Download pdf - Mechanics of Mine Backfill - research-repository.uwa.edu.au · Thought the publications listed are not part of the thesis, the work included in them forms a central part of the thesis

Mechanics of Mine Backfill

By

Matthew Helinski

This thesis is presented for the

Degree of Doctor of Philosophy

The University of Western Australia

School of Civil and Resource Engineering

December 2007

DECLARATION FOR THESES CONTAINING PUBLISHED WORK AND/OR WORK PREPARED FOR PUBLICATION

The examination of the thesis is an examination of the work of the student. The work must have been substantially conducted by the student during enrolment in the degree. Where the thesis includes work to which others have contributed, the thesis must include a statement that makes the student’s contribution clear to the examiners. This may be in the form of a description of the precise contribution of the student to the work presented for examination and/or a statement of the percentage of the work that was done by the student. In addition, in the case of co-authored publications included in the thesis, each author must give their signed permission for the work to be included. If signatures from all the authors cannot be obtained, the statement detailing the student’s contribution to the work must be signed by the coordinating supervisor. Please sign one of the statements below. 1. This thesis does not contain work that I have published, nor work under review for publication. (Note: A number of journal and conference papers have been published on various aspects of the work, as listed Page v at the start of the Thesis. However, these are not part of the thesis per se.)

Signature: Thought the publications listed are not part of the thesis, the work included in them forms a central part of the thesis. The candidate, Mr Helinski, is first author on all of the publications, and can claim a contribution of > 70% to each of them.

Signature: (Martin Fahey, coordinating supervisor) 2. This thesis contains only sole-authored work, some of which has been published and/or prepared for publication under sole authorship. The bibliographical details of the work and where it appears in the thesis are outlined below. Signature......................................................................................................................................................... 3. This thesis contains published work and/or work prepared for publication, some of which has been co-authored. The bibliographical details of the work and where it appears in the thesis are outlined below. The student must attach to this declaration a statement for each publication that clarifies the contribution of the student to the work. This may be in the form of a description of the precise contributions of the student to the published work and/or a statement of percent contribution by the student. This statement must be signed by all authors. If signatures from all the authors cannot be obtained, the statement detailing the student’s contribution to the published work must be signed by the coordinating supervisor. Signatures......................................................................................................................................................... Signatures.........................................................................................................................................................

Mechanics of Mine Backfill Matthew Helinski The University of Western Australia

i

ABSTRACT

Mine backfilling is the process of filling large underground mining voids (“stopes”)

with a combination of tailings, water and small amounts of cement, to promote regional

stability. Stopes are often in excess of 20 m × 20 m in plan dimensions and 40-50 m tall,

and can be filled within a week. Barricades are constructed in all tunnels (“drives”) that

access the stope to contain the backfill material. In recent years, a significant number of

failures of mine backfill barricades have occurred, resulting in the inrush of slurry

backfill into the mine workings. In addition, sampling has shown material strengths in

situ to be far greater than equivalent mixes cured in the laboratory (indicating the

potential for reducing the cement content). The purpose of this thesis is to apply soil

mechanics principles to the mine backfill deposition process with the intent of providing

some insight into these issues.

In many cases, filling, consolidation and cement hydration all take place at a similar

timescale, and therefore, to understand the cemented mine backfill deposition process it

was necessary to appropriately couple these activities. Developing appropriate models

for these mechanisms, and coupling them into a finite element code, forms the core of

this thesis.

Firstly, the fundamental processes involved in the cementing mine backfill deposition

process are investigated and represented using theory founded on basic physical

observations.

Using this theory, one- and two-dimensional finite element models (called CeMinTaCo

and Minefill-2D, respectively) are developed to fully couple each of the individual

mechanisms.

A centrifuge experiment was undertaken to investigate the interaction between

consolidation and total stress distribution in a cementing soil. The results of this

experiment were also used to verify the performance of Minefill–2D. Due to scale

effects, the centrifuge experiment was unable to fully couple the interaction of the

cement hydration and consolidation timescales. To achieve this, a full scale field

experiment was undertaken. The simulated behaviour achieved using Minefill-2D (with

independently derived material properties) provided a good representation of the

consolidation behaviour.


ii

Finally, a sensitivity study carried out using Minefill-2D is presented. This study

enables some useful suggestions to be provided for managing the risk of excessive

barricade stress, and for preparing laboratory samples to more appropriately represent in

situ curing conditions.


iii

ACKNOWLEDGEMENTS

Firstly I would like to acknowledge the support of my wonderful family throughout the

period of my studies. My wife Libby, who after initially being somewhat apprehensive

about my decision to return to university, has provided me with undivided support

throughout this period. Jessica who was undesirably juggled during my early years of

study always had a wonder smile to greet me with and Lucy, our recent addition, who I

am equally proud of. To my parents, grandparents and sister who have provided me

with the wonderful gift of education and support throughout my life, I am forever

grateful of this.

To my supervisor Professor Martin Fahey, a true professor in the way he can make the

most complicated aspect of soil mechanics appear so clear and simple through the

application of his fundamental knowledge. This is something I aspire to. My supervisor

Professor Andy Fourie, whose guidance and friendship during my research was

essential in developing this project. Andy, I feel very fortunate that you arrived in

Australia and supported me when you did. Also, thanks to Dr Mostafa Ismail who

assisted me in the laboratory component of this work and Professor Jack Barrett who

helped shape this project during the early stages.

Thanks to all of my university colleagues, in particular James Schneider and James

Doherty and Shambu Sharma, I am extremely appreciative of your supervision and

guidance throughout this thesis.

Also my industry colleagues Cameron Tucker, Mat Revell and Tony Grice, I appreciate

all of your support and encouragement with this work.

Thanks to all of the academic and support staff in the Civil Engineering department in

particular Binaya, Clair and Natalia (who sadly passed away during this thesis) for their

ongoing patience with my chaotic style in the laboratory as well as Tuarn, John, Shane,

Phil, Bart, Don and Neil for their assistance with centrifuge testing.

Finally, this work would not have been possible without the wonderful post graduate

scholarship foundation at The University of Western Australia. The late Robert John

Gledden for establishing the Gledden trust that provided the majority of financial

support throughout this work. Merriwa for their wonderful “top-up” scholarship that


iv

provided both financial and equipment support. Mrs N. Shaw who established the

F.S.Shaw scholarship in memory of her late husband, which provided much needed

funding towards the latter stages of this research. And the UWA travel scholarship

which allowed me to attend the Minefill ’07 conference in Canada.


v

DECLARATION

I hereby declare that, except where specific reference is made in the text to work of

others, the contents of this thesis are original and have not been submitted to any other

university.

During the compilation of this thesis some of the work has been published in various

journals and conference proceedings. I acknowledge the contribution of my co-authors

in preparing these publications. Details of these publications are as follows:

Journal publications

Helinski, M. Fahey, M. and Fourie, A.B. (2007) Numerical modelling of cemented mine

backfill deposition, ASCE Journal of Geotechnical and Geoenvironmental Engineering,

Vol. 133, Issue 10, 1308-1319.

Helinski, M., Fourie, A.B. Fahey, M. and Ismail, M. (2007). The self desiccation process in cemented mine backfill. Canadian Geotechnical Journal. Vol. 44, No. 10, 1148-1156. Helinski, M. Fahey, M. Fourie, A.B. (2007) An effective stress approach to modelling

mine backfilling, CIM technical paper, Issue No. 5, August, Vol.2.

Fourie, A.B. Helinski, M. Fahey, M. (2007) Using effective stress theory to characterise

the behaviour of backfill. CIM technical paper, Issue No.5, August, Vol. 2

Conference publications

Helinski, M., Fourie, A.B. and Fahey, M. (2006) Mechanics of early age cemented paste

backfill. Paste ’06, Limerick April 3-7, Australian Centre for Geomechanics, ISBN 0-

9756756-5-6.

Helinski, M. Coltrona, A.B. Fourie, A.B. and Fahey, M. (2007) Influence of tailings

type on barricade loads in backfilled stopes. Paste ’07, Perth, March 13-15, Australian

Centre for Geomechanics, ISBN 0-9756756-7-2. 95-104.

Helinski, M. Fahey, M. Fourie, A.B. (2007) An effective stress approach to modelling

mine backfilling, Minefill ’07, 9th International Symposium on Mining with Backfill,

Montreal, Paper # 2478.


vi

Fourie, A.B. Helinski, M. Fahey, M. (2007). Using effective stress theory to

characterise the behaviour of backfill. Minefill ’07, 9th International Symposium on

Mining with Backfill, Montreal, Paper # 2480.

Helinski, M. Tucker, C. Grice, A.G. (2007) Water management in hydraulic fill

operations. Minefill ’07, 9th International Symposium on Mining with Backfill,

Montreal, Paper # 2479.

…………………………………………

Matthew Helinski

December 2007


vii

TABLE OF CONTENTS

Abstract...........................................................................................................................i

Acknowledgements...................................................................................................... iii

Declaration.....................................................................................................................v

Table of Contents ....................................................................................................... vii

List of Figures................................................................................................................x

List of Tables ............................................................................................................ xvii

Chapter 1 Introduction..............................................................................................1.1 1.1 Significance of consolidation to mine backfill ...................................................1.4 1.2 Project methodology...........................................................................................1.5

Chapter 2 Background & literature review ............................................................2.1 2.1 Introduction.........................................................................................................2.1 2.2 Mine backfill literature .......................................................................................2.1

2.2.1 Influence of consolidation on barricade stresses.....................................2.1 2.2.2 Influence of consolidation on in situ strengths........................................2.7 2.2.3 Influence of consolidation on exposure stability.....................................2.9 2.2.4 Summary ...............................................................................................2.10

2.3 Consolidation....................................................................................................2.10 2.3.1 Consolidation behaviour of cementing soil...........................................2.11

2.4 Structured soil ...................................................................................................2.13 2.4.1 Modelling structured soil behaviour......................................................2.16

2.5 Cementation......................................................................................................2.17 2.5.1 Cementation behaviour..........................................................................2.20

2.6 Summary...........................................................................................................2.20

Chapter 3 Behaviour of cementing slurries .............................................................3.1 3.1 Introduction.........................................................................................................3.1 3.2 Strength and stiffness..........................................................................................3.1

3.2.1 Uncemented material response................................................................3.1 3.2.2 Stress-strain behaviour of cemented fill ..................................................3.2 3.2.3 Hardening ................................................................................................3.3 3.2.4 Damage due to yielding during hydration (dD) ......................................3.6 3.2.5 Unconfined compression strength (qu) ....................................................3.7 3.2.6 Stiffness ...................................................................................................3.7 3.2.7 Stress-strain behaviour: summary ...........................................................3.8

3.3 Permeability........................................................................................................3.9 3.3.1 Uncemented permeability........................................................................3.9 3.3.2 Cemented permeability..........................................................................3.10

3.4 Self desiccation.................................................................................................3.11 3.4.1 Cementation reactions ...........................................................................3.12 3.4.2 Impact on pore pressure ........................................................................3.14 3.4.3 Analytical model ...................................................................................3.15 3.4.4 Experimental demonstration of effect of self desiccation .....................3.17 3.4.5 Material properties influencing self desiccation ...................................3.18 3.4.6 Experimental derivation of parameters .................................................3.21


viii

3.5 Temperature......................................................................................................3.25 3.6 Material characterisation technique..................................................................3.27 3.7 Conclusion ........................................................................................................3.28

Chapter 4 One-dimensional consolidation modelling.............................................4.1 4.1 Introduction.........................................................................................................4.1 4.2 Model development ............................................................................................4.1

4.2.1 Modelling the behaviour of uncemented tailings: the MinTaCo Program4.1 4.2.2 Modelling the behaviour of cemented tailings: the CeMinTaCo

Program ...................................................................................................4.3 4.2.3 CeMinTaCo governing equations ...........................................................4.5

4.3 Numerical implementation .................................................................................4.9 4.4 Model verification ............................................................................................4.11

4.4.1 Compressibility .....................................................................................4.11 4.4.2 Self desiccation......................................................................................4.11

4.5 Sensitivity study................................................................................................4.12 4.5.1 Influence of cementation .......................................................................4.12 4.5.2 Influence of permeability ......................................................................4.13 4.5.3 Typical damage scenario .......................................................................4.15 4.5.4 Strain requirements................................................................................4.19 4.5.5 Comparison with data from in situ monitoring of filled stopes ............4.20

4.6 Conclusion ........................................................................................................4.22

Chapter 5 Two-dimensional consolidation analysis (Minefill-2D) ........................5.1 5.1 Introduction.........................................................................................................5.1 5.2 Programming requirements ................................................................................5.2 5.3 Programming Methodology................................................................................5.4

5.3.1 Introduction .............................................................................................5.4 5.3.2 The finite element method.......................................................................5.4 5.3.3 Boundary conditions..............................................................................5.14 5.3.4 Solution to the global equations ............................................................5.18

5.4 Material Behaviour ...........................................................................................5.20 5.4.1 Influence of cementation on governing equations ................................5.20 5.4.2 Constitutive model, ( )[ ]( )[ ]cG CetDK ,,′ ...............................................5.22

5.4.3 Permeability model, ( )[ ] ( )[ ]cGcG CetnCet ,,,,,Φ .................................5.26

5.4.4 Self desiccation, Q(t,e,C).....................................................................5.27 5.5 Model Verification............................................................................................5.27

5.5.1 Comparison with analytical/numerical solutions ..................................5.27 5.5.2 Comparison with CeMinTaCo ..............................................................5.29 5.5.3 Stope mesh details .................................................................................5.30 5.5.4 Comparison with in situ measurements.................................................5.32 5.5.5 Investigation of the arching mechanism................................................5.34

5.6 Conclusion ........................................................................................................5.36

Chapter 6 Centrifuge modelling ...............................................................................6.1 6.1 Introduction.........................................................................................................6.1 6.2 Experimental Apparatus .....................................................................................6.2 6.3 Calibration ..........................................................................................................6.4 6.4 Experiment..........................................................................................................6.7

6.4.1 Material ...................................................................................................6.7


ix

6.4.2 Experimental procedure ..........................................................................6.8 6.4.3 Experimental results ................................................................................6.9

6.5 Numerical back analysis ...................................................................................6.11 6.5.1 Material characterisation .......................................................................6.11 6.5.2 Numerical back analysis........................................................................6.13

6.6 Conclusion ........................................................................................................6.15

Chapter 7 Sensitivity study .......................................................................................7.1 7.1 Introduction.........................................................................................................7.1 7.2 Comparision of hydraulic fill and paste fill ........................................................7.1

7.2.1 Experimental results ................................................................................7.2 7.2.2 Modelling ................................................................................................7.3 7.2.3 Comparison of hydraulic fill and paste fill..............................................7.6

7.3 Consolidating fill ................................................................................................7.6 7.3.1 Influence of stope geometry ....................................................................7.7 7.3.2 Influence of permeability ........................................................................7.8 7.3.3 Influence of cementation .........................................................................7.9 7.3.4 Influence of filling rate..........................................................................7.11 7.3.5 Consolidating fill: discussion ................................................................7.11 7.3.6 Consolidating fill: conclusion ...............................................................7.13

7.4 Non-consolidating fill .......................................................................................7.13 7.4.1 Influence of stope geometry ..................................................................7.14 7.4.2 Influence of permeability ......................................................................7.15 7.4.3 Influence of cementation .......................................................................7.16 7.4.4 Filling rate .............................................................................................7.17 7.4.5 Non-consolidating fill: discussion.........................................................7.17 7.4.6 Non-consolidating fill: conclusion ........................................................7.19

7.5 Development of effective stress during curing.................................................7.20 7.5.1 Comparision between consolidating and non-consolidating fill ...........7.20 7.5.2 Development of effective stress in consolidating fill ............................7.21 7.5.3 Development of effective stress in non-consolidating fill.....................7.22 7.5.4 Curing of fill: discussion and conclusion ..............................................7.23

7.6 Conclusion ........................................................................................................7.25

Chapter 8 Concluding remarks and recommendations for future work..............8.1 8.1 Concluding remarks............................................................................................8.1 8.2 Main outcomes....................................................................................................8.1 8.3 Recommendations for future work .....................................................................8.4

Chapter 9 References.................................................................................................9.1


x

LIST OF FIGURES

Figure 1.1 Schematic of a typical mine tailings based backfill system (contributed

by Cobar Management Pty Ltd).

Figure 1.2 Schematic showing a typical stope filling situation.

Figure 1.3 Photograph showing a failed barricade (from Revell and Sainsbury,

2007).

Figure 2.1 Stress distribution down the centreline of a stope assuming “drained”

and “undrained” filling.

Figure 2.2 The impact of drained and undrained filling on barricade stress.

Figure 2.3 Conversion from vertical total stress to horizontal stress.

Figure 2.4 Gibson's(1958) consolidation chart with typical minefills.

Figure 2.5 Comparison between structured and unstructured compression

behaviour.

Figure 2.6 Comparison between structured and unstructured yield surfaces.

Figure 2.7 Powers illustration of the Cement hydration process (from Illstron et al.

1979).

Figure 2.8 Relationship between void ratio and binder content to achieve critical

porosity and typical mine backfill range.

Figure 3.1 Incremental yield stress as it is defined in this thesis.

Figure 3.2

(a)

Relationship between void ratio and qu for CSA hydraulic fill.

Figure 3.2

(b)

Relationship between void ratio and qu for Cannington paste fill from

Rankin (2004).

Figure 3.3 Normalised qu against time for CSA hydraulic fill and Cannington

paste fill.

Figure 3.4

(a)

Incremental small strain shear stiffness against qu for CSA hydraulic

fill.

Figure 3.4

(b)

Young's modulus (at large strains) against qu for Cannington paste fill.


xi

Figure 3.5 Comparison between one-dimensional compression experiments and

the model results.

Figure 3.6 Comparison between eff and permeability.

Figure 3.7 Particle size distribution curves.

Figure 3.8 Pore water pressure (u) and effective stress changes in triaxial samples

hydrating under constant total stress and undrained boundary

conditions.

Figure 3.9 Typical result from ‘bender element’ test.

Figure 3.10 Typical pore water pressure (u) and effective stress changes in a

triaxial sample (CSA hydraulic fill material with 5% cement) hydrating

under constant total stress and undrained boundary conditions (with

periodic re-establishment of back pressure, to minimise effective stress

change).

Figure 3.11 The development of bulk stiffness Ks with time for CSA hydraulic fill:

experimental data (symbols) and Equation 3.31 (lines).

Figure 3.12 Rate of pore water pressure (u) reduction with time after initial set for

various cement contents for CSA hydraulic fill.

Figure 3.13 Normalised apparent water loss rate plotted against time for different

cement contents for CSA hydraulic fill: experimental data compared

with Equation 3.32.

Figure 3.14 Comparison of experimental reduction of pore water pressure (u)

against time and adjusted theoretical solution for CSA hydraulic fill.

Figure 3.15 Predicted and measured reduction in pore water pressure (u) for KB

paste backfill.

Figure 3.16 Temperature variation across stope half-space after 20 hours.

Figure 3.17 Hydration test setup.

Figure 4.1 Schematic representation showing the relationship between a, ξ and x

in the convective coordinate system.

Figure 4.2 Schematic representing pore water continuity across an element ∂a.


xii

Figure 4.3 Schematic showing mesh used in CeMinTaCo finite difference

approximation.

Figure 4.4 Comparison between the self desiccation pore pressure reduction in a

hydration test and CeMinTaCo output.

Figure 4.5 Idealisation of the base boundary conditions used to represent a stope

in CeMinTaCo.

Figure 4.6 CeMinTaCo output illustrating the influence of the cement induced

mechanisms on the pore pressure response.

Figure 4.7 Variation in permeability against time

Figure 4.8 Pore pressure against time for the different cases analysed.

Figure 4.9 Pore pressure isochrones for the different permeability cases analysed.

Figure 4.10 e against σv for different damage parameters.

Figure 4.11 CeMinTaCo output for different damage parameters.

Figure 4.12 Development of material strength against time for different damage

parameters.

Figure 4.13 CeMinTaCo output for different damage parameters in free draining

material Figure 4.14 Development of material strength for different damage parameters with

free draining fill.

Figure 4.15 Axial strain levels for different filling scenarios.

Figure 4.16 Comparison between CeMinTaCo and in situ pore pressure

measurements.

Figure 5.1 Element geometry adopted for plane-strain displacement and pore

pressure finite element calculations in this thesis.

Figure 5.2 8 noded isoparametric element (taken from Potts and Zdravković,

1999) showing (a) the parent element and (b) the global element.

Figure 5.3 Element geometry adopted for axi-symmetric displacement and pore

pressure finite element calculations in this thesis.

Figure 5.4 (a) shear stress against axial strain and (b) shear stress against mean

stress for a triaxial test.


xiii

Figure 5.5 Tangent shear stiffness normalised by small strain shear stiffness

against shear stress normalised by the peak shear strength.

Figure 5.6 Illustration of one-dimensional consolidation problem.

Figure 5.7 Comparison between Minefill-2D and the analytical solution for one-

dimensional consolidation analysis.

Figure 5.8 Illustration showing the one-dimensional self weight consolidation

problem used in the Minefill-2D verification.

Figure 5.9 Comparison between Minefill-2D and Plaxis for a self weight

consolidation problem.

Figure 5.10 Numerical simulation undertaken to verify the performance of the self

desiccation mechanism.

Figure 5.11 Comparison between Minefill-2D and the analytical solution for self

desiccation.

Figure 5.12 Numerical geometry for comparison between Minefill 2D and Darcy's

law for a falling head permeability test.

Figure 5.13 Comparison with Minefill-2D and Darcy's law for the flow through the

surface layer of the fill.

Figure 5.14 Comparison between Cemintaco and Minefill 2D.

Figure 5.15 Comparison between Cemintaco and Minefill 2D with a modified

"initial set" point.

Figure 5.16 Finite element mesh used to represent (a) coarse mesh, (b) medium

mesh and (c) a fine mesh.

Figure 5.17 Calculated pore pressure in the centre of the stope floor for different

mesh shapes.

Figure 5.18 Calculated barricade stress in the centre of the stope floor for different

mesh shapes.

Figure 5.19 Vertical total stress contours at the completion of filling for the (a)

coarse mesh, (b) medium mesh and (c) the fine mesh.

Figure 5.20 Comparison between Minefill-2D and in situ measurements.


xiv

Figure 5.21 Illustration showing the boundary conditions adopted for the (a) fixed-

BC and (b) free-BC case in the "arching" analysis.

Figure 5.22 Comparison between u and σv in a stope with fixed and free vertical

displacement boundary conditions.

Figure 5.23 σv contours for a stope with (a) fixed vertical displacement boundary

conditions and (b) with free vertical displacement boundary conditions

Figure 5.24 Total vertical stress along the stope centreline for the fixed and free

BC.

Figure 6.1 Schematic showing a section through the sample container.

Figure 6.2 (a) Photograph of strain gauged cylinder that was used to represent the

stope walls and (b) the inside of the cylinder showing the rough

cylinder walls. Figure 6.3 Photograph of the false base and loadcells that were used in the

experiment.

Figure 6.4 Experimental apparatus positioned in a strong box on the UWA

geotechnical centrifuge.

Figure 6.5 Change in pressure and stress during Stage 1 loading.

Figure 6.6 Incremental change in u during Stage 2 loading.

Figure 6.7 Incremental load / stress distribution in second stage of loading.

Figure 6.8 Relationship between vertical effective stress and void ratio from the

Rowe cell test.

Figure 6.9 Relationship between void ratio and permeability from Rowe cell.

Figure 6.10 Comparison between measured and calculated pore pressure in Stage 1.

Figure 6.11 Comparison between the measured and calculated load distribution in

Stage 1.

Figure 6.12 Evolution of Go and qu against time for the kaolin with 25% cement

mix.

Figure 6.13 Comparison between measured and calculated pore pressure in Stage 2.

Figure 6.14 Comparison between the measured and calculated load distribution in

Stage 2.


xv

Figure 7.1 Particle size distribution of backfills tested.

Figure 7.2 Evolution of permeability against time for different mine backfills.

Figure 7.3 Evolution of cohesion against time for different mine backfills.

Figure 7.4 Minefill 2D results of barricade stress against time for different backfill

types.

Figure 7.5 Development of pore pressure against time for different mine backfills.

Figure 7.6 Pore pressure isochrones for different mine backfills.

Figure 7.7 Influence of drawpoint permeability on pore pressure at the base of a

stope with consolidating fill.

Figure 7.8 Pore pressure isochrones for consolidating fills with various drawpoint

permeabilities.

Figure 7.9 Barricade stress against time for different drawpoint permeabilities

with consolidating fills.

Figure 7.10 Pore pressure against time for consolidating fills with different

permeabilities.

Figure 7.11 Barricade stress against time for consolidating fills with different

permeabilities.

Figure 7.12 Pore water pressure against time for consolidating fill with different

binder contents.

Figure 7.13 Barricade stress against time for consolidating fills with different

binder contents.

Figure 7.14 Comparison between applied shear stress and cohesion for a boundary

element.

Figure 7.15 Contour of cohesion at the end of filling for the (a) the 3.0% cement

and (b) the 1.5% cement case.

Figure 7.16 Total vertical stress calculated for the (a) 3.0% cement and (b) the

1.5% cement case.

Figure 7.17 Influence of filling rate on consolidating fill pore pressures.


xvi

Figure 7.18 Influence of filling rate on consolidating fill barricade stress.

Figure 7.19 Relationship between pore pressure and barricade stress in a

consolidating fill.

Figure 7.20 Pore pressure against time for non-consolidating fills with different

drawpoint permeabilities.

Figure 7.21 Barricade stress against time for non-consolidating fills with different

drawpoint permeabilities.

Figure 7.22 Pore pressure profile at the end of filling for (a) kdp=10kstope and (b)

kdp=0.1kstope.


permeabilities.


permeabilities.


cement contents.


cement contents.

Figure 7.27 Barricade Stress and pore pressure against time for non-consolidating

fill with a bonded and unbonded interface


filling rates.


filling rates.

Figure 7.30 Development of effective stress within an element of consolidating and

non-consolidating fill against time.

Figure 7.31 Development of effective stress against time in a consolidating fill.

Figure 7.32 Development of effective stress against time in a non-consolidating fill.

Figure 7.33 Development of effective stress against time at different elevations in a

non-consolidating fill.


xvii

LIST OF TABLES

Table 5.1 Material properties adopted for CeMinTaCo - Minefill-2D comparison.

Table 5.2 P.F.-A material properties (from Helinski et al. 2007) adopted for back

analysis of in situ test results.

Table 5.3 Material properties adopted in the investigation of the arching

mechanism.

Table 6.1 Material properties for kaolin with 25% cement content.

Table 7.1 Comparison of hydraulic fill and paste fill properties.

Table 7.2 Material Properties.

Mechanics of Mine Backfill Matthew Helinski Introduction The University of Western Australia

1.1

CHAPTER 1

INTRODUCTION

Many underground hard-rock mining operations adopt an open stoping technique,

which involves the extraction of ore in large underground blocks called stopes. Stope

sizes are dictated by geotechnical conditions, but the extraction of an orebody generally

requires many, often hundreds of stopes. In order to maintain geotechnical stability on

both a local and regional scale, significant pillars containing valuable ore must be left

between stopes, but this can significantly reduce the quantity of ore recovered. To

increase recovery, many mines choose to re-fill previously mined stopes.

The filling process involves placing mine waste materials into previously mined stopes,

in order to provide a number of services to the mining operation. These services

include:

• Providing support to the surrounding rockmass

• Creating a working surface for production activities

• Disposal of mining waste products.

The primary reason for adopting a mine backfill strategy is to increase the quantity of

ore that may be recovered and reduce the amount of ore dilution that occurs during

stoping. In addition, mine backfill can be used to improve ground conditions by

replacing poor natural host rock with an engineered material, in regions that are

sensitive to mining.

Mine backfilling can be carried out in a number of different ways including hydraulic

fills, which use the coarse component of the tailings stream; paste backfill, whose

source is full-stream tailings, and rockfill, which may be generated from quarried rock

or mining waste rock. The main advantage of hydraulic fill and paste fill over rockfill is

their ability to be transported hydraulically. This provides benefits regarding material

handling costs, but once placed within a stope the transportation water can reduce

stability if not managed appropriately.


1.2

This thesis is focused on tailings-based backfill, which includes both hydraulic and

paste fills. These are grouped under the term “tailings-based backfill” throughout this

thesis. Figure 1.1 provides an illustration of the processes involved at a typical tailings-

based backfill site. This figure illustrates the interaction of mining, processing and

filling activities. The relevant features of Figure 1.1 with respect to the backfill process

are as follows (the numbers refer to the key in Figure 1.1):

3. Shows ore being extracted from a stope.

27. Shows the concentrator, where the ore is crushed and the commodity

extracted.

36. Shows the backfill plant, which is where the tailings from the concentrator

are post-processed to generate the desired backfill product (this often

includes cycloning, thickening, filtration and cement mixing).

23. Shows the underground backfill delivery borehole/ pipeline system.

6. Shows the backfill slurry being deposited into a stope.

4. Shows a stope being blasted, which leads to the adjacent backfill mass being

exposed vertically, and the overlying backfill mass being exposed

horizontally.

The focus of this work is to improve the understanding of the processes involved during

the deposition of mine backfill into a stope. Figure 1.2 presents a schematic showing

backfill being deposited into a stope. This figure shows a typical stope with a

“drawpoint” that would previously have been used to extract ore from the stope. Fill

would be deposited into the stope from the top and containment barricades (also

referred to as bulkheads) would be constructed in the drawpoint to retain the fill from

flowing out of the stope and into the active mining environment. These barricades are

typically constructed from permeable bricks or sprayed fibrecrete. The terminology

presented in Figure 1.2 will be used throughout this thesis.

Figure 1.1 illustrates that, during the extraction of ore around existing fill masses, the

material is exposed vertically and horizontally. In order to maintain stability during

these exposures, small proportions of binder (cement) are often added to the tailings


1.3

mix. As conveyed throughout this thesis, the addition of cement to the fill mass results

in additional complexities when attempting to characterise the deposition behaviour.

Traditionally the use of tailings-based backfill has involved the removal of fines from

the tailings stream (referred to in the industry as “classification”) to create a coarse

material, which is transported through pipelines in a turbulent manner with large

amounts of water (Thomas and Holtham 1989). The purpose of removing the fines is to

increase the hydraulic conductivity of the material so, when placed, transportation water

can drain away freely. Recently there have been significant developments in the field of

tailings-based mine backfill with the introduction of full-stream tailings into the

underground environment. This type of fill is transported with lower water contents than

hydraulic fills and the presence of fines allows the material to be transported at slower

velocities without creating segregation in the reticulation system. This material is

termed “paste backfill” and is comprehensively addressed by Landriault (1995, 2006).

The main focus of this thesis is to investigate the processes and mechanisms associated

with the placement and consolidation of tailings-based backfill, and develop a sound

methodology for understanding the mechanisms, and interaction of mechanisms, that

occurs during the filling process. The thesis examines the influence of these

mechanisms on total stresses applied to containment barricades as well as the

development of effective stress within cemented mine backfill during the hydration

process. Only by applying a rigorous approach to these problems, can certainty be

developed regarding these areas of concern.

In the mining industry there has, in the past, been an acceptance of operational “rules of

thumb”, which were developed through experience at other sites, or through experience

at the site of interest. These ‘rules of thumb” can result in a successful outcome, but as

noted by Baldwin (2004) “each tailing stream is unique and the resulting paste

geomaterial behaviour can and does vary dramatically from one operation to another”.

Therefore, without a fundamental understanding of the processes involved, it is

impossible to determine when subtle characteristics associated with a given situation

will result in the “rules of thumb” becoming invalid. In this situation, a variation from

the expected behaviour can result in catastrophic consequences such as the failure of


1.4

containment barricades and inrush of fill material, or the failure of a fill mass during

exposure.

Between the period of December 2003 and December 2004, there were seven tailings-

based fill barricade failures worldwide; in 2006 there were at least five barricade

failures. Due to confidentially reasons barricade failures are often not reported in

literature. One example is that reported by Revell and Sainsbury (2007). These authors

present a number of different examples of barricade failures. Included in this document

are two examples where rapid filling rates resulted in excessive loading of barricade

structures. These failures resulted in a very large energy release with paste fill flowing

up to 250 m from the original bulkhead location. Figure 1.3 presents a photograph of a

failed barricade from this paper. In addition, this paper discussed various barricade (or

bulkhead) designs and presents details relating to the structural failure mechanisms.

Another hydraulic fill barricade failure, that was documented in a coroner’s report

(Coroner’s Report, 2001), is that at the Bronzwing mine in Western Australia where

three miners were killed. The overall conclusion of this investigation suggested that

inadequate stope drainage was the aspect that resulted in excessive loads on the

barricade structure.

In addition to addressing the problem of barricade loads, by developing a model that

rigorously captures the most important mechanisms associated with cemented mine

backfill processes, filling conditions can be varied throughout the whole spectrum of

tailings-based fill types without having to adopt simplifying assumptions to achieve a

result. This approach provides an understanding of which parameters control the

behaviour and which fundamental relationships need to be satisfied in order to deem

various “rules of thumb” appropriate.

1.1 SIGNIFICANCE OF CONSOLIDATION TO MINE

BACKFILL

Tailings-based backfill that is transported hydraulically, is a multi-phase system

consisting of a solid phase and water phase. Due to the large compressive stiffness of

the pore water, relative to the soil structure, the application of load (due to the accretion

of overlying material) creates an increase in the pore fluid pressure. Should there be no

dissipation of pore fluid pressure, there would be no increase in effective stress and the


1.5

situation is said to be “undrained”. If the pore pressure is dissipated immediately, any

applied load would be immediately placed on the soil matrix in the form of effective

stress, and the situation is said to be “drained”.

Various mine sites have fill types that possess different mineralogy and particle size

distribution, while filling rates and stope sizes vary from site to site. As a result, the

degree of consolidation that occurs during filling also varies.

To complicate the consolidation process further, most mine backfills contain a small

component of cement, which acts to modify the consolidation properties by increasing

the stiffness and reducing the permeability.

It is important to appreciate that throughout this thesis, consolidation is defined as the

transfer of stress from the water phase to the soil phase. This should not be confused

with the compression of the soil matrix or the bonding of material, through cement

hydration, as has been noted throughout mine backfill literature. An appropriate

definition of consolidation is particularly important in relation to stiff cemented soil

where only small amounts of compression is required to mobilise large stresses.

Given the theoretical developments that are generated in this work the results will be

applied to mine backfill problems such as;

• Providing a rigorous technique for estimating loads placed on barricade

structures

• Providing an understanding of in situ curing conditions relative to those in the

laboratory

1.2 PROJECT METHODOLOGY

The overall objective of this thesis was to develop a means of representing the cemented

mine backfill deposition process. As will be outlined throughout this thesis, the

cemented mine backfill process involves the interaction of a number of complex

mechanisms, and in order to achieve the desired outcome simplification of many of

these mechanism was required.

The methodology adopted is to develop an understanding of the consolidation behaviour

of cementing soils through an assessment of past research in relevant fields. On this


1.6

basis an assessment was undertaken of the applicability and limitations of previous

work to the mine backfill situation. Using previous work, a rational approach to

simulating the cemented mine backfill deposition process is formulated.

The second component of this project focuses on the utilisation of existing literature as

well as experimental testing, to formulate suitable models to represent various

mechanisms that occur during the mine backfill deposition process. Areas investigated

include the characterisation of strength, stiffness and permeability of the material prior

to cementation, but unlike in conventional soil mechanics, a major focus is placed on

the evolution of these properties due to cement hydration. Hydrating cement acts to

develop a structure that increases the material stiffness and yield strength, yet the

application of stress can potentially destroy this cemented structure. Furthermore, the

growth of cement hydrates has been shown to reduce the material permeability. In

addition, the cement hydration reaction creates a net volume reduction, which is termed

self desiccation. In later chapters this volume change is shown to have a significant

influence on the overall consolidation behaviour and must be incorporated into the

understanding of the mine backfill deposition process.

Cemented mine backfill placement essentially involves the interaction of three time-

dependent relationships, which include filling rate, consolidation rate and hydration

rate. In order to appropriately link these mechanisms, they are coupled numerically. The

first numerical stage included incorporation of the cementing soil’s material

characteristics into the one-dimensional, large strain, tailings consolidation program

MinTaCo (Seneviratne et al., 1996). This modified model was renamed CeMinTaCo,

and is used in a sensitivity analysis to investigate the interaction of mechanisms during

typical mine backfill runs. From this sensitivity analysis, the most significant

characteristics associated with the consolidation of cemented mine backfill were

identified.

A new two-dimensional (plane strain and axi-symmetric) fully coupled consolidation

model named Minefill-2D is then presented. Minefill-2D incorporates all of the relevant

cemented mine backfill mechanisms, as well as the ability to simulate the progressive

accretion of material and any stress redistribution onto the surrounding stiff rockmass.

This model is verified against a number of established analytical solutions as well as


1.7

laboratory experiments (including both element testing and centrifuge modelling) and in

situ data.

Having gained appropriate confidence in Minefill-2D, a sensitivity study was

undertaken. This study investigates the fundamental difference in mechanisms between

full-stream tailings backfill (paste fill) and classified-tailings backfill (hydraulic fill). A

sensitivity study was undertaken for both full-stream and classified-tailings backfills, to

highlight what are likely to be important, and less important, characteristics when

dealing with the various fill types.

The results of the sensitivity study are used to provide some guidance when designing

and managing filling operations.

Mechanics of Mine Backfill Matthew Helinski Background & Literature Review The University of Western Australia

2.1

CHAPTER 2

BACKGROUND & LITERATURE REVIEW

2.1 INTRODUCTION

The purpose of this chapter is to provide an overview of the literature that is relevant to

this thesis. Firstly, there is a discussion regarding the “state of the art” in mine backfill.

This provides an overview of existing methods being applied in the mining industry and

highlights a number of areas where further research can deliver an improved

understanding.

This is followed by a review of previous work that is considered to be relevant to this

thesis. Specifically, topics addressed include consolidation theory, structured-soil

mechanics, and cement technology. In addition to the overview of previous work, at the

end of each section there is a brief description of how the literature has been applied in

the context of mine backfill throughout this thesis.

2.2 MINE BACKFILL LITERATURE

In conventional surface tailings disposal, consolidation is important since this

mechanism dictates the settlement of the tailings mass and therefore the quantity of

material that can be placed into a storage facility. In addition, the stress history of

tailings is important when determining the undrained shear strength of the material. As a

result, authors such as Gibson (1967), Williams (1988), Toh (1992), Seneviratne et al.

(1996) and Newson et al. (1996) have thoroughly investigated the consolidation

behaviour of surface tailings facilities.

In an underground environment, the degree of settlement is not of major importance and

since the material is often cemented, the undrained shear strength is less likely to be

influenced by stress history. Therefore the relevance of consolidation might be

questioned.

2.2.1 Influence of consolidation on barricade stresses

In the underground backfill environment, the surrounding rockmass is significantly

stiffer than the material being deposited. Rankin (2004) investigated numerically the


2.2

development of stress in the backfill during filling and found that much of the vertical

stress can be redistributed to the surrounding rockmass. This work neglected pore

pressures in the calculation of the stress distribution and as shown later in the thesis, this

approach can lead to a gross oversimplification of the process.

To understand how stress is redistributed to the surrounding rockmass requires an

understanding of the effective stress. And in order to understand effective stress, an

understanding of the consolidation process is required.

To demonstrate the significance of consolidation (or specifically the influence of pore

water pressure) on the stress distribution in a backfill mass, Helinski et al. (2006)

undertook a series of numerical simulations using the finite difference program FLAC

(Fast Lagrangian Analysis of Continua). This analysis involved filling a plane strain

stope (20 m wide by 50 m high), with fully hydrated cemented paste backfill, assuming

either fully drained or undrained conditions. The fully drained case neglected the

influence of pore water pressure, while the undrained case assumed that the material is

placed without any consolidation. Neglecting the influence of pore water pressure in the

fully drained case is considered a valid representation of the “best case scenario” as the

water table is assumed to have been drawn to the bottom of the stope, and with a low air

entry suction value (for non-plastic tailings), this would result in atmospheric pressures

existing throughout most of the fill mass.

Material properties adopted in this analysis were those quoted by Rankin et al. (2001)

for Cannington paste fill. These included a unit weight of 20 kN/m3,Young’s modulus

(E) of 60 MPa and Poisson’s ratio (ν′) of 0.25. These parameters equate to a shear

modulus (G) of 24 MPa and a drained bulk modulus (K) of 40 MPa. The friction angle

(φ′) adopted was 25º and, to demonstrate the influence of bond strength (or lack

thereof), an artificially high cohesion (c′) of 25 MPa was adopted.

Figure 2.1 presents the calculated total vertical stress down the centreline of the stope at

the end of filling, when the material has been placed in both a drained and an undrained

manner. Also presented in Figure 2.1 is the total vertical stress assuming no stress

redistribution to the surrounding rockmass.

Figure 2.1 demonstrates that there is a significant difference between the total vertical

stress down the centreline of a stope, if filling is carried out under fully consolidated


2.3

(drained) or fully unconsolidated (undrained) conditions. With fine-grained material

(with a high air entry suction value) drawing the water table down through the fill mass

may cause suctions to develop within the fill mass. The development of suctions would

increase the amount of arching in the “drained” case, increasing the influence of pore

pressure on the arching process.

Even with fully-hydrated cemented backfill, if there is no consolidation there is very

little stress redistribution to the surrounding rockmass, even with an inflated value of

cohesion. In order to mobilise any shear stress at the fill/rock interface, shear strains are

required. To generate shear strain the material must settle, but under undrained

conditions the compressive stiffness of the bulk material is that of water, which is very

high, and therefore, very little settlement occurs. It is not until water is squeezed out of

the fill mass that soil compression (settlement) can occur and shear strains at the

interface can occur, generating the “arching” effect. The lower vertical stress for the

drained case in Figure 2.1, is due to this arching effect.

It is interesting to note that, in the lower 10 m of the stope in the drained case, there is a

linear increase in vertical total stress. The reason for this is that, towards the stiff base of

the stope, the total amount of settlement (vertical deformation) is reduced, resulting in

less shear strain being mobilised at the interface and therefore less shear stress. As a

result less stress redistribution or “arching” occurs towards the base even in a drained

situation. In addition, as the name implies, a certain vertical height is required to

accommodate the “arch” in the material, so that arching only takes effect above a

certain distance from the base.

The results from this numerical study can be extended to the total horizontal stress

placed on the barricade for the two extreme cases. It should be noted that in both cases

the pore pressure immediately behind the barricade is set to zero. The total horizontal

stress calculated at the barricade location is plotted against height up the barricade in

Figure 2.2 for both the drained and undrained cases. This Figure illustrates that if filling

is carried out “undrained”, barricade stresses are very high (≈ 800 kPa) while “drained”

filling results in much lower barricade stresses (≈ 80 kPa).

Figure 2.1 demonstrates that without consolidation, there is little stress redistribution

and high vertical total stresses. In addition to these high total vertical stresses within the


2.4

stope, the undrained filling case also results in higher horizontal total stress for a given

vertical total stress. This may be understood with reference to Figure 2.3, which

illustrates Rankin’s lateral earth pressure theory. This theory relates the vertical total

stress ( vσ ), vertical effective stress (vσ′ ), pore pressure (u) to the horizontal total stress

( hσ ) in accordance with Rankin’s lateral earth pressure coefficient K0. For most

uncemented tailings K0 is typically in the range of 0.3-0.5.

If all of the self-weight stress were supported by the water phase, the horizontal total

stress would be equal to the vertical total stress. As consolidation occurs and the self-

weight stress is transferred off the water phase and onto the soil structure, the horizontal

total stress becomes less than half of the vertical total stress, for typical Ko values.

Consolidation also influences the horizontal effective stress within a stope. In order to

generate frictional shear strength between the fill mass and the surrounding rockmass,

horizontal effective stress is required. If all of the self weight vertical stress is being

carried by the water phase, the horizontal total stress and pore pressure would be equal.

In this case, the horizontal effective stress would be zero. Consolidation reduces the

pore pressure, increasing the horizontal effective stress and allows some frictional shear

strength to exist at the rock/fill interface.

Gibson (1958) investigated analytically the amount of consolidation in a deposit of a

saturated soil where the thickness of the deposit is increasing with time. He derived a

relationship between the development of excess pore pressure (uex), the coefficient of

consolidation (cv) , the filling rate (m) and the duration that filling has been ongoing (t),

in a one-dimensional situation.

Applying this analytical solution, Gibson (1958) developed a chart to relate a non-

dimensional time term (T) to the excess pore pressure (uex). In this solution, uex is

represented by a gradient of uex against depth relative to the gradient of uex that would

be created with no consolidation. This ratio is defined as (du/dz)/γ′. If this ratio is equal

to unity, the total stress and pore pressure are equal (meaning that there is no

consolidation) while if equal to zero there is no excess pore pressure (i.e. complete

consolidation).

The non-dimensional time constant is defined as;


2.5

vc

tmT

.2

= (2.1)

Gibson’s chart to relate the degree of consolidation that occurs during placement to the

non-dimensional time constant is reproduced as Figure 2.4. The relevance of this figure

to tailings backfill is discussed further later.

The situation analysed is well suited to the case of tailings-based backfill placement into

an open stope. While it might be argued that the placement of minefill into a stope does

not strictly conform to the one-dimensional assumption due to the potential for arching

to the surrounding rockmass, neglecting arching during the early stages of placement

can provide a reasonable representation of most situations.

The other point of question may relate to the base boundary conditions. In most

situations it is reasonable to consider free-draining conditions at the barricade location.

But, as illustrated in Figure 1.2, the drawpoint flow area is often significantly smaller

than that of the stope. Furthermore, as filling progresses away from the base, the

distance to this boundary increases, making drainage towards the top boundary more

likely. As a result, it may be more appropriate to ultimately assume an impermeable

condition at the base. Gibson (1958) analysed both permeable and impermeable

boundary conditions at the base.

