Use of MWD data for detecting discontinuities

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Dirk van Oosterhout 21.06.2016

Use of MWD data for detecting

discontinuities

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Use of MWD data for detecting discontinuities

By

D. van Oosterhout

in partial fulfilment of the requirements for the degree of

Master of Science in Geo-Engineering

at the Delft University of Technology,

to be defended publicly on Thursday June 30, 2016 at 12:00.

Supervisor: Dr. Ir. D.J.M. Ngan-Tillard TU Delft Thesis committee: Prof. Dr. G. Bertotti TU Delft Dr. J. Benndorf, TU Delft Prof. Dr. A. Bruland NTNU Dr. Ir. P.D. Jakobsen NTNU

Ir. M.L Arntsen, Norwegian Public Roads Administration

An electronic version of this thesis will available at http://repository.tudelft.nl/.

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Abstract

In the last decades, measurement while drilling, or MWD, technology has set foot in the drill and blast tunnelling industry. Penetration rate, thrust, torque pressure, percussive pressure, rotation speed, water flow and water pressure are registered on a centimetre scale and processed to parameters more dependent on geology. These parameters could ideally be used to adapt the blast design for a more efficient blast and to predict the amount of rock support needed. In reality, MWD technology is often only used to document geology. The main reasons for this could be that the workflow is not fully adapted to the MWD technology, the knowledge about MWD is not sufficient or the ability of MWD to represent the geology has not been extensively investigated and verified for drill and blast tunnelling.

MWD has great potential since it is a relatively cheap and simple method of collecting a larger amount of data, which does not interfere with the workflow in drill and blast tunnelling. The aim is to investigate the ability to detect discontinuities and their geometrical properties in MWD data and to evaluate the usability of MWD data in terms of detecting discontinuities.

The first of five objectives is a literature review on the subjects of MWD technology, discontinuities in rock masses, previous research and statistical data analysis methods. Raw MWD parameters are processed and filtered by software, which can somewhat be seen as eliminating influences such as depth dependency and percussive pressure. This results in modified penetration rate, torque or water pressure which represents rock mass properties. Previous research showed the inability to compare MWD data and available geological reporting about fractures was due to a large difference in scale. For statistical analysis of MWD data in this study 4 methods are considered. Principle component analysis and k-means cluster analyses are forms of unsupervised learning and can potentially help to understand and reduce complexity of multivariate datasets. Linear and logistic regressions are forms of supervised learning that can give insight into predictability and potentially predict the presence discontinuities.

The second objective is to gather data, which is appropriate and detailed enough to study relations between MWD data and discontinuities. Two tunnels under construction are visited where limestone and highly foliated phyllite are the dominant rock types. These are the Solbakktunnelen and Bjørnegårdtunnelen. While not disturbing the construction work, different methods of detailed geological mapping are used. Blasthole remains used as scanlines for mapping discontinuities and mapping discontinuities in the contour and face led to a dataset reflecting the geological situation in tunnels. Another method for mapping discontinuities, which is not influenced as much by blasting, is borehole inspection. The use of an inspection camera and an optical televiewer resulted in 11 video footages and 25 detailed recordings of 5 meter long boreholes.

The third objective is to evaluate the data by a visual comparisons of geological data and MWD data.

Comparing the mapped geology and 3D images of MWD data showed that fractures with a certain infill or aperture are visible in MWD data. The more detailed geological data showed that an open fracture or a fracture with soft infill and an aperture wider than 1cm often leads to a peak in penetration rate, rotation pressure, processed penetration and processed rotation pressure.

The fourth objective is to apply statistical methods to come to a more in depth understanding of the relation between MWD data and discontinuities and confirm findings in objective 3. Since it is suspected that only the actual location and aperture can be predicted, a vector is made by assigning the number 1 to each MWD sampling depth between the upper and lower boundary of a discontinuity. For intact rock, a 0 is assigned to each MWD sampling depth. The principle component analyses showed that the dataset could be reduced to a manageable number of 5 to 7 components and that around 80% of the variability was retained. K-means cluster analyses is found to be an appropriate analysis for 2 out of 4 datasets. It led to the understanding that responses in MWD data due to lithological discontinuities without an aperture cannot be separated from intact rock. Training the data with logistic regression

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analyses confirmed this finding. Logistic regression did however differentiate MWD data of open fractures from other MWD data in half of the collected data. 2 out of 3 fractures were predicted, but the exact location and size of predicted fractures differ slightly from the real location. The regression for the fractures with soft infill was successful for a quarter of the data. 6 out of 9 fractures with clayey infill were predicted, again with a small deviation in size. Testing the regression equations on test datasets, which were not part of the input for data training, did not lead to the correct prediction of fractures.

The last objective is to discuss the current and future usability of MWD data for the Norwegian Public Roads Administration. Even though the statistical analyses did not fully succeed in separating responses of fractures in MWD data, visually responses are found to be characteristic. The fact that not all discontinuities give a distinctive response, makes calculations of rock quality designation unreliable.

Therefore, in terms of rock support, MWD data can only assist in decision making concerning spot bolting to secure wedges due to large fractures. This research might contribute to help understand and predict grout volumes. The use of 3D images of MWD data could give a better understanding of the in situ fracture structure. Ideally, this knowledge can be used to anticipate possible under- and overbreak due to these fractures before blasting. Considering the findings in this study, it is still presumed that MWD technology has great potential even if it might not lead to the prediction of each type of discontinuity.

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Acknowledgments

During this project I got help of many different parties and individuals. Firstly I would like to thank every Norwegian for showing patience with my Norwegian language and not shifting to English too easily. You have contributed a great deal to my Norwegian language skills.

I would like to thank the team from the Norwegian Public Roads Administration working on the Bjørnegårdtunnelen and Marco Filipponi from Marti AS at the Solbakktunnelen site. Not only has gathering of data been essential for my thesis, it was special to learn about tunnel construction outside lecture rooms.

The help of Thorvald Wetlesen from Bever Control AS has been crucial to get to this result. Thanks for your openness in MWD processing method, assistance with gathering MWD data and support with data management. In addition, I would like to thank Harald Elvebakk from NGU for driving a long way to provide the televiewer service.

Essential for me in writing this thesis have been five academics and one engineer from the Norwegian Public Roads Administration. I would like to thank Amund Bruland, Pål Drevland Jakobsen and Mari Lie Arntsen for providing data and contacts, taking care of finances, giving valuable feedback and much more. It means a great deal to me to be welcomed as an outsider and be given this much trust. At TU Delft I would like to thank Giovanni Bertotti for support in the geological field and Jörg Benndorf for support with data analysis. I want to express special thanks to Dominique Ngan-Tillard who has been my direct supervisor. She has supported me through the last years in my choices of academic ambitions.

Overall, the supervision has been perfect, giving me the freedom to steer my own project.

To finish I would like to express my enormous gratitude towards my family and Kari. Thanks!

