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Am und Brulan dHa rd Rock Tunnel Boring

DrillabilitySta tistics of D rilla bility Test Resu lts

Tr on

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D octora l thes es a t NTNU 1998:81

Vol. 10 of 10

F a c ul t y

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g S c i e n

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g e ni r
http://www.ntnu.no/indexe.htmlhttp://www.bygg.ntnu.no/batek/ba_eng.htm

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PREFACE 1

0 GENERAL

0.1 Project Reports about Drillability

0.2 Background

3

3

5

1 STATISTICS

1.0 General

1.1 Presentation of Data

1.2 Parameter Analysis

1.21 DRI

1.22 BWI

1.23 CLI

1.3 Parameter Correlation

6

6

7

8

8

12

18

24

2 PARAMETER DISTRIBUTION

2.1 The Total Database

2.2 Rock Type Vs Indices

2.3 Rock Type Overview

26

26

31

81

3 USE OF DATA

3.1 Parameter Distributions

3.2 Generating Distributions

3.3 Extreme Values

3.4 Planning and Contracts

95

95

99

102

105

APPENDICES

A. Previous Editions

B. Research Partners

C. Laboratory Testing

108

108

109

110

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PREFACE

1

DRILLABILITY Statistics of Drillability Test ResultsProject Report 13C-98

The report is one of three reports about drillability of rocks:

13A-98 DRILLABILITY Test Methods 13B-98 DRILLABILITY Catalogue of Drillability Indices 13C-98 DRILLABILITY Statistics of Drillability Test Results

Combined with the other reports in the Project Report Series from the Department ofBuilding and Construction Engineering at NTNU, the reports present an updated andsystematised material on rock excavation and tunnelling to be used for:

Economic dimensioning Choice of alternative Time planning Cost estimates, tender, budgeting and cost control Choice of excavation method and equipment.

A list of available Project Reports may be requested from the Department of Buildingand Construction Engineering at NTNU.

The Drillability Catalogue also exists as a digital database of test results (Excel file).

The basis of the report is the results from the comprehensive testing which has beendone at the Engineering Geological Laboratory at NTNU and SINTEF in Trondheim.

At present, more than 2100 samples have been tested. The report is published in theProject Report Series of the Department of Building and Construction Engineering because of the relation to the other reports in the series.

The report is prepared by Amund Bruland and is part of his dr.ing thesis abouthard rock tunnel boring. The report is included in the thesis as a necessary basisfor use and understanding of the prognosis model for hard rock tunnel boring.

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0. GENERAL 0.1 Project Reports about Drillability

3

0.1 PROJECT REPORTS ABOUT DRILLABILITY

13C-98

The Drilling Rate Index DRI, the Bit Wear Index BWI and the Cutter Life Index CLIare indirect measures for the drillability of a rock type.

The report presents statistics of laboratory test data of 2038 rock samples tested at theEngineering Geological Laboratory at NTNU and SINTEF Rock and MineralEngineering.

In Chapter 1 the laboratory tested parameters and computed drillability indices areanalysed with regard to statistical relation or independence. A comparison ofvariability in the existing database and Lien's original data from 1961 is also shown.

Chapter 2 shows distribution curves and variability for each parameter and index forthe database as a whole. Distribution curves and variability of the drillability indicesgrouped by rock type are given in the same chapter.

Chapter 3 shows some statistical distributions that may be used when the test resultsare to be represented by curve fitting. Some examples of curve fitting to given

parameter distributions are also shown.

Other Reports

The Project Report 13A-98 DRILLABILITY Test Methods describes the

laboratory methods used to determine DRI, BWI and CLI. The methods have beendeveloped at NTNU from 1960 and onward. Test apparatus and procedures are notdescribed in detail. Such information may be obtained from the Department ofGeology and Mineral Resources Engineering or the Department of Building andConstruction Engineering at NTNU.

Project Report 13B-98 DRILLABILITY Catalogue of Drillability Indices contains detailed test results for approximately 2050 samples. The report is updatedregularly, and is also available as a digital database.

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0. GENERAL 0.2 Background

5

0.2 BACKGROUND

The Drilling Rate Index, the Bit Wear Index and the Cutter Life Index are based onlaboratory test results.

For rock blasting and tunnelling, the drillability has a major influence on

Time consumption and costs Choice of method and equipment.

