Step 2 5E-7 s^-1

Mode step 2

5×10-7 s-1

88

(b)

(c)

89

(d)

Figure 3.5. Log-log plot of strain rate vs. differential stress including the results of stress relaxation steps. Closed triangles are the

steady state/maximum differential stress values obtained at the end of each step, closed rectangles are the mode values of the

calculated strain rate data. Three slopes representing the n-values of 1, 5 and 10 are included to be compared with the trend during

relaxation, represented by the free-hand drawn dashed line. a) selected example of the collected data (close diamonds), showing the

scatter due to sudden change of stress during stick slip events, and open square symbols are the mode corresponding mode values, b)

halite1, c) halite2, d) halite3

90


Two samples were prepared for microstructural study. Halite1 (fine grained,

reagent grade pure synthetic polycrystalline sample) shows a microstructure

of a dense aggregate of flattened grains. The grains show lobate and locally

bulged grain boundaries indicating dynamic recrystallization. The grain

boundaries often intersect at triple points with angles deviating from 120o.

Sub-grain walls and sub-grains are recognizable close to at least some of the

grain boundaries, but overall, the internal parts of the grains do not show

well-developed substructures. This sample was allowed to relax under stress

for one week, under 50 MPa confinement at 125 oC, after deformation at a

strain rate of 5×10-7

s-1

. Halite2 (coarse grained, natural polycrystalline)

sample with a grain size of 2-5 mm. The sample was deformed at 5×10-5

s-1

as last step of its stepping test, and was not relaxed but was taken out of the

machine for microstructural steady. Microstructure shows slightly open

grain boundaries but no sign of dislocation substructures, but recrystallized

and shows flattened grains. The open grain boundaries are due to handling

effects, as, at the end of experiment, the confining pressure (50 MPa) was

taken off before the sample was properly cooled down (to below the boiling

point of water).

91

Figure 3.6. Microstructures after tests, deformation direction is horizontal, wet

samples (H2O ≈30 ppm) A) synthetic salt halite 1, recrystallized grains with no

internal structure, average grain size of ~300 μm, B) natural salt halite 2, grain size

2-5 mm, slightly open grain boundaries, no dislocation structures.

100 μm A

10 mm B

92

3.4 DISCUSSION

The aim of this study was to investigate if a transition can be observed from

creep behaviour of halite governed by dislocation mechanisms to creep

behaviour controlled by a solution-precipitation mechanism, and if so, what

the conditions of this transition are in terms of strain rate. Below, we will

discuss our observations and compare the strength of the halite and its

change with decreasing strain rate with the mechanical behaviour

established in other studies.

3.4.1 n-value

Fitting the stress-strain rate data obtained during the constant strain rate

parts of the multi-step experiments to a conventional power law creep of the

type 𝜀̇ = 𝐴𝜎𝑛 resulted in a value for n larger than 10. Microphysical models

for creep controlled by dislocation climb generally result in power law creep

equations (e.g. see Chapter 2), but the values for n usually range 3-4.5 for

climb controlled by lattice diffusion, or up to 6.5 in case of climb controlled

by dislocation core (pipe) diffusion (Senseny et al. 1992, Carter et al. 1993,

Franssen 1994) . The value of n > 10 appears to rule out climb control for

the creep behaviour of wet polycrystalline halite for the conditions tested.

Rather, a glide or cross slip controlled creep model may apply (cf. De

Bresser et al. 2002). The results presented in Chapter 2 on the dry rock salt

showed a low sensitivity of the stress on the strain rate similar to the wet

halite reported here, at comparable conditions of temperature and pressure,

at 125 oC and 50 MPa. For the dry halite, it was concluded that a glide

mechanism (Weertman 1957, Poirier 1985) rather than a cross slip

mechanism (cf. Auten et al. 1973, Skrotzki et al. 1981) controls flow at the

given conditions. Though we have not tested the effect of pressure on the

93

Figure 3.7. Log-log plot of strain rate vs. differential stress, comparing the current

results with the results of previous studies on wet and dry halite at 125 oC. (Heard

1972, Wawersik & Zeuch 1986, Carter et al. 1993, Ter Heege et al. 2005a), (see

Table 3.2 for details).

strength of wet halite, which may serve as a way of discriminating between

mechanisms (Chapter 2), we infer that the conclusion regarding glide

control also holds for the current wet halite.

The stress relaxation behaviour of the wet halite (Figs. 3.5a-d) shows that

the n-value gradually decreases with decreasing stress and strain rate,

reaching ~1 at strain rates below 10-8

s-1

. This trend is observed in both

synthetic and natural halite samples. This strongly suggests that a transition

takes place towards grain size sensitive (GSS) creep (Spiers et al. 1990, Ter

Heege et al. 2005a).

If we compare our work with previous studies on halite by using their

flow laws, parameters given in Table 3.4, (Heard 1972, Wawersik & Zeuch

-12

-10

-8

-6

-4

-2

0

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Log (

stra

in r

ate

[s-1

])

Log (differential stress [MPa])

Halite1

Halite2

Halite3

Heard 1972

Wawersik & Zeuch 1986

Carter et al. 1993_high

Carter et al. 1993_Low

Ter Heege et al 2005a

94

1986, Carter et al. 1993 and Ter Heege et al. 2005a), for 125 oC, we see in

Figure 3.7 that the current data on natural halite2 and 3 have got the upper

limit by Wawersik & Zeuch (1986) (unknown water content) and Ter Heege

et al. 2005a (wet), whereas the lower bounds are given by Carter et al. 1993

(dry). The data of synthetic sample halite1 show weaker behaviour and lie in

approximation of Wawersik & Zeuch (1986) and Ter Heege et al. (2005a).

3.4.2 Composite flow law

Provided physical conditions (like pressure and temperature) are fixed, the

microstructure of the sample may be expected to remain constant during

stress relaxation with limited straining (see Rutter & Mainprice, 1978),

while processes such as dynamic (syn-deformational) recrystallization and

grain growth are likely to affect the microstructure during deformation that

results in substantial increase in strain. The relaxation data show that the

dependence of strain rate on stress approaches linearity at low stress and

slow strain rate, which observation has been used above to suggest that

grain size sensitive behaviour might play a role.

We thus should consider if the flow behaviour of wet halite should be

described by a composite flow equation of grain size insensitive (GSI) and

grain size sensitive (GSS) behaviour as follows

𝜀̇ = 𝐴∗𝜎𝑛 + 𝐵∗𝜎𝑑−𝑝 (3.3)

Where A* and B* are constants at a given temperature, n is the usual stress

exponent and p is the grain size exponent.

95

Table 3.2. The updated Table of flow law parameters after Ter Heege et al. 2005a.

Material/

composition

H2O

[ppm]

P

[MPa] 𝜀̇

[s-1]

T

[oC]

σ

[MPa]

LOGA

[MPa-n s-1]

Stress

exponent n

ΔU

[kJmol-1]

Source/

comments Synthetic pure rocksalt

5-10 50-600 4×10-7 to 10-4 250-350 2.8-15.2 -14.4 ±1.4 4.7 ±0.3 126 This study (Chapter 2)

Synthetic pure

rocksalt 20–45 200 10-1 to 10-8 23-400 1.6-47 5.58 ±0.8 5.5 ±0.4 98 ±8 Heard (1972)

Synthetic pure

rocksalt 20–45 200 10-1 to 10-8 23-400 1.6-47 0.7 ±0.4 5.8 ±0.2 96 ±3

Heard & Ryerson

(1986)

Natural (>95% rocksalt)a

? 14, 21 10-6 to 10-11 23-160 8.3-24 3.36-6.03 4.1 ±6.3 50-83 Wawersik & Zeuch (1986)

Natural

(>99% rocksalt)b <100 2.5-20.7 10-6 to 10-9 50-200 6.9-20.7 3.8 5.3 ±0.4 68 ±4

Carter et al.

(1993)

high 𝜀̇, σ

Natural

(>99% rocksalt)b <100 2.5-20.7 10-7 to 10-9 100-200 2.5-10.3 4.09 3.4 ±0.1 52 ±1

Carter et al.

(1993)

low 𝜀̇, σ

Synthetic pure

rocksalt Dry Uncof. 10-3 to 10-7 250-780 0.4-14.8 -0.76 ±0.2 5.7 ±0.3 129 ±8

Franssen (1994)

Low T

Natural (rocksalt)c ? Unconf.

+ 15-20 10-3 to 10-11 30-250 1.7-40 -- 7 110

Hunsche & Hampel

(1999)d

Natural

(>98% rocksalt)c 500 3-30 3.5×10-7 150 11-13 -- -- --

Peach et al.

2001

Synthetic pure

rocksalt 9–46 50 10-4 to 10-7 75-200 7.2-22.4 1.56 ±0.54 5.6 ±0.5 80 ±6

Ter Heege et

al 2005

a: Range of parameters for natural rocksalt from five different locations: Salado (New Mexico), West Hackberry and Bayou Choctaw (Louisiana), Bryan Mound

(Texas) and Asse (Germany).

b: Avery Island (Louisiana). c : Asse Speisesalz (Germany).

d: In this study, mechanical data were fitted to a composite law. Stress exponent and activation energy quoted here are from their best fit to a power law equation.

96

In order to evaluate Equation (3.3), we need to estimate what the grain

size was during deformation of our halite samples. We do this by using a

conventional Piezometric relation, allowing predicting what the dynamically

recrystallized grain size was at a certain stress value (e.g. De Bresser et al.

2001)

𝑑 = 𝐾𝜎 −𝑚 (3.4)

where K and m are material and mechanism specific constants. This

relationship between stress and recrystallized grain size is generally

assumed to be independent of temperature, although that there is evidence

that this assumption is not generally valid.

Ter Heege et al. (2005b) established a Piezometric relation between the

grain size d and differential stress σ by measuring the grain size of

experimentally deformed synthetic halite samples. The data by the authors

are shown in the Figure 3.8 along with the best fit linear trend. The halite

samples tested here (halite2 and 3) are natural salt samples, but we assume

that the same piezometer relation holds at current conditions of temperature

and pressure; 125 oC and 50 MPa respectively.

Using the slope and intercept values of the best fit line in Figure 3.8, we

obtained values for K and m as 27.1 and 1.75 respectively, so the Equation

(3.4) reduces to

𝑑 = 27.1𝜎 −1.76 (3.5)

Using this Equation, the grain size at different stress values were

calculated and are given in Table 3.3. These values represent the grain sizes

97

at the end of the constant strain rate parts of the experiments, and hence, the

grain sizes at the start of the relaxation parts. Assuming now that the

microstructure remains constant during relaxation, these are also the grain

sizes applicable at the behaviour at n ≈ 1. This allows us to estimate the

value for p of Equation (3.3), in which stress is linearly dependent on strain

rate. Taking logarithms and simplifying Equation (3.3), we get

𝑙𝑜𝑔𝜀 ̇ = (𝑙𝑜𝑔𝐵∗ + 𝑙𝑜𝑔𝜎) − 𝑝𝑙𝑜𝑔𝑑 (3.6)

Or

𝑙𝑜𝑔𝜀 ̇ = 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 − 𝑝𝑙𝑜𝑔𝑑 (3.7)

To keep the intercept part of this equation as a true constant, a fixed value of

log stress (0.8) was selected (i.e. 6.3 MPa). For this fixed value of stress, log

strain rate values were picked from the stress relaxation curves (Figs. 3.5c-

d) (see relaxation data in Table 3.4). Note that halite1 was not used in this

analysis being different. The selected strain rate values are thus plotted

against the calculated grain size d values in Figure 3.9.

Regression analysis revealed a p-value of -1.1 (±0.3). This p-value

supports the hypothesis that during stress relaxation, grain size sensitive

(GSS) creep might play a role. It is well known that (GSS) solution-

precipitation mechanisms may play an important role in the creep of fine

grained halite, creep (e.g. Raj, 1982, Spiers et al. 1990, Schutjens 1991,

Cox & Paterson 1991, Schutjens & Spiers 1999). According to these

authors, a p-value of about 1 suggests, that the rate controlling step in the

process will be dissolution or precipitation rather than diffusion.

Accordingly, we infer that dissolution/precipitation controlled pressure

98

Figure 3.8. Log-log plot of differential stress vs. grain size for wet synthetic halite

(Ter Heege 2005b).

Figure 3.9. Strain rates picked from relaxation curves at fixed stress value (σ

=6.3[MPa]) against the recrystallized grain size calculated using the piezometer

relation of Eq. 3.5.

y = -0.5688x + 0.8151

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

-1.0 -0.8 -0.6 -0.4 -0.2 0.0

Log (

stre

ss [

MP

a])

Log (grain size [mm]

-8.6

-8.5

-8.4

-8.3

-8.2

-8.1

-8.0

-7.9

-7.8

-1.0 -0.8 -0.6 -0.4

Lo

g (

stra

in r

ate

[s-1

])

Log (grain size [mm])

Halite2 and 3

99

Table 3.3. Calculated grain size using piezometer using maximum stress at the end

of deformation step

Sample Step 𝜀̇

[s-1

]

σ

[MPa]

d

[mm]

Halite 1

1 5×10-7

7.7 0.750

2 5×10-7

8.7 0.603

3 5×10-7

9.2 0.542

Halite2

1 5×10-5

22.6 0.113

2 5×10-6

21.9 0.120

3 5×10-7

16.0 0.206

4 5×10-8

13.1 0.294

5 5×10-7

15.7 0.213

6 5×10-6

20.3 0.136

7 5×10-5

21.1 0.127

Halite3

1 5×10-5

21.8 0.120

2 5×10-6

20.9 0.129

3 5×10-7

15.3 0.224

4 5×10-8

11.9 0.347

5 5×10-7

15.2 0.228

6 5×10-6

19.5 0.146

7 5×10-5

21.9 0.119

𝜀̇ is the strain rate

σ is the differential stress value at the end of the deformation step

d is the calculated recrystallized grain size, applying Eq. 3.5

solution processes dominates the creep of wet halite at low stress and strain

rate, at 125 oC.

Now using the intercept value of the best fit line in Figure 3.9, the

unknown constant B* gets the value of 1.68x10-10

(MPa-1

mm1.1

s-1

), so the

GSS creep equation becomes

100

Table 3.4: Data picked from relaxation curves at similar differential stress values

Sample Deformation

strain rate [s-1

] 𝜀̇

[s-1

]

LOG

(𝜀̇[s-1])

σ

[MPa]

LOG

(σ[MPa])

Halite1

5×10-7

4×10-8

-7.4 6.3 0.8

5×10-7

4.3×10-8

-7.4 6.3 0.8

5×10-7

3.4×10-8

-7.5 6.3 0.8

Halite2

5×10-6

8.6×10-9

-8.1 6.3 0.8

5×10-8

4.7×10-9

-8.3 6.3 0.8

5×10-6

7.0×10-9

-8.2 6.3 0.8

Halite3

5×10-6

1.4×10-8

-7.9 6.3 0.8

5×10-8

2.9×10-9

-8.5 6.3 0.8

5×10-7

9.7×10-9

-8.0 6.3 0.8

𝜀̇ is the strain rate values picked from stress relaxation curves at fixed differential

stress value (6.3 MPa)

Deformation strain rates are the values used to deform the sample and set the stress

value for relaxation.

σ is the fixed differential stress selected to pick the data from relaxation curves

𝜀�̇�𝑆𝑆 = 1.68 × 10−10𝜎𝑑−1.1 (3.8)

For the GSI part of Equation (3.3), we assume that conventional power law

is applicable; plotting the steady points of halite2 and 3, against the

deformation strain rates (Figure 3.10), the values of n and A* come out to be

~11 and 4.365×10-20

s-1

MPa-11

, so the GSI part can be written as

𝜀�̇�𝑆𝐼̇ = 4.365 × 10−20𝜎11 (3.9)

The GSS flow law (Eq. 3.8) is based on the calculated grain size - strain rate

data at σ = 6.3 MPa under the assumption that there is no influence of GSI

flow at that condition. So, the GSS flow law (Eq. 3.8) is the right-handed

101

Figure 3.10. Log-log plot for conventional power law (𝜀̇ = σn). The slope of the

curve represents the stress exponent n-value. Three slopes lines corresponding to n

= 1, 5 and 10 are also projected according to scale. The slope of halite2 and 3

combined data very high (i.e. n ~ 11).

𝜀�̇�𝑆𝐼̇ = 4.365 × 10−20𝜎11 (3.9)

end member of the composite description of Equation (3.3). Its trends for

four different grain sizes are plotted in Figure 3.11, where the trend for the

steady state data (halite1 and 2) is included, as described by Equation (3.9).

Equation (3.9), however, cannot simply be regarded as the left-hand (GSI)

end member of the composite flow law (Eq. 3.3), since grain size sensitive

behaviour might have influenced the steady state creep without realizing it.

We thus took the data of halite2 and 3 from Table 3.1 and fitted them to

Equation 3.3, using the established values for n, p and B* and applied non-

linear regression. This resulted in a value of 6.42×10-20

(MPa-11

s-1

) for A*.

The composite flow law (Eq. 3.3) now can be written, as

y = 10.97x - 19.36

-8.0

-7.5

-7.0

-6.5

-6.0

-5.5

-5.0

-4.5

-4.0

1.0 1.1 1.2 1.3 1.4

Log (

stra

in r

ate

[s-1

])

Log ( flow stress [MPa])

Halite 2 and 3

n = 1

n = 5

n = 10

102

Figure 3.11. Log-log plot of strain rate and differential stress showing the predicted trends for GSS creep applying Eq. 3.8 for

different grain sizes (GSS1, 2, 3 and 4 for d = 0.1, 0.2, 0.3 and 0.4 mm respectively), satisfying the lower stress and strain rate data.

Note that higher grain sizes are lower in strain rates. The trend for GSI creep applying Eq. 3.9, satisfies the steady state values of

constant deformation data.

-9.0

-8.5

-8.0

-7.5

-7.0

-6.5

-6.0

-5.5

-5.0

-4.5

-4.0

0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

Log (

stra

in r

ate

[s-1

])


Halite 2 and 3 steady state data

GSI

GSS1

GSS2

GSS3

GSS4

Halite2 and 3 data from relaxation curves

103

Figure 3.12. Log-log plot of strain rate and differential stress showing the predicted trends applying the composite creep Eq. 3.10, for

a grain size of 0.1 mm (composite1), 0.2 mm (composite 2),0.3 mm (composite 3) and 0.4 mm (composite 4).

-9.0

-8.5

-8.0

-7.5

-7.0

-6.5

-6.0

-5.5

-5.0

-4.5

-4.0

0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

Log (

stra

in r

ate

[s-1

])


Halite2 and 3 steady state data

composite1

composite2

composite3

composite4

Halite2 and 3 data from relaxation curves

104

𝜀̇ = 6.42 × 10−20𝜎11 + 1.68 × 10−10𝜎𝑑−1.1 (3.10)

The trend lines in Figure 3.12 show that the influence of grain size is

effective at lower stresses and strain rates. For higher stresses, these curves

satisfy the steady state points, whereas on lower stress/strain rates, these

trends satisfy the data picked from relaxation curves. So the composite flow

law gives a complete picture of the creep characteristics of natural wet halite

samples, in two regimes of GSI (n ~ 11) and GSS (n ~ 1) that gradually pass

into each other on higher stress and strain rate side.

CONCLUSIONS

The main research question addressed in this chapter was if a transition can

be observed, in wet polycrystalline halite, from creep behaviour governed

by a (grain size insensitive) dislocation mechanisms to creep behaviour

controlled by a (grain size sensitive) solution-precipitation mechanism, and

if so, what the conditions of this transition are in terms of strain rate.

The experiments on the synthetic and natural halite samples at a confining

pressure of 50 MPa and temperature of 125 oC revealed that at faster strain

rates and higher stresses, dislocation creep (GSI) plays its role, which can be

described by a conventional power law creep equation with n = 11. With

such a high value, dislocation climb is unlikely to be rate controlling, but a

dislocation glide mechanism should be considered. During the stress

relaxation parts of the experiments, the n-value decreased to ~1 and a grain

size sensitive creep mechanism, most probably pressure solution, becomes

operative with the dissolution/precipitation step as rate controlling, as

105

revealed by an analysis of the grain size exponent of creep (p ~ 1), using a

flow equation of the type 𝜀̇ = 𝐵∗𝜎𝑑−𝑝.

The transition from (presumably) glide controlled dislocation creep with

high power law n-value to grain size sensitive creep at n ~ 1, at 125 oC,

occurs at a strain rate of about 10-9

s-1

. So, at slow strain rates ~10

-9 s

-1, at a

depth equivalent to an overburden/hydrostatic pressure of 50 MPa, grain

size sensitive creep mechanism plays a more important role than dislocation

mechanisms.

The number of experiments performed at the given conditions are

limited, i.e. one experiment on reagent grade synthetic fine grain

polycrystalline salt (halite1) and two on natural coarse grained salt samples

(halite2 and 3), whereas the composite flow law is proposed for natural salt

for at in situ conditions. Doing more experimentation on different grain

sized halite samples, both on synthetic and natural would help to make more

general flow law. However, the story (i.e. high n-value for faster strain rate

and higher stress and low n-value for slower strain rate and lower stress)

does not seem to change much as we have seen in the current work.

107

Chapter 4

Creep behaviour of bischofite,

carnallite and mixed bischofite-

carnallite-halite salt rock at in situ

conditions

108

4.1 INTRODUCTION

The salt deposits at Veendam (northern part of the Netherlands) are mainly

composed of the evaporites bischofite, carnallite and halite in the form of

layers and mixtures, with sulphates in minor quantities. In order to solution

mine the caverns, it is important to know the rheology of the different salts

at real in situ conditions, so that the rate of inflow into the caverns as well as

surface subsidence can be predicted. The strain rate of such salts in

underground mines is normally in the range of 10-8

to 10-15

s-1

(Heard 1972,

Van Eekelen et al. 1981, Jackson & Talbot 1986) which is a rate that cannot

be achieved easily in laboratory scale experiments. However, laboratory

experiments can be used to define a flow law that allows extrapolation to

real in situ conditions. In order to perform such extrapolation in a reliable

manner, good understanding of the deformation mechanism of the material

is needed, so that the characteristics of the flow law can be related to the

microphysical mechanism controlling creep. In this case study, the

mechanical properties of rock salts bearing bischofite, carnallite and their

mixtures, are studied with the main aim of producing constitutive flow laws

than can be applied at real in situ conditions.

Van Eekelen et al. (1981) and Urai (1983) have tested the creep

behaviour of bischofite at a fixed confining pressure of 28 MPa, in the

temperature range of 40-80 °C, with varying water content including dry

samples. The authors suggested that a conventional power law of the type

𝜀̇~𝜎𝑛, relating strain rate 𝜀̇ to stress , can be used to describe the flow

behaviour of bischofite, as long as two regimes were defined, one at low and

one at relatively high differential stress. The flow laws of the two regimes

show different values of the power law stress exponent n, namely 1.5 and 4

for the low and high stress regime, respectively. However, the nature of the

109

two regimes was not fully understood and accordingly, a good basis for

establishing the rate of inflow relevant in the case of cavern evolution

associated with solution mining is still missing.

The creep properties of dry and wet carnallite have been studied by Urai

(1985), by performing triaxial deformation experiments at a temperature of

60 oC, using a range of strain rates and confining pressures. Urai (1985)

proposed a conventional power law for steady state creep of wet carnallite

with stress exponent n = 4.8 ± 0.1. The strength of carnallite was found to be

substantially higher than that of bishofite. It is yet unknown what the

rheology of mixtures of bishofite and carnallite is like, and which of these

salts dominates creep in a mixture.

Also halite, both as natural single and poly-crystals and as artificially

prepared dense aggregates, has been studied before for its creep properties

under dry and wet conditions (Heard 1972, Heard & Ryerson 1986,

Wawersik & Zeuch 1986, Urai et al. 1986, Spiers et al, 1990, Senseny et al.