Delft, University of Technology Dirk van Oosterhout

June 5^th, 2016

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Table of content

Abstract ... I Acknowledgments ... III Table of content ... IV List of figures ... VIII List of tables ... X

1. Introduction ... 1

1.1 MWD technology in drill and blast tunnelling ... 1

1.2 Drill and blast tunnelling ... 1

1.3 The Norwegian Public Roads Administration ... 2

1.4 Problem definition, aim and objectives ... 3

1.5 Research questions ... 4

1.6 Limitations 5 1.7 Scope and constraints ... 6

1.8 Thesis outline ... 6

2. Literature study ... 7

2.1 MWD technology... 7

2.2 Discontinuities and discontinuity mapping ... 7

2.3 The drilling process ... 8

2.4 MWD responses to discontinuities ... 9

2.5 Common practise of geological mapping in Norwegian tunnels ... 9

2.6 Data processing ... 10

2.7 Multivariate statistics ... 13

2.7.1 Principle Component Analysis ... 13

2.7.2 K-means cluster analysis ... 15

2.7.3 Multiple linear regression analysis ... 16

2.7.4 Multiple logistic regression... 17

2.7.5 Overview of statistical analyses ... 20

2.8 Correlation between MWD and geology ... 20

2.8.1 Grouting volumes and MWD data ... 20

2.8.2 Geological boundaries and zones of weaknesses ... 21

2.8.3 Mechanical properties of rock and MWD data... 22

2.8.4 Mapped geology and MWD data ... 22

2.8.5 Findings in research in the field of MWD technology ... 22

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3. Data gathering and collected data ... 23

3.1 Preparation of fieldwork at Bjørnegårdtunnelen ... 23

3.1.1 Project ... 23

3.1.2 Geology ... 23

3.2 Preparation of fieldwork at Solbakktunnelen ... 24

3.2.1 Project ... 24

3.2.2 Geology ... 24

3.3 Geological mapping ... 25

3.3.1 Tunnel wall mapping ... 25

3.3.2 Borehole inspection ... 26

3.4 Fieldwork at Bjørnegardtunnelen ... 26

3.4.1 Tunnel wall mapping and MWD data ... 27

3.4.2 Borehole inspection and MWD data ... 30

3.4.3 Overview of collected data ... 34

3.5 Fieldwork at Solbakktunnelen ... 34

3.5.1 Tunnel wall mapping and MWD data ... 34

3.5.2 Borehole inspection and MWD data ... 35

3.5.3 Overview of collected data ... 36

4. Visual validity assessment of MWD data ... 37

4.1 Tunnel wall mapping data ... 37

4.1.1 Overview of observations in MWD data and mapped geology ... 39

4.2 Televiewer data ... 39

4.2.1 Data preparation ... 39

4.2.2 Borehole 1 ... 40

4.2.3 Borehole 2 ... 40

4.2.4 Borehole 3 ... 41

4.2.5 Borehole 4 ... 41

4.2.6 Borehole 5 ... 42

4.2.7 Borehole 6 ... 42

4.2.8 Borehole 7 ... 42

4.2.9 Borehole 8 ... 43

4.2.9 Borehole 9 and 10 ... 43

4.2.10 Borehole 11 to 15 ... 43

4.2.11 Borehole 16 to 20 ... 44

4.2.12 Borehole 21 to 25 ... 45

4.2.13 Overview of observations in MWD data and mapped geology with televiewer ... 46

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4.3 Borehole camera data ... 46

5. Statistical validity assessment of MWD data ... 48

5.1 Data sets 48 5.2 Principle component analysis ... 50

5.2.1 Determining the number of principle components ... 50

5.2.2 Orthogonal and oblique rotation ... 51

5.2.3 PCA outcome dataset 1 ... 52

5.2.7 Overview of PCA analyses ... 59

5.3 Cluster analysis ... 59

5.3.1 K-means cluster analysis ... 59

5.3.2 Cross tabulation clusters and discontinuity groups ... 60

5.3.2.1 Dataset 1 ... 60

5.3.2.2 Dataset 2 ... 62

5.3.2.2 Dataset 3 and 4... 62

5.3.3 Overview of cluster analysis outcome ... 63

5.4 Logistic regression ... 63

5.4.1 Training dataset 1 ... 63

5.4.1.1 All discontinuities ... 63

5.4.1.2 Discontinuities with an aperture>0 ... 64

5.4.1.3 Discontinuities with an aperture>0 and no infill ... 64

5.4.4.1 Discontinuities and with an aperture>0 ... 67

5.4.4.2 Discontinuities with an aperture>0 and soft or no infill ... 67

5.4.5 Summary of logistic regression analyses ... 68

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5.5 Regression equation ... 69

5.5.1 Testing regression outcome from dataset 1 ... 69

5.5.5 Overview of predicted discontinuities ... 70

6. Discussion ... 71

6.1 Literature study ... 71

6.2 Data gathering and collected data ... 71

6.3 Visual validity assessment of MWD data ... 71

6.4 Statistical validity assessment of MWD data ... 72

6.5 Current usability of MWD ... 74

7. Conclusion and recommendations ... 75

Research questions ... 75

Recommendations ... 77

Bibliography ... 79

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List of figures

Figure 1. Illustration of the drill and blast cycle, starting in the top with drilling and loading and continuing with blasting, ventilating, mucking, scaling, installing rock support and surveying (Heiniö,

1999). ... 2

Figure 2. Top view of tunnelling sites and tunnel section with in the top Solbakktunnelen and below the Bjørnegårdtunnelen (The Norwegian Public Roads Administration, 2014). ... 4

Figure 3. Illustration of primary geometrical properties of discontinuities in rock (Hudson & Harrison, 1997). ... 8

Figure 4. Illustration of feed, rotation and percussion impact for the top hammer drilling method (Olsen V. , 2009). ... 9

Figure 5. 2D documentation of discontinuities by the Norwegian Public Roads Administration (Lillevik, 2011). ... 10

Figure 6. Two dimensional illustration of Principle Component Analysis (Powell & Lehe, u.d.). ... 14

Figure 7. Illustration of binary outcome in a linear regression scatter plot. ... 17

Figure 8. The logit function of logistic regression. ... 17

Figure 9. Illustration of how Hjelme placed boreholes in a spread out tunnel contour sheet for comparing MWD data to mapped geology. ... 21

Figure 10. Map of southern Norway with tunnel site locations. ... 23

Figure 11. Cross sections of geology encountered with constructing the two tunnel profiles (GEOVITA, 2014). ... 24

Figure 12. Geological map with Solbakktunnelen section, the yellow line is approximately 2km (Multiconsult, 2009). ... 25

Figure 13. Illustration of an optical televiewer (NGU, 2015). ... 26

Figure 14. Mapping at tunnel wall in tunnel A at profile 955 of an injection borehole remain. Person length is 1.75m. ... 27

Figure 15. Graphical representation of calcite infilled discontinuity in tunnel A at profile 505. ... 28