Qiu and Sego (2001) undertook a series of laboratory experiments on full-stream gold

and copper tailings. One component of this work included large strain consolidation

testing of this material to determine cv. The tests indicated cv values of 14 m2/yr and 25

m2/yr for the gold and copper tailings, respectively, over the density range typical for

paste backfill. Vick (1983) suggests that cv for classified tailings (which would be

representative of hydraulic fill) ranges between 1500 m2/yr and 300,000 m2/yr and cv for

full-stream tailings ranges from 3 m2/yr to 300 m2/yr.

To develop an understanding of the degree of consolidation likely to occur during filling

in typical mine backfill operations, these suggested cv values were combined with a

filling rate of rise of 5 m/day (a typical filling rate) and a 40 m high stope to calculate

the respective dimensionless time factor (T). The location of the various material types

is superimposed onto Gibson’s consolidation chart in Figure 2.4.


2.6

Figure 2.4 therefore indicates that during the placement of hydraulic fill it is unlikely

that excess pore pressures would develop unless very high filling rates are adopted. In

contrast, for full-stream tailings (paste fill), it indicates that it is very unlikely that

consolidation would occur. This suggests that, following the logic outlined earlier, loads

applied to barricade structures can be extremely high in full-stream tailings backfill in

an uncemented state. It should be noted that Gibson’s chart only considers excess pore

pressures, neglecting hydrostatic pore pressures. However, as discussed later in this

document, the presence of “hydrostatic” type pore pressures (generated as a result of a

flow restriction through the drawpoint area) also make the influence of pore water

pressure relevant to a hydraulic filling scenario.

To the author’s knowledge, the only case where the influence of pore pressure has been

incorporated into the analysis of mine backfill deposition mechanics is in the work

described by Kuganathan (2002). This work presented an analytical solution for

estimating barricade stresses in hydraulic fill stopes, which incorporates “steady state”

seepage-induced pore pressures1 within the stope drawpoint. This solution is based on a

limit state analysis, which incorporates the influence of pore pressures only within the

drawpoint of a stope. Being a limit state method, this approach assumes the mobilisation

of the ultimate material strength at the rock/fill interface and there is no consideration of

the influence of pore pressures on the stress distribution within the stope, nor is there

consideration of excess pore pressures that may be created during filling. Therefore,

while this technique may provide a reasonable indication of barricade stresses under

some conditions, these limitations can lead to oversimplification in many cases

(particularly cases involving fine-grained full-stream tailings backfill).

Another approach that has previously been adopted to establish an understanding of the

stresses placed on barricades is direct stress measurement using diaphragm-type earth-

pressure cells. Revell (2002) and Belem et al. (2004) used total pressure cells to

measure the loads placed on paste fill retaining structures during filling. Based on the

1 “Steady-state seepage pore pressures” will be properly defined later. Briefly, this is the pore pressure profile that is reached when steady-state seepage is established within the stope, in equilibrium with the boundary total head conditions (the boundaries being the top fill surface and the barricade).


2.7

measurements, it was concluded that the amount of load transferred to the wall reduced

as the cement hydration proceeded.

Clayton and Bica (1993) demonstrated that the stress measurements from earth-pressure

cells are typically lower than the true values; this is called “under-registration”. The

degree of under-registration is related to the relative stiffness between the cell and the

surrounding soil. As hydration proceeds, the stiffness of a cemented soil increases

significantly, and therefore the degree of under-registration in such circumstances could

also change. Therefore, questions may arise as to whether the reduction in stress

measured by Revell (2002) and Belem at al. (2004) is a true reduction in barricade

stress or if it is simply a result of the change in under-registration due to the progress of

hydration.

Stone (personal communications 2007) suggests that the biggest problem facing the

mining industry with regard to mine backfill is uncertainty over barricade loads. The

need for further research into loads being placed on mine backfill retaining structures

has also been recognised by Le Roux (2004) who suggests that there is a need for a

“renewed focus on barricade design with high rates of filling”. McCarthy (2007)

suggests that mine backfill barricades are a problem in the mining industry and that “the

problem is technically complex” and there is a need for more research in this area.

2.2.2 Influence of consolidation on in situ strengths

It has been documented that in situ backfill strengths are often significantly greater than

those measured in the laboratory, for the same mix (Cayouette, 2003, Revell 2004). It

has also been well established that the application of effective stress to a cementing soil

prior to or during hydration can increase the material strength (Blight and Spearing

1996, Consoli 2000, Rotta 2003). The improvement in strength is said to be a result of

soil matrix compression (which leads to an increased density) as well as an

improvement in the intimacy of the contact points. This topic has been researched

experimentally by a number of different authors such as Blight and Spearing (1996), Le

Roux at al. (2002) and Belem et al. (2006).


2.8

The work by Blight and Spearing (1996) focused on investigating the influence of

closure strains2 on the strength of mine backfill. This work demonstrated that as the

strain rate is increased there is an associated increase in strength. As this work was

carried out in the context of strains induced by ground movement in classified tailings

backfill, a strain criterion was adopted and there was no need for an effective stress

consideration. The loading rate adopted by these authors is less likely to be relevant to a

large open stoping situation where the application of total stress during filling is usually

dependent on the self weight of the overlying fill mass.

Le Roux et al.(2002) investigated the impact of applying load in a one-dimensional

situation to a sample during curing. The results indicated that higher cement contents

reduced the degree of compression for the same loading sequence. The deficiency with

this work was that the rate of loading adopted was in accordance with the rate of

application of self weight total stresses in a typical filling situation rather than that of

effective vertical stress. In order to develop a rational approach to the loading rate that

should be applied, it is the rate of development of effective stress in the field that must

be matched, rather than the total stress. As demonstrated in this thesis, this is

particularly relevant during the early stages of loading where the pore pressures in a

stope can increase at the same rate as the total stress, resulting in no change in effective

stress during the early stages of hydration.

Belem (2006) undertook a series of “column filling tests”. The columns used in this

work were 3 m high, and 300 mm square in plan. Three columns were tested: the first

had impermeable vertical boundaries, the second had an impermeable top half and a

permeable bottom half and the third had completely permeable boundaries. These

columns were filled with paste backfill containing cement. At the end of the tests, the

resulting cemented material was investigated. This investigation indicated that drainage

created a significant increase in density which resulted in an increase in material

strengths. These tests were meant to represent possible conditions within a stope, but

due to the significant reduction in drainage path length associated with the boundary

2 “Closure strains” refer to the inward movement of the walls of a stope after the fill is placed and the hydration process is occurring.


2.9

the rate of effective stress development is not considered representative of the field

situation1.

Therefore, in order to improve the understanding of the mine backfill deposition process

and to start to develop a rational approach for understanding the interaction of cement

hydration and the application of effective stress, an understanding of the mine backfill

consolidation process is required. This aspect has been recognised by Le Roux (2004)

who suggests that it is necessary to understand “… the influence of hydrating cement on

the consolidation properties of the paste fill and how this influences the final material

properties and affects the performance of the material”.

2.2.3 Influence of consolidation on exposure stability

During the removal of stopes adjacent to a cemented fill mass (as illustrated in Figure

1.1 point number 3), there is a reduction in confining stress, which reduces the stability

of the fill mass. If the fill mass has insufficient cohesive strength, fill failure can occur,

resulting in dilution of the ore being mined in the adjacent stope.

A number of authors have proposed analytical solutions for estimating vertical exposure

strength requirements. The most commonly adopted analytical solutions include the

upper bound mechanisms by Mitchell and Wong (1982) and those based on the limit

state arching theory of Marston (1930) and Terzaghi (1943) (such as those presented by

Winch 1999 and Aubertin et al. 2003). The interesting point about these two commonly

adopted limit state techniques is the strength parameters used to represent the contact

between the fill mass and the surrounding rockmass. In the upper bound mechanism

proposed by Mitchell and Wong.(1982), it is assumed that the interface is cohesive,

while the technique presented by Winch (1999) and Aubertin et al. (2003) is based on a

frictional contact strength only.

During the filling process, the interaction between the development of shear strength

and the application of shear stress may modify the cohesive properties at this interface.

Such interaction is dependent on the material properties, boundary conditions, filling 1 The limitations of using scaled models (whether on a geotechnical centrifuge or at 1g) for this type of investigation is that the timescale of consolidation/drainage is reduced by reducing the scale, but the timescale for hydration is not. This is explained in much more detail in Chapter 6.


2.10

rate and the consolidation rate, but without appropriately understanding the filling

process it is difficult to establish an understanding of this important characteristic.

2.2.4 Summary

This section has presented previous work in the field of mine backfill and demonstrated

the need for a soil mechanics approach to understanding the mine backfill deposition

behaviour. The remainder of this chapter focuses on work carried out in the fields of

consolidation, structured-soil and cementation which is considered relevant to the

cemented mine backfill application.

2.3 CONSOLIDATION

A solution for the process of consolidation in a saturated soil was developed by

Terzaghi, on the basis of a number of simplifying assumptions, such as:

• the pore water is infinitely stiff relative to the soil skeleton, such that an

application of external stress results in generation of a pore pressure equal to

that stress

• the permeability (hydraulic conductivity) and compressibility of the soil does

not change during a loading increment

• Darcy’s law applies – i.e. the rate of water flow in the soil depends on the

permeability and the gradient in the total head.

For slurries consolidating under self-weight stresses, many authors, such as Carrier

(1982), pointed out that the assumption of constant permeability and compressibility of

the matrix is not correct, due to the large changes in void ratio that occur as

consolidation proceeds, resulting in significant change in compressibility, and even

more significant change in permeability.

The Terzaghi model was extended by Gibson (1958) to simulate the progressive

sedimentation of material, as discussed in the previous section. This model was based

on small-strain theory and restricted to material properties that remain constant

throughout the consolidation process. The main advancement in this work was to take

account analytically of an increase in drainage path length as well as the inclusion of

self-weight stresses.


2.11

In order to take account of the significant nonlinearity in large-strain consolidation

problems, researchers began investigating finite strain consolidation models. This

included work by Mikasa (1965) and Gibson et al. (1967, 1981). The methodology uses

a Lagrangian coordinate system where the boundaries move in accordance with the

evolving soil dimensions. Through applying this theory numerically, the authors were

able to rigorously account for variations in geometry as well as variations in

permeability and stiffness during compression. Based on this work, Gibson et al. (1981)

demonstrated that conventional small-strain theory had the potential to significantly

underestimate excess pore pressures. Tan and Scott (1988) continued the comparison of

small- and large-strain theory, suggesting that Terzaghi’s small-strain solutions were

only applicable for strains less than 20%.

With modern developments in computational efficiency, numerical programs

specifically focused on solving the large-strain consolidation equations for the purpose

of understanding the mine tailings deposition process, have been generated (Williams et

al., 1989, Tao, 1992 and Seneviratne et al., 1996).

In addition to the numerical and analytical developments, significant research effort has

been dedicated to understanding material parameters including oedometer testing,

constant and falling head permeability tests as well as Rowe cell testing that captures

volume and permeability changes under various confining stresses. Based on results

from this type of testwork, authors such as Carrier et al. (1983) developed models to

represent the large strain compressive behaviour of soil.

2.3.1 Consolidation behaviour of cementing soil

The development of a one-dimensional consolidation model for soil undergoing

cementation (CeMinTaCo) is described in detail in Chapters 3 and 4. However, a brief

overview is given here, to show where it fits with respect to other models in the

literature.

The basis for this model is the large-strain consolidation equation derived by Gibson et

al. (1981). The governing equation is derived through combining equilibrium of the soil

and water phases using Darcy’s law to represent flow. Combining these equations and

maintaining continuity, the following governing equation was derived to represent one-

dimensional large strain consolidation of uncemented slurry.


2.12

( ){

( )

( ) ( ) ( ){

BCDA

1

11

ta

k

a

u

e

ek

aee

t

u vo

w

vo δ

δσ=

δδ+

δδ

++

γδδ

δσ′δ++

δδ

44444 344444 2144 344 21

(2.2)

where a is a Lagrangian coordinate, u is pore pressure, k is hydraulic conductivity

(permeability), and σ′v and σv are the vertical effective and total stresses, respectively.

In this equation, term A is the rate of change in pore pressure as a result of a rate of

application of total stress (term B), term C is the volumetric strain, which is dictated by

the hydraulic conductivity (k) of the material, and term D is the current stiffness of the

material.

During the consolidation of uncemented mine tailings from an initial slurry state, both

the stiffness (compressibility) and the permeability of the material change as the void

ratio reduces. When cement is added, these changes still occur but a number of other

mechanisms associated with cement hydration are introduced. These include the

development of cement-induced stiffness and strength, a reduction in permeability and

the introduction of a new mechanism that is referred to as “self desiccation”.

The modified governing equation is presented here:

( )

( )( ) ( ) ( )

( ) ( ){(B)(E)

(C)

0

(D)

0

)A(

,,,,

1

11,,,

,,,1

tt

CtVeCt

e

a

ek

a

u

e

eek

aeeCt

e

eCteK

e

t

u

vcshvc

v

eff

w

effvc

v

vcv

w

δδσ=

δδσ′

δσ′δ+

δδ

+

δδ

++

γδδ

+σ′

δσ′δ+

σ′

δσ′δ−

δδ

44444 344444 21

4444444 34444444 214444 34444 21

444444 3444444 21

(2.3)

In this equation, the modified terms are identified using the same labels as the

equivalent unmodified terms (in Equation 2.2) but there is an additional term (term E)

that does not have an equivalent term in the unmodified equation.

Due to the soil matrix stiffness potentially approaching that of water, the change in pore

pressure (term A in Equation 2.2) resulting from a change in total stress, requires


2.13

modification to take account of the cemented matrix stiffness (ev

δσ′δ

) and the bulk

modulus of water (Kw) to satisfy strain compatibility.

The volumetric strain term (term C in Equation 2.2) requires modification to take into

account the fact that the permeability (k) is affected not just by the normal void ratio

reduction due to consolidation, but also by the formation of cement gel in the void

space.

The stiffness term (term D in Equation 2.2) requires modification to express the material

stiffness (ev

δσ′δ

) as a function of cement hydration, current stress state and previous

stress excursions.

An additional term (term E) needs to be introduced to take account of volumetric

changes (t

Vsh

δδ

) associated with the cement hydration process (the self-desiccation

process referred to above).

The derivation of the modified material models is presented in Chapter 3 while the

derivation of the modified governing equation for one-dimensional consolidation of a

cementing soil (Equation 2.3) is presented in Chapter 4.

2.4 STRUCTURED SOIL

The term “structured soil” refers to any soil that has a true cohesive strength. This may

include artificially-cemented soils or natural soils that may have been cemented through

natural processes, such as calcite precipitation.

Clough et al. (1981) pioneered the research into cemented soils by investigating

experimentally the impact of cementation on both naturally-cemented and artificially-

cemented soils. This work demonstrated that cementation creates true cohesion but has

little impact on the friction angle. It was also shown that density, grain-size distribution,

and grain shape all have a significant influence on the behaviour of cemented soils.

Clough et al. (1989) continued this work on cemented soils with experimental

investigations into the cyclic loading of cemented soils.


2.14

In the late 1970’s - early 1980’s during the construction of offshore oil and gas

platforms on the North West shelf of Australia, piling problems were encountered. As

discussed in Jewell et al. (1988), the major reason for these problems was associated

with a lack of understanding regarding the behaviour of structured soils.

In response to these problems, a significant focus was placed on understanding the

behaviour of structured soils. Leroueil and Vaughan (1990) were the first to present a

comprehensive framework for understanding structured soils, with a particular focus on

the behaviour of residual soils. They discuss how the shape of the yield surface varies

with curing stresses. The different failure modes that would occur through loading along

different stress paths were also discussed. In this framework it was shown that shearing

would produce a localised failure plane, while compressive stresses would destroy the

structure more uniformly, leading to volumetric contraction. The authors also

introduced the concept of the “structure-permitted” space, which is illustrated in Figure

2.5. This is a region in volumetric compression space (e - p′) where only material with

structure can exist.

Coop and Atkinson (1993) presented a framework for understanding the behaviour of

cemented carbonate sand. This work showed that when sheared, the materials in either a

cemented or uncemented state approach the same critical state. Also, they suggest that

the cemented friction angle is slightly lower than the uncemented equivalent. This is

attributed to surface coating. They demonstrate that, as with overconsolidated soils,

shearing under low stress results in high stress ratios with post-yield strain softening,

while shearing under high mean stress results in the cementation having little influence

on the ultimate strength. It was also shown that cementation can significantly increase

the elastic compressive stiffness.

Cuccovillo and Coop (1997) investigated the yielding and pre-failure deformation of

cemented soils. They demonstrated that a cemented soil showed two major yield points

in loading, these being the stress where the material stiffness starts to reduce below the

small strain stiffness (termed Y1 yield stress) and the point where significant reduction

in stiffness is observed (termed Y2 yield stress). Y1 is said to be the first onset of

structural breakdown. The rate of stiffness change at Y2 was shown to be a function of


2.15

the state of the soil fabric. It was shown that a loose calcarenite reduces in stiffness

significantly more than dense silica sandstone.

Asaoka et al. (2000) investigated the significance of structure in clayey soil on the

consolidation/ compression behaviour. It was concluded that prior to yield, the higher

stiffness of the structured soil (relative to the destructured soil) resulted in faster rates of

consolidation. However, as the material was loaded beyond its yield point (Y2), the

stiffness of the structured soil was less than that of the destructured soil (under the same

stress) and, as a result, consolidation of the structured material occurred over a longer

period with greater settlement.

More recently, there has been renewed interest in the behaviour of soils cemented

artificially for the purpose of soil improvement. This research effort has been primarily

driven by Consoli and his co-workers, as detailed below.

Consoli et al. (2000) showed that the stress state during curing plays a significant role in

the mechanical behaviour of the soil. Schnaid et al. (2001) investigated the triaxial

behaviour of cemented soils experimentally. They showed that the shear strength of a

cemented soil can be appropriately determined from the unconfined compressive

strength and the uncemented friction angle. For the confining stresses used in the

testwork, the secant modulus is unaffected by the confining stress, suggesting that the

stiffness is more a measure of the bond strength.

Rotta et al. (2003) investigated isotropic yielding of a cemented soil. This work

involved an experimental investigation of material cemented at different densities,

under different stress levels. They introduced the concept of the incremental yield

strength, which is considered to be the contribution of cementation to the increase in

yield stress of the material. The focus of this work was to develop a rational approach to

determining the material characteristics that influence this incremental yield strength. It

was demonstrated that this value is dependent on the degree of cementation and the

material state.

Finally, Consoli et al. (2006) combined the results of Schnaid et al. (2001) and Rotta et

al. (2003) to develop a unified framework for understanding the strength of cemented

soils. This work demonstrated that the incremental isotropic yield stress and initial bulk


2.16

modulus can be linearly related to the unconfined compressive strength for a cemented

material.

Yin and Fang (2006) undertook experimental studies into the influence of cement-

treated clay columns on the consolidation of an otherwise untreated clay mass. These

results indicated that the presence of the cement-treated material played a significant

role in accelerating the consolidation of the mass. This was primarily attributed to the

increase in material stiffness.

A number of different constitutive models have been developed to represent the

behaviour of structured soils (Gens and Nova, 1993; Lagioia and Nova, 1995; Rouainia

and Wood, 2000; Kavvadas and Amorosi, 2000). Comparison with experimental data

indicates that these models provide a good representation of the soil behaviour. But in

order to provide this representation, significant mathematical detail is required. While

these types of models are considered superior to those presented in this thesis, at the

time of writing this thesis, such complexity was considered a second order effect in the

context of this work.

Liu and Carter (2002, 2005) present a modification of the well known Cam-Clay model

to represent the behaviour of structured soil. This model is referred to as the Structured

Cam-Clay model. The concept behind this model is that the yield surface for the

cemented soil is simply an expansion of the original yield surface for the uncemented

soil, and the magnitude of this expansion is dependent on the degree of cementation.

This concept is illustrated in Figure 2.6. As the soil is loaded, the model allows for the

degradation of the structured yield surface and hardening of the uncemented yield

surface. This can occur at the yield point (virgin yielding) as well as for loading

excursions within the yield surface (sub-yielding), but beyond a particular stress level

(Y1 as defined by Cuccovillo and Coop, 1997). This logic is the same in both the

compression and shearing stress paths.

2.4.1 Modelling structured soil behaviour

In order to characterise the material response for one-dimensional compression

modelling, a modified version of the Structured Cam-Clay model was adopted. This

model provides the flexibility to represent the compression behaviour initially in

accordance with the uncemented Cam-Clay model and to take account of the presence


2.17

of cementation through an increased yield surface. The Structured Cam-Clay model also

allows for the yield surface to be degraded (potentially back to that of the uncemented

soil) in accordance with the destructuring functions suggested by Carter and Liu (2005).

To represent the size of the yield surface, the methodology presented by Rotta et al.

(2003) and Consoli et al. (2006) is used. The concept of an incremental yield stress is

incorporated to separate the cemented yield stress from the uncemented yield stress. The

magnitude of the incremental yield stress is said to be a function of the degree of

cementation and material state in accordance with the function suggested by Rotta et al.

(2003). Furthermore, based on the findings of Consoli et al. (2006), the unconfined

compressive strength and small-strain bulk stiffness is said to be proportional to the

incremental yield stress along the isotropic and one-dimensional stress paths. Details of

this approach are presented in Section 3.2.

2.5 CEMENTATION

Combining Sections 2.3 and 2.4, a rational methodology for the consolidation analysis

of a cemented soil can be developed. However, in order to appropriately represent the

cemented mine backfill process, a model that can appropriately represent the

consolidation of a cementing soil is required. In this work, previous work in the field of

cement and concrete research was taken into account.

Pioneering work in the field of cement research is described in a series of publications

by Powers and Brownyard (1947). These publications were the culmination of a

research program, by the Portland cement association, aimed at understanding the

behaviour of Portland cement paste. This work was later summarised in a single concise

document by Brouwers (2004).

This, and subsequent work by Powers (1958, 1979), developed the first model for

understanding cement hydration. When the cement particles are undergoing hydration, a

number of chemical reactions take place. These reactions result in the growth of

hydrates that effectively act to connect particles. An illustration of this process (taken

from Illstron et al., 1960) is presented in Figure 2.7. Powers and Brownyard (1947)

suggest that the cemented structure is made up of solid particles and cement “gel”. With

this, they introduce the concept of non-evaporable water, which is bound within the


2.18

solid material, and gel water, which exits between gel particles. Due to the large surface

area of the very fine gel particles, van der Waals forces bind gel water within the gel

phase.

Based on their research, Powers and Brownyard (1947) determined that the specific

gravity of the unhydrated cement is 3.17 while that of the hydrated gel solids is 2.43 and

that of the gel including pores is 1.76. This indicates that, when combined with water in

the hydration process, the unhydrated cement volume increases by approximately 80%

(including gel products).

It was also found that the weight of chemically-bound water (termed non-evaporable

water) used in cement hydration is 23% of the weight of unhydrated cement.

Furthermore, it was found that due to the change in volume stoichiometries during the

cement reactions, there is a net reduction in volume from the unhydrated cement and

water to the final hydrated cement product. This change in volume (in cm3) was shown

to be 27% of the weight of non-evaporable water. In conventional concrete literature,

this volume reduction is termed “self desiccation” as it acts to desaturate lean concrete

mixes. This mechanism is important with respect to conventional concrete mechanics

because of the way that it influences shrinkage cracking (termed “autogenous

shrinkage”). Researchers such as Powers and Brownyard (1947), Hua et al. (1995),

Koenders and Van Breugel (1997), Bentz (1995) and Brouwers (2004) investigated the

impact of this mechanism on the shrinkage of conventional concrete.

Illstron (1979) presents the rate of hydration for the various compounds that make up

cement paste. This work indicated that the four main compounds react at vastly different

rates, ranging from C3S, which achieved 70% of its ultimate strength after 28 days, to

C2S which has achieved only 5% of its strength after 28 days.

Rather than simulating the rate of hydration for each individual compounds, other

researchers have developed empirical relationships to represent the rate of hydration for

the overall cement product (Rastrup, 1956, Guo, 1989 and Sideris, 1993). These authors

term the rate of hydration “maturity” and essentially fit various curves to the

development of cement related characteristics (maturity) against time.

The growth of cement hydrates increase the material stiffness and strength, due to the

bonding of particles. This has been well documented by authors such as Powers and


2.19

Brownyard (1947), Illstron (1979) and Sideris et al. (2004). The strength achieved is

said to be a function of the cement content as well as the water-cement ratio. For a

saturated soil, this is consistent with the findings of the cemented soil literature, which

suggests that the strength is dependent on the density of the cemented soil (Consoli. et

al. 2006).

During the hydration process, some of the water is converted from a free liquid to either

solid or gel product, which forms a component of the soil structure and occupies some

of the previous void space. As already mentioned, Powers and Brownyard (1947)

suggest that the hydrated solid and gel is 80% greater than the original unhydrated

cement volume. Just as with a reduction in void space from soil compression, the

infilling of voids by cement gel acts to reduce the permeability of the material. This

aspect has been researched in the concrete literature for the purpose of reinforced

concrete corrosion resistance (Garboczi and Bentz,1995, Breysse and Gerard, 1997, and

Bentz et al. 1998).

Garboczi and Bentz (1995) present the concept of critical porosity. This is defined as

the point where the cement has enlarged sufficiently that the combination of the cement

solids and the gel structure create a seal across the entire cross-sectional area of the

sample. Since the cement gel is composed of platelets with very large surface areas, this

situation produces a significant reduction in permeability; in fact, at this point the

material is considered to be impermeable.

Based on the volumetric changes suggested by Powers and Brownyard (1947), Figure

2.8 was developed to illustrate the relationship between void ratio and cement content

required to achieve the critical porosity (as described by Garboczi and Bentz, 1995).

Also presented in Figure 2.8 is the range over which typical mine backfills are

produced. This indicates that, due to the relatively low density and small cement

contents, it is very unlikely that a typical mine backfill would ever approach critical

porosity. Therefore, while the presence of cementation acts to reduce the permeability

(and should be taken into account), this reduction is not expected to render the material

impermeable.


2.20

2.5.1 Cementation behaviour

In order to represent the cementation process, research in the field of concrete

technology (which was presented in the previous section) was investigated. A brief

overview of how this logic is applied has been provided in this section.

While each of the maturity functions (discussed in the previous section) appears to

provide a reasonable fit to experimental data, the exponential relationship suggested by

Rastrup (1956) was adopted to represent the maturity of cement throughout this thesis.

This work provides a simple exponential relationship between cement hydration and

time. Investigations presented later in this thesis indicate that the rate of change of

strength, stiffness, permeability and volume can all be appropriately represented using

the same maturity relationship. Details of this approach are provided in Section 3.2.

Combining the total volumetric changes recommended by Powers and Brownyard

(1947) with the maturity function presented by Rastrup (1956), a function is developed

to represent the rate of volumetric change that occurs with time due to the self

desiccation mechanism. This approach is detailed in Section 3.4.

To represent the influence of cement hydration on permeability, the relationship

between void ratio and permeability suggested by Carrier et al (1983) is combined with

the volumetric changes during cement hydration as recommended by Powers and

Brownyard (1947) and the maturity relationship of Rastrup (1956). Details of this

relationship are provided in Section 3.3.

2.6 SUMMARY

This chapter has presented an overview of previous work in the field of mine backfill. In

addition, some simple examples were presented to demonstrate the significance of some

of the assumptions inherent in existing solutions. Specifically, these examples

demonstrate that gaining an understanding of the degree of consolidation that occurs

during placement is essential in attempting to determine the stress distribution around a

stope.

This chapter continues with a description of literature relevant to understanding the

consolidation that takes place during the deposition of cemented mine backfill. The

fields covered included consolidation, structured soil and cement hydration. Following a


2.21

description of background literature, a brief description is provided in each of these

areas to explain how this previous work is applied to the cemented mine backfill

problem throughout this thesis.

The next chapter will expand on this brief description and develop these ideas to form a

unified framework to represent the individual mechanisms relevant to the cemented

mine backfill deposition process.

Mechanics of Mine Backfill Matthew Helinski Behaviour of Cementing Slurries The University of Western Australia

3.1

CHAPTER 3

BEHAVIOUR OF CEMENTING SLURRIES

3.1 INTRODUCTION

During the placement of mine backfill, the material initially behaves in accordance with

the uncemented material characteristics, but as cement hydrates the behaviour of the

material changes. Due to the increase in stiffness, reduction in permeability, and the self

desiccation mechanism, the change in material behaviour can have a significant

influence on the consolidation response. This chapter presents a description of the

behaviour of a tailings material undergoing simultaneous consolidation and

cementation, and develops equations to characterise this behaviour. These equations

will form the basis of the numerical models presented later in the thesis.

3.2 STRENGTH AND STIFFNESS

Terms A, D and E in the governing consolidation equation (Equation 2.3) are all

influenced by the stiffness of the material. Therefore, it is important that an appropriate

model be developed to represent the evolution of the material stiffness throughout the

filling process. This model must take account of the response of the material prior to the

formation of any cementation as well as the evolution of the material properties with

time. Due to the interaction of filling and cement hydration, this model must be capable

of representing the formation of cement bonds as well as the possible breakdown of

these bonds as a result of stresses that exceed the current bond strength.

3.2.1 Uncemented material response

As the eventual goal is to adopt the Structured Cam-Clay model to represent the

behaviour of the material in a cemented state, a convenient method of representing the

compression behaviour of the uncemented soil is through the Cam-Clay model. This

relationship is represented by Equations 3.1 and 3.2.

( )( )

σ′σ′

λ−=∆−1

.iv

ivne l

(3.1)


3.2

σ′σ′

κ−=∆− )1(

)(.iv

ivne l

(3.2)

where ∆e is the change in void ratio in the current time increment, λ and κ are the

conventional Cam-Clay parameters describing the gradient of the compression curve,

and σ′v(i-1) and σ′v(i) are the vertical effective stresses at the start and end of the

increment respectively. The ‘normally consolidated’ relationship (Equation 3.1) applies

to loading of the material on or above the uncemented compression line while the elastic

compression relationship (Equation 3.2) applies for material undergoing compression at

stress levels below the uncemented compression line (i.e. material that has been

overconsolidated).

3.2.2 Stress-strain behaviour of cemented fill

To incorporate the effect of cementation on strength, a convenient starting point is the

Structured Cam-Clay model developed by Liu and co-workers at Sydney University

(Liu et al., 1998; Liu and Carter, 2002; and Carter and Liu, 2005). In this approach,

‘structure’ (which could include cementation) has the effect of increasing the isotropic

(or one-dimensional) compression yield stress in a manner analogous to

overconsolidation. In the case of cemented mine backfill, the yield stress in

compression is a function of void ratio and cementation, and consequently it changes

with time as both of these change. A considerable extension to the Structured Cam-

Clay model is required in this case, to deal with the combined effects of growth of

‘structure’ (e.g. cement gel) as hydration occurs and damage to this structure due to

possible yielding with increasing effective stress.

The principle that has been adopted to determine the cement contribution to

compression resistance follows the concept suggested by Rotta et al. (2003). Rotta et al.

(2003) propose the concept of the incremental isotropic yield stress (∆p′y) and define

this as being the difference between the primary yield stress and the isotropic curing

stress. The concept of incremental yield stress has been illustrated in Figure 3.1, which

presents a plot of mean effective stress (p′) versus void ratio (e) for soil in uncemented

and cemented states during isotropic compression. As mine backfill material is placed

and consolidated along the normally consolidated line, it is assumed that the curing


3.3

stress can be appropriately represented by the yield stress of the material in an

uncemented state. Therefore, the incremental yield stress is said to represent the

difference between the yield stresses for the uncemented and cemented material.

Rotta et al. (2003) suggested that ∆p′y is a measure of the bond strength, and Consoli et

al. (2006) continued this concept to show that ∆p′y is proportional to the unconfined

compressive strength (qu). Given these findings, it is considered reasonable to assume

that this proportionality would continue along the one-dimensional compression stress

path. Therefore, the incremental one-dimensional vertical yield stress (∆σ′vy, the

preconsolidation stress) for a cemented soil has been assumed to be adequately

represented by the superposition of an uncemented and a cemented component (the ∆p′y

contribution). Furthermore, based on the findings of Consoli et al. (2006) it has been

assumed that ∆σ′vy can be linearly related to qu.

During the mine backfill deposition process, previously placed fill is subjected to

mechanical processes that cause changes to the one-dimensional yield stress (∆σ′vy).

These include:

• conventional soil hardening due to void ratio reduction (dH);

• increases in yield stress with time due to cementation (dHyd);

• a potential reduction in strength due to plastic deformation – effectively,

yielding of the cement bonds as compression occurs simultaneously with

hydration (dD).

These characteristics are accounted for by cumulating the changes in each of these

individual characteristics over a particular timestep (dt):

t

DHydH

tvy

dddd

d−+=

σ′∆ (3.3)

3.2.3 Hardening

Hardening in the model results from void ratio reduction as for conventional

uncemented soil and also from the hydration process.


3.4

The conventional soil strain hardening term (dH) applies to an increase in the

uncemented yield strength as a result of the compression of the soil matrix. This

hardening is a function of the uncemented soil properties λ and Γ:

κ−λ∆−Γ=

peH expd

(3.4)

where λ and κ are as defined above (Equations 3.1 and 3.2), Γ corresponds to the void

ratio on the normal consolidation line at a vertical effective stress of 1 kPa, and ∆ep is

the plastic change in void ratio.

The additional, hardening (strength increase) that occurs due to hydration (dHyd) is

assumed to be a function of cement content, tailings density at the time of the hydration

increment and the time from the start of hydration. It has been well documented

(Leroueil and Vaughan, 1990; Consoli et al., 2000; Li and Aubertin, 2003; and Rotta et

al., 2003) that an increase in either cement content or density increases the strength of a

cemented soil. Rotta et al. (2003) developed an empirical equation to relate the

incremental isotropic yield strength (∆p′y) to both cement content and void ratio:

+−+

=∆WZ.C

eY X.Cp'

c

cy exp

(3.5)

where Cc is cement content (weight of cement per unit weight of solids), e is void ratio

and X, Y, Z and W are dimensionless constants and ∆p′y is in kPa. As it stands, this

equation implies that there is some cement component of strength even when the

cement content is zero. In order to ensure that there is zero cement component of

strength at zero cement content, the Y constant has been replaced by a ‘cement power’

term and the function adopted is shown in Equation 3.6. In addition, a constant

multiplier A (with units of kPa) has been introduced.

+−+

=∆WZ.C

eCX.CAp'

c

ccy

1.0

exp.

(3.6)

Assuming that ∆σ′vy, qu and ∆p′y are all proportional (as discussed earlier), data on any

of the stress paths may be used to derive the constant terms (X, Y, Z and W), and by

adjusting the constant A (according to the ratio of proportionality between the various


3.5

cemented strength components) the cement component of strength along other stress

paths may be determined. An example of this is given in Figures 3.2(a) and 3.2(b),

which show how Equation 3.6 can be fitted to a series of unconfined compression test

results on CSA hydraulic fill and Cannington mine paste fill data (Rankin, 2004),

respectively. This indicates that Equation 3.6 can appropriately represent the

development of cementation in a range of typical cemented mine backfill materials. For

one-dimensional compression analysis the most direct method of determining all

constants (A, X, W and Z) is through regression analysis on a series of one-dimensional

compression tests.

The ‘maturity relationship’ adopted to represent the progress of hydration with time is

an exponential relationship originally presented by Rastrup (1956) and republished by

Illston (1979). This relationship is presented as:

−=*

expt

dm (3.7)

where m is the degree of maturity (0 at the start of the process, 1 at the end), d is a

maturity constant (day-1/2), t* is the time (in days) since “initial set”. While it is

acknowledged that Equation 3.7 is not dimensionally independent, to maintain

consistency with previous work, the published form was preserved with t* always

specified in units of days and d in terms of day1/2.

A series of unconfined compression tests was carried out at different stages of hydration

to assess the development of this bond strength with time. Figure 3.3 shows qu

(normalised by dividing by the maximum qu) against the time in hours for both

Cannington paste fill (PF) (Rankin, 2004) and CSA hydraulic fill (HF).

Based on regression of the two data sets in Figure 3.3, maturity constants (d) of 0.9

day1/2 and 2.6 day1/2 provided a very close match to the hydraulic fill and the finer paste

fill, respectively, with the duration until initial set (to) being 4 hours (0.16 days) in both

cases.

The maturity relationship (Equation 3.7) may be combined with the strength increment

relationship (Equation 3.6) to determine the increment of bond strength (dHyd) over a

given time interval (∆t):


3.6

+−+

−−

∆+

−=WZ.C

eC X.C.A.

t

d

tt

dHyd

c

.cc

10

**expexpexpd (3.8)

It should be noted that the change in bond strength is incremented in accordance with

the material state at t*, the time at the start of that increment. This ensures that any strain

hardening of the soil matrix is accounted for when evaluating hardening due to

hydration over the next time increment.

3.2.4 Damage due to yielding during hydration (dD)

As hydration may be occurring simultaneously with an increase in effectives stress (due

to consolidation) the newly-forming ‘structure’ may experience damage due to the

evolving yield stress being exceeded. This damage may occur as a result of loading

within the yield surface as well as loading on the yield surface (virgin yielding).

The damage relationship adopted here follows the approach used in the Structured Cam-

Clay model (Liu et al., 1998; Liu and Carter, 2002; and Carter and Liu, 2005). In this

approach, incremental plastic volumetric strain induces damage, which is manifest as a

reduction in the size of the yield surface.

The function adopted to account for plastic volumetric strain in the model follows the

work of Carter and Liu (2005) where the plastic component of strain may be represented

by Equation 3.9.

( )

′+′α+′κ−λα

Μη−=ε

s

ccpv pe

pbp

)1(

dd1d

3**

*

(3.9)

where the asterix (*) indicates uncemented properties, η is the stress ratio (q/p′), M is

the stress ratio at critical state, p′c is the applied effective stress, b is a constant

representing the structural breakdown, and α is a measure of the kinematic hardening

given by:

′−′′−′

=αus

uc

pp

pp

(3.10)

where p′u is the stress at which kinematic hardening or destruction occurs, and p′s is the

isotropic stress on the yield surface.


3.7

Given the plastic strain increment, the associated reduction in compressive yield

strength may be determined as:

( )

( )

−

′′

−

′′

+κ−λ

ε′+= c

p

p

cp

pb

pbeD

o

s

o

s

pvs

n

n1

d1d

**

l

l

(3.11)

where c is the constant separating the limiting compression lines of the cemented and

uncemented soils (for the very low cement contents commonly used in mine backfill

this term is equal to zero), and p′o is the stress required to place the uncemented soil in

the same state on the normal consolidation line.

While changes in Poisson’s ratio (due to cementation) can modify the stress path in one-

dimensional compression, CeMinTaCo has been simplified by replacing all mean stress

terms in Equations 3.9 – 3.11 by vertical effective stress (σ′v), and setting the stress ratio

term (η) to zero.

3.2.5 Unconfined compression strength (qu)

As explained earlier, it is assumed that the incremental one-dimensional yield stress is

linearly related to qu. In this analysis, the total one-dimensional yield stress and the

equivalent uncemented one-dimensional yield stress are monitored. By subtracting the

latter from the former, and applying the constant of proportionality, qu is determined.

This assumption has little impact on the overall consolidation behaviour. However, it is

common to use qu when referring to material strengths in the mining industry therefore

it is useful to gain an understanding of the impact of the various mechanisms on qu

throughout the filling process.

3.2.6 Stiffness

The previous section addressed the change in yield stress due to strain hardening,

cement hydration and damage. As with strength, these characteristics also influence the

material stiffness and in order to undertake consolidation analysis it is therefore

essential to characterize any material stiffness changes that occur. In an approach

similar to that used for strength, it is assumed that the stiffness of the cemented soil is a

combination of the stiffness due to the uncemented soil skeleton and that due to the


3.8

cementation. The uncemented stiffness is determined in accordance with Equations 3.1

and 3.2, while the cemented component of stiffness is assumed to be proportional to the

cemented component of strength (∆σ′vy, qu or ∆p′y).

A series of experiments was carried out to assess the validity of the assumption that the

cement induced stiffness and cement induced strength could be linearly related. These

experiments involved the measurement of small strain shear stiffness (Go) using bender

elements prior to unconfined compression testing of these specimens. Figure 3.4(a)

shows the results of incremental shear stiffness (Go(inc)) relative to qu for a variety of

combinations of CSA hydraulic fill mixes. Figure 3.4(b) illustrates the relationship

between qu and Young’s Modulus for Cannington Paste fill as published by Rankin

(2004).

Figures 3.4(a) and 3.4(b) indicate that for a range of material strengths and material

types there appears to be a linear correlation between the cement component of stiffness

and cemented strength (qu). Therefore, if ∆σ'vy or qu are known, it is reasonable to

assume that a constant of proportionality may be applied to calculate the cement

component of the stiffness.

These Young’s modulus or shear modulus values can be converted to constrained

modulus values using Poisson’s ratio and these may be combined with the uncemented

constrained modulus values to give total values of constrained modulus for every stage

of hydration.

Assuming that the strength and stiffness are proportional, it may be useful to utilise non-

destructive stiffness measurement techniques such as bender elements (Baig et al.,

1977) to assess the rate of cementation development with time. Experiments on CSA

hydraulic fill indicate that the maturity factor (d in Equation 3.7) to represent the

development of stiffness with time was 1.0 which is very close to that determined for

the development of strength with time (0.9).

3.2.7 Stress-strain behaviour: summary

This section has presented the details of how the various constitutive aspects have been

related in order to characterize the mechanical response of the cemented mine tailings

during filling. Combining these aspects, the stiffness term in Equation 2.3 can be


3.9

determined as a function of material density (i.e. void ratio e), cement content (Cc),

hydration duration (t) and effective stress (σ’v) as illustrated in Equation 3.12.

),,,( '

'

vcv tCef

eσ

δδσ =

(3.12)

In order to demonstrate its applicability, the proposed constitutive relationship was used

to simulate a series of one-dimensional compression experiments on cemented CSA

hydraulic fill. In these experiments the specimens were prepared at different densities

and allowed to cure for different periods of time prior to loading them in one-

dimensional compression. The material constants d, X, W and Z (from Equation 3.8)

were determined from qu and bender element experiments. The parameters λ*and κ*

(from Equation 3.9) were determined from one-dimensional compression tests on

uncemented material and through modifying the terms A (from Equation 3.6) and b

(from Equation 3.9 and 3.11) the one-dimensional compression response could be

adequately represented. A comparison between the experimental results and the

proposed model is presented in Figure 3.5. Note that different initial void ratios were

used in the three tests, which explains why the 16-day result plots above the 5-day

result, initially. Once the cementation bonds are broken, all three results tend to

converge to the same compression line.

Figure 3.5 indicates that, given suitable experimental results, the proposed constitutive

relationship provides a good representation of the material behaviour when subject to

curing, compression and cementation breakdown.

3.3 PERMEABILITY

Term C in Equation 2.3 is highly dependent on the material permeability. This is the

term that controls the rate water is expelled from the system. As a result, permeability

can have a significant influence on the overall consolidation behaviour.

3.3.1 Uncemented permeability

During the compression of a soil matrix, the void volume reduces, which can lead to a

reduction in permeability. Carrier et al. (1983) developed a relationship that has been

shown to provide a good representation of the relationship between void ratio and


3.10

permeability for mineral waste materials. This function was adopted for this study and is

presented as equation 3.13

( ))1( e

eck

kdk

+=

(3.13)

where k is the permeability, e is the void ratio and ck and d k are constants.

3.3.2 Cemented permeability

The hydration of cement is associated with a growth of cement products. These products

are in the form of solid cement hydrates as well as cement gel. This product growth fills

some of the void volume, which further reduces the permeability. Due to the relatively

low permeability of the cement gel itself, it is suggested that in addition to the growth of

cement solids the entire gel volume should be taken into account in determining the

reduction in permeability. Powers and Brownyard (1947) suggest that when combined

with water, the solids and gel volume created (after full hydration) are 80% greater than

the initial unhydrated cement volume.

In order to account for this characteristic, Equation 3.13 is modified to be in terms of

effective void ratio (eeff). The calculation of effective void ratio is based on the void

space determined in the conventional manner as well as that calculated in accordance

with the hydrating cement products. This concept is illustrated in Equations 3.14 and

3.15.

),,( tCefe ceff = (3.14)

( ))1( e

eck

kdeffk

+=

(3.15)

The rate at which the growth of cement products takes place is simulated using the

maturity relationship (Equation 3.7).

A series of permeability experiments was conducted to assess the applicability of this

relationship to cementing tailings. These tests were conducted in a permeability cell

where the cell pressure was maintained at 520 kPa. The hydraulic gradient was

established by setting the back pressure at the top of the sample to 510 kPa and that at


3.11

the base to 490 kPa. Testing at these elevated back pressures ensured full saturation

throughout the test. As curing progressed, permeability measurements were taken at

regular intervals. At the completion of the test, the sample dimensions were measured

and, based on the initial dry weight, the void ratio could be calculated. The results of

tests on cemented hydraulic fill with cement contents of 2%, 5% and 10% are presented

in Figure 3.6, which shows the calculated effective void ratio against measured

permeability for the different experiments, along with the model estimate.

Figure 3.6 indicates that a reasonable fit to the measured data may be achieved using the

proposed method. However, it is suggested that the constant terms (in Equation 3.15)

representing compression and those representing cement growth may vary. Further

work may be required to develop the understanding of the contribution of these two

mechanisms to the reduction in permeability.