1992, Carter et al. 1993, Spiers & Carter 1998, Ter Heege et al. 2005b,

Muhammad et al. 2012). Also for this material, a conventional power law

appears to describe the behaviour well. For wet salt, the proposed stress

exponent n lies in the range of 4.1 to 5.7, in the temperature range of 23 to

400 oC.

In the current work, we have performed triaxial deformation experiments

on polycrystalline natural samples of bischofite, carnallite and their mixture

with halite, at real in situ conditions of confining pressure 40 MPa and at a

fixed temperature of 70 oC. All deformation tests were done in strain rate

stepping mode, with several steps being followed by stress relaxation

(Rutter & Mainprice 1978), with the aim to achieve strain rates as low as ~

10-9

s-1

, approaching the natural strain rates in salt caverns. Aims of the

110

work were: 1) to determine the creep behaviour of relatively pure bishofite

and carnallite under in situ conditions, 2) to establish the role of dislocation

creep, recrystallization and, possibly, pressure solution creep in the

behaviour of bishofite and carnallite, and construct creep laws that allow

reliable extrapolation, and 3) obtain a first order impression of the creep

behaviour of mixtures of bishofite, carnallite and halite, and compare this

with the behaviour of the end members.

The mechanical data of the samples tested confirmed that bischofite is

much weaker than carnallite, and revealed that carnallite is weaker than the

bishofite-carnallite-halite mixture. During stress relaxation, we observed

that, at 70 oC, the n-value for bischofite and carnallite gradually changed

with changing conditions, from n = 5 at higher stress (and higher strain rate)

to n = 1 for lower stress (and corresponding lower strain rate). For the

mixtures, the n-value is observed to be rather high at relatively high stress (n

> 10), but also reduced to n = 1 during relaxation to slow strain arte and low

stress. A higher n-value (n > 3) is usually related to grain size insensitive

(GSI) dislocation creep processes and a lower n-value is consistent with

grain size sensitive (GSS) mechanisms such as pressure solution. We have

evidence that the rate controlling mechanism might not be governed solely

by dislocation motion, but may also be grain size dependent, depending on

deformation conditions. Accordingly, the flow behaviour of bischofite and

carnallite can be explained by flow laws combining GSI and GSS creep. We

therefore suggest that the established flow laws for bischofite and carnallite

(Urai 1983, 1985) require modifications. These results help putting

constraints on the behaviour of salt mixtures, as for example in the case of

the salt deposits at Veendam.

111

4.2 METHOD


The natural cores of bischofite, carnallite and their mixture with halite,

extracted by Nedmag Industries Mining & Manufacturing B.V. during the

so-called TR9 drilling project, were provided with 100 mm diameter and 1

m length, along with the description. The selection of the cores was initially

based on the description, later on; compositional analysis was done locally

using micro XRF technique.

The cores were first cut down to rectangular rods of about 100 mm

length and 50 mm diameter using a hand saw. These rods were then shaped

down to samples with the required dimensions of 35 mm diameter and 85

mm (average) length, using Silicone Carbide papers. Since the salts under

investigation are hygroscopic, the samples were prepared in a low humidity

room with relative humidity (R.H.) < 15% to control the water content.

Natural salts in general are wet (Roedder & Bassett 1981, Urai 1983). In

order to create a deliquescence condition in our samples, comparable to that

at in-situ conditions, the samples were first equilibrated with air with R.H. >

30% (Urai 1985, Christov 2009) and, in parallel, carefully measured for

increase in weight by water absorption. This was followed by wrapping up

the samples in a double layer of perforated glass fibre sheet (0.3 mm starting

thickness) creating an equilibrated humid environment around the sample.

These wrapped samples were further sealed in 1.0 mm thick polymer

“ethylene propylene diene monomer (EPDM)” jackets to avoid

contamination of the samples by the confining medium (silicone oil) used in

the deformation apparatus. The deformation pistons were inserted in the

open ends of the jacket. To seal the ends, stainless steel wires were tightly

112

wound in grooves of the steel pistons from over the jacket. After the

experiments, the samples were taken out immediately, sealed in plastic

wrapper and stored at -20 oC to freeze the microstructures by preventing

fluid-assisted recrystallization processes.

In order to obtain a first-order insight into the composition of the mixed

salt rock samples used, the micro XRF (X-ray Fluorescence) technique was

applied. In this technique, flat surfaced samples were prepared by cutting

and polishing, and these surfaces were analysed for the number of counts

being received as per characteristic X-Rays of the elements. The output data

obtained from the XRF analysis contains a list of elements and their atomic

and weight percentage present at the surface of the selected area. These

elements can be combined according to their contribution in the chemical

formulae of the salts involved, and the results then show in wt. % the

composition. Unfortunately, the XRF machine used is not calibrated for

elements with atomic number smaller than 10. So the lighter elements

hydrogen and oxygen could not be detected. As a consequence, the water

content of our mixtures could not be studied.

4.2.2 Deformation apparatus

The apparatus used for this study was the so-called “Shuttle vessel” (Fig.

4.1) of the experimental rock deformation (HPT) laboratory at the

department of Earth Sciences at Utrecht University. The Shuttle vessel

machine consists of an internally heated 100 MPa confining pressure vessel

mounted on a standard Instron 1362 loading frame with a servo controlled

positioning system. This machine can be used to deform the sample at a

constant piston speed, approaching constant strain rate if total strains are

kept relatively low. The machine is provided with a (Instron standard) +/- 50

113

Figure 4.1. Shuttle vessel triaxial deformation apparatus.

Figure 4.2. Sample with piston assembly and steel discs

35 mm

LVDT_2

Deformation piston

Thermocouples

connections

Pressure vessel

containing sample

assembly

114

mm linear variable differential transformer (LVDT_1), but to come to an

accurate measurement of the sample deformation, another LVDT (LVDT_2)

with a 25 mm stroke from Jensen was installed at the top of the vessel and

near the sample, to reduce the effect of the elastic distortion of the apparatus

and measure accurately the shortening of the sample, especially during

stress relaxation, where very limited axial strain in the order of ~0.1% is to

be monitored. The temperature was measured by thermocouples at two

locations inside the vessel; one was positioned close to the middle of sample

and, the other was at the top of the sample. K-type thermocouples were

used, which are accurate within ± 1 oC. The axial load on the sample was

measured using a 100 kN load cell accurate within 0.1% of the full scale.

The confining pressure was created by using silicone oil which is kept at

constant pressure within ± 0.1 MPa using a servo pump. Measurement of the

pressure was done using a diaphragm pressure transducer (Teledyne 2403,

100 MPa range). To avoid rusting of the deformation pistons and related

contamination of the samples, two grooved stainless steel discs having 2.0

mm thickness and 35.0 mm diameter were used as separators, along with 50

μm thin PTFE sheets to reduce the friction between sample and the

deforming pistons (Fig. 4.2). The triaxial apparatus used is very sensitive to

the environmental conditions. For example, a little variation in laboratory

temperature not only causes a drift in the load cell signal, but also may

cause a small change in the pressure, which would influence the load cell

signal. Such (small) change in pressure will result in some elastic

expansion/contraction of the pressure vessel, hampering straightforward

processing of the data from the LVDT_2. Therefore the apparatus was

carefully calibrated for the effect of pressure and temperature on the load

cell. The elastic distortion of machine was corrected on the basis of tests

using a steel dummy sample of known Young’s modulus. This was done by

115

applying a gradually increasing axial load to the dummy and measuring the

LVDT_2 reading in parallel, then using a 10th order polynomial to relate the

LVDT_2 value to the internal load.

4.2.3 Experiments

In this study, multistep experiments were performed. A typical experiment

consisted of a few steps at constant strain rate, in the range 10-5

to 10-8

s-1

,

interrupted by periods of stress relaxation. During the constant strain rate

part of the test, the sample was deformed until a steady (or near steady) state

of stress was reached. This usually required about 2-4% of shortening. Then

the piston was arrested and the stress on the sample was allowed to relax

until the diminishing force on the sample reached the limits of the load cell

resolution. The duration of each relaxation step was a few days.

In detail, each experiment included a maximum of seven strain rate steps

(10-5

, 10-6

, 10-7

, 10-8

, 10-7

, 10-6

, 10-5

s-1

), followed by stress relaxation; after

each step in case of bischofite and after three steps (10-6

, 10-8

, 10-6

see Table

4.1) in case of carnallite and mixture samples. The experiments were

performed at 70 oC sample temperature and 40 MPa confining pressure for

real in situ conditions, whereas the bischofite was additionally tested at 70

MPa confining pressure to obtain a first-order impression of the pressure

sensitivity of creep.

4.2.4 Data acquisition and processing

Confining pressure, temperature, load and position (LVDT_1 and 2) were

logged throughout the test. The stress on the sample was calculated from the

load values by assuming constant volume deformation, correcting the

instantaneous area value for progressive change in length of the sample. The

116

cumulative strain (shortening) of the sample was calculated as the ratio of

the change in length of sample and the initial length of sample. The zero of

the internal load signal was tested before the deformation piston touched the

sample and after unloading at the end of experiment. If found necessary, a

correction was applied for zero-level shift. The data acquired during stress

relaxation was analysed with a dedicated code to produce the plastic strain

rate of the sample.

The stress relaxation technique is based on the following. During

deformation at constant rate (imposed by a moving piston), some energy

gets stored inside the material as elastically stored energy. During

relaxation, when the loading piston is arrested, this energy is dissipated

through plastic deformation of the sample. Ideally, this requires an infinitely

stiff machine which does not participate by means of the elastically stored

energy in its own frame. In practice, such a machine does not exist, so the

elastic modulus of machine should be taken into account. In other words, the

elastically stored energy inside the active part (under force) of the machine

also dissipates through the plastic strain of the sample, so the data also need

to be corrected for the stiffness of machine. In order to calculate the sample

straining, we take the simple assumption that the stress is proportional to

strain, provided that other physical conditions (confining pressure,

temperature, microstructure) are constant (Rutter & Mainprice 1978). The

strain rate at any instant will then be proportional to the stress relaxation

rate, with the elastic (Young’s) modulus of sample as a constant of

proportionality.

The measured total displacement” xtotal” (from LVDT_2) can be written

as the sum of the sample deformation (elastic + plastic) and elastic distortion

of apparatus

117

𝑥𝑡𝑜𝑡𝑎𝑙 = 𝑥𝑠𝑎𝑚𝑝𝑙𝑒 + 𝑥𝑎𝑝𝑝𝑎𝑟𝑎𝑡𝑢𝑠 (4.1)

After differentiating w.r.t. time and normalizing this Equation using the

instantaneous length of the sample, the following relation of plastic strain

rate of the sample is obtained:

𝜀�̇�𝑙𝑎𝑠𝑡𝑖𝑐 = 𝜀�̇�𝑜𝑡𝑎𝑙 −1

𝐸𝑠𝑎𝑚𝑝𝑙𝑒(�̇�𝑠𝑎𝑚𝑝𝑙𝑒) −

1

𝐿𝑡𝑆 (

𝜕𝐹

𝜕𝑡) (4.2)

where,

𝜀�̇�𝑙𝑎𝑠𝑡𝑖𝑐 = plastic strain rate of sample [s-1

]

𝜀�̇�𝑜𝑡𝑎𝑙 = total strain rate measured by LVDT_2 [s-1

]

𝐸𝑠𝑎𝑚𝑝𝑙𝑒 = Young’s modulus of sample [MPa]

�̇�𝑠𝑎𝑚𝑝𝑙𝑒 = sample stress relaxation rate [MPa s-1

]

𝐿𝑡 = instantaneous length of sample [m]

𝑆 = machine stiffness correction constant [m N-1

]

(𝜕𝐹

𝜕𝑡) = rate of change of force [N s

-1]

We then have to determine the total strain rate, stress relaxation rate and

the rate of change of force, as on right hand side of Equation (4.2), to

calculate the plastic strain rate of the sample. The first term, the total strain

rate (𝜀�̇�𝑜𝑡𝑎𝑙), was directly measured using the external LVDT_2 attached at

the top of the vessel. The second and third terms contain the calculation of

the change of the force and stress on the sample as a function of time, which

was done by defining a variable window size on each data point with

118

minimum 10% of its value on high and low side of the data series of force

and stress.

4.2.5 Young’s modulus measurement

The second term of Equation (4.2) contains the Young’s modulus E of the

sample material. Unfortunately, its value for bischofite and carnallite is not

reported in literature. We thus determined these values for the material

tested, by performing ultra-sonic time of flight sound velocity measurements

on unconfined samples of bischofite, carnallite and the mixture under study,

using the facilities at Technical University Delft. The results thus obtained

are given in Table (4.2).

4.2.6 Microstructures (only carnallite)

Three carnallite samples were selected for microstructural study, in

particular with the aim to determine the grain size. The samples were cut

along the cylindrical axis at the middle. Subsequently, the halves were

ground using silicon carbide papers, followed by polishing and etching to

reveal the grain boundaries in reflected light microscopy. The thick sections

of the samples were photographed with a high resolution photographic

camera. The line-intercept method was used to determine values for the

average grain size of the samples.

4.3 RESULTS

The mechanical results of bischofite, carnallite and mixture samples, along

with the experimental conditions have been tabulated in Table (4.1), where

the differential stress values obtained at the end of each step are given. Since

the main aim of this study is to produce a flow law to be applied at in situ

119

conditions, we will assess how the obtained mechanical data fit to

conventional power laws (Van Eekelen et al, 1981, Urai 1983, Ter Heege et

al. 2005b), describing grain size insensitive (GSI – dislocation) creep and/or

grain size sensitive (GSS – diffusion/pressure solution) creep, as given

below

GSI: 𝜀̇ = 𝐴∗𝜎𝑛 (4.3)

GSS: 𝜀 ̇ = 𝐵∗𝜎𝑑−𝑝 (4.4)

where 𝜀̇ is the strain rate, A* is a substituted constant term for Aexp(-Q/RT),

where A is constant (for constant temperature), Q is the activation energy, R

is the gas constant, T is the temperature, B* is also constant at a given

temperature T, σ is the flow stress of the sample, n is the stress exponent, d

is the average grain diameter, p is the grain size exponent.

4.3.1 Bischofite

(i) Stress vs. strain curves

In total, six experiments were performed on bischofite, all at a temperature

of 70 oC. Samples bischofite 5, 6 and 7 were tested at in situ condition of 40

MPa confining pressure, while bischofite 2, 3 and 4 were tested at 70 MPa

confining pressure (see Table 4.1). Figures 4.3a-c show the differential

stress vs. natural strain, d-f show the differential stress vs. time. Bischofite5

was a 7-step strain-rate stepping stress-relaxation experiment with relaxation

periods between every constant strain rate part. Bischofite6 was a 5-step

stepping experiments with stress relaxation followed by each step. The first

two steps of bischofite6 were performed at the same strain rate (10-6

s-1

) but

the stress obtained at the end of the first step was slightly lower than that at

120

(a)

(b)

121

(c)

(d)

122

(e)

(f)

Figure 4.3. Mechanical data bischofite5, 6 and 7, (a-c) differential stress vs. natural

strain (d-f), differential stress vs. time

123

the end of the second step (see Table 4.1), demonstrating that steady state

was not yet reached during the first step. Bischofite7 was a repeat of the

bischofite5 experiment, with the only difference being that the sample was

given comparatively more time for stress relaxation (see Table 4.1). This

test gave reasonably reproducible/overlapping differential stress values at

similar strain rates.

(ii) Effect of confining pressure

Bischofite 2, 3 and 4 were tested at 70 MPa confining pressure. Figures

4.4a-c show the stress-strain curves of these experiments. The stress values

obtained were very similar to the results at 40 MPa confining pressure

(Table 4.1).

(a)

124

(b)

(c)

Figure 4.4. Mechanical data bischofite2, 3 and 4, (a-c) differential stress vs. natural

strain

125

The current experimental data are shown in Figures 4.5a-b. Data from

Urai (1983), at temperatures 60 and 80 oC, at similar strain rate and fixed

confining pressure 28 MPa, are included in the Figure. Comparison of the

results revealed that there is no measurable effect of confining pressure on

the flow stress of bischofite in the range 40-70 MPa.

(a)

(b)

Figure 4.5. Pressure sensitivity of differential stress as compared with Urai (1983),

a) this study (70 oC) vs. Urai’s (60

oC), b) this study (70

oC) vs. Urai’s (80

oC).

126

Table 4.1: Test conditions and results of constant deformation parts, bischofite,

carnallite and mixture

Test

P

[MPa]

𝜀̇

[s-1

]

σ

[MPa]

Experiment

duration

[hrs.]

Bischofite5

40 10-5

5.3

576

40 10-6

3.8

40 10-7

2.3

40 10-8

1.2

40 10-7

2.2

40 10-6

3.4

40 10-5

5.0

Bischofite6

40 10-6

3.2

520

40 10-6

3.8

40 10-5

5.7

40 10-5

5.5

40 10-7

2.3

Bischofite7

40 10-5

5.2

1338

40 10-6

3.4

40 10-7

2.1

40 10-8

1.2

40 10-7

2.0

40 10-6

3.5

40 10-5

5.3

Bischofite2

70 10-6

3.7

45.3 70 10-5

5.9

70 10-4

9.5

Bischofite3

70 10-6

3.4

66.3

70 10-6

3.5

70 10-6

3.5

70 10-5

5.5

70 10-5

5.3

127

Table 4.1: contd.

Test

P

[MPa]

𝜀̇

[s-1

]

σ

[MPa]

Experiment

duration

[hrs.]

Bischofite4

70 10-5

5.5

106

70 10-6

3.0

70 10-7

2.0

70 10-8

---

70 10-7

2.2

70 10-6

3.2

70 10-5

4.9

Carnallite1

40 10-5

20.8

1050

40 10-6

13.2

40 10-7

9.0

40 10-8

5.5

40 10-7

9.0

40 10-6

14.0

40 10-5

24

Carnallite2

40 10-5

21.5

953

40 10-6

13.4

40 10-7

9.0

40 10-8

5.2

40 10-7

9.0

40 10-6

14.5

40 10-5

24.3

Carnallite3

40 10-5

28.1

73 40 10-6

18.8

40 10-7

11.1

Carnallite4 40 10-5

17.4 143

128

Table 4.1: contd.

Test

P

[MPa]

𝜀̇

[s-1

]

σ

[MPa]

Experiment

duration

[hrs.]

Carnallite5

40 10-5

21.9

579

40 10-6

13.8

40 10-7

9.4

40 10-8

6.1

40 10-7

10.2

40 10-6

15.2

40 10-5

23.8

Mixture1

40 10-5

25.7

1014

40 10-6

26.1

40 10-7

23.2

40 10-8

20.6

40 10-7

23.3

40 10-6

27.7

40 10-5

33.3

Mixture2

40 10-5

24.9

611

40 10-6

21.6

40 10-7

16.8

40 10-8

10.8

40 10-7

16.7

40 10-6

21.1

40 10-5

25.2

P is the confining pressure

σ is flow/steady state stress (at the end of each deformation step)

𝜀̇ is strain rate of deformation

(iii) Flow behaviour

All stress values obtained at the ends of the constant strain rate steps (Table

4.1), approaching steady state, are plotted against corresponding

deformation strain rates in Figure 4.6. Note that the dependent variable

(stress) is plotted along the x-axis in this figure, to allow easier comparison

129

with the relaxation data presented below. Best fit linear regression (in log-

log-space) resulted in n = 4.8 ±0.2 when applying the conventional power

law of Equation (4.3).

The steady state stress values have also been used to calculate n-values (cf.

Eq. 4.3) for every individual step in strain rate of experiments bischofite 5-

6-7. The resulting values are plotted in Figure (4.7). The n-value changes

from about 6 at the higher stress to about 4 at the lower end of the stress

range. This shows that a simple power law of the type of Equation (4.3)

might not be applicable to the full data set for bischofite. This will be

explored further in the Discussion part of this Chapter.

Table 4.2. Elastic modulus of the specimens

Sample ρ

[kg m-3

]

Vp

[m s-1

]

Vs

[m s-1

] ν

G

[GPa]

E

[GPa]

Carnallite 1600* 3938 1988 0.33 6.3 16.8

Bischofite 1600* 4312 2037 0.36 6.6 18.0

Mixture 1600* 3970 2207 0.28 7.8 19.8

Halite 2100* -- -- -- -- 39*

ρ: density of the material

Vp: longitudinal component of velocity (measured)

Vs: shear component of velocity (measured)

ν: Poisson’s ratio (calculated)

G: shear modulus (calculated)

E: Young’s modulus (calculated)

*From literature

130

Figure 4.6. Complete data of bischofite tests at 40 MPa confining pressure.

Figure 4.7. n-value at different steady state stress values in bischofite5, 6 and 7.

-8.5

-8.0

-7.5

-7.0

-6.5

-6.0

-5.5

-5.0

-4.5

-4.0

0.0 0.2 0.4 0.6 0.8

Log (

stra

in r

ate[

s-1])

Log (flow stress [MPa])

Bischofite data

0

1

2

3

4

5

6

7

8

-1.0 -0.5 0.0 0.5 1.0

n-v

alue


n = 4.8 ±0.2

131

(iv) Stress relaxation

The stress relaxation results obtained for the individual bischofite

experiments at 40 MPa confining pressure are plotted in Figures 4.8a-j. The

steady state stress values obtained at the end of each strain rate step are

included in the graphs and form the starting points for relaxation. Results at

similar strain rate are combined. Generally, the graphs show that the

evaluated plastic strain rate at the start of each relaxation fit to a trend with

relatively high n-value (n ~ 5), implying that stress is relatively insensitive

to strain rate. During relaxation then, the stress-strain rate sensitivity

gradually increases and the n-value appears to approach n = 1 near the end

of each relaxation step. Strikingly, the individual relaxation curves, starting

at a particular strain rate and gradually decreasing in strain rate, do not pass

through the steady state values obtained during the constant strain rate parts

at lower rates. If compared at the same strain rate, the strength of the

material during relaxation is always less than that during the constant strain

rate part. It is noted that occasionally, there were stick slip events during the

steps, occurring due to piston/seal friction (see irregularities in the curves).

This resulted in apparent sudden rise in calculated plastic strain rate, but it

did not change the trend as it regained its progression toward low n-value

after every event.

132

(a) (b) (c)

(d) (e) (f)

133

(g) (h) (i)

(j)

Figure 4.8. Stress relaxation curves bischofite tests at P = 40 MPa, for

comparison, the relaxation curves of similar strain rate deformation steps

are combined, a) Bischofite5, step1 and step7 𝜀̇ = 10-5

s-1

, b) Bischofite5,

step2 and step6 𝜀̇ = 10-6

s-1

, c) Bischofite5, step3 and step5 𝜀̇ = 10-7

s-1

, d)

Bischofite5, step4 𝜀̇ = 10-8

s-1

, e) Bischofite6, step1 and step2 𝜀̇ = 10-6

s-1

, f)

Bischofite6, step3 and step4 𝜀̇ = 10-5

s-1

, g) Bischofite7, step1 and step7 𝜀̇ =

10-5

s-1

h) Bischofite7, step2 and step6 𝜀̇ = 10-6

s-1

, i) Bischofite7, step3 and

step5 𝜀̇ = 10-7

s-1

, j) Bischofite7, step4 with strain rate 10-8

s-1

134

4.3.2 Carnallite


Five carnallite samples were tested and their stresses vs. natural strain data

(Table 4.1) are shown in Figures 4.9a-e. Carnallite1 and 2 were both 7-step

strain-rate stepping tests with three relaxation periods after constant strain

rate deformation steps at 10-6

, 10-8

and 10-6

s-1

, respectively. Carnallite3 was

a 3-step stepping test without relaxation, carnallite4 was a single step

deformation test followed by stress relaxation, and carnallite5 was a repeat

experiment of carnallite 1 and 2. The samples showed strain rate sensitivity

of stress, and strengths at the end of similar (repeat) strain rates were

slightly higher for steps at higher total strains (see Table 4.1). The strengths

of carnallite1, 2 and 5 are in good agreement with each other, demonstrating

reproducibility. Carnallite3 was comparatively too strong when compared

with carnallite 1, 2 and 5 at similar strain rates, while carnallite4 was found

to be slightly weaker than the other samples.