Figure 16. Graphical approximation of positions of discontinuities seen along tunnel face 975 in tunnel tube A. ... 28

Figure 17. View along the tunnel face 975 tunnel A. The packers are separated by approximately 1.2m (top left), the packers stick approximately 30 to 40 cm out of the wall (top right), the rock bolts in the shotcrete have a diameter of 20cm (lower right)... 29

Figure 18. Approximate location holes 1 and 2 drilled with angles of 20° to 30° from the tunnel axis. 30 Figure 19. Approximate location holes 3 to 10 drilled with angles of 55° and 90° from the tunnel axis. ... 31

Figure 20. Approximate location holes 11 to 15 close to 975 and holes 16 to 20 close to 960, drilled with angles of 40° to 60° from the tunnel axis. ... 31

Figure 21. Approximate location holes 21 to 25 drilled with angles of 20° to 30° from the tunnel axis. ... 32

Figure 22. Graph showing drops in feeder pressure due to jamming of the drill bit caused by difficulties with aligning drilling direction of the large hole. ... 33

Figure 23. The inspection camera and portable computer. ... 35

Figure 24. Screenshots of typical video footages. ... 36

Figure 25. View from underneath the tunnel, or the tunnel floor, of RMS normalised penetration with a moving average of 4 values showing possible locations of mapped discontinuities. ... 38

Figure 26. Top view of RMS normalised penetration with a moving average of 4 values of the contour showing possible locations of mapped discontinuities. ... 38

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Figure 27. Illustration of mismatch between televiewer depth and MWD data. ... 46 Figure 28. Zones with light coloured minerals which might give a response in MWD data. Left in borehole 1 at a depth of 4.8m and right in borehole 4 at a depth of 3.5m. ... 47 Figure 29. Scree plot for dataset 1 to determine the number of statistically significant components. . 51

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List of tables

Table 1. Over view of statistical analyses. ... 20

Table 2. Geometrical properties of discontinuities crossing an injection borehole remain close to profile 955 in tunnel A. ... 27

Table 3. Overview of collected data at the Bjørnegårdtunnelen. ... 34

Table 4. Overview of collected data at the Solbakktunnelen. ... 36

Table 5. Overview of observations in MWD data and mapped geology. ... 39

Table 6. Overview of observation in MWD data and geological data from the televiewer inspections.47 Table 7. Table showing how depth sampling of discontinuity location vector is done. ... 49

Table 8. Component correlation matrices with an oblique rotation for all datasets. Highlighted in green are the highest Pearson correlations... 51

Table 9. Total variance explained by principle components. ... 53

Table 10. Pattern matrix giving the correlation between parameters and principle components for dataset 1. ... 54

Table 14. Overview of PCA analyses. ... 59

Table 15. The outcome of Variance Ration Criterion. ... 59

Table 16. Cross tabulation of MWD clusters and discontinuity groups for dataset 1. ... 61

Table 17. Cross tabulation of principle component clusters and discontinuity groups for dataset 1. ... 61

Table 18. Cross tabulation of MWD clusters and discontinuity groups for dataset 2. ... 62

Table 19. Cross tabulation of PC clusters and discontinuity groups for dataset 2. ... 63

Table 20. Overview if cluster analysis outcome. ... 63

Table 21. Outcome of sensitivity analysis of regression analysis with discontinuities with an aperture >0 and no infill. ... 65

Table 22. Outcome of sensitivity analysis of regression analysis with discontinuities with an aperture >0. ... 65

Table 25. Outcome of sensitivity analysis of regression analysis with discontinuities with an aperture >0 and soft or no infill. ... 68

Table 27. Overview of the best predicting models which meet the Wald statistics and Hosmer and Lemeshow test. ... 69

Table 28. Overview of predictions in the test datasets. ... 70

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1. Introduction

In this first chapter readers will be introduced to MWD technology, tunnelling methods and the company which assigned this thesis. Next, the problem statement and objectives will be given followed by research questions and limitations.

1.1 MWD technology in drill and blast tunnelling

In the beginning of the 20^th century, Schlumberger pioneered with downhole logging for the oil industry with the aim of increasing the understanding of geology in oil fields. In the 1970’s the technology was introduced in the mining industry to detect ore bodies (Valli, 2010). In the last decades MWD has also set foot in the tunnelling industry and since 1997 MWD tools are equipped standardly on drilling rigs.

MWD stands for measurement while drilling and it is in principle the registration of drilling parameters.

These drilling parameters are processed. The raw and processed drilling parameters are interpreted to predict geology and improve drilling efficiency, this is often called Drill Parameter Interpretation. MWD technology in tunnelling leads to large amounts of data. Nowadays computers and software packages make it possible to process this data and visualize it in 3D. Ideally, these outcomes are used to adapt the blast design for a more efficient blast and to predict the amount of rock support needed (Nilsen &

Palmstrom, 2013). In reality, it is often only used to document geology.

Nevertheless, MWD technology has great potential as it is a relatively cheap and simple method of collecting a larger amount of data, which does not intervene with the workflow in drill and blast tunnelling. In the next section the use of MWD technology in drill and blast tunnelling is introduced.

1.2 Drill and blast tunnelling

Two commonly used tunnelling techniques are tunnelling with a tunnel boring machine and drill and blast tunnelling. Both involve measurement while drilling, but this thesis is merely focussed on drill and blast tunnelling. Drill and blast tunnelling consists of a series of actions, where each cycle typically ends with a 5 meter tunnelling advance depending on rock mass quality and blast vibrations. It starts with drilling blast holes, usually of 5m long. Several tens of holes are drilled, but an average number of holes is hard to give since the number of holes depend on the rock, wanted perfection of tunnel contour and tunnel dimensions. MWD data is collected for each blast hole. The next step is charging and blasting.

After ventilation to reduce dust and dangerous gas concentrations, the blasted rock is transported out of the tunnel by trucks or a conveyor belt. At this stage the rock mass might still be unstable so the rock surfaces are scaled by machine and hand to remove loose hanging blocks. After this, it is up to the geologist or engineering geologist and the contractor to decide what kind of rock support will be used to support the rock on the long term. In Norway this is often called ‘byggherrens halvtime’, which directly translated means ‘the client’s half hour’. It is a contracted activity where no other activities should take place than geological mapping and deciding on rock support. The next step in this process is the installation of the rock support, which can be bolts, reinforced ribs of sprayed concrete, spiling bolts, reinforced shotcrete or a combination of these support types. Often these are installed directly after removal of blasted rock. In some cases these types of rock support are temporary. Permanent rock support might be the installation of additional rock support or cast in place concrete lining. The final step is a survey to prepare the next cycle. The cycle is illustrated in Figure 1. Tunnelling is an expensive activity, time efficiency is therefor of the essence.

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As will be discussed later, this thesis will be mainly focused on the detection of discontinuities. If discontinuities can be identified during probe or blast hole drilling this could help in different fields.