3.4 SELF DESICCATION

The process known as “self desiccation” has been well documented with respect to its

impact on concrete behaviour. The basis of this process is that following cement

hydration, the resulting hydrated volume is less than the combined volume of the

unhydrated constituents (cement and water). Researchers such as Powers and

Brownyard (1947), Hua et al. (1995), Koenders and Van Breugel (1997), Bentz (1995)

and Brouwers (2004) have investigated the impact of this mechanism on the shrinkage

of conventional concrete. Most conventional concrete masses have lean (low) water

contents and are placed in thin horizontal layers resulting in low total vertical stress.

Therefore, the volume reduction of the cement/water constituents can result in

development of negative pore pressure and desaturation of the mixture – hence the term

“self desiccation”.

However, cemented mine backfills have much higher water contents (and lower cement-

water ratios) than conventional concrete and can be subjected to high self-weight total

stresses due to rapid rates of rise in typical stope-filling operations. In fine-grained

(paste) fills, this can result in high positive pore pressures. As a result, the processes

involved in self desiccation act, in these circumstances, to reduce the build-up of

positive pore pressure rather than desaturating the material and creating negative pore

pressures. Consequently there is no “self desiccation” per se. Thus, when reference is


3.12

made to self desiccation in this thesis, this refers to reduction in pore pressure resulting

from cement hydration, rather than desaturation (desiccation) of the material. The term

“self desiccation” has been used to preserve consistency with the mechanism of

hydration-induced water volume reduction, rather than implying any actual “drying out”

(desaturation). In saying this, given the appropriate conditions, this mechanism does

have the potential to generate negative pore pressures and potentially desaturate the

mass.

The aims of the work described in this section are to show that the self-desiccation

process can have a significant effect on the behaviour of the backfill (during the

hydration process), to derive a model for describing the process and to devise a

laboratory testing procedure to enable the model parameters to be determined for any

fill/cement combination.

3.4.1 Cementation reactions

The reactions associated with cement hydration involve the chemical combination of

cement and water. If it is assumed that an enclosed volume of the soil-cement-water

slurry prior to cement hydration contains a water volume of Vw, and an unhydrated

cement volume of Vcu. After hydration, the hydrated cement volume is Vch, such that Vch

– Vcu = ∆Vhyd. In this reaction, the increase ∆Vhyd is less than the volume of water used

in hydration, Vwh. In keeping with the terminology used in the concrete literature, this

loss of volume is denoted ∆Vsh (the ‘chemical shrinkage’ volume).

For the purposes of the calculations that follow, the total water volume used in

hydration (Vwh) can conveniently be thought of as being composed of two parts – an

amount converted directly into solid volume equal to ∆Vhyd, and a volume equal to ∆Vsh

that is lost from the system as if removed via an internal water “sink”.

Vwh = ∆Vhyd + ∆Vsh (3.16)

Thus, using this approach, ∆Vsh represents an apparent water volume lost from the

system due to the hydration reaction, whereas ∆Vhyd represents water volume that is

substituted by solid volume, and hence has no overall effect on total volume or water

pressure.


3.13

All of this assumes that the soil voids can compress to accommodate the lost volume

(∆Vsh) in a completely unrestrained way, and ∆Vsh, when integrated over the total

volume, would give the total shrinkage. This would be the case in a slurry where the

soil matrix has zero stiffness, and the voids can compress without any change in

effective stress or any change in the pressure in the remaining water. Thus, it is only in

this case that ∆Vsh in Equation 3.16 represents the apparent “unrestrained” water volume

lost via the internal sink, and, when integrated, gives the overall slurry shrinkage.

Conversely, in the hypothetical case of a soil matrix with infinite stiffness (assuming a

fully-saturated state and no inflow of water allowed), no overall volume change can

occur, and the chemical shrinkage can only be accommodated by a volume expansion of

the remaining water equal to ∆Vsh, leading to a drop in pore pressure equal to the bulk

modulus of water multiplied by ∆Vsh/(Vw – Vwh). For the general case of a soil matrix of

finite stiffness, some of the volume loss is accommodated by soil matrix compression

(and hence some increase in effective stress), and some by expansion of the remaining

water (and hence some reduction in pore pressure). This will be discussed further in the

next section.

It should be remembered that mine backfill slurries are fully saturated, typically with

initial water content (mass of water per unit dry mass of soil) of 100% or greater, and

cement content (mass of cement per unit dry mass of soil) typically 2 – 5%. Therefore,

the water-cement ratio is much greater than for conventional concrete (for 100% water

content, and 2% and 5% cement content, the water-cement ratio would be 50 and 20,

respectively, in mass terms, corresponding to about 160 and 62, respectively, in volume

terms). Thus, the actual volume of water involved in hydration is relatively small, and

hence volumetric strains in the water can be calculated relative to the original total

volume of water (Vw), rather than the final volume (Vw–Vwh). In fact, in the numerical

implementation of the equations, all calculations are performed in incremental fashion,

so that volumes are continually updated, and strains are therefore calculated using the

appropriate water volume.

It should also be noted that, following the convention used in soil mechanics,

compressive stresses and strains are considered positive, while tensile stresses and

strains are considered negative. Thus, volume reduction is considered positive (and

hence chemical shrinkage ∆Vsh is positive).


3.14

Powers and Brownyard (1947) found experimentally that, for a fully hydrated system,

∆Vsh for a cement paste could be related to the mass of chemically-combined water (Wn)

through Equation 3.17:

∆Vsh = 0.279 Wn (3.17)

where ∆Vsh is the volume reduction in cm3 and Wn is in gram (and thus the “constant”

has units of cm3/g). From a series of laboratory experiments, they found that Wn could

be related to the proportion of the compounds that make up the cement product and the

mass of unhydrated cement (Wc) in accordance with Equation 3.18.

Wn/Wc = 0.187XC3S + 0.158XC2S + 0.665XC3A + 0.213XC4AF (3.18)

where X is the proportion by mass of the subscript compound in the cement. For the

proportions contained in most General Portland cements, they established empirically

that the Wn can be approximately related to Wc via Equation 3.19:

Wn/Wc = 0.23 (3.19)

Combining Equations 3.17 and 3.19 allows the shrinkage volume (in cm3) that would

occur in a General Portland cement paste over the full hydration period to be

determined. This relationship is shown in Equation 3.20 as a function of the original

mass (in g) of cement:

∆Vsh = 0.064 Wc (3.20)

3.4.2 Impact on pore pressure

As mentioned above, the apparent “unrestrained” volume change in the water resulting

from hydration (∆Vsh) could occur under undrained conditions only if the soil skeleton

were of zero stiffness, and this volume change would result in an equal compression of

the soil skeleton. To calculate the actual volume changes and pore pressure changes, it

is necessary to consider the water and soil matrix stiffnesses, and use principles of strain

compatibility and stress equilibrium to calculate the actual behaviour.

The change in pore pressure is a function of the difference between the shrinkage

volume (∆Vsh), as defined in Equation 3.16, and the actual reduction in void volume


3.15

(∆Vv) resulting from soil matrix compression. The difference between these two

volumes is denoted ∆Vrel:

∆Vrel = ∆Vv – ∆Vsh (3.21)

Effectively, strain compatibility requires that the water must expand by ∆Vrel to

accommodate the fact that the actual void volume reduction ∆Vv is less than ∆Vsh (and

hence ∆Vrel as defined by Equation 3.21 is negative, signifying expansion).

Initially, when the soil matrix has a very low stiffness, the void volume reduction (∆Vv)

is close to ∆Vsh, and hence there is very little pore pressure change. However, in the

case of soil containing cement, an increase in stiffness comes about not just as a result

of ongoing compression, as with uncemented soils, but also due to the formation of

cement bonds so that as hydration proceeds the pore pressure reduction can be quite

substantial.

A major difference between self desiccation and evaporative desiccation is that, with

evaporation, the water “sink” is at the (top) boundary, which sets up internal hydraulic

gradients to feed water to the evaporation process. However, in the hydration process,

internal “sinks” are set up within every pore throughout the material. Therefore the

mechanism is purely intrinsic and the incremental reduction in pore pressure is

dependent on the hydration time and not on any length scale in the problem.

3.4.3 Analytical model

An analysis relating fundamental material properties to the reduction in pore pressure is

discussed below. The analysis assumes that:

• the material is in an undrained state (with respect to water flows across the

external boundary);

• the soil compressibility is linear, corresponding to the current small-strain bulk

modulus, at any stage of hydration (though changing with ongoing hydration);

• soil particles are incompressible;

• the water bulk modulus (Kw) is constant;

• the material is fully saturated at all stages of the process; and


3.16

• the water density is independent of pressure.

In the experimental work described later, full saturation at all stages has been assured by

using high initial back pressure, such that positive pore pressure exists at all stages, even

following the pore pressure reduction resulting from the hydration process.

Equilibrium of the pore water system requires:

w

w

relwv K

V

VKu

∆=ε∆=∆ . (3.22)

where ∆u is the change in pore pressure in the current increment, ∆εv is the increment of

volumetric strain in the water required to maintain strain compatibility with the soil

skeleton, Kw is the bulk modulus of the water, ∆Vrel is the relative pore volume

reduction (as defined by Equation 3.21), and Vw is the total volume of the pore water.

Since ∆Vrel is negative (expansion), both ∆εv (expansion) and ∆u (pore pressure

reduction) are also negative.

The change in soil bulk volume is proportional to the change in effective stress. With a

constant total stress, the change in effective stress (∆σ′) is equal in magnitude and

opposite in sign to the change in pore pressure:

∆σ′ = –∆u (3.23)

The incremental volumetric strain in the soil matrix (∆εv-soil) is a function of the change

in effective stress (∆σ′) as well as the bulk modulus of the soil matrix (Ks):

sT

vsoilv KV

V σ′∆=∆=ε∆ − (3.24)

where VT is the total volume of the combined soil and water (bulk volume) and ∆Vv is

the actual change in the void volume due to compression (which is identical to the

change in the bulk volume ∆VT, since the soil particles are taken to be incompressible).

Combining the behaviour of the pore water (Equation 3.22) with the behaviour of the

soil matrix (Equation 3.24) via Equation 3.23 gives:

w

w

rels

T

v KV

VK

V

V..

∆−=∆

(3.25)


3.17

Equation 3.21 may then be substituted into Equation 3.25 to derive a relationship

between the actual incremental contraction of the pore volume (∆Vv) and the chemical

shrinkage volume (∆Vsh):

w

w

T

s

w

wsh

v

VK

VK

VKV

V+

∆

=∆

.

(3.26)

which indicates, as expected, that ∆Vv = ∆Vsh when Ks = 0. By combining Equations

3.26, 3.24 and 3.23 and rearranging, a relationship can be obtained between the

incremental change in pore pressure (∆u), the bulk stiffnesses of the soil (Ks) and water

(Kw), the porosity of the material (a function of Vw and VT) and the incremental change

in volume associated with the hydration reaction (∆Vw):

( )sw

w

T

sh

w

w

T

s

sw

Tw

shKKn

K

V

V

VK

VK

KK

VV

Vu

+∆−=

+

∆−=∆ ... (3.27)

This gives ∆u → 0 as Ks → 0, and ∆u → – Kw{ ∆Vsh/(n.VT)} as Ks → ∞, as expected.

3.4.4 Experimental demonstration of effect of self desiccation

A series of preliminary tests was carried out to demonstrate the validity and relevance of

the self-desiccation concept as applied to cemented tailings backfill. These experiments

used a silty silica sand hydraulic fill (HF) from the CSA mine and a silt-sized paste fill

(PF) from Kanowna Belle (KB) mine. These materials were mixed with 5% General

Portland cement from the Kandos Cement Plant (Kandos, NSW, Australia) and

Cockburn Cement (Perth, WA, Australia), respectively. In this thesis, the cement

content is defined as the mass of dry cement divided by the total dry mass of solids.

Particle size distribution curves for the two tailings materials are presented in Figure

3.7. The specific gravity (Gs) of CSA material is 2.81 while that for the KB material is

2.72.

The tests were carried out on samples set up in a triaxial cell in the conventional

manner. The specimens were prepared using the dry sand preparation technique

explained by Ismail et al. (2000). This technique involves preparing the specimens dry


3.18

before purging with CO2 and back-pressure saturating the samples. While this sample

preparation technique does not represent the mine filling process, the technique was

adopted to ensure consistency between samples. Both samples were prepared at a void

ratio of 0.80. After saturation in the triaxial cell, the cell pressure was increased to 550

kPa and the back pressure to 500 kPa. The purpose of the high back pressure was to

ensure positive pore pressure and full saturation throughout the test, given the large pore

pressure reductions expected from the self-desiccation process. For both tests, the

Skempton B-value was checked and found to be greater than 0.95. At this point, the

back pressure valve was closed and the pore pressure was monitored with time. The

results of the tests are presented in Figure 3.8, which shows the applied total stress, the

pore pressure and the effective stress, plotted against time from the start of the test.

As may be seen in Figure 3.8, even with cement content as low as 5%, the hydration

process creates a significant reduction in pore pressure, with both material types. With a

constant total stress, this pore pressure reduction is associated with an effective stress

increase of equal magnitude. The figure shows that the rate and final amount of pore

pressure reduction for the CSA HF specimen are significantly greater than for the finer

KB PF specimen. Consequently the impact of the self-desiccation process depends on

material type, as well as other factors discussed below.

These tests provide a graphic illustration of the changes in pore pressure that result from

the cement hydration process and the resulting change in effective stress, even where

the samples are subjected to undrained boundary conditions. Therefore, it is apparent

that this self-desiccation phenomenon needs to be considered when analysing the

behaviour of cemented mine backfill, particularly where filling rates are rapid and fine-

grained (i.e. low permeability) tailings are used, resulting in the hydration process

occurring under undrained conditions.

3.4.5 Material properties influencing self desiccation

Equation 3.27 indicates that the reduction of excess pore pressure is sensitive to the

water and soil bulk moduli (Ks and Kw) as well as to the rate of water consumption and

the total volume of water consumed during the hydration process.


3.19

Material stiffness

Due to the growth and strengthening of hydrates, the soil matrix undergoes an increase

in stiffness during hydration. A non-destructive test that is often used in soil mechanics

to monitor the ‘small strain’ shear stiffness (Gmax, also called Go) of a soil matrix

involves the measurement of shear wave velocity (Dyvik and Olsen, 1989, Baig et al.

1997, Fernandez and Santamarina, 2001). This technique consists of generating a shear

wave pulse at one end of a sample using a piezoceramic ‘bender element’, and

measuring the arrival time at the opposite end of the sample using a second ‘bender

element’.

Figure 3.9 shows an example of the data from one of the tests carried out in this study.

In this case, the transmitting bender element is excited by a single sine wave pulse,

nominally of 10 V amplitude, and the arrival of this shear wave at the other end of the

sample is picked up by the receiver bender element. Based on the time of transmission

and the length of the sample, the shear wave velocity (Vs) can be obtained. From this

value of Vs and the bulk density of the material (ρ), the value of Gmax may be inferred

using Equation 3.28.

2smax V.G ρ= (3.28)

This test can be carried out at intervals during the hydration process to monitor the

development of the shear modulus with time. The corresponding ‘small strain’ effective

bulk modulus Kmax can be related to Gmax via the Poisson’s ratio (ν):

maxmax G

)(

)(K

νν213

12

−+=

(3.29)

In this paper, this value of Kmax is assumed to be equivalent to the soil matrix stiffness

Ks mentioned earlier (e.g. Equation 3.24), which is equivalent to assuming that soil

matrix stiffness is linear over the range of strain relevant to this work. Santamarina et

al. (2001) and Jamiolkowski et al. (1994) suggest that a ‘small strain’ drained Poisson’s

ratio of 0.1 to 0.15 is appropriate for many soils, and thus, for the interpretation of the

results in this paper, a small strain Poisson’s ratio of 0.125 has been adopted. It should

be noted that varying the Poisson’s ratio over this range has minimal impact on the

results.


3.20

At the University of Western Australia, bender elements are fitted as standard in triaxial

setups, allowing shear wave velocity (and hence Gmax) to be determined routinely.

Measuring the compression wave velocity Vp (and the equivalent Emax) could also be

used to indicate the progress of hydration, but doing so in the triaxial apparatus was not

possible with the equipment available.

Water consumption during hydration

The process that determines the rate at which pore water volume is consumed is very

complex and is made particularly difficult to quantify theoretically due to:

• the hydration of cement involving at least 8 different chemical reactions;

• each reaction consuming different volumes of water;

• each reaction producing a different hydrate volume;

• each reaction commencing at a different time after the start of hydration;

• each reaction occurring at a different rate;

• only cement surfaces exposed to pore water reacting;

• the cement being made up of different proportions of each constituent;

• the reactions being dictated by the random collision of various cement

constituents;

• not all of the total cement content in the mix may react.

Cement technology researchers have developed detailed microscopic models to predict

this process for the purpose of concrete shrinkage predictions (Bentz, 1995). These are

complex models that involve the input of many fundamental cement properties, and

further discussion of them is beyond the scope of this work.

The other complicating factor associated specifically with mine backfill is that in

addition to different cement types, different tailings mineralogy and chemicals

contained in the tailings after processing may have an impact on the chemical reactions

that take place. Therefore, it is suggested that the most practical method of determining

the net volumetric change and the rate at which this change occurs is through direct

experiment with each cement/tailings combination. Furthermore, it is suggested that


3.21

rather than adopting the total volume change (6.4% of the unhydrated cement weight,

Equation 3.20) as determined by Powers and Brownyard (1947), the volume change

should be defined as a variable (Eh) for each particular cement/tailings combination.

Therefore, Equation 3.20 is re-written as Equation 3.30, where Eh is defined as the total

volumetric change ∆Vsh per unit mass of cement Wc:

∆Vsh = Eh. Wc (3.30)

3.4.6 Experimental derivation of parameters

By measuring the incremental pore pressure reduction and monitoring the material

stiffness, the rate of water volume consumption may be back-calculated using the

proposed analytical solution (Equation 3.27). The rate of hydration (d in Equation 3.7)

and hydration efficiency (Eh) are considered fundamental material properties. Therefore,

once determined, these parameters may be incorporated into a coupled analysis model

to account for the impact of this mechanism on the consolidation and filling process.

Experimental procedure

A series of pore pressure reduction experiments was carried out to verify the proposed

theory, provide examples of how the experimental process may be conducted and

demonstrate how the relevant material parameters may be derived. The material used in

these experiments was again silty sand (hydraulic fill) from the CSA mine and silt

(paste fill) from Kanowna Belle. These materials were mixed with General Portland

cement from the Kandos Cement Plant (Kandos, NSW, Australia) and the Cockburn

Cement Company (Perth, WA, Australia), respectively, in various proportions.

The experiments were conducted in a triaxial cell, with the specimens being prepared

using the dry sand preparation technique explained by Ismail et al. (2000). During

saturation, the amount of water added to the system was measured (as this would be the

volume of water subject to the volumetric changes).

As was shown in a previous section, (Figure 3.8) the hydration process results in a

reduction in water volume, which leads to a reduction in pore pressure and a

corresponding increase in effective confining stress. This increase in effective stress

could lead to yielding of the hydrating matrix, which could invalidate the assumption

that the small strain stiffness Kmax is the relevant bulk stiffness Ks for the soil. Also,


3.22

depending on the initial back pressure, the reduction in pore pressure could lead to air

coming out of solution, thereby changing the bulk modulus of the pore fluid.

To avoid any of these potential problems associated with a decreasing pore pressure, the

back pressure and cell pressure were initially set at values well above those

recommended by Bishop and Henkel (1962) for complete saturation. To avoid the

possibility of yielding due to increasing effective stress, the effective stress was kept

low by regularly restoring the back pressure to its original value by opening the

drainage valve at various stages during the test. This restoration of back pressure means

that, strictly speaking, the experiment was not conducted under undrained conditions,

but since the material properties are only determined during the undrained stages (i.e.

while the back pressure valves are closed) the application of Equation 3.27 remains

valid. At different stages during the tests, shear wave velocity measurements were

made, using bender elements, to monitor the evolution of stiffness (Gmax) with time.

Figure 3.10 presents the results of one of the tests on the CSA HF (hydraulic fill)

material. This shows the actual pore pressure behaviour – i.e. reduction in pore pressure

while the drainage valve was shut, followed by restoration of the initial back pressure in

the brief intervals when the valve was opened. From this, the cumulative pore pressure

change was determined to be of the order of 800 kPa for this test. The actual effective

stresses during the test are also shown, with the procedure adopted limiting the effective

stress to a maximum of less than 200 kPa.

An identical test on an uncemented specimen was carried out prior to those on the

cemented specimens to assess the compliance of the system. The system indicated a

pore pressure change of less than 5 kPa for the uncemented specimen over a 3 day

period, indicating that the system was free of any leaks.

Stiffness development

From the measurements of Gmax made as hydration proceeded, Equation 3.29 was used

with a Poisson’s ratio of 0.125 to determine the soil matrix small strain bulk modulus

Kmax, which was taken to be equivalent to Ks. Figure 3.11 shows how this calculated

value of Ks increased with time during the various experiments.


3.23

The curves shown fitted to the data in Figure 3.11 are based on the exponential

‘maturity relationship’ (for cement hydration) published in Illston et al. (1979). For this

application, this relationship takes the form:

−∆+= −− *exp.

t

dKKK fsiss (3.31)

where Ks-i is the initial bulk modulus and ∆Ks-f is the increase in bulk modulus at the

completion of the hydration period, d is a ‘maturity’ constant, and t* is the time since the

commencement of hydration. The curves in Figure 3.11 were obtained using d = 0.9

day1/2 with all cement contents. The time until initial set was found to be reasonably

consistent at about 4 hours for all these tests.

Pore pressure reduction

The test procedure used in these tests involved opening the drainage valve at regular

intervals during the test, thereby re-applying the initial back pressure. The data from

pore pressure reduction in the undrained phases that followed each of these re-

applications of back pressure can be combined to form a continuous pore pressure

reduction curve for each test, as shown in Figure 3.10. By dividing the pore pressure

reduction into one-hour increments, the incremental rate of pore pressure reduction was

determined for the duration of the test. Figure 3.12 shows this incremental reduction

rate plotted against time for the CSA hydraulic fill material with different cement

contents.

While there is some fluctuation in the pore pressure measurements, it can be seen that

the rate of reduction diminishes with time over the duration of the test (from the start of

initial set). Figure 3.12 also indicates that the rate of pore pressure reduction increases

with an increase in cement content. It should be noted that the pore pressure fluctuation

is temperature sensitive (fluctuating on a 24 hour cycle), suggesting that these tests

should have been conducted in a temperature-controlled environment.

Pore water volume decrease

In order to incorporate the self-desiccation mechanism into a finite element (or other

numerical) computer code, the incremental water volume change with time is required.

By substituting the instantaneous bulk modulus and the pore pressure reduction over a


3.24

given time period into the analytical solution (Equation 3.27) and rearranging, the pore

water volume change over that given time period may be back calculated.

Direct measurement of water volume consumption was also attempted in these

experiments. However, the volume measuring system used proved to have insufficient

resolution and accuracy, given that the volumes involved were of the order of tenths of a

cm3 per day. An improved system of volume-change measurement is a priority for

inclusion in future experiments.

After calculating the rate of water volume change throughout the experiment as

described above, the results can be divided by the relevant cement mass to determine a

rate of volume change per unit mass of cement. The results of this analysis are presented

in Figure 3.13 as the rate of water volume consumption per unit mass cement (∆Vw/Wc)

plotted against time for tests with three different cement contents.

The ‘maturity model’ presented in Illston et al. (1979) was combined with Equation

3.30 (for total water consumption) to estimate the total water volume change after a

given hydration time (t). This relationship has been differentiated and divided by the

mass of unhydrated cement (Wc) to derive a function for the rate of volume change per

unit mass of cement. This function is presented as Equation 3.32:

( ) ( )

( )

−

==

*exp.

*.

21

δ

δ

δ

δ5.1 t

d

t

dE

t

WV

t

WVh

cshcw (3.32)

The same maturity constant (d = 0.9 day1/2) as that found for the rate of stiffness

development was substituted into Equation 3.32, and the efficiency term (Eh) was

adjusted to achieve the best fit to the experimental data, resulting in a best-fit value of

Eh = 0.035 cm3/g. The derived curve is compared with the experimental data in Figure

3.13. In this case, the fit was obtained by taking t as applying from the start of the test,

rather than the initial set; slightly different parameters would be obtained if the latter

had been used.

Cumulative pore pressure reduction

Combining the experimentally derived terms for hydration efficiency (Eh = 0.035

cm3/g) with the maturity constant (d), the rate of pore pressure change can be

determined. This rate may be integrated over a given time period to predict the


3.25

cumulative pore pressure drop. The experimental results are compared with the

analytical solution in Figure 3.14 for CSA material, with d = 0.9 day0.5 and Eh = 0.035

cm3/g.

Figure 3.14 indicates that the predicted pore pressure reduction due to cementation can

be estimated accurately using the proposed analytical solution with appropriate values

of d and Eh. The values of d and Eh have been shown to be unique for a given

cement/tailings combination over the range of typical cement contents. The value of Eh

determined for the CSA fill (0.035 cm3/g) is somewhat less than the value of 0.064

cm3/g suggested by Powers and Brownyard (1947) for cement paste.

Kanowna Belle paste fill experiments

Experiments were carried out using silt sized Paste backfill material from the Kanowna

Belle (KB) mine (with cement contents of 2% and 5%) to assess the applicability of the

proposed approach to a different type of minefill. The experimental technique used was

identical to that described for the CSA test work. From the results of these experiments,

values of d and Eh of 2.5 day1/2and 0.055 cm3/g, respectively, were determined. These

values were substituted into Equations 3.31 and 3.32 before combining them in

Equation 3.27 to predict the cumulative drop in pore pressure with time and this

prediction is compared with experimental results in Figure 3.15. It can be seen that the

analytical solution compares well with the experimental results in this figure. It should

be noted that, again, the maturity constant (d) representing the rate of hydration appears

similar for both the rate of pore water volume consumption as well as the development

of shear stiffness with time. For the KB Paste backfill the Eh term of 0.055 cm3/g

corresponds closely to the value of 0.064 cm3/g suggested by Powers and Brownyard

(1947) for cement paste, whereas a significantly lower value (0.035 cm3/g) appears

relevant for the CSA hydraulic fill.

3.5 TEMPERATURE

As cement hydration is an exothermic reaction, in a bulk filling situation hydration of

cemented mine backfill can lead to temperature increases. However, as cement contents

in minefill are often very low, temperatures typically range from 20 – 30ºC in a typical

cemented mine backfill situation. Temperature increases greater than 5ºC act to reduce

the water density, increasing the water volume. This was taken into consideration, as a


3.26

volume increase has the potential to negate volumetric reductions from self desiccation.

Assessment of the magnitude of volumetric change over this range indicates the

potential for a maximum 0.1% increase in water volume throughout a typical filling

period. In comparison with volumetric changes associated with the self desiccation

process, this change was shown to be a second order influence and was therefore not

addressed in this thesis.

Turcry et al. (2002) demonstrated that thermal volumetric changes can simply be

superimposed onto chemical volumetric changes to achieve a net volumetric change.

Therefore, to incorporate temperature variation into the analysis of the influences of any

volumetric changes, it could simply be incorporated as an independent mechanism in

the analysis.

Temperature variations also have the potential to influence the rate of hydration.

Therefore, rather than superimposing the influence of temperature changes at the

analysis stage, consideration was given to incorporating the influence of temperature in

the experimental process. This work is ongoing, but to investigate the appropriateness of

carrying out the hydration test with an insulated specimen a numerical analysis was

carried out to assess the appropriateness of a fully insulated assumption in a typical

mine backfill scenario. This study utilised the numerical code Temp/W1 to assess the

likelihood of heat transfer to the surrounding rockmass in a typical mine backfill

scenario. The analysis involved establishing an initial temperature of 30ºC throughout a

10 m wide, 40 m tall plane-strain stope with a boundary condition of 20ºC. The

material properties adopted included a thermal conductivity of 1 J/s/m/°K and a heat

capacity of 3 MJ/m3/°K, which are considered suitable for a saturated soil at a void ratio

of 1.0.

Figure 3.16 presents the calculated temperature profile laterally across the analysed

half-space after 20 days (a typical filling period). The results indicate that only the outer

1 m of the fill mass is significantly influenced by the heat exchange at the fill-rockmass

boundary, and the majority of the material remains in an insulated state. Based on this

1 Temp/W is a part of the GeoStudio suite of programs from Geo-Slope International Ltd, Calgary, Alberta, Canada, www.geo-slope.com


3.27

result, it may be more appropriate to undertake hydration testwork (as discussed in

Section 3.6) in a fully insulated environment, which would address both water

volumetric changes (through a modified Eh in Equation 3.32) and the influence of

temperature on hydration rate (through a modified d term in Equation 3.7).

3.6 MATERIAL CHARACTERISATION TECHNIQUE

This chapter has addressed details of the mechanisms that are considered to be relevant

to the deposition and consolidation of cemented mine backfill. Being a complicated

interaction of different mechanisms, it is important to characterise the influence of

different materials on each of these mechanisms via fundamental material properties.

Keeping in mind the properties required, an experimental technique was devised to

capture most of the important material properties. This technique generally only

requires a hydration test, a triaxial test, and a Rowe cell test.

The hydration test is similar to that described in Section 3.4.6. Using the technique

described an understanding of the development of small-strain stiffness against time as

well as the self-desiccation characteristics can be obtained. In addition, a hydraulic

gradient can be established across the sample, at any time during hydration, to measure

the permeability of the material and assess how this changes with cement hydration.

Figure 3.17 presents an illustration of the experimental setup for a hydration test.

The hydration test can be combined with a conventional consolidated drained triaxial

test to determine the shear strength parameters such as cement induced bond strength

and frictional characteristics. If equipped with a local strain measurement system, it is

possible to use this experiment to determine non-linear elastic stiffness parameters and,

if the sample is strained to sufficient levels, the rate of cementation breakdown with

plastic strain can also be determined.

Finally one-dimensional compression (or Rowe cell) testing can be used to define the

stiffness and permeability characteristics during the compression of the material in

either a cemented or uncemented state.


3.28

3.7 CONCLUSION

Background citations and experimental data have been presented to demonstrate the

mechanisms and material models that are used throughout this thesis. In addition,

experimental techniques have been presented for determining material properties that

are considered to most significantly influence the cemented mine backfill deposition

process. With this basis of understanding, the remainder of this thesis is focused on the

combination of these mechanisms and how they influence the overall filling behaviour.

Mechanics of Mine Backfill Matthew Helinski One-dimensional Consolidation Modelling The University of Western Australia

4.1

CHAPTER 4

ONE-DIMENSIONAL CONSOLIDATION MODELLING

4.1 INTRODUCTION

In Chapter 2, Gibson’s governing equations for one-dimensional consolidation were

introduced and the influence of cement hydration on these equations was discussed. In

Chapter 3, a description of the different processes that are expected to occur during

filling with cemented mine backfill was presented, and equations to describe these

processes were developed. This chapter is focused on incorporating these mechanisms

into Gibson’s one-dimensional consolidation equations. These modified equations are

then solved using a modified version of the one-dimensional finite element tailings

consolidation program MinTaCo. This program has been renamed CeMinTaCo, and is

used in a sensitivity study to demonstrate the interaction of the different consolidation

mechanisms.

4.2 MODEL DEVELOPMENT

4.2.1 Modelling the behaviour of uncemented tailings: the MinTaCo Program

In previous work carried out some 10 years ago at UWA by others, a finite element

program was developed to model the consolidation and evaporation behaviour of mine

tailings, within the context of conventional tailings deposition in above-ground tailings

storage facilities (TSFs). This program, named MinTaCo (Mine Tailings

Consolidation) forms the basis of the new program. The new program has been named

CeMinTaCo, to indicate it deals with cemented mine tailings consolidation. A full

description of the MinTaCo model is provided by Seneviratne et al. (1996), and a

summary of some of its features that are relevant to cemented backfill is provided in the

following section:

• MinTaCo is a one-dimensional model, which uses a large-strain formulation

with Lagrangian coordinates and Gibson’s consolidation equations (Gibson

1967) to deal with the large volume changes. The form of the Gibson

consolidation equation was presented as Equation 2.2:


4.2

( ){

( )

( ) ( ) ( ){

BCDA

1

11

ta

k

a

u

e

ek

aee

t

u vo

w

vo δ

δσ=

δδ+

δδ

++

γδδ

δσ′δ++

δδ

44444 344444 2144 344 21

(2.2bis)

where a is a Lagrangian coordinate, u is pore pressure, k is hydraulic

conductivity (permeability), σ'v and σv are the vertical effective and total

stresses, respectively. In this equation, term A is the rate of change in pore

pressure as a result of a rate of application of total stress (term B), term C is

the volumetric strain, which is dictated by the hydraulic conductivity (k) of the

material, and term D is the current stiffness of the material. As with tailings

placed into surface TSFs, paste fill placed underground may undergo large

settlements as it drains and consolidates. Incorporating a large strain

formulation into the model was regarded as important. MinTaCo provided this.

• Fresh tailings slurry can be added at any desired rate, and this rate can be

changed at any stage during filling. Details of this aspect can be found in Toh

(1992) and Seneviratne et al (1996).

• The properties of the fresh layers can be different from preceding layers.

• The ‘settled density’ of the material is taken as the starting point for

consolidation. Thus if very wet (low solids content) slurry were used, the

model is able to account for the generation of ‘bleed’ water and update the

initial void ratio of the fill to account for this.

• The base of the storage area can be perfectly permeable, perfectly

impermeable, or any state in between.

The input data required to run the program are: the material parameters; the filling

schedule and the drainage conditions. The material parameters are:

• The specific gravity Gs of the tailings material.

• The initial ‘settled density’ of the tailings.

• The k–e (permeability – void ratio) and e–σ'v (void ratio – effective stress)

relationships, which are generally very non-linear, are expressed using power

functions suggested by Carrier (1983):


4.3

( )( )

e

eck

aek

c

dk

bvc

+=

′=

1

σ

(4.1)

where ac, bc represent soil compression constants and ck, dk represent

permeability constants. The large volume changes that occur during paste fill

consolidation referred to earlier mean that large void ratio changes occur and it

is essential to account for the effects of these changes on parameters such as

permeability.

• The “air entry suction” value – the point where desaturation starts to occur

during drying. This allows an important feature of a consolidating fill mass,

development of a partially saturated matrix, to be accounted for.

• Estimates of shear strength and its variation with time may be made using the

Cam Clay model, so that values of the Cam Clay parameters (λ, κ, M, Γ) are

required for the material.

• Drainage occurs in the vertical direction only (upwards or downwards,

depending on hydraulic gradient), and strains are vertical only.

The MinTaCo program has been used extensively for modelling a wide variety of

tailings filling operations. Some examples of its application may be found in Fahey and

Newson (1997) and Fahey et al. (2002).

4.2.2 Modelling the behaviour of cemented tailings: the CeMinTaCo Program

Section 2.2 showed that regardless of the ultimate cured strength, the loads applied to

(backfill) barricades during the filling process are highly dependent on the degree of

consolidation. Furthermore, it was demonstrated that in an uncemented state, very little

consolidation is likely to occur in paste fill during a typical filling sequence. As a result,

barricade stresses are more appropriately calculated assuming undrained conditions.

However, as discussed in Chapter 3, the addition of cement to backfill complicates the

rate of pore pressure change and in most cases where paste fill is used, the behaviour is

likely to be neither fully drained or fully undrained, but somewhere in between. Use of a

model such as that described in this thesis makes it possible to determine where a

particular fill is located between these two extremes.


4.4

Because it provides full coupling between filling rates, boundary drainage, and stiffness

and permeability changes within the tailings, the MinTaCo program appeared to provide

the ideal basis for the development of a program to model the consolidation behaviour

of backfill. However, to be of general application to the backfilling problem, additional

features were required, relating particularly to the effect of adding cement in various

quantities to the tailings.

During the consolidation of uncemented mine tailings from an initial slurry state, the

material behaviour that is most important are the changes in soil stiffness and

permeability that occur due to the reduction in void ratio as consolidation progresses.

The rate of increase of the fill stiffness is important as it governs, inter alia, the amount

of stress transfer due to arching that can occur. In the case of cemented mine backfill, a

number of other mechanisms associated with cement hydration are introduced, which

also need to be addressed during modelling. These include:

• the development of an appropriate material stiffness that takes account of soil

volumetric changes, cement hydration and damage that may occur to cement

bonds during the filling process (and thus, changes are required in term D of

Equation 2.2);

• changes in permeability, not only with changes in void ratio, but also with the

growth of cement gel in the voids (and thus, changes are required in term C in

Equation 2.2);

• ‘self desiccation’ of the hydrating cement paste – the water volume changes

that occur due to chemical reaction in the hydration process (an additional term

in Equation 2.2);

• the large increase in stiffness of the cementing soil matrix, leading to the matrix

bulk stiffness being comparable to that of water, which must be taken into

account in estimating pore pressure changes due to increases in total vertical

stress. (and hence changes are required in term A in Equation 2.2); as shown by

Black and Lee (1973), when the stiffness of a soil matrix becomes similar to

that of water, the change in pore pressure due to load application cannot be


4.5

estimated using conventional approaches but must account for the relative

stiffnesses.

4.2.3 CeMinTaCo governing equations

The following section provides the derivation of the governing equations for the large

strain consolidation of a cementing soil. The description provided follows that of

Gibson et al. (1981), but these equations are modified to take into account the influence

of cement hydration. In the derivation, convective forces are ignored and the motion of

pore fluid relative to the solids is assumed to be governed by Darcy’s law.

For this analysis, an updated Lagrangian coordinate system is adopted. Figure 4.1

presents the definition of this coordinate system over a consolidation timestep t to t+∆t.

With reference to Figure 4.1, a is the original element height, x is the equivalent height

of soil solids, and ξ is the real coordinate system, which is required for the calculation of

hydraulic gradients. These terms can be related through:

)1(d

)1(d

dee

ax

o +ξ=

+= (4.2)

As illustrated in Figure 4.2, the weight of fluid flow out of an element of thickness aδ

is given by:

( )[ ] ana sww δν−νγ

∂∂

(4.3)

where n is the porosity, wν is the velocity of water sν is the velocity of soil and wγ is

the unit weight of water.

The change in water volume in an element of height aδ as a result of self desiccation

over time ( t∂ ) is be given by:

( )

∂∆

+∂

t

V

e

a sh

01 (4.4)

where ( shV∆ ) is the change in volume per bulk unit volume of solids as a result of self

desiccation.


4.6

Assuming the water volume is independent of the water pressure, Equations 4.3 and 4.4

can be combined to determine a relationship between the change in stored water in an

element of height a∂ with time (t

Vf

∂∂

).

( ) ( )[ ]t

Van

at

V

e

a fsww

sh

∂∂

=δν−νγ∂∂+

∂∆

+∂

01 (4.5)

Assuming laminar flow conditions, the fluid velocity (wν ) relative to the soil velocity

( sν ) can be determined using Darcy’s law, which is defined as:

ξ∂∂

γ=− ex

wsw

ukvvn )( (4.6)

where ( sw ν−ν ) is the relative velocity between the soil and the fluid, k is the

coefficient of permeability and ξ∂

∂ exu is the excess pore pressure gradient.

Combining Darcy’s law with the coordinate transformation relationship (Equation 4.2)

Equation 4.5 becomes:

( ) t

Va

a

u

e

ek

at

V

e

a fex

w

sh

∂∂

=∂

∂∂

++

γ∂∂+

∂∆

+∂

11

10

0 (4.7)

In most, if not all, stopes free-draining barricades are constructed at the base. This free

draining condition acts as a base drain and draws down the phreatic surface. The

gradual drawdown of the phreatic surface combined with the accretion of overlying

material makes the it difficult to define excess pore pressures. Due to these reasons, it is

inconvenient to undertake calculations in terms of excess pore pressures and it is more

suitable to perform calculations in terms of total pore pressure (u). When converting

from uex to u Equation 4.7 becomes:

( ) t

Va

e

e

a

u

e

ek

at

V

e

a fw

ow

sh

∂∂

=∂

γ

+++

∂∂

++

γ∂∂+

∂∆

+∂

1

1

1

1

10

0 (4.8)

In conventional soil mechanics, it is common to assume that the stiffness of the water

phase is significantly greater than that of the soil skeleton and as a result the volumetric


4.7

soil compression is considered to be equal to removed water. However, in the case of

cementing soil, the soil stiffness may be comparable to that of water. In order to take

account of the relative stiffness between the soil and water phases, Hooke’s law can be

applied to the water phase to derive pore pressure changes. If the soil particles are

assumed to be incompressible, this may be written as:

wsf

wf

s

f

f Ke

e

t

V

ae

e

t

V

aK

V

V

tV

V

tt

u

+∂

∂∂∂−+

∂∂

∂∂=

∂∂∂−

∂∂∂=

∂∂ )1()1( 00

(4.9)

where sV∂ is the change in soil volume in an element of height a∂ .

Assuming a constant stiffness (eδσ′δ

) over the timestep (t∂ ), the constitutive relationship

may be represented as:

( ) ( )11

11

00 +σ′δδ

∂∂−

∂σ∂=

+σ′δδ

∂σ′∂=

∂ε∂=

∂∂

∂∂

e

e

t

u

te

e

ttt

V

avvss

(4.10)

where vσ′∂ and vσ∂ are the change in vertical effective and total stress, respectively,

and sε∂ is the change in vertical strain in the element.

Substituting Equations 4.8 and 4.10 into Equation 4.9 and rearranging:

( )

δδ+

δδ

++

γδδ+

δσ′δ+

δδ

δσ′δ+

δσ′δ−

δδ=

δδσ

a

k

a

u

e

ek

ae

e

t

V

eeK

e

t

u

t

o

wo

v

shvv

w

v

11

1

1

(4.11)

If Kw is significantly greater than e

v

δσδ ′

and ( shVδ ) is equal to zero Equation 4.11 takes

the form of Gibson’s large strain consolidation equation (Equation 2.2) for conventional

soils.

As explained in Chapter 3 the material stiffness ( )

+′

01 ee

v

δσδ

permeability )(k and

self desiccation induced volumetric shrinkage ( )shVδ can all be represented by

functions involving various combinations of effective stress( )vσ′ , void ratio( )e cement


4.8

content ( )cC , time ( )t and effective void ratio ( )effe . Substituting these dependent

variables into the appropriate terms of Equation 4.11 gives Equation 2.3, which has

been implemented and solved using CeMinTaCo.

( )

( )( ) ( ) ( )

( ) ( ){(B)(E)

(C)(D)

)A(

,,,,

1

1,,,1

,,,1

tt

CtVeCt

e

a

ek

a

u

e

eek

aeCte

e

eCteK

e

t

u

vcshvc

v

effo

w

effvco

v

vcv

w

δδσ=

δδσ′

δσ′δ+

δδ

+

δδ

++

γδδ

σ′+

δσ′δ+

σ′

δσ′δ−

δδ

44444 344444 21

4444444 34444444 214444 34444 21

444444 3444444 21

(2.3bis)

In this equation, the modified terms are identified using the same labels used to identify

the equivalent terms in the unmodified equation (Equation 2.2), but there is also an

additional term (E), which does not have an equivalent term in the unmodified equation.

As the stiffness of the cemented soil matrix may be comparable to that of pore water,

the change in pore pressure (term A in Equation 2.2) due to a change in total stress, is

modified to take account of the stiffness of the cemented matrix (ev

δσ′δ

) and that of

water ( wK ). This formulation incorporates strain compatibility to achieve an

appropriate distribution of total stress.

The volumetric strain term (term C in Equation 2.2) is modified to take into account the

fact that the permeability (k) is affected not just by normal void ratio reduction due to

consolidation, but also by the formation of cement gel in the void space. This aspect

was addressed in Section 3.3.

The stiffness term (term D in Equation 2.2) is modified to take account of the fact that

the material stiffness (ev

δσ′δ

) is now a function of cement hydration, current stress state

and previous stress excursions as documented in Section 3.2.


4.9

In addition to these modified terms, an additional term (term E) has been included to

quantify the impact of volume changes (t

Vsh

δδ ) associated with the ‘self desiccation’

mechanism, as discussed in Section 3.4.

4.3 NUMERICAL IMPLEMENTATION

The solution to Equation 2.3 is obtained through implementation into the one-

dimensional tailings consolidation program MinTaCo. This program, which has been

renamed CeMinTaCo in its modified form, solves these equations using an implicit

finite element formulation for the space variable, and an explicit finite difference time

marching scheme.

Figure 4.3 shows the geometric layout adopted in the finite difference solution to

Equation 2.3. Each finite element is represented using a single nodal point. Node i has

nodal points i-1 and i+1 in the adjacent elements with the vertical spacing between these

points being a1 and a2 respectively. Assume a time increment that is defined as ∆t where

∆t = tj+1-tj. The finite difference representation of Equation 2.3 is given by:

{ } ( ) ( )[ ]{ }{ }

( ) ( )ji

jishffv

jiw

fji

jifff

jifffjifff

e

VS

aa

tS

eK

eSu

uDKaS

uaaKaaDSuDKaS

ji

,

,

21,,

1,1212

1,2111221,1211

12

.

1

.1 ,

+

∆−

∆−σ∆+

++

=δ−δ

++δ−−δ+δ+δ

+−

+++

(4.2)

where the coefficients are defined as:

)(

2

21211 aaaa

t

+∆=δ

221

2)(4 aa

t

+∆=δ

( ) ( )1,11,21,1,11 +−++++ −+−= jijijijiperm kkakkaK

( )ji

ji

vf e

eS ,

1,

1d

d+

′=

+

σ


4.10

++

γ=

+

+

1,

,1,

1

1

ji

ji

w

jif e

ekK

++

−

++

+

++

−

++

γ=

+−

−+−

++

++

++

+++

1,1

,11,1

1,

,1,2

1,

,1,

1,1

,11,11

1

1

1

1

1

1

1

1

1

ji

jiji

ji

jiji

ji

jiji

ji

jiji

wf

e

ek

e

eka

e

ek

e

eka

D

where Kw is the bulk modulus of the water phase and shV∆ is the volumetric change that

occurs over the time increment (∆t) due to self desiccation. This may be calculated as:

( )

−

∆=∆

*exp.