(ii) Flow behaviour

All stress values obtained at the ends of the constant strain rate steps (Table

4.1), approaching steady state, are plotted against strain rate in Figure 4.10.

As was the case in Figure 4.6, the dependent variable (stress) is plotted

along the x-axis in this figure, to allow easier comparison with the

relaxation data presented below. Best fit linear regression (in log-log-space,

Fig. 4.11) resulted in n = 5.1 ±0.3 when applying the conventional power

law of Equation (4.3).

135

(a)

(b)

136

(c)

(d)

137

(e)

(f)

138

(g)

(h)

139

(i)

(j)

Figure 4.9. Mechanical data carnallite1-5, (a-e) differential stress vs. natural strain,

(f-j) differential stress vs. time.

140

Figure 4.10. Steady state stress values of carnallite samples against the strain rate on

log space. Note: the strain rate is independent in this work, but it is plotted on

dependent axis (Y-axis) to compare with the relaxation data.

Figure 4.11. n-values at different steady state values of carnallite experiments

-8.5

-8.0

-7.5

-7.0

-6.5

-6.0

-5.5

-5.0

-4.5

-4.0

0.5 0.7 0.9 1.1 1.3 1.5

Log (

stra

in r

ate[

s-1])

Log (stress [MPa])

Carnallite all data

0

1

2

3

4

5

6

7

0.5 0.7 0.9 1.1 1.3 1.5

n-v

alu

e

Log Stress [MPa]

n = 5.1 ±0.3

141


The stress relaxation results obtained for carnallite tests are plotted in Figure

4.12. The steady state values obtained at the end of each deformation step

are included in the graphs and form the starting points of the relaxation. For

comparison, similar strain rate deformation steps are combined. Generally,

the graphs show that the evaluated plastic strain rate at the start of each

relaxation fit to a trend with relatively high n-value (n ~ 5), implying that

stress is relatively insensitive to strain rate. During relaxation then, the

stress-strain rate sensitivity gradually increases and the n-value appears to

approach n = 1 near the end of each relaxation step. The relaxation curves

found not passing through the steady state values obtained during the

constant deformation steps, but stay on lower stress side. i.e. the strength of

the material is low during relaxation if compared at similar strain rates. It is

noted that occasionally, there were stick slip events during the steps,

occurring due to piston/seal friction (see irregularities in the curves). This

resulted in apparent sudden rise in calculated plastic strain rate, but it did not

change the trend as it regained its progression toward low n-value after

every event.

142

(a) (b) (c)

(d) (e) (f)

143

(g)

Figure 4.12. Stress relaxation curves bischofite tests at P = 40 MPa, for comparison, the relaxation curves of similar strain rate

deformation steps are combined, a) Carnallite1 step2 and step6 𝜀̇ = 10-6

s-1

, b) Carnallite1 step4 𝜀̇ = 10-8

s-1

, c) Carnallite2 step2 and

step6 𝜀̇ = 10-6

s-1

,d) Carnallite2 step4 𝜀̇ = 10-8

s-1

, e) Carnallite4; The only relaxation step 𝜀̇ = 10-5

s-1

, f) Carnallite5 step2 and step6 𝜀̇ =

10-6

s-1

, g) Carnallite5 step4 𝜀̇ = 10-8

s-1

,

144

(iv) Microstructures

Samples carnallite1, 3 and 4 and one undeformed sample have been used for

microstructural analysis. The undeformed microstructure (Fig. 4.13a) shows

a dense aggregate of grains with an average grain size of 4.9 mm. The grain

size resulting at the end of the multi-step (strain rate stepping and

relaxation) experiment carnallite1 was measured to be 2.3 mm. Carnallite3

only included strain rate steps, no relaxation, and resulted in an average

grain size of 3.5 mm. Carnallite4 was one step (10-5

s-1

) deformation

experiment followed by relaxation. The grain size measured is 5.4 mm. The

measurements are summarized in Table (4.3).

Table 4.3 Measured grain sizes of different carnallite samples

Sample 𝜀̇

[s-1

]

σ

[MPa]

d

[mm]

Stress

Relaxation

ε

Undeformed -- -- 4.865 -- --

Carnallite1 10-5

24 2.335 No 0.16

Carnallite3 10-7

11.1 3.535 No 0.96

Carnallite4 10-5

17.4 5.425 Yes 0.54

𝜀̇: deformation strain rate

σ: maximum/steady stress at the end of the corresponding strain rate step

d: measured grain size from microstructure of sample, using line intercept method

ε: maximum natural strain at the end of the constant strain rate deformation

(a)

10 mm

145

(b)

(c)

10 mm

10 mm

146

(d)

Figure 4.13. The microstructures of carnallite samples, a) carnallite undeformed;

showing dense aggregate of grains in grey scale, with average grain size 4.9 mm, b)

Carnallite1, σ = 24 MPa (at the end of experiment), deformation strain rate 𝜀̇= 10-5

s-1

, without relaxation, showing deformed (slightly flattened) grains by deformation,

compression direction is horizontal, c) carnallite3, σ = 11.1 MPa (at the end of

experiment), deformation strain rate 𝜀̇= 10-7

s-1

, without relaxation, compression

direction horizontal. The grain boundaries look slightly opened up, which might be

due to handling of sample while preparing for microstructural analysis, d)

Carnallite4 (after stress relaxation), deformation strain rate 𝜀̇= 10-5

s-1

, compression

direction horizontal. The grains appear slightly grown during relaxation. The

average grain size showing is 5.4 mm, which is bigger than other three measured

samples (i.e. undeformed, carnallite1 and 3).

4.3.3 Mixture samples of bischofite, carnallite and halite


Two multistep experiments were performed on mixed bischofite-carnallite-

halite samples. mixture1 was a 7-step strain-rate stepping test with three

relaxation periods after constant strain rate steps at 10-6

, 10-8

and 10-6

s-1

,

respectively (see Table 4.1). The sample showed strain hardening in all

10 mm Fracture line during sample preparation

147

constants strain rate steps (Fig. 4.14a), except for the one at the lowest rate.

Mixture 2 was also a 7-step strain-rate stepping test with three relaxation

periods (Table 4.1), following the same sequence of steps as applied in

mixture1 (Fig. 4.14a). The sample mixture2 contained a distinct carnallite

band of ~14 mm width, appearing as a ~30o tilted disc in the middle of the

sample (see Figure 4.15b). Mixture 2 was found to be weaker than mixture

1, and did not show the strain hardening as observed in mixture 1, but rather

approached steady state stress behaviour in individual steps (Figure 4.15a).

At the end of the experiment, the sample was taken out of the testing

machine and localized strain along the pre-existing carnallite band (Figure

4.15b) was observed. This localized shear strain at the carnallite band most

probably caused some leakage of the rubber jacket in the final stage of the

experiment, which allowed some silicon oil to effuse through jacket and

contaminate the sample.

(ii) Flow behaviour

The sensitivity of stress to strain rate of the two mixtures is illustrated in

Figures 4.16a-b, plotting the stress values at the end of each step as a

function of strain rate, again with strain rate along the y-axis. Figure 4.16a

quite clearly illustrates the hardening behaviour of mixture1 and shows that

the sensitivity of the differential stress to strain rate is rather low (high n-

value). Figure 4.16b shows that the flow behaviour of mixture2 does not

follow a linear trend in log-log space. Expressed using the power law n-

value (Eq. 4.3), the trend is from n ~ 10 at the higher stress and faster strain

rate, to n ~ 5 at lower stress and slower strain rate.

148

(a)

(b)

Figure 4.14. a) Stress-strain curve for mixture1, b) mixture1 sample after

deformation, loading direction vertical.

10 mm

149

(a)

(b)

Figure 4.15. a) Stress strain curve for mixture2, b) mixture2 sample before and after

deformation, loading direction vertical.

10 mm

150

(a) (b)

Figure 4.16 Steady state (or maximum) stress values at each step, showing the strain

history. a) Mixture1 has higher stress values towards higher strain; b) mixture2 has

reproducible stress values for similar strain rates. Note: Scale along stress axis is

not same and mixture1 is stronger at the end, if compared at similar strain rates.

151


The stress relaxation data of mixtures are shown in Figures 4.17(a-d). The

steady state values obtained at the end of each deformation step are included

in the graphs and from the starting points of relaxation. For comparison,

similar strain rate steps are combined. At start of relaxation, the n-value is

high (n > 10) showing steep slope, implying that the stress is relatively

insensitive to strain rate. During relaxation then, the n-value decreases and

appears to approach n = 1 near the end of each relaxation step. Distinctly,

mixture1 relaxation curves progressively, pass through the steady state

points obtained during deformation steps (compare Figs. 4.17a and c),

pointing that the mixture2 shows weaker behaviour during relaxation than

during deformation. A similar trend was observed during stress relaxation of

bischofite and carnallite (compare with Figs. 4.8 and 4.12). Note that the

relaxation curves showed crest-troughs due to day and night temperature

rhythm, which is quite substantial.

152

(a) (b)

(c) (d)

Figure 4.17. Stress relaxation behaviour of mixture samples. a-b) mixture1, c-d) mixture2. Note the x-axis (Log stress) scale of

mixture 2 is different from that of mixture1.

153

4.3.4 Elemental analysis using micro X-Ray Fluoroscopy (μ-XRF)

In order to obtain some first-order insight into the composition of the

samples used in the experiments, the micro XRF (X-ray Fluorescence)

technique was applied. In total 5 number of samples were analysed;

carnallite1, 3 and 5, mixture1 and 2.

As a first step, a relatively large cross-section of the sample was mapped

for different elements. This gave a qualitative overview. After this step, one

smaller rectangular area per sample (20 × 5 mm2), taken as representative of

the whole sample (e.g. mixture1 and 2, Figs. 4.18a-b), was selected for

detailed elemental analysis. The results for the selected areas are visualized

in Figure 4.19. In the figures, darker colour reflects higher wt. % of the

contributing salts. The figures show that carnallite samples (1, 3 and 5)

contain; higher percentage of carnallite (KMgCl3), i.e. 64 to 66 wt. %,

bischofite 17 to 19 wt. % and halite as 6 to 8 wt. % and other trace elements.

The mixture1 has higher halite wt. % (65%), the next abundant mineral is

bischofite (14.15%) followed by carnallite (4.13%) and traces are 14.18%.

Mixture2 has got bischofite (18.6%), halite (29.8%) and carnallite (36.8 wt.

%). In short, all samples contain the neighbour minerals and not very pure in

composition. In mixture1, the wt. % of halite is rather high, 65.4%, while

bischofite is 14.2%, carnallite is 4.1% and the remaining elements are

considered as trace elements as their contribution is very limited. In

mixture2, the halite composition is less than in mixture1, and is ~30%,

carnallite is slightly higher than in mixture1, ~37%, and bischofite is 18.6%.

154

(a)

(b)

Figure 4.18. Selection of area for detailed inspection of elements for micro XRF. a)

mixture1,b) mixture2

10 mm

10 mm

155

Carnallite1

156

Carnallite3

157

Carnallite5

158

Mixture1

159

Miixture2

Figure 4.19. Micro XRF analyses of the samples showing composition in wt. %.

Bischofite (MgCl2), Carnallite (KMgCl3), Halite (NaCl)

160

4.4 DISCUSSION

4.4.1 Mechanical behaviour

The stress strain plots of the three salts tested; bischofite (Figures 4.3 and

4.4), carnallite (Figure 4.9) and their mixture including halite (Figures 4.14

and 4.15) showed that these materials have different strengths for similar

strain rate and temperature. Bischofite was found the weakest in the series.

Carnallite appeared stronger than bischofite and the mixture was found even

stronger than carnallite. Note that mixture1 showed strain hardening

throughout the test and was found the strongest in the series, while mixture2

approached steady state behaviour. The stress values reached at the end of

the constant strain rate tests were related to the strain rates via the standard

power law of Equation (4.3), resulting in n = 4.8 ±0.2 for bischofite, n = 5.1

±0.3 for carnallite, and n ~ 5-10 for mixtures. Commonly, n-values ranging

3 to 4.5 are related to dislocation climb as the rate controlling mechanism,

involving bulk vacancy diffusion though the lattice (Weertman 1968,

Sherby & Weertman 1979, Poirier 1985), where the n-value may rise to 6.5

if pipe diffusion along dislocation cores plays a controlling role (Frost &

Ashby 1982, De Bresser 1991). Climb controlled dislocation creep is a grain

size insensitive (GSI) mechanism. The stress relaxation trend of all three

materials showed rather low sensitivity of stress to strain rate at the start (n

~ 5 for bischofite and carnallite and n > 5 for mixtures), but this sensitivity

changed towards the end of relaxation, when the n-value approached 1.

Such low n-values are usually interpreted as indicating grain size sensitive

(GSS) behaviour.

We will now first consider the flow law for bischofite and carnallite

taking only the data resulting from the constant strain rate tests into account,

161

i.e. representing the GSI behaviour of the materials, and then discuss how to

use the relaxation data to come to a more complete description of the salts

and their mixture. Two important elements need to be taken into account in

this discussion: i) the gradual change to n ~ 1 observed towards slow strain

rate during relaxation, and ii) the observations that the relaxation curves of

all three salts tested, gradually covering slower strain rates, did not pass

through the steady state values determined at slower rates than where

started.

(i) Creep law for bishofite using stresses at the end of constant

strain rate steps

The stress exponent n determined for every individual step in strain rate of

experiments Bischofite 5-6-7 (Fig. 4.8) changed from about 6 at the higher

stress to about 4 at the lower end of the stress range, showing that a simple

power law of the type of Equation (4.3) might not be applicable. Rather, a

general flow equation may be used (De Bresser et al. 2002, Renner et al.

2002), of the type

𝜀̇ = 𝐴𝜎𝑛𝑒𝑥𝑝 (𝜎

𝐵) 𝑒𝑥𝑝 (

−𝑄

𝑅𝑇) 𝑑−𝑝 (4.5)

where A and B are constants, Q represents the activation energy of the rate

controlling process, and R is the gas constant. The exp(σ/B) term in this

equation makes that stress-strain rate data plotted in log-space do not follow

linear trends. Comparing the current bischofite data at temperature 70 oC (as

N70) with Urai’s 1983 at temperatures 60 and 80 oC (as U60 and U80),

Figure 4.20, we see that the trend of N70 is slightly different, as it shows

slightly weaker behaviour for faster strain rates (10-6

s-1

and higher) and

stronger behaviour for slower strain rates (10-7.5

s-1

and beyond).

162

Figure 4.20. Bischofite current steady state stress values (at 70 oC) comparison

with Urai's 1983 (at 60 and 80 oC).

For constant temperature conditions, the second exponential term drops out

and assuming, for now, grain size independent behaviour, Equation (4.5) is

reduced to

𝜀̇ = 𝐴′𝜎𝑛𝑒𝑥𝑝 (𝜎

𝐵) (4.6)

Taking the stress-strain rate data at steady state (Table 4.1) and applying

non-linear regression analysis, the following best fit values of the

parameters included in Equation (4.6) were found: n = 3.4, 𝐴′= 10(-8.519)

, and

B = 2.261 (correlation coefficient, R2 = 0.99). According to this best fitting,

the n-value approaches 3.4 at low stress of 0.1 MPa and increases to ~ 6 at

higher stress (~0.6 MPa, cf. Fig. 4.7).

-10

-9

-8

-7

-6

-5

-4

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Log (

stra

in r

ate

[s-1

])


U60 U80 N70

163

Of course, in this analysis, it is assumed that a single GSI creep law

applies to the data. Later this discussion, we will discuss the possibility that

a composite creep law combining GSI and GSS might suit the observations

better.

(ii) Creep law for carnallite using stresses at the end of constant

strain rate steps

The conventional power law of the type of Equation (4.3) can be written

in full as:

𝜀̇ = 𝐴𝑜𝑒𝑥𝑝 (−𝑄

𝑅𝑇) 𝜎𝑛 (4.7)

where Ao is a constant, Q represents the activation energy of the rate

controlling process, and R is the gas constant. Since all our experiments

were carried out at the same temperature (70 oC), our data do not allow

determining a value for the activation energy Q. However, we can compare

our data with the results of Urai (1985) on carnallite. Using the steady state

(or the maximum) stress values for each step and plotting these against the

strain rate in the corresponding step, all data are plotted in Figure 4.21. The

graph shows that the current results are in good agreement with Urai’s wet

sample results. Urai (1985) obtained n = 4.5 ±1.0 for steady state flow of

wet carnallite. The value obtained for the stress exponent n in the current

work is 5.1 ± 0.3, hence is in agreement with the result of Urai. More

importantly, it is a far more accurate determination of n than previously

established. Given the agreement of our n-value with that of Urai (1985),

taking the errors into account, it is justified to apply the Q-value determined

by Urai to our data, which is 83700 (± 20000) J/mole.

164

Figure 4.21. Current study carnallite data vs. Urai (1985) dry and wet carnallite

sample data.

Taking the steady state data of all carnallite samples, the temperature

used T = 70 oC (343 K), n = 5.1 and Q = 83700 Jmol

-1, a value of 6.4 (MPa

-

5.1 s

-1) was thus determined for Ao. With these values for Ao, n and Q,

Equation (4.7) can now be used to describe the steady state flow of

carnallite at various temperatures:

𝜀̇ = 6.4 𝑒𝑥𝑝 (−83700

𝑅𝑇) 𝜎5.1 (4.8)

For the in situ temperature of 70 oC (343 K), Equation (4.8) reduces to:

𝜀̇ = 1.13 × 10−12𝜎5.1 (4.9)

-10

-9

-8

-7

-6

-5

-4

0.0 0.5 1.0 1.5 2.0

Log (

stra

in r

ate

[s-1

])


Carnallite

Urai_Dry

Urai_B1.15%

This study

165

(iii) Comparison of steady state values

For a comparison of the strengths measured as steady state values of

bischofite, carnallite and mixture, averaged values at similar strain rates

were used to calculate strength ratios and plotted in Figure 4.22. The

comparison shows that the strength ratio is higher at slower strain rates.

Carnallite is 4.3 times and mixture is 5.1 times stronger than bischofite at a

strain rate of 10-5

s-1

; this ratio increases towards slower deformation strain

rates, resulting in values 4.7 times and 13 times at strain rate of 10-8

s-1

,

respectively The strength of the mixture is 1.2 times larger than that of

carnallite for a strain rate of 10-5

s-1

and 2.8 times at 10-8

s-1

. If we compare

our work with previous studies on halite by Heard (1972), Wawersik &

Zeuch (1986), Carter (1993) and Ter Heege et al. (2005a), we see (Figure

4.23a) that the upper limit (highest stress at a given strain rate) is

constrained by the flow law by Heard (1972 - confined tests on

polycrystalline natural halite aggregates) at the temperature of 70 oC.

Carnallite is weaker and lies around the flow law given by Wawersik &

Zeuch (1986), whereas the bischofite is clearly the weaker end in the family.

(iv) Relating the relaxation behaviour to the creep at near steady

state

We observed that the behaviour of bischofite, carnallite and (notably)

mixture2 during relaxation is different from that during the constant strain

rate parts of the testing; in all three multi-step experiments, the material was

weaker during relaxation than during deformation at constant strain rate, if

compared at the same strain rate or stress. In addition, if the dependence of

strain rate on stress is considered by means of the power law n-value (Eq.

166

Figure 4.22. Strength ratios of mixture by taking bischofite and carnallite as

reference. B/B: bischofite to bischofite, C/B: carnallite to bischofite, M/B: mixture

to bischofite and M/C is mixture to bischofite strength ratio at similar strain rates.

(a)

0

2

4

6

8

10

12

14

1.E-09 1.E-07 1.E-05

Str

ength

rat

io

Strain rate [s-1]

B/B

C/B

M/B

M/C

-14

-12

-10

-8

-6

-4

-2

0.0 0.5 1.0 1.5 2.0

Lo

g (

stra

in r

ate

[s-1

])

Log(flow stress [MPa])

Bischofite Carnallite

Mixture1 Mixture2

Ter Heege 2005a Heard 1972

Carter 1993 Wawersik&Zeuch1986

167

(b)

Figure 4.23 a) Projected curves for flow laws of wet halite from previous studies, b)

steady state values comparison of bischofite, carnallite and mixture (with halite%

composition)

4.3), the n-value during relaxation is lower than at constant strain rate, again

if compared at the same strain rate or stress.

During relaxation, when changes in strain are very limited, the

microstructure may be expected to remain constant (see Rutter & Mainprice

1978), while processes such as dynamic (syn-deformational)

recrystallization and grain growth are likely to affect the microstructure

during deformation covering substantial changes in strain (De Bresser et al.

2001, Ter Heege et al. 2005a). The relaxation data suggest that dependence

of strain rate on stress may approach linearity (i.e. n-value approaching 1),

which suggests that grain size sensitive behaviour might play a role at low

stress (Spiers et al. 1990, Ter Heege et al. 2005a). We thus speculate that

during relaxation, the creep behaviour of bischofite, carnallite and mixtures

-14

-12

-10

-8

-6

-4

-2

0.0 0.5 1.0 1.5 2.0

Log (

stra

in r

ate[

s-1])

Log ( flow stress[MPa])

Bischofite Carnallite Mixture1 Mixture2

168

might go through a transition from GSI creep (Eq. 4.3) at the faster strain

rates (at the start of relaxation) to GSS creep (Eq. 4.4) at relatively slow

rates. This transition then would occur at constant structure, notably at

constant grain size, while the transition from GSI to GSS creep might be

prevented during steady state creep when microstructural modification is

effective. Since our study did not systematically involve experiments on

materials with different grain size, we explore the possible role of GSS

creep using predictions on the basis of recrystallized grain size piezometers

for the salts under consideration. In a recrystallized grain size piezometer,

the size of the grains is directly related to the differential stress (e.g. Twiss

1977, Shimizu 2008, De Bresser et al. 2001) according to:

𝑑 = 𝐾𝜎 −𝑚 (4.10)

Or

𝜎 = 𝐾1

𝑚 𝑑−1

𝑚 (4.11)

where K and m are material and mechanism specific constants. This

relationship between stress and recrystallized grain size is generally

assumed to be independent of temperature, although that there is evidence

that this assumption is not generally valid (de Bresser et al. 2001).

Bischofite

Van Eekelen et al. (1981) measured the recrystallized grain size in a number

of bischofite samples experimentally deformed at 60 °C (Figure 4.24). We

used their data to calibrate the values for K and m in Equations (4.10) and

(4.11) by simply applying

169

Figure 4.24. Flow stress vs. mean grain size at 60oC

𝑑 = 𝐾(𝜎)−1

𝑠𝑙𝑜𝑝𝑒⁄ (4.12)

The resulting Piezometric relation for bischofite is:

𝑑 = 4.725𝜎 −1.15 (4.13)

Using the piezometer of Equation 4.13, we can now estimate the

recrystallized grain size at any stress, under the assumption the dynamic

recrystallization was fully effective at the conditions imposed. We have

done this for the average stresses relevant for our bischofite samples at the

start of the relaxation periods, after steps at constant strain rate of 10-5

, 10-6

,

10-7

and 10-8

s-1

. The results are given in Table (4.4). The role of grain size

can now be further evaluated by (1) assuming that during relaxation the

grain sizes will remain the same, and (2) that a GSS creep law of the type of

Equation 4.4, with n = 1, applies at the final stages of relaxation, i.e. at the

y = -0.8686x + 0.5858

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

-1.0 -0.5 0.0 0.5

Log (

flow

str

ess

[MP

a])


Van Eekelen et al. 1986 bischofite data

170

Figure 4.25. Log strain rate values picked from relaxation curves at similar stress of

1.0 MPa

very slow strain rates, This allows calculating the p-value (Equation 4.4).