Fracturing has great influence on the rock mass quality and therefore the amount of rock support needed. For example, a fractured rock with small discontinuity spacing can require multiple forms of rock support like shotcrete, bolts, spiling bolts etc. A rock mass with multiple discontinuity sets could lead to the formation of wedges, which can collapse. Large wedges can be supported by spot bolting.

Another form of rock support is injection of grout. Grout injection is done to increase the water tightness. Large volumes of grout are injected in fractures in rock masses. The understanding of where and how rocks are fractured could potentially help to predict the volume of grout that is needed.

Another example when detection of large discontinuities can be useful is to prevent under- and overbreak. Excavating too much or too little rock would require additional shotcrete or reblasts to get the desired tunnel contour. Fracturing in the rock mass is one of the causes of under- and overbreak.

To summarize, detection of discontinuities before excavation would help to characterize rock masses early and to anticipate to these rock mass conditions before excavation.

1.3 The Norwegian Public Roads Administration

The Norwegian Public Roads Administration, or NPRA, is responsible for planning, construction and operation of the national and county road network. This road network also includes about 1000 road tunnels with an added length of about 800km. Two tunnels which are assigned by the NPRA have been visited to collect data for this thesis: Solbakktunnelen and Bjørnegårdtunnelen. In Figure 2 illustrations of both tunnels are given. The Solbakktunnel will be a 14.3km tunnel, which will make it world-longest subsea road tunnel with the deepest point at 290m below sea level. The Bjørnegårdtunnel will be a 2.3km tunnel and it is built to reduce traffic in Sandvika. This thesis is written in collaboration with the Norwegian Public Roads Administration.

Figure 1. Illustration of the drill and blast cycle, starting in the top with drilling and loading and continuing with blasting, ventilating, mucking, scaling, installing rock support and surveying (Heiniö, 1999).

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1.4 Problem definition, aim and objectives

MWD technology in drill and blast tunnelling is rather new. Like mentioned before, it is often only used to document geology while it has the potential to improve the drill and blast tunnelling process. The main reasons for this could be that MWD technology is not fully adapted to the drill and blast workflow, the knowledge about MWD is not sufficient or the ability of MWD to represent the geology has not been extensively investigated and verified. Apart from rock hardness, the little amount of MWD research in fracturing and water conditions have not shown overwhelming results. Concerning fracturing, one main obstacle, which has been encountered in previous research, is the difference in scale between MWD data and available geological information. MWD data has a typical sampling interval of 2 to 5cm. The most detailed geological information available from tunnel sites is often mapped geology by engineering geologist. Since the objective of this geological mapping is to document geology and agree on rock support types, a cm scale accuracy is not relevant and far too time consuming in the drill and blast tunnelling. Only large structures like intrusions, rock type changes and large discontinuities are mapped. This is often done by different engineers and locations of structures are estimated. This might be sufficient for the objective of the geological mapping, but for comparing geology and MWD data, this is too inaccurate and unprecise. The Norwegian Public Roads Administration spends money on facilitating MWD software and MWD services, while the ability of some parts of MWD technology has not been verified. The Norwegian Public Roads Administration defines the use of MWD for their projects in their process code (The Norwegian Public Roads Administration, Prosesskode 1 - Standard beskrivelsetekster for vegkontrakter, hovedprosess 1-7., 2012). It is stated that all drilling rigs must be equipped with logging equipment and used for at least 90% of the borehole length.

The aim of this thesis is to investigate the ability to detect discontinuities and their geometrical properties in MWD data and to evaluate the usability of MWD data in terms of detecting discontinuities for the NPRA as the client in future tunnelling projects.

Five objectives are established for this project.

1. Firstly, the subjects of MWD technology, discontinuities in rock masses and previous research need to be studied. In addition, the literature study should be focussed on possible statistical data analysis methods, which can be used to evaluate MWD data.

2. The second objective is to gather data, which is appropriate to study relations between MWD data and discontinuities. This objective will include preparation and execution of fieldwork.

3. The third objective is to evaluate the data by visual comparisons of geological data collected during fieldwork and MWD data.

4. The fourth objective will be to apply statistical methods to come to a more in depth understanding of the relation between MWD data and discontinuities and confirm findings in objective 3.

5. The last objective will be to discuss the current and future usability of MWD data for the NPRA.

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1.5 Research questions

The main research question is: To what extent can discontinuities be detected by MWD data and used for reporting geology in a tunnel, predicting geology ahead of the tunnel face and predicting the amount of rock support needed? This will be answered by achieving the listed objectives and answering the following research questions.

1. Conduct a literature study of the subject MWD technology, discontinuities in rock masses, statistical analysis that can be used to evaluate MWD data and previous research in the subject of MWD validity.

- What is MWD technology in drill and blast tunnelling?

- What kind of discontinuities can be encountered?

- How is geology mapped in tunnels by the Norwegian Public Roads Administration?

- How is MWD data filtered and processed?

- What statistical analyses are appropriate for analysing MWD data to enhance and understand the predictability of discontinuities?

- What is the result of previous research on the validity and usability of MWD?

Figure 2. Top view of tunnelling sites and tunnel section with in the top Solbakktunnelen and below the Bjørnegårdtunnelen (The Norwegian Public Roads Administration, 2014).

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2. Prepare site visits and conduct fieldwork.

- What is the local geology of the tunnel sites?

- What methods can be used to map discontinuities in tunnels?

- What are the parameters to obtain during fieldwork?

- To what extent is it possible to work on sites where the degree of fracturing is the only variable parameter?

- What is the quality of the collected data?

3. Assess the validity of MWD data by visually comparing the geological data and MWD data.

- What kind of discontinuities are visible in MWD data or what kind of geometrical properties make discontinuities visible in MWD data?

- Is there a characteristic response of MWD data to discontinuities?

4. Assess the validity of MWD data through statistical analyses.

- What geological data can be used for statistical analyses?

- How should geological data be translated to statistical input?

- Are the statistical analyses appropriate for the MWD data collected?

- Can discontinuities and/or certain geometrical properties be predicted by use of statistical methods?

5. Discuss the current and future usability of MWD data for the Norwegian Public Roads Administration and contractors

- To what extent are discontinuities visible in MWD data?

- In which way could the outcome of this study be used to improve the process of drill and blast tunnelling ?

- What significance do detected discontinuities have for rock support determination?

1.6 Limitations

In advance it can be stated that performing fieldwork in tunnels under construction does not allow much freedom. An outsider is limited in where he or she can be mapping geology and how much time he or she may get. Both client and contractor are bound to contracts, which involve large amounts of money. It is therefore unwanted to disturb the tunnelling processes. By good communication and planning, these limitation will be minimized.

Next to that the conditions under which geological mapping is done in a tunnel are different from above ground. Artificial light, accessibility and noise could influence the ability of gathering data. As much as possible, these limitations should be taken into account when designing data gathering methods and preparing fieldwork. Moreover, there is always a possibility that rock masses do not show a wide variety of discontinuities. This limitation cannot be foreseen.