The DRI and BWI were developed at the Department of Geology at NTH 1 in theyears 1958 61 (Reidar Lien, Rolf Selmer-Olsen). The method was tested in the fieldduring the next ten years, resulting in minor adjustments.

The CLI was developed at The Department of Construction Engineering at NTH 2 inthe years 1980 - 83.

Systematic follow-up of drilling and boring in rock quarries and tunnels has beencarried out since 1972. The data have been normalised and related to the drillability

indices of representative rock samples. The results are presented as drilling ratediagrams. The various reports in the Project Report Series show relevant drilling ratediagrams and how to estimate capacity and costs based on that information.

Registrations show that DRI and CLI give a good and reproducible measure of thedrillability and abrasiveness of rocks. The BWI has been found to have someweaknesses, one being that the DRI value to a large extent influences the BWI of arock sample (see Section 1.3 and Figure 1.5 in PR13A-98 3). We are currently workingto replace the BWI with VHNR, see Section 1.5 of the same report.

It is only when the drillability indices are related to performance throughdrilling rate diagrams and to costs for varying rock conditions throughestimation models of drilling capacity and excavation costs that the indices gettheir full user value.

1 The present Department of Geology and Mineral Resources Engineering at NTNU2 The present Department of Building and Construction Engineering at NTNU3 Project Report 13A-98 DRILLABILITY Test Methods, published by us.

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1. STATISTICS 1.0 General

6

1.0 GENERAL

Except when noted, all statistics, distributions, presentation of data and similar in thisreport are based on the database BORBAR as given in the version dated 31 January1998.

As a general reference and textbook on statistics, we have used

Andrew F. Siegel STATISTICS AND DATA ANALYSIS An Introduction, JohnWiley & Sons, 1988

Furthermore, the statistical tools in Microsoft EXCEL have been used for dataanalysis and graphical presentation.

When using mean values, standard deviation, cumulative distributions, etc. from thereport, one must bear in mind that the database most likely is not representative of theglobal rock mass. When testing rock samples, it is more interesting to test samples oflow drillability or high abrasivity than samples of good drillability or low abrasivity,since the latter seldom represents any risk regarding time consumption and costs.

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1. STATISTICS 1.1 Presentation of Data

7

1.1 PRESENTATION OF DATA

In general, the data are presented as

cumulative distributions bivariate plots.

The bivariate plots (xy plots) are used to show correlation or lack of such betweenlaboratory tested parameters and/or indices.

The correlation of data is analysed using different trend lines. In most cases, the datahave been tested for the following relationships:

linear logarithmic polynomial geometric exponential.

From these, the trend line giving the best correlation coefficient has been selected toshow the relationship between two variables.

The cumulative distributions are used to

show variability in the data estimate drillability and wear parameters analyse risk with regard to drillability and wear parameters.

Except when noted, all relevant data are plotted. Outliers or extreme values may befound in many of the plots, but are still included in regression analyses, cumulative

percentages and similar. Suggested treatment of outliers and extreme values is foundin Section 3.3.

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1. STATISTICS 1.2 Parameter Analysis

8

1.2 PARAMETER ANALYSIS

1.21 DRI

The DRI value should be interpreted as a corrected Brittleness Value with regard tothe Sievers' J-value. Hence, the two parameters that constitute the DRI should beindependent of each other in order to reflect different rock properties.

Figure 1.1 shows a bivariate plot of the Brittleness Value and the Sievers' J-value forthe complete database. The linear regression line is also shown. The linear correlationcoefficient between S 20 and SJ is r = 0.17, indicating that the two parameters are moreor less independent of each other. This is also visually confirmed by Figure 1.1.

Plotting the same parameters for a given rock type results in a similar conclusion, seeexamples in Figure 1.2. The linear correlation is r = 0.24 for granite and r = 0.14 forgarnet-mica schist.

Figure 1.1 Bivariate plot of the Brittleness Value and the Sievers' J-value for thetotal database. Trend line: y = 0.3995x + 4.42, r 2 = 0.0273.

0

50

100

150

200

0 20 40 60 80 100

Britt leness Value, S20

S i e v e r s

' J - v a l u e , S

J

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9

Figure 1.2 Bivariate plot of the Brittleness Value and the Sievers' J-value forgranite and garnet-mica schist. Trend line granite: y = 0.165x - 1.45, r 2 = 0.056. Trend line garnet-mica schist: y = 0.477x + 30.47, r 2 = 0.020.