Taking logarithm and simplifying the Equation (4.4) we get

𝑙𝑜𝑔𝜀 ̇ = 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 − 𝑝𝑙𝑜𝑔𝑑 (4.14)

The intercept includes the stress and is only a constant if data are

considered at single value of stress. For this, we picked σ = 1.0 MPa (i.e.

Logσ = 0) in the stress relaxation curves (Figures 4.8(a-j)), determined the

strain rate values at the various relaxation curves, and plotted the results, in

log-log space (cf. Eq. 4.14, see Fig. 4.25), against the values for the grain

size from Table (4.4). Then using Equation 4.14, the grain size exponent ‘p’

can be determined as from the slope of the best fit line (Figure 4.25).

As is clear from the Figure 4.25, the scatter is quite substantial, so the

resulting value for p, 0.8 ±0.2, must be regarded as only a crude estimate.

Nevertheless, the result confirms the suggestion that grain size sensitive

y = -0.7539x - 7.4049

-8

-7.9

-7.8

-7.7

-7.6

-7.5

-7.4

-7.3

-7.2

-7.1

-7

-0.5 0 0.5 1

Lo

g (

stra

in r

ate

[s-1

])


Bischofite this study

171

Table 4.4: Estimated grain size from piezometer

Salt 𝜎𝑎𝑣𝑒𝑟𝑎𝑔𝑒

[MPa]

𝜀̇ [s

-1]

d

[mm]

Bis

cho

fite

5.3 10-5

0.69

3.5 10-6

1.10

2.2 10-7

1.91

1.2 10-8

3.83

Car

nal

lite

22.7 10-5

1.81

14.7 10-6

2.99

9.5 10-7

4.92

5.6 10-8

9.06

𝜎𝑎𝑣𝑒𝑟𝑎𝑔𝑒 : average stress value for similar strain rate of deformation,

taken from Table 4.1

𝜀̇: deformation strain rate

d: estimated grain size from piezometer

behaviour is likely to play a role in the flow behaviour of bischofite, at least

during the relaxation. A possible mechanism controlling flow in this GSS

regime is dissolution or precipitation controlled pressure solution creep (e.g.

Spiers et al. 1990, Schutjens 1991). A possible mechanism controlling flow

in this GSS regime is dissolution or precipitation controlled pressure

solution creep (e.g. Spiers et al. 1990, Schutjens 1991). According to these

studies, the inter-granular pressure solution creep (IPS) is a serial process

comprising of three steps; dissolution of material at high stress zones,

transportation via diffusion to lower stress zones and precipitation at low

stress zones. The slowest of these will determine the creep rate. The creep

rate is inversely related to the grain size (‘d-p

’), where p = 1, 2 and 3 are the

sensitivities of the rate controlling mechanism to grain size, defining

dissolution, diffusion and precipitation respectively.

It cannot be excluded that during the long time spans needed for

relaxation down to slow strain rates, some microstructural modifications has

172

taken place, notably (static) grain growth. This then undermines our

assumption of constant structure. However, the range of (predicted) grains

sizes in our samples is rather limited (Table 4.4), the durations of the

various relaxation steps are quite comparable, and all tests were done at the

same temperature. Consequently, the possible change in grain size during

relaxation due to grain growth will be almost the same for all steps, hardly

affecting estimates of the value for p.

Using the intercept value of the best fit line (Fig. 4.25), the unknown

constant B* of Equation (4.4) was calculated to be 3.94×10-8

(MPa-1

mm0.8

s-

1). Hence, the GSS flow law for bischofite at 70

oC, with grain size d in mm

is

𝜀�̇�𝑆𝑆 = 3.94 × 10−8𝜎𝑑−0.8 (4.15)

Carnallite

No recrystallized grain size Piezometric relation is available in the literature

for carnallite. We plotted our grain size data of two carnallite samples as a

function of stress together with the data for halite (Ter Heege et al. 2002b)

and bischofite (Van Eekelen et al. 1981) in Figure 4.26. Bischofite and

halite follow very comparable trends, but the grain size of carnallite at a

given stress is substantially larger than that of halite and bischofite. We

assumed that the trend observed for halite and bischofite also holds for

carnallite, coming from the same family of materials. We thus suggest that

the recrystallized grain size Piezometric relation for carnallite (Fig. 4.26) is:

𝑑 = 65.92𝜎 −1.15 (4.16)

173

Figure 4.26. Carnallite measured grain sizes in log space with halite and bischofite

Figure 4.27. Strain rate values picked from relaxation data plotted against stress

equivalent grain size from piezometer

Now doing the same exercise for carnallite as carried out for bischofite,

applying Equations 4.4 and 4.14 under the assumption of constant structure

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

-1.5 -0.5 0.5

Log (

flow

str

ess

[MP

a])


Bischofite Halite

Carnallite Estimated grain size

y = -1.079x - 7.3413

-9

-8.8

-8.6

-8.4

-8.2

-8

-7.8

-7.6

-7.4

-7.2

-7

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Lo

g (

stra

in r

ate

[s-1

])


Carnallite

174

(grain size) during relaxation, we can obtain a crude estimate for the p-value

for carnallite. We picked σ = 4.0 MPa (i.e. Logσ = 0.6) in the stress

relaxation curves (Figures 4.12a-g), determined the strain rate values at the

various relaxation curves, and plotted the results, in log-log space against

the values for the grain size from Table (4.4), see Figure 4.27. The resulting

value for p was: 1.0 ±0.26.

Using the intercept value of the best fit line (Figure 4.27), the unknown

constant B* of Equation (4.4) was calculated to be 1.01×10-8

(MPa-1

mm1.0

s-

1). Hence, the GSS flow law for bischofite at 70

oC, with grain size d in mm

is

𝜀�̇�𝑆𝑆 = 1.01 × 10−8𝜎𝑑−1.0 (4.17)

In literature, the value p = 1 is suggested for dissolution or precipitation

controlled pressure solution creep), while p = 3 for diffusion controlled

pressure solution creep (e.g. Raj, 1982).

Mixture

The mixture samples have shown a change in the trend of relaxation

comparable with bischofite and carnallite; starting with a relatively high n-

value at the higher stress and approaching n = 1 towards the end of the

relaxation curve. Hence, the suggestion made for bischofite and carnallite

that a transition occurs from GSI to GSS creep during relaxation may also

hold for the mixtures. The relaxation curve of mixture2 (halite 30%,

carnallite 37%, bischofite 18.6%) does not pass through the steady state

stress values obtained during constant deformation steps, at slower strain

rate, whereas the relaxation curve of mixture1 (halite 65%, carnallite 4%,

175

bischofite is 14%) does seem to pass through the slower strain rate steady

state points. We infer that the mixture2 has experienced grain size evolution

during relaxation. The data set on the mixtures is not extensive enough to

allow a meaningful definition of the creep behaviour in terms creep GSS

equation cf. Equation 4.4.

Table 4.5: Data picked from relaxation curves at similar differential stress values

Sample Deformation

strain rate [s-1

] 𝜀̇

[s-1

]

LOG

(𝜀̇[s-1])

σ

[MPa]

LOG

(σ[MPa])

Bischofite5

10-5

8.6×10-8

-7.1 1.0 0

10-6

3.0×10-8

-7.5 1.0 0

10-7

1.6×10-8

-7.8 1.0 0

10-8

1.4×10-8

-7.9 1.0 0

Bischofite6 10

-5 5.3×10

-8 -7.3 1.0 0

10-6

2.1×10-8

-7.7 1.0 0

Bischofite7

10-5

5.1×10-8

-7.3 1.0 0

10-6

4.2×10-8

-7.4 1.0 0

10-7

3.1×10-8

-7.5 1.0 0

10-8

2.0×10-8

-7.7 1.0 0

Carnallite1

10-6

9.3×10-9

-8.0 4.0 0.6

10-8

4.7×10-9

-8.3 4.0 0.6

10-6

1.2×10-8

-7.9 4.0 0.6

Carnallite2

10-6

1.9×10-8

-7.7 4.0 0.6

10-8

4.1×10-9

-8.4 4.0 0.6

10-6

2.4×10-8

-7.6 4.0 0.6

Carnallite4 10-5

3.0×10-8

-7.5 4.0 0.6

Carnallite5

10-6

1.2×10-8

-7.9 4.0 0.6

10-8

4.0×10-9

-8.4 4.0 0.6

10-6

5.1×10-9

-8.3 4.0 0.6

𝜀̇ : the strain rate values picked from stress relaxation curves at fixed differential

stress value (6.3 MPa)

Deformation strain rates are the values used to deform the sample and set the stress

value for relaxation.

σ : the fixed differential stress selected to pick the data from relaxation curves

176

(v) Composite flow laws

In the above, we have established creep laws for the GSI deformation

behaviour of bischofite and carnallite, Equations (4.6) and (4.9)

respectively, and for the GSS behaviour, (4.15) and (4.17) respectively. The

basis for determining these flow laws were the data obtained during the

deformation at constants strain rate, providing near steady state stresses, and

the analysis of the relaxation curves under the assumption of constant

structure. We will now evaluate if combining GSS and GSS creep in the

form of a composite creep law is of added value. We start from:

𝜀̇ = 𝐴∗𝜎𝑛 + 𝐵∗𝜎𝑑−𝑝 (4.18)

Equation (4.18), however, cannot simply be regarded as the sum of the GSI

and GSS creep laws defined separately, since grain size sensitive behaviour

might have influenced the steady state creep while this was not taken into

account in performing the best fitting exercise. In other words, the

established GSI creep law might not hold for the complete stress – strain

rate range covered. We assume now that at the highest stress, GSI creep is

robust. Regression analysis taking only the data into account at strain rate

10-6

and 10-5

s-1

, i.e. at the higher stresses, then results in n = 5.4 ±0.4 for

bischofite and n = 5.3 ±0.7 for carnallite. Using these new values for the

stress exponent n, holding for the GSI part of the composite Equation 4.18,

and taking the established GSS flow equations, non-linear regression best

fitting resulted in values for A* of Equation 4.18.

For bischofite:

𝜀̇ = 1.1 × 10−9𝜎5.4 + 3.94 × 10−8𝜎𝑑−0.8 (4.19)

177

For carnallite:

𝜀̇ = 3.70 × 10−13𝜎5.3 + 1.01 × 10−8𝜎𝑑−1 (4.20)

The trends representing composite flow for bischofite and carnallite

following Equations 4.19 and 4.20 are shown in Figures 4.28 and 4.29.

The trend lines in Figures (4.28-4.29) show that the influence of grain

size is effective at lower stresses and strain rates. For higher stresses, these

curves satisfy the steady state points, whereas on lower stress/strain rates,

these trends satisfy the data picked from relaxation curves. In Figure 4.28b,

the trend lines to Urai’s (1983) 60 and 80 oC data are also plotted along

using best fit polynomial. The two isotherms seem to present lower and

upper limits of the composite flow, whereas the grain size (Eq. 4.19) looks

to play role to suggest the strain rate at lower stress region.

(a)

-10

-9

-8

-7

-6

-5

-4

-0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Lo

g (

stra

in r

ate

[s-1

])


Bischofite steady state data

Data picked at 0 from relaxation curves

composite 1

composite 2

composite 3

composite 4

178

(b)

Figure 4.28. a) Trends resulting from the composite GSI + GSS flow law (19) for

bischofite, covering the steady state behaviour (diamond data points) as well as the

gradual decrease in n-value during relaxation (from n ~ 5 to n ~ 1 when going

towards low stress and strain rate), b) comparison with Urai’s data and

prediction on lower stresses and strain rates

So the composite flow laws give a complete picture of the creep

characteristics of bischofite and carnallite, in two regimes of GSI (n ~ 5) and

GSS (n ~ 1) that gradually pass into each other.

The final question to be addressed now is what flow law to use, the laws

determined on the basis of the steady state stress-strain rate values (Eqs. 4.6

and 4.9), or the composite laws (4.19 and 4.20). It is recalled here that the

GSS creep laws were determined using the relaxation data under the

assumption of constant structure. During deformation in nature, ongoing

-10

-9

-8

-7

-6

-5

-4

-0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Log (

stra

in r

ate

[s-1

])


Bischofite steady state data

Data picked at 0 from relaxation curves

composite 1

composite 2

composite 3

composite 4

U80 oC

U60 oC

U80 oC

U60 oC

179

Figure 4.29. Trends resulting from the composite GSI + GSS flow law (20) for

carnallite, covering the steady state behaviour (diamond data points) as well as the

gradual decrease in n-value during relaxation (from n ~ 5 to n ~ 1 when going

towards low stress and strain rate)

microstructural modification is likely to occur. De Bresser et al. (2001)

proposed that in the GSI creep field, dynamic recrystallization will reduce

the grain size, moving the material to the boundary with the GSS creep

field, so increasing the contribution of a grain size sensitive mechanism to

the overall creep rate. On the other hand, fine grained starting material

deforming by a GSS mechanism might show grain growth, also moving the

material towards the GSS-GSI boundary, now increasing the contribution of

a grain size insensitive mechanism.

Flow behaviour within the boundary zone between GSI and GSS creep

should be described by a composite flow law of the type: 𝜀�̇�𝑜𝑡𝑎𝑙 = 𝜀�̇�𝑆𝐼 +

𝜀�̇�𝑆𝑆, cf. Equations (4.19 and 4.20, bischofite and carnallite respectively). In

-10

-9

-8

-7

-6

-5

-4

0.0 0.4 0.8 1.2 1.6 2.0

Log (

stra

in r

ate

[s-1

])


Carnallite steady stress

Data picked at 0.6 from relaxation curves

composite 1

composite 2

composite 3

composite 4

180

case, however, that the grain size reduction related to the GSI part of

composite creep is balanced by grain growth associated with GSS flow of

fine grained material, both mechanisms may contribute about equally to the

overall flow rate so, 𝜀�̇�𝑆𝐼 ≈ 𝜀�̇�𝑆𝑆. The composite Equation then boils down

to a flow law without grain size sensitivity:

𝜀�̇�𝑜𝑡𝑎𝑙 = 2𝜀�̇�𝑆𝐼 (4.21)

The factor of 2 included in Equation (4.21) holds if GSI and GSS creep both

contribute half to the total creep rate. This not necessary is the case, while a

balance between the two mechanisms might still be maintained (see De

Bresser et al. 2001). We suggest that our experimental data indicate that

during straining at constant strain rate, the microstructure is continuously

being reworked; allowing some balance to develop at the boundary between

the GSI and GSS mechanisms, cf. Equation (4.21). The GSI flow laws as

established for bischofite and carnallite, Equations (4.6) and (4.9), then form

solid descriptions of the creep behaviour of these materials.

However, in cases that effective microstructural modification cannot be

assumed, as for example during transient creep in the walls of salt caverns,

the composite creep laws established form better descriptions.

4.4.2 Effect of composition

The mixture1 sample was found to be stronger than mixture2. The XRF

analysis of the samples (Fig. 4.19) has shown a higher halite wt. % in

mixture1 compared to mixture2, ~65% and 30%, respectively, while the

difference in bischofite wt. % is limited, namely 14 and 19%, respectively.

Samples carnallite 1, 3 and 5 (Fig. 4.19) were obtained from a different part

181

Figure 4.30. Strengths of the mixtures 1 and 2 and samples carnallite 1 and 5 (that

have limited amounts of halite and hence can also be considered as mixtures),

against wt. % halite, carnallite and bischofite. The plot shows that the higher the

halite % in the mixture, the higher the strength of the material.

182

of the TR-9 core that formed the source of our samples. The micro XRF

analysis (carnallite 1, 3 and 5) revealed that these samples were not pure

carnallite samples, as they contain up to 6-8% halite and 17-19% bischofite.

So these samples can, to a first-order, be considered as mixtures as well, and

their mechanical behaviour can be compared with that of the “true” mixtures

1 and 2.

Accordingly, the strengths of mixtures 1 and 2 and carnallite samples 1

and are plotted against the wt. % of halite, carnallite and bischofite in Figure

4.30. The Figure shows that there is a systematic dependence of strength of

materials tested, notably on the halite content. With increasing halite

content, the mixed salt becomes 2 to 4 times stronger (at 10-6

, 10-8

s-1

respectively) than the carnallite material tested. We thus infer that the

difference in strength from one mixture to the next is best explained by the

difference in halite wt. % between the samples.

SUMMARY AND CONCLUSIONS

Deformation experiments were conducted on bischofite, carnallite and

mixed bischofite-carnallite-halite samples obtained from natural cores. Main

aim was to produce constitutive flow laws that can be applied at real in situ

conditions. The experiments were carried out at a confining pressure of 40

MPa and a temperature of 70 ºC. The experiments were multi-step tests

consisting of constant strain rate parts and stress relaxation parts. The flow

laws developed are mainly on the basis of mechanical data, microstructural

work is for future.

The main findings are:

183

1. Carnallite is 4-5 times stronger than bischofite. The bischofite-

carnallite-halite mixtures, at their turn, are stronger than carnallite,

and hence also stronger than bischofite. With increasing halite

content, the mixed salt becomes 2 to 4 times stronger (at strain rates

10-6

, 10-8

s-1

respectively) than the carnallite material tested. We

infer that the difference in strength from one mixture to the next is

best explained by differences in halite wt. %.

2. The constant strain rate parts of the multistep experiments allowed

defining (dislocation/grain size insensitive GSI) creep laws for

bischofite and carnallite.

3. For bischofite as well as carnallite, we observed that during stress

relaxation, the conventional power law stress exponent in the creep

laws changes from ~5 at 10-5

to ~1 at 10-9

s-1

. This is interpreted as

reflecting a change from grain size insensitive (GSI) dislocation

creep at the faster strain rates to grain size sensitive (GSS)

behaviour at slow strain rate.

4. Assuming that recrystallization was effective during deformation at

constant strain rate, and that the recrystallized grain size remained

constant during relaxation, composite creep laws combining GSI

creep and GSS creep, holding at 70 oC were established for

bischofite and carnallite.

5. If during deformation of bischofite and carnallite the microstructure

is continuously being reworked, some balance might develop

between the GSI and GSS mechanisms, at the boundary between the

creep regimes. The established single GSI flow laws then form solid

descriptions of the creep behaviour of these materials. In cases that

effective microstructural modification cannot be assumed, as for

184

example during transient creep in the walls of salt caverns, the

composite creep laws form better descriptions.

187

Chapter 5

Permeability of interfaces in layered

rock salt under different stresses and

geometries

Muhammad, N., C.J. Spiers, C.J. Peach, J.H.P. de Bresser & W. Liu, 2015

Mechanical Behavior of Salt VIII.

L. Wei, Nawaz Muhammad, Y. Li, C.J. Spiers, C. Yang & H. Ma, 2014

Yanshilixue Yu Gongcheng Xuebao

188

1.1 INTRODUCTION

Salt formations have been of great importance for storage of gas and liquid

fuel for the last few decades due to easy solution mining and excellent

sealing capacity. In order to fully assess the potential, it is important to

know the permeability of the salt cavern walls. The permeability is mainly

an inter-crystalline phenomenon or through fractures (Gloyna & Reynolds

1961). In contrast to domal salt, layered salt has the additional feature of

interfaces between different compositional layers. Due to the multilayer

character, it is not only important to know the bulk permeability, but also

important to know the permeability through interfaces and any changes,

such as damage from material incompatibility, due to application of

differential stress. Selected and cored samples with various interface

geometries were tested for their permeability to argon gas. Five samples

(NP1 to NP5: Batch-I) were provided from the Jintan salt mine at a depth of

(873-1047 m) and three samples (NP6 to NP8: Batch-II) from the Yunying

salt mine at a shallower depth of (811-815 m) from Hubei province in

China. In order to simulate the near real in situ conditions of caverns, the

samples were tested at a confining pressure of 20 and (for shallower depth)

10 MPa respectively. Data for the dilatancy, permeability and damage for

pure salt are readily available (Peach & Spiers 1996, Hatzor & Heyman

1997, Stormont 1997, Popp et al. 2012), but very little is known about the

permeability of layered salt under various differential stresses. There is

some indication (Hatzor & Heyman 1997) from effects of bedding

anisotropy on dilation that there could be effects on permeability. In

particular, little is known regarding the effect of differential stress and

bedding orientation on permeability through interfaces between salt layers

(Liang et al. 2007 and 2012). Models exist relating damage to estimates of

189

permeability (Arson & Pereira 2013, Pereira & Arson 2013), but it is

beyond the scope of these experiments to provide a full quantification of

porous microstructure to test such models, where radial permeability

measurements and exact mapping of porosity would be necessary.

For the first time, in this research work, focus is made on the response of

interlayer bond integrity of interfaces to differential stress, by measuring the

permeability at various steps of increasing differential stress, using argon

gas as pore fluid.

5.2 METHOD

5.2.1 Samples source, composition and preparation for experiments

The sample preparation was done at the laboratory of rock and soil

mechanics and engineering, Wuhan Institute of Rock and Soil Mechanics

(IRSM), Chinese Academy of Sciences. The salt cores were extracted from

two different mines. Batch-I samples (NP1 to NP5) from Jintan mines,

formed in Cenozoic, Paleogene system，Palaeocene to Eocene series.

Batch-II samples (NP6 to NP8) from Yunying basin, which is located in the

northeast part of Jianghan Sunken. The salt mine locates in the centre

location of Yunying salt basin. This was an inland fault-bounded salt lake,

formed during the Cretaceous through to the early Tertiary period.

The salt cores (under investigation) were located in Lower Paleogene,

Gypsum and Salt Group, and are composed of halite and glauberite as bulk

minerals, whereas the interlayer itself is, fine grained, white coloured and

argillaceous (Figure 5.1). The mineralogical components in the cores of

Batch-I were determined by dissolution method, which revealed that

190

composition of this interlayer varies; NaCl: 17.50%-23.62%, Na2SO4:

11.19%-19.43%, CaSO4: 23.86%-26.35%, remainder of insoluble minerals

such as quartz, feldspar, argillaceous minerals etc. The sample bulk is

mainly salt NaCl > 95% and rest is glauberite Na2SO4·CaSO4. The fine

material in the interlayers of Batch-I is clay-rich (see Appendix III). Only

one sample from Batch-II was analysed for its bulk composition using XRD

and the results revealed the composition; glauberite: 78.42%, halite:

11.88%, dolomite: 4%, quartz: 2.53%, magnesite: 3.16%.

Cylindrical cores (of ~100 cm length and 10 cm diameter) were extracted

by drilling vertically into the horizontal salt beds. From these cores, samples

were prepared incorporating interfaces oriented, vertical, oblique and

horizontal to deformation direction, by hand sawing. The blocks were then

machined into cylinders by saw-cuts followed by Silicon Carbide paper

grinding and polishing to reach the final required diameter of 50 mm.