The most important limitation is that no matter how interesting a fresh rock contour or face might be, it cannot be studied in an unsafe situation, both in terms of rock stability and construction activities.

This will always be discussed before entering tunnels with client and contractor and during data gathering with staff.

A limitation with the use of MWD technology is that a misconception might rise that MWD data gives all the information you need to know about rock mass conditions. This is incorrect. Geological mapping gives a much better idea of the variability of the geology than MWD technology can.As a result, the aim of this study is not to replace geological mapping, but to support the geologist and improve drill and blast tunnelling.

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1.7 Scope and constraints

This thesis is mainly focused on the detection and prediction of discontinuities from MWD data.

Objective 5, the actual usefulness of the results of this study, is covered in much less detail. Although it would be interesting, the scope of this study does not cover the implications of discontinuity detection on the drill and blast workflow and costs. It also does not aim to predict discontinuities based on MWD data for an entire tunnelling project. The main reason that this study does not aim to cover the two mentioned points is that these require extensive knowledge about the extent to which discontinuities can be detected. The available sources of information do not give this knowledge. In fact, none of the available resources attempted to study discontinuities and MWD data as detailed as is attempted with this study.

1.8 Thesis outline

This thesis starts with a general introduction to MWD technology, including problem definition, aim and objectives, research questions and limitations. Chapter 2 provides background information of all the different aspects involved in this project. MWD technology, discontinuities and discontinuity mapping, the drilling process, common practise of geological mapping in Norwegian tunnels, data analysis, multivariate statistics and previous research in the correlation between MWD technology and geology is summarized in the literature study.

Chapter 3 includes introductions to the tunnel sites visited for data gathering: Solbakktunnelen and Bjørnegårdtunnelen. This is followed by descriptions of the preparations for data gathering, a short summary of the fieldwork and the results of the fieldwork.

Next, the data is analysed. In chapter 4 this is done visually. Here, a mismatch between scales of geological mapping and MWD data is still allowed. In chapter 5, only the detailed geological records are used for a statistical analysis.

In the discussion the potential of MWD technology in the field of fracturing is discussed. In the conclusion the findings and answers to the research questions will be summarized. Furthermore, the main limitations and their possible solutions will be discussed and recommended.

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2. Literature study

Here, the literature study on the subjects MWD technology, discontinuities in rock, the drilling process, geological mapping in Norwegian tunnels, data processing, statistical analyses and previous research in the field of MWD is summarized. The 4 main sources of literature are the library at NTNU, the library at TU Delft, a database of the Norwegian Public Roads Administration and the internet.

2.1 MWD technology

Like stated, MWD technology deals with recording drilling parameters and processing these parameters. In the past it used to be only penetration rate, which was measured, whereas today the systems installed on the drilling rigs register 9 parameters: Penetration rate, thrust, torque pressure, percussive pressure, rotation speed, water flow, water pressure, depth and sampling time. The drilling rigs and measuring systems are calibrated either at the site or by use of previous projects. The parameters are filtered and processed by software to visualize measures of the hardness, fracturing and water conditions. Some software packages put more focus on defining these three outcomes, while other software leaves it to the user to interpret the different outcomes.

The amount of data collected with one advance round can be enormous. For example, if one advance round consists of 80 blast holes, all 9 parameters plus 6 processed parameters are stored. With a common sampling interval of 2cm, this gives 300000 data points.

2.2 Discontinuities and discontinuity mapping

A discontinuity is defined by Hudson and Harrison as ‘’any separation in the rock continuum having effectively zero tensile strength.’’ (Hudson & Harrison, 1997). Hudson and Harrison state that discontinuities can be the single most important factor governing the deformability, strength and permeability. Therefore, discontinuities can critically effect the stability of a tunnel. There are different type of discontinuities. In this thesis, four different types of discontinuities are considered (Shanghal &

Gupta, 2010).

1. Lithological discontinuities, the layering in sedimentary rock.

2. Foliation, discontinuous planes caused by parallel alignment of minerals due to stress.

3. Fracture, discontinuous planes where stress caused partial loss of cohesion.

4. Faults and shear zones, discontinuities caused by movement due to shear stress.

5. Other geological discontinuities, for example intrusive contact and veins.

In addition, there can be blast induced fractures present.

Several geometrical properties are defined. These include spacing, orientation, persistence, termination, roughness, aperture, discontinuity sets and presence of water (see Figure 3).

Spacing is the distance between discontinuity intersections with a scanline. Orientation is defined as the dip direction, the horizontal angle between the normal of the discontinuity plane and north, and dip angle of the plane. Persistence is the length or size of a discontinuity plane. Termination is the ending of a fracture due to another fracture. Aperture is the perpendicular distance between two adjacent discontinuities.

In practise, it would be too time consuming and costly to map these properties for all discontinuities in a tunnel under construction. Several classification systems are designed to classify the quality of the rock. In the Norwegian tunnelling industry, the Q-system is used. The Q-systems gives a value between

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0.001 and 1000, which indicates the quality of the rock (NGI, 2013). This value can also be used to estimate the amount of rock support needed. The Q-value is a computation of six different parameters:

𝑄 =𝑅𝑄𝐷 𝐽_𝑛 ∗𝐽_𝑟

𝐽_𝑎∗ 𝐽_𝑤 𝑆𝑅𝐹

Rock Quality Designation, or 𝑅𝑄𝐷, is the sum of the length of all core pieces longer than 10 cm as a percentage of the total length of the core. It can also be estimated by counting the number of fractures per m³. 𝐽_𝑛 is the joint set number, which represents the number of joint sets and random joints.

Together the first term represents the relative block size. 𝐽_𝑟 is the joint roughness number representing both small scale roughness (rough, smooth and slickenside) and large scale roughness (stepped, undulating and planar). 𝐽_𝑎 represents the joint friction or shear strength. The second term is an approximation of the actual friction angle. 𝐽𝑤 is the joint water reduction factor which represents the presence of water and 𝑆𝑅𝐹 is the stress reduction factor which represents the relation between rock strength and stress.

2.3 The drilling process

In the drill and blast tunnelling industry the drilling method used is top hammer drilling. It is a combination of applying feed, rotation and percussion impact transmitted through the drilling steel (Figure 4) (Olsen V. , 2009). All the energy is transferred through the drilling string. The drill bit is covered with several indenters, which are either small hemispheres or cones. If an indenter is forced in to the rock, the stress in the rock increases and a zone around the indenter is deformed plastically. A small zone directly under the indenter is crushed to rock powder. Just outside the zone where rock is pulverized the stress can reach the peak strength and the rock can break. In a larger hemisphere around the indenter, cracks are induced and some of these cracks can find a path out to the free surface. This is called chip formation (Olsen V. , 2009). The indenters on a drilling bit are forced in the rock by the percussion pressure. The position of the indenters is changed continuously by the rotation and the drilling bit is kept in contact with the rock by the feed pressure.