Figure 1.3 shows that the DRI value is strongly dependent on the Brittleness Value.The overall variation in the database due to the Sievers' J-value is roughly +14 unitsand -11 units. Very few tests are outside this range. One should note that the variationdue to the SJ-value is approximately the same for low as for high values of S 20. Thismay be interpreted as folows:

Since samples with a high Brittleness Value combined with a high Sievers' J-value will result in very or extremely high DRI values, such samples would beless important to test than samples with an expected low DRI value, and aretherefore not fully represented in the database.

The S 20 and the SJ-value are independent parameters, describing independent properties of the rock samples.

The correction of the Brittleness Value due to the Sievers' J-value in the original dataused by Lien in 1961, is shown in Figure 1.4 1. One may conclude that the variation inthe original data is sufficiently large to cover most of the variation in the more than2000 samples in the database. For S 20 less than 30, Lien's data are few while theBORBAR database contains 145 samples with a Brittleness Value less than or equalto 30. For this range of S 20 values, the current DRI laboratory testing to some extentextrapolates Lien's data, but within reasonable limits.

1 Lien's DRI values are according to the revised method published by R. Selmer-Olsen and O. T.

Blindheim: On the Drillability of Rock by Percussive Drilling. Proc. 2 nd Congress of ISRM, Belgrade 1970.

GARNET-MICA SCHIST

0

20

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60

80

100

120

0 20 40 60 80

Brittleness Value, S20

S i e v e r s

' J - v a l u e , S

J

GRANITE

0

10

20

30

40

50

0 20 40 60 80


S i e v e r s

' J - v a l u e , S

J

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10

Figure 1.3 Variation of the DRI due to correction of the Brittleness Value S 20 for

Sievers' J-value 10. Trend line: y = 1.1122x -3.66, r 2 = 0.80.

Figure 1.4 Variation of the DRI due to correction of the Brittleness Value S 20 for

Sievers' J-value 10 in Lien's original data.

0

20

40

60

80

100

0 20 40 60 80 100


D r i

l l i n g

R a t e

I n d e x ,

D R I

0

20

40

60

80

100

120

0 10 20 30 40 50 60 70 80 90


D r i l l i n g

R a t e

I n d e x , D

R I

Trendline for the total database

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11

The Sievers' J-value should have less influence than the Brittleness value on the DRI,

according to Lien. This is confirmed when comparing Figure 2.x and Figure 2.x.

Figure 1.5 Bivariate plot of Sievers' J-value and the Drilling Rate Index for the totaldatabase. Trend line: y = 7.396ln(x) + 29.9, r 2 = 0.38.

0

20

40

60

80

100

0,1 1 10 100 1000

Sievers' J-value, SJ

D r i

l l i n g

R a t e I n d e x , D

R I

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12

1.22 BWI

The BWI was designed to represent the time dependent wear adjusted for drilling rateto express the drill bit life in drilled metres. The BWI is found by adjusting theAbrasion Value AV by the DRI value according to Figure 1.5 in the Project Report13A-98 DRILLABILITY Test Methods. Figure 1.6 shows a bivariate plot of AV andDRI for the complete database, confirming that AV and DRI are independentvariables. The linear correlation coefficient is as low as r = 0.04.

Plotting the same parameters for a given rock type results in a similar conclusion, seeexamples in Figure 1.7. The linear correlation is r = 0.19 for granite and r = 0.30 forgarnet-mica schist.

Figure 1.6 Bivariate plot of the Abrasion Value and the Drilling Rate Index for thetotal database. Trend line: y = -0.0334x + 48.4, r 2 = 0.002.

0

20

40

60

80

100

0 20 40 60 80 100 120 140 160

Abras ion Val ue, AV

D r i

l l i n g

R a t e

I n d e x , D

R I

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13

Figure 1.7 Bivariate plot of the Abrasion Value and the Drilling Rate Index for

granite and garnet-mica schist. Trend line granite: y = 0.19x - 45.4,r 2 = 0.037. Trend line garnet-mica schist: y = 0.37x + 58.8, r 2 = 0.09.

The Figures 1.8 and 1.9 show bivariate plots of AV vs S 20 and AV vs SJ respectively.The linear correlation coefficients confirm that the Abrasion Value AV and two

parameters that make up the DRI also are more or less independent variables.