*..

21

5.1 t

d

t

dEWtV hcsh (3.32bis)

where Wc is the weight of cement per unit volume of material, t* is the time since the

commencement of hydration, Eh is the efficiency of hydration (as defined in Section

3.4) and d is the hydration maturity constant.

The duration of each consolidation timestep is initially estimated based on Terzagi’s

time factor for individual layers. This time factor is then used along with a user-defined

allowable strain level to make an initial estimate for the allowable time increment.

Using the defined timestep, a solution (based on a void ratio convergence criterion) is

sought through a maximum of 40 successive iterations. Should the solution not

converge, a smaller timestep is established and the calculation repeated. After

converging to an acceptable solution, the maximum induced strain is determined and

compared with a user-defined tolerance. Should the tolerance be exceeded, the time

increment is halved and the calculation repeated until the strains obtained are less than

the allowable strains.

Over each timestep, the material properties are assumed to remain constant, but at the

completion of each timestep, the material properties are updated in accordance with the

time increment and strains that occurred during that timestep.


4.11

4.4 MODEL VERIFICATION

4.4.1 Compressibility

In order to demonstrate its applicability in modelling compressibility, the proposed

approach has been used to simulate a series of one-dimensional compression tests on

cemented CSA hydraulic fill. In these experiments, the specimens were prepared at

different densities and allowed to cure for different times prior to loading. The material

constants d, X, W and Z (in Equation 3.5) were determined from the measured values of

qu and from Go values obtained from bender elements. The parameters λ* and κ* (in

Equation 3.1 and 3.2) were determined from one-dimensional compression tests on

uncemented material, and through modifying the terms A (in Equation 3.5) and b (in

Equation 3.11), the one-dimensional compression response could be adequately

represented, as was previously presented in Figure 3.5.

4.4.2 Self desiccation

To verify the self-desiccation aspect of the model, a hydration test was carried out, and

the CeMinTaCo program was used to reproduce the reduction in pore pressure induced

by self desiccation observed in the experiment. The test involved preparing a fully

saturated sample of CSA hydraulic fill, at a void ratio of 0.7 and cement content of 5%,

in the form of a triaxial test sample. This was mounted in a triaxial cell, and enclosed in

a latex membrane in the usual way. The sample was subjected to a total cell pressure of

850 kPa and an initial back pressure of 830 kPa. Then, the back-pressure valve was

closed, so that the hydration process could take place in a completely undrained state.

The results are shown in Figure 4.4 as a plot of measured pore pressure versus time. In

this case, the self-desiccation mechanism has reduced the pore pressure from the initial

back pressure value of 830 kPa to a final value close to zero. (This suggests that it might

have been appropriate to start from an even higher back pressure in this case, to ensure a

final pore pressure well above zero). The response fitted using the CeMinTaCo program

is also shown in Figure 4.4, which indicates that the program is capable of reproducing

the observed experimental results quite well. It should be noted that the CeMinTaCo

output was modified in accordance with the Poisson’s ratio to convert from a one-

dimensional situation to an isotropic situation.


4.12

This experiment shows how effective the self-desiccation mechanism can be in reducing

pore pressure (and hence in increasing effective stress). In this case, this occurs in the

absence of any external drainage effects, but in a real stope, it would combine with any

‘consolidation drainage’ to potentially produce a faster pore pressure reduction than

would otherwise be the case.

4.5 SENSITIVITY STUDY

A limited sensitivity study was undertaken to illustrate the effect of varying some of the

input parameters on the response when modelling the filling of a stope. The filling

strategy used in the study was based on a common paste fill schedule, and involved

filling an initial ‘plug’ at 0.4 m/hr for 16 hours, followed by a 24-hour rest period, and

then completing filling the remaining 30 m at a rate of 0.4 m/hr. The base-case set of

input parameters used in the study is given in Table 4.1; these parameters correspond to

typical paste backfill properties, and except where otherwise indicated these parameters

are used in all the examples that follow.

Proper simulation of the three-dimensional geometry of a real stope and drawpoint

(illustrated schematically in Figure 1.2) would require a three-dimensional FE program,

or at least a two-dimensional or axi-symmetric program. However, since CeMinTaCo is

only one dimensional, a means of simulating the restriction to drainage resulting from

the reduced drawpoint cross-section was required. The method adopted is illustrated in

Figure 4.5, which consisted of introducing a 5 m thick layer with reduced permeability

(1/8 of the value adopted for the bulk of the material at a corresponding void ratio) at the

base of the stope. Note, however, that the material in this region had zero cement

content, so none of the effects of self desiccation apply in this region.

In the following sections, the effect of changing a number of parameters is investigated.

These parameters include cementation, permeability, and damage.

4.5.1 Influence of cementation

To illustrate the effect of cementation on the consolidation response, analysis was first

carried out using uncemented material. Then, the analysis was repeated with cement

content (Cc) of 5%, in one case with the self-desiccation mechanism disabled in the

model, and the other with it enabled.


4.13

Figure 4.6 presents the results of these analyses as plots of pore pressure (2 m above the

base drainage layer) versus time. Also shown is a plot of the total vertical stress versus

time at the same point in the profile. These plots indicate that for the case without any

cement, the increase in pore pressure is similar to the increase in total stress, and hence

very little effective stress is generated during filling. After the completion of filling, the

rate of dissipation of pore pressure is slow, and very little consolidation has occurred at

the end of the period modelled (250 hours). This indicates that, in the absence of

cementation, paste fill barricade stresses would be well represented by the “undrained”

case that was discussed on Section 2.2.

For the second case, it may be seen from Figure 4.6 that, even with the self-desiccation

mechanism disabled, pore pressures are significantly less than for the uncemented case

once hydration begins. The effect of adding cement is to produce an increase in soil

stiffness (after the start of hydration) and a reduction in permeability, as previously

discussed. Since the rate of pore pressure reduction (consolidation) is dictated by the

product of stiffness and permeability, this result indicates that the effect of the increase

in stiffness outweighs the effect of the reduction in permeability, and there is some

increase in the rate of pore pressure dissipation, even during filling. However, it should

be noted that there are still significant excess pore pressures present at the end of filling.

Due to the increased stiffness, these dissipate somewhat more rapidly after completion

of filling than in the previous case.

In the third case, with self desiccation enabled, there is a significant increase in the

degree of pore pressure reduction that takes place, indicating the potential importance of

the self-desiccation mechanism in promoting dissipation of pore pressure. It should be

noted that the dissipation of pore pressure would act to increase the effective stress,

promoting arching, which would further reduce the pore pressure. This will be shown

with reference to in situ measurements later, and also when two-dimensional modelling

results are presented in Chapter 7.

4.5.2 Influence of permeability

To illustrate the influence of permeability on the overall filling response, analyses were

carried out using the filling sequence and material properties described above, with Cc

of 5%, but using three different permeability relationships (i.e. three different values of


4.14

the permeability parameter ck in Equation 3.15). The resulting three permeability

functions (denoted k1, k2 and k3) are plotted against curing time in Figure 4.7. In this

plot, the change in permeability with time shown for each case is due only to cement

growth, whereas in a modelling situation, the change could be greater with the added

effect of void ratio reduction due to compression.

Figure 4.8 shows the pore pressure during and following filling for a point 7 m above

the base (i.e. 2 m above the lower-permeability ‘drawpoint’ region) for the three cases

considered. Figure 4.9 shows the pore pressure profile down through the stope at the

end of filling. Also shown in Figure 4.9 is the final ‘steady state pore pressure’ (SSPP)

for the k1 case (the SSPP lines for the other two cases are practically coincidental). In

Figure 4.8, the final steady state equilibrium has been reached at about 230 hours for the

k1 case, whereas changes were still occurring for the other two cases at this stage.

In Figure 4.9, the line labelled ‘k1 SSPP’ refers to the steady state pore pressure that

results from maintaining a water table in the stope at 33.65 m height (the final filled

height) and zero pore pressure at the base of the drawpoint, with the permeability in the

lower 5 m being about 8 times less than the permeability in the stope proper for each

case. Note that the permeability in the stope is not uniform with depth, so the ratio of 8

refers to average values. In Figure 4.9, the difference between the pore pressure at the

end of filling and the SSPP line is the excess pore pressure at this stage. Thus, there are

excess pore pressures in the stope for each of the three cases at the end of filling, but

these are different for the three cases.

These results appear to be counterintuitive, since conventional consolidation theory

suggests that high permeability material should dissipate pore pressures more quickly

than low permeability material. Thus, in Figure 4.8, while the lowest permeability case

(k3) shows the highest pore pressure in the first filling stage, it shows pore pressures

very much less than the higher permeability cases during the rest period and at all times

thereafter. Examination of the pore pressure plot at the end of filling for this case in

Figure 4.9 shows that from the surface down to about 25 m above the base, the pore

pressure gradient corresponds to the total overburden stress gradient – i.e. there is no

pore pressure dissipation in this region at this stage, and hence the effective stresses are

zero. However, below about 25 m, the pattern changes completely. In this region,


4.15

hydration and self desiccation are occurring, setting up high negative excess pore

pressures. Though this results in a very steep downward hydraulic gradient (from 25 m

down to 13 m), the low permeability prevents sufficient internal water flow from

dissipating these negative pore pressures. If later pore pressure isochrones for this case

were plotted, these would show the point of minimum pore pressure gradually moving

upwards until it reached the surface (as hydration progressed). Then, slow internal

flows would gradually move the pore pressures onto the steady state line.

For the highest permeability case (k1), the same internal volume change occurs due to

hydration, and thus the potential pore pressure reduction resulting from this is the same.

However, the higher permeability in this case means that high internal hydraulic

gradients are not sustainable, due to the ease of generating internal water flow to smooth

out the pore pressure profile. Thus, at the end of filling, the pore pressures for the k1

case are not very different from the SSPP values. There is still evidence of the self

desiccation process occurring in this plot – i.e. the slight concave-upward curvature of

the pore pressure profile from about 10 to 20 m would not be present if self desiccation

was not influencing the process.

The intermediate permeability case (k2) shows behaviour similar to the k1 case,

commensurate with the fact that the permeability is not very much lower than for the k1

case, as shown in Figure 4.7.

4.5.3 Typical damage scenario

As discussed throughout this thesis, the filling process involves the interaction of three

time-dependent processes: the rate of filling, cement hydration and consolidation.

Researchers such as Le Roux at al. (2002) and Belem et al. (2006) have investigated the

mine backfill process experimentally. In this work, the authors apply effective stress to

curing cemented paste fill at a rate equivalent to the accumulation of total stress from

the fill self weight. Through adopting a total stress approach, rather than an effective

stress approach, the third of the time-dependent processes (consolidation) has been

neglected. This section presents a numerical investigation of the interaction of the three

time-dependent processes with specific emphasis on the influence that damage (from

excessive vertical effective stress on fragile cement bonds during the early stages of

hydration) has on the consolidation process.


4.16

The purpose of this analysis is to select a material that possesses an ultimate strength

that is suitable for eventual vertical exposure, and determine if this material can be

damaged during a typical filling sequence. The focus of the analysis is the early stages

of hydration, where fragile cement bonds may be damaged by the application of

compressive stress. The material properties from Table 4.1 were adopted, but in order to

produce a material with an ultimate qu that is equal to the final vertical effective stress,

the void ratio has been increased to 1.25. The property that dictates the response of the

material to damage is the damage coefficient (b) in Equation 3.11; in this analysis,

damage coefficients of 0.05 and 3.0 have been adopted. These values are considered

appropriate for representing the entire range of damage coefficients for mine backfill.

The impact of this variation on the structural breakdown has been demonstrated in

Figure 4.10, which presents the results of a simulated one-dimensional compression test

on a fully hydrated sample. Figure 4.10 indicates that prior to yield, the behaviour is

largely independent of b, but after yield the rate of cementation breakdown is very

sensitive to the value of b.

The analysis has considered two materials, one with the value of the permeability term a

given in Table 4.1, and the other with the value of a increased by two orders of

magnitude. These are meant to represent a paste fill example and a hydraulic fill

example, respectively.

Paste fill modelling

The results of the paste backfill modelling are presented in Figures 4.11 and 4.12.

Figure 4.11 shows the development of pore pressure (u), vertical total stress (σv) and

vertical effective stress (σ′v) against time, at a point 2 m above the base of the stope,

using both damage coefficients (b). The results of the simulation with b = 3 are plotted

as lines, while those with b = 0.05 are plotted as symbols. Figure 4.11 indicates that in a

typical paste fill situation, compressive damage is unlikely to influence the

consolidation behaviour.

The main reason for independence is as follows:

• The application of total stress (due to the accumulation of overlying material) is

resulting in an equal increase in pore pressure, and therefore there is no change

in effective stress, and no possibility of damage being caused.


4.17

• Due to the low coefficient of consolidation (associated with the fine grained

nature of paste fill) the cement hydration is required to achieve consolidation

(i.e. pore pressure reduction, rather than conventional “consolidation”).

As a result, the hydration timescale dictates the timescale of consolidation (or

application of effective stress). Therefore, softer/weaker material consolidates more

slowly, allowing bonds to mature appropriately, while stiff/strong material rapidly

develops sufficient strength to overcome the associated rapid application of effective

stress.

Figure 4.12 presents the application of vertical effective stress (σ′v) and one-

dimensional yield stress (σ′vy) against time for the element. Initially both σ′v and σ′vy

are very low. After reaching “initial set” σ′vy increases at a significantly faster rate than

σ′v therefore eliminating the likelihood of damage. This would typically be the case in a

paste fill situation. Also presented in Figure 4.12 is the calculated unconfined

compressive strength (qu) for the in situ material and that for material cured under no

stress (as would be the case in the laboratory). Comparison of these indicates that the

application of effective stress during filling can actually increase the material strength

(by reducing the final density) rather than damaging fragile cement bonds.

This behaviour is in accordance with that observed by Blight and Spearing (1996), who

investigated the effect of stope lateral strain (i.e. stope closure) on cementing backfill,

and showed that such strain (i.e. the resulting effective stress increase), resulted in

higher final strengths. It is also in accordance with many field observations (Revell,

2004, Cayouette, 2003), where the unconfined compression strengths obtained from

cores taken from filled stopes are often significantly greater than the control samples

taken from the material as it is filled and cured under zero confining pressure.

Hydraulic fill modelling

It has been demonstrated that in a typical paste fill situation the damage coefficient,

which represents the rate of cementation breakdown with strain, has little influence on

the consolidation and hydration behaviour because in this case it is the hydration

process that generates effective stress. However, in the case of hydraulic fill, the

material often has a much higher permeability. As a result (if it is assumed that


4.18

immediate consolidation occurs) the rate of development of effective stress is more

closely related to the filling rate.

In order to simulate a typical hydraulic filling situation, the same material properties as

those adopted for the paste fill example are adopted, but the permeability is increased by

two orders of magnitude. Furthermore, rather than a filling rate of 0.5 m/hr with a single

long rest period (as in the paste fill case) a constant filling rate of 3 m/day was adopted

without a rest period. This is expected to be indicative of typical hydraulic filling rates,

when taking account of fill and rest periods that are commonly adopted to avoid piping

type failures (Cowling et al. 1987).

The results of this modelling are presented in Figures 4.13. Figure 4.13 presents the

development of pore pressure (u), vertical total stress (σv) and vertical effective stress

(σ′v) against time for a point 2 m above the base of the stope. Again the results of

modelling with a damage coefficient b = 3 are presented as lines while those with a

damage coefficient b = 0.05 are presented as symbols. It is clear from this figure that,

as in the paste fill example, the damage coefficient has little influence on consolidation

in a typical hydraulic fill situation. This is most likely to be related to the fact that (as

indicated in Section 2.2 using Gibson’s (1958) analytical solution) the combination of

permeability and stiffness immediately after placement of hydraulic fills results in

excess pore pressures dissipating rapidly. Hence, water pressures in a hydraulic fill

stope are dictated by the restriction at the drawpoint, rather than the dissipation of

excess pore pressures. This point was also evident in the high permeability example in

Section 4.4.2.

Figure 4.14 presents the development of one-dimensional yield stress (σ′vy) and applied

vertical effective stress (σ′v) against time in an element 2 m above the stope floor.

Unlike with the paste-fill case, the application of vertical total stress (from the accretion

of material) creates an immediate increase in vertical effective stress. This acts to

compress the soil, increasing σ′vy even prior to the onset of cement hydration. This

creates some initial hardening of the material and, as with the paste-fill case, the onset

of cement hydration causes σ′vy to increase significantly faster than σ′v. Again this

reduces the likelihood of damage.


4.19

Also presented in Figure 4.14 is the calculated qu against time for material in situ and

that expected for the material cured under zero applied stress. As with the paste-fill

case, qu for material cured in situ is greater than that for material cured under zero

stress. But it is important to note that even with the reduced filling rate (relative to the

paste fill situation), the increase in qu of the in situ material relative to that cured under

zero stress is significantly greater. The increased ratio is a result of the soil compression

that occurred immediately after deposition. This compression increased the material

density, which leads to the higher strengths.

Summary

Overall, it can be concluded that, under most conditions, the interaction of effective

stress and the growth of fragile cement bonds during filling is unlikely to adversely

influence the consolidation behaviour or damage the fragile cement bonds in either a

paste or hydraulic fill situations. In fact, modelling indicates that in most cases this

interaction will actually lead to higher material strengths in situ due to soil compression.

4.5.4 Strain requirements

One component that is often incorporated into tailings consolidation models is large

strain consolidation theory. This is important when analysing the consolidation of large

storage facilities containing compressible tailings. But in a tailings-based backfill

situation material is either cycloned (to remove fine particles) or, if placed as full-stream

tailings, combined with cement to avoid the material liquefying after placement.

In addition to reducing the risk of liquefaction, the removal of fines from a tailings

stream (as in a hydraulic fill) increases the material stiffness (in an uncemented state)

and therefore reduces the amount of compression, while, as noted by Le Roux et al.

(2005) the presence of cementation in full-stream tailings backfill (paste fill) acts to

reduce the compression that occurs during the filling process. For these reasons large-

strain numerical formulation may be unnecessary when undertaking consolidation

analysis of mine backfill.

To investigate this aspect, the vertical strain calculated for the paste fill example

presented in Section 4.5.3 is plotted against time in Figure 4.15. This figure indicates

that vertical strain levels of 4% occurred for the cemented paste example.


4.20

As hydraulic fill can be placed without any cement, it is important to consider the likely

strains that would be generated for a typical uncemented hydraulic fill. The values of

uncemented compression parameters (λ = 0.06, κ = 0.006) that were adopted for the

previous study are considered to be greater than the values relevant to a typical

hydraulic fill, and hence using these parameters would overestimate strains in a

hydraulic fill situation. Based on Rowe cell testing of hydraulic fills, compression

parameters of λ = 0.035, κ = 0.0035 are considered more appropriate. These

compression parameters were adopted, along with the other material properties for the

hydraulic fill example in Section 4.5.3, and zero cement content, in an analysis to

investigate the degree of compression likely to occur in a typical uncemented hydraulic

fill situation. The calculated axial strain is plotted against time in Figure 4.15, indicating

that a maximum strain of 6% occurred in this example.

The axial strains calculated for both the paste and hydraulic fill examples are both

significantly less than 20%, which was specified by Tan and Scott (1988) as the strain

levels requiring large strain formulation. This result indicates that the large strain

approach (involving a Lagrangian coordinate system and very small timesteps) adopted

in CeMinTaCo is unnecessary, and it would appear that a conventional Cartesian

coordinate system can provide a suitable representation of most mine backfill situations.

This is the approach adopted in the two-dimensional consolidation program, which is

presented in Chapter 5.

4.5.5 Comparison with data from in situ monitoring of filled stopes

To determine how well the CeMinTaCo program can reproduce the behaviour in an

actual mine backfilling situation, the program was used to simulate the deposition of a

fine-grained cemented paste fill at the Cayeli mine in Turkey. The properties of the as-

placed material adopted in the modelling were in accordance with those in the field.

These included a placed void ratio of 1.0, a cement content of 8%, and a fully hydrated

qu of 1 MPa. However, some of the other relevant material properties could not be

obtained, and thus, in order to gain a reasonable estimate of appropriate material

properties, those determined for a similar tailings material with the same cement content

were adopted. This material had grain size distribution, and mineralogical and cement


4.21

characteristics, similar to those encountered at Cayeli and was therefore expected to

have similar properties.

The values chosen in this way include the efficiency and rate of hydration (Eh = 0.032, d

= 1.5), the ratio of qu to ∆σ′vy (6), the uncemented compression parameters (λ = 0.06, κ

= 0.009) and permeability parameters (k ≈ 5×10-8 m/s), the ratio between cemented

stiffness and strength (1300) and the damage coefficient (b = 0.5). The method adopted

to account for the flow restriction due to the drawpoint is the same as that used earlier in

the parametric study, and is illustrated in Figure 4.5.

The modelling was carried out by increasing the fill height at the same rate as that

adopted in the field. The filling rate was a constant rate of rise of 0.4 m/hr for the first

24 hours followed by a 9-hour rest period, and then filling the remainder of the stope at

a rate of 0.4 m/hr over a 100-hour period. Figure 4.16 shows a plot of pore pressure

versus time obtained from the modelling, compared to the field measurements. The

monitoring location for the in situ measurements was 1.0 m above the stope floor, and

the CeMinTaCo results plotted refer to the same elevation.

In Figure 4.16, the response during the initial stage of filling is linear (and, though not

shown, coincides with the total stress increase during this period). However, the onset

of initial set coincides with a reduction in the rate of pore pressure increase, such that

from about 20 hr onwards, the pore pressure is actually reducing for both the measured

and model values even as filling continues (up to 24 hr). When filling recommences (at

approximately 33 hr) the initial pore pressure behaviour appears to be reasonably well

modelled, but as filling continues the model and in situ results start to diverge. For the

in situ case, it is likely that, due to consolidation, some of the fill/rock interface strength

is mobilised, resulting in a stress redistribution to the surrounding rockmass (arching).

This reduces the total vertical stress imposed on the material at the monitoring point,

resulting in a lower pore pressure increase than would otherwise have occurred. In fact,

any tendency for pore pressure increase beyond this point is completely counteracted by

on-going drainage (and self desiccation), with the result that the pore pressure at the

monitoring point continues to reduce. Clearly, the one-dimensional CeMinTaCo model

is not able to account for the arching mechanism, and in this case it predicts an increase,

rather than a decrease, in pore pressure when filling recommences.


4.22

While many of the material parameters used in the modelling have not been derived

directly for the material being modelled, the ability of the model to reproduce the

significant characteristic of the filling process based on properties of similar material

illustrates that the model is capturing the most significant mechanisms associated with

mine backfill placement. However, it is also clear that a two-dimensional model (plane

strain or axi-symmetric), or even a full three-dimensional model, is required to capture

the complete behaviour.

4.6 CONCLUSION

Overall, this section has demonstrated that the mine backfill process is a complex

interaction of mechanisms. This interaction of mechanisms can actually create

circumstances that produce counterintuitive outcomes, as was demonstrated in the

permeability sensitivity study (Section 4.5.2). For example, contrary to ‘rules of thumb’

used in industry, filling a stope with low-permeability material can result in very low

pore pressures being present in the fill at the end of filling – pore pressures much lower

than those in a free-draining fill. Therefore, in order to predict the overall response, the

individual mechanisms need to be fully coupled into a program such as CeMinTaCo. It

would be unwise to speculate about the impact of a single mechanism on the overall

response and it would be unwise to attempt to superimpose the impact of individual

mechanisms in an effort to understand the cumulative response.

This work has demonstrated that compressive yielding during placement is unlikely to

occur in a typical mine backfill situation. In addition, analysis of typical strains levels

during filling indicate that, under normal conditions, small-strain formulation is

sufficient to capture the consolidation behaviour of mine backfill.

Comparison with in situ monitoring demonstrated that the one-dimensional model

(CeMinTaCo) was capable of accurately representing the early age behaviour; but

diverged from in situ measurements during the later stages of filling. This is believed to

be a result of stress redistribution to the surrounding rockmass. To appropriately address

this mechanism, a two- or three-dimensional model is required. The development of a

new fully-coupled two-dimensional finite element model is presented in Chapter 5 of

this thesis.


4.23

Mechanics of Mine Backfill Matthew Helinski Two-dimensional consolidation analysis (Minefill 2D) The University of Western Australia

5.1

CHAPTER 5

TWO-DIMENSIONAL CONSOLIDATION ANALYSIS

(MINEFILL-2D)

5.1 INTRODUCTION

In Chapter 4, a computer code (CeMinTaCo) for modelling the behaviour of backfill

material undergoing consolidation and cement hydration during and following

placement in a stope was presented. Being one-dimensional, the model can not, of

course, deal with any of the two-dimensional or three-dimensional aspects of the

behaviour in a real stope. For example, in comparing the numerical output from

CeMinTaCo with the in situ measurements, e.g. as presented in Section 4.5.6, one

drawback that becomes evident is the inability of the one-dimensional model to

appropriately capture the redistribution of stress to the surrounding rockmass (arching),

and thus it cannot take account of the reduced vertical stress that can result from

arching. It is likewise incapable of representing the stope drawpoint in a geometrically

correct fashion. Without being able to represent the stope drawpoint correctly, artificial

base boundary conditions are required to represent the drainage restrictions through the

drawpoint, such as those described in Figure 4.3. In addition, a one-dimensional model

cannot appropriately represent the horizontal stresses placed on barricades. In order to

take these aspects into account, a two- or three-dimensional model is required.

While the one-dimensional nature of CeMinTaCo has these drawbacks, it has shown

that some aspects of cemented mine backfill behaviour that were previously thought to

be important were, in fact, not so important after all in most situations. These were the

requirement to use large-strain formulation, and the possibility of yielding of cement

bonds as they formed due to the development of excessive confined vertical

compressive stresses.

With regard to the first aspect, the sensitivity study in Chapter 4 demonstrated that the

presence of cementation (in paste fill) or the removal of fines (in hydraulic fill) result in

strain levels that are far less than 20% (strains in the order of 6% were calculated). Tan

and Scott (1988) suggest that for strains less than 20%, a small-strain formulation


5.2

provides accurate solutions. Therefore, it is considered acceptable to perform the

calculations using the conventional Cartesian coordinate system rather than the

Lagrangian coordinate system that was used in CeMinTaCo.

With regard to the second aspect, a study into the influence of structural damage from

excessive compressive stress indicates that, provided the material has sufficient strength

to support the ultimate stress state, effective stress generated during the early stages of

hydration is unlikely to damage cement bonds as they form. Therefore, it is considered

appropriate to undertake calculations where compressive yield of the cemented structure

is neglected and a Mohr Coulomb yield surface is used to represent the behaviour of the

cemented material. It should be noted that compressive yield of the material in an

uncemented state is taken into account to address any compression that occurs prior to

the onset of hydration, which was shown to be relevant in Section 4.5.3.

This chapter begins by outlining the unique requirements of a model to represent the

mine backfill deposition process. This is followed by a description of the governing

equations and numerical formulations developed within the program Minefill-2D. An

overview of the material models adopted in this program is then provided. Minefill-2D

is then compared with various well-established analytical solutions and CeMinTaCo to

verify the performance of the model. Finally, a comparison against in situ

measurements is undertaken to verify the applicability of the program to the mine

backfill deposition process.

Many of the basic ideas incorporated into Minefill-2D are the same as those

incorporated into CeMinTaCo, and these ideas have been thoroughly explored in

previous chapters. Nevertheless, there is a considerable amount of repetition of this

material in this chapter; this has been done for the sake of completeness, and to make

this chapter more coherent.

5.2 PROGRAMMING REQUIREMENTS

The main features required in this model included the following:

• fully coupled analysis – i.e. full coupling between compression, water flow, and

the cementation processes;


5.3

• calculations in terms of total water head;

• ability to vary boundary conditions on the upper surface, to enable fresh material

to be added, and to deal with various water outflow or inflow conditions;

• ability to take account of water accumulation above the fill surface (influencing

surface total stresses and pore pressures);

• a constitutive model that takes account of cement hydration;

• a permeability model that takes account of cement hydration;

• a self-desiccation model;

• strain softening of the fill mass due to interface shear during filling.

In order to achieve these requirements, a number of commercially-available programs,

including FLAC, Plaxis and AFENA, were examined. None of these programs proved

to be suitable due primarily to problems associated with simulating the accretion of soft

soil whose properties evolve with time under fully coupled conditions. Specifically this

related to dynamic waves generated during the consolidation of soft material disrupting

the calculation scheme (in FLAC), problems associated with undertaking calculations in

terms of total water head and problems associated with establishing boundary

conditions along the surface nodes and then including these surface nodes back into the

calculation scheme at a later stage. Because of these problems, it was decided that the

most appropriate approach would be to develop a new two-dimensional (plane-strain or

axi-symmetric) model, which specifically addressed the described criteria. This program

was coded in Visual Fortran 90 and named ‘Minefill-2D’.


5.4

5.3 PROGRAMMING METHODOLOGY

5.3.1 Introduction

This section presents the relevant numerical components incorporated into the program

Minefill-2D. It includes an introduction of the numerical technique, a description of the

calculation sequence, an outline of the governing equations, as well as a description of

how other numerical difficulties were addressed. Throughout this section, all

relationships are formulated for the condition of plane strain analysis. Section 5.3.6

presents a description of how the equations are converted for axi-symmetric analysis.

5.3.2 The finite element method

The numerical technique adopted is the finite element method. As described in Potts

and Zdravković (1999) the finite element method involves 6 main steps. These include:

• Element discretisation

• Primary variable approximation

• Element equations

• Global equations

• Boundary conditions

• Solution to the global equations

Element discretisation

The first step in the finite element formulation is to discretise the problem geometry into

small domains, (elements). These individual element are then connected by a series of

points (nodes). The most important feature of defining a suitable discretisation of the

problem geometry is to increase the number of elements in regions where unknowns

vary rapidly, such as displacements (shear strains) at the fill/rock interface.

In two-dimensional problems, triangular or quadrilateral elements are commonly

adopted. Throughout this thesis, quadrilateral elements were adopted with 8 boundary


5.5

nodes to represent displacement and 4 boundary nodes to represent pore pressures, as

illustrated in Figure 5.1.

Primary variable approximation

The primary unknown variables adopted in Minefill-2D are displacement and pore

pressure. Stresses and strains are determined as a function of the calculated

displacements field. In the two-dimensional analysis presented, global displacements u

and v are determined in the x and y direction respectively (typically the conventional

symbols adopted for displacements are u and v but to avoid confusion with pore

pressures and Poisson’s ratio these modified symbols were used).

Across each element, the displacements are assumed to vary in accordance with a

polynomial shape function, where the order of the polynomial depends on the number

of nodes in the element. Displacement (u , v ) at any point within an element are defined

in accordance with nodal displacements and the matrix of shape functions [ ]dN such

that:

[ ]{ }821821 ˆˆˆˆˆˆˆ

ˆnnnnnnd v,...,v,v,u,...,u,uN

v

u=

(5.1)

where u and v are the displacements at any point within the element and niu , niv are

the displacements (in the x and y directions respectively) at nodal points i.

If displacements vary quadratically across an element, strains and therefore effective

stresses vary linearly across the element. To ensure that effective stress and pore

pressure vary in the same way across an element, it is conventional to adopted 4-noded

elements to represent pore pressure variations. Therefore, pore pressures (u) within an

element are related to the four nodal pore pressures by:

[ ] [ ]{ }421 nnnp ,...,u,uuNu= (5.2)

where niu is the nodal pore pressure at location i and pN is the shape function.

To assist with the numerical formulation, most finite element programs (including

Minefill-2D) uses isoparametric elements, where the global coordinates (x, y) of a point

in an element are expressed as a function of the global nodal coordinates (xi, yi) and


5.6

local shape (interpolation) functions Ni(s,t) . For the elements shown in Figure 5.2, the

global coordinates of a point in the element can be expressed by coordinate

interpolation of the form:

( )∑=8

1

, ii xtsNx and ( )∑=8

1

, ii ytsNy (5.3)

where s and t are local coordinates which vary from -1 to 1 across each element. The

purpose of introducing this coordinate system is to allow a solution to be sought through

Gaussian integration. The term isoperimetric come from the fact that the geometry is

approximated using the same shape function as that for displacements, which simplifies

the element equations.

Element equations

a. Co-ordinate transformation

The element equations govern the deformation of each element. The formation of

element equations combines compatibility with equilibrium and the constitutive

relationship.

Using the primary variable approximation, presented previously, the compatibility

equations can be represented as:

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

=

εγεε

8

8

1

1

8811

81

81

ˆ

...

ˆ

00000

0

000

000

v

u

v

u

x

N

y

N

x

N

y

Ny

N

y

Nx

N

x

N

zxy

y

x

&&

&&

(5.4)

which can be more conveniently expressed as:

{ } [ ]{ }ndB ∆=ε∆ (5.5)

where [ ]B contains the derivatives of the shape functions [Ni],and { }nd∆ contains a list

of the nodal displacements for a single element. The shape functions [Ni] depend only

on the local coordinates (S and T). Therefore, in order to calculate the derivatives of

these shape functions relative to the global coordinate system (x and y), a chain rule is


5.7

required to relate the x and y derivatives to derivatives with respect to S and T. Using the

chain rule:

Tii

Tii

y

N

x

NJ

T

N

S

N

∂∂

∂∂=

∂∂

∂∂

(5.6)

where J is defined as the Jacobian matrix:

∂∂

∂∂

∂∂

∂∂

=

T

y

T

xS

y

S

x

J (5.7)

the global derivatives of the shape functions (used in Equation 5.4) can be obtained by

inverting Equation 5.6.

Time-dependent consolidation requires the material constitutive model to be combined

with equilibrium and Biot’s consolidation equations. Coupling these leads to the

development of the governing equations of finite element consolidation as follows.

b. Constitutive model

Assuming elastic behaviour over a given loading increment (σ∆ ), Hooke’s law states

that the relationship between stress and strain can be represented as:

{ } [ ]{ }ε∆′=σ′∆ D (5.8)

where { } [ ]Txyyx τ∆σ∆σ∆=σ′∆ ,, '' and { } [ ]Txyyx γ∆ε∆ε∆=ε∆ ,, are the incremental

effective stress and strain vectors in plane strain respectively, and [ ]D′ is the assumed

relationship between these vectors. [ ]D′ is based on the drained Young’s modulus (E′)

and the drained Poisson’s ratio (ν′) such that:

[ ]

ν′−′

ν′−ν′+ν′−′

ν′−ν′+ν′

ν′−ν′+ν′

ν′−ν′+ν′−′

=′

)21(300

0)21)(1(

)1()21)(1(

0)21)(1()21)(1(

)1(

E

EE

EE

D (5.9)


5.8

Terzaghi’s principle of effective stress states that:

{ } { } { }u∆+σ′∆=σ∆ (5.10)

where σ∆ is the change in total stress,σ ′∆ is the change in effective stress and u∆ is

the change in pore pressure. Substituting Equation 5.8 into Equation 5.10 gives:

{ } [ ]{ } { }uD ∆+ε∆′=σ∆ (5.11)

where ε∆ is the strain matrix.

c. Continuity

The equation for pore fluid continuity is:

t

εQ

yxvyx

∂∂=−

∂∨∂

+∂∨∂

(5.12)

where ∨ x, and ∨ y are the components of pore fluid velocity in the coordinate directions

and Q is any source or sink term.

Assume the pore fluid flow is in accordance with Darcy’s law:

∂∂∂∂

−=

∨∨

y

hx

h

kk

kk

yyyx

xyxx

y

x (5.13)

or { } [ ]{ }hk ∆−=∨

where kij is the coefficient of hydraulic conductivity for the soil, [ ]k is the hydraulic

conductivity matrix and h is the hydraulic head, defined as:

( )gygxw

iyixu

h .. ++=γ (5.14)

Vector { } { }Tgygxg iii ,= is the unit vector parallel to, but in the opposite direction to,

gravity and γw is the unit weight of water.

d. Equilibrium and governing equations


5.9

Rather that solving for force equilibrium, a more convenient formulation is brought

about through considering conservation of energy, (i.e. internal (W∆∂ ) and external

work ( L∆∂ ) must be equal):

0=∆∂−∆∂ LW (5.15)

The internal work is given by the integration of the increment of total stress multiplied

by the increment of strain across the element:

{ } { } VolWVol

T d2

1∫ σ∆ε∆=∆ (5.16)

Using Equation 5.11, Equation 5.16 can be split into soil matrix and pore pressure

terms, and re-written as:

{ } [ ]{ } { } { }[ ] VoluDWVol

TT d2

1∫ ∆ε∆+ε∆′ε∆=∆ (5.17)

The work done by the incremental applied loads (L∆ ) can be divided into contributions

from body forces and surface tractions, and can be expressed as:

{ } { } { } { }dSrfTddVolFdLT

Srf

T

Vol

∆∆+∆∆=∆ ∫∫ (5.18)

Combining the above, the equilibrium condition is satisfied during the consolidation

step when

[ ]{ } [ ]{ } { }EE RuLdK ∆=∆+∆ (5.19)

where d∆ is the nodal displacements vector, and

[ ] [ ] [ ][ ] VolBDBKT

VolE d′= ∫ (5.20)

which is termed the element stiffness matrix, and [ ]B is the derivative of the shape

functions as discussed previously. [ ]EL is termed the element volume matrix and is

defined as:


5.10

[ ] { }[ ] [ ]∫=Vol

pT

E VolNBmL d (5.21)

where [Np] is the matrix of shape functions for pore fluid pressure interpolation and

{ } { }000111=Tm

Using the principle of virtual work, the continuity equation (5.6) can be written as:

{ } ( ){ }∫ =∆−

∆∂ε∂+∆∇∨

Vol

vT uQVolut

u 0d (5.22)

Substituting Darcy’s law (Equation 5.13) into Equation 5.22 gives:

{ } [ ] ( ){ }∫ ∆=

∆∂ε∂+∆∇∇

Vol

vT uQVolut

ukh d (5.23)

where [ ]k is the permeability matrix and { }h∇ is the gradient of total water head. h∇

takes account of both elevation head { }gi and total pore pressure { }u∆ so that

calculations can be carried out in terms of total water head rather than excess pore

pressures. It is important for Minefill-2D to carry out analysis in terms of total water

head, as the combination of on-going filling and drainage (through base barricades)

make it difficult to define hydrostatic conditions. The sink term (Q ) becomes

particularly important when accounting for self-desiccation volumetric changes.

If tv

∂∂ε

is approximated as tv

∆∆ε

, equation 5.23 can be re-written as:

[ ] { } [ ]{ } [ ] Qnut

dL EnE

nTE +=Φ−

∆∆

(5.24)

where

[ ] [ ][ ]

VolEkE

Vol w

T

E d .

∫=Φγ (5.25)

represents the element permeability matrix,


5.11

[ ] [ ]{ } VolikEn g

Vol

TE d ∫= (5.26)

represents flows due to gravitational forces, and

[ ]T

ppp

z

N

y

N

x

NE

∂∂

∂∂

∂∂

= ,, (5.27)

represents the derivative of the shape functions for pore water pressure interpolation.

Equations 5.24 and 5.19 are solved using a time-marching process such that if the nodal

pore pressure { }nu and displacements { }nd∆ are known at time t1, then the solution for

nodal pore pressures and displacements is sought at time t2 = t1 + ∆t. If a finite

difference approach is adopted, and assuming a linear interpolation in time, the resulting

equation is:

[ ]{ } [ ] { }( ) ( ) { }( )[ ] tuutu nnEn

t

tE ∆β−+βΦ=Φ∫ 1d 12

2

1

(5.28)

Booker and Small (1975) demonstrated that, in order to form a stable solution to

Equation 5.28 , the value of β must be greater than or equal to 0.5. To maintain an

implicit time-marching solution, a value of 1.0 was adopted for β throughout this work.

Substituting equation 5.28 into 5.24 gives:

[ ]{ } [ ]{ } [ ] { }( ) [ ]( ) tnQuutdL EnEnEnE ∆++∆Φ=∆Φ∆−∆ 1 (5.29)

Combining equations 5.13 and 5.23, the governing equations for finite element

consolidation analysis can be developed. These governing equations are presented as

Equation 5.30:

[ ] [ ][ ] [ ]

{ }{ }

{ }[ ] [ ]{ }( )

Φ++=

Φ− tuQn

R

u

d

tL

LK

nEE

E

n

n

ET

E

EE

∆

∆

∆

∆

∆ 1 (5.30)

where [ ]EK represents the element stiffness matrix, [ ]EL represents the element volume

submatrix, [ ]EΦ represents the permeability submatrix, { }ER∆ is the vector of boundary

stresses, [ ]En represents flow due to gravitational forces, Q represents an internal sink


5.12

term, {∆u}n is the vector of nodal total pore pressure increments, {∆d}n is vector of

nodal displacement increments.

Global equations

The global system of finite element equations for the consolidation problem is simply

the assembly of terms from Equation 5.30, across the entire problem domain in

accordance with corresponding nodes.

[ ] [ ][ ] [ ]

{ }{ }

{ }[ ] [ ]{ }( )

Φ++=

Φ− tuQn

R

u

d

tL

LK

nGG

G

n

n

GT

G

GG

∆

∆

∆

∆

∆ 1 (5.31)

where:

[ ] [ ]i

N

iEG KK ∑

==

1 (5.32)

[ ] [ ]i

N

iEG LL ∑

==

1 (5.33)

[ ] [ ]i

N

iEG ∑

=Φ=Φ

1 (5.34)

[ ] [ ]i

N

iEG RR ∑

==

1 (5.35)

[ ] [ ]i

N

iEG nn ∑

=

=1

(5.36)

where N is the number of elements in the problem domain.

Extension to axi-symmetric conditions

To model the complexities of the stope drawpoint geometry would require the

development of a full three-dimensional version of the two-dimensional (plane strain)

model. This is beyond the scope of this thesis. The plane-strain Minefill-2D model is

capable of providing very good representation of the behaviour in many stopes,

especially where the length-to-breath ratio is high. However, in some situations, an axi-

symmetric model might provide a better representation of reality. In addition, Chapter 6


5.13

presents the results of an axi-symmetric centrifuge test, and clearly an axi-symmetric

model would be more appropriate for modelling this test.

All of the previous discussion relating to the development of Minefill-2D was based on

a plane-strain formulation. Axi-symmetric analysis follows the same calculation

methodology as that for plane strain conditions, but rather than analysing an element of

unit depth, the analysis is carried out on a one-radian slice through an axi-symmetric

geometry (i.e. through a cylinder) as illustrated in Figure 5.3. As is well documented in

the literature (Naylor et al., 1981, Potts and Zdravković ,1999, Smith and Griffiths,

1998), rather than calculations being carried out in terms of x and y coordinates (as is

the case in plane strain) calculations are carried out using a cylindrical coordinate

system (r, z, θ).

As the calculations progress outwards from the centreline, the thickness of the slice is

always equal to the radius (since a one-radian slice is considered). In order to account

for the increase in thickness, a number of minor numerical adjustments are required.

These include the following:

• The conversion of surface stress into nodal forces needs to be modified to

account for the increasing radius and therefore increased force applied to the

surface nodes with an increase in radius.

• The terms in the stiffness matrix for both the “undrained” and “consolidation”

calculation steps need to be multiplied by the respective Gauss-point radius.

• The volume submatrix [ ]EL must be multiplied by the respective Gauss-point

radius to account for the increase in volume that occurs as the radius increases.

These modifications were made to Minefill-2D to allow the program to be used in either

plane-strain or axi-symmetric mode.


5.14

5.3.3 Boundary conditions

Initial conditions

The methodology adopted in Minefill-2D is to simulate the continuous placement of

material by activating discrete layers of material at a defined rate. The initial placement

of each layer involves an undrained step. As this step is assumed to occur over an

infinitely short time and as the material stiffness of each new layer is initially very low,

it is assumed that the layer being placed demonstrates completely undrained conditions

(i.e. within the new layer, the increase in total stress and pore pressure with depth are

equal).

The existing fill mass is loaded with a vertical stress that is equal to the weight of the

new layer. The response of the existing layer to this vertical force is calculated with an

undrained calculation step.

The reason for undertaking this undrained step is to provide a consistent match between

model geometry and applied self weight, and to independently establish the stress

distribution throughout the matrix in accordance with strain compatibility between the

water and soil phases.

The undrained loading step in Minefill-2D is undertaken using effective stress

parameters. When undertaking undrained analysis Equation 5.19 simplifies to:

[ ]{ } { }EnE RdK =∆ (5.37)

or in global form:

[ ]{ } { }GGnG RdK =∆ (5.38)

While the formation of the element stiffness matrix remains the same, the constitutive

matrix [ ]D′ is modified to [ ]D , which accounts for the compressive stiffness of the

water phase through its bulk modulus Kw. Therefore, in an undrained situation the plane

strain stiffness matrix [ ]D takes the form:


5.15

[ ]

′−′

+′−′+

′−′+

′−′+′′

+′−′+

′′+

′−′+′−′

=

)21(300

0)21)(1(

)1(

)21)(1(

0)21)(1()21)(1(

)1(

ν

ννν

ννν

ννν

ννν

E

KE

KE

KE

KE

D Ww

wW

(5.39)

After the placement of each new layer, Equation 5.38 is solved to derive the nodal

displacements and, like with the consolidation case, Equation 5.4 is used to derive the

strains increment (∆ε). These strains are then used to determine the associated changes

in effective stress, total stress and pore pressure in accordance with

ε∆′=σ′∆ .D (5.40)

ε∆=σ∆ .D (5.41)

ε∆=∆ .wKu (5.42)

As discussed previously, a fully-coupled analysis requires the pore pressures to be

calculated at the element nodal points rather than the integration points. Therefore, pore

pressures calculated at the integration points must be converted to nodal pore pressures

for the consolidation calculation phase. A number of stress-recovery techniques have

been proposed by researchers such as Zienkiewicz and Zhu (1992). These authors note

that if the variation of properties is linear across the element, then a straightforward

averaging technique would provide accurate results. As the flow calculations are carried

out using 4-noded elements, the shape functions vary linearly across the element and

linear interpolation is suitable. Therefore, in order to recover the nodal pore pressures,

the integration-point pore pore-pressure tensor is multiplied by the inverse of the shape

function to calculate the contribution of each integration point to the particular node.