Thrust, rotation speed and percussion pressure are parameters which are controlled by the operator or automatic drilling system. Therefore, these parameters are independent. The drilling system is programmed to drill as fast as possible without jamming the drill bit. Jamming can for example be

Figure 3. Illustration of primary geometrical properties of discontinuities in rock (Hudson &

Harrison, 1997).

Termination

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caused by a too high thrust. In that case, the contact of the drill bit with the rock is continuous and rotation and indentation are obstructed. The dependent parameters are penetration rate and torque.

These are dependent on the independent parameters and are the possible cause of variation.

2.4 MWD responses to discontinuities

The drilling behaviour when crossing an open discontinuity has been researched. Schunnesson summarises the findings of Barr in 1984 in his PhD thesis (Schunnesson H. , 1996). Most or all of the following events happened in an artificial set-up of rock blocks including discontinuities with known orientation aperture and infilling.

When a discontinuity was met, the following was observed:

- A short increase in penetration rate.

- A small increase in rotational speed followed by a sharp decrease when re-establishing rock contact.

- A drop in torque pressure followed by sharp increase on re-establishing rock contact.

- A drop in water pressure until equal pressure in the void or rock is established.

- A drop in feed pressure followed by a sharp increase on re-establishing rock contact. This might only be visible for discontinuities with a large aperture.

An infilled fracture can dampen the events. The most reliable event is the increase in penetration rate.

Schunnesson found in his own research that the intensity of fracturing can cause the penetration rate, torque pressure and rotational speed to increase.

2.5 Common practise of geological mapping in Norwegian tunnels

In the Norwegian tunnelling industry, it is common that geological inspection and documentation is done by a geologist or an engineering geologist employed by the client. After the removal of blasted rock and the cleaning of the surfaces for the application of shotcrete, the client has a 30 to 45 minutes window, in which there is no other activity in the tunnel, to document the rock mass properties (Rongved, u.d.). In common practise this means the documentation of the Q-values, classification of rock types, mapping of fractures. This is an interactive process between client and contractor. When rock mass quality is high, the geological mapping is often done during operation and the drill and blast activities are not put on a hold. Afterwards the client stores the information digitally. The Norwegian Public Roads Administration uses the program Novapoint from Vianova Systems AS which gives the options to document foliation, discontinuities, joint sets, joints with infill, weakness zones < 1m, weakness zones > 1m, rock type, Q values and water leakage (Vianova Systems AS, 2011). Novapoint gives a 2 dimensional representation of the exposed tunnel contour, meaning that the (engineering) geologist has to document in 2 dimensions. The tunnel contour is split in four parts, shown as dashed

Figure 4. Illustration of feed, rotation and percussion impact for the top hammer drilling method (Olsen V. , 2009).

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lines parallel to the tunnel axis in Figure 5. The tunnel floor is not included in mapping. The geological features are transformed from the 3 dimensional space to the 2 dimensional as illustrated in Figure 5.

The Norwegian Public Roads Administration defines this work facet in their process code (The Norwegian Public Roads Administration, Prosesskode 1 - Standard beskrivelsetekster for vegkontrakter, hovedprosess 1-7., 2012). Documentation and mapping of the geology is done to help planning rock support installation, to have documentation of geology and to see the link between geology and installed rock support.

2.6 Data processing

The common practise of processing MWD data is based on a doctoral thesis written by Schunnesson.

Schunnesson aimed to develop a method for analysing MWD data and reducing the need for calibration of rock properties against MWD data (Schunnesson H. , 1996) (Schunnesson H. , 1997) (Schunnesson &

Holme, 1997) (Schunnesson & Sturk, 1997). The data used in his thesis came from the Viscaria mine, the Zinkgruvan mine, the Glodberget tunnel and the Hallandsåsen tunnel. Schunnesson proposed a method to separate the two main groups of parameters, namely the independent parameters, which are feeder pressure, rotation speed and percussion pressure, and dependent parameters, which are penetration rate and torque pressure. First, the length dependency along the boreholes should be taken into account for all parameters. Length dependent behaviour is caused by for example the reflection of energy with the addition of each drilling rod, increase in friction with the rock and the decrease of flushing efficiency. Next, the applied differences in thrust should be normalized for penetration rate and torque pressure. Finally, the influence of penetration rate on torque should be normalized. The resulting data consists of systematic variations caused by the drill rig itself. This should be subtracted from the original data set to remain with the unsystematic variations or rock mass variation. A straight forward way to do this is to withdraw the gradient of the trend line of every dataset from every dataset.

Figure 5. 2D documentation of discontinuities by the Norwegian Public Roads Administration (Lillevik, 2011).

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Schunnesson stated that after applying this method, only the rock dependent variations are left in the data. He found that the magnitude of penetration rate and torque pressure generally are good indicators for rock hardness and that both increase in fractured rock. However, responses based on the magnitude of penetration rate and torque pressure differ from site to site. The variability of penetration rate and torque pressure usually has a more general relation to fracturing. Schunnesson gave several examples from his data that showed this. He used principle component analyses (PCA) to investigate the correlation between penetration rate and torque pressure. For the Glodberget tunnel, Schunnesson showed that less fractures gave a smoother curve.

There are a number of software packages which process the raw MWD data. Both normalisation and root mean square calculations, abbreviated as RMS, are used to separate dependent and independent variables and to amplify responses. In contrast with most software developers, Bever Control AS is open about how raw MWD data is used to get to the three standard evaluations (hardness, fracturing and water conditions (Håkonsen & Wetlesen, 2008) (Bever Team as, 2009)). Developers sometimes explicitly define hardness based on a modified penetration rate, fracturing based on a modified torque pressure and water conditions based on both modified water pressure and water flow. The developers of Bever Team 3 leave interpretation up to the user and they do not assign the terms hardness, fracturing or water conditions. Instead, the outcome is called normalized penetration, normalized rotation pressure, normalized water, RMS normalized penetration, RMS normalized rotation pressure and RMS normalized water. All outcome is expressed as %. These parameters are influenced by:

1. External influences like drill bit wear and the number of drilling rods.

2. The dependent parameter percussive pressure 3. Hole depth

4. Rock mass properties

In a way the steps explained below can be seen as eliminating influences 1, 2 and 3 to end up with a modified penetration rate, torque or water pressure which represents rock mass properties in a better way. The steps are generally the same for penetration rate, torque and water pressure and for simplicity, these will be called parameter, or P, in the following steps.

Step 1. Influences which do not contain relevant information about rock properties like adding of drilling rods are removed from the data. Generally, penetration rates lower than 1 m/min, unrealistic high values for penetration rate and unrealistic low values for percussion pressures.