Figure 1.8 Bivariate plot of the Brittleness Value and the Abrasion Value for thetotal database. Trend line: y = 0.3916x + 3.77, r 2 = 0.054.

GRANITE

0

20

40

60

80

100

0 10 20 30 40 50 60

Abra sio n Valu e, AV

D r i

l l i n g

R a t e

I n d e x ,

D R I

GARNET-MICA SCHIST

0

20

40

60

80

100

0 10 20 30 40 50 60

Abra sio n Valu e, AV

D r i

l l i n g

R a t e

I n d e x ,

D R I

0

20

40

60

80

100

120

140

160

0 20 40 60 80 100

Britt leness Value S20

A b r a s i o n

V a l u e

A V

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14

Figure 1.9 Bivariate plot of the Sievers' J-value and the Abrasion Value for the total

database. Trend line: y = 53.33x -0.6413 , r 2 = 0.054.

Figure 1.10 Bivariate plot of Drilling Rate Index and Bit Wear Index for the total

database. Trend line: y = 0.0123x2

- 2.24x +115, r 2

= 0.70.

0

20

40

60

80

100

0 20 40 60 80 100

Drilling Rate Index, DRI

B i t W e a r

I n d e x , B

W I

0

20

40

60

80

100

120

140

160

0 50 100 150 200

Sievers' J-value SJ

A b r a s i o n

V a l u e

A V

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15

Figure 1.10 shows that there is a quite strong correlation between the Bit Wear Index

and the Drilling Rate Index. The correlation becomes even stronger when the data aregrouped according to quartz content, see Figure 1.11. The trend lines in Figure 1.11may be used to estimate the BWI when DRI and quartz content are known.

Figure 1.11 Bit Wear Index as a function of Drilling Rate Index and rock quartzcontent in percent. Normalised from the data in Figure 1.10. Line Equation r 2

1 y = 0.007x 2 - 1.39x + 78 0.97

2 y = 0.009x 2 - 1.77x + 94 0.92

3 y = 0.013x 2 - 2.32x + 121 0.88

4 y = 0.014x 2 - 2.58x + 133 0.75

5 y = 0.017x 2 - 2.99x + 149 0.67

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16

The Abrasion Value has less influence than the DRI value on the BWI, as seen when

comparing the Figures 1.10 and 1.12. The strong influence of the DRI on the BWI isone of the reasons why the BWI for some time has been considered as not being quitesuitable for description of the rock wear properties concerning drilling equipment.This has resulted in the development of new wear parameters such as the Cutter LifeIndex CLI and the Vickers Hardness Number Rock VHNR, see Project Report 13A-98 DRILLABILITY Test Methods.

Figure 1.12 Bivariate plot of Abrasion Value and Bit Wear Index for the totaldatabase. Trend line: y = 19.266x 0.2382 , r 2 = 0.39

The variation of BWI as a function of DRI in the data used by Lien in 1961 whenestablishing the BWI is shown in Figure 1.13. The variation is roughly +12 and -25BWI units compared to the trendline for the total database (in the DRI range of 35 -60). Compared to the total database shown in Figure 1.10, where the variation isroughly +16 and -24 BWI units in the DRI range of 25 - 75, one may conclude thatthe current BWI laboratory testing do not extrapolate Lien's data outside reasonablelimits.

0

20

40

60

80

100

120

0,1 1 10 100 1000

Abras ion Value, AV

B i t W e a r

I n d e x ,

B W I

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Figure 1.13 Variation of BWI as a function of DRI in Lien's original data. Thetrendline is from Figure 1.10.

0

10

20

30

40

50

60

70

80

0 20 40 60 80 100 120

Drillin g Rate Index, DRI

B i t W e a r

I n d e x , B

W I

Trendline for the total database

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18

1.23 CLI

The CLI was designed to express the time dependent wear of single disc cutters withsteel rings used in TBM tunnelling. The CLI is expressed by a regression formulaincorporating the Abrasion Value Steel AVS and the Sievers' J-value SJ as shown inthe Project Report 13A-98 DRILLABILITY Test Methods.

Figure 1.14 shows a bivariate plot of AVS and SJ for the complete database,confirming that AVS and SJ are nearly independent variables. The geometriccorrelation coeffisient is r = 0.53.