The eight samples obtained (denoted “NP1” to “NP8”) had an average

diameter of 50 mm and lengths in the range 85 to 100 mm. Three different

geometries have been investigated, namely interfaces that are oriented

vertical, horizontal and oblique to the sample axis or show more complex

configurations (“mixed” e.g. NP3, Figure 5.1). All permeability

measurements were taken parallel to the cylindrical axis, with gas

transmission via the end faces. Three samples (NP2, 4 and 8) were prepared

with their interface at an oblique and one sample NP7 with interface

oriented horizontal to measurement direction. Consequently, the interface

between layers was not necessarily directly accessible by argon gas from

flat end faces and interfacial effects could therefore be masked by

impermeable sample ends. To study the permeability characteristics at the

interface, it was devised to drill perpendicular holes in both flat faces till

191

Figure 5.1. Pictures of the samples with different interface geometries and their

schematic diagrams. The two main layers are marked with their abbreviations;

halite (H) and glauberite (G)

Sal

t

H

H H

H

G

G

G G

NP1 NP2 NP3 NP4

15 mm

NP6 NP7 NP8

H

H

H

G

G

G

H

G

NP5

15 mm

192

interface depth in order to provide a direct access for argon gas. A 2.5 mm

diameter drill was used for all samples, whereas the depth of each hole

purely depends upon the distance of the interface from a flat face (see Table

5.2 for more details).

The samples were placed between steel pistons, and were subsequently

jacketed with butyl rubber jackets, to allow even confinement and avoid

contamination of samples with the confining medium, silicone oil. The

jacket was stretched on both ends, rolled over the pistons and tied with

stainless steel wires embedded in circular grooves within the pistons. The

pistons were perforated at centre with a 2.5 mm hole for the argon gas

passage. For uniform spread of gas on the both flat faces of the sample, a

double layer of fine glass fibre sheeting was incorporated on both sides. To

reduce the friction between the polished pistons and sample plus glass fibre,

during deformation, a 50 µm thick perforated PTFE

(polytetrafluoroethylene) sheet was inserted in between.

5.2.2 Apparatus and testing conditions

The experiments were carried out by coupling two instruments, namely a

“Heard” triaxial deformation apparatus (named after its original designer,

the late H.C. Heard, Lawrence Livermore Lab., CA), and a transient-step

argon gas permeameter (designed and fabricated at HPT laboratory Utrecht

University) which works on the basic principle given by Sutherland and

Cave (1980), for measurement of low-permeability samples. For more

details see Peach and Spiers (1996). The tests were conducted at room

temperature and confining pressures of 20 and 10 MPa for Batch-I and

Batch-II respectively. The confining medium used was silicone oil and

pressure was maintained using a servo pump control system accurate within

193

0.01 MPa. The displacement of the confining pressure control system pump

acted as a dilatometer (with a resolution of ± 0.1l), allowing the

measurement of the change in total confining fluid volume to be interpreted

as bulk compaction/dilatancy of the sample, after correction for machine

distortion.

The samples were deformed at a strain rate ( ) of about 10-5

s-1

, reached

by employing a constant piston displacement rate of 1.086 µm/s, at 50:1

drive-gear ratio of the Heard apparatus and the differential stress on sample

was measured. Displacement was measured externally by an LVDT (linear

variable differential transformer) with 25 mm range. Axial load was

measured using a semi-internal force gauge with 400 kN capacity,

insensitive to seal friction but affected by confining pressure. This

sensitivity was corrected by calibration against confining pressure measured

using the 100 MPa pressure system control transducer (type Jensen HFJ PE

1000 LS). All signals were computer logged using a 16-channel, 16-bit

resolution, 250 kSamples/sec analogue to digital data acquisition system

(National Instruments, USB-6221). After every 10 MPa increase in

differential stress, the deformation piston was arrested and permeability was

measured using the argon gas transient-step permeametry. For permeability

measurement, the mean Argon-gas pressure used was ≥ 1.5 MPa, which is

high enough (Peach and Spiers 1996) to suppress the Klinkenberg gas

slippage effect (Klinkenberg, 1941) (in salt samples for κ > 10-19

m2). For

Argon gas pressure, two absolute pressure transducers (Keller PR33X, 2

MPa range, high precision 0.01% and accuracy of 0.05%, with 16 bit

precision data transfer and temperature compensation) monitored the

upstream pressure decay and downstream pressure rise following the

194

approach to a new equilibrium. During equilibration, the drop in pressure of

the gas was logged until equilibrium was reached.

5.2.3 Calibrations

Both triaxial deformation machine and the gas permeameter were carefully

calibrated for the testing conditions. The triaxial apparatus was calibrated

for the machine stiffness (axial elastic distortion) by using a stainless steel

dummy (length = 100 mm and diameter = 50 mm) of known Young’s

modulus, recording elastic distortion as a function of the axial load, at 10

and 20 MPa confining pressures. Volumetric distortion was determined at

constant pressure, using the volumometer control system during the axial

stiffness determinations. Since the apparatus is also volumetrically sensitive

to temperature, a small change in temperature can cause expansion or

contraction of the vessel thereby changing the signal of dilatometer, it was

also calibrated for volume versus temperature.

For transient-step permeametry, the precise attached volumes on both

sides of the sample, including volume of pipes and reservoirs on upstream

and downstream sides are required. An impermeable plastic dummy sample

was used to separate the two system halves and the connected volumes

determined by use of Boyle’s law (PV = constant). The unknown volumes

were calculated by monitoring the drop of pressure at constant temperature

relative to an evacuated pre-calibrated volume in the attached permeameter

by opening a connecting valve.

5.2.4 Experimental procedure and data processing

Before permeability measurement, the system, including gas pipes and

sample assembly, was evacuated and flushed with argon gas three times to

195

drive out any traces of air molecules. The sample was then equilibrated with

> 1.5 MPa argon mean gas pressure for a few hours, to fill the gas into the

pores of the sample. Then the pressure step (down) of 0.2 MPa was created

in the reservoir on one side of the sample and rapidly applied to the pre-

equilibrated sample, by opening a valve to start the transient test. The

pressure difference across the sample versus time data were digitally

recorded until the pressure transient dissipated to below 10% of its starting

value. To study any reversible permeability response of the samples (elastic

response of the crack networks), the permeability at zero-load conditions

was measured at two confining pressure values (5 and 20 MPa for Batch-I; 7

and 10 MPa for Batch-II) at the beginning and end of the test sequence.

Assuming negligible sample storage as compared to the reservoirs

attached, constant volume of the system plus sample at the provided

pressure values and no gas slippage at the boundaries of the walls and

keeping temperature constant, applying the following exponential pressure

decay equation with time as given by Sutherland and Cave (1980):

𝛥𝑃 = (∆𝑃𝑜)𝑒−∝𝑡 (5.1)

∝= 𝜅 (𝐴

𝑙) (

𝑉1+𝑉2

𝑉1𝑉2) (

1

𝜇𝛽) (5.2)

𝜅 =𝑑

𝑑𝑡(𝑙𝑛 (

∆𝑃

∆𝑃𝑜))

𝑙

𝐴(𝑉1𝑉2

𝑉1+𝑉2)𝜇𝛽 (5.3)

where

ΔPo = initial pressure difference [Pa]

ΔP = pressure difference at time t [Pa]

196

α = constant for given sample and experimental conditions [s-1

]

t = time [seconds]

κ = permeability [m2]

A = cross-sectional area of sample [m2]

l = length of sample [m]

V1, V2 = volumes of gas reservoirs on two sides of sample assembly [m3]

µ = dynamic viscosity of argon gas at room temperature [Pa s]

β = argon compressibility [Pa-1

]

The value of the permeability (κ) can be directly determined from the slope

of a graphical plot of ln(ΔP/ΔPo) against time (t). This analysis was

performed by a dedicated computer program (Peach, 1991) with argon gas

properties determined from a virial equation of state and interpolated

viscosity values for the mean temperature and pressure of the argon gas used

in each test.

5.2.5 Preparations for Microstructural study

The deformed samples were studied for the permeable pathways by slicing

into halves along the length. Prior to that, the samples were impregnated

with a low viscosity dark blue resin. The resin was prepared in a hollow

cylinder and the samples were submersed in it. The assembly was first

placed in a vacuum chamber for one hour to drive out the gas/air molecules

from inside the samples and then it was brought to normal atmospheric

pressure which helped drive the resin into the sample through open grain

boundaries. It was kept for 24 hours to allow the resin to set. Later the

samples were taken out and halved along the length (and perpendicular to

interface) using a hand-saw and subsequently were polished with SiC papers

197

to reveal the resin impregnation marks. The porous locations then appeared

dark in greyscale of scanned images. Five out of total eight numbers of

samples were selected for such microstructural study.

5.3 RESULTS


The mechanical response of the tested samples is shown in Figure 5.2. The

measured stress and volumetric strain of all samples is plotted against the

axial strain. The maximum axial strain (𝜀𝑎𝑥𝑖𝑎𝑙) imparted to any individual

sample was less than 3.5%, except for NP3 (𝜀𝑎𝑥𝑖𝑎𝑙 ~ 7%). The bulk

volumetric strain was also measured during deformation and was found

negative for all samples, indicating compaction of the samples. None of the

samples macroscopically failed during deformation, neither at the interface

nor elsewhere. At the end of the experiments the samples were measured for

their final dimensions. Such measurement on the vertical interface sample

NP6 revealed that the halite half was relatively shorter and plastically

deformed, whereas the glauberite half behaved elastically.

198

(a)

(b)

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0

10

20

30

40

50

60

0 1 2 3

com

pac

tio

n ɛ

v [

%]

dil

atio

n

Dif

fere

nti

al S

tres

s [M

Pa]

Axial strain [%]

NP1

Stress vs. axial strain

Volumetric strain

vs. axial strain

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0

10

20

30

40

50

60

0 1 2 3

com

pac

tion ɛ

v [

%]

dil

atio

n

Dif

fere

nti

al S

tres

s [M

Pa]

Axial strain [%]

NP2

Stress vs. axial

strain

Volumetric strain vs.

axial strain

199

(c)

(d)

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0

10

20

30

40

50

60

0 1 2 3 4 5 6 7

com

pac

tion ɛ

v [

%]

dil

atio

n

Dif

fere

nti

al S

tres

s [M

Pa]

Axial strain [%]

NP3

Stress vs. axial

strain


axial strain

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0

10

20

30

40

50

60

0 1 2 3

com

pac

tio

n ɛ

v [

%]

dil

atio

n

Dif

fere

nti

al S

tres

s [M

Pa]

Axial strain [%]

NP4

Stress vs. axial

strain


axial strain

200

(e)

(f)

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0

10

20

30

40

50

60

0 1 2 3

com

pac

tion ɛ

v [

%]

dil

atio

n

Dif

fere

nti

al S

tres

s [M

Pa]

Axial strain [%]

NP5

Stress vs. axial

strain


axial strain

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0

5

10

15

20

25

30

35

40

0 1 2 3

com

pac

tio

n ɛ

v [

%]

dil

atio

n

Dif

fere

nti

al S

tres

s [M

Pa]

Axial strain [%]

NP6

Stress vs. axial

strain


axial strain

201

(g)

(h)

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0

5

10

15

20

25

30

35

40

0 1 2 3

com

pac

tion ɛ

v [

%]

dil

atio

n

Dif

fere

nti

al S

tres

s [M

Pa]

Axial strain [%]

NP7

Stress vs. axial

strain


axial strain

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0

5

10

15

20

25

30

35

40

0 1 2 3

com

pac

tio

n ɛ

v [

%]

dil

atio

n

Dif

fere

nti

al S

tres

s [M

Pa]

Axial strain [%]

NP8

Stress vs. axial

strain


axial strain

202

(i)

Figure 5.2. Mechanical data showing differential stress and volumetric strain vs.

axial strain, a-h) NP1-NP8 and i) retest NP4

5.3.2 Permeability

The interface permeability (κ) to argon gas was measured as response; to

hydrostatic confinement (at start and at the end of each experiment) and to

stepwise increase in differential stress. The change in permeability with

hydrostatic pressure was studied to see the elastic response of permeable

pathways, necessarily at zero differential loading. The response of sample

permeable pathways to differential stress was done at constant confining

pressures of (20 and 10 MPa for Batch-I and II respectively). The stepwise

obtained permeability values are plotted in Figures 5.3 and 5.4.

As a group, all samples of both batches, exhibit a wide range of initial

permeability (10-15

to < 10-20

m2). This makes comparison difficult, so it

becomes necessary to concentrate on relative change. Taking the starting

zero-load (zero differential stress) permeability (κo) as reference value (at

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0

10

20

30

40

50

60

0 1 2 3

com

pac

tion ɛ

v [

%]

dil

atio

n

Dif

fere

nti

al S

tres

s [M

Pa]

Axial strain [%]

NP4_retest

Stress vs. axial

strain Volumetric strain vs.

axial strain

203

confining pressure 20 or 10 MPa for Batch-I or II respectively) and κ as the

instantaneous permeability at each higher differential stress, relative

permeability values (κ/κo) were calculated and plotted against the axial and

volumetric strain Figures 5.5 and 5.6.

5.3.3 Results Batch-I (20MPa confinement)

(i) NP1 (vertical interface)

The initial permeability measured at zero differential stress and Pc = 20 MPa

was 1.07×10-16

m2. It progressively went down with differential stress and

decreased to 4.71×10-17

m2 at the maximum differential stress of 30 MPa.

The sample was fully unloaded before starting a second run on the same

sample. During this second run, the differential stress has stepwise increased

to values higher than reached in the first run, to a maximum value of 55

MPa, and the permeability found decreasing and reached final value of

1.61×10-17

m2.

The relative change in permeability κ/κo, with differential stress, is plotted

against; axial strain in Figure 5.5a and volumetric strain in Figure 5.5b.

Figures 5.5 (a, b) show that with (stepwise increase in differential stress and

corresponding) axial and volumetric strain of the sample, the relative

permeability is decreasing. After the first run of experiment (0-10-20-30

MPa differential stress), the sample was fully unloaded by pulling back the

piston. Thereafter, the value of permeability was measured as zero-load

value, resulting in a permeability that was nearly the same as the last under

load value (at 30 MPa differential stress). This shows that some permanent

change (notably compaction) has taken place in the sample. This was further

confirmed by analysing the strain of the sample at the initial stage of the

second run. Most of the strain at the first part of second run is elastic, from 0

204

to 20 MPa differential stress, during which part of the test the permeability

hardly changed. Only after exceeding the previous maximum differential

stress, did the permeability resume its decrease for the remaining test steps.

(ii) NP2 (oblique interface)

The permeability measured with increasing differential stress is plotted in

Figure 5.3b, which shows a decreasing trend. The zero-load permeability

value at Pc = 20 MPa was found to be 2.9×10-17

m2, which decreased with

differential stress till last step at a differential stress of 40 MPa and value

found to be 6.21×10-18

m2. The only increase in permeability at the end of

the test is due to hydrostatic pressure decrease at zero differential stress.

The relative change in permeability κ/κo is plotted in Figures 5.5(c, d). The

decrease in κ/κo is systematic and appears directly related to axial and

volumetric (compaction) strain. The deformation is steady and permeability

is decreased to about 80% of its initial value at the end of test for maximum

differential stress of 40 MPa.

(iii) NP3 (mixed)

Initially, under zero differential load and Pc = 20 MPa the sample did show

a measurable permeability (6×10-17

m2). Providing the first step differential

stress of 10 MPa, the permeability decreased by 20% (1.29×10-17

m2). For

the subsequent steps of differential loading of 20 MPa and higher, the

permeability became too low to be measured by the system (i.e. κ < 10-21

m2). While measuring the permeability of the sample at 20 MPa differential

stress, it took so long (a few days) that the stress on the sample was relaxed.

For a repeat measurement of permeability, the sample was deformed again

205

to 20 MPa differential stress, the permeability was still too low (i.e. κ < 10-21

m2) to be measured.

The relative permeability κ/κo measured showed a steep fall to a value of

0.21κo for 10 MPa differential stress, but for the following steps, no

information could be retrieved, as the absolute permeability dropped below

the apparatus limit (<10-21

m2).

(iv) NP4 (oblique interface)

Sample NP4 is an impure salt rock showing an oblique interface of salt with

glauberite. Overall, the sample shows a decreasing trend of permeability

with differential stress (Figure 5.3d). At the unloaded condition of step5,

which is a repeat of step4, a slight increase in permeability was observed.

This difference was attributed to non-equilibration of argon gas pressure

within the sample before starting the transient test in step 4 (step5 was given

a longer equilibration time before the permeability test).So, the starting

permeability at zero differential stress and Pc = 20 MPa is 1.16×10-17

m2,

which shows decreasing trend and reduced to 3.93×10-19

m2 for differential

stress of 30 MPa. For next steps its values remains almost the same for

further deformation to 40 MPa and also completely unloading the

differential stress.

The relative permeability κ/κo calculated is plotted against axial and

volumetric strain in Figures 5.5(g, h). Graph shows there is much change in

κ/κo during first three deformation steps (i.e. for differential stress of 10, 20

and 30 MPa). For the subsequent step of 40 MPa, the curve does not show

much change and shows final value as 0.04κo.

206

(v) NP5 (interlayer with salt)

This salt sample had the lowest permeability among the other samples in

Batch-I. The starting permeability value at zero differential stress and Pc =

20 MPa was found 1.07×10-20

m2, which almost remained the same for first

step deformation to 10 MPa. Subsequent deformation lowered the

permeability value of the sample, finishing with 7.26×10-21

m2 for a

maximum differential stress of 30 MPa. The corresponding relative

permeability κ/κo is plotted against axial and volumetric strain in Figures

5.5(i, j). This shows a negligible change for the first step deformation of 10

MPa followed by progressive decrease and finishing with 0.68κo for a

maximum differential stress of 30 MPa.

(a)

0

10

20

30

40

50

60

1.E-21

1.E-20

1.E-19

1.E-18

1.E-17

1.E-16

1.E-15

1.E-14

0 1 2 3 4 5 6 7 8 9 1011121314151617

[MP

a]

Per

mea

bil

ity [

m2]

Number of test steps

NP1 PermeabilityDifferential StressConfining Pressure

207

(b)

(c)

0

10

20

30

40

50

60

1.E-21

1.E-20

1.E-19

1.E-18

1.E-17

1.E-16

1.E-15

1.E-14

0 1 2 3 4 5 6 7 8 9 10

[MP

a]

Per

mea

bil

ity [

m2]


NP2 Permeability

Differential Stress

Confining Pressure

0

10

20

30

40

50

60

1.E-21

1.E-20

1.E-19

1.E-18

1.E-17

1.E-16

1.E-15

1.E-14

0 1 2 3 4 5 6 7 8 9 10

[MP

a]

Per

mea

bil

ity [

m2]


NP3 Permeability

Differential Stress

Confining Pressure

208

(d)

(e)

Figure 5.3. Permeability of Batch-I samples, (a-e) (NP1-NP5) as measured at

different steps in sequence of increasing differential stress for Batch-I samples.

Confining pressure and the differential stress are plotted on secondary y-axis.

0

10

20

30

40

50

60

1.E-21

1.E-20

1.E-19

1.E-18

1.E-17

1.E-16

1.E-15

1.E-14

0 1 2 3 4 5 6 7 8 9 10 11 12 13

[MP

a]

Per

mea

bil

ity [

m2]


NP4 Permeability

Differential Stress

Confining Pressure

0

10

20

30

40

50

60

1.E-21

1.E-20

1.E-19

1.E-18

1.E-17

1.E-16

1.E-15

1.E-14

0 1 2 3 4 5 6 7 8

[MP

a]

Per

mea

bil

ity [

m2]


NP5

Permeability

Differential Stress

Confining Pressure

209

5.3.4 Results Batch-II (10 MPa confinement)

(i) NP6 (vertical interface)

Distinctly, this sample has shown an increasing trend of permeability with

differential stress (Figure 5.4a). The initial value at zero load and at Pc = 10

MPa was found 4.54×10-20

m2 that increased to 6.1×10

-19 m

2 for a maximum

differential stress of 30 MPa.

The relative permeability (κ/κo) is plotted against axial and volumetric strain

in Figures 5.6(a, b). In Figures we see the gradual rise in relative value with

strain and reaching to 13κo for maximum strain with a maximum differential

stress of 30 MPa.

(ii) NP7 (horizontal interface)

The starting permeability at zero differential loading and Pc = 10 MPa was

found 6.13×10-18

m2. The permeability was found to decrease at first during

stepwise increasing differential stress to 10 MPa (Figure 5.4b), but

decreased for the subsequent steps to 20 and 30 MPa, ending at about twice

the value at start 1.26×10-17

m2.

The relative permeability (κ/κo) plotted in Figures 5.6(c, d) which shows a

small dip for differential loading of 10 MPa, recovery to original value at 20

MPa and a further increase to ~2κo for final differential stress of 30 MPa.

(iii) NP8 (oblique interface)

This sample had a high starting permeability 6.09×10-16

m2 as measured at

zero load and at Pc = 10 MPa. With stepwise increase in differential stress,

its permeability value was found to decrease (Figure 5.4c), ending up with

210

an order of magnitude lower value 7.06×10-17

m2, than at start for a

maximum differential stress of 30 MPa.

The relative permeability (κ/κo) plot is shown in Figures 5.6(e, f), which

shows an almost linear trend of decreasing permeability with axial and

volumetric strain and finishing with 0.12κo for maximum differential stress

30 MPa.

(iv) NP4-Re-test (oblique interface)

The sample NP4 was tested again at lower confining pressure Pc = 10 MPa

for a comparative study. The results appeared to be consistent as the

permeability decreased with increasing differential stress (Figure 5.4d). As

compared with the first test at 20 MPa confining pressure, this time the

sample was given more time to become fully equilibrated with argon gas

before starting experiment, and therefore no anomalies were found in the

trend of the permeability change with differential stress. Starting

permeability at zero differential stress was found almost same as was in the

first test, i.e. 1.02×10-17

m2. Deforming the sample caused the reduction of

permeability as measured in stepwise order; the final value appeared to be

4.60×10-18

m2.

The relative permeability (κ/κo) plots (Figures 5.6(g, h)) show that the

maximum decrease in permeability is 0.45κo which is comparatively less

than its first test where it reduced to 0.21κo.

211

(a)

(b)

0

10

20

30

40

50

60

1.E-21

1.E-20

1.E-19

1.E-18

1.E-17

1.E-16

1.E-15

1.E-14

0 1 2 3 4 5 6 7 8

[MP

a]

Per

mea

bil

ity [

m2]


NP6

Permeability

Differential Stress

Confining Pressure

0

10

20

30

40

50

60

1.E-21

1.E-20

1.E-19

1.E-18

1.E-17

1.E-16

1.E-15

1.E-14

0 1 2 3 4 5 6 7 8

[MP

a]

Per

mea

bil

ity [

m2]


NP7

Permeability

Differential Stress

Confining Pressure

212

(c)

(d)

Figure 5.4. Permeability of Batch-II samples, (a-d) (NP6-NP8 & NP4-retest) as

measured at different steps in sequence of increasing differential stress for Batch-II

samples. Confining pressure and the differential stress are plotted on secondary y-

axis.