Step 2. An attempt is made to normalize the wear of the drill bit and the drilling settings. It is noted in literature that this cannot be fully successful. The formula used to normalize hammer pressure, penetration rate, rotation pressure, water pressure and water flow in Bever Team 3 is:

𝑃_{𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑} =(𝑃_{𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑}− 𝑃_{𝑚𝑒𝑎𝑛}) 𝑃_{𝑚𝑒𝑎𝑛}

⁄

In which the mean parameter 𝑃_{𝑚𝑒𝑎𝑛} is calculated over one single whole borehole length.

Step 3. After this normalization the most significant influencing factors on the penetration rate and rotation pressure are believed to be percussion pressure, friction between drilling rods and borehole (or depth dependency) and the rock mass property. Thrust and rotation speed mentioned as dependent parameters by Schunnesson, are not considered by Bever Team 3. It is assumed that the relation between the parameter, its rock mass property (𝑅𝑀𝑃) and percussive pressure (PP) is linear.

𝑃_{𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑}= 𝑅𝑀𝑃 + 𝑘 ∗ 𝑃𝑃

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The constant 𝑘 is found by plotting the raw parameter, without the peaks of adding a rod, against the percussion pressure and obtaining the linear trend.

Step 4. With this known constant 𝑘 the rock mass properties, or 𝑅𝑀𝑃, can be calculated by filtering out the influence of the hammer pressure and the drilling depth from the normalized penetration. The equation below is the result of rearranging the previous equation plus a correction for the drilling depth.

𝑅𝑀𝑃 = 𝑃𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 − 𝑘 ∗ 𝑃𝑃 +𝐶𝐻𝐿 100∗ 𝑠

Where 𝐶𝐻𝐿 is a predefined value for the correction of hole length and 𝑠 the sampling depth. It should be noted that for an unknown reason this is not done for the normalized rotation pressure.

Step 5. The water parameter 𝑃_{𝑤𝑎𝑡𝑒𝑟} is calculated with the formula below.

𝑃_{𝑤𝑎𝑡𝑒𝑟}= 𝑃_{𝑤𝑎𝑡𝑒𝑟𝑓𝑙𝑜𝑤}∗ (1 − 𝑃𝑤𝑎𝑡𝑒𝑟𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒2) ∗ 𝑊𝑃𝐹

Where 𝑃_{𝑤𝑎𝑡𝑒𝑟𝑓𝑙𝑜𝑤} is the water flow in l/min, 𝑃𝑤𝑎𝑡𝑒𝑟𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 the water pressure in bar, and 𝑊𝑃𝐹 is the water pressure factor which is a predefined value. 𝑃_{𝑤𝑎𝑡𝑒𝑟𝑓𝑙𝑜𝑤} is not corrected for the depth but for the number of drilling rods since the water is pumped through all drilling rods which are in use. For example, drilling at a depth of 7m requires 2 drilling rods of 5 meter. Water is then pumped through 10m.

Step 6. The output given as normalized penetration, normalized rotation pressure and normalized water, or 𝑃𝑜𝑢𝑡𝑝𝑢𝑡 1,𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑, is calculated with a moving average of 𝑁 values

𝑃𝑜𝑢𝑡𝑝𝑢𝑡 1,𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 = 𝐴 − ∑ 𝑃_𝑖

𝑖₀+𝑁

𝑖=𝑖₀

𝑁

⁄

Where 𝐴 is either 𝑅𝑀𝑃, 𝑃𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 𝑟𝑜𝑡𝑎𝑡𝑖𝑜𝑛 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 or 𝑃_{𝑤𝑎𝑡𝑒𝑟}, 𝑖₀ is the index of the value to be calculated, 𝑃_𝑖 is the value of a parameter at index 𝑖.

Step 7. This operation influences the dynamic property of curves. A moving root mean square calculation is done to represent the fluctuations of rock mass properties better. The formula used for this is:

𝑃𝑜𝑢𝑡𝑝𝑢𝑡 2,𝑅𝑜𝑜𝑡𝑀𝑒𝑎𝑛𝑆𝑞𝑢𝑎𝑟𝑒

= √∑ (𝑃^𝑁 𝑜𝑢𝑡𝑝𝑢𝑡 1,𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑− 𝑃̅𝑜𝑢𝑡𝑝𝑢𝑡 1,𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 𝑚𝑜𝑣𝑖𝑛𝑔 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑜𝑓 𝑁 𝑣𝑎𝑙𝑢𝑒𝑠)² 𝑁

N is the number of measurements taken for the root means square computation and it influences how dynamic the response is to changes in the original curve. If 𝑃𝑜𝑢𝑡𝑝𝑢𝑡 2,𝑅𝑜𝑜𝑡𝑀𝑒𝑎𝑛𝑆𝑞𝑢𝑎𝑟𝑒 𝑤𝑎𝑡𝑒𝑟 is larger than 0.7 or smaller than the original water flow value, it is set to 0.

Bever Team 3 allows the user to display every individual curve of every step and 3 dimensional images with colour scales. These colour scales can be adjusted manually.

Another method to characterize rock masses is by use of specific energy, the energy required to break one unit volume of rock (Ghosh, 2015) (Rai, Schunnesson, Lundqvist, & Kamur, 2015) (Ghosh, Schunnesson, & Kumar, 2014). Ghosh et all and Rai et all had the aim to determine an unique geotechnical description of the rock mass excavated by rotary core drilling. The description of specific energy used in their research is 𝐸 =^𝐹_𝐴+^{2𝜋𝑁𝑇}_60𝐴𝑢, in which E is the specific energy, F is the thrust, A is the area of the cross section of the drill bit, N is the rotary speed, T is torque and u is penetration rate. The

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relation between specific energy and compressive strength of the rock has often been verified and is found to be best in rock masses with changing conditions. Specific energy has not been introduced in percussion drilling in tunnelling.

2.7 Multivariate statistics

For this thesis the Bever Team 3 software is used to extract raw and processed MWD data. It is suspected that the moving averages used as described in section 2.6 influences the ability to detect discontinuities. Therefore processed MWD parameters are generated with different moving averages.

This makes the number of variables even larger. To handle a large amount of variables it is chosen to apply multivariate statistical analyses. Wuensch listed a number of available multivariate analyses (Wuensch, 2013). In addition he stated that it is relatively easy to perform a multivariate analysis, but not easy to interpret the outcome of such an analysis. Wuensch also warns that for each individual method, multiple choices are to be made and therefore outcomes of analyses may differ from analyser to analyser. The outcome of a multivariate analysis for this research should enhance the understanding of the interdependency of MWD parameters, it should give an overview of the most important parameters influencing fracturing and it should clarify the type of response of a parameter when encountering a discontinuity.

There are two principle methods to approach sets of data: Supervised and unsupervised learning (Bergen & Ioannidis, 2015). Unsupervised learning aims to understand relationships between variables.

Therefore, the input is data without an associated response. Examples of unsupervised learning methods are dimension reduction and cluster analysis. For this study, one dimension reduction method and one type of cluster analysis are found to be useful, namely Principle Component Analysis (PCA) and k-means cluster analysis. The input data for these methods will merely be MWD data. Supervised learning includes the associated response variable, which for this study are the presence and geometrical properties of discontinuities. The goal of supervised learning is to generalize to new data.