The contributions of all integration points (from elements surrounding the particular

node) are averaged to recover the appropriate nodal point value. These values can then

be used during the consolidation calculation phase.

Phreatic surface control

During the deposition of saturated slurry material, the solids may immediately settle,

creating a free surface of water above the solids mass. Also, due to the bulk unit weight


5.16

being greater than that of water, undrained placement creates a hydraulic gradient that is

steeper than hydrostatic. This gradient causes upward water flow, which leads to water

ponding on the surface.

A surface water pond applies a total stress and (an equal) pore pressure at the fill

surface. The magnitude of the total stress and pore pressure is proportional to the depth

of the pond, and since they affect the total stress distribution throughout the fill mass

and the hydraulic gradients, it is necessary to accurately take account of the

accumulation of water above the fill surface.

In Minefill-2D, changes in surface ponding are accounted for by monitoring the water

exchange through the surface layer, in a manner almost identical to that employed in

CeMinTaCo (and in the original MinTaCo). The characteristics that are taken into

account in estimating the water exchange include flows through the surface layer,

volumetric changes that occur in the surface layer and any self-desiccation volumetric

changes. Based on the cumulative impact of these three mechanisms, the change in

phreatic surface elevation is determined.

During the placement of a new layer, any existing ponded water is transferred directly

to the surface of the new layer. Often when delivering mine backfill to a stope, the water

content required for transportation results in the solids settling (almost immediately) and

free water accumulating on the surface. If this is the case, any surplus water is added to

the existing surface water and consolidation calculations begin at what is defined as the

“settled density”.

All modelling described in this thesis was carried out assuming completely saturated

conditions. Therefore, the only relevance of the phreatic surface is that it defines a

surface on which the pore pressure is equal to atmospheric pressure. As a result, if base

drainage is occurring (without the addition of an equal quantity of water at the surface),

the phreatic surface would eventually be drawn below the fill surface. As discussed by

Fredlund and Rahardjo (1993), in order to maintain equilibrium, water above the

phreatic surface develops negative pore pressures that increase in magnitude with height

according to the unit weight of water. Full saturation assumes that the pore suctions at

the fill surface are always less than the air-entry suction of the fill, no matter how large

these suctions become. In real stope filling, desaturation can occur, though it is


5.17

generally where high cement contents are adopted, or it occurs late in the process, well

after the development of maximum barricade loads. Therefore, at this stage, extension

of the model to deal with unsaturated behaviour has not been attempted, but this is

certainly a desirable aspect that could be investigated in future work.

Boundary node control

Changes in boundary conditions occur during the transition from an undrained loading

calculation step to a consolidation calculation step. During this change in calculation

routine, the pore pressures at the controlled boundaries change from the value calculated

during the undrained step to that specified by the boundary condition. This change in

pore pressure can be accounted for by reassigning the nodal pore pressure values, but

this change in pore pressure must be reflected in a change in effective stress and

associated strains.

Also, as discussed in the previous section, the initial placement of material can create a

surface water pond or an upward hydraulic gradient which allows water to accumulate

on the fill surface. Any accumulated water would apply a total stress and pore pressure

to the surface nodes, with the magnitude being a function of the water depth. This

condition cannot be managed by eliminating the surface nodes from the calculation

scheme, as later they must be reintroduced into the calculation scheme after the

placement of the next layer.

In both cases, the initial and eventual nodal pore pressures are known, and therefore the

technique that is commonly adopted to apply known nodal displacement increments can

be utilised to address these issues. The following section presents how this logic can be

applied to the situation of changing nodal pore pressures along a boundary.

Assume the problem to be solved is:

{ }

{ }

{ }

[ ]{ }( )

[ ]{ }( )

[ ]{ }( )

∆Φ+

∆Φ+

∆Φ+

=

∆

∆

∆

tu

tu

tu

u

u

u

kkk

kkk

kkk

nngG

jngG

ngG

n

j

nnnjn

jniji

nj

....

....

....

...

...

......

...............

......

...............

...... 11

1

1

1111

(5.43)


5.18

When progressing from an initial condition ({ }Undrainedu ) to a condition specified by

the boundary condition ({ }BCu ) the change in pore pressure { } ju∆ can be determined in

accordance with:

{ } { } { } { }UndrainedBCconsj uuuu −=∆=∆ (5.44)

This situation occurs when progressing from the undrained calculation step to the

boundary condition of atmospheric pressure at the barricade location or due to a change

in surface nodal pore pressure and total stress from a change in surface pond elevation.

Therefore, { } { }consj uu ∆=∆ can be simply substituted into the j th row of the

consolidation matrix and all other terms in the j th row of the [k] matrix can be removed.

Also, as the value of { }ju∆ is now known, it can be subtracted from both sides of the

equation such that:

{ }

{ }

{ }

[ ]{ }( ) [ ] { }( )( ){ }

[ ]{ }( ) [ ] { }( )( )

∆∆Φ+−∆Φ+

∆

∆∆Φ+−∆Φ+

=

∆

∆

∆

tuktu

u

tuktu

u

u

u

kk

kk

jconsGnjnngG

cons

jconsGjngG

n

j

nnn

n

.........

...

...

.........

...

...

...0...

...............

0...1...0

...............

...0... 111

1

111

(5.45)

Given this procedure, the pore pressure change can be incorporated into the calculation

scheme such that it is appropriately reflected in changes to effective stress and strain in

addition to pore pressures. Furthermore, by maintaining the terms in the calculation

matrices, they can be included into the conventional calculation scheme when required.

5.3.4 Solution to the global equations

As will be described in Section 5.4, a non-linear constitutive equation is adopted to

represent the cemented mine backfill. In order to solve the non-linear constitutive

relationship, the visco-plasticity technique (Zienkiewicz and Cormeau, 1967) was

adopted. The associated numerical code is taken from Smith and Griffiths (1998).


5.19

The visco-plasticity technique allows the material to be loaded to a stress state that is

beyond the yield surface. If the yield function [Fy] is positive (i.e. yielding has occurred)

this function is combined with the flow rule

σ∂∂Q

and viscosity parameter ( )µ to

determine the visco-plastic strain rate ( )vpε& in accordance with:

σ∂∂µ=ε Q

F yvp ..& (5.46)

Ideally, µ should be determined experimentally, but as the main interest is in

determining steady-state stress and plastic strains, the transient stress path is not

important. It will be shown later (in Equation 5.48) that when determining stress states

and unbalanced forces, µ cancels, making the result independent of the chosen value.

The visco-plastic strain rate vpε& is combined with a pseudo-time step ( )crt∆ to

determine the increment of plastic strain vpε . The time step used in the time-marching

process (∆t) must be limited to maintain stability. For the Mohr-Coulomb yield surface,

which is adopted in Minefill-2D, it has been shown that the maximum stable timestep

(∆tcr) is given by:

( )

( )φ+ν′−µν′−=∆

2sin21

212

Gtcr (5.47)

where G is the shear modulus, ν′ is the Poisson’s ratio and φ is the friction angle.

The visco-plastic strains are combined with the material stiffness to evaluate the stress

increment σ∂ .

[ ] crtQ

DFD ∂σ∂

δφµ−ε∂=σ∂ .. (5.48)

where D is the elastic stiffness matrix.

In addition, the last term in Equation 5.48 is used to derive the unbalanced body

stresses. These body stresses are integrated over each Gauss point to determine

unbalanced body forces, which are redistributed to other nodes in the finite element

mesh during subsequent iterations. The solution is iterated until no Gauss-point stress


5.20

state violates the yield criterion (within a certain tolerance). The convergence tolerance

adopted throughout this thesis was 0.0001.

During each calculation step, it is assumed that the material properties remain constant

but these properties are updated after each increment of load or time. A flaw that exists

with this approach is the implementation of the strain-softening criteria into the visco-

plasticity solution scheme. Inherent in the visco-plasticity solution is the assumption of

perfect plasticity, and therefore body forces are calculated based on the assumption of

plastic strains not absorbing (or releasing) energy. But the degradation of material

strength with plastic strain does result in an energy release. Therefore, a rigorous

solution should take account of this energy release when calculating the body forces. By

updating the yield strength (taking account of this strength degradation) at the end of

each increment, and mapping the stress state back onto the yield surface during the

following timestep the energy release is, to some degree, taken into account. Detailed

and rigorous treatment of this aspect is beyond the scope of the thesis but future work

may consider applying a secant stiffness solution algorithm, which is better suited to

managing strain softening.

To minimise the likelihood of numerical drift, the maximum strain increment is

maintained below 0.001 in any calculation increment. If this tolerance is exceeded in the

undrained load calculation, the load increment is reduced, or if exceeded in the

consolidation calculation the consolidation timestep is reduced, and the calculation

repeated to ensure that this tolerance criterion is satisfied. Currently this process is

carried out manually, but future versions of Minefill-2D will combine the coefficient of

consolidation with the element size to derive a suitable timestep in a similar way to that

suggested by Yong et al. (1983) for the one-dimensional consolidation situation. This

approach would increase the efficiency of this process by maximising the timestep

increment without exceeding the strain criteria.

5.4 MATERIAL BEHAVIOUR

5.4.1 Influence of cementation on governing equations

Immediately after placement, and before the cemented mine backfill has reached initial

set, the material is assumed to behave in accordance with the uncemented material


5.21

properties. However, as demonstrated in Chapter 4 (using CeMinTaCo), the time-scale

associated with consolidation may be similar to that of the hydration process. As a

result, the cement hydration process must be fully coupled with the consolidation

process.

As discussed previously (in Chapters 3 and 4), the cement-hydration process influences

the consolidation behaviour. This influence was shown to be most significantly

associated with:

• Stiffness: Aspects that can influence the material stiffness include the initial

uncemented density, cement hydration, and damage to the cement bonds due to

excessive strain. The evolution of these influences the constitutive matrix [ ]D′ ,

which influences the global stiffness matrix [ ]GK .

• Strength: This can be influenced by cement hydration as well as by destruction

of cement bonds due to excessive stress. Strength or yield stress influences the

constitutive matrix [ ]D′ and the global stiffness matrix [ ]GK as it governs the

selection of stiffness properties.

• Permeability: This can be influenced by material density, particle size

distribution and cement hydrate growth. These mechanisms interact to influence

the permeability matrix [ ]GΦ .

• Self desiccation: This refers to the volume changes that occur during the

hydration process (as discussed in Chapter 3) and can be taken into account

through the internal sink term Q.

Therefore, in order to take account of the cement hydration processes during the

consolidation process, the governing consolidation equations (Equation 5.31) are solved

such that the relevant terms are a function of time, material state (void ratio), and

cement content (t, e and Cc):


5.22

( )[ ] [ ][ ] ( )[ ]

{ }{ }

{ }( )[ ] ( ) ( )[ ]{ }( )

Φ++=

Φ− tuCetCetQCetn

R

u

d

CettL

LCetK

nGcGccG

G

nG

nG

cGT

G

GcG

∆,,,,,,

∆

∆

∆

,,.∆

,,

(5.49)

Details of the cemented material relationships incorporated into Equation 5.49 were

discussed previously in Chapter 3, and are discussed further in the following section.

5.4.2 Constitutive model, ( )[ ]( )[ ]cG CetDK ,,′

The overall approach to the material model used in Minefill-2D is similar to that

described in Section 3.2, where the cemented and uncemented material behaviour is

superimposed to represent the overall response, and the small strain stiffness is linearly

related to the material strength while the secant stiffness is degraded in accordance with

the proximity of the loading surface to the yielded surface. Section 3.2 focused on a

model to represent one-dimensional loading, while the description that follows here

focuses on the response of the material under two-dimensional loading conditions. In

what follows, there is considerable repetition of material previously dealt with in

Chapter 3; this has been done for completeness, and to make it easier to follow the

developments.

In order to represent the behaviour of the material after placement but prior to “initial

set” of the cement, a power law was adopted to relate the void ratio to the applied

effective stress. This power law takes the form of:

( ) cbcae σ ′= (5.50)

where e is the void ratio and σ ′ is the mean effective stress, while ac and bc are curve

fitting constants. This function has been successfully applied to the compression

behaviour of uncemented mine tailings (Fahey and Newson, 1997 and Fahey et al.,

2002). Note that this differs from the Cam Clay approach to representing material

compression used in Chapter 3 (Equations 3.1 and 3.2). By differentiating Equation

5.50 and combining the result with well known elastic relationships, the uncemented

shear stiffness )(uncemG can be derived such that:


5.23

( )( )

( )

−

′++=

′++

∂∂=

11

)( 12

1

12

)1( cb

cccuncem a

e

ba

ee

eG

ννσ

(5.51)

where ν′ is the drained Poisson’s ratio.

Once the “initial set” point is reached, it is also necessary to take account of the

influence of cementation on the behaviour. The material model used in Minefill-2D

assumes a Mohr-Coulomb failure criterion, where the size of the yield surface is

governed by the material state and degree of hydration. The shear stiffness is dependent

on the size of the yield surface and the mobilised stress relative to the yield stress. The

compressive stiffness is then related to the shear stiffness in accordance with an

assumed value of Poisson’s ratio. This is a much simpler approach than that used in

CeMinTaCo, where a model similar to the Structured Cam Clay model was used to take

account of possible yielding on the compression side of the yield surface, an aspect that,

as explained earlier, has not been incorporated into Minefill-2D.

In the Mohr-Coulomb yield surface, it is assumed that the friction angle is independent

of cementation, and during hydration, only the cohesive component evolves. This is

consistent with the findings of Clough et al. (1981) and Schnaid et al. (2001), who

suggest that cementation has little influence on the friction angle. The cohesive

component of strength increases as a result of cement hydration and decreases due to

damage in accordance with:

pS

D

t

Hydc

ε∂∂−

∂∂=′∂ (5.52)

where c′∂ is the change in the effective cohesion, t

Hyd

∂∂

is the change in c′ due to

hydration with time and pS

D

ε∂∂

is the degredation in c′ with time due to plastic shear

strain ( pSε∂ ).

This differs from the approach taken in CeMinTaCo where, firstly, the damage term is a

function of the vertical compressive strain, and secondly, in addition to a damage term

degrading the cement contribution to the yield surface, a hardening term increases the


5.24

size of the uncemented yield surface. This hardening term is not included in Equation

5.52, but, as the cohesive strength is a function of the cement content and void ratio (in

accordance with Equation 5.53), any soil compression will manifest in an increase in

Hyd∂ over subsequent timesteps.

Soil hardening is accounted for in the hydration function by calculating the hydration

component as a function of both void ratio (e) and cement content Cc, expressed as a

percentage. It was shown in Section 3.2 that the unconfined compressive strength (qu)

can be related to e and Cc by Equation (3.6). Since the friction angle is assumed to be

constant, cohesion (c′) is linearly related to qu. This implies that a modified version of

Equation 3.6 can be used to relate Cc and e to c′ (in kPa). The modification involved the

introduction of another constant term (Ac) which is ratio between c′ and qu.

+−+=′

WCZ

eCCXAc

c

ccc .

.exp

1.0

(5.53)

where Ac, X, Z and W are curve fitting constants.

As in CeMinTaCo, the exponential relationship proposed by Rastrup (1956) (Equation

3.7) is used to relate the cumulative evolution of cement hydration (or maturity, m)

against time. By differentiating Equation 3.7 and combining this with Equation 5.53 the

rate of development of cohesion with time can be represented. This function is

( )

+−+

−

=

∂′∂

WCZ

eCCXA

t

d

t

d

t

c

c

cc

..

exp.*

exp.*2

1 1.0

5.1 (5.54)

If the material is strained beyond yield, progressive breakdown of the bond strength can

occur. This mechanism has been accounted for by reducing c′ linearly as a function of

the plastic shear strain pSε (i.e the pS

D

ε∂∂

term in Equation 5.52).

The breakdown of cementation can be characterised using a triaxial test. An example

showing the stress-strain plot from a triaxial test on cemented paste fill is presented in

Figure 5.4 (a). Figure 5.4 (b) shows the assumed evolution of the Mohr-Coulomb yield

surface during this test.


5.25

Figure 5.4 (a) shows that as the material is loaded beyond yield, there is a progressive

reduction in the shear strength until it plateaus. The strength reduction is considered to

be a result of a progressive breakdown in the cement bonds until eventually all of the

bond strength is destroyed and the shear strength is purely a function of the frictional

strength and confining stress. The impact of cementation breakdown on the yield

surface is demonstrated in Figure 5.4 (b), where the gradient of the yield surface

remains constant (due to the assumption of a constant friction angle), but c′ is degraded

between the fully cemented and uncemented surfaces. The rate of breakdown of c′ is

assumed to be linearly related to the plastic shear strain according to the behaviour in

triaxial compression.

In Section 3.2.6, it was shown that the cement-induced component of stiffness can be

linearly related to qu. Therefore, the cement-induced component of stiffness can also be

linearly related to c′, assuming a constant friction angle. This assumption is convenient

for modelling since, by evolving the cohesive intercept in accordance with Equation

5.52, the cement-induced component of stiffness can be linearly related to this value in

accordance with a constant rigidity term.

To represent the pre-yield response, a non-linear stiffness function was adopted. This

function degrades the material tangential stiffness linearly as the shear stress approaches

yield in accordance with:

−=

max0 1

τ

τfGG mob

(cem)t(cem) (5.55)

where mobτ is the mobilised shear stress, maxτ is the yield stress, Gt(cem ) is the cement

contribution to the tangential shear stiffness, G0(cem) is the cement component of the

small strain shear stiffness and f is a curve fitting constant.

If the uncemented soil contribution to the material stiffness is very low and f is equal

to 1, infinite strain is required to reach the ultimate shear strength (τmax). Thus the peak

is never reached and softening never occurs. For a model that has a similar drawback,

Fahey and Carter (1993) suggested the introduction of a constant term f, which if less

than 1, ensures that the material fails at finite strain. The actual value for f can be

derived from a triaxial stress-strain curve.


5.26

Figure 5.5 compares the adopted model with experimental data from local strain gauges

on a cemented backfill sample loaded in a triaxial compression. The comparison

suggests that for this particular material, the proposed model provides a reasonable

representation with f = 0.85.

Others (Fahey and Carter, 1993) suggest that the secant stiffness degrades in accordance

with a hyperbolic function while the tangential stiffness degrades in accordance with the

square of the hyperbolic function. While a more complex model may provide an

improved representation, the linear relationship was adopted because it provides

modelling convenience and appears to represent the experimental data reasonably well.

After the cement-induced component of stiffness is calculated, it is directly added to the

uncemented stiffness (from Equation 5.51) to determine an appropriate stiffness for the

cemented soil mass. The superposition of the cemented and uncemented properties

provides a convenient method of addressing the evolution from an uncemented material

to a fully-cemented material. If required, the approach is also suitable for simulating the

breakdown of the cementation due to excessive shear stress.

Modelling has assumed a constant Poisson’s ratio. Therefore, after an appropriate shear

stiffness is evaluated, this value can be used to derive the bulk modulus in accordance

with well documented elastic relationships. It is recognised that this approach neglects

the potential for strain localisation but with appropriately sized boundary elements, this

approach is considered to be reasonable for this thesis.

5.4.3 Permeability model, ( )[ ] ( )[ ]cGcG CetnCet ,,,,,Φ

The permeability function adopted in Minefill-2D is the same as that presented in

Section 3.3. This model is a modified version of that originally suggested by Carrier et

al. (1983), but in this case the void ratio term is modified to account for both cement

hydrate growth as well as soil compression. This relationship was previously presented

as Equation 3.15 and is repeated below:

( )

e

eck

kdeffk

+=

1 (3.15 bis)


5.27

5.4.4 Self desiccation, Q(t,e,C)

The process of self desiccation was addressed in Section 3.4, where a relationship

between the rate of volume change in an element ( )cCetQ ,, , the cement weight per

element (Wc,), the efficiency of hydration (Eh) and a constant to represent the rate of

hydration (d) was presented. This relationship was implemented into Minefill-2D as an

internal sink term and is repeated below:

( )

−

−=

*5.1*exp...

2

1,,

t

d

t

dWECetQ chc (3.32 bis)

5.5 MODEL VERIFICATION

5.5.1 Comparison with analytical/numerical solutions

In the following section, Minefill-2D is compared with a range of analytical and

numerical solutions to verify its performance.

The first simulation involved an elastic, weightless, one-dimensional consolidation

problem, with 2-way drainage – the most basic problem encountered in any

undergraduate textbook treatment of Terzaghi’s consolidation solution. This analysis

assumed a Young’s modulus of 100 MPa and a permeability of 1x10-6 m/hr. Figure 5.6

presents an illustration showing the problem geometry. The proportion of excess pore

pressure at the various elevations after 30 and 50 hours of consolidation are shown in

Figure 5.7. Also shown in Figure 5.7 is the well-known analytical solution to this

problem, for the same times. This demonstrates that the conventional consolidation

behaviour can be well represented by Minefill-2D.

To assess the performance of Minefill-2D with respect to self-weight consolidation, a

comparison between the Minefill-2D program and the commercially-available program

Plaxis (Vermeer and Brinkgreve, 1998) was undertaken. The development and

dissipation of excess pore pressures due to the deposition of a fresh layer of material

was simulated using these two programs. This analysis involved placing a 4 m thick

layer of material with a saturated unit weight of 19.5 kN/m3, a Young’s modulus of 100

MPa and a permeability of 1x10-6 m/hr. The problem is illustrated in Figure 5.8.


5.28

Immediately after placement, the base and top boundaries were set to atmospheric

pressure and consolidation was initiated. For the Minefill-2D case, the initial pore

pressure profile was determined using an undrained step (based on self-weight loading)

followed by the top and base boundary conditions being reset, in accordance the

technique described previously in this chapter.

Figure 5.9 indicates that the undrained calculation step (in Minefill-2D) provides an

accurate method of establishing the initial conditions, and the subsequent consolidation

calculations are consistent with results from Plaxis.

To assess the performance of the self-desiccation mechanism in Minefill-2D, the model

was compared with the analytical solution (Equation 3.27). The problem simulated was

what was referred to as a “Hydration Test” in Section 3.4.6. Modelling represented a

sample placed into a triaxial cell where the cell pressure was increased to 500 kPa with

the back pressure valves closed. The material properties included a void ratio of 1.05, a

cement content of 5%, an initial effective bulk modulus of 20 MPa and an ultimate bulk

modulus of 420 MPa. The rate of hydration was assumed to be in accordance with

Equation 3.7, with a hydration coefficient (d) value of -1.5 days1/2, and an efficiency of

hydration (Eh) of 6.4%. The “initial set” time was 12 hours. This example is illustrated

in Figure 5.10.

Figure 5.11 compares the variation in pore pressure (u) and the development of effective

stress (σ′) against time, for an element test as determined using Minefill-2D and the

analytical solution presented in Section 3.4.3 for this problem. The analytical solution

for undrained self desiccation (Equation 3.27) is presented as symbols while the

Minefill-2D results are presented as lines.

Figure 5.11 indicates that the self-desiccation component of the model is performing in

the appropriate manner. It should also be noted that cement-induced development of

stiffness against time for Minefill-2D was also compared with the measured results and

found to provide a match. The combination of these is evidence that the cementation

component of Minefill-2D is providing accurate results.

The final modelling carried out to assess the performance of Minefill-2D (against

analytical solutions) was a falling head permeability test. The purpose of this was to

ensure the algorithm controlling the elevation of the phreatic surface above the fill mass


5.29

is operating appropriately and also to ensure that flow calculations are performed

appropriately in terms of total water head.

Modelling involved establishing a 4-m thick saturated soil layer with 0.8 m of water

above the layer and atmospheric pressure specified along the base boundary. The

material was assigned a Young’s modulus of 1×1020 kPa (to ensure that volumetric

changes were minimal) and a permeability of 5x10-5 m/s. An illustration showing this

problem is presented in Figure 5.12.

Figure 5.13 shows a comparison between the elevation of the phreatic surface (above

the fill surface) calculated using Minefill-2D and that calculated according to Darcy’s

law, against time.

Figure 5.13 indicates that the change in phreatic surface elevation determined using

Minefill-2D is consistent with that calculated using Darcy’s law. This demonstrates that

the algorithm controlling the movements of the phreatic surface above the fill surface

and the component controlling flows due to gravitational forces, are providing accurate

results.

5.5.2 Comparison with CeMinTaCo

Because CeMinTaCo is a modification of the “well tried” tailings consolidation

program MinTaCo, which takes account of the influence of cementation on the

consolidation process, this provides an excellent basis to validate the performance of the

new finite element program Minefill-2D. Furthermore, because CeMinTaCo uses a

Lagrangian coordinate system and takes full account of yielding in one-dimensional

compression, this comparison provides an opportunity to investigate the significance of

these characteristics on the numerical results.

The material properties adopted for this comparison are those deemed typical for a

cemented paste backfill. These properties are presented in Table 5.1.

Using these properties, a one-dimensional filling situation was simulated, adopting an

impermeable base condition. This simulation involved the accretion of material at a

constant rate of 4 m/day for a period of 4 days. Figure 5.14 presents the development of

total vertical stress (σv) and pore pressure (u) at a point 2.0 m above the base against

time.


5.30

The results presented in Figure 5.14 indicate that the pore pressure calculated using

CeMinTaCo is greater than that calculated using Minefill-2D. It is also clear that the

point where the curves representing the pore pressure and total vertical stress diverge

also differs for the two models.

Examination of the output from the two models indicates that during the very early

stages of strength and stiffness development, these material properties begin to change

(i.e. reach “initial set”) at a slightly different times in the two programs. In CeMinTaCo,

the cemented strength and stiffness are dependent on the difference between the

cemented and uncemented yield surfaces in one-dimensional compression, while in

Minefill-2D the cemented strength and stiffness are independent of the uncemented

yield surface. Therefore, in CeMinTaCo during the early stages of cement hydration,

any compression of the soil matrix hardens this material and softens the cemented yield

surface, effectively merging these surfaces. However, in Minefill-2D, hardening of the

uncemented soil simply acts to increase the density and therefore increase the influence

of cementation in the next timestep.

The overall influence of this behaviour is to effectively delay the “initial set” point, but

the calculated behaviour is essentially the same beyond this point. This is demonstrated

in Figure 5.15, which again presents the calculated pore pressure and vertical stress, for

the one-dimensional accretion of material at 4 m/day, but in this case the initial set point

for the Minefill-2D example has been delayed an additional 0.4 days. By making this

adjustment the results from the two programs are equal.

While this “initial set” point has been shown to have an influence on the result of the

modelling, and is therefore an aspect that should be addressed, it is suggested that

curing samples under effective stresses induced by self desiccation (as suggested in

Chapter 3), and adopting the measured “initial set”, Minefill-2D can provide a good

representation of the behaviour.

5.5.3 Stope mesh details

Element size

To investigate the influence of mesh size on the modelling results, and choose an

appropriate mesh size for the sensitivity study in Chapter 7, a convergence study was


5.31

undertaken. This study adopted typical paste backfill material properties and involved

identical simulations of the filling process using Minefill-2D in plane strain mode with

various mesh sizes. The stope geometry simulated was 10 m wide and 40 m tall with a 6

m high drawpoint, 5 m in length. Mesh sizes adopted in the analysis included:

• A coarse mesh consisting of 5 elements horizontally across the stope width, 2

elements along the drawpoint length, 3 elements representing the drawpoint

height and 20 elements to represent the stope height. This mesh is presented in

Figure 5.16a.

• A medium mesh consisting of 10 elements horizontally across the stope, 5

elements along the drawpoint, 6 elements representing the drawpoint height and

50 elements representing the stope height. This mesh is presented in Figure

5.16b.

• A fine mesh consisting of 40 elements horizontally across the stope, 10 elements

representing the drawpoint length, 10 elements representing the drawpoint

height and 80 elements representing the stope height. This mesh is presented in

Figure 5.16c.

These meshes were used to simulate the same filling sequence, which consisted of

filling the stope at a constant rate of 0.5 m/hr for 12 hours, at which time filling was

suspended for 24 hours prior to a second filling at a constant rate of rise of 0.5 m/hr

from 6 m to the top of the 40 m high stope. In this analysis, all boundary nodes (apart

from those along the fill surface) were fixed against displacement in both the vertical

and horizontal direction. Nodes along the barricade boundary were maintained at zero

pore pressure.

The calculated pore pressure, at the centre of the stope floor is plotted against time for

each of the meshes in Figure 5.17, while the calculated barricade stress is plotted against

time for each mesh in Figure 5.18. These figures indicate that the coarse mesh produces

considerable different results to the other meshes, but the results from the medium and

fine mesh appear very close.

To investigate the influence of element size throughout the mesh the vertical total stress

(σv) contours at the completion of filling for the coarse, medium and fine meshes are


5.32

shown in Figures 5.19 a, b and c respectively. Again, comparison of these images

indicates that the coarse mesh produces significantly different results to the fine and

medium mesh. Figures 5.19 b and c are very similar with the fine mesh indicating

slightly higher stresses than the medium mesh.

The accurate results with the medium sized mesh are due to the relatively low pore

pressure and effective stress gradients throughout the simulated geometry.

Considering the minor variation in results between the fine and medium mesh and the

significant difference in computational time, it is considered most suitable to adopt the

medium mesh in the remainder of the calculations in this chapter as well as the

sensitivity study presented in Chapter 7.

Interface behaviour

In Minefill-2D, the interface between the fill and surrounding rockmass was represented

using conventional elements where the boundary nodes (corresponding to the interface)

are fixed against displacement in both directions. The significance of deformation at this

interface is evident in Figure 5.19, where the σv contours change sharply in direction

near the stope boundaries, indicating a stress discontinuity. Reducing the element size

reduces the region of influence such that it is difficult to identify shear planes in the fine

mesh. As shear planes are most likely to form immediately adjacent to the interface, the

boundary elements were reduced in size so that any yielding was concentrated at the

interface. Apart from the influence on the stress transfer to the surrounding rockmass,

the development of shear planes in these elements would have minimal influence on the

overall consolidation behaviour.

An alternative approach would have been to introduce interface elements to concentrate

any yielding along a defined plane. This may be considered in future developments.

5.5.4 Comparison with in situ measurements

To assess the ability of Minefill-2D to capture the important aspects associated with the

mine backfill deposition process, the model output was compared with in situ

measurements. In this analysis, the calculated pore pressure at the centre of a stope is

compared with actual pore pressures measurements during filling at site Paste Fill A


5.33

(PFA) in August 2007. This is the same material used in the sensitivity study presented

in Chapter 7.

The plan dimensions of the stope were 15 m x 18 m and 50 m tall. Using data collected

on the log sheets from the paste-fill plant, the volume of placed material was combined

with the actual stope cross sectional area (at various elevations) to determine the

elevation of the fill surface against time. This approach is considered valid as this

material typically does not experience significant volumetric changes during placement

and subsequent consolidation. The filling sequence consisted of filling the first 10 m at

a vertical rate of rise of 0.2-0.5 m/hr prior to a 24-hour rest period. After the rest period,

filling continued at a vertical rate of rise of 0.3-0.6 m/hr until the stope was filled. It

should be noted that the rate of rise adopted in the modelling was varied to match the

actual rate for each individual layer.

While the axi-symmetric geometry could have been more appropriate to represent the

stope geometry, the plane strain version of Minefill-2D was adopted to allow the

drawpoint to be represented. Based on a numerical comparison between an equivalent

axi-symmetric and plane strain stope, an 11 m wide plane-strain stope was deemed

appropriate to represent a stope of 15 m x 18 m plan dimensions.

Pore pressure (ucl) in the field was measured using a vibrating wire piezometer that was

installed on the floor of the stope prior to the commencement of filling. Readings were

taken on an automatic data logger at 2 minute intervals throughout the filling process.

The material used to fill the stope was PFA mixed with 3.1% cement and delivered at a

density of 75% solids by weight. Material properties used in the back analysis were

derived using a 1-D compression test, a hydration test and a triaxial test. Laboratory

testwork was actually carried out for PFA material at the same density (75% solids by

weight) but containing 3% cement, prior to field testing (Helinski et al., 2007). Due to

the close match of the tested material to the actual mix adopted, further testing was not

undertaken with 3.1% cement. The material properties adopted for the model are

presented in Table 5.2.

Figure 5.20 presents a comparison between the measured pore pressure and that

calculated using Minefill-2D. Also shown in Figure 5.20 is the total vertical stress (σv)

that would be applied to the stope floor if no arching occurred.


5.34

Because of the low permeability and stiffness of the PFA material (in the uncemented

state) soon after placement, ucl initially increases at the same rate as σv. This is an

indication that no consolidation is occurring, and that the fill mass is fully saturated and

it also provides confidence that the vibrating wire piezometer is fully saturated, and

measuring water pressures accurately.

Soon after the material reaches “initial set”, ucl diverges from σv. However, as fill

continues to be deposited, and the increase in ucl due to the accretion of material is

greater than the reduction from consolidation, ucl continues to increase. After 35 hours,

filling stops, but as consolidation continues ucl decreases rapidly.

When filling resumes (at 59 hours), there is an increase in ucl, but as filling extends up

into the stope, some of the fill self weight is redistributed to the surrounding rockmass.

As a result, the incremental increase in σv at the piezometer location reduces. This

results in ucl plateauing and then reducing at the later stages of filling.

Overall, Figure 5.20 indicates that using independently-determined material properties

Minefill-2D provides a very good representation of the pore pressure in the centre of the

stope floor during filling, which indicates that Minefill-2D appears to be representing

the consolidation behaviour of a cemented paste backfill accurately.

5.5.5 Investigation of the arching mechanism

A study was undertaken using Minefill-2D to investigate the significance of the arching

mechanism in a typical mine backfill scenario. Minefill-2D was used to simulate a 13 m

wide, 40 m tall plane-strain stope that was filled at a constant rate of rise of 0.4 m/hr.

The material properties adopted in this study where considered typical for a cemented

paste backfill and were the same for both scenarios analysed. These properties are

presented in Table 5.3. To investigate the significance of stress redistribution onto the

surrounding rockmass (“arching”), analysis was undertaken assuming boundary nodes

that were fully fixed in both directions (“fixed BC”) and boundary nodes that were fixed

against horizontal displacement but free to displace in a vertical direction (“free BC”).

The fixed-BC and free-BC cases are illustrated in Figure 5.21a and b, respectively.

The calculated pore pressure (u) and total vertical stress (σv) on the stope centre line 1 m

above the stope floor are plotted against time during filling in Figures 5.22 for both


5.35

cases. Also shown in Figure 5.22 is the vertical total self-weight stress from the

overlying fill calculated assuming no arching.

Figure 5.22 shows that during the early stages of deposition both u and σv are equal to

the vertical self-weight stress for both cases. This is because there is no consolidation,

and even with consolidation the ratio of fill height to width is insufficient to create any

noticeable stress redistribution away from the centre of the stope. After about 12 hours,

u diverges from σv (indicating consolidation) but the ratio of consolidated fill height to

width is insufficient to create a stress redistribution. After 30 hours, 12 m of fill is in

place and, of this, the bottom 6 m has achieved a considerable amount of consolidation.

In the fixed-BC scenario, the rate of increase in σv is less than that for the free-BC case,

because some of the applied vertical stress from the accretion of fill material is

redistributed to the fixed boundary (which represents stiff rockmass) as “arching”. It is

interesting to note that, even though the consolidation characteristics are the same for

both scenarios, the calculated u values also diverge at this point. This is because

“arching”, which is occurring in the fixed BC case, is reducing the amount of total stress

transferred to the stope floor during the accretion of additional material.

Finally, it is interesting to note that in the free-BC case, σv is not equal to the total self-

weight stress, as would be expected in a true one-dimensional case. The reason for this

result is a stress redistribution that is occurring around the drawpoint opening. This

stress redistribution acts to spread some of the vertical stress around the drawpoint

opening, which actually reduces σv in the centre of the stope floor. This will be

discussed in further detail below.

Contours of σv at the end of filling for the fixed BC and free BC case are presented in

Figures 5.23a and b respectively. In addition, the σv along the centreline for both cases

and that due to self-weight stress without arching is presented in Figure 5.24.

Comparison of these figures indicates that for the upper 10-15 m, the total vertical stress

for both scenarios is approximately the same. This is a consequence of reduced

consolidation in this area and an insufficient height-to-width ratio to generate “arching”.

But progressing further from the top of the stope, the contour plots are significantly

different. Figures 5.23a and 5.24 indicate that in the fixed-BC case, σv (along the centre


5.36

line) remains relatively constant at approximately 200 kPa for the entire height of the

stope. This is an indication that significant arching is occurring.

Figures 5.23b and 5.24 indicates for the free-BC case no “arching” occurs throughout

the stope, resulting in an increase in stress with depth that is equal to the self-weight

stresses. Approaching the drawpoint, the rate of stress increase with depth reduces,

which is a consequence of arching around the relatively soft drawpoint opening. Even

though stress cannot be transferred vertically along the stope walls, a semi-circular

“stress arch” is established between the corner of the stope floor (opposite the

drawpoint) to above the drawpoint, as illustrated in Figure 5.23b.

This section has demonstrated that stress redistribution to the surrounding rockmass can

make a significant contribution to reducing the vertical stress in a typical mine backfill

stope. Two extreme cases were presented, but the trends are applicable for stopes of

different plan dimensions. As the stope plan area increases, the situation tends towards

the free-BC case,where little arching occurs, while a reduction in stope plan area would

cause the result to trend towards the fixed-BC case, or, in the case of even narrower

stopes than that presented, would promote additional stress redistribution leading to

even lower vertical stresses.

5.6 CONCLUSION

This chapter has presented the basis of the two-dimensional cemented tailings

consolidation program Minefill-2D. The program provides results that are consistent

with well-established analytical solutions to drainage-, consolidation- and cementation-

type problems. When compared with in situ monitoring data, Minefill-2D was shown to

provide a very good representation of the mine backfill deposition process. Overall, this

assessment provides confidence that Minefill-2D is performing appropriately and can be

used to represent the mine filling process.

Finally, a brief study was undertaken to investigate the arching mechanism in a typical

mine backfill situation. This study revealed that stress “arching” to the stiff surrounding

rockmass can make a significant contribution to reducing vertical total stresses in a

typical mine backfill stope.

Mechanics of Mine Backfill Matthew Helinski Centrifuge Modelling The University of Western Australia

6.1

CHAPTER 6

CENTRIFUGE MODELLING

6.1 INTRODUCTION

A centrifuge modelling experiment was undertaken to demonstrate experimentally some

of the points that have been made in this thesis and to verify the performance of

Minefill-2D for representing the consolidation and arching processes in a cementing

backfill. In this experiment, a 3-D stope was represented by a cylindrical container – i.e.

an axi-symmetric representation. This axi-symmetric geometry was chosen for practical

experimental reasons outlined later, but also because the axi-symmetric geometry could

be modelled numerically using Minefill-2D.

Centrifuge modelling (Schofield 1980) is an experimental technique commonly adopted

in geotechnical research. The concept behind centrifuge modelling is that by rotating a

scale model, the centrifugal forces increase the gravitational forces, increasing the stress

levels within the soil mass. By increasing the gravitational forces the model size can be

proportionally reduced while still creating an equivalent self-weight stress distribution.

In soil mechanics, it is important to reproduce similar stress conditions, as soil behaves

differently (particularly with respect to volume changes during shearing) under different

stress levels. In the language of centrifuge modelling, a centrifuge imposes an

acceleration level of N times the acceleration due to the earth’s gravity (g) – i.e. an

acceleration of Ng. Provided the soil in the model is of the same density as that in the

prototype, an acceleration of Ng increases the unit weight by a factor of N, such that at a

depth z in the model, the vertical stress is the same as that at a depth Nz in the prototype.

The factor N is therefore thought of as being the length scaling factor of the model test.

Since the time-scale for consolidation depends on the square of the drainage path length,

the time for consolidation in the model is N2 times faster than in the prototype.

Therefore, the centrifuge is an ideal tool for investigating problems involving

consolidation. However, in this case, the interest is in consolidation and cement

hydration in mine backfill, where the time-scales of the two processes are similar, and

hence where these two processes are coupled. However, unlike for consolidation, the

time-dependency of cement hydration does not depend on any length scale, and hence


6.2

the time for hydration in the prototype is not reduced in the model. Therefore, if the

time-scales of consolidation and hydration are similar in the prototype, they cannot be

similar in a centrifuge model in which the same materials are used, and therefore the

coupling between these processes cannot be studied directly in a centrifuge model.

The aim of the centrifuge experiment was to investigate the interaction between

consolidation and the total stress distribution for a consolidating soil undergoing

cementing in a model that represents an idealised stope. This test specifically focused on

how consolidation influenced the stress transferred through the soil mass and that

transferred as shear to the surrounding stiff container. This concept is fundamental to all

of the work discussed in this thesis.

The aim of this work had originally been to conduct an experiment that coupled the

time-dependent processes of loading, consolidation and cement hydration. Coupling of

these processes proved to be impossible due to the small scale of the model, as

explained above. Although the stress field could be scaled up in the experiment, the

consolidation time was still dictated by the actual drainage path length in the model.

This created very high hydraulic gradients that accelerated conventional drainage-type

consolidation, such that the time-scale for consolidation was very much less than that

for hydration. As a result, the material completely consolidated prior to the

commencement of hydration.

6.2 EXPERIMENTAL APPARATUS

The experimental apparatus is designed to capture the important aspects relating to the

distribution of stress around a stope during the placement of fill material. A schematic

showing a section view of the apparatus is presented in Figure 6.1.

The apparatus consists of a hollow cylinder (620 mm high and 180 mm in diameter with

an average wall thickness of 6 mm), machined on the inside to provide a rough interface

with the fill material. The cylinder is fitted with six axial and six hoop Wheatstone

bridge strain-gauge sets spaced at 100 mm centres along the vertical axis of the

cylinder. Each strain-gauge set consists of 4 gauges spaced at 90° intervals around the

cylinder circumference. The readings from each of the strain gauges in the set are


6.3

averaged to provide the value at that particular elevation. The Wheatstone bridges are

completed in each case by external resistors.

The purpose of the strain gauges is to measure the hoop and axial strains in the cylinder.

As will be discussed later, the axial and hoop strains can be combined to determine the

axial and hoop stress in the cylinder. As the strain gauges are sensitive to any

temperature variations, each strain gauge site is fitted with a thermocouple for ongoing

temperature measurements. Photographs of the strain gauged cylinder are shown in

Figures 6.2 (a) and (b).

A “floating” base is inserted into the bottom of the cylinder. This base fits into a smooth

section of the cylinder to ensure a water-tight O-ring seal. The base rests on three

loadcells that measure the load carried by the base throughout the test. A drainage hole

is drilled into the centre of the base, with a filter placed immediately above this surface.

The drainage hole is connected to a pore pressure transducer to monitor the change in

pore pressure at the base location throughout the experiment. A photograph of the base

arrangement showing the floating base, loadcells and the base stand is presented in

Figure 6.3.

The purpose of the floating base resting on stiff loadcells is to provide a true measure of

the stress transferred vertically through the fill mass to the base. Due to the high

stiffness of the base loadcells, the displacement of the “floating” base is negligible,

relative to the soil stiffness. This boundary can therefore be considered as being rigid,

and the loads measured by the loadcells considered equal to those placed on a rigid

boundary, such as the base of a stope.

It would have been useful to also measure the stresses at discrete points within the fill

mass. However, the measurement of stress within a soil mass is very difficult, since this

generally requires inclusion of transducers with different relative stiffnesses. As

discussed in Sections 2.2, this is particularly problematic in cemented materials, where

the soil stiffness can become significantly greater than the diaphragm of an earth

pressure cell. These problems have been well documented by authors such as Clayton

and Bica (1993), and Take and Valsangkar (2001).


6.4

During testing, the experimental apparatus was placed within an aluminium “strong

box”, which was mounted on the swinging platform of the geotechnical centrifuge.

Figure 4 presents a photograph of the apparatus in place on the centrifuge.

6.3 CALIBRATION

The process of calibrating the load cells and strain gauges attached to the cylinder walls

was carried out on the centrifuge, where known weights were accelerated to known

levels, to create a known force (or stress). Details of this calibration process are

presented below.

Base readings

All of the model testing discussed later was carried out at 100g. Therefore, the first

stage of calibration involved placing the empty cylinder on the centrifuge and

accelerating the centrifuge to 100g. The increment of strain measured on each

instrument when ramping up from 1g to 100g was due purely to the weight of the

apparatus itself. This value was deducted from all subsequent experimental results

recorded in the model tests. The empty apparatus was also subjected to different g-

levels to determine base-line readings to be deducted from calibration measurements at

different g-levels.

Loadcell calibration

For the calibration of the base loadcells, various weights were placed on the floating

base and the centrifuge accelerated to 100g. Knowing the weight and the radius to the

weight as well as the angular velocity, the force could be calculated. The force

increments were then used to form a linear correlation with the loadcell output.

Calibrating the loadcells using the centrifuge rather than at 1g meant that the same

logging system as that used in the experiment was used as well as taking into account

any friction loss between the O-ring and cylinder.

Strain gauges

One of the potential concerns regarding the strain gauge output was the influence of

temperature on the output. As only half Wheatstone bridge strain gauges were used in

either direction, all bridge outputs had to be adjusted for temperature changes. To

calibrate for the effect of temperature, the cylinder was filled with warm water (at a


6.5

temperature of 40°C) and left stationary (at 1g) overnight. During this period, the

cylinder temperature (as measured by the thermocouples mounted on the outer surface

of the cylinder at each site) and bridge output was logged. Due to the high thermal

conductivity of the aluminium cylinder, this temperature measurement was considered

representative of the average cylinder temperature.