0

10

20

30

40

50

60

1.E-21

1.E-20

1.E-19

1.E-18

1.E-17

1.E-16

1.E-15

1.E-14

0 1 2 3 4 5 6 7 8

[MP

a]

Per

mea

bil

ity [

m2]


NP8

Permeability

Differential Stress

Confining Pressure

0

10

20

30

40

50

60

1.E-21

1.E-20

1.E-19

1.E-18

1.E-17

1.E-16

1.E-15

1.E-14

0 1 2 3 4 5 6 7 8

[MP

a]

Per

mea

bil

ity [

m2]


NP4-retest

Permeability

Differential Stress

Confining Pressure

213

(a) (b)

(c) (d)

(e) (f)

214

(g) (h)

(i) (j)

Figure 5.5 (i-j). Relative permeability vs. axial and volumetric strains of Batch-I

(confining pressure 20 MPa) semi logarithmic plots

(a) (b)

215

(c) (d)

(e) (f)

(g) (h)

Figure 5.6. Relative permeability vs. axial and volumetric strains of Batch-

II (confining pressure 10 MPa) semi logarithmic plots (a-h)

216

Table 5.1 Step wise permeability values for Batch-I and II, and the conditions used

Sample No of

step

Confining

pressure

[MPa]

Differential

stress [MPa]

Average

Argon

pressure

[MPa]

Permeability

[m2]

NP

1

(ver

tica

l in

terf

aced

)

1 5 0 1.4 1×10-15

2 5 0 1.5 1×10-15

3 20 0 1.6 1×10-16

4 20 0 1.6 1×10-16

5 20 10 1.6 9×10-17

6 20 20 1.6 7×10-17

7 20 30 1.6 5×10-17

8 5 0 1.6 8×10-17

9 5 0 1.6 8×10-17

10 20 0 1.6 4×10-17

11 20 20 1.6 4×10-17

12 20 40 1.6 3×10-17

13 20 55 1.6 2×10-17

14 20 55 1.6 2×10-17

15 20 0 1.6 2×10-17

16 5 0 1.6 3×10-17

NP

2

(ob

liq

ue

inte

rfac

ed)

1 5 0 1.5 6×10-17

2 20 0 1.7 3×10-17

3 20 0 1.7 3×10-17

4 20 10 1.7 3×10-17

5 20 20 1.7 2×10-17

6 20 30 1.7 1×10-17

7 20 40 1.7 6×10-18

8 20 0 1.7 7×10-18

9 5 0 1.7 2×10-17

NP

3

(mix

ed)

1 5 0 1.6 1×10-16

2 5 0 1.6 1×10-16

3 20 0 1.6 6×10-17

4 20 10 1.6 1×10-17

5 20 20 --- <10-21

6 20 30 1.6 <10-21

7 20 40 1.6 <10-21

8 20 0 1.6 <10-21

9 5 0 1.6 <10-21

NP

4

(ob

liq

ue

inte

rfac

ed) 1 5 0 1.6 1×10

-15

2 5 0 1.6 1×10-15

3 5 0 1.6 1×10-15

4 20 0 1.6 *2.×10-18

5 20 0 1.6 1×10-17

217

Table 5.1: contd.

Sample No of

step

Confining

pressure

[MPa]

Differential

stress [MPa]

Average

Argon

pressure

[MPa]

Permeability

[m2]

NP

4

(ob

liq

ue

inte

rfac

ed)

6 20 10 1.6 4×10-18

7 20 10 1.7 2×10-18

8 20 20 1.7 3×10-19

9 20 30 1.6 4×10-19

10 20 40 1.6 4×10-19

11 20 0 1.6 4×10-19

12 5 0 1.7 8×10-19

NP

5

(in

terl

ayer

) 1 5 0 1.5 3×10-20

2 20 0 1.5 1×10-20

3 20 10 1.5 1×10-20

4 20 20 1.5 8×10-21

5 20 30 1.5 7×10-21

NP

6

(ver

tica

l

inte

rfac

ed)

1 7 0 1.9 5×10-20

2 10 0 1.9 5×10-20

3 10 10 1.9 5×10-20

4 10 20 1.9 1×10-19

5 10 30 1.9 6×10-19

6 10 0 1.9 8×10-19

7 7 0 1.9 8×10-19

NP

7

(ho

rizo

nta

l

inte

rfac

ed)

1 7 0 1.9 1×10-17

2 10 0 1.9 6×10-18

3 10 10 1.9 5×10-18

4 10 20 1.9 5×10-18

5 10 30 1.9 1×10-17

6 10 0 1.9 1×10-17

7 7 0 1.9 2×10-17

NP

8

(ob

liq

ue

inte

rfac

ed)

1 7 0 1.9 7×10-16

2 10 0 1.9 6×10-16

3 10 10 1.9 3×10-16

4 10 20 1.9 2×10-16

5 10 30 1.9 7×10-17

6 10 0 1.9 7×10-17

7 7 0 1.9 9×10-17

218

Table 5.1: contd.

Sample No of

step

Confining

pressure

[MPa]

Differential

stress [MPa]

Average

Argon

pressure

[MPa]

Permeability

[m2]

NP

4 (

rete

st)

(ob

liq

ue

inte

rfac

ed)

1 7 0 1.9 1×10-17

2 10 0 1.9 1×10-17

3 10 10 1.9 7×10-18

4 10 20 1.9 5×10-18

5 10 30 1.9 5×10-18

6 10 0 1.9 5×10-18

7 7 0 1.9 6×10-18

*Non-equilibrated start of test (poor value) repeated correctly in following step

Table 5.2. Sample dimensions and changes after test

Test

Initial

length

[mm]

Final

length

[mm]

Initial

dia.

[mm]

Final

dia.

[mm]

Max.

Axial

strain

[%]

Max.

Volume

strain

[%]

NP1 87.50 *87.33

**86.93 49.75 49.753 0.7 -0.32

NP2 86.02 84.37 49.87 *51.48

**49.85 2.4 -0.3

NP3 92.63 86.6 49.94 53.13 6.8 -0.82

NP4 87.64 84.93 49.82 *50.11

**50.46 3.23 -0.44

NP5 85.13 85.1 50.0 50.02 0.275 -0.41

NP6 85.25 *85.22

**84.84 50.01 50.13 0.70 -0.24

NP7 100 98.75 49.84 *49.86

**50.41 1.55 -0.08

NP8 84.47 *82.85

**82.63 49.81 49.95 2.56 -0.48

NP4

retest 84.93 -- 50.26 0.5 -0.5

* glauberite half

** salt half

Note that the initial and final lengths were measured outside the machine, whereas

strains were measured during deformation.

219

5.4 Microstructures

Five deformed samples were selected for microstructural study, considering

the different geometries tested NP3, 4, 6, 7 and 8. These were prepared for

an optical inspection by resin impregnation, cutting and polishing. Cross-

sectional views of these samples are shown in Figure 5.7. In this series of

views, the original cylindrical sample is shown on the left (A), its cross-

section at centre (B) and a magnified view of the interface of (B) on the

right (C). The dark bands, related to resin impregnation, indicate the zones

with permeable channels, which appear as micro-fractures parallel to the

interface.

(i) NP3, A) cylindrical view, upper half glauberite rich, lower half halite rich B)

cross-sectional view of upper and lower halves (at same scale as A), C) magnified

view of encircled region showing resin impregnation marks.

15 mm

A B

C

Resin

7.5 mm

220

(i) NP3 (mixed)

It is a sample without a visible interface. Figure 5.7i shows three different

views; (A) is the cylindrical view where we see the glauberite and halite as

dark and light grey areas. The upper half appears more dominated by

glauberite and the lower half is dominated by halite. The cross-sectional

view (B) shows the upper and lower half of the sample. The glauberite rich

upper half does not show any sign of impregnation, while the lower halite

rich half has a few resin-filled trans granular fractures which appear

disconnected in this two-dimensional view (magnified view C), but must be

connected in depth (to be impregnated).

(ii) NP4 (oblique interface)

The oblique interface of the layers of glauberite and halite is clearly visible

in cylindrical view Figure 5.7ii (A) where the upper half is halite rich

appearing as light and the lower half is glauberite rich and is appearing as

dark grey. The cross-sectional view of the interface is shown in (B). The

encircled area is shown in (C) as magnified image, where we see the resin

impregnated pathways (inter-granular partings) as black lines around grains.

(iii) NP6 (vertical interface)

Figure 5.7iii shows the vertical interface sample. The cylindrical view (A)

of the sample before test shows two layers; the left half is halite-rich and the

right half dominantly consists of glauberite. The cross sectional view (B)

shows the impregnated parts appearing very dark in this grey scale image.

The right half (glauberite-rich) contains only a limited amount of resin,

whereas the halite-half has far more resin impregnation, visible via dark

bands. There is a clear pathway parallel to the interface (see magnified

image (C)). Not only the interface, but also the bulk material away from the

221

(ii) NP4, A) cylindrical view, upper half glauberite rich, lower half halite rich, white

dotted lines show the drilling positions B) cross-sectional view of upper and lower

halves (at same scale as A), C) magnified view of encircled region showing

permeable pathways at interface as resin impregnated.

interface contains parted grains and permeable paths visible as resin filled

dark grey channels (dark grey in micrograph).

(iv) NP7 (horizontal interface)

The cylindrical sample view (Figure 5.7iv (A)) of the horizontal interface

sample clearly shows the two halves; the upper half which is halite-rich and

the lower half which is sulphate-rich (light and dark grey colours,

respectively). The cross-sectional view (B) shows that the halite-rich half

contains more resin that the half with glauberite, which hardly shows any

permeable pathways. At the interface, there is a network of connected paths,

appearing as blackish lines in (B and C) forming a rectangular pull apart

15 mm

A

B

Resin

C

7.5 mm

222

(iii) NP6, A) cylindrical view, left half is halite-rich and right half is glauberite-rich

B) cross-sectional view (at same scale as A) with outlined interface C) magnified

view of clearly connected pathways at interface appearing as darker line.

lattice resembling boudinage. The sample had drilled holes (2.5 mm

diameter) in both flat faces, but the walls of the holes were not sealed, so the

resin also gained access to the sample via these holes, resulting in local

darkening the halite.

(v) NP8 (oblique interface)

In the cylindrical view of the oblique interface sample, the salt-rich part

shows loosely bound grains (Figure 5.7v (A)) as well as inter-granular paths

that appear black upon impregnation (B). In this sample, flat face at top of

sample has a clearly visible interface, while the flat face at the bottom of

sample was drilled, until the interface was reached. In the magnified image

15 mm

B C

Resin 7.5 mm

A

223

(iv) NP7, A) cylindrical view, upper half halite-rich, lower half glauberite-rich,

white dotted lines show the drilling positions B) cross-sectional view (at same scale

as A) with highlighted interface, C) magnified view of highlighted region showing

marks of resin impregnation.

(C), a set of connected and continuous dark lines along the interface are

clearly visible, which appear to anastomose.

5.5 DISCUSSION

5.5.1 Summary of results

(i) Comparison of Batch-I results

Five samples tested at room temperature and confining pressure of 20 MPa

showed a decreasing trend of permeability with differential stress. The

absolute permeability value is different depending upon the interface

Partly intersected, resin

filled, drilled hole.

15 mm

Resin

7.5 mm

C

B A

224

(v) NP8, A) cylindrical view, top half glauberite-rich, bottom half halite-rich, white

dotted lines show the drilling positions B) cross-sectional view of interface (at same

scale as A), C) magnified view of encircled region showing marks of resin

impregnation at the interface.

Figure 5.7. Three different views of each sample. Dotted white lines show the drill-

hole position and depth. The deformation direction is vertical. A) Side view of

cylindrical sample B) cross-sectional view (at same scale as A) and C) (at least) × 2

magnified view of interface.

orientation to loading, as these were similar in terms of extraction location

and depth (i.e. from the same mine and core). Glauberite is found

considerably stronger than salt, and remains elastic with limited plastic

deformation. The bonding at the interface is found strong enough to

withstand the applied differential stress and no general failure occurred. The

volumetric strain in all samples is found negative i.e. compaction.

15 mm

7.5 mm

A B C

Resin

225

(ii) Comparison of Batch-II results

Three samples (NP6, 7 and 8) extracted from a different mine and one

sample from Batch-I (NP4) were tested for shallower depth conditions using

a confining pressure of 10 MPa. The vertical interfaced sample (NP6)

showed a significant increase in permeability with differential stress and

deformation, the horizontal interfaced sample (NP7) sample did not show

any significant change in the permeability, if compared the initial and final

permeability values, though there was change in trend from decrease to

increase with differential stress. The oblique interfaced sample NP8 showed

progressive decrease of permeability with deformation, and NP4-retest

showed a further minor decrease in permeability maintaining its trend in

Batch-I (i.e. at Pc = 20 MPa). The volumetric strain for all of the samples

was negative, i.e. compaction.

5.5.2 Effect of confining pressure

The permeability is mainly an inter-crystalline phenomenon or through

fractures (Gloyna & Reynolds 1961). Under mine conditions, salt rocks are

always in compressed state due to hydrostatic confinement, that makes the

inter-crystalline pathways compacted (Walsh 1965) and reduces the pore

fluid transport and hence permeability. Further, the deformation of salt rocks

also causes dilatancy with strain (Hunsche 1998, Schulze et al. 2001), in the

form of crack opening, intra-crystalline fractures or intra-granular tensile

cracks which in turn creates more pathways by spreading and percolating

(Stormont and Daemen 1992) causing increase in permeability. The

threshold value of confining pressure to suppress the dilatancy is reported to

be Pc > 17.5 MPa (Peach and Spiers 1996). So there is a direct effect of

226

confining pressure on permeability, i.e. higher confining pressure causes

compaction that in turn reduces permeability.

5.5.3 Elastic response of existing cracks to the hydrostatic

pressure

The data obtained on the basis of the experiments show that there is a

permanent change in permeability with respect to differential stress, as the

final permeability was always different from the starting value and did not

reverse on unloading. However, a minor elastic response of the material can

be recognized. We have plotted the permeability values measured by

changing the confining pressure from 5 to 20 MPa at the start and from 20

back to 5 MPa at the end of the experiments of Batch-I (Figure 5.8), and

also the similar treatment using 7 and 10 MPa of Batch-II, under zero

differential load conditions (Figure 5.9). The graph shows that the

permeability at the higher confining pressure is less than at the lower

confining pressure. On the basis of the classical crack-closure model by

Walsh (1981), the permeability is proportional to the 3rd

power of mean

crack width (i.e. κ ∝ <ω>3), which highlights the sensitivity of permeability

to confining pressure by elastic strain, seen in each of the tests. Hence, we

infer that this change in permeability is due to elastic response of crack

width to the hydrostatic loading. This elastic response is only instantaneous,

and gives a qualitative picture of existing cracks and permeable pathways,

which can be predicted to be healed/sealed on long time scales ~1000 years

if salt is dry (Koelemeijer et al. 2012) or on short time scales ≥ 2 years for

relative humidity of 75% (Houben et al. 2013). That is also the reason why

salt rocks are the good choice for underground storage.

227

Figure 5.8. Elastic response of existing cracks to hydrostatic (confining) pressure

Batch-I

Figure 5.9. Elastic response of existing cracks to hydrostatic (confining) pressure

Batch-II

1.E-21

1.E-20

1.E-19

1.E-18

1.E-17

1.E-16

1.E-15

1.E-14P

erm

eabil

ity [

m2]

NP1 Δκ start NP2 Δκ start NP3 Δκ start

NP4 Δκ start NP5 Δκ start NP1 Δκ end

NP2 Δκ end NP4 Δκ end

5 20 20 5 MPa

1.E-21

1.E-20

1.E-19

1.E-18

1.E-17

1.E-16

1.E-15

1.E-14

Per

mea

bil

ity [

m2]

NP6 κ start NP7 κ start NP8 κ start NP6 κ end NP7 κ end NP8 κ end NP4 redo Δκ start NP4 redo Δκ end

10 7 10 7 MPa

228

5.5.4 Compaction and dilatancy

According to Peach & Spiers (1996), halite can be expected to show

dilatancy at confining pressures lower than 18 MPa. However, none of our

test specimens showed bulk dilatancy. This is probably due to the fact that

the total strain imparted < 3%, (except for NP3 that contained comparatively

higher wt. %age of halite) was not high enough to actually take the sample

into the dilatant field, where Peach & Spiers reached final axial strains of

10%, and to the fact that the glauberite layers are stronger than halite and

thus load supporting. In fact, resin impregnation into permeable pathways,

after the experiments, suggests there actually is some localised dilatancy

near to the interfaces.

5.5.5 Localised dilatancy at interface

Overall the permeability of the samples has showed a decreasing trend with

differential stress, especially the Batch-I tests (NP1-NP5) which were all

performed at 20 MPa confining pressure (well above dilatancy limit, Peach

and Spiers 1996). This is interpreted as that compaction and plastic

deformation during loading stages have caused closure of already existing

pathways in the bulk volume of the samples. The vertical interface NP6 has

shown an increasing trend in permeability with differential stress and the

horizontal interface NP7 has shown an increase in permeability towards the

end of test. The mechanical data showed that both of these samples were

compacted by stepwise increase in differential stress. We speculate that the

compaction of the samples is measured as for the bulk, whereas the increase

in permeability is associated to the local dilatancy on the interface and

additionally by more connectivity of already existing pore networks. Indeed,

resin filling at interfaces shows clear evidence of local crack linkage

pathways along interfaces (Figure 5.7). On the other hand, the decrease in

229

the permeability of oblique interface (NP8) is due to bulk compaction by

choking the already existing pathways. However, the resin filling at the

interface shows a localized dilation and permeable connectivity which we

infer is masked by the bulk compaction.


The cross-sectional views of the selected samples are shown in Figures

5.7(i-v) B and C. In general the glauberite-rich parts did not show any

visible sign of impregnation, but still we found non-zero permeability of the

samples. For example, the sample NP5, which is glauberite rich, presented a

low. but measurable, permeability. So there must be some connected

pathways inside the sample inaccessible to the resin. The halite-rich parts

also appear to contain resin, indicative of dilatation, despite all samples

showing overall compaction. NP3, which is halite-rich, showed high

permeability at start of test, its microstructure shows resin filling around

grains, but in the form of discontinuous networks. This sample also

achieved comparatively higher strain, which might have partly closed the

pre-existing cracks that resulted in a dramatic loss of permeability. This

suggests pre-existing inter- and intra-granular crack networks in the halite,

possibly due to damage and present before the deformation.

NP4 was tested twice; its microstructure has prominent resin

impregnation networks connecting through the interface. Although the

sample has shown compaction at both conditions of confining pressures,

locally, dilatancy is visible on the interface as impregnation, which must

have been masked in magnitude by the bulk compaction.

NP6 (vertical interface) sample was initially low permeability and

presented a different trend, i.e. increase in permeability with differential

230

stress. Its microstructure shows that not only the interface, but also the bulk

material away from the interface contains parted grains and permeable paths

visible as resin filled sub-horizontal dark grey channels (dark grey in

micrograph). Again, the bulk showed compaction, which shows that the

permeability increase is due to connectivity of local dilatancy along the

interface, where resin highlights the pathways. The spread of dilatancy

horizontally into the halite from the interface probably reflects the

differential unloading of the halite after its plastic deformation relative to

the more elastic glauberitic half (semi-circular disking fractures confined to

the halite half).

The horizontal interfaced NP7 had a slightly tilted interface inside the

sample. The decrease in permeability at start might be due to closure the

existing connected pathways running sub-horizontally along interface, but

due to confinement within the dilatant regime, further straining of the

sample caused some shear slippage on the interface resulting in crack

opening in lateral directions and increase in permeability. These interfacial

cracks are resin filled along with some sub-horizontal inter-granular

fractures in the halite half, especially close to the resin filled drill hole.

The widespread resin impregnated cross-section of the halite rich part of

NP8 shows that the halite grains were loosely bound (even at the end of

testing). The bulk compaction of the sample with differential stress and drop

in permeability shows that the plastic straining of the samples has caused

narrowing down of the permeable pathways through the bulk, whereas the

local dilatancy which is visible at the oblique interface is masked by this

bulk compaction.

231

5.5.7 Consequences of drilling the interfaces

The permeability values given in Table 5.1 are calculated at sample scale,

using the full sample length and diameter, but the samples NP2, 4, 7 and 8

were actually drilled till the interface of the layers and we measured the

properties of interface with that of sample volume.

The exact path followed by argon is hard to describe, because:

a) the gas was spread uniformly on both faces of the sample and

b) walls of the holes were not sealed or isolated from argon gas

So, there was a potential chance that the Argon gas volume received on

downstream side is the sum of; volume passed through interface only plus

the volume through the bulk of the sample.

The basic principle implicitly used in Equation 5.3 is the empirical law

given by Darcy (1856), which is given as

𝑄 =−𝜅𝐴𝛥𝑃

𝜇𝐿 (5.4)

Where, Q is volume flow rate (m3-s

-1), κ is the permeability of the

medium (m2), A is the cross-sectional area of the sample (m

2), μ is the

dynamic viscosity of the fluid (Pa-s) and (ΔP/L) is the macroscopic fluid

pressure gradient (Pa-m-1

). Re-arranging Equation 5.4 for permeability:

𝜅 = −𝑄𝜇𝐿

𝐴𝛥𝑃 (5.5)

232

Figure 5.10. NP7 schematic diagram, A) cylindrical transparent view, B) cross-

sectional view of interface showing tips of the drilled holes and the cubical

rectangle connecting, C) dimensions of cubical rectangle with (t is the thickness of

area facing)

The permeability is inversely proportional to the pressure gradient

‘ΔP/L’ and directly proportional to the area ‘A’ open to flow for a fixed Q

and μ.

The listed permeability values (Table 5.1) are calculated for all samples

including the drilled-hole samples at the full sample scale.

If only the pathway at the drilled interface is considered, the effective

length ‘L’ is actually the tip to tip distance of the drilled holes, and the

cross-sectional area ‘A’ is the area perpendicular to the connected interfacial

path. This area is hard to estimate due to multiple pathways in the interface

from tip to tip (some of these pathways were highlighted by resin

Drilled holes

A B

28.6 mm

50.0 mm

t

C

233

impregnation). A possible connected path is represented by a rectangular

cube with its length as tip-to-tip distance, breadth as 35.35 mm calculated as

base of a right triangle with its hypotenuse as diagonal of the rectangle (i.e.

diameter of the sample, which is 50 mm for all samples) and thickness ‘t’

can be estimated from the impregnated pathways in the microstructures.

For simplicity, we consider the horizontal interfaced sample NP7, for

which the tip-to-tip inter-holes distance ‘L’ is measured to be 28.6 mm

(Figure 5.10). The thickness ‘t’, estimated from Figure 5.7(iv) is ~ 0.1 mm.

Consider the step4 permeability value (5.05×10-18

m2), calculated at sample

scale (L = 100 mm and diameter = 50 mm) measured at confining pressure

of 10 MPa and differential stress of 20 MPa. Now changing the length ‘L’ to

the new constant value of 28.6 mm and calculating the permeability value

‘κ’ for an new area of 3.535 mm2, we get the value 7.32×10

-16 m

2, which is

~102 times higher than what is listed in Table 5.1. It is important to note that

the main idea behind this work was to test the differential stress sensitivity

of permeability characteristics at the interface of layers. So the absolute

value is less important.

5.5.8 Permeability: bulk and interface

As explained above, that the drilling of a few samples was devised to

provide direct access of Argon gas to the interface, but as a consequence,

the absolute permeability of the samples becomes uncertain. For example;

two samples NP3 and NP5 are the example of relatively dominant minerals

halite and glauberite respectively. Both of these samples were tested without

drilling holes. The starting permeability for NP3 was found in the order of

10-16

m2, which dropped by an order of magnitude for differential stress of

10 MPa. However, further deformation caused the decrease of permeability

234

to become too low to be measured by the apparatus used and it was only

realized after 10 days period while sample was under permeability test with

20 MPa differential stress. NP5 was found less permeable than other

samples, from the start, κ ~10-20

m2 and the sample took several days to be

filled in by Argon gas and reach a starting equilibrium pressure before test

could be started. In short, it was indispensable to drill the oblique and

horizontal interface samples and by-pass the low permeable bulk to

investigate the effects of the interfaces.

As a matter of fact, the Argon gas could not be restricted to pass through

the interface only, since the hole surfaces were not sealed. The permeability

values thus reported have uncertainty in the absolute values, but more

importantly, response of interface permeability of the samples to differential

stress was still measurable and can give guidance about possible leakage

under the real in situ conditions for gas storage.

5.5.9 Comparison with previous work and implications

The potential of using rock salt caverns repositories has already been widely

discussed in the literature and representative cores have been tested for

transport properties (e.g. Gloyna & Reynolds 1961, Sutherland & Cave

1980, Stormont & Daemen 1992, Peach & Spiers 1996, Schulze 2001, Zhou

et al. 2009). All of these studies have reported that rock salt, in general, is a

very suitable choice for repositories, for its sealing and healing capabilities.