Plotting the same parameters for a given rock type results in a similar conclusion, seeexamples in Figure 1.15. The linear correlation is r = 0.16 for granite and r = 0.13 forgreenschist.

Figure 1.14 Bivariate plot of the Sievers' J-value and the Abrasion Value Steel for thetotal database. Trend line: y =46.694x -0.5584 , r 2 = 0.28.

)AVS

SJ(13.84=CLI

0.3847

[1.1]

0

20

40

60

80

0 50 100 150 200

Sievers' J-value

A b r a s i o n

V a l u e

S t e e l

A V S

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19

Figure 1.15 Bivariate plot of the Sievers' J-value and the Abrasion Value Steel forgranite and greenschist. Trend line granite: y = 0.08x + 33, r 2 = 0.027.Trend line greenschist: y = -0.04x + 11.7, r 2 = 0.016.

Figure 1.16 Bivariate plot of the Abrasion Value Steel and the Cutter Life Index forthe total database. Trend line: y = 56.6x -0.577 , r 2 = 0.78.

Figure 1.16 shows a quite strong correlation between the Abrasion Value Steel andthe Cutter Life Index.

The Sievers' J-value and the AVS influence the CLI to approximately the same

extent, as seen when comparing the Figures 1.16 and 1.17.

GRANITE

0

10

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30

40

50

60

0 10 20 30 40 50


A b r a s

i o n

V a l u e

S t e e l , A

V S

GREENSCHIST

0

5

10

15

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25

0 20 40 60 80 100


A b r a s

i o n

V a l u e

S t e e l , A

V S

0

50

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150

200

0 10 20 30 40 50 60 70

Abras ion Value Steel , AVS

C u t

t e r

L i f e I n

d e x , C

L I

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21

AVS, but the trendline of these rock types is close to the trendline of the total

database shown in the Figures 1.17 and 1.19 respectively.

Figure 1.18 Cutter Life Index as a function of Sievers' J-value and rock quartzcontent in percent. Normalised from the data in Figure 1.17. Line Equation r 2

1 y = 4.2346x 0.6234 0.69

2 y = 4.7835x 0.5366 0.53

3 y = 3.7432x 0,5399 0.77

4 y = 3.242x 0.5165 0.81

5 y = 3.7428x 0.4317 0.85

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22

Figure 1.19 Bivariate plot of the Abrasion Value and the Abrasion Value Steel for thetotal database. Trend line: y = 1.781x 0.779 , r 2 = 0.766.

0

20

40

60

80

0 20 40 60 80 100 120

Abras ion Value AV

A b r a s

i o n

V a l u e

S t e e l

A V S

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23

Figure 1.20 The Abrasion Value Steel as a function of the Abrasion Value and rockquartz content in percent. Normalised from the data in Figure 1.19. Line Equation r 2

1 y = 1.4743x 1.0387 0.70

2 y = 1.4836x 0.8611 0.79

3 y = 1.5491x 0.8183 0.75

4 y = 1.4588x0.7796

0.595 y = 3.1383x 0.5604 0.27

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1. STATISTICS 1.3 Parameter Correlation

25

Parameters Best Fit r 2 Reference

Quartz content - DRI linear 0.0008

Quartz content -BWI linear 0.134

Quartz content -CLI exponential 0.22

DRI - BWI polynomial 0.695 Figure 1.10

DRI - BWI grouped by quartz content polynomial 0.68 - 0.97 Figure 1.11

DRI - CLI linear 0.075

BWI - CLI geometric 0.61

Table 1.1b Bivariate correlation of drillability parameters.

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2. PARAMETER DISTRIBUTION 2.1 The Total Database

26

2.1 THE TOTAL DATABASE

The Figures 2.1 - 2.8 show plots of the cumulative distributions of the laboratorytested parameters and the calculated indices for the total database BORBAR .

The cumulative distribution is found by sorting all test results for a given parameter inascending order. The relative position or rank of each parameter value is thencalculated in a scale of 0 - 100 %. The highest parameter value represents the 100 %mark. As suggested by Siegel 1, the lowest parameter value represents the percentage:

The table to the right of the cumulative distribution plots list significant percentilevalues for the given index as calculated by the Microsoft EXCEL spreadsheet.EXCEL calculates the percentiles differently from Siegel, see Section 2.3.