Temperature measurements indicated that the water initially heated the cylinder to 40°C

and overnight the cylinder temperature reduced to 20°C. As the stress conditions

remained constant over this period the strain gauge half bridges could be calibrated for

temperature variations. This calibration was then used to correct the bridge output for

temperature variations throughout the calibration and testing stages.

The strain gauges used were manufactured from aluminium and as the cylinder was also

aluminium the temperature correction was minimal.

As strains can be linearly related to the strain gauge electrical resistivity (via a gauge

factor) and strains can be linearly related to applied stresses or forces the calibration and

the interpretation strategy adopted in the study was to simply relate the strain gauge

voltage output to an applied force or stress.

To calibrate the apparatus for axial force (F), a top cap was placed over the empty

cylinder and various weights were stacked onto this top cap. Once the weights were in

place, the centrifuge was accelerated to 50, 100, 150 and 200g to vary the axial force

applied to the cylinder. This process applied an axial force (F) without any change in

internal radial pressure (P). For calibration of radial stress the cylinder was filled with

water before applying 50, 100, 150 and 200g. After deducting the influence of the

cylinder self-weight stresses, this procedure provided an increase in radial pressure (P)

without changing the axial force (F).

When applying only an axial force (F) a voltage change was measured across the axial

and hoop bridges. If we denote the axial and hoop bridge voltage change as VAF and

VHA, respectively these can be related to F via calibration factors AF and HF in

accordance with:

( )FAF AFV .= ( )FHA HFV −= . (6.1)


6.6

By accelerating the water-filled container an internal pressure (P) is generated which

induces axial and hoop bridge outputs of VAP and VHP respectively. After deducting the

apparatus self-weight voltage changes, P can be related to the axial and hoop bridge

outputs (VAP and VHP respectively) via calibration factors AP and HP in accordance with:

( )PAP APV −= . ( )PHP HPV .= (6.2)

The changes in bridge voltages due to both an axial force and radial pressure are given

by:

APAFA VVV += HPHAP VVV += (6.3)

Substituting 6.1 and 6.2 into 6.3

−−

=

P

F

HH

AA

V

V

PF

PF

H

A

(6.4)

Using this approach calibration factors AF, AP, HF and HP were derived.

To interpret the experimental results Equation 6.4 must be rearranged such that F and P

can be derived from the measured values of VA and VH. Inverting the matrix of

calibration factors and rearranging Equation 6.4 gives:

−=

H

A

FF

PP

PFPF V

V

AH

AH

AHHAP

F 1 (6.5)

Therefore, the bridge outputs were simply adjusted for temperature variations and the

apparatus self-weight prior to direct substitution into Equation 6.5 to calculate the axial

force and radial stress throughout the experiment.

Pore pressure transducer

During the calibration with the water-filled cylinder, the standpipe pore-pressure

transducer was in place. From the calculated water pressure at the transducer location,

the calibration factor supplied with the transducer was verified.

The previously-described calibration routine provided suitable calibration factors for the

various instruments. This calibration yielded excellent consistency, providing

confidence in the performance of the data collection system.


6.7

6.4 EXPERIMENT

Only one experiment was undertaken in this investigation. The aim of this experiment

was to investigate the interaction between consolidation and stress distribution in a

typical mine backfill situation.

6.4.1 Material

In a centrifuge model of thickness d representing a full-scale prototype of thickness D

(where d = D/N, and N is the acceleration multiplier), the time-scale for consolidation is

reduced by a factor N2 compared to the time-scale for the prototype. However, the

time-scale for hydration is unaffected by the g-level, so that the time until initial set, and

the total time for hydration, are the same for the model and the full-scale prototype.

Thus, if the time-scales for consolidation and hydration are similar in the full-scale

prototype, they are completely different for the model, assuming that the same material

is used in the model as in the prototype.

In an effort to prolong the consolidation time (with the aim being to investigate the

interaction of consolidation / stress arching and cement hydration), a material with a low

coefficient of consolidation was required, as the use of conventional mine tailings (even

a fine grained paste fill) would result in very rapid consolidation at the scale of the

centrifuge experiment. In order to prolong the consolidation rates, commercially-

available kaolin clay was adopted for this test.

The aim of the experiment was to investigate the interaction of the loading,

consolidation and cementation time-dependent processes. Therefore, cement was added

to the kaolin mix. Due to the high compressibility of the kaolin clay and the high water

contents required to achieve a flowable mix, 25% cement was required to achieve an

appropriate development of stiffness with time. Without sufficient cementation, it would

have been difficult to identify the influence of cementation on the overall consolidation

behaviour.

To maximise the strength gain for minimum cement content, and minimise the material

permeability, the water content was maintained at the minimum level that the mix

would be sufficiently free flowing to remove entrained air. The water content adopted


6.8

was 62%, which corresponded to a placed void ratio of 2.20, assuming fully saturated

conditions.

As will be shown in this chapter, these high cement contents altered the coefficient of

consolidation such that consolidation was complete prior to the onset of initial set. Thus,

even with the use of the kaolin clay, the interaction of consolidation and hydration could

not be investigated in this experiment. Nevertheless, some interesting results are

presented.

6.4.2 Experimental procedure

The experiment involved filling the cylinder with the kaolin/cement/water mix in two

layers. The first of the layers was 250 mm high and the second 240 mm high.

Prior to the placement of the first layer, 5 mm of water was placed in the base of the

cylinder to assist with the removal of air during the filling process. The first layer was

placed in 5 sub-layers, each 50 mm high, with each layer being tamped 20 times to

ensure that all entrained air was removed. After placement of the first layer, water was

added above the material. This water filled the cylinder until it reached the overflow

valves at the top of the cylinder, where it was directed out of the “strong box”. The

water level in the cylinder was kept constant by continually adding water to maintain an

overflow, to make up for any water lost via evaporation. The high water level also

provided a back pressure within the soil, which assisted with ensuring full saturation

throughout the consolidation period. With the first layer in place, the centrifuge was

ramped up to 100g and this was maintained for 20 hours.

After 20 hours the centrifuge was stopped, resulting in a total stress reduction in the soil

at all depths. Initially the total stress reduction created an equivalent reduction in pore

pressure, and therefore there was no change in effective stress. But due to the short

drainage path, and increased material stiffness, stopping the centrifuge allowed the

negative pore pressures to increase to hydrostatic levels at 1g. This led to a reduction in

effective stress.

Should the total stress again be increased (through ramping up the centrifuge), the stress

distributed to the surrounding cylinder would be different to that before ramping down,

as there has been a change in shear stiffness at the soil / cylinder interface that was


6.9

brought about due to cement hydration (this was demonstrated numerically by Rankin,

2004) . To remove the influence of any changes in stress distribution from the stress

cycling, the centrifuge was again ramped up to 100g where new baseline readings were

taken, which were subsequently used to determine the incremental change in stress due

to the application of the second layer.

A second layer of material (with the same mix proportions as the first) was then added

above the original material. This layer was 240 mm thick and was placed in the same

way as described for the first layer. The centrifuge was again ramped up to 100g and the

material was allowed to consolidate until equilibrium was achieved.

6.4.3 Experimental results

The results of the experiment have been divided into two sections, namely Stage 1

loading and Stage 2 loading. Stage 1 loading contains data collected during the

consolidation of the initial layer and Stage 2 loading contains data gathered during the

placement and consolidation of the second layer.

Stage 1 loading

During the placement of the first layer, the relationship between degree of consolidation

(as measured by the base pore pressure measurement) and the distribution of total stress

around the cylinder was investigated. These results are presented in Figure 6.5, which

shows the vertical force resulting from the soil and overlying water weight within the

cylinder (“Total soil force”), as well as the total force measured on the base load cells

(“Base load cells force”) and the cylinder (wall) axial load (“Cylinder axial force”)

plotted against time. Also plotted on the right axis of Figure 6.5 is the measured pore

pressure at the base of the cylinder (“Base u”), plotted against time.

Initially, after the material is placed and the centrifuge reaches the operating speed, the

measured pore pressure at the base of the cylinder was 600 kPa, which corresponds to

the total self-weight stress of the overlying material (assuming no arching). This

indicates that at this stage, the material is fully saturated and in an undrained state (i.e.

no consolidation has occurred). It can also be seen that initially the entire load is being

transferred through the saturated soil to the base loadcells, and no arching is occurring.

This is verified by the fact that no load is transferred axially through the cylinder (apart

from the cylinder self-weight).


6.10

As consolidation takes place (indicated by the reduction in base u), there is a gradual

reduction in load measured on the base and an increase in the axial load on the

surrounding cylinder walls. This demonstrates that without consolidation there can be

little arching, but as consolidation occurs (even with a very low-strength clay material)

arching can create a significant amount of stress distribution onto the surrounding

cylinder.

At approximately 2.25 hours, the pore pressure at the base of the cylinder has reached

hydrostatic levels, and the system is therefore in equilibrium at this stage. As the pore

pressure reaches a constant value, there is no further change in effective stress and no

further change in any other measurements. This demonstrates that it is consolidation,

and not cement hydration bond strength, that is most important for arching.

Stage 2 loading

During the second loading stage, a 240-mm layer of slurry was placed over the original

layer. At the time of placement of the second layer, the original layer had been allowed

to cement to an unconfined compressive strength of approximately 300 kPa. The

incremental changes in pore pressure, base stress and axial stress that resulted from the

application of this second layer and subsequent ramping back up to 100g are presented

in Figures 6.6 and 6.7.

Figure 6.6 shows an incremental increase of 95 kPa in the pore pressure at the base of

the cylinder. The total vertical stress generated by the new layer was 105 kPa, so even

after developing a significant cemented strength, most of the applied load is still being

supported by the water phase and not being distributed to the surrounding cylinder

through arching.

Figure 6.7 shows the increment of force applied from the second layer (“Applied force

increment”) as well as the incremental change in force measured by the base loadcells

(“Base loadcells force”) and that measured as axial force in the cylinder (“Cylinder

(wall) axial load”). The results indicate that even with cemented material in the lower

part of the cylinder (which is expected to have qu in excess of 300 kPa), immediately

after placement almost all of the applied stress is transferred to the base. But as

consolidation takes place (which is indicated by a reduction in base u) force is

transferred off the base and onto the surrounding cylinder.


6.11

Using the strain gauges at the #5 location, the total horizontal stress increment (“∆σh

#5”) applied to the cylinder was monitored and is plotted, using the right hand axis, in

Figure 6.7. This strain-gauge set was installed 80 mm above the floating base, making

the location adjacent to the cemented layer (Layer 1). The measurements indicate that

immediately after the placement of the second layer, the increase in horizontal total

stress is 100 kPa, which is almost equal to the applied total vertical stress (105 kPa).

Therefore, even within the cemented mass, the horizontal stress increase is

approximately the same as the applied vertical stress if no consolidation takes place.

But, as consolidation takes place, σh reduces significantly such that after complete

consolidation ∆σh reduces to approximately 30 kPa, or 30% of the applied total stress

increment.

6.5 NUMERICAL BACK ANALYSIS

As explained previously, it was not possible to conduct a centrifuge experiment in

which the time-scales of consolidation and hydration would be similar, and hence it was

not possible to study the entire interaction of mechanisms. Nevertheless, the experiment

has shown an interesting interaction between consolidation and the distribution of stress

around a stope-shaped container. The purpose of this section is to use the numerical

program (Minefill-2D) to simulate the consolidation behaviour, and replicate the

distribution of stress that was measured during the experiment.

6.5.1 Material characterisation

Consolidation in Stage 1 of the experiment was primarily conventional drainage-type

consolidation (rather than self desiccation), so back analysis of the results is most

sensitive to the consolidation characteristics of material in an uncemented state. For the

purposes of the numerical modelling, the one-dimensional consolidation properties of

the material were determined using a Rowe Cell consolidation test.

The Rowe Cell is a one-dimensional loading apparatus for measuring the consolidation

characteristics of soil. Load increments are applied via a flexible membrane, rather than

via a solid piston, as in a standard oedometer apparatus. With the Rowe Cell setup used

at UWA, the permeability can be directly determined at the end of each loading

increment. The test is carried out using one-way drainage, with the pore pressure


6.12

response at the undrained boundary being measured directly. The test is performed

under elevated back pressure, which helps ensure full saturation (and also ensures fast

response in the base pore pressure transducer).

The material used in the element testing was identical to that used in the centrifuge

experiment. The material consisted of 75% commercially available kaolin clay and 25%

ordinary Portland cement, by dry weight, which was mixed to a water content of 62%.

Axial stresses of 220, 250, 300, 350, 400, and 500 kPa were applied with a constant

back pressure of 200 kPa. Throughout the consolidation period, the pore pressure at the

base (the undrained end of the sample) and the settlement of the sample were measured

to determine the confined modulus and permeability over a range of densities.

Direct permeability measurements were taken by establishing a hydraulic gradient

across the sample after completion of consolidation under axial effective stresses of 50,

100, 200 and 300 kPa.

The results of these tests are presented in Figures 6.8 and 6.9. Figure 6.8 presents the

relationship between applied vertical effective stress and void ratio, and Figure 6.9

presents the relationship between permeability and void ratio. Also presented in these

figures are the material relationships that were adopted in the numerical back analysis.

While the relationship between vertical effective stress and void ratio departs from the

experimental results at higher stress levels, over the range of vertical effective stresses

encountered in Stage 1 of the test (0-150 kPa) the relationship provides a good

representation. Note that normally a linear relationship in semi-logarithmic space (e –

log σ′v) would be used to describe such a relationship, but in this case the linear

relationship shown is more than adequate for the purpose required.

Stage 2 of the experiment involved the consolidation of both cemented and uncemented

layers. Therefore, the consolidation characteristics of Layer 1 (taking account of cement

hydration) at the time of the application of the second layer were required. To

characterise the cemented material properties, a hydration cell and triaxial test (after 77

hours of hydration) was carried out on kaolin with 25% added cement.

Using the experiments, the influence of cementation on the material behaviour was

determined. The relevant material properties are presented in Table 6.1. Figure 6.12


6.13

presents the experimental measurements of small strain shear stiffness (Go) and

unconfined compressive strength (qu) as well as the relationship assumed in the back

analysis plotted against time. After 22 hours of hydration (the time when the second

layer is applied in the centrifuge test) the material is expected to have a Go of 180 MPa

and a qu of 300 kPa. In addition, an internal friction angle of 23º (Randolph and Hope,

2004) was adopted, assuming that the friction response was in accordance with that of

pure kaolin.

One aspect that complicates the derivation of appropriate cemented material properties

in Stage 2 is the significant density change that occurs due to conventional drainage-

type consolidation in Stage 1. Any density increase would lead to higher cement-

induced strength/stiffness than that measured in the element test where no (drainage-

type) consolidation took place. To address this complexity, the stiffness and strength

results were extrapolated to different densities using the exponential relationship

between void ratio and strength that was defined in Section 3.2.3, for Cannington Paste

backfill.

To account for the effect of cement hydration on the material permeability, the

relationship between void ratio and permeability for the uncemented material was

maintained, but the influence of cement hydrate growth was taken into account via the

“effective void ratio” term as described in Section 3.3.2.

6.5.2 Numerical back analysis

The program Minefill-2D, which was presented in Chapter 5, was used in axi-

symmetric mode for back analysis of the experiment results. The material relationships

are those described in Section 6.5.1.

Figure 6.10 presents a comparison between the measured base pore pressure and that

predicted using Minefill-2D during Stage 1. This figure indicates that the experimental

pore pressure reduction is only slightly more rapid than that calculated using Minefill-

2D. This provides confidence that Minefill-2D is providing an accurate representation

of the consolidation behaviour (albeit conventional drainage-type consolidation).

Figure 6.11 presents a comparison between the experimental and numerical results for

the distribution of vertical stress between the floating base and the surrounding cylinder.


6.14

The experimental results are represented by solid lines while the numerical results are

represented by symbols. This comparison indicates that Minefill-2D provides a good

representation of the initial stress distribution as well as the redistribution of stress

during the consolidation period.

Initially, both experimental and numerical results indicate that without consolidation all

of the soil weight is transferred through the saturated soil to the floating base. But as

consolidation takes place, the force transferred to the base reduces and that transferred

through the surrounding cylinder (through arching) increases. The transfer of force off

the base and onto the surrounding cylinder continues as the pore pressure reduces (or as

consolidation takes place), but when the pore pressure plateaus, this force transfer stops.

It can be seen that the slightly faster consolidation rates measured in the experiment are

associated with a slightly faster increase in axial stress in the cylinder.

The calculated incremental change in pore pressure during Stage 2 is compared with the

experimental measurements in Figure 6.13. Again the calculated increase in pore

pressure due to the application of Layer 2 and the subsequent reduction in pore pressure

are well represented.

Figure 6.14 presents a comparison between calculated and measured incremental

changes in vertical forces acting on the floating base and transferred to the surrounding

cylinder when the centrifuge was restarted after Layer 2 was added. In addition, the

measured and calculated total horizontal stress at the strain gauge #5 level in the

cylinder is shown on the right axis. The measured results are presented as solid lines

while the calculated results are represented by symbols.

The calculated incremental change in total stress distribution slightly overestimates the

measured amount of arching. The overestimation of arching could have resulted from an

inappropriate relationship to represent the influence of density on cement-induced

strength and stiffness. This could have led to the model overestimating the actual

material stiffness, which would have promoted additional arching.

It should be noted that the bulk modulus of the material used in this experiment is at the

lower end of what would be expected in a real cemented mine backfill situation. Should

this stiffness be increased, the transfer of stress (through the cemented layer) due to the

undrained application of total stress would reduce in accordance with strain


6.15

compatibility between the soil and water phases. Strain compatibility has been taken

into account when establishing the initial conditions in Minefill-2D to address this

aspect.

6.6 CONCLUSION

This chapter has presented a centrifuge experiment that was designed to investigate the

interaction of consolidation, cement hydration and the distribution of stress. However,

where the time-scales of consolidation and cement hydration are similar in a full-scale

stope (and hence these processed are coupled), the times-scales are very different in a

reduced-scale model, since the consolidation time is reduced (by a factor N2), but the

hydration time is unaltered. Thus, it was not possible to devise an experiment where

these processes could be fully coupled. However, the results have experimentally

confirmed a number of key aspects relating to this thesis. These include:

• The distribution of stress is heavily influenced by consolidation and largely

independent of the cement-induced bond strength.

• Even in a material with an unconfined compressive strength of 300 kPa, if

saturated, the application of stress initially results in the load being supported by

the water phase, with very little arching occurring.

• Even in a material with an unconfined compressive strength of 300 kPa, if

saturated, the undrained application of vertical stress results in an increase in

horizontal total stress of equal magnitude.

• As consolidation takes place, the material is able to mobilise shear strength at

the soil/boundary interface and redistribute some of the vertical stress onto the

surrounding stiff medium.

• Minefill-2D is capable of providing a reasonable representation of the

conventional consolidation and arching behaviour, using material parameters

measured in element testing.

Mechanics of Mine Backfill Matthew Helinski Sensitivity Study The University of Western Australia

7.1

CHAPTER 7

SENSITIVITY STUDY

7.1 INTRODUCTION

The preceding chapters have described the development of a rigorous numerical model

for simulating the mine backfill deposition process. This model is based on fundamental

material properties and, through comparison with well established analytical solutions,

was shown to provide a good representation of individual mechanisms. It was

demonstrated experimentally that the model is capable of accurately coupling the

interaction between consolidation and stress development in conditions similar to those

that are likely to be encountered in a stope filling environment. This provides

confidence that the Minefill-2D program is capable of providing a good representation

of the cemented mine backfill process and that the tool can be used with confidence.

This section uses Minefill-2D to assess the sensitivity of the overall filling response to

various characteristics. The aim of this work is to understand the backfill process and

provide strategies for managing the process that are based on sound logic. Sections 7.2

involves a comparison between hydraulic and paste fill. This is followed by two

sensitivity analyses, one on material that consolidates immediately after placement

(typically hydraulic fill) and another on material that does not consolidate immediately

after placement (typically paste fill). Throughout the sensitivity analysis, emphasis is

placed on the resulting barricade loads, but the final section (Section 7.5) considers the

effect of the application of effective stress to in situ material during curing.

7.2 COMPARISION OF HYDRAULIC FILL AND PASTE FILL

In the mining industry, slurry mine backfills are commonly divided into two main

groups, paste fill and hydraulic fill. As Minefill-2D undertakes analysis using

fundamental material properties, it provides an opportunity to investigate the

relationship between paste and hydraulic fills without introducing simplifications that

“pre-empt” the final outcome.

When considered from a fundamental soil mechanics point of view, hydraulic fill and

paste fill are essentially the same product. The main difference is that hydraulic fill


7.2

generally contains less fines than paste fill. The typical consequences of this difference

are highlighted in Table 7.1

In order to investigate the significance of these characteristics on the overall filling

response, an experimental and numerical study was undertaken. This involved testing 4

different cemented mine backfills using the (previously described) hydration test,

triaxial test and Rowe Cell test to determine both cemented and uncemented material

properties. Testing was carried out on two hydraulic fills and two paste fills. Hydraulic

Fill A (HFA) is from a zinc mine, Hydraulic Fill B (HFB) is from a copper mine, Paste

Fill A (PFA) is from a gold mine tailings and Paste Fill B (PFB) is from a nickel mine.

7.2.1 Experimental results

The experimental program commenced with particle size distribution analysis of each

tailings specimen. The results of this analysis are presented in Figure 7.1. As expected,

Figure 7.1 indicates that the hydraulic fill materials have far less fines than the paste

fills.

The aim of this investigation is to assess how the tailings characteristics influence the

filling behaviour. Therefore, in order to maintain consistency, testing was carried out

with each of the materials combined with 3% ordinary Portland cement and each mixed

with water to achieve an equivalent void ratio of 0.9, assuming fully saturated

conditions. Each mix was subject to a hydration test to determine the cement hydration

properties (as discussed in Chapter 3) followed by a triaxial test to determine the

strength properties. Rowe Cell testing was also undertaken on the tailings material

(without cement) to determine properties that represent the behaviour prior to the onset

of cement hydration.

A summary of the material properties for the various fill types is presented in Table 7.2.

From Table 7.2, it can be seen that the final unconfined compressive strengths (qu-f) are

very similar for the four samples, even though the materials have different rates of

hydration (d), efficiency of hydration (Eh), and hydraulic conductivity parameters (ck

and dk). Figures 7.2 and 7.3 show how the hydraulic conductivity (k) and cohesion (c′)

evolve with time, respectively.


7.3

7.2.2 Modelling

In order to assess the impact of the various material properties on the filling process,

Minefill-2D was used (in plane strain mode) to simulate the filling of a plane strain

stope 20 m wide and 40 m high. A drawpoint height of 5 m was adopted with a

barricade offset distance of 5 m. A boundary condition of atmospheric pore pressure

was assigned along the boundary that represents the barricade. To allow direct

comparison between the various materials, a standard filling sequence was adopted.

This sequence consisted of filling the first 8 m over a 16-hour period (0.5 m/hr)

followed by a 14-hour rest period, and then filling the remaining 32 m over a period of

64 hours (0.5 m/hr).

In an actual stope, the drawpoint width is typically less than the side length of the stope,

whereas in the plane strain representation it occupies the full side length. This means

that the actual drawpoint represents a greater “choke” to outflow than the plane strain

representation. In order to account for this, the hydraulic conductivity in the drawpoint

area was halved.

Modelling was undertaken using the material properties presented in Table 7.2 to assess

the impact of tailings type on the consolidation behaviour and on the resultant barricade

stresses.

Figure 7.4 shows a plot of the total horizontal stress, developed at a point immediately

behind the barricades, for the various fill materials, using the described filling sequence.

This indicates that barricade stress reaches 108 kPa for PFA, 150 kPa for both HFB and

HFB and 240 kPa for PFB. Thus, even with fills that reach the same ultimate strength

(qu-f), stresses applied to barricades can vary significantly.

Furthermore, there is no obvious relationship between any one material property and the

resulting barricade stresses. For example, barricade loads for PFA are the lowest, even

though the hydraulic conductivities of HFA and HFB are higher, while that of PFB is

lower. Also, HFA and HFB show a faster rate of hydration (lowest d value) and a higher

efficiency of hydration (highest Eh value), when compared with the paste fill materials,

but ranks in the middle in terms of ultimate barricade stress.


7.4

The reasons for the stress variation may be better understood with reference to the

development of pore pressure at the opposite side of the stope to the barricade. This is

presented in Figure 7.5 along with the “steady state seepage pore pressure” that is

created when the water table is maintained at the fill surface and atmospheric pore

pressures are maintained at the barricade boundary. This is calculated in accordance

with the relationship presented by Helinski and Grice (2007). Pore pressures greater

than “steady state” indicate that the material has not fully consolidated, while pore

pressures equal to this value indicate that the material has completely consolidated.

This is a somewhat artificial situation, since ongoing water flow without further

addition of water to the stope would result in lowering of the water table (with the

possibility of further consolidation as the equilibrium situation changes) but it does

provide a reference for assessment of excess pore pressures.

Comparison between Figures 7.4 and 7.5 indicates that there is a clear relationship

between the development of pore pressure and the stresses placed on barricades. This is

logical, as higher pore pressures are associated with less consolidation and lower

effective stress. As discussed in Chapter 2, with less effective stress, less interface shear

strength is mobilised resulting in higher total vertical stresses in the stope. In addition,

the conversion from total vertical stress to total horizontal stress adjacent to the

drawpoint is dependent both on the proportion of the load being carried by the soil

skeleton (effective stress) and that carried by the pore water (pore pressure), in

accordance with Equation 7.1:

uKovh +σ′=σ . (7.1)

where hσ is the total horizontal stress, vσ′ is the vertical effective stress, oK is the

lateral earth pressure coefficient (≈ 0.3-0.5) and u is the pore pressure.

Therefore, if all of the total vertical stress is supported by the water phase (vu σ= ) the

vertical and horizontal total stresses would be equal, but if the pore pressure is zero, the

horizontal total stress would approximately 30% to 50% of the total vertical stress.

The other aspect to note about Figure 7.5 is with respect to the development of pore

pressure (for the different mine backfill materials) relative to the steady state seepage

pore pressure. Comparing the pore pressures for the four cases with the steady state


7.5

seepage pore pressure, it is clear that both HFA and HFB hydraulic fills exhibit close to

steady state seepage pore pressures throughout the filling process, indicating immediate

consolidation, PFB develops pore pressures that are greater than steady state seepage

pore pressures indicating that consolidation is not complete, and PFA exhibits pore

pressures that are even less than steady state seepage pore pressures. This may be more

clearly depicted in Figure 7.6, which shows the pore pressure isochrones along the stope

centre line at the completion of filling. Also shown in Figure 7.6 is the line representing

the steady state seepage pore pressures for the stope.

The reason for the three different types of behaviour is as follows:

HFA and HFB

Due to the initial high value of the coefficient of consolidation (i.e. higher permeability

and stiffness compared to the paste fill materials), excess pore pressures dissipate

immediately and the pore pressures in the fill mass are the steady state seepage pore

pressures resulting from the reduced flow area in the drawpoint. It is also interesting to

note that the efficiency of hydration for the HFA hydraulic fill is double that of the HFB

hydraulic fill but the pore pressures and barricade loads are almost identical. This

suggest that this mechanism plays little role in the consolidation of hydraulic fills.

PFA

For PFA, the initial low stiffness and low hydraulic conductivity result in very little

conventional drainage-type consolidation prior to “initial set”. Close inspection of

Figure 7.5 indicates that during the early stages of filling, pore pressures in PFA are

higher than in HFA and HFB. This is reflected in higher barricade loads during this

period. However, this material has a high propensity for self desiccation after “initial

set”, where the water volume reduction from self desiccation combines with the rapidly

increasing material stiffness to reduce the pore pressures. For higher permeability

materials, this would be counteracted by an inflow of water from above that would

restore steady state seepage pore pressures (as shown for the hydraulic fills), but for

PFA, the permeability is so low that volumes being consumed by the self-desiccation

mechanism are greater than the inflow from above. Therefore, the very steep hydraulic

gradients being generated by the low pore pressures can be maintained. This suggests


7.6

that very low pore pressures, below the steady state line, may be produced by self

desiccation in association with low hydraulic conductivity.

PFB

Like PFA, the initial value of the coefficient of consolidation of PFB is very low (i.e.

low permeability and high stiffness), and therefore drainage-induced consolidation is

insufficient to dissipate excess pore pressures. However, unlike PFA, the prosperity for

self desiccation is too low to give a significant pore pressure reduction, with the result

being significant pore pressure development. Also, even though the material is gaining

stiffness, the low permeability is preventing any conventional dissipation of excess pore

pressures. The resulting high pore pressures (low levels of consolidation) are reflected

in high barricade loads.

This situation seems to be most prominent when the tailings being used to form the

paste have high active clay content. Clay particles reduce the coefficient of

consolidation (suppressing conventional consolidation) and have also been shown to

adversely influence the cement hydration process. This is the case with PFB.

7.2.3 Comparison of hydraulic fill and paste fill

This analysis has identified two significantly different responses depending on whether

the material undergoes immediate consolidation or if very little consolidation takes

place prior to the onset of hydration. Broadly, it may be assumed that hydraulic fills

consolidate immediately while paste fills require cement hydration to achieve

consolidation, but this outcome will be dependent on both the coefficient of

consolidation and the filling rate. Therefore, both of these factors must be taken into

account when characterising the expected behaviour. One method of characterising the

combination of material properties and filling rate is through Gibson’s (1958) analytical

solution that was introduced in Section 2.2.

The following two sections describe sensitivity studies that investigate the behaviour of

firstly consolidating fills and secondly non-consolidating fills.

7.3 CONSOLIDATING FILL

This section refers to fill types that when first deposited, at the specified rate of rise,

have a coefficient of consolidation that is sufficient to dissipate any excess pore


7.7

pressures while filling is in progress. This characteristic is most commonly associated

with hydraulic fills, but is equally applicable to coarse paste fills that are placed with

low rates of rise. The analysis carried out to investigate the sensitivity of consolidating

fills has used the HFB parameters, which were presented in Table 7.2. In each case the

stope geometry simulated was a 40 m tall, 13 m wide plane-strain stope, with a 5m long

and 5 m high drawpoint. The 13 m wide plane-strain stope was selected as this

dimension is expected to provide a similar vertical stress distribution to a stope with

plan dimensions of 20 m x 20 m, which is considered typical, and the plane-strain

configuration allows the drawpoint to be represented. In most consolidating fill

situations, fill rates are often much slower than 0.5 m/hr, which was adopted in Section

7.2 for direct comparison with paste fills. Therefore, in order to provide more realistic

results, the analysis in this section is carried out using a constant fill rate of 3 m per day

or approximately 0.125 m/hr.

7.3.1 Influence of stope geometry

Stopes often have different configurations with regard to plan dimensions and the

number and size of drawpoints. Different configurations will lead to differences in the

restriction to flow at the base of the stope. This section is focused on investigating the

influence of the drawpoint restriction on barricade loads.

To represent different drawpoint restrictions the stope geometry has been maintained

constant but the drawpoint permeability was modified by an order of magnitude. This

modification has the equivalent impact as modifying the number of drawpoint openings

or the installation of drains through this region. In addition, to demonstrate the extreme

situation, an impermeable barricade was simulated.

The development of pore pressure at a point 2 m above the stope floor on the opposite

side of the stope has been plotted against time for each of these cases, in Figure 7.7.

Figure 7.7 indicates that the pore pressure at the opposite side of the stope to the

drawpoint is heavily influenced by the restriction created at the base of the stope. It

should be noted that the reduced pore pressures (at the base of the stope) coincide with a

significant change in pore pressure distribution throughout the stope rather than a

significantly different phreatic surface elevation. This point is demonstrated in Figure

7.8, which presents the pore pressure isochrones along the centre line of the stope for


7.8

the different cases. It can be seen that the phreatic surface elevation is effectively the

same for each of the cases, but the rate of pressure increase (with depth) is significantly

reduced as the restriction to flow through the drawpoint reduces (or the drawpoint

permeability increases).

The impact of the different drawpoint restrictions on barricade stress is illustrated in

Figure 7.9, which presents the total horizontal stress placed on the barricade against

time for the different cases.

Figure 7.9 indicates that the reduction in pore pressure and increase in effective stress

associated with the reduced drawpoint restriction significantly influences loads applied

to consolidating fill barricade structures. Even with the same phreatic surface elevation,

the different drawpoint restrictions can have a significant influence on the distribution

of total stress and hence on barricade loads. This is most significant in the extreme case

of the impermeable barricade. In this case there is no water flow and the resulting

hydrostatic pore pressures leads to very high barricade stresses.

This result is consistent with the analytical analysis results published by Kuganathan

(2002), who also suggested that the installation of engineered drainage systems in the

stope drawpoint can minimise barricade stresses.


To investigate the significance of changes in the permeability of a consolidating fill

material, the HFB permeability was modified by an order of magnitude in both a

positive (k=10×kHFB) and negative (k=0.1×kHFB) direction. It should be noted that,

with the change in permeability, the coefficient of consolidation remained sufficiently

large to ensure that there was no build up of excess pore pressures during filling.

Figure 7.10 indicates that, until approximately 220 hours, the material permeability has

little influence on the pore pressure that develops in a stope. At 220 hours, the high-

permeability material allows the phreatic surface to fall below the fill surface, which

leads to reduced pore pressures. But for the same phreatic surface elevation, the pore

pressures are independent of the permeability. The reason for the independence is that,

provided the permeability is sufficient to dissipate the build up of excess pore pressures,

in situ pore pressures would be dictated by the relative flow resistance between the


7.9

stope and drawpoint. Provided the relative flow resistance (between the stope and

drawpoint) is constant, for a given water table elevation, the pore pressure profile will

be similar.

Should the permeability be further reduced, there is potential to accumulate excess pore

pressures, which would change the deposition behaviour. This is discussed in Section

7.3.4.

The impact of fill mass permeability on barricade stress is presented in Figure 7.11,

which shows the development of barricade stresses against time for the various cases.

As with the pore pressure, it can be seen that for the same phreatic surface elevation the

barricade loads remain largely independent of permeability.

It is interesting to note that, for the k=10×kHFB case, when the phreatic surface falls

below the fill surface at approximately 220 hours, there is an associated significant

decrease in barricade stress. The reduction in pore pressure is associated with an

increase in effective stress, which acts to mobilise more shear stress (within the fill

mass) and reduce the total stress transferred to the barricade.


The following sensitivity study investigates the influence of cementation on the

barricade loads in a consolidating fill. Again the HFB material is adopted but the

cement content is varied between 0%, 1.5%, 3% and 8%.

Figure 7.12 shows the development of pore pressure at the base of the stope (on the

opposite side of the stope to the barricade) against time for the different cement

contents. Based on the results, it appears that the development of pore pressure against

time in a consolidating fill is largely independent of cement content. This is expected to

be due to the high initial coefficient of consolidation, which rapidly creates and sustains

“steady state” conditions (as discussed in Section 7.2.2). Consequently cementation is

not required in the consolidation process.

Figure 7.13 presents the development of barricade stresses in a consolidating fill mass

against time with varying cement contents. It can be seen that between cement contents

of 3 and 8 %, the presence of cementation has little influence on the calculated barricade

stresses, but as the cement content drops to 1.5 %, there is an increase in barricade


7.10

stress. The barricade stress for the 1.5% case is similar to the 0% case. This increase in

stress is a result of the weaker material (associated with the lower cement contents)

yielding at the fill/rock interface. To demonstrate this point, Figure 7.14 presents the

calculated shear stress and cohesive strength against time for an element at the interface

between the fill and the rockmass, 7 m above the stope floor. This result indicates that

with 3% cement, the cohesive component of strength is sufficient to support the applied

shear stress, and no softening occurs. But in the 1.5% cement case, there is some strain

softening and subsequent breakdown of the cementation at the fill/rock interface, which

is indicated by the reduction in cohesion from approximately 80 hours onward. Another

illustration of this cementation breakdown is shown in Figures 7.15 (a) and (b), which

show contours of cohesion for the 3.0% and 1.5% cases, respectively. Figure 7.15 (a)

shows relatively constant cohesion horizontally across the stope while Figure 7.15 (b)

shows a dramatic reduction in cohesion at the fill/rock interface.

A consequence of this softening is that stress that was previously supported in shear by

the boundary element is redistributed, increasing the vertical stress within the fill mass,

and therefore increasing the barricade stresses. The influence of strain softening on the

vertical total stress is illustrated in Figure 7.16 (a) and (b), which show vertical total

stress contours at the completion of filling for the 3 % cement and 1.5 % cement cases,

respectively. Comparison of these figures indicates that strain softening (associated with

the 1.5% case) results in a 150 kPa increase in vertical total stress at the base of the

stope.

This increase in total vertical stress does not induce an associated increase in pore

pressure, since the coefficient of consolidation is sufficient to dissipate any excess pore

pressures that are created, but this increase in total vertical stress creates an associated

increase in horizontal effective stress, which contributes to barricade stresses.

In addition to the implications of interface strain softening on barricade stress, this

mechanism should also be considered when assessing fill exposure stability (as

discussed in Section 2.2.3). For example, the assumption of a fully cohesive fill/rock

interface (Mitchell and Wong 1982) would not be valid in the 1.5% cement example,

and instead a friction-only interface should be considered when undertaking exposure

stability analysis for this case. By reducing the filling rate, such that the development of


7.11

shear strength exceeded the application of shear stress, it could be possible to avoid

yield at the interface, which would result in increased fill stability at the time of

exposure.

7.3.4 Influence of filling rate

The following section presents an investigation into the influence of placement rate on

material that might be considered to be consolidating fill. Again the HFB parameters

(from Table 7.2) have been adopted, but the rate of fill rise is varied from a constant

0.06 m/hr to 4 m/hr. The development of pore pressure is presented against time for

each of the cases in Figure 7.17.

Figure 7.17 indicates that the maximum attained pore pressure for all filling rates up to

0.6 m/hr is relatively constant at 200 kPa. However, for filling rates of 2 m/hr and 4

m/hr, pore pressures reach a higher maximum before reducing to around the same

constant value. These higher pore pressures are excess pore pressures resulting from the

higher filling rates.

Figure 7.18 presents the calculated barricade stresses against time for the different

filling rates. As with the development of pore pressure, the maximum barricade load

remains relatively constant (at approximately 130-140 kPa) up to a filling rate of 0.6

m/hr. But with the filling rates of 2 m/hr and 4 m/hr the peak barricade stress is

significantly greater. The higher barricade stresses are a result of the excess pore

pressures, which change the loading mechanism.

7.3.5 Consolidating fill: discussion

The modelling results presented indicate that aspects such as drawpoint restriction,

cement content and filling rate can influence loads applied to barricade structures for

consolidating fill. But, apart from the drawpoint restriction, barricade stresses appear

relatively constant over a range of cement contents and filling rates. It was demonstrated

that if these factors vary beyond a given thresholds, there is a “step-change”, where the

deposition behaviour is modified. Specifically, the change in mechanism involves strain

softening at the rock/fill interface and the development of excess pore pressures. The

discrete change in behaviour results in a change to barricade stresses. Therefore, when

estimating barricade stresses with consolidating fill, it is first necessary to define if the


7.12

fill/rock interface is likely to yield during deposition and secondly to define the rate of

rise that would allow excess pore pressures to develop. Provided that excess pore

pressures are not generated and the calculation of vertical stress within the stope takes

account of the fill/rock interface behaviour, barricade stresses should remain relatively

independent of these factors.

Section 7.3.4 showed that steady state seepage pore pressures are dependent on the

elevation of the phreatic surface and the restriction to flow through the drawpoint.

Helinski and Grice (2007) showed that the restriction to flow through the drawpoint can

vary significantly between stopes due to the presence of macro pores, which can

dominate the drainage behaviour through the drawpoint region.

Comparison between Figures 7.8 and 7.9 indicates a trend between barricade stresses

and the pore pressure on the floor of the stope opposite the drawpoint. To examine this

relationship, the calculated pore pressure was plotted against the barricade stress in

Figure 7.19, for each of the cases analysed in Section 7.3.1. This figure indicates a

unique relationship between barricade stress and this pore pressure. The significant

dependence on pore pressure is problematic from a design point of view (as it is

difficult to accurately predict pore pressures), but since it is very easy to measure

positive water pressure accurately, these measurements can be used to efficiently

manage filling activities.

For example, based on an assumed drawpoint restriction, the required barricade capacity

can be estimated. As the most significant assumption in the design is the drawpoint flow

restriction, pore pressure measurements can be used in operation to manage filling

operations such that the actual pore pressures do not exceed those assumed in the

design. For example, consider the case presented in Section 7.31. If the design assumes

a drawpoint resistance that is equivalent to kdp = kst, an ultimate barricade stress of 118

kPa would be expected. Applying the relationship between pore pressure and barricade

stress presented in Figure 7.19, filling should be undertaken such that the pore pressure

at the opposite side of the stope floor to the barricade does not exceed 196 kPa (the

estimated peak pore pressure for this condition). If the pore pressures increased at a rate

faster than expected, filling should be suspended prior to the pore pressures reaching

196 kPa. Filling would then continue, ensuring that this target is not surpassed.


7.13

Alternatively, should pore pressures remain low, filling could be accelerated, ensuring

that excess pore pressures are not generated. The relationship presented in Figure 7.19

can be used along with the peak pore pressure to estimate the ultimate barricade stress.

7.3.6 Consolidating fill: conclusion

Based on the consolidating fill sensitivity study, it can be concluded that the important

aspects to consider in determining barricade stress level are:

• Should the placement rate be limited to ensure that no excess pore pressures

develop, the calculated barricade loads would be largely independent of filling

rate and permeability.

• A step change in barricade stress was shown to occur depending on whether or

not the material yields at the fill/rock interface during placement. For both the

yielding and non-yielding cases, the barricade stresses are largely independent

of cement content.

• The restriction to flow through the drawpoint dictates the pore pressure

distribution within a consolidating fill stope. This pore pressure distribution

significantly influences the effective stress and therefore barricade stresses.

• For the same stope geometry with different drawpoint restrictions, a unique

relationship exists between pore pressure and barricade stress. This unique

relationship can provide a useful means of managing filling activities.

7.4 NON-CONSOLIDATING FILL

The definition of non-consolidating fill means that, during fill deposition, very little

conventional drainage-type consolidation occurs. This scenario would most frequently

be associated with paste fill, but could be equally applicable to fine hydraulic fills that

are placed at fast rates of rise.

For the purpose of the non-consolidating fill sensitivity study, PFA material properties

(from Table 7.2) were adopted. The filling sequence involved the first 8 m of material

being placed over a 16-hour period (0.5 m/hr), followed by a 14-hour rest period, and

then filling the remaining 32 m over a period of 64 hours (0.5 m/hr filling rate). The

stope geometry adopted represents a 13 m wide, 40 m high plane strain stope with a 5m


7.14

long drawpoint. Through the drawpoint the fill permeability is reduced by 50% to

represent the reduction in drawpoint flow area. The aspects that were covered in the

consolidating fill sensitivity study have been addressed here also. These include the

influence of stope geometry, permeability, cementation and filling rate.

7.4.1 Influence of stope geometry

This study involved varying the permeability of the stope drawpoint area, which in turn

varied the restriction to conventional drainage-type consolidation through this region. In

this study the drawpoint permeability was increased (kdp= 10×kstope) and decreased (kdp=

0.1×kstope) by an order of magnitude.

Figure 7.20 presents the development of pore pressure against time during filling for a

point on the stope floor on the opposite side of the stope to the drawpoint. This figure

indicates that during the early stages of filling, the pore pressure is relatively

independent of the drawpoint permeability. The reason for this is that the dissipation of

pore pressure, at the opposite side of the stope to the drawpoint, is primarily dictated by

self desiccation rather than conventional drainage-type consolidation. At the later stages

of filling, when water migrates down to the base of the stope, the restriction to flow at

the drawpoint becomes more influential on the pore pressures.

The influence of the drawpoint permeability on barricade stress is presented in Figure

7.21, which shows the development of barricade stress with time for the different cases.

This result indicates that, even during the early stages of filling, the drawpoint

restriction can influence barricade stresses. This is also the case later in the filling cycle.

This is due to the hydraulic gradient that exists through the drawpoint region. With

higher resistance to flow through the drawpoint the hydraulic gradient is steeper, which

effectively results in lower effective stresses and less stress being transferred to the

surrounding rockmass. This is illustrated in Figures 7.22 (a) and (b), which presents

pore pressure contours at the completion of filling for the “kdp=0.1×kstope” and

“kdp=10×kstope” cases respectively. Figure 7.22a shows an almost linear reduction in

pore pressure when progressing across the stope floor, but Figure 7.22b shows much

higher, almost constant, pore pressures within the stope and a very steep hydraulic

gradient in through the drawpoint. It is this pore pressure profile that creates the

difference in barricade stress.


7.15


To investigate the influence of permeability on non-consolidating fill deposition,

sensitivity modelling was undertaken using PFA material properties, but with the

hydraulic conductivity increased (k=10×kPFA) and decreased (k=0.1×kPFA) by an order

of magnitude.

Figure 7.23 presents the evolution of pore pressure with time at a point on the stope

floor at the opposite side of the stope to the drawpoint. This result suggests that

permeability significantly influences the consolidation behaviour. Soon after placement,

a reduction in permeability creates an increase in pore pressure. This is consistent with

conventional consolidation theory. But interestingly, during the later stages of filling a

reduction in permeability is associated with lower pore pressures.