However, the characteristics of the salt formations vary substantially from

location to location, in particular regarding homogeneity or interlayering

with other associated minerals. Bedded salt rocks with different layers and

interfaces have never been tested before regarding permeability

characteristics with effect of differential stress included. There is some work

235

on permeability of bedded salt (Stormont & Daemen 1992, Stormont 1997),

but the cores used were without interface of layers. The current study

focusses in particular on layered halite-glauberite salt and presents some of

the interface properties of different layers in bedded salt in different

geometries, covering various possibilities in repositories.

Undisturbed domal salt (5 m deep in cavern walls) has very low

permeability ≤ 10-21

m2, but for the first 1 m depth, this permeability often

has higher values reaching 10-16

m2 (Sutherland and Cave 1980, Peach 1991,

Stormont and Daemen 1992, Stormont 1997) as a result of dilatational creep

in the excavation damage zone. For repositories, such caverns are apparently

a suitable choice.

Different geometries of interface were tested for permeability change

with increasing differential stress, and the absolute magnitude of

permeability was found to vary per sample. The permeability measured, lies

in the wide range of 10-15

to < 10-21

m2. These cores were just extracted by

vertically drilling the horizontal beds, but do show signs of damage and the

initial permeabilities were very high for cavern use. Most of the deformation

effects are masked by this initial dilatation and all samples compacted,

under stress, as a result. More samples from deeper in walls should be tested

to check this hypothesis, but the effect of interfaces is clear in that local

dilatancy will increase permeability in their vicinity, when stressed, and

fluid could therefore escape along these deformation-induced pathways.

CONCLUSIONS

The permeability of layered rock salt with different geometries has been

studied by triaxial testing, with emphasis on interface response to

236

differential stress. Two batches were made according to confining pressure

values; 20 and 10 MPa, simulating depths of ~1000 and 600 m respectively.

The samples were multi-layered (mainly halite and glauberite), often with a

fine grained layer (argillaceous Batch-I) at the major interface. The interface

orientation ranges from horizontal to vertical through oblique direction.

The main findings are follows:

1) Generally, the samples showed an instantaneous response of

permeability to straightforward hydrostatic confinement at the start/end

of the tests. This is interpreted as indicating simple elastic

closure/opening of pre-existing cracks and planar pathways;

2) The absolute values for the permeability varied per sample, due to

differences in interlayer/interface character and initial damage. The high

initial permeability of some of the samples suggests already damaged

material and masked the subsequent effect of the localised deformation

induced damage.

3) All samples showed a decrease in bulk volume with axial strain,

demonstrating progressive bulk compaction with increasing differential

stress; presumably due to crack closure in the bulk.

4) In layer parallel shortening, the applied stress is mostly supported by

harder layer of glauberite in elastic manner, whereas the halite half is

plastically deformed at the same time, as confirmed by the measurement

of the final dimension of the samples after tests.

5) On the basis of the results of our experiments, pre-existing fractures in

the halite are expected to become closed at higher stress values.

6) The interfaces with fine grained material (clay in Batch-I) do not appear

to become debonded.

237

7) The observed decrease in the permeability, with differential stress, of

vertical interface NP1 (high initial permeability) is inferred as due to

closure of grain boundaries and associated sealing of inter-granular

pathways, but the increase in permeability of vertical interface NP6 is

due to local dilatancy at the interface, as confirmed by resin

impregnation after test and a much lower initial permeability.

8) The oblique interfaced samples (NP2, 4 and 8) all showed decrease in

permeability.

9) The samples with higher volume of halite (e.g. NP3) compacted more

and became much less permeable (at the deformation conditions

employed) than that of the other samples, with permeability values

beyond the limit of measurement of our system (i.e., κ<10-21

m2).

10) Since the permeability increases, inferred from microstructural

observations (resin filled pathways), are masked by the bulk compaction

and permeability reduction of pre-existing damage, future work should

endeavour to test less damaged material better reflecting in situ

permeabilities. Without microstructural examination of the interface, the

dilatational effects of the interfaces would have been unnoticed.

238

Data supplied by Chinese Academy of Sciences (CAS) for Batch-I (Appendix I-III)

Appendix I

Petro physical information of samples

Sample Length

[mm]

Diameter

[mm]

Depth

[m] Lithotypes

Density

[g/cm3]

Porosity

[%]

NP1 87.50 49.75 972.74-973.25 horizontal

interface 2.44 4.5

NP2 86.02 49.87 897.11-897.71 inclined

interface 2.33 1.4

NP3 92.63 49.94 968.41-968.86 pure rock

salt 2.23 1.5

NP4 87.64 49.82 873.75-874.1 impure

rock salt 2.26 1.7

NP5 85.13 50.0 1047.1-1047.5 interlayer

with salt 2.59 5.2

Appendix II

Compositions solution results for each sample

Reference

No.

Cl-

[%]

SO42-

[%]

Na+

[%]

K+

[%]

Ca2+

[%]

Mg2+

[%]

Insolution

[%]

Total

[%]

NP1 52.92 1.31 34.8 0.02 0.46 0.01 10.48 100

NP2 57.28 0.84 37.36 0.01 0.29 0.02 4.2 100

NP3 56.73 0.87 37 0.03 0.34 0.01 5.02 100

NP4 53.82 0.24 34.97 0.01 0.19 0.02 10.75 100

NP5 16.47 5.73 11.51 0.02 1.83 0.04 64.4 100

Appendix III

Mineralogical determination of the (nonsaline) interlayers using XRD (Batch-I).

Minerals [%]

Quartz 34.865

Analcime-C 11.645

Montmorillonite-14A 7.635

Halite,syn 2.67

Illite 11.01

Montmorillonite-chlorite 11.155

Feldspar 8.36

Albite 7.2

Pyrite 5.46

Total 100

241

Chapter 6

Conclusions

242

The focus of this thesis was on the deformation and transport

processes in salt rocks. The study was an experimental study with

special emphasis on the effects of confining pressure and stress

relaxation. Below, the aims of the study, as outlined in Chapter 1, are

repeated and the main conclusions are given, following the chapter

organization of the thesis.

In Chapter 2, the results are presented of new experiments on jacketed

samples of dry synthetic rock salt. The aim was to determine the

microphysical mechanism controlling dislocation creep of halite at

20-350 C, and to develop a mechanism-based flow law providing a

solid basis for extrapolation of lab data to long time scales. One way

of distinguishing between the various dislocation mechanisms that

may control creep in dry rock salt is by the effect of confining

pressure. For that reason, systematic pressure stepping tests were

carried out across a range of pressures not attempted before (50-600

MPa). The following was concluded:

In the temperature range of 22 to 350 oC, the rate controlling

dislocation mechanism changes from Peierls resistance

controlled glide at room temperature to climb controlled creep

governed by dislocation core diffusion at 350 oC. At all

conditions tested, the dry rock salt is stronger if the confining

pressure is higher. The activation volume for creep was found

to be about 0.58Vm for the Peierls resistance controlled glide,

and about 0.66Vm for climb controlled creep, where Vm is the

molecular volume of halite.

243

The resulting creep equations are:

𝜀̇ = 1.26

× 1017 (𝜎

𝜇)2.5

𝑒𝑥𝑝 [−(138 + 𝑃(0.58𝑉𝑚))

𝑘𝑇(1

−𝜎

𝜎𝑜

𝜋

2)]

for Peierls resistance controlled glide

and

𝜀̇ = 2.51 × 1014𝜎4.7𝑒𝑥𝑝 [−126 + 𝑃(0.66𝑉𝑚)

𝑘𝑇]

for climb controlled creep

The temperature at which the transition from glide to climb

control takes place was found to lie in between 125 and 250

oC, at a stress of about 16 MPa. Given the slow strain rates

and low stresses normally relevant for in situ conditions,

dislocation creep of rocksalt in nature will likely be controlled

by dislocation climb.

In Chapter 3, the results are presented of experiments on dense

aggregates of both synthetic and natural wet halite. The aim was to

establish, for this wet material, if a transition can be observed from

creep behaviour governed by dislocation mechanisms to creep

244

behaviour controlled by a solution-precipitation mechanism, and if so,

what the conditions of this transition are in terms of strain rate. All

experiments were multi-step experiments at a temperature of 125 oC,

consisting of constant strain rate parts and stress relaxation parts.

Strain rates as low as 10-9

s-1

were achieved during stress relaxation.

The following was concluded:

The stress exponent n obtained by fitting the mechanical data

to a conventional power law is very high (> 10), suggesting

that dislocation glide may play a role as rate controlling

mechanism, as concluded for dry rock salt deformed at

relatively low temperature. During stress relaxation, a

progressive decrease in the n-value was observed, reaching to

a value of ~1 at the slowest strain rates attained. Such value of

n of ~1 points to a grain size sensitive mechanism controlling

creep at slow strain rate and low stress, likely to be solution-

precipitation in the case of wet halite.

Assuming i) that recrystallization was effective during the

deformation at constant strain rate, modifying the grain size in

relation to the differential stress, and ii) that the grain size

remained constant during relaxation, allowed to establish a

composite creep law combining grain size insensitive

(dislocation/GSI) creep and grain size sensitive (solution-

precipitation/GSS) creep, holding at 125 oC. This composite

creep law is as follows:

245

𝜀̇ = 6.42 × 10−20𝜎11 + 1.68 × 10−10𝜎𝑑−1.1

Natural salt appeared stronger than synthetic salt at otherwise

similar conditions, which is inferred to be due to the

impurities in natural salt.

Chapter 4 reports on the creep behaviour of bischofite, carnallite and

mixtures of bischofite-carnallite-halite. Aims were: 1) to determine

the creep behaviour of these salt rocks under in situ conditions, 2) to

establish the role of dislocation creep, recrystallization and, possibly,

pressure solution creep in their behaviour, and to construct creep laws

that allow reliable extrapolation to natural conditions, and 3) to obtain

a first order impression of the difference in strength between mixtures

of bishofite-carnallite-halite mixtures and their end members.

Experiments have been carried out at real in situ conditions of

confining pressure 40 MPa and at a fixed temperature of 70 oC. All

experiments were multi-step experiments at a temperature of 70 oC,

consisting of constant strain rate parts and stress relaxation parts. The

following was concluded:

The strength of bischofite is much less than that of carnallite

and bishofite-carnallite-halite mixtures.

The constant strain rate parts of the multistep experiments

allowed defining (dislocation/GSI) creep laws for bischofite

and carnallite:

246

𝜀̇ = 10−8.519𝜎3.4𝑒𝑥𝑝 (𝜎

2.261)

𝜀̇ = 1.13 × 10−12𝜎5.1

Making the same assumptions as done for wet halite (Chapter

3), namely i) that recrystallization was effective during the

deformation at constant strain rate, modifying the grain size in

relation to the differential stress, and ii) that the grain size

remained constant during relaxation, composite creep laws

combining grain size insensitive (dislocation/GSI) creep and

grain size sensitive (GSS) creep, holding at 70 oC were

established for bischofite and carnallite:

𝜀̇ = 1.1 × 10−9𝜎5.4 + 3.94 × 10−8𝜎𝑑−0.8

𝜀̇ = 3.70 × 10−13𝜎5.3 + 1.01 × 10−8𝜎𝑑−1

If during deformation of bischofite and carnallite the

microstructure is continuously being reworked, some balance

might develop between the GSI and GSS mechanisms, at the

boundary between the creep regimes. The established GSI

flow laws then form solid descriptions of the creep behaviour

of these materials. In cases that effective microstructural

modification cannot be assumed, as for example during

247

transient creep in the walls of salt caverns, the composite

creep laws form better descriptions.

The bischofite-carnallite-halite mixtures are stronger than

carnallite, and hence also stronger than bischofite. With

increasing halite content, the mixed salt becomes 2 to 4 times

stronger (at 10-6

, 10-8

s-1

respectively) than the carnallite

material tested. We inferred that the difference in strength

from one mixture to the next is best explained by the

difference in halite wt. % between the samples.

Chapter 5 describes the results of permeability measurements on

experimentally deformed samples of layered rocksalt from mines in

the Hubei province China. The aim was to test the permeability as

response to differential stress using various geometries/orientation to

deformation direction. By studying the bulk and local

compaction/dilation (at the interface) with the help of dilatometry in

conjunction with the deformation apparatus and microstructural

studies of interface of pre-tested samples. Permeability was

determined using argon gas transient step permeametry, throughout

the deformation. The following was concluded

Hydrostatic and differential stresses both have immediate

effect on permeability, due to initial damage of samples.

The differential stress can cause compaction and permeability

reduction at bulk level if the initial damage levels are high and

may mask dilation at the local interface level. Since both may

248

occur together, it is of utmost importance to study the specific

interlayer characteristics of the walls of potential underground

storage. Local dilatation due to differential stress will cause

local increase in permeability at interfaces in layered salt

rocks similar to those tested here, based on the observations

from resin impregnation and permeametry

Less damaged samples should be tested to better quantify the

effects of local dilation at interfaces and measure the

permeability increases revealed by microstructural analysis

following impregnation. Damaged samples already possess

permeabilities above those expected for storage cavern use.

Relatively pure salt is less permeable and has a better sealing

capacity than sulphates like glauberite.

Suggestions for further research and refinement

In this thesis project, new data have been obtained on the creep

behaviour of dry synthetic rock salt (Chapter 2), wet synthetic and

natural rock salt (Chapter 3), and on polycrystalline bischofite,

carnallite and their mixtures (Chapter 4). In addition, the permeability

of interfaces in salt samples was investigated, in various geometries

(Chapter 5). Although a substantial body of new data was obtained, a

number of uncertainties remained. The following suggestions for

future work are made:

Though a positive pressure sensitivity of flow stress was

found throughout the temperature and strain rate ranges tested,

249

the number of data obtained at low temperature is still limited.

More data for the temperature range 22-125 oC are needed to

further check if the conclusions that under common in situ

conditions, at relatively low stress, climb controlled creep is

the process governing salt flow. Additional tests are

particularly needed to constrain more exactly, than currently

established, what the temperature-stress conditions are of the

transition from glide to climb control.

The number of experiments performed on wet synthetic and

natural polycrystalline halite was relatively limited, partly

owing to the long-time duration of the type of experiments

performed, including stress relaxation. Nevertheless, a

transition was inferred from grain size insensitive (dislocation

– GSI) creep at high stress to grain size sensitive (likely

pressure solution- GSS) at low stress. Grain sizes were

estimated on the basis of application of a recrystallized grain

size piezometers for halite. Independent measurements of

grain sizes are needed to investigate to what extent the

approach that was followed is robust. This concerns both

samples deformed at constant strain rate, assumed to

microstructurally adjust themselves to the operative stress, as

to samples there were let to relax, in which constant structure

was applied. In addition, experiments were only carried out at

125 oC – additional data at higher temperature, where

recrystallization is more prominent, are needed to further

250

constrain the composite GSI-GSS creep law, notably

regarding the activation energy for the GSS-part.

An important outcome of the work on bischofite, carnallite

and their mixtures was the apparent dependence of the

strength of mixtures on the relative wt.% of the various salts

that are present, notably the wt.% halite. In order to study the

contribution of each salt (bischofite, carnallite and halite) in a

systematic way, reagent grade synthetic salt samples should be

prepared and tested for their creep properties. This then can be

followed by the preparation of a series of mixtures with

known composition, and subsequently testing these under the

same conditions as applied on the single salt samples. This

will help to quantify the participation of each member in the

composition, and make a flow law according to volume

contribution of each salt. The results need to be compared

with predictions of models of creep behaviour of

polymineralic minerals.

In investigations of layered salt permeability, the difficulty of

measuring layer parallel permeability changes at high angles

to applied differential stress could be lessened by using radial

permeability tests, rather than relying on pathway

modifications by drilling to allow axial permeability

measurement. In any case, samples with less initial damage

should be used. Impregnation with coloured low viscosity

251

resin and microstructural analysis remains a valuable tool in

elucidating permeable pathways.

Finally, the results of this work are directly relevant for the modelling

of flow of salt in settings varying from salt diapirs to solution–mined

cavities and the stability and integrity of bore holes through sediment

packages containing salt horizons. It would be most useful if the creep

equations for glide and climb controlled creep for dry halite, the

composite creep law obtained for wet halite, and the (composite)

creep laws for bischofite and carnallite are included in models, to

evaluate their full implications.

253

REFERENCES

Aladag, E., L.A. Davis & R.B. Gordon, 1970. Cross slip and the plastic

deformation of NaCl single and polycrystals at high pressure.

Philosophical Magazine, 21, 469-478.

Arson, C. & J.M. Pereira, 2013. Influence of damage on pore size

distribution and permeability of rocks. International Journal for

Numerical and Analytical Methods in Geomechanics, 37(8), 810-831.

Auten, T.A., L.A., Davis, & R.B. Gordon, 1973. Hydrostatic pressure and

the mechanical properties of NaCl polycrystals. Philosophical Magazine,

28, 335-341.

Barr, L.W., J.A. Morrison, & P.A. Schroeder. Anion diffusion in crystals of

NaCl. Journal of Applied Physics 36.2 1965: 624-631.

Cannon, W.R., & T.G. Langdon, 1983. Creep of ceramics. Journal of

Materials Science, 18(1), 1-50.

Carter, N.L. & F.D. Hansen, 1983. Creep of rocksalt. Tectonophysics, 92(4),

275-333.

Carter, N.L., S.T. Horseman, J.E. Russell & J. Handin, 1993. Rheology of

rocksalt. Journal of Structural Geology, 15 (9-10), 1257-1271.

Christov C., 2009. Isopiestic Determination of the Osmotic Coefficients of

an Aqueous MgCl2 + CaCl2 Mixed Solution at (25 and 50) °C. Chemical

Equilibrium Model of Solution Behavior and Solubility in the MgCl2 +

H2O and MgCl2 + CaCl2 + H2O Systems to High Concentration at (25

and 50) °C J. Chem. Eng. Data 2009, 54, 627–635.

Clark, S.P. (Ed.). 1966. Handbook of physical constants (Vol. 97).

Geological Society of America.

Conrad, H. & D. Yang, 1999. The rate-controlling mechanism(s) during

plastic deformation of polycrystalline NaCl at 0.28--0.75 Tm. Journal of

materials science, 34 (4), 821-826.

Cosenza, Ph., M. Ghoreychi, B. Bazargan-Sabet & G.De Marsily, 1999. In

situ rock salt permeability measurement for long term safety assessment

of storage. International Journal of Rock Mechanics and Mining

Sciences 36, no. 4: 509-526.

254

Cox, S.F.& M.S. Paterson, 1991. Experimental dissolution‐precipitation

creep in quartz aggregates at high temperatures. Geophysical Research

Letters 18.8: 1401-1404.

De Bresser, J.H.P.,1991. Intracrystalline deformation of calcite, Geol.

Ultraiectina, 79, Ph.D. thesis, Utrecht Univ., The Netherlands.

De Bresser, J.H.P., J.H. Ter Heege & C.J. Spiers, 2001. Grain size reduction

by dynamic recrystallization: can it result in major rheological

weakening?. International Journal of Earth Sciences, 90(1), 28-45.

De Bresser, J.H.P., B. Evans & J. Renner, 2002. On estimating the strength

of calcite rocks under natural conditions. Geological Society, London,

Special Publications 200, no. 1: 309-329.

De Bresser, J.H.P., 2002. On the mechanism of dislocation creep of calcite

at high temperature: Inferences from experimentally measured pressure

sensitivity and strain rate sensitivity of flow stress. Journal of

geophysical research, 107 (B12), 2337.

Desbois, G., P. Závada, , Z. Schléder & J.L. Urai, 2010. Deformation and

recrystallization mechanisms in actively extruding salt fountain:

Microstructural evidence for a switch in deformation mechanisms with

increased availability of meteoric water and decreased grain size (Qum

Kuh, central Iran). Journal of Structural Geology, 32(4), 580-594.

Dienes, J.K., 1982. Permeability, percolation and statistical crack

mechanics. In: R.E. Goodman and F.E. Heuze (Editors), Issues in Rock

Mechanics. American Institute of Mining, Metallurgical and Petroleum

Engineering, New York, NY.

Escaig, B., 1968a. Sur le glissement de´vie´ des dislocations dans la

structure cubique a` faces centre´es, J. Phys., 29, 225– 239.

Escaig, B., 1968b. L’activation thermique des de´viations sous faibles

contraintes dans les structures h.c. et c.c, Phys. Status Solidi, 28, 463–

474.

Fontaine, G., 1968. Dissociation des dislocations sur les plans (110) dans les

cristaux ioniques du type NaCl. Journal of Physics and Chemistry of

Solids 29.2: 209-214.

255

Fontaine, G. & P. Haasen, 1969. Hydrostatic pressure and plastic

deformation of the alkali halides. physica status solidi (b) 31.1: K67-

K70.

Franssen, R.C. 1994. The rheology of synthetic rocksalt in uniaxial

compression. Tectonophysics, 233(1), 1-40.

Frost, H.J. & M.F. Ashby, 1982. Deformation mechanism maps: the

plasticity and creep of metals and ceramics. Pergamon press.

Gloyna, E.F. & T.D. Reynolds, 1961. Permeability measurements of rock

salt. Journal of Geophysical Research 66.11: 3913-3921.

Hatzor, Y.H. & Eli P. Heyman, 1997. Dilation of anisotropic rock salt:

Evidence from Mount Sedom diapir. Journal of Geophysical Research:

Solid Earth (1978–2012) 102.B7 : 14853-14868.

Heard, H.C. 1972. Steady‐State Flow in Polycrystalline Halite at Pressure of

2 Kilo bars. Flow and Fracture of Rocks, 191-209.

Heard, H.C. & F.J. Ryerson, 1986. Effect of Cation Impurities on Steady‐

State Flow of Salt. Mineral and Rock Deformation: Laboratory Studies:

The Paterson Volume, 99-115.

Houben, M.E., A. ten Hove, C.J. Peach and C.J. Spiers, 2013. Crack healing

in rocksalt via diffusion in adsorbed aqueous films: Microphysical

modelling versus experiments. Physics and Chemistry of the Earth, Parts

A/B/C 64 : 95-104.

Hudec, M.R. & M.P. Jackson, 2007. Terra infirma: understanding salt

tectonics. Earth-Science Reviews, 82(1), 1-28.

Hull, D. & D.J. Bacon, 1983. Introduction to Dislocations, 3rd ed., Int. Ser.

Mater. Sci. Technol., 37, Pergamon, New York. Kennedy, L. A., and J.

M. Logan, The role of veining and dissolution.

Hunsche, U., 1998. Determination of the dilatancy boundary and damage up

to failure for four types of rock salt at different stress geometries. In:

Aubertin, M., Hardy Jr., H.R. (Eds.), The Mechanical Behaviour of salt

IV. Proceedings of the fourth conference.

256

Hunsche, U., & A. Hampel, 1999. Rock salt—the mechanical properties of

the host rock material for a radioactive waste repository. Engineering

geology, 52(3), 271-291.

Istvan J.A., L.J. Evans, J.H. Weber & C. Devine, 1997. Rock mechanics for

gas storage in bedded salt caverns. International Journal of Rock

Mechanics and Mining Sciences 34, no. 3: 142-e1.

Jackson, M.P.A. & C.J. Talbot, 1986. External shapes, strain rates, and

dynamics of salt structures. Geological Society of America Bulletin 97.3:

305-323.

Karato, Shun-ichiro, 2008. Deformation of earth materials: An introduction

to the rheology of solid earth. Cambridge University Press.

Klinkenberg L.J. 1941. The permeability of porous media to liquids and

gases. Drill. Prod. Pract. 2, 200.

Liang, W.G., C.H. Yang, Y.S. Zhao, M.B. Dusseault & J. Liu, 2007.