One type of supervised learning is of special interest for this study, namely regression. A regression could help to predict responses of new data. More specific for this study, regression could help to predict discontinuities ahead of the tunnel face. In the following sections, two types of regressions are discussed. They are multiple linear regression analysis and multiple logistic regression.

At the end, an overview of the advantages, disadvantages and data requirements for this thesis is given.

2.7.1 Principle Component Analysis

Principle component analysis, or PCA, is a form of unsupervised learning. PCA is a widely used and well- developed statistical method. Schunnesson used PCA to investigate the interdependency of MWD parameters. Jolliffe describes PCA as: ‘The reduction of the dimensionality of a data set consisting of a large number of interrelated variables, while retaining as much as possible of the variation present in the data set’ (Jolliffe, 2002). Wackernagel states that PCA can be used for data compression, multivariate outlier detection, deciphering a correlation matrix, identifying underlying factors and detecting intrinsic correlation (Wackernagel, 2003). The interdependent variables are transformed to a new, uncorrelated set of variables, the principle components. The first few of these principle components contain most of the variation present in all of the original variables. Schunnesson observed that the MWD parameters penetration rate and torque pressure preserve most of the information captured by all the MWD parameters.

Below an image of a hypothetical dataset with 2 parameters is given. In the left graphs shows the original dataset with parameters x and y. If one would try to compress this dataset by deleting 1

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parameter, the choice of deleting either x or y is not simple. By deleting either of them, a significant amount of variability is lost as can be seen in the image below the graph.

PCA finds a coordinate system that preserves more of the variation (Powell & Lehe, u.d.). The rotated axes are called the principle components. In Figure 6, the right graph visualizes the new coordinate system for the hypothetical dataset. As can be seen below the right graph, the first principle component contributes most to the variation in the dataset. The second principle component contributes much less to the variation compared to principle component 1 or x and y. By dropping the second principle component, the data is compressed and still a fair part of the variability is maintained.

For a higher dimensional dataset this is hard to visualize, but the principle is the same. The first principle component represents most of the variation. The aim is to choose enough principle components so that a significant part of the variation is preserved and at the same time to reduce number of variables.

A normal approach to investigating the number of principle components required is to look at the scree plot. This is a plot of eigenvalues versus the component number. The eigenvalues decrease for an increasing component number. In the scree plot one would look for the transition where the eigenvalues are decreasing rapidly to where the eigenvalues are relatively small and of the same size.

This is not always an obvious point. A parallel analysis is a more objective way for determining the number of components needed (O'Connor, 2000). A common parallel analysis is the Monte Carlo analysis, where data is generated either randomly based or generated based on permutations of the raw data. The latter option is more suitable to data which is not normally distributed. If the eigenvalue of the n^th component of the parallel analysis is smaller than the eigenvalue of the n^th component of the original dimension reduction analysis, this n^th component is to be considered as statistically significant.

Other input which needs to be defined for a parallel analysis is the variables for the PCA, a desired number of data parallel sets and a desired percentile for statistical significance testing.

Another important aspect of PCA is the type choice of rotation used to convert the variables in principle components. There are two type of rotations oblique and orthogonal. Like stated before, PCA creates an uncorrelated sets of variables, i.e. the principle components. It is therefore straightforward to choose an orthogonal rotation, which forces the principle components to be uncorrelated and makes the large loadings larger and the small loadings smaller, either within a component or with a variable.

It is also possible to use an oblique rotation, where the principle components are allowed to be

Figure 6. Two dimensional illustration of Principle Component Analysis (Powell & Lehe, u.d.).

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correlated with each other. The thought behind it is that an oblique rotation could be orthogonal if that is the most appropriate solution for the data. If the most appropriate solution is a non-orthogonal relation between principle components and principle components are slightly correlated, it is also allowed by an oblique rotation. In most cases there will be some correlation between factors or components. If the correlation coefficient between principle components is 0.32 or higher, it means there is an overlap of 10% or more in variance among principle components. If there is no theoretical reason for using an orthogonal rotation, an oblique rotation is recommended (Brown, 2009). When using a regression analysis an important reason to not use an oblique rotation is the risk of (multi)collinearity. This will be explained later in this chapter.

The question of whether a principle component analysis should be used or not is answered by a test called Kaiser-Meyer-Oklin measure of sampling adequacy, or KMO. This is an evaluation including the off-diagonal elements of the original correlations and rotated correlations. As a rule of thumb, an outcome below 0.5 indicates no reason to perform a PCA. The higher above 0.5 the more appropriate a PCA becomes (Dziuban & Shirkey, 1974). Another method of justifying the use of a PCA is by looking at the percentage of variance that is being accounted for by the PCA, or communalities. The higher these percentages, the better.

2.7.2 K-means cluster analysis

A cluster analysis is a type of unsupervised learning, where the goal is to identify and understand possible clusters in the data. A cluster analysis is designed to partition data into subsets with common characteristics. There are different types of clustering analysis. A good analysis to assess large amounts of data is the k-means cluster analysis. With k-means clustering, a data point can only be in one cluster, whereas with other methods, data points can be in multiple clusters. This is also called hard and soft boundaries. One important aspect is that the number of clusters in the data needs to be predefined.

Unfortunately there is no good way to decide on the correct number of clusters. Only in special cases one could decide the correct number. For example if the data exist out of grading digits 0 to 9, the obvious chose is 10 clusters.

The k-means cluster analysis starts with defining the number of clusters k. Next k random initial cluster centres are generated in the dataspace. Boundaries of equal distance between cluster centres are computed and every data point within a boundary of a cluster centre is assigned to the cluster with that random initial centre point. The next step is that new cluster centres are calculated for each cluster based on the average of the data points in a cluster. New boundaries of equal distance between the new cluster centres are computed and all data points are redistributed to the new cluster centre. This is repeated until the cluster centres are not changing.

In this thesis the following considerations are made to assess the number of clusters.

1. Number of iterations: If it takes a high number of iterations to find stable cluster centres, it indicates that software has to readjust centres often due to a lack of clustering in the data. A point of attention is that the higher k is defined, the more iterations are needed.

2. Variance Ratio Criterion (VRC). The criterion is given by VRC𝑘 = (

SS_𝑏

K − 1)/( SS_𝑤 𝑁 − 𝐾)

Where SS_𝑏 is the between cluster variation, SS_𝑤 the within cluster variation, K the number of clusters and 𝑁 the number of objects. VRC𝑘 is in fact the F-value of an one-way ANOVA. To determine the correct number of clusters, 𝜔_𝑘 should be calculated for every cluster. The smallest 𝜔_𝑘 indicates the best number of clusters.

𝜔𝑘 = (VRC_𝑘+1− VRC𝑘) − (VRC_𝑘− VRC𝑘−1)