The reason for this unusual response is that, after cement hydration begins to create an

increase in material stiffness, the consolidation behaviour is dictated by the self-

desiccation mechanism. If the propensity to self desiccation is high, very large hydraulic

gradients can be created in the fill mass (due to the material being at different stages of

hydration). If the permeability is low, these hydraulic gradients can be sustained,

effectively suppressing the development of pore pressures. But if the permeability is

increased, the hydraulic gradients will cause water to flow, recharging voids that were

previously depleted due to self desiccation. This will re-establish steady state seepage

pore pressures. An example of this is demonstrated in Figure 7.23 for the k=10.kPFA

case. Here the permeability is high enough for water to flow through the fill mass, and

pore pressures are dictated by the build up that occurs at the drawpoint as discussed in

Section 7.3.

Figure 7.24 presents the calculated barricade stress against time for the different

material permeabilities. The barricade stress trends closely follows those for pore

pressure, with lower permeabilities initially creating higher barricade stresses (due to a

reduction in conventional drainage-type consolidation) but as filling continues the lower

permeability material produces lower barricade stresses.


7.16


To investigate the influence of cementation on the filling response, modelling involving

PFA with cement contents of 1.5% and 4.5% in addition to the base case of 3.0% was

undertaken.

Figure 7.25 presents the development of pore pressure with time for the different

cement contents, at point on the stope floor on the opposite side of the stope to the

barricade. This figure indicates that even minor variation in cement content can have a

significant influence on the development of pore pressure within a paste-fill stope. The

significant impact is due to the increased stiffness achieved by the higher cement

contents as well as the increase in self-desiccation volumes that come about from higher

cement contents.

Figure 7.26 presents the calculated barricade stress against time for PFA with the

various cement contents. As with pore pressures, changes in cement content

significantly influence barricade stresses for non-consolidating fill. In this particular

case, an increase in cement content from 3% to 4.5% results in a barricade stress

reduction of over 50%, while a reduction in cement content from 3% to 1.5% results in

a 150% increase in barricade stress. Again, the change in barricade stresses can be

attributed to the influence of cementation on the consolidation behaviour, which in turn

influences the total stress distribution. In addition to the influence that cementation has

on the consolidation behaviour, a reduction in cement content also increases the

likelihood of yielding at the rock/fill interface. As discussed in Section 7.3.3, yielding at

the rock/fill interface can increases the vertical total stress within the stope, which

increases barricade stresses.

To investigate the influence of the interface behaviour, an analysis was undertaken

using the base case material properties (PFA with 3% cement) but in this analysis the

cohesive bond along the rock/fill interface was set to zero. The calculated barricade

stresses and pore pressure at the opposite side of the stope to the drawpoint are

presented in Figure 7.27, along with the results for the fully bonded case. Figure 7.27

indicates that yielding at the fill/rock interface can increase barricade stresses, but

unlike the consolidating fill case, this yielding is associated with an increase in pore

pressure. This is because with non-consolidating fill material the increased vertical total


7.17

stress creates an increase in excess pore pressure, and due to the low coefficient of

consolidation these pressures cannot be dissipated rapidly.

7.4.4 Filling rate

During the deposition of cemented mine backfill three different time scales interact,

these being the rate of hydration, rate of consolidation and rate of placement. In order to

investigate the influence of the third timescale (rate of placement) a series of numerical

experiments were undertaken. These experiments used PFA material with filling rates of

0.2 m/hr, 2.5 m/hr as well as the base case of 0.5 m/hr. The filling sequence adopted

involved filling the first 8 m followed by a 14 hour rest period before filling the

remaining 32 m.

The development of pore pressure, at the opposite side of the stope to the barricade, is

plotted against time in Figure 7.28. As expected increasing the filling rate caused an

increase in pore pressures. Increasing the filling rate increases the rate of total stress

application but as pore pressures are being dissipated primarily as a result of self

desiccation (which is independent of the pore pressure magnitude) faster filling rates

will create an overall increases increase in pore pressure. The reverse occurs when

filling rates are reduced. In the 0.2 m/hr case the rate of application of total stress is

reduced but the rate of (self desiccation induced) pore pressure reduction remains

constant resulting in lower pore pressures. But, the other influence of slowing filling

rates is to extend the loading timescale to be comparable to the timescale associated

conventional drainage-type consolidation. In this case, drainage-type consolidation acts

to restore steady state seepage pore pressures” leading to an increase in pore pressures.

The calculated barricade stress against time is presented in Figure 7.29 for the different

filling rates. Again the trend of the pore pressure and barricade stress plots are similar,

with the highest filling rates being associated with the highest barricade stresses. The

higher stresses can be attributed to reduced consolidation.

7.4.5 Non-consolidating fill: discussion

As with consolidating fills, the overall result of this study indicates that barricade

stresses are closely related to the degree of consolidation (or the pore pressures). But it

is interesting to note that material properties that appeared to have little influence on the


7.18

behaviour of consolidating fill, such as cement content and permeability, had a

significant impact on the behaviour of non-consolidating fills. The fundamental reason

for the significant influence of these characteristics is their influence on the

consolidation mechanism.

As with consolidating fills, the significant influence of pore pressures on barricade

stresses poses a problem for mine backfill designers, since pore pressures are very

difficult to predict numerically. However, this dependence presents the opportunity to

manage the situation using in situ pore pressure measurements. Due to the complex

interaction of mechanisms in a non-consolidating fill a unique relationship cannot be

developed between pore pressure and barricade stress. But pore pressure measurements

can provide an indication of the field situation varying from the design.

Using fully-coupled numerical modelling, and the associated laboratory experiments to

define the material characteristics (as outline in Chapter 3), a reasonable understanding

of the likely behaviour during filling can be developed. This provides a rational

approach to defining an initial filling sequence. From the analysis, barricade stresses can

be estimated as well as providing an understanding of the expected pore pressure

regime.

As illustrated in Section 7.4, the modelling results can be significantly influenced by a

number of different characteristics and it is usually necessary to assess the performance

of the model results in situ. Clayton and Bica (1993), Take and Valsangkar (2001) and

Fourie et al. (2007) suggest that the direct measurement of stress within a soil can be

problematic due to the inclusion of a loadcell that possesses a different stiffness to the

soil medium. This problem is exacerbated when attempting to measure stress in a soil,

such as a cementing minefill, in which the stiffness changes (often by an order of

magnitude) with time. Therefore, managing filling operations based on loadcell

measurements is considered unreliable.

However, as demonstrated in this thesis, with non-consolidating fills most variations

from the design assumptions (such as delayed initial set, permeability changes,

excessive drawpoint flow resistance, fill/rock interface softening or inappropriate

material stiffness development) result in higher pore pressures. Therefore, during filling

in situ pore pressure measurements may be compared with modelling results to assess if


7.19

the proposed sequence is suitable. Should the measured pore pressures vary from the

predicted value, the schedule can be adjusted accordingly. As barricade stresses

progressively increase during filling, the information gathered during the early stages of

filling can be used to manage filling activities in the later stages, where barricade

stresses may approach their maximum. This approach may not clearly identify the root

cause of any problem, but in most cases it can identify if the actual situation varies from

the design assumptions and hence avert barricade failure.

7.4.6 Non-consolidating fill: conclusion

The two-dimensional mine backfill consolidation program Minefill-2D was used to

undertake a sensitivity study on cemented mine backfill that would be unlikely to

consolidate during the filling process without the assistance of cement hydration. This

study highlighted a number of interesting aspects that should be considered when using

this type of fill. These include:

• As with consolidating fills, the degree of consolidation (or increase in pore

pressure) has a significant influence on barricade stresses.

• The resistance to flow through the drawpoint region can influence loads

applied to barricade structures. This suggested that the use of free-draining

barricades help to reduce the barricade stresses during filling.

• During the initial placement of non-consolidating fill, an increase in

permeability may increase the amount of conventional drainage-type

consolidation, reducing pore pressures and barricade loads.

• Contrary to conventional consolidation theory, a reduction in permeability can

actually lead to higher consolidation and lower barricade stresses after cement

hydration is initiated.

• The most significant factor influencing loads applied to barricade structures

from non-consolidating fills is cement content. Non-consolidating fills are

highly dependent on cementation to achieve consolidation due to the stiffness

increase and self-desiccation characteristics that cementation imparts. Other

properties that influence these characteristics, such as placed density and


7.20

mineralogy, can have a comparable influence on consolidation and barricade

stresses.

• A number of different factors were shown to influence stresses applied to non-

consolidating fill barricade. The most significant of these factors result in

higher pore pressures. Therefore, it is suggested that fully-coupled numerical

analysis, combined with appropriate in situ monitoring, can provide a safe and

efficient means of managing filling activities.

7.5 DEVELOPMENT OF EFFECTIVE STRESS DURING

CURING

7.5.1 Comparision between consolidating and non-consolidating fill

Coring of in situ cemented backfill has shown in situ strengths to be frequently greater

than those measured in the laboratory, for the same mix (Revell 2004, le Roux et al.

2002, Belem et al. 2002). The higher in situ strengths are expected to be a result of

different curing conditions. One aspect that differs between material cured in situ and

that cured in the laboratory, is the level of effective stress during curing. Application of

effective stress during curing has been shown to increase material strengths by

increasing the number of contact points and improving the intimacy of the contacts

(Blight 2000, Rotta et al. 2003, Consoli et al. 2000).

While the development of total stress to an element within a stope is relatively easy to

predict, it is the rate that effective stress develops relative to the hydration period that

must be appropriately understood to develop a more representative approach to sample

preparation. For example, application of effective stress at the same rate as the total

stress will result in an initial compression of the soil matrix and hydration at an

increased density, while application of the entire self-weight stress at the completion of

filling may result in crushing of weak cement bonds, and may thus have a detrimental,

rather than a positive, effect on strength.

As Minefill-2D is a fully coupled model, it can be used to estimate the rate and

magnitude that effective stress develops in material within a stope. Given the rate of

effective stress development in situ, the significance of this with respect to the final

strength of the material can be understood.


7.21

To investigate the impact of different fill types on the rate at which effective stress

develops, the Paste fill B (PFB) and Hydraulic Fill A (HFA) modelling results, from

Section 7.2, are plotted in Figure 7.30. This shows a plot against time of the

development of vertical effective stress (σ′v) at a point located 12 m above the stope

floor, at the opposite side to the drawpoint, for the HFA (HFA σ′v) and PFB (PFB σ′v).

Also plotted in Figure 7.30 are the total self-weight stress (σv) and the effective self-

weight stress (σ′v) that would develop in the absence of any arching. Assuming the same

density, for the same filling sequence, this would be equal for both fill types. The other

information presented in Figure 7.30 is the magnitude of decrease in pore pressure for

the two materials due to self desiccation in isolation (∆u SD only) (using Equation

3.27).

The first point to note is that effective stress develops in HFA material immediately

after placement, while no effective stress develops in PFB until approximately 6 hours.

Also, in the first 30 hours of curing, the rate of development of effective stress in the

HFA material is almost double that in PFB. Finally, the rate of effective stress

development is relatively constant with the HFA material, while that with PFB is

initially very slow but then increases exponentially.

7.5.2 Development of effective stress in consolidating fill

Figure 7.30 suggests that the rate of development of effective stress in the HFA material

is in accordance with the effective self-weight stress. The reason is that the coarse

nature of HFA causes immediate dissipation of excess pore pressures, but due to the

restriction (to flow) created at the drawpoint a phreatic surface is established within the

fill mass. This phreatic surface creates approximately hydrostatic pore pressures within

the stope and, if arching is neglected, this would result in effective stress developing in

accordance with the effective unit weight of the material.

If arching occurs as filling progresses, the effective stress applied is less than the

effective self-weight stress. The significance of this increases as the stope plan area is

reduced, with the consequence of reduced vertical total stress and a reduced rate of

development of vertical effective stress . Another factor that could influence this

response is the restriction at the drawpoint. As illustrated in Section 7.3.1, the resistance

to flow through the drawpoint modifies the gradient of the pore pressure isochrones


7.22

within the stope. Using the effective unit weight and the filling rate to define the

effective self-weight stress assumes hydrostatic pore pressures. A reduction in flow

resistance through the drawpoint area would act to reduce pore pressures leading to an

increase in vertical effective stress.

To investigate the applicability of this theory for different filling rates, the effective

stress at the same point was monitored for different filling rates using HFA. Figure 7.31

presents the development of vertical effective stress against time for a point 12 m above

the base of the stope with different filling rates. Also presented in Figure 7.31 are the

self-weight stresses, for each filling rate, if arching is neglected.

In each case, the actual effective stress is very similar to the effective self-weight stress.

The rate of development of effective self-weight stress is dependent on the filling rate

and the effective unit weight of the material and independent of the rate of cementation.

Obviously, the maximum effective stress in this case depends on the amount of material

placed above the location of interest.

It is also interesting to note that, for the HFA material, the calculating the effective

stress using the dissipation of pore pressure that would occur due to self desiccation in

isolation significantly overestimates the effective stress for this material. This is because

with the high permeability of HFA, only very small hydraulic gradients are required to

recharge water volumes removed through self desiccation. These pores are recharged

and steady state seepage pore pressures are re-established.

7.5.3 Development of effective stress in non-consolidating fill

Figure 7.30 indicates that the rate of development of vertical effective stress in PFB

material is approximately equal to the rate that pore pressure is dissipated as a result of

self desiccation alone. This is because the low coefficient of consolidation allows very

little conventional (drainage-type) consolidation to take place. Furthermore, with little

conventional consolidation taking place, the application of total self-weight stress (from

fill accretion) creates an equivalent increase in pore pressure and no change in effective

stress. As the only mechanism causing dissipation of any significant proportion of pore

pressure is self desiccation, this mechanism alone can appropriately capture the rate at

which effective stress develops in the soil matrix.


7.23

To investigate this theory in more detail, modelling was undertaken using PFB and the

same fill/rest schedule as before, but this time with filling rates varying from 0.05 m/hr

to 1.0 m/hr. The calculated vertical effective stress is plotted against time, for a point 12

m above the base of the stope, in Figure 7.32. Also presented in Figure 7.32 is the

dissipation of pore pressure as a result of self desiccation occurring in isolation. As this

characteristic is material dependent, the relationship is consistent for all cases.

Figure 7.32 indicates that, the development of vertical effective stress is similar for all

filling rates greater than 0.05 m/hr, and that these are close to the magnitude of pore

pressure reduction from self desiccation alone. This is particularly the case during the

early stages of hydration, where the effective stress level has the greatest influence on

the cured strength.

The exception is the slowest filling rate of 0.05 m/hr. At this filling rate, the time

required to fill the stope is of the same order as the time required for conventional

drainage-type consolidation to take place. With reference to Gibson’s (1958)

consolidation chart (Figure 2.4) this situation corresponds to a dimensionless time factor

(T=m2t/cv) equal to 0.5. Figure 2.4 suggests that this time factor corresponds to

(du/dx)/γ′ equal to 0.15, indicating drained filling conditions. This essentially changes

the situation to that of a consolidating-type fill, where the effective stress is similar to

the effective self weight.

To investigate the spatial variation around a stope, the base case (PFB with a filling rate

of 0.5 m/hr) was selected and the development of vertical effective stress at different

elevations was monitored, and the results plotted in Figure 7.33. Also presented in

Figure 7.33 is the total vertical self-weight stress (from the accumulating fill mass) as

well as the reduction in pore pressure from self desiccation alone.

Figure 7.33 indicates that for non-consolidating fills, the development of vertical

effective stress throughout a stope can be appropriately represented by the self

desiccation mechanism in isolation.

7.5.4 Curing of fill: discussion and conclusion

From the above discussion, it is clear that effective stress should be applied to

laboratory control samples during curing at the same rate that they develop in situ,


7.24

otherwise the cured strengths of the laboratory samples will not be the same as the in

situ cured strengths. One approach to doing so is to simulate each individual filling

sequence using a tool such as Minefill-2D, and, based on the results, the laboratory

specimen could be loaded to create an equivalent stress regime throughout the curing

period. However, the results from the previous sensitivity analyses can also provide

some useful guidance in formulating an appropriate curing technique.

For material with a high uncemented coefficient of consolidation relative to the filling

rate (such as the HFA case presented above), the development of vertical effective stress

was shown to be in accordance with the effective self weight vertical stress. This logic

assumes:

• Excess pore pressures are immediately dissipated

• Hydrostatic pore pressures are established within the fill mass due to the

restriction at the drawpoint

• There is no arching.

It is also important to note that the maximum effective stress depends on the depth of

the sample within the fill mass.

For material with a very low coefficient of consolidation relative to the filling rate (such

as the PFB case presented above), it is expected that effective stress develops due to the

drop in pore pressure that occurs from self desiccation occurring in isolation. In this

case, the setup similar to the hydration experimental setup described previously (Section

3.6) can be used to allow the effective stress to develop as hydration proceeds. In this

setup, high total stress is applied to the saturated sample enclosed in a membrane, which

generates pore pressure practically equal to the applied total stress, and thus there is

initially practically zero effective stress, just as in the stope. However, the process of

hydration causes pore pressures to reduce (and effective stresses to increase) due to the

self-desiccation mechanism, in a manner that exactly mimics what happens within the

stope. Thus, at all stages of the test, the effective stress develops at exactly the same

rate as it does within the stope – assuming of course that the material is sufficiently fine-

grained to prevent any conventional consolidation occurring prior to hydration.


7.25

Modelling demonstrated that the rate of development of vertical effective stress is the

same throughout the fill mass in the stope, which suggests that a single experiment may

suitably define the material strengths throughout the stope. This logic assumes:

• The material remains saturated in the field

• No conventional drainage-type consolidation takes place.

It is important to note that an increase in the coefficient of consolidation can have the

effect of increasing or decreasing the rate of development of effective stress.

Conventional consolidation acts to restore steady state seepage pore pressures.

Therefore, if the self-desiccation mechanism is unable to reduce pore pressures below

the “steady state” condition (as explained in Section 7.2.2), conventional consolidation

acts to assist with the dissipation of pore pressures and thus, in this case, this increases

the rate of development of effective stress. This is the case where a filling rate of 0.5

m/hr is adopted with PFB. On the other hand, should the self-desiccation mechanism be

capable of reducing the pore pressures below “steady state” (as was demonstrated with

PFA in Section 7.2.2), conventional consolidation causes water to flow downwards,

recharging the pores, and re-establishing steady state seepage pore pressures. This

reduces the rate that effective stress develops.

7.6 CONCLUSION

The tools developed throughout this thesis have been used in this chapter to investigate

the behaviour of tailings-based mine backfill. This investigation addressed a comparison

between a range of tailings-based fill types, focusing on barricade stresses and the

development of effective stress during curing. At the completion of each section, a

specific conclusion section was provided. Some of the major conclusions that resulted

from this analysis are presented below.

Regardless of the fill properties, the most significant factor influencing barricade

stresses is consolidation. Reduced consolidation resulted in higher barricade stresses.

Broadly speaking, tailings-based fills can be divided into two groups: fills that

consolidate immediately after placement (consolidating fills) and those that are unlikely

to consolidate without the influence of cementation (non-consolidating fills). The

fundamental difference between these fill types is that the mobilisation of strength in


7.26

consolidating fills is dependent on the rate of deposition, while the mobilisation of

strength in non-consolidating fills is dependent on the rate of cement hydration.

Pore pressures in consolidating fills are largely independent of cementation,

permeability (for a given phreatic surface elevation) and filling rates, but are influenced

by the flow restriction through the drawpoint at the base of a stope. Reducing this flow

restriction can significantly reduce pore pressures throughout the stope, thereby

increasing effective stresses and reducing barricade stresses.

Cementation, permeability, drawpoint restriction and filling rate can all have a

significant influence on the barricade stresses from non-consolidating fill. A variation in

any of these factors results in a pore pressure change, which leads to higher barricade

stresses.

Mechanics of Mine Backfill Matthew Helinski Concluding Remarks and Recommendations of Future Work The University of Western Australia

8.1

CHAPTER 8

CONCLUDING REMARKS AND RECOMMENDATIONS

FOR FUTURE WORK

8.1 CONCLUDING REMARKS

This thesis has presented an investigation into the mine backfill deposition process that

is based on fundamental soil mechanics principles. The main feature of the work was to

investigate and numerically couple three time-dependent processes that interact during

the cemented tailings backfill process, these being: the loading rate (or filling rate), the

conventional consolidation rate and the cement hydration rate.

Based on the interaction of these different processes, a number of useful results were

obtained that are relevant to the cemented mine backfill process. These results and some

concluding remarks are contained in this chapter.

8.2 MAIN OUTCOMES

The first significant result from this work was to highlight the importance of

consolidation in estimating barricade stresses. It was demonstrated numerically that

stresses applied to mine backfill barricade structures can vary by an order of magnitude

depending on the degree of consolidation that occurs during filling. The significance of

consolidation on the total stress distribution was also demonstrated experimentally

using geotechnical centrifuge modelling.

Furthermore, it was demonstrated that, without the presence of cement, the degree of

consolidation during filling for typical tailings-based backfills can range from fully

drained to fully undrained conditions.

Investigation of the fundamental characteristics that influence the consolidation of

cemented mine backfill showed that even with the minor amounts of cement typically

added to mine backfill (2% to 10%), the material properties can change significantly.

Specifically these changes include:

• An increase in stiffness, which can be greater than an order of magnitude.


8.2

• A reduction in permeability, which can also be greater than an order of

magnitude.

• A volumetric reduction, which, while only very small, can lead to a significant

drop in pore pressure when combined with the high material stiffness achieved

through cement hydration (this is the so called “self-dessication” effect).

By modifying the tailings consolidation program MinTaCo, the time-dependent process

of cement hydration was successfully coupled with filling and conventional

consolidation to assess the influence of cementation on the filling process. This

modified program (termed CeMinTaCo) demonstrated that:

• The cement-induced increase in stiffness and self desiccation can make a

significant contribution to the mine backfill consolidation process

• Because of the substantial influence of cementation on the consolidation

behaviour, cement content can have a major influence on the consolidation of

some cemented mine backfills.

• Contrary to conventional consolidation theory, the combination of cementation

with low permeability material can act to generate lower pore pressures (higher

consolidation) than higher permeability material.

To investigate the influence of stress arching (onto the surrounding rockmass) during

filling, a new two-dimensional consolidation program (termed Minefill-2D) was

developed. Like CeMinTaCo, Minefill-2D coupled the three time-dependent processes,

but, unlike CeMinTaCo, Minefill-2D also takes account of the influence of the stiff

surrounding rockmass on the stress distribution. In addition, Minefill-2D allowed the

stope drawpoint geometry to be incorporated (albeit in plane strain), which allowed

stresses applied to barricade structures to be determined. This new model was compared

with results from a series of laboratory tests and shown to provide a good representation

of the process.

To investigate the ability of Minefill-2D to represent the consolidation behaviour in an

actual filling situation, modelling results were compared with in situ measurements. A

comparison was carried out between the measured pore pressure in the centre of the

stope floor and that predicted using Minefill-2D, using material properties that were


8.3

independently derived using the material characterisation technique described in Section

3.6. This comparison indicated that Minefill-2D can provide a very good representation

of the consolidation behaviour.

A sensitivity study to investigate barricade stresses using Minefill-2D indicated:

• Broadly speaking, tailings-based fills can be divided into two groups: fills that

consolidate immediately after placement (“consolidating fills”) and those that

are unlikely to consolidate (during the filling period) without the influence of

cementation (“non-consolidating fills”). The fundamental difference between

these fill types is that the mobilisation of strength in consolidating fills is

dependent on the rate of deposition, while the mobilisation of strength in non-

consolidating fills is dependent on the rate of cement hydration.

• Provided that no excess pore pressures are generated during deposition (i.e.

consolidating fills as defined in Chapter 7) pore pressure is largely independent

of cementation, permeability (for a given phreatic surface elevation) and filling

rates, but is influenced by the flow restriction through the drawpoint at the base

of the stope. Reducing this flow restriction can significantly reduce pore

pressures throughout the stope, resulting in an increase in effective stress and a

reduction in barricade stresses.

• Cementation, permeability and filling rate can all have a significant influence

on the barricade stresses imposed by a non-consolidating fill. A variation in

any of these characteristics results in a pore pressure change, which leads to

changes in barricade stresses.

• As consolidation is the characteristic that most significantly influences

barricade stresses (in both fill types), it is recommended that the most

appropriate means of managing the risk of barricade failure is through in situ

pore pressure monitoring strategies. The recommended management strategies

for “consolidating fills” differ from those for “non-consolidating fills”.

A sensitivity study to investigate the development of effective stress during curing using

Minefill-2D indicated:


8.4

• The application of effective stress (at rates similar to those experienced in situ)

during curing increases the final strength of the material. This was primarily

due to an increase in density, which is consistent with the results of previous

experimental studies.

• The development of effective stress during curing in a “consolidating fill” can

be closely related to the accumulation of effective self-weight stress from the

overlying fill mass

• The development of effective stress during curing in a “non-consolidating fill”

can be closely related to the reduction in pore pressure from self desiccation in

isolation.

8.3 RECOMMENDATIONS FOR FUTURE WORK

The main focus of this thesis was to develop a framework for understanding the

cemented mine backfill deposition process that may be used to assess the significance of

various aspects and help with the interpretation of in situ monitoring results. In

achieving the final outcome, a series of assumptions and simplifications were made to

firstly represent the material behaviour and secondly simulate the behaviour. Much of

this work should be revisited with the view of refining some of the material

characteristics that were shown to be most critical. Specifically material modelling

should focus on:

• Improved techniques for quantifying the self-desiccation process, including

directly quantifying volumetric changes that occur during the hydration process

and taking account of temperature changes during the hydration process.

• An improved model to represent the influence of cement hydration and soil

compression on the permeability of the material.

• Additional experimental and constitutive modelling to more appropriately

represent the variation in material strength and stiffness during the cement

hydration process.

Minefill-2D is a new finite element model that was developed specifically for the

purpose of representing the cemented mine backfill deposition process. In its current


8.5

state, the program is considered suitably rigorous for the applications in this thesis, but

nevertheless improvements to some of the calculation algorithms would probably result

in increased calculation speed and accuracy. Specifically these improvements might

include:

• An improved time-stepping algorithm. This algorithm would calculate the most

appropriate time-stepping size based on the element size, coefficient of

consolidation and information from previous calculations in a manner similar

to that adopted by Yong at al. (1983).

• Implementation of a constitutive model that takes account of yielding due to

volumetric compression as well as a more rigorous approach to numerically

accounting for strain softening. This would be useful when investigating the

behaviour of very weak material.

• Implementation of interface elements to more appropriately represent the

behaviour of the interface between the fill and the surrounding rockmass.

• Extension of the geometry to more appropriately represent the stope drawpoint.

This may include extension from two to three dimensions or coupling of the

axi-symmetric version of Minefill-2D (to represent the stope) with another axi-

symmetric version of Minefil-2D to represent the drawpoint.

• The stress distribution around a stiff fill mass can be influenced by the

deformation behaviour of the barricade structure. Consideration should be

given to implementing beam elements to represent any flexibility in the

barricade structure.

• The combination of slow filling rates and high self-desiccation rates can lead to

the development of large matrix suctions. As discussed by Grabinski and

Simms (2006) these suctions have the potential to desaturate the fill matrix

which could change the modelling response. Consideration should be given to

taking account of matrix desaturation in the numerical analysis.

This thesis demonstrated that devising a centrifuge experiment in which the three time-

dependent processes can interact is very difficult, and in order to achieve this, full-scale

field testing is required. While the repetitive nature of stoping and backfilling provides


8.6

opportunities to undertake full scale parametric studies, full scale field testing

introduces problems regarding the suitability of instrumentation. Gathering quality data

from cemented mine backfill stopes can be difficult and care should be taken to address

the following concerns;

• It is well documented (Clayton and Bica, 1993, Take and Valsangkar 2001)

that the deformation of earth pressure cells can lead to “under registration” (i.e.

the cell measures less than the actual stress). The degree of under registration

depends on the stiffness of the cell relative to the surrounding soil. As

cemented mine backfill can gain very high stiffness during the hydration

process, care should be taken to ensure that the cell stiffness matches the

material stiffness appropriately.

• In the centre of a large backfill mass, the cement hydration process can lead to

temperature changes that are in the order of 20ºC. With fluid-filled pressure

cells, this can cause the internal fluid to expand, leading to an artificial pressure

increase in the cell. Should this type of pressure cell be adopted, care must be

taken to ensure the fluid has an appropriately low coefficient of thermal

expansion to eliminate or minimise this error

• The measurement of positive pore pressure can be successfully achieved using

vibrating wire piezometers, but when (and if) pore pressures become negative,

the porous disk at the face of the piezometer can desaturate, creating a capillary

block. In order to gather accurate negative pore pressure measurements, care

should be taken to select a porous disk with an appropriate pore size to avoid

desaturation. Also, to minimise the likelihood of desaturation, the porous disk

should be saturated with a low-viscosity fluid under vacuum. Grabinski at al.

(2007) adopted heat dissipation sensors in an attempt to measure pore water

suctions, but are yet to report on the success of this approach.

An obvious model verification strategy is to use in situ monitoring results to further

verify the performance of the modelling approach presented in this thesis. However,

prior to undertaking such back analysis, it is considered imperative that a number of

assumptions regarding boundary conditions should be more clearly defined. Aspects

that should be investigated include pore pressure accumulation immediately behind


8.7

barricade structures (assumed to be zero in this analysis) and the pore pressure

boundary condition within the stope at the fill / rock interface.

Mechanics of Mine Backfill Matthew Helinski References The University of Western Australia

9.1

CHAPTER 9

REFERENCES

Asaoka, A. Naknao, M. Noda, T and Kaneda, K. (2000). Delayed compression /

consolidation of natural clay due to degradation of soil structure. Soils and Foundations,

Vol. 40, No. 3, 75-85.

Aubertin, M. Li, L. Arnoldi, S. Belem, T. Bussiére, B. Benzaazoua M. and Simon, R.

(2003). Interaction between backfill and rock mass in narrow stopes. Soil and Rock

America (Calligan Einstein and Whittle eds.), V1, 1157-1164.

Baig, S. Picornell, M. and Nazarian, S. (1997). Low strain shear moduli of cemented

sands. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 123,

No. 6, 540-545.

Baldwin.W.F. (2004). Responses to requests to comment, Handbood on Mine fill (eds.

Potvin, Thomas, Fourie), Australian Centre for Geomechanics, ISBN 0-9756756-2-1.

Bentz, D.P. (1995). A three-dimensional cement hydration and microstructure program.

Hydration rate, heat of hydration, and chemical shrinkage. Building and Fire Research

Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland

20899, USA. Available from http://fire.nist.gov/bfrlpubs/build96/art095.html (last

accessed 19 April 2007).

Bentz. D.P, Garboczi. E.J, Lagergren. E.S (1998). Multi-scale microstructure and

transport properties of concrete. Construction and Building Materials, Vol. 10, No. 5,

293-300.

Bentz. D.P. Garboczi. E. J. and Lagergren. E. S (1998). Multi-scale microstructure

modelling of concrete diffusivity: identification of significant variables. Cement,

Concrete, and Aggregates, CCAGDP, Vol. 20, No. 1, 129-139.

Belem, T. Benzaazoua, M. Bussiére, B. and Dagenais, A.M. (2002). Effects of

settlement and drainage on strength development within mine paste backfill. Tailings

and Mine Waste ’02, Swets & Zeitlinger, ISBN 90 5809 353 0, 139-148.


9.2

Belem, T. H, A. Simon, R. and Aubertin, M. (2004). Measurement and prediction of

internal stresses in an underground opening during filling with cemented fill. Proc. of

the Fifth International Symposium on Ground Support, Villaescusa and Potvin (eds),

Balkema Publishers, 28-30 September, Western Australia, ISBN 9058096408, p. 619-

630.

Belem,T. El Aatar, O. Bussiere, B. Benzaazoua, M. Fall, and M.Yilmaz, E. (2006).

Characterisation of self-weight consolidated paste backfill. Paste ’06, (Jewell, Lawson

& Newman eds.). Limerick, Ireland, 333-345.

Biot, M.A. (1941). “General theory of three-dimensional consolidation”, Journal of

Applied Physics, Vol. 12, 155-164.

Bishop, A.W. and Henkel, D.J. (1962). Measuring Soil Properties in the Triaxial Test.

2nd ed, Edward Arnold, London.

Black, D.K. and Lee, K.L. (1973). Saturating laboratory samples by back pressure.

Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 99, No. SM1, 75-

93.

Blight, G.E. (2000). The use of mine waste as a structural underground support. Geo-

eng 2000, V1: Invited paper, Technomic, ISBN No. 1-58715-067-6.

Blight, G.E. and Spearing, A.J.S. (1996). The properties of cemented silicated backfill

for use in narrow, hard-rock, tabular mines. Journal of South African Institute of Mining

and Metallurgy, January/February 1996, 17-28.

Breysse, D. and Gerard, B, (1997). Modelling of permeability in cement-based

materials: Part 1- Uncracked medium. Cement and Concrete Research, Vol.27, No. 5,

761-775

Brouwers, H.J.H. (2004). The work of Powers and Brownyard revisited: Part 1. Cement

and Concrete Research, Vol. 34, 1697-1716.

Carrier, W.D. Bromwell, L.G. and Somogyi, F. (1983). Design capacity of slurried

mineral waste ponds. Journal Geotechnical Engineering Division, ASCE, 109(GT5), p.

699-716.


9.3

Cayouette, J. (2003). Optimization of paste backfill plant at Louvicourt mine. Canadian

Institute of Mining Bulletin , 96, 1075, 51-57.

Clayton, C.R.I. and Bica, A.V.D. (1993). Design of diaphragm-type boundary total

stress cells. Géotechnique, 43 (4), 523-535.

Clough, G.W. Sitar, N. Bachus, R.C. and Nader, S.R. (1981). Cemented sands under

static loading. Journal of the Geotechnical Engineering Division, ASCE, Vol. 107,

GT6, 799-817.

Clough, G.W. Iwabuchi, J. Rad, N.S. and Kuppusamy, T, (1989). Influence of

cementation on liquefaction of sands. Journal of Geotechnical Engineering, ASCE,

Vol. 115, No. 8, 1102-1117.

Consoli, N. C. Rotta, G.V. and Prietto, P.D.M. (2000). Influence of curing under stress

on the triaxial response of cemented soils. Géotechnique 50(1), 99-105.

Consoli, N.C. and Sills, G.C. (2000). Soil formation from tailings: comparison of

predictions and field measurements. Géotechnique 50(1), 25-33.

Consoli, N. C, Foppa, D, Festugato, L. and Heineck, K. S. (2006). Key parameters for

strength control of artificially cemented soils. Journal of Geotech. and

Geoenvironmental Engrg, ASCE, vol. 133, No. 2, 197-205.

Coop, M. R. and Atkinson, J. A. (1993). Mechanics of cemented carbonate sands.

Géotechnique, 43(1), 53-67.

Coroner’s Report (2001) Ref No 20/01, Record of investigation into death.

Cowling R, Grice A.G. and Isaacs L.T. (1987). Simulation of hydraulic filling of large

underground mining excavations. Numerical Methods in Geomechanics, (Innsbruck

1988), Swoboda (ed.), Balkema, ISBN 90 6191 809 X, 1869-1876.

Cuccovillo, T. and Coop, M.R. (1997). Yielding and pre-failure deformation of

structured sands. Géotechnique, 47(3), 491-508.

Dyvik, R. and Olsen, T.S. (1989). Gmax measured in oedometer and DSS tests using

bender elements. Proceedings of the 12th International Conference on Soil Mechanics

and Foundation Engineering, Rio de Janeiro, Vol. 1, 39–42, Balkema, Rotterdam.


9.4

Fahey, M. and Carter, J.P. (1993). A finite element study of the pressuremeter test in

sand using a non-linear elastic plastic model. Canadian Geotechnical Journal, 30, 348–

362.

Fahey, M. Finnie, I. Hensley, P.J. Jewell, R.J. Randolph, M.F. Stewart, D.P. Stone,

K.J.L. Toh, S.H. and Windsor, C.S. (1990). Geotechnical centrifuge modelling at the

University of Western Australia. Australian Geomechanics, No. 19, 33-49.

Fahey, M. and Newson, T.A. (1997). Aspects of the geotechnics of mining wastes and

tailings dams. Theme Lecture, GeoEnvironment 97: Proc. of the 1st Australia - New

Zealand Conference on Environmental Geotechnics, Melbourne, Australia, 115–134,

Balkema, Rotterdam.

Fahey, M. Newson, T.A. and Fujiyasu, Y. (2002). Engineering with tailings. Keynote

Lecture, Proc. 4th International Conference on Environmental Geotechnics, Rio de

Janeiro, Brazil, Vol. 2, 947-973, Balkema, Lisse.

Fernandez, A. and Santamarina, J. C. (2001). Effect of cementation on the small strain

parameters of sand. Canadian Geotechnical Journal, 38(1), 191–199.

Fredlund, D.G. and Rahardjo, H. (1993). Role of unsaturated soil behaviour in

geotechnical engineering practice. Proc. Southeast Asian Geotechnical Conference, 11,

SEAGC, Singapore, May, 37–49.

Fourie, A.B. Helinski, M. Fahey, M. (2007). Using effective stress theory to

characterise the behaviour of backfill. Minefill ’07, Montreal, Paper # 2480.

Garboczi, E.J. and Bentz, D.P. (1996). Modelling of the microstructure and transport

properties of concrete. Construction and Building Materials, Vol. 10, No. 5, 293-300.

Gens, A. and Nova, R. (1993). Conceptual bases for a constitutive model for bonded

soils and weak rocks. Geotechnical Engineering of Hard Soils – Soft Rocks, R4

Anagnostopoulos, A., Schlosser, F., Kalteziotis, N. and Frank, R. (eds), Balkema,

Rotterdam, 1: 485-494.

Gibson, R.E. (1958). The process of consolidation in a clay layer increasing in thickness

with time. Géotechnique, 8(4), 177-182.


9.5

Gibson, R.E. England G.L. and Hussey, M.J.L. (1967). The theory of one-dimensional

consolidation of saturated clays. I. Finite non-linear consolidation of thin homogeneous

layers. Géotechnique, 17(3), 261-273.

Gibson, R.E. Schiffman, R.L. and Cargill, K.W. (1981). The theory of one-dimensional

consolidation of saturated clays. II. Finite non-linear consolidation of thick

homogeneous layers. Canadian Geotechnical Journal, 18, No.2, 280-293.

Grabinski, M. and Simms, P. (2006). Self-desiccation of cemented paste backfill and

implications on mine design. Paste ’06, Limerick April 3-7, Australian Centre for

Geomechanics, ISBN 0-9756756-5-6.

Grabinski, M. and Bawden, W.F. (2007). In situ measurements for geomechanical

design of cemented paste backfill systems. Canadian Institute of Mining Bulletin,

Special Edition on Mining with Backfill (August 2007).

Guo, J. (1989). Maturity of concrete: method for predicting early-stage strength, ACI

Mater J., 86 (1989). (4), 341–353.

Helinski, M., Fourie, A.B. and Fahey, M. (2006). Mechanics of early age cemented

paste backfill. Paste ’06, Limerick April 3-7, Australian Centre for Geomechanics,

ISBN 0-9756756-5-6.

Helinski, M. and Grice, A.G. (2007). Water management in hydraulic fill operations.

Minefill ’07, Montreal, Paper # 2481.

Hua, C. Acker, P. and Ehrlacher, A. (1995). Analysis and models of autogenous

shrinkage of hardening cement paste. Cement and Concrete Research, Vol. 25, No. 7,

1457–1468

Illston, J.M. Dinwoodie, J.M. and Smith, A.A. (1979). Concrete, Timber and Metals.

Van Nostrand Reinhold Company, New York. ISBN 0419154701.

Ismail, M.A., Joer, H. and Randolph, M.F. (2000). Sample preparation technique for

artificially cemented soils. Geotechnical Testing Journal, ASTM. Vol. 23, No. 2, 171–

177.

Jamiolkowski, M. Lancellotta, R. Lo Presti, D.C.F. and Pallara, O. (1994). Stiffness of

Toyoura sand at small and intermediate strain. Proceedings of the 13th International


9.6

Conference on Soil Mechanics and Foundation Engineering, New Delhi, India, Vol. 1,

169–172, Balkema, Rotterdam.

Jewell, R.J. Andrews, D.C. and Khorsid, M.S. (eds). (1988). Engineering for

Calcareous Sediments: Proceedings of the International Conference on Calcareous

Sediments, Perth, 15-18 March. Proceedings, Vol. 1-2.

Kavvadas, M. and Amorosi, A. (2000). Constitutive model for structured soils.

Géotechnique, 50(3), 263-273.

Koenders, E.A.B. and Van Breugel, K. (1997). Numerical modelling of autogenous

shrinkage of hardening cement paste. Cement and Concrete Research, Vol. 27, No. 10,

1489–1499.

Kuganathan, K. (2002). A method to design efficient mine backfill drainage systems to

improve safety and stability of backfill bulkheads and fills. Proceedings of the 7th

Underground Operators Conference, Townsville, Qld., Australasian Institute of Mining

and Metallurgy, 191-188

Lagioia, R. and Nova, R. (1995). Experimental and theoretical study of the behaviour of

calcarenite in triaxial compression, Géotechnique, 45(4), 633-648.

Landriault, D. (2006). They said “It will never work”- 25 years of paste backfill 1981-

2006. Paste ’06, Limerick, Ireland, Australian Centre for Geomechanics, ISBN 0-

9756756-5-6, 277 – 292.

Landriault, D. (1995). Paste backfill mix design for Canadian underground hardrock

mining. Canadian Institute of Mining Report, V22, No.1, 11-13.

Le Roux, K.A. Bawden, W.F. and Grabinski, M.W.F. (2002). Assessing the interaction

between hydration rate and fill rate for a cemented paste backfill. Proceedings on the

55th Canadian Geotechnical and 3rd joint IAH-CNC Groundwater Specialty Conference,

Niagara falls, Ontario, October 20-23, 2002, pp.427-432.

Le Roux, K. (2004). Responses to requests to comment. Handbood on Mine Fill (eds.

Potvin, Thomas, Fourie), Australian Centre for Geomechanics, ISBN 0-9756756-2-1.


9.7

Le Roux, K.A. Bawden, W.F. and Grabinski, M.W.F. (2005). Field properties of

cemented paste backfill at the Golden Giant Mine. Proceedings of the 8th International

Symposium on Mining with Backfill, Beijing, September, 233-241.

Leroueil, S. and Vaughan, P.R.(1990). The general and congruent effects of structure in

natural soils and weak rocks. Géotechnique 40(3), pp.467-488.

LI, L. and Aubertin, M. (2003). A general relationship between porosity and uniaxial

strength of engineering materials. Canadian Journal of Civil Engineering, August ’03,

Vol. 30, No.4, 644-658.

Liu, M.D. Carter, J.P. Desai, C.S. and Xu, K.J. (1998). Analysis of the compression of

structured soils using the disturbed state concept. University of Sydney, Department of

Civil Engineering, Research Report R770.

Liu, M.D. and Carter, J.P. (2002). A Structured Cam-Clay model. Canadian

Geotechnical Journal, Vol ??, No 39, 1313-1332.

Liu, M.D. and Carter, M.D. (2005). Some applications of the Sydney Soil Model.

Proceedings of the 16th International Conference on Soil Mechanics and Geotechnical

Engineering, Osaka, September, 2005. Proceedings, vol. 2, 881-884.

Marston, A. (1930). The theory of external loads on closed conduits in the light of latest

experiments. Bulletion No.96, Iowa Engineering Experiment Station, Ames, Iowa.

McCarthy, P. (2007). Digging Deeper. AMC Newsletter, March ’07.

Mitchell, R.J. and Wong, B.C. (1982). Behaviour of cemented sands. Canadian

Geotechnical Journal, Vol. 19, 289-295.

Mikasa, M. (1965). The consolidation of soft clay, a new consolidation theory and its

application. Japanese Society of Civil Engineers (Reprint from Civil Engineering in

Japan 1965): 21-26.

Naylor, D.J. Pande, G.N. Simpson, B. and Tabb, R. (1981) Finite elements in

geotechnical engineering, Pineridge press, Swansea, U.K. ISBN 0-906674-11-5.

Potts, M.D. and Zdravković, L. (1999). Finite element analysis in geotechnical

engineering (theory), Thomas Telford, ISBN 0 7277 2783 4.


9.8

Potvin, Y. Thomas, E. and Fourie, A. (eds.). (1995). Handbook on Mine Fill. Australian

Centre for Geomechanics, ISBN 0-9756756-2-1.

Powers, T.C. and Brownyard, T.L. (1947). Studies of the physical properties of

hardened Portland cement paste. Bull. 22, Res. Lab. of Portland Cement Association,

Skokie, IL, U.S.A., reprinted from J. Am. Concr. Inst. (Proc.), Vol. 43, 1901-132, 247-

336, 469-505, 549-602, 669-712, 845-880, 933-992.

Powers, T.C. (1956). Structure and physical properties of hardened Portland cement

paste. Bull. 94, Res. Lab. of Portland Cement Association, Skokie, ILK, U.S., J. Am.

Ceram. Soc. 41, 1-6

Powers, T.C. (1979). The specific surface area of hydrated cement obtained from

permeability data. Materials and Structures, Vol. 12, No. 3, 159-168, Springer.

Qiu, Y. and Sego, D.C. (2001). Laboratory properties of mine tailings. Canadian

Geotechnical Journal, Feb 2001, No.38, 183-190.

Randolph, M. F. and S. Hope (2004). Effect of cone velocity on cone resistance and

excess pore pressures. IS Osaka - Engineering Practice and Performance of Soft

Deposits, Osaka, Japan, n/a: 147-152

Rankin, R. (2004). Geotechnical characterisation and stability of paste fill stopes at

Cannington mine. PhD thesis, James Cook University.

Rastrup, E. (1956). The temperature function for heat of hydration in concrete.

Proceedings of the RILEM Symposium on Winter Concreting, Copenhagen, Danish

National Institute for Building Research, Session B11. 3-20.