Experimental investigation of mechanical properties of bedded salt rock.

International Journal of Rock Mechanics and Mining Sciences. 44(3),

400-411.

L. Wei, N. Muhammad, Y. Li, C.J. Spiers, C. Yang & H. Ma, 2014.

Experimental study of permeability of salt rock and its application to

deep underground gas storage. Yanshilixue Yu Gongcheng Xuebao, 33

(10), (pp. 1953-1961) (9 p.)

Liang, W.G., C. Zhang, H. Gao, X. Yang, S. Xu & Y. Zhao, 2012.

Experiments on mechanical properties of salt rocks under cyclic loading.

Journal of Rock Mechanics and Geotechnical Engineering. 4(1), 54-61.

McDonnell, R.D., C.J. Peach & C.J. Spiers, 1999. Flow behavior of fine‐

grained synthetic dunite in the presence of 0.5 wt. % H2O. Journal of

Geophysical Research: Solid Earth (1978–2012) 104.B8: 17823-17845.

Mehrer, H., 2011. Diffusion in Solids under Pressure. DIMETA-82 Defect

and Diffusion Forum (Vol. 309, pp. 91-112).

Mohamed, F.A. & T.G. Langdon, 1974. Method of estimating stacking‐fault

energies in alkali halide crystals using creep data. Journal of Applied

Physics, 45(5), 1965-1967.

257

Muhammad, N., C.J. Spiers, C.J. Peach & J.H.P. de Bresser, 2012. Effect of

confining pressure on plastic flow of salt at 125 oC. In: Bérest, P.,

Ghoreychi, M., Hadj-Hassen, F., and Tijani, M. eds. Mechanical

behaviour of salt VII, CRC press, pp. 57-64.

Muhammad, N., C.J. Spiers, C.J. Peach, J.H.P. de Bresser & W. Liu, 2015.

Permeability of layered rock salt at different stresses and geometries. In:

Roberts, Mellegard & Hansen (Eds). Mechanical Behavior of Salt VIII,

CRC press, pp. 23-33.

Peach, C.J., 1991. Influence of deformation on the fluid transport properties

of salt rocks. Geologica ultraiectina, 77, 1-238.

Peach, C.J. & C.J. Spiers, 1996. Influence of crystal plastic deformation on

dilatancy and permeability development in synthetic salt rock.

Tectonophysics, Vol.256, pp101-128.

Peach, C.J., C.J. Spiers, & P.W. Trimby, 2001. Effect of confining pressure

on dilatation, recrystallization, and flow of rock salt at 150 C. Journal of

Geophysical Research: Solid Earth (1978–2012) 106.B7: 13315-13328.

Pereira, J.M. & C. Arson, 2013. Retention and permeability properties of

damaged porous rocks. Computers and Geotechnics, 48, 272-282.

Poirier, J.P. 1976. On the symmetrical role of cross-slip of screw

dislocations and climb of edge dislocations as recovery processes

controlling high-temperature creep. Revue de Physique Appliqu'e, 11 (6),

731-738.

Poirier, J.P. 1985. Creep of crystals: high-temperature deformation

processes in metals, ceramics and minerals. Cambridge University Press.

Popp, T., W. Minkley, K. Salzer & O. Schulze, 2012. Gas transport

properties of rock salt—synoptic view. In: Berest, P., Ghoreychi, M.,

Hadj-Hassen, F. & Tijani, M.: Mechanical Behavior of Salt VII. Taylor

& Francis group, London N, ISBN 978-0-415-62122-9, 143-153.

Raj, Rishi, 1982. Creep in polycrystalline aggregates by matter transport

through a liquid phase. Journal of Geophysical Research: Solid Earth

(1978–2012)87.B6: 4731-4739.

258

Renner, Jörg & Brian Evans, 2002. Do calcite rocks obey the power-law

creep equation? Geological Society, London, Special Publications 200.1:

293-307.

Roedder, E. & R.L. Bassett, 1981. Problems in determination of the water

content of rock-salt samples and its significance in nuclear-waste storage

siting. Geology 9, no. 11: 525-530.

Rouby, D., S. Raillard, F. Guillocheau, R. Bouroullec & T. Nalpas, 2002.

Kinematics of a growth fault/raft system on the West African margin

using 3-D restoration. Journal of Structural Geology, 24(4), 783-796.

Rutter, E.H. & D.H. Mainprice, 1978. The effect of water on stress

relaxation of faulted and unfaulted sandstone. Pure and Applied

geophysics 116.4-5: 634-654.

Schulze, Otto, Till Popp & Hartmut Kern, 2001. Development of damage

and permeability in deforming rock salt. Engineering Geology 61.2: 163-

180.

Schutjens, P.M.T.M., 1991. Intergranular pressure solution in halite

aggregates and quartz sands: an experimental investigation. Geologica

Ultraiectina, 76, 1-233.

Seeger, A., 1956. The mechanism of glide and work hardening in face-

centered cubic and hexagonal close-packed metals, in Dislocations and

Mechanical Properties of Crystals, edited by J. C. Fisher, W. G.

Johnston, R. Thomson, and T. Vreeland, pp. 243–329, John Wiley, New

York.

Senseny, P.E., F.D. Hansen, J.E. Russell, N.L. Carter & J.W. Handin, 1992.

Mechanical behaviour of rock salt: phenomenology and

micromechanisms. International journal of rock mechanics and mining

sciences & geomechanics abstracts, vol. 29, no. 4, pp. 363-378.

Pergamon.

Sherby, O.D. & J. Weertman, 1979. Diffusion-controlled dislocation creep:

a defense. Acta Metallurgica 27, no. 3: 387-400.

Shimizu, I., 2008. Theories and applicability of grain size piezometers: The

role of dynamic recrystallization mechanisms. J. Struct. Geol. 30, 899-

917.

259

Simmons, G. & H. Wang, 1971. Single Crystal Elastic Con-stants and

Calculated Aggregate Properties: A Handbook, 2nd edition, 370 pp, MIT

Press, Cambridge, MA.

Skrotzki, W., O. Frommeyer, & P. Haasen 1981. Plasticity of

polycrystalline ionic solids. physica status solidi (a), 66 (1), 219-228.

Skrotzki, W. & Z.G. Liu, 1982. Analysis of the cross slip process in alkali

halides. physica status solidi (a), 73 (2), K225-K229.

Skrotzki, W. & P. Welch, 1983. Development of texture and microstructure

in extruded ionic polycrystalline aggregates. Tectonophysics 99.1: 47-61.

Spiers, C.J., J.L. Urai, G.S. Lister, J.N. Boland & H.J. Zwart, 1986. The

influence of fluid-rock interaction on the rheology of salt rock.

Commission of the European Communities, Luxembourg.

Spiers, C.J., P.M.T.M. Schutjens, R.H. Brzesowsky, C.J. Peach, J.L.

Liezenberg & H.J. Zwart, 1990. Experimental determination of

constitutive parameters governing creep of rocksalt by pressure solution.

Geological Society, London, Special Publications 54, no. 1: 215-227.

Spiers, C.J. & N.L. Carter, 1998. Microphysics of Rocksalt Flow in Nature,

The Mechanical Behaviour of Salt IV, Proceedings of the Fourth

Conference. M. Aubertin,H. R. Hardy Jr.,115–128, Trans. Tech.,

Clausthal-Zellerfeld,Germany.

Spiers, C.J. & P.M.T.M. Schutjens, 1999. Intergranular pressure solution in

NaCl: Grain-to-grain contact experiments under the optical microscope.

Oil & Gas Science and Technology, 54(6), 729-750.

Stocker, R.L. & M.F. Ashby, 1973. On the rheology of the up-per mantle.

Reviews of Geophysics, 11(2), 391-426.

Stormont, J.C. & J.J.K. Daemen, 1992. Laboratory study of gas permeability

changes in rock salt during deformation. International journal of rock

mechanics and mining sciences & geomechanics abstracts. Vol. 29. No.

4. Pergamon.

Stormont, J.C. 1997. Conduct and interpretation of gas permeability

measurements in rock salt. International Journal of Rock Mechanics and

Mining Sciences 34.3 : 303-e1.

260

Sutherland, H.J. & S.P. Cave,1980. Argon gas permeability of New Mexico

rock salt under hydrostatic compression. Int. J.Rock Mech. Min. Sci.

Geomech., Abstr., 17: 281-288.

Talbot, C.J. Fold trains in a glacier of salt in southern Iran. Journal of

Structural Geology 1.1 (1979): 5-18.

Tasker, P.W.& T.J. Bullough, 1981. An atomistic calculation of extended

planar defects in ionic crystals Application to stacking faults in the alkali

halides. Philosophical Magazine A 43.2: 313-324.

Ter Heege, J.H., J.H.P. De Bresser & C.J. Spiers, 2005a. Rheological

behaviour of synthetic rocksalt: The interplay between water, dynamic

recrystallization and deformation mechanisms. J. Struct. Geol. 27, 948-

963.

Ter Heege, J.H., J.H.P. De Bresser & C.J. Spiers, 2005b. Dynamic

recrystallization of wet synthetic polycrystalline halite: dependence of

grain size distribution on flow stress, temperature and strain.

Tectonophysics 396.1: 35-57.

Twiss, R.J., 1977. Theory and applicability of a recrystallized grain size

paleopiezometer. Pure and applied Geophysics 115, 227-244.

Urai, J.L. 1983. Water assisted dynamic recrystallization and weakening in

polycrystalline bischofite. Tectonophysics 96.1: 125-157.

Urai, J.L., 1985. Water-enhanced dynamic recrystallization and solution

transfer in experimentally deformed carnallite. Tectonophysics, 120(3),

285-317.

Urai, J.L., C.J. Spiers, H.J. Zwart & G.S. Lister 1986. Weakening of rock

salt by water during long-term creep.

Urai, J.L., C.J. Spiers, C.J. Peach, R.C.M.W. Franssen & J.L. Liezenberg,

1987. Deformation mechanisms operating in naturally deformed halite

rocks as deduced from microstructural investigations. Geologie en

Mijnbouw 66, no. 2: 165-176.

Van Eekelen, H.A., T. Hulsebos & J.L. Urai, 1984. Creep of bischofite, The

Mechanical Behavior of Salt: Proceedings of the First Conference Held

261

at the Pennsylvania State University, University Park, Pennsylvania,

November 9-11, 1981. Gulf Pub Co.

Vendeville, B. Ci & M.P.A. Jackson, 1991. The rise of diapirs during thin-

skinned extension. Marine and Petroleum Geology 9, no. 4 : 331-354.

Verrall, R.A., R.J. Fields & M.F. Ashby, 1977. Deformation‐Mechanism

Maps for LiF and NaCl. Journal of the American Ceramic Society 60,

no. 5‐6: 211-216.

Walsh, J.B., 1981. Effect of pore pressure and confining pressure on fracture

permeability. Int. J. Rock Mech. Min. Sci. and Geomech. Abstr., Vol. 18,

pp. 429-435.

Watanabe, T. & C.J. Peach, 2002. Electrical impedance measurement of

plastically deforming halite rocks at 125 oC and 50 MPa. Journal of

Geophysical Research: Solid Earth (1978–2012), 107(B1), ECV-2.

Wawersik, W.R. & D.H., Zeuch, 1986. Modeling and mechanistic

interpretation of creep of rock salt below 200 oC. Tectonophysics, 121(2),

125-152.

Weertman, J., 1955. Theory of Steady‐State Creep Based on Dislocation

Climb. Journal of Applied Physics 26, no. 10: 1213-1217.

Weertman, J., 1957. Steady‐State Creep of Crystals. Journal of Applied

Physics, 28(10), 1185-1189.

Weertman, J., 1968. Dislocation climb theory of steady-state creep. ASM

TRANS QUART 61.4: 681-694.

Werner M. & H. Mehrer, 1983. Diffusion in Metals and Alloys, F.J.

Kedves, D.L. Beke (Eds.), Trans Tech Publications, Diffusion and

Defect Monograph Series No. 7, 392.

Wolf, H. 1960. Die Aktivierungsenergie für die Quergleitung aufgespaltener

Schrauben versetzungen, Z. Naturforsch, 15A, 180– 193.

Zhou, H., J. He & Z. Wu, 2009. Permeability and meso-structure

characteristics of bedded salt rock. Chinese Journal of Rock Mechanics

and Engineering, 28(10), 2068-2073.

263

Samenvatting

264

De aanwezigheid van evaporitische lagen in sedimentaire bekkens,

vaak gedomineerd door het zoutmineraal haliet, heeft grote invloed op

de ontwikkeling van structuren tijdens tektonische activiteit. Ook zijn

op veel plekken in evaporitische zoutlagen cavernes te vinden die

ontstaan zijn door oplossingsmijnbouw. Deze cavernes worden

steeds meer gebruikt voor strategische opslag van energiebronnen in

de vorm van gasvormige of vloeibare brandstoffen, en voor de opslag

van energie tijdens daluren in de vorm van perslucht. Daarnaast

worden conventionele mijngangen gebruikt voor lange termijn opslag

van gevaarlijk afval. De lage permeabiliteit van de meeste

zoutgesteenten, met lage mechanische sterkte en de neiging tot zelf-

afdichting, vormt de belangrijkste reden voor ingenieurs om

zoutformaties te gebruiken voor dergelijke opslagprojecten. De

Zechstein zoutafzettingen in de ondergrond van Nederland bestaan uit

zowel de oorspronkelijke afzettingen als gemigreerde zout

diapieren/pijlers die kunnen zijn uitgegroeid tot op kilometer-schaal.

Sommigen zoutafzettingen bevatten economisch waardevolle

magnesiumrijke zouten welke worden gewonnen door middel van

oplossingsmijnbouw. De cavernes die op deze manier ontstaan

midden in deze gemakkelijk oplosbare en mechanisch zwakke

materialen brengen verdere uitdagingen met zich mee met betrekking

tot lange-termijn opslag van afval. Zorgvuldig beheer van de met

water gevulde cavernes vereist een uitgebreide kennis van het

reologisch- en transportgedrag van de omliggende zout formaties, ten

einde de veiligheid van toekomstige exploitatie te garanderen.

265

Dit proefschrift adresseert een aantal tekortkomingen in de huidige

kennis over het mechanisch gedrag van zout, met name met

betrekking tot kruip van haliet en van mengsels van haliet met

magnesium zouten. In het bijzonder is de afhankelijkheid van kruip

van de alzijdige druk onderzocht, gebruik makend van synthetisch en

natuurlijk halietgesteente, met als doel de samengestelde

mechanismen te identificeren welke bijdragen aan het totale

deformatie proces. Dit alles met het oog op het beter begrijpen van de

natuurkunde van het kruipen van zout. Tevens is de reologie van

magnesium bevattende zouten, carnalliet en bischofiet, onderzocht,

met speciale aandacht voor het mechanische gedrag van mengsels van

deze zouten met haliet. Naast de reologische aspecten zijn ook de

effecten van de samengestelde gelaagdheid op de doorlaatbaarheid

(permeabiliteit) van door uitgraving beschadigde zones rondom

gemijnde holtes bestudeerd, gebruik makend van natuurlijk gelaagd

materiaal uit mijnen in China. Doel hierbij was om beter inzicht te

krijgen in de effecten van de oriëntatie van de gelaagdheid ten

opzichte van de deformerende differentiaalspanning in holtes en

mijngangen op diepte.

Hoofdstuk 1 omvat een literatuurstudie met betrekking tot zout

reologie, en beschrijft de hoofddoelen van deze studie en de planning

van het proefschrift.

Hoofdstuk 2 gaat over het snelheidsbepalende mechanisme van de

kruip van droog polykristallijn zout. Het temperatuurbereik dat dit

deel van de studie omvat is 22 tot 350 °C. De gebruikte

266

vervormingssnelheden liggen tussen de 4x10-7

s-1

en 10-4

s-1

. Een

aantal testen werden uitgevoerd bij constante vervormingssnelheid,

andere testen omvatten systematische stappen in de

vervormingssnelheid. De gedachte achter dit gedeelte van de studie is

om onderscheid te maken tussen verschillende mechanismen van

dislocatiekruip, zoals het klimmen van dislocaties (“dislocation

climb”), het schuiven van dislocaties van het ene glijvlak naar het

andere (“dislocation cross-slip”) en het glijden van dislocaties binnen

één vlak (“dislocation glide”), gebruik makend van de druk-

afhankelijkheid van de vloeispanning van droog zout. De theorie stelt

dat er een atomistische activeringsenergie of -volume is, welke

geassocieerd is met vastestofvloei door dislocatie kruip. Volgens

theoretische modellen zou het zout in het geval van een positief

activeringsvolume, bij hogere druk een grotere sterkte moeten

hebben, gerelateerd aan het snelheidsbepalende mechanisme van

kruip. Voor deze analyse werd de omvattende (alzijdige) druk

gevarieerd tussen 50 en 600 MPa, iets wat nog niet eerder

systematisch was gedaan voor volledig omvat zout. Het zout werd

sterker bevonden bij hogere omvattende druk, en op basis van de

experimentele gegevens werd geconcludeerd dat het mechanisme dat

de snelheid van kruip bepaalt, onder de geteste omstandigheden, in

het overgangsgebied ligt van dislocatie glij naar dislocatie klim.

Hoofdstuk 3 gaat over de vloeiwet bij in situ condities van water

houdend haliet, gebruik makend van synthetische en natuurlijke zout

monsters. De toegepaste temperatuur en omvattende druk waren

267

125 °C en 50 MPa, respectievelijk. De monsters werden getest in

multi-stap experimenten met constante vervormingssnelheid gedeeltes

(5x10-5

– 5x10-8

s-1

), gevolgd door spanningsrelaxatie na

geselecteerde stappen. De relaxatie data laten zien dat het

snelheidsbepalende mechanisme niet hetzelfde blijft, maar verandert

van kruip gecontroleerd door dislocatie activiteit (bij hogere

spanningen en vervormingssnelheden), naar korrelgrootte-

afhankelijke kruip (waarschijnlijk drukoplossing) tegen het einde van

de relaxatie (i.e. bij lagere spanningen en reksnelheden).

Hoofdstuk 4 is een compilatie van testen gedaan op bischofiet,

carnalliet en hun mengsels met haliet, uitgevoerd onder in situ

condities met een omvattende druk van 40 MPa en een temperatuur

van 70 °C. Deze testen werden uitgevoerd op polykristallijne

monsters verkregen uit boorkernen van natuurlijk materiaal. Hierbij

werden vochtabsorberende condities toegepast rondom de monsters.

De monsters werden op dezelfde manier getest als de haliet

gerapporteerd in Hoofdstuk 3, namelijk in multi-stap experimenten

met constante vervormingssnelheid gedeeltes (10-5

– 10-8

s-1

), gevolgd

door spanningsrelaxatie na geselecteerde stappen. De resultaten

toonden aan dat de carnalliet sterker is dan de bischofiet, en dat

mengsels met haliet op hun beurt sterker zijn dan carnalliet. De

sterkte van het mengel lijkt direct gerelateerd te zijn aan het massa

percentage van haliet, i.e. hogere massa percentages haliet maken het

mengsel sterker. De samenstelling van de verschillende monsters

werden getest met behulp van een micro-XRF techniek.

268

Spanningsrelaxatie toonde aan dat een verandering in het

vloeimechanisme plaatsvond, van kruip gecontroleerd door dislocatie

activiteit bij hogere spanningen en reksnelheden (aan het begin van

de relaxatie) naar korrelgrootte-afhankelijke kruip bij lagere

spanningen en reksnelheden (tegen het einde van de relaxatie). Op

basis van de resultaten werden samengestelde vloeiwetten voor

bischofiet en carnalliet opgesteld, met een combinatie van

korrelgrootte-onafhankelijke dislocatie kruip en korrelgrootte-

afhankelijke (drukoplossing) kruip die het mechanisch gedrag bij

hogere en lagere spanningen beschrijven, respectievelijk.

Hoofdstuk 5 gaat over de transporteigenschappen van gelaagde zout

uit zout mijnen in China. De monsters werden getest op hun

permeabiliteit langs het contact van twee verschillende lagen, haliet

en glauberiet, gebruik makend van de argon gas permeametrie

techniek, onder toenemende differentiaalspanningen. De

experimenten werden geclassificeerd in twee groepen: groep-I

omvatte relatief grote omvattende druk (20 MPa, releatief grote

diepte), en groep-II omvat kleinere omvattende druk (10 MPa,

kleinere diepte). Verschillende oriëntaties van het contact ten

opzichte van de richting van deformatie werden getest (verticaal,

onder een hoek en horizontaal) waarbij de differentiaalspanning werd

vergroot in stappen van 10 MPa. De axiale en volumetrische

vervormingen werden tijdens de experimenten gemeten, wat

aantoonde dat alle monsters compacteerden, ondanks en toename of

afname in permeabiliteit. Microstructurele analyse toonde aan dat

269

lokale dilatatie plaatsvond op de contacten, wat een lokale toename

van de permeabiliteit moet hebben veroorzaakt, maar welke werd

verborgen door de bulk compactie van de samples.

271

Acknowledgements

272

I am really grateful to all my teachers for their endless support,

encouragement and feedback throughout my studies. Special thanks to

Professor Chris Spiers for his loving nature and generosity that he arranged

all the funds and enabled me to continue my studies. I have learnt many

teaching skills while assisting him during practical classes. Dr. Colin Peach

is thanked for sharing his knowledge and explaining the complications of

state of art equipment in HPT laboratory, and solving the technical issues in

a wink of an eye. The efforts of Dr. Hans de Bresser are highly appreciated,

for his timeless, prompt and constructive feedbacks on write-ups, which

helped the work go smoothly.

All staff of the Higher Education Commission (HEC) of Pakistan, especially

former chairman Dr. Atta-Ur-Rahman is heartily thanked for initiating PhD

scholarships. The programme is very useful for upgrading the education

level in our country. The support of my alma mater GC University Lahore is

also highly appreciated.

I also want to thank to my “paranimfen”, Amir Raoof and Martijn Van den

Ende, who, other than taking care of my thesis, were very helpful in making

the computer code for complex data analysis.

While staying in Netherlands, I felt like at home. Especially at HPT

laboratory, all members were very co-operative. I want to thank all of you.

My room fellows Anne Pluymakers, Amir Raoof, Tim Wolterbeek and Miao

Zhang were all very helpful in creating a good environment for studies.

Bart, Andre, Jon, Suzanne, Ross, Chen, Elisenda, Michiyo, Yu, Luuk,

George, Ayumi, Evangelos, Mariska and Ronald were all very caring

fellows. We had great time throughout my research period at HPT. Caring

273

Magda will always be remembered for her kindness and sincerity. All the

technical staff, Peter Van Krieken, Gert Kastelein, Eimert de Graaff and

Thony Van de Gon Netscher is thanked for their fantastic support. All of my

country fellows in Netherlands; Imran, Bilal, Fraz, Qamar, Mehboob, Zahid

are thanked for their moral support and hospitality.

Deep respect for my sincere teachers at all levels of my studies. My wife

Nida and our little angel like daughter Khadeejah were very supportive in

boosting up my morale. At the end, I want to say special thanks to my

parents, who were patient enough to allow me to have higher education

abroad. My brother Eijaz, sister Humaira, students Attique and Tahir and

sincere friend Qaiser Butt were looking after back home in my absence. This

milestone was not being possible to achieve without their support.

Nawaz Muhammad

275

Curriculum vitae Full Name Nawaz Muhammad

Date of birth 15th December 1975

Place of birth Lahore Pakistan

Matriculation Government Iqbal Hussain

high school Lahore.

Intermediate and graduation Government Islamia

college Railway road

Lahore

Masters (Physics) Government College

University Lahore.

Teaching/job experience at CASP GC University Lahore:

Research Assistant 2001-2002

Lecturer 2002-2006

Assistant professor 2006 to date

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