Revell, M. (2002). Underground mining at Aurion gold Kanowna Belle. AusIMM

Bulletin, May/June, 37-41.

Revell, M.B. (2004). Paste – How strong is it? Proceedings of the 8th International

Symposium on Mining with Backfill, September, Beijing, The Nonferrous Metals

Society of China, 286-294.

Revell, M. and Sainsbury, D (2007) Paste bulkhead failures, Minefill ’07, Montreal,

Paper # 2472.


9.9

Rouainia, M. and Wood, D.M. (2000). Kinematic hardening constitutive model for

natural clays with loss of structure. Géotechnique, 50(2), 153-164

Rotta, G.V. Consoli, N.C. Prietto, P.D.M. Coop, M.R. and Graham, J. (2003). Isotropic

yielding in an artificially cemented soil cured under stress. Géotechnique 53(5), 493-

501.

Santamarina, J. C., Klein, K. A., and Fam, M. (2001). Soils and Waves – Particulate

Materials: Behaviour , Characterisation and Process Monitoring. Wiley, Chichester,

England.

Schnaid, F, Prietto, P.D.M. and Consoli, N.C. (2001). Characterization of cemented

sand in triaxial compression. Journal of Geotechnical and Geoenvironmental

Engineering, ASCE, Vol. 127, No. 10, 857-868.

Schofield, A.N. (1980). Cambridge Geotechnical Centrifuge operations. Géotechnique

30(3), pp.227-268.

Seneviratne, N., Fahey, M., Newson, T.A. and Fujiyasu, Y. (1996). Numerical

modelling of consolidation and evaporation of slurried mine tailings. International

Journal for Numerical and Analytical Methods in Geomechanics, Vol. 20, No. 9, 647–

671.

Sideris K. (1993). The cement hydration equation. Zem-Kalk-Gips;12:E337-55, Edition

B.

Sideris, K.K. Manita, P. and Sideris, K. (2004). Estimation of the ultimate modulus of

elasticity and Poisson’s ratio of normal concrete. Cement & Concrete Composites, No

(not Vol??) 26, 623-631.

Smith, I.M. and Griffiths, D.V. (1998). Programming the Finite Element Method. 3rd

edition. John Wiley and Sons, ISBN 0 471 96542 1.

Tan, T.S. and Scott, R.F. (1988). Finite strain consolidation – a study of convection.

Soils and Foundations, Vol. 28, No. 2, 64-74.

Take, W.A. and Valsangkar, A.J. (2001). Earth pressures on unyielding retaining walls

of narrow backfill width. Canadian Geotechnical Journal, Vol. 38, No. 6, 1220-1230.


9.10

Terzaghi, K. (1943). Theoretical Soil Mechanics. John Wiley & Sons, New York.

Thomas, E.G. and Holtham, P.N. (1989). The basics of preparation of de-slimed mill

tailings hydraulic fill. Innovations in Mining Backfill Technology, Hassani et al. (eds),

Balkema, Rotterdam. 425-431.

Toh, S.H. (1992). Numerical and centrifuge modelling of mine tailings consolidation.

PhD thesis, The University of Western Australia.

Turcry, P. Loukili, A. Barcelo, L. and Casabonne, J.M. (2002). Can the maturity

concept be used to separate the autogenous shrinkage and thermal deformation of

cement paste at early age? Cement and Concrete Research, Vol. 32, 1443-1450.

Vermeer and Brinkgreve (1998). Plaxis – Finite element code for soil and rock analysis.

Balkema, Rotterdam.

Vick, S.G. (1983). Planning, design and analysis of tailings dams. John Wiley and

Sons, New York.

Winch, C.M. (1999). Geotechnical characterisation and stability of paste backfill at

BHP Cannington Mine. Undergraduate thesis, School of Engineering, James Cook

University, Australia.

Williams, D.J. Carter, J.P. and Morris, P.H. (1989). Modelling numerically the lifecycle

of coal mine tailings. Proc. 12th Int. Conf. Soil Mech. Found. Engrg, 3, Rio de Janeiro,

1919-1923.

Yin. J. H and Fang. Z, (2006). Physical modelling of consolidation behaviour of a

composite foundation consisting of a cement-mixed soil column and untreated soft

marine clay. Géotechnique 56(1), 63-68.

Yong, R.N. Siu, S.K.H and Sheeran, D.E. (1983). On the stability and settling of

suspended solids in settling ponds. Part 1. Piecewise linear consolidation analysis of

sediment layer. Canadian Geotechnical Journal, Vol. 20, 817-826.

Zienkiewicz, O.C. and Cormeau, I.C. (1967). Viscoplasticity, plasticity and creep in

elastic solids. A unified numerical solution approach. Int. J. Num. Meth. Eng., No.8,

821-845.


9.11

Zienkiewicz, O.C. and Zhu, J.Z. (1992), The superconvergent patch recovery and a

posteriori error estimates. Part 1: The recovery technique. International Journal for

Numerical Methods in Engineering, Vol. 33, 1331-1364.


Figures

Mechanics of Mine Backfill Ch 1 Introduction - Figures

Matthew HelinskiThe University of Western Australia

Figure 1.1. Schematic of a typical mine tailings based backfill system (contributed by Cobar Management Pty Ltd).

1.1

Mechanics of Mine Backfill Ch 1 Introduction - Figures


Figure 1.2. Schematic showing a typical stope filling situation (with typical dimensions).

Figure 1.3. Photograph showing a failed barricade (from Revell and Sainsbury 2007).

Containment barricade

Drawpoint

Stope

Fill deposition point

Saturated fill material

≈ 5 - 6 m

≈ 5 - 6 m

≈ 5 - 6 m

≈ 20 - 100 m

≈ 10 - 40 m

1.2

Mechanics of Mine Backfill Ch 2 Background Literature Review - Figures


Figure 2.1. Stress distribution down the centreline of a stope assuming “drained” and “undrained” filling.

Figure 2.2. The impact of drained and undrained filling on barricade stress.

0

1

2

3

4

5

6

7

0 100 200 300 400 500 600 700 800 900Barricade stress, σx (kPa)

Hei

ght u

p ba

rric

ade

(m) Undrained

analysis

Drained analysis

σx

0

5

10

15

20

25

30

35

40

45

50

0 100 200 300 400 500 600 700 800 900 1000Vertical total stress, σv (kPa)

Hei

ght a

bove

bas

e (m

)

Self weight stress

Undrained

Drained

σv

σv

F2.1



Figure 2.4. Gibson's(1958) consolidation chart with typical minefills.

Figure 2.3. Conversion from vertical total stress to horizontal stress.

0

0.2

0.4

0.6

0.8

1

1.2

0.01 0.1 1 10 100 1000 10000 100000T=m2t/cv

(du/

dx)/ γ

' at

surf

ace

Impermeable base

Permeable base

Classified tailings Vick (1983)

Cu tailings, Qiu and Sego (2001)

Ag tailings, Qiu and Sego (2001)

Full-stream tailings Vick (1983)

σh=σ′v.K0 + u

σv=σ′v+ u

F2.2



Figure 2.6. Comparison between structured and unstructured yield surfaces.

Figure 2.5. Comparison between structured and unstructured compression behaviour.

Deviator stress, q

Mean stress, p′

p′sp′cp′0

Equivalent unstructured yield surface

Critical state line

Structured yield surface

Loading surface

Compression of bonded material

Compression of destructured material

Mean stress, p’

Void ratio, e

Structure permitted space

F2.3



Figure 2.8. Relationship between void ratio and binder content to achieve critical porosity and typical mine backfill range.

Figure 2.7. Powers illustration of the Cement hydration process (from Illstron et al. 1979).

0

10

20

30

40

50

60

70

0 0.2 0.4 0.6 0.8 1 1.2 1.4Void ratio, e

Cem

ent c

onte

nt re

quire

d (%

)

Critical porosity

Typical cemented minefill operating range

F2.4

Mechanics of Mine Backfill Ch 3 Behaviour of Cementing Slurries- Figures


Figure 3.1. Incremental yield stress as it is defined in this thesis.

Figure 3.2 (a). Relationship between void ratio and qu for CSA hydraulic fill.

0

400

800

1200

1600

2000

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1Void ratio, e

Unc

onfin

ed c

ompr

essi

on st

reng

th, q

u (kP

a)

Cc = 10%, 28 day

Cc = 5%, 7 day

Lines: Eq. 3.6Points: Data

Void Ratio,e

Mean effective stress, p′

Uncemented yield

Uncemented yield

Cemented compression

curve

Cemented yield p′y

Yield stress incrementΔp′y

F3.1



Figure 3.2 (b). Relationship between void ratio and qu for Cannington paste fill from Rankin (2004).

Figure 3.3. Normalised qu against time for CSA hydraulic fill and Cannington paste fill.

0

500

1000

1500

2000

2500

0.5 0.7 0.9 1.1 1.3Void ratio, e

Unc

onfin

ed c

ompr

essi

on st

reng

th, q

u (kP

a)

Cc = 6%

Lines: Eq. 3.6Points: Data(All at 28 days)

Cc = 4%

Cc = 2%

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20 25 30Time, t (day)

q u/q

u(m

ax)

CSA H.F.Cannington P.F.

⎟⎠

⎞⎜⎝

⎛−−

=16.0

6.2exp(max) tqq

u

u

⎟⎠

⎞⎜⎝

⎛−−

=16.0

9.0exp(max) tqq

u

u

F3.2



Figure 3.4 (a). Incremental small strain shear stiffness against q u for CSA hydraulic fill.

Figure 3.4 (b). Young's modulus (at large strains) against qu for Cannington paste fill.

R2 = 0.9137

0

400

800

1200

1600

2000

0 0.5 1 1.5 2 2.5Unconfined compression strength, qu (MPa)

Incr

emen

tal G

o (M

Pa)

R2 = 0.9809

0

50

100

150

200

250

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6Unconfined compression strength, qu (MPa)

You

ng's

mod

ulus

, E (M

Pa)

F3.3



Figure 3.5. Comparison between one-dimensional compression experiments and the model results.

Figure 3.6. Comparison between eff and permeability.

0.6

0.7

0.8

0.9

1

1.1

10 100 1000 10000Vertical effective stress, σ'v (kPa)

Voi

d ra

tio, e

Cc = 5%, 5 day

Uncemented

Lines: modelPoints: data

Cc = 5%, 1 day

Cc = 5%, 16 day

0.0E+00

1.0E-06

2.0E-06

3.0E-06

4.0E-06

5.0E-06

6.0E-06

7.0E-06

8.0E-06

0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.82

Effective void ratio, eeff

Perm

eabi

lity,

k (m

/s)

10%5%2%Model

F3.4



Figure 3.7. Particle size distribution curves.

Figure 3.8. Pore water pressure (u ) and effective stress changes in triaxial samples hydrating under constant total stress and undrained boundary conditions.

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1 10 100 1000Size (microns)

Perc

enta

ge p

assi

ng

CSA HF

KB Paste

0

100

200

300

400

500

600

0 20 40 60 80 100 120 140 160

Time, t (hr)

Pres

sure

(kPa

)

Confining

KB PF u

CSA HF uKB PF σ'

CSA HF σ'

KB PF: Kanowna Bell Paste FillCSA HF: CSA mine Hydraulic Fill

F3.5



Figure 3.9. Typical result from ‘bender element’ test.

Figure 3.10. Typical pore water pressure (u ) and effective stress changes in a triaxial sample (CSA hydraulic fill material with 5% cement) hydrating under constant total stress and undrained boundary conditions (with periodic re-establishment of back pressure, to minimise effective stress change).

-8

-6

-4

-2

0

2

4

6

8

-100 0 100 200 300 400 500 600 700 800 900Time, t (μ Seconds)

Sent

wav

e am

plitu

de

-0.01

-0.008

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

0.008

0.01

Rec

eive

d w

ave

ampl

itude

0

100

200

300

400

500

600

700

800

900

1000

0 50 100 150 200 250Time, t (hr)

Pres

sure

(kPa

)

p'

u

Total stress

Cumulative u drop

u backup to minimise effective stress

F3.6



Figure 3.11. The development of bulk stiffness Ks with time for CSA hydraulic fill: experimental data (symbols) and Equation 3.31 (lines).

Figure 3.12. Rate of pore water pressure (u ) reduction with time after initial set for various cement contents for CSA hydraulic fill.

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250Time, t (hr)

Soil

bulk

mod

ulus

, Ks (

MPa

)

10% Binder (Maturity relation, eqn 3.31)10%Binder (from Go experiment)5% Binder (Maturity relation, eqn 3.31)5% Binder (from Go experiment)2% Binder (Maturity relation, eqn 3.31)2% Binder (from Go experiment)

0

5

10

15

20

25

30

0 20 40 60 80 100 120 140 160 180 200 220 240 260Time, t (hr)

Incr

emen

tal u

redu

ctio

n (k

Pa/h

r)

10% Binder

5% Binder

2% Binder

F3.7



Figure 3.13. Normalised apparent water loss rate plotted against time for different cement contents for CSA hydraulic fill: experimental data compared with Equation 3.32.

Figure 3.14. Comparison of experimental reduction of pore water pressure (u ) against time and adjusted theoretical solution for CSA hydraulic fill.

0

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

0.001

0 20 40 60 80 100 120 140 160 180 200 220 240 260Time, t (hr)

Nor

mal

ised

wat

er c

onsu

mpt

ion

rate

(c

m3/

cem

gra

m/h

r)10% Binder

5% Binder

2% Binder

0

500

1000

1500

2000

2500

3000

3500

4000

0 40 80 120 160 200 240Time, t (hr)

Cum

ulat

ive

pore

pre

ssur

e re

duct

ion,

Δu

(kPa

) 10% Theoretical10% Experiment5% Theoretical5% Experiment2% Theoretical2% Experiment0% Experiment

F3.8



Figure 3.15. Predicted and measured reduction in pore water pressure (u ) for KB paste backfill.

Figure 3.16. Temperature variation across stope half-space after 20 hours.

0

100

200

300

400

500

600

0 20 40 60 80 100 120 140Time, t (hr)

Cum

ulat

ive

pore

pre

ssur

e re

duct

ion,

Δu

(kPa

)2% Binder Prediction

2% Binder Experiment

5% Binder Preciction

5% Binder Experiment

0

5

10

15

20

25

30

35

0 1 2 3 4 5

x-coordinate (m)

Tem

pera

ture

(ºC

)

0 m 5 m

tBC =20ºC t0 =30ºC

Monitoring location

F3.9



Figure 3.17. Hydration test setup.

Top back-pressure control

Base back-pressure control

Bender Element processing system

Cell pressurecontrol


Cell

Sample enclosed in membraneBender elements

Top back-pressure control

Base back-pressure control

Bender Element processing system

Cell pressurecontrol


Cell

Sample enclosed in membraneBender elements

F3.10

Mechanics of Mine Backfill Ch 4 One Dimensional Consolidation Modelling - Figures


Figure 4.2. Schematic representing pore water continuity across an element ∂a.

Figure 4.1. Schematic representation showing the relationship between a, ξ and x in the convective coordinate system.

1

δa

δx

a

a + da

δξ

δx1

ξ(a+da,t)

ξ(a,t)

δa

( ) ( )[ ] avvna

vvn wswwsw ∂−∂∂

+− γγ

( ) wsw vvn γ−

⎟⎠

⎞⎜⎝

⎛∂∂

∂t

Va sh

F4.1



Figure 4.4. Comparison between the self desiccation pore pressure reduction in a hydration test and CeMinTaCo output.

Figure 4.3. Schematic showing mesh used in CeMinTaCo finite difference approximation.

0

100

200

300

400

500

600

700

800

900

0 50 100 150 200 250 300Time, t (hr)

Pore

pre

ssur

e, u

(kPa

)

Experiment: CSA HF, Cc = 5%, e = 0.7

CeMinTaCo

i+1

i

i-1

a2

a1

F4.2



Figure 4.5. Idealisation of the base boundary conditions used to represent a stope in CeMinTaCo.

Figure 4.6. CeMinTaCo output illustrating the influence of the cement induced mechanisms on the pore pressure response.

Typical stope

geometry

Idealisedone-

dimensional stope

Drainage through

draw-point

Vertical drainage

0

100

200

300

400

500

600

0 50 100 150 200 250 300

Time, t (hr)

Pore

pre

ssur

e, u

(kPa

)

Total vertical stress

No cement

Cc = 5%, no self desiccation

Cc = 5%, with self desiccation

Drainage through drawpoint

Typical stope geometry

Idealised one-dimensional stope

Vertical drainage

F4.3



Figure 4.7. Variation in permeability against time

Figure 4.8. Pore pressure against time for the different cases analysed.

1.0E-09

1.0E-08

1.0E-07

1.0E-06

0 50 100 150 200 250 300Curing time, t (hr)

Perm

eabi

lity,

k (m

/s)

k1

k2

k3

0

20

40

60

80

100

120

140

160

180

0 50 100 150 200 250 300Time, t (hr)

Pore

pre

ssur

e, u

(kPa

)

k1

k2

k3

F4.4



Figure 4.9. Pore pressure isochrones for the different permeability cases analysed.

Figure 4.10. e against σv for different damage parameters.

0

5

10

15

20

25

30

35

40

0 20 40 60 80 100 120 140 160 180 200Pore pressure, u (kPa)

Hei

ght a

bove

bas

e, h

(m

)

k1

k2

k3

k1

SSPP

Stope

Drawpoint

5 m

0.80

0.85

0.90

0.95

1.00

1.05

1.10

1.15

1.20

1.25

1.30

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Vertical effective stress, σv' (kPa)

e

b=3.0

b=0.05

F4.5



Figure 4.12. Development of material strength against time for different damage parameters.

Figure 4.11. CeMinTaCo output for different damage parameters.

0

50

100

150

200

250

300

350

400

450

500

0 50 100 150 200 250Time, t (hr)

Pore

pre

ssur

e, u

/ Ef

fect

ive

stre

ss, σ

' v / T

otal

stre

ss,

σ v (k

Pa)

σv'

u

σv

0

50

100

150

200

250

300

350

400

0 50 100 150 200 250 300 350 400Time, t (hr)

Stre

ss, σ

v′ /

Stre

ngth

, qu,

σvy

' (kP

a) qu (in situ )

σv′

qu (unstressed )

One-dimensional yield stress

F4.6



Figure 4.13. CeMinTaCo output for different damage parameters in free draining material

Figure 4.14. Development of material strength for different damage parameters with free draining fill.

0

50

100

150

200

250

300

350

400

450

500

0 50 100 150 200 250Time, t (hr)

Pore

pre

ssur

e, u

/ Ef

fect

ive

stre

ss, σ

' v / T

otal

stre

ss,

σ v (k

Pa)

σv'

u

σv

0

50

100

150

200

250

300

350

400

0 50 100 150 200 250 300Time, t (hr)

Stre

ss, σ

v′ /

Stre

ngth

, qu, σ'

vy (

kPa)

One-dimensional yield stress

qu (in situ)

σv'

qu ( without σv')

F4.7



Figure 4.15. Axial strain levels for different filling scenarios.

Figure 4.16. Comparison between CeMinTaCo and in situ pore pressure measurements.

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60 70Time, t (hr)

Pore

pre

ssur

e, u

(kPa

)

u, CeMinTaCo

u, In situ measurement

0%

1%

2%

3%

4%

5%

6%

7%

0 50 100 150 200 250 300Time, t (hr)

Ver

tical

stra

in, ε

v

Hydraulic fill, 0% cement

Paste fill, 5% cement

F4.8

Mechanics of Mine Backfill Ch 5 Two Dimensional Consolidation analysis (Minefill 2D) - Figures


(a) (b)

Figure 5.2. 8 noded isoparametric element (taken from Potts and Zdravković, 1999) showing (a) the parent element and (b) the global element.

Figure 5.1. Element geometry adopted for plane-strain displacement and pore pressure finite element calculations in this thesis.

1

Displacement only nodes

Displacement and pore pressure nodes

x

z

y

F5.1



(a) (b)

Figure 5.3. Element geometry adopted for axi-symmetric displacement and pore pressure finite element calculations in this thesis.

Figure 5.4. (a) shear stress against axial strain and (b) shear stress against mean stress for a triaxial test.

0

1000

2000

3000

4000

5000

6000

0 2000 4000 6000 8000Mean stress, p (kPa)

Shea

r stre

ss, τ

(kPa

)

Cemented yield surface

Triaxial stress path

Uncemented yield surface

0

1000

2000

3000

4000

5000

6000

0 5 10Axial strain, εq (%)

Shea

r stre

ss, τ

(kPa

)

Peak strength Residual

strength

Plastic shear strain to destroy

i

r2

r2

CL r1r1

1 radian

r

θ

z

Displacement only nodes

Displacement and water pressure nodes

F5.2



Figure 5.6. Illustration of one-dimensional consolidation problem.

Figure 5.5. Tangent shear stiffness normalised by small strain shear stiffness against shear stress normalised by the peak shear strength.

0.0

0.2

0.4

0.6

0.8

1.0

0 0.2 0.4 0.6 0.8 1 1.2t/tmax

Gt(c

em) /

G0(

cem

)

Experimental Model

1 m

4 mE = 100 MPa,k=1e-6 m/hr

u=0

u=0

F5.3



Figure 5.8. Illustration showing the one-dimensional self weight consolidation problem used in the Minefill-2D verification.

Figure 5.7. Comparison between Minefill-2D and the analytical solution for one-dimensional consolidation analysis.

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1Excess pore pressure normalised against initial value, uex/uex0

Dep

th (m

)

Initial pressure

Analytical 30 hr

Analytical 50 hr

Minefill-2D 30 hr

Minefill-2D 50 hr

4 mE = 100 MPa,k=1e-6 m/hr,γ=19.5 kN/m3

u=0

u=0

1 m

F5.4



Figure 5.10. Numerical simulation undertaken to verify the performance of the self desiccation mechanism.

Figure 5.9. Comparison between Minefill-2D and Plaxis for a self weight consolidation problem.

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 10 20 30 40 50 60 70 80 90Excess pore pressure, uex (kPa)

Dep

th (m

)Initial pressure 0 hr

Plaxis 6 hr

Plaxis 20 hr

Minefill-2D 6 hr

Minefill-2D 20 hr

500 kPa

500 kPa500 kPa Impermeable

F5.5



Figure 5.12. Numerical geometry for comparison between Minefill 2D and Darcy's law for a falling head permeability test.

Figure 5.11. Comparison between Minefill-2D and the analytical solution for self desiccation.

0

100

200

300

400

500

600

0 20 40 60 80 100 120 140

Time, t (hr)

Pore

pre

ssur

e, u

/ M

ean

stre

ss, p

' (kP

a)

p'

u

Analytical

Minefill-2D

4 mE = 1x1020 kPa,k=5x10-5 m/sec

u=0

Phreatic surface height

F5.6



Figure 5.13. Comparison with Minefill-2D and Darcy's law for the flow through the surface layer of the fill.

Figure 5.14. Comparison between Cemintaco and Minefill 2D.

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 5000 10000 15000 20000 25000Time, t (sec)

Phre

atic

surf

ace

heig

ht (m

)

Analytical

Minefill-2D

0

50

100

150

200

250

300

0 20 40 60 80 100 120 140 160 180 200Time, t (hr)

Pore

pre

ssur

e, u

/ V

ertic

al to

tal s

tress

, σv (

kPa)

u, Minefill-2D

u, CeMinTaCo

σv, CeMinTaCo

σv, Minefill-2D

4 m/day

u

F5.7



(a) (b) (c)

Figure 5.16. Finite element mesh used to represent (a) coarse mesh, (b) medium mesh and (c) a fine mesh.

Figure 5.15. Comparison between Cemintaco and Minefill 2D with a modified "initial set" point.

0

50

100

150

200

250

300

0 20 40 60 80 100 120 140

Time, t (hr)

Pore

pre

ssur

e, u

/ Ver

tical

tota

l stre

ss, σ

v (kP

a)

u, Minefill-2D

u, CeMinTaCo

σv, CeMinTaCo

σv, Minefill-2D

4 m/day

u

F5.8



Figure 5.17. Calculated pore pressure in the centre of the stope floor for different mesh shapes.

Figure 5.18. Calculated barricade stress in the centre of the stope floor for different mesh shapes.

0

20

40

60

80

100

120

140

160

180

0 20 40 60 80 100 120

Time, t (hr)

Cen

tre-li

ne p

ore

pres

sure

, u-c

l (kP

a)

Fine mesh

Medium mesh

Coarse mesh

u

0

20

40

60

80

100

120

140

0 20 40 60 80 100 120

Time, t (hr)

Bar

ricad

e st

ress

, σx (

kPa) Fine mesh

Medium mesh

Coarse mesh

σx

F5.9



(a) (b) (c)

Figure 5.19. Vertical total stress contours at the completion of filling for the (a) coarse mesh, (b) medium mesh and (c) the fine mesh.

Figure 5.20. Comparison between Minefill-2D and in situ measurements.

0

50

100

150

200

250

300

0 20 40 60 80 100 120 140 160 180Time, t (hr)

Ver

tical

tota

l stre

ss, σ

v / C

entre

-line

por

e pr

essu

re,

u cl (

kPa)

σv, No arching

ucl, In situ measurement ucl, Minefill-2D

σv

F5.10



(a) (b)

Figure 5.21. Illustration showing the boundary conditions adopted for the (a) fixed-BC and (b) free-BC case in the "arching" analysis.

Figure 5.22. Comparison between u and σv in a stope with fixed and free vertical displacement boundary conditions.

0

100

200

300

400

500

600

700

800

900

1000

0 20 40 60 80 100 120Time, t (hr)

Ver

tical

tota

l stre

ss, σ

v/ Po

re p

ress

ure,

u (

kPa)

u, free-BCu, fixed-BC

Self weight stress

σv, fixed-BC

σv, free-BCσv

u

40 m

13 m13 m

5 m5 m

5 m 5 m

F5.11



(a) (b)

Figure 5.23. σv contours for a stope with (a) fixed vertical displacement boundary conditions and (b) with free vertical displacement boundary conditions.

Figure 5.24. Total vertical stress along the stope centreline for the fixed and free BC.

σvσv

0

5

10

15

20

25

30

35

40

0 100 200 300 400 500 600 700 800 900Total vertical stress, σv (kPa)

Hei

ght (

m)

σv, fixed-BC

σv, free-BC

Self weight stress

F5.12

Mechanics of Mine Backfill Ch 6 Centrifuge Modelling - Figures


Figure 6.1. Schematic showing a section through the sample container.

Figure 6.2.(a) Photograph of strain gauged cylinder that was used to represent the stope walls and (b) the inside of the cylinder showing the rough cylinder walls.


Strain gauge set

Base load cells

Water overflow line 180

Rough wall

1

2

3

4

5

6

1

2

3

4

5

6

620

100

505

Base plate

O-ring seal


Strain gauge set

Base load cells

Water overflow line 180

Rough wall

1

2

3

4

5

6

1

2

3

4

5

6

620

100

505

Base plate

O-ring seal

F6.1



Figure 6.3. Photograph of the false base and loadcells that were used in the experiment.

Figure 6.4. Experimental apparatus positioned in a strong box on the UWA geotechnical centrifuge.

F6.2



Figure 6.5. Change in pressure and stress during Stage 1 loading.

Figure 6.6. Incremental change in u during Stage 2 loading.

0

20

40

60

80

100

22.3 22.8 23.3 23.8 24.3Time, t (hr)

Por

e pr

essu

re in

crem

ent, Δu

(kPa

)

Base Δu


u

σv, Layer 2

0

2

4

6

8

10

12

14

16

18

0 1 2 3 4 5 6 7 8

Time, t (hr)

Ver

tical

forc

e (k

N)

0

100

200

300

400

500

600

700

800

900

Pore

pre

ssur

e, u

(kPa

)

Total soil force

Base load cell force

Base u

Cylinder axial force

F6.3



Figure 6.6

Figure 6.7. Incremental load / stress distribution in second stage of loading.

Figure 6.8. Relationship between vertical effective stress and void ratio from the Rowe cell test.

1.5

1.6

1.7

1.8

1.9

2

2.1

2.2

2.3

2.4

2.5

0 20 40 60 80 100 120 140 160 180 200

Effective vertical stress, σ′v (kPa)

Voi

d ra

tio, e

Test data

Fitted relationship used in the modelling

0

1

2

3

4

22.4 22.9 23.4 23.9 24.4 24.9 25.4

Time, t (hr)

Ver

tical

forc

e in

crem

ent (

kN)

0

10

20

30

40

50

60

70

80

90

100

Hor

izon

tal t

otal

stre

ss in

crem

ent,

Δσ h

(kPa

)

Cylinder (wall) axial force (#6)

Base loadcells force

Applied force increment

σh #5

#6

#5σh

F6.4



Figure 6.9 Relationship between void ratio and permeability from Rowe cell.

Figure 6.10. Comparison between measured and calculated pore pressure in Stage 1.

1.0E-09

1.0E-08

1.0E-07

1.0E-06

1.0E-05

1.8 1.9 2 2.1 2.2

Void ratio, e

Perm

eabi

lity,

k (m

/s)

Fitted relationship used in the modelling

Direct measurementFrom cv obtained from displacement rateFrom cv obtained from pore pressure dissipation

0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8Time, t (hr)

Bas

e po

re p

ress

ure,

u (k

Pa)

Minefill-2D

Experiment

u

F6.5



Figure 6.11. Comparison between the measured and calculated load distribution in Stage 1.

Figure 6.12. Evolution of Go and qu against time for the kaolin with 25% cement mix.

Base

0

2

4

6

8

10

12

14

16

18

0 1 2 3 4 5 6 7 8Time, t (hr)

Ver

tical

forc

e (k

N)

Minefill -2D Base Force

Minefill-2D Axial Force

Applied force

Base loadcells

Cylinder (wall) axial load (#6)

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70 80 90 100Time, t (hr)

Smal

l stra

in sh

ear s

tiffn

ess,

Go

(MPa

)

0

100

200

300

400

500

600

700

Unc

onfin

ed c

ompr

essi

ve st

reng

th, q

u

(kPa

)

Go measurement

qu measurement

Application of layer 2 G o fit

q u fit

F6.6



Figure 6.13. Comparison between measured and calculated pore pressure in Stage 2.

Figure 6.14. Comparison between the measured and calculated load distribution in Stage 2.

0

1

2

3

4

22.4 22.9 23.4 23.9 24.4 24.9Time, t (hr)

Ver

tical

forc

e In

crem

ent (

kN

)

0

10

20

30

40

50

60

70

80

90

100

Cylinder (wall) axial force (#6)

Base loadcells force

Applied force increment

#6

#5 σh

Minefill-2D, Incremental axial forceMinefill-2D, Incremental base forceMinefill-2D, Incremental σh

Δσh

Incr

emen

t of h

oriz

onta

l tot

al s

tress

, Δσ h

(kPa

)

0

20

40

60

80

100

22 23 23 24 24 25Time, t (hr)

Por

e pr

essu

re in

crem

ent, Δu

(kPa

)

Base u


u

σv, Layer 2

Minefill-2D, Base u

F6.7

Mechanics of Mine Backfill Ch 7 Sensitivity Study - Figures


Figure 7.2. Evolution of permeability against time for different mine backfills.

Figure 7.1. Particle size distribution of backfills tested.

0

20

40

60

80

100

120

1 10 100 1000Size (micron)

Porti

on p

assi

ngHFA

HFB

PFA

PFB

1.0E-11

1.0E-09

1.0E-07

1.0E-05

0 50 100 150 200 250Time, t (hr)

Perm

eabi

lity,

k (m

/s) HFB

PFA

PFB

HFA

F7.1



Figure 7.3. Evolution of cohesion against time for different mine backfills.

Figure 7.4. Minefill 2D results of barricade stress against time for different backfill types.

0

20

40

60

80

100

120

0 20 40 60 80 100 120 140 160 180 200Time, t (hr)

Coh

esio

n, c

' (kP

a)

PFB

PFA

HFB HFA

0

50

100

150

200

250

0 20 40 60 80 100 120 140 160 180 200Time, t (hr)

Bar

ricad

e st

ress

, σx (

kPa)

PFB

PFA

HFA HFBσx

F7.2



Figure 7.5. Development of pore pressure against time for different mine backfills.

Figure 7.6. Pore pressure isochrones for different mine backfills.

0

5

10

15

20

25

30

35

40

0 50 100 150 200 250 300 350 400Pore pressure, u (kPa)

Hei

ght,

h (m

)

PFB

HFAPFA

Steady state seepage pore pressure

HFB

0

50

100

150

200

250

300

350

0 20 40 60 80 100 120 140 160 180 200Time, t (hr)

Pore

pre

ssur

e, u

(kPa

)

PFA

HFA

PFB

HFB

Steady state seepage pore pressure

u

F7.3



Figure 7.7. Influence of drawpoint permeability on pore pressure at the base of a stope with consolidating fill.

Figure 7.8. Pore pressure isochrones for consolidating fills with various drawpoint permeabilities.

0

50

100

150

200

250

300

350

400

450

500

0 100 200 300 400 500 600

Time, t (hr)

Pore

pre

ssur

e, u

(kPa

) kdp=0.1×kstope

kdp=10×kstope

Impermeable barricadeu

kdp=kstope

0

5

10

15

20

25

30

35

40

45

0 50 100 150 200 250 300 350 400 450Pore pressure, u (kPa)

Hei

ght,

h (m

)

Impermeable Barricade

kdp=0.1×kstopekdp=10×kstope

kdp=kstope

F7.4



Figure 7.9. Barricade stress against time for different drawpoint permeabilities with consolidating fills.

Figure 7.10. Pore pressure against time for consolidating fills with different permeabilities.

0

50

100

150

200

250

300

350

400

450

0 100 200 300 400 500 600

Time, t (hr)

Bar

ricad

e st

ress

, σx (k

Pa)

kdp=0.1×kstope

kdp=10×kstope

Impermeable barricadeσx

kdp=kstope

0

50

100

150

200

250

0 100 200 300 400 500 600Time, t (hr)

Pore

pre

ssur

e, u

(kPa

)

u

k=0.1×kHFB

k=10×kHFB

k=kHFB

F7.5



Figure 7.11. Barricade stress against time for consolidating fills with different permeabilities.

Figure 7.12. Pore water pressure against time for consolidating fill with different binder contents.

0

20

40

60

80

100

120

140

0 100 200 300 400 500 600Time, t (hr)

Bar

ricad

e st

ress

, σx (

kPa)

σx

k=10×kHFB

k=kHFB

k=0.1×kHFB

0

50

100

150

200

250

0 100 200 300 400 500 600Time, t (hr)

Pore

pre

ssur

e, u

(kPa

)

0.0% cement1.5% cement

3.0% cement8.0% cement

u

F7.6



Figure 7.13. Barricade stress against time for consolidating fills with different binder contents.

Figure 7.14. Comparison between applied shear stress and cohesion for a boundary element.

0

20

40

60

80

100

120

140

160

180

200

0 100 200 300 400 500 600Time, t (hr)

Bar

ricad

e st

ress

, σx

(kPa

)

0.0% cementσx

1.5% cement

3.0% cement

8.0% cement

0

20

40

60

80

100

120

140

160

0 100 200 300 400 500 600Time, t (hr)

Shea

r stre

ss, τ

/Coh

esio

n, c

' (kP

a)

1.5% cement, cohesion

3.0% cement, shear stress

1.5% cement, shear stress

3.0% cement, cohesion

τ

F7.7



(a) (b)

(a) (b)

Figure 7.15. Contour of cohesion at the end of filling for the (a) the 3.0% cement and (b) the 1.5% cement case.

Figure 7.16 Total vertical stress calculated for the (a) 3.0% cement and (b) the 1.5% cement case.

Interface shear induced softening

F7.8



Figure 7.17. Influence of filling rate on consolidating fill pore pressures.

Figure 7.18. Influence of filling rate on consolidating fill barricade stress.

0

50

100

150

200

250

300

350

0 100 200 300 400 500 600Time, t (hr)

Bar

ricad

e st

ress

, σx (

kPa)

σx

0.12 m/hr 0.06 m/hr

.0.6 m/hr

4 m/hr

2 m/hr

0

50

100

150

200

250

300

350

400

450

0 100 200 300 400 500 600

Time, t (hr)

Pore

pre

ssur

e, u

(kPa

)

0.06 m/hr

4 m/hr

u

0.12 m/hr0.6 m/hr

2 m/hr

F7.9



Figure 7.19. Relationship between pore pressure and barricade stress in a consolidating fill.

Figure 7.20. Pore pressure against time for non-consolidating fills with different drawpoint permeabilities.

0

50

100

150

200

250

300

350

400

0 50 100 150 200 250

Barricade stress, σx (kPa)

Pore

pre

ssur

e, u

(kPa

)

Kdp=Kstope

Kdp=0.1×Kstope

kdp=10×Kstope

σxu

0

50

100

150

200

250

0 20 40 60 80 100 120 140 160 180 200

Time, t (hr)

Pore

pre

ssur

e, u

(kP

a)

kdp=0.1×kstope

kdp=kstope

kdp=10×kstope

u

F7.10



(a) (b)

Figure 7.21. Barricade stress against time for non-consolidating fills with different drawpoint permeabilities.

Figure 7.22. Pore pressure profile at the end of filling for (a) kdp=10k stope and (b) kdp=0.1kstope.

0

20

40

60

80

100

120

140

160

180

200

0 20 40 60 80 100 120 140 160 180 200Time, t (hr)

Bar

ricad

e st

ress

, σx (

kPa)

kdp=0.1×kstope

kdp=kstope

kdp=10×kstope

σx

F7.11



Figure 7.23. Pore pressure against time for non-consolidating fills with different permeabilities.

Figure 7.24. Barricade stress against time for non-consolidating fills with different permeabilities.

0

50

100

150

200

250

0 20 40 60 80 100 120 140 160 180 200

Time, t (hr)

Pore

pre

ssur

e, u

(kPa

)

k=10×kPFAu

k=kPFA

k=0.1×kPFA

0

20

40

60

80

100

120

140

160

0 20 40 60 80 100 120 140 160 180 200Time, t (hr)

Bar

ricad

e st

ress

, σx (k

Pa)

σx k=10×kPFA

k=kPFA

k=0.1×kPFA

F7.12



Figure 7.25. Pore pressure against time for non-consolidating fills with different cement contents.

Figure 7.26. Barricade stress against time for non-consolidating fills with different cement contents.

0

50

100

150

200

250

300

350

400

0 20 40 60 80 100 120 140 160 180 200Time, t (hr)

Pore

pre

ssur

e, u

(kPa

)

.

1.5% cement

3.0% cement

4.5% cement

u

0

50

100

150

200

250

300

0 20 40 60 80 100 120 140 160 180 200

Time, t (hr)

Bar

ricad

e st

ress

, σx (

kPa) 1.5% cement

3.0% cement

4.5% cement

σx

F7.13



Figure 7.28. Pore pressure against time for non-consolidating fills with different filling rates.

Figure 7.27. Barricade Stress and pore pressure against time for non-consolidating fill with a bonded and unbonded interface.

0

50

100

150

200

250

300

350

400

450

500

0 20 40 60 80 100 120 140 160 180 200Time, t (hr)

Pore

pre

ssur

e, u

(kPa

)

0.2 m/hr

2.5 m/hr

0.5 m/hr

u

0

20

40

60

80

100

120

140

160

180

200

0 20 40 60 80 100 120 140

Time, t (hr)

Bar

ricad

e st

ress

, σx /

Por

e pr

essu

re, u

(kPa

)

σx , Cohesionless interface

u , Cohesionless interface

σx , Bonded interface

u , Bonded interface

σxu

F7.14



Figure 7.29. Barricade stress against time for non-consolidating fills with different filling rates.

Figure 7.30. Development of effective stress within an element of consolidating and non-consolidating fill against time.

0

50

100

150

200

250

300

350

400

450

500

0 10 20 30 40 50 60 70 80 90 100Time, t (hr)

Ver

tical

eff

ectiv

e st

ress

, σv'

/ Ver

tical

tota

l st

ress

, σv / P

ore

pres

sure

, u (k

Pa)

σv(self weight) HFA, -Δu S.D. only

σ′v(self weight)

HFA, σv'

PFB, σv'

PFB, Δu S.D. only

0

50

100

150

200

250

300

350

0 20 40 60 80 100 120 140 160 180 200

Time, t (hr)

Bar

ricad

e st

ress

, σ x

(kP

a)

2.5 m/hr

0.5 m/hr

0.2 m/hr

σx

F7.15



Figure 7.31. Development of effective stress against time in a consolidating fill.

Figure 7.32. Development of effective stress against time in a non-consolidating fill.

0

50

100

150

200

250

300

350

400

0 50 100 150 200 250 300 350 400 450 500Time, t (hr)

Ver

tical

eff

ectiv

e st

ress

, σv'

(kPa

)

σv' 0.05 m/hr (minefill-2D)

Effective self weight 0.05 m/hr

Effective self weight 0.5 m/hr



Effective self weight 1 m/hr

0

50

100

150

200

250

300

350

0 50 100 150 200 250 300 350 400

Time, t (hr)

Ver

tical

eff

ectiv

e st

ress

, σv'

(kPa

)

1 m/hr

0.5 m/hr

0.15 m/hr 0.05 m/hr

Self desiccation -Δu

F7.16



Figure 7.33. Development of effective stress against time at different elevations in a non-consolidating fill.

0

100

200

300

400

500

600

0 20 40 60 80 100 120 140 160 180 200Time, t (hr)

Ver

tical

eff

ectiv

e st

ress

, σv'

(kPa

)

2 m

15 m

19 m25 m 29 m

Self desiccation -Δu

σv from fill self weight without arching

F7.17


Tables

Mechanics of Mine Backfill Ch 5 Two Dimensional Consolidation analysis (Minefill 2D) - Tables


Value1.2-0.11.40.5

0.032

5.00E-0640125330

60003

0.1

Permeability parameter (Eqn 4.1), d k (-)

Uncemented compression parameter (Eqn 4.1), ac

Material Property

Uncemented compression parameter (Eqn 4.1), bc

Rate of hydration parameter, d (day1/2)

Cement Content (% by weight)Damage Constant, b

Table 5.1. Material properties adopted for CeMinTaCo - Minefill-2D comparison.

Ultimate cohesion, c′ max (kPa)Ration between 1D compressive yield and CFriction angle, degrees (º)Rigidity

Initial set, t o (day)

Efficiency of hydration, E h (cm3/g)Permeability parameter (Eqn 4.1), c k (m/s)

T5.1

Mechanics of Mine Backfill Ch 5 Two Dimensional Consolidation analysis (Minefill 2D) - Tables


Table 5.2. P.F.-A material properties (from Helinski et al. 2007) adopted for back analysis of in situ test results.

Initial bulk modulus,

K max-i (MPa)

Ultimate bulk modulus,

K max-f (MPa)

Rate of hydration

parameter, d (day1/2)

Initial set, to (day)

Efficiency of hydration, Eh

(cm3/g)

Permeability parameter,

ck (m/s)


dk (-)

Ultimate cohesion, c′-f (kPa)

Friction angle,

degrees (º)

Ultimate unconfined

compressive strength, qu-f

(kPa)

50 750 1.4 0.3 0.032 5.0x10-6 40 125 30 433

Table 5.3. Material properties adopted in the investigation of the arching mechanism.

Initial bulk modulus,

K max-i (MPa)

Ultimate bulk modulus,

K max-f (MPa)

Rate of hydration


Initial set, to (day)

Efficiency of hydration, Eh

(cm3/g)


ck (m/s)


dk (-)


Friction angle,

degrees (º)

35 650 0.9 0.4 0.032 5.36 15 400 35

T5.2

Mechanics of Mine Backfill Ch 6 Centrifuge Modelling - Tables


Table 6.1. Material properties for kaolin with 25% cement content.

Initial bulk

modulus, K max-i

(MPa)

Ultimate bulk

modulus, K max-f

(MPa)

Rate of hydration


Initial set, to

(day)

Efficiency of hydration, Eh (cm3/g)

Uncemented compression

parameter (Eqn 5.5), ac

Uncemented compression

parameter (Eqn 5.5), bc


ck (m/s)


dk (-)


Friction angle,

degrees (º)

Ultimate unconfined

compressive strength, qu-f

(kPa)

40 530 0.9 0.2 0.025 -2.0x10-3 1 3.0x10-15 25 287 23 870

T6.1

Mechanics of Mine Backfill Ch 7 Sensitivity Study - Tables


Property Symbol & Units Hydraulic Fill A (HFA)

Hydraulic Fill B (HFB)

Paste Fill A (PFA)

Paste Fill B (PFB)

Initial bulk modulus

K max-i (MPa) 80 60 50 31

Ultimate bulk modulus

K max-f (MPa) 630 690 750 950

Rate of hydration parameter

d (day1/2) 1.2 0.9 1.4 2.3

Initial set t o (day) 0.3 0.3 0.3 0.3Efficiency of

hydrationE h (cm3/g) 0.064 0.032 0.032 0.018

Permeability parameter

c k (m/s) 2.5x10-1 6.2x10-4 5.0x10-6 5.0x10-8

Permeability parameter

d k (-) 80 15 40 10

Ultimate cohesion

c′ max (kPa) 110 120 125 116

Friction angle φ′ (º) 35 35 30 28Ultimate

unconfined compressive

strength

q u-f (kPa) 422 461 433 380

Low permeabilityLow uncemented stiffness

Generally slower rates of cement hydration

Hydraulic Fill (classified tailings)

Generally faster rates of cement hydration

High uncemented stiffnessHigh permeability

Table 7.1. Comparison of hydraulic fill and paste fill properties.

Table 7.2. Material Properties.

Paste Fill (full-stream tailings)

Greater than 15-20 % finer than 20 μmTransported in a laminar flow regime at

lower water contentsNon-settling on placementSettles on placement, creating

surface water

Transported in a turbulent manner with high water contents

Less than 10 % finer than 10 μm

T7.1