The difference may be significant when the distribution is based on few observations,e.g. less than 10. In such cases there may be a notable deviation between the observeddata and the adapted distribution. See Chapter 3 for examples, discussion andsuggestions of how to handle the problem in a contract or a similar situation.

1 Andrew F. Siegel STATISTICS AND DATA ANALYSIS An Introduction, John Wiley & Son 1988

%10011 = n p n = number of test results [2.1]

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27

Figure 2.1 Cumulative distribution of the Brittleness Value for 2007 samples.

Figure 2.2 Cumulative distribution of Sievers' J-value for 2038 samples.

0

20

40

60

80

100

0 10 20 30 40 50 60 70 80 90


C u m u l a t

i v e p e r c e n t a g e

0

20

40

60

80

100

0 20 40 60 80 100 120 140 160 180 200


C u m u l a t


Low 15

10 % 31

25 % 37

Median 45

75 % 54

90 % 62

High 87

Low 0.5

10 % 2.4

25 % 4.0

Median 9.2

75 % 30

90 % 71

High 200

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Figure 2.3 Cumulative distribution of the Abrasion Value for 1893 samples.

Figure 2.4 Cumulative distribution of the Abrasion Value Steel for 863 samples.

0

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100

0 20 40 60 80 100 120 140 160

Abr asio n Valu e, AV

C u m u l a t

i v e p e r c e n

t a g e

0

20

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60

80

100

0 10 20 30 40 50 60 70

Abr asio n Value St eel, AVS

C u m u l a t


Low 0.1

10 % 1.5

25 % 4.9

Median 17

75 % 34

90 % 49

High 156

Low 0.1

10 % 2.0

25 % 7.0

Median 19

75 % 30

90 % 39

High 63

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29

Figure 2.5 Cumulative distribution of the quartz content for 1486 samples.

Figure 2.6 Cumulative distribution of the Drilling Rate Index for 2011 samples.

0

20

40

60

80

100

0 10 20 30 40 50 60 70 80 90 100

Quartz content in percent

C u m u l a t

i v e p e r c e n

t a g e

Low 0

10 % 5

25 % 15

Median 25

75 % 32

90 % 49

High 98

Low 4

10 % 29

25 % 36

Median 46

75 % 58

90 % 68

High 100

0

20

40

60

80

100

0 10 20 30 40 50 60 70 80 90 100

Drilling Rate Index, DRI

C u m u l a t

i v e p e r c e n

t a g e

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30

Figure 2.7 Cumulative distribution of the Bit Wear Index for 1888 samples.

Figure 2.8 Cumulative distribution of the Cutter Life Index for 867 samples.

0

20

40

60

80

100

0 20 40 60 80 100 120

Bit Wear Index, BWI

C u m u l a t

i v e p e r c e n

t a g e

0

20

40

60

80

100

0 20 40 60 80 100 120 140 160 180 200

Cutter Life Index, CLI

C u m u l a t

i v e p e r c e n

t a g e

Low 4

10 % 18

25 % 26

Median 36

75 % 50

90 % 65

High 108

Low 3.3

10 % 5.6

25 % 7.0

Median 10.8

75 % 23

90 % 45

High 197

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2. PARAMETER DISTRIBUTION 2.2 Rock Type Vs Indices

31

2.2 ROCK TYPE VS INDICES

The pages 32 - 80 show the cumulative distribution of the drillability indices for therock types found in the database BORBAR . Only rock types and indices with 4 ormore test results are shown. Section 2.3 shows a complete overview of all rock typesand indices.

The cumulative distribution is found by sorting all test results for a given parameter inascending order. The relative position or rank of each parameter value is thencalculated in a scale of 0 - 100 %. The highest parameter value represents the 100 %mark. As suggested by Siegel 1, the lowest parameter value represents the percentage:

The table to the right of the cumulative distribution plots list significant percentilevalues for the given index as calculated by the Microsoft EXCEL spreadsheet.EXCEL calculates the percentiles differently from Siegel, see Section 2.3.

The difference may be significant when the distribution is based on few observations,e.g. less than 10. In such cases there may be a notable deviation between the observeddata and the adapted distribution. See Chapter 3 for examples, discussion andsuggestions of how to handle the problem in a contract or a similar situation.

1 Andrew F. Siegel STATISTICS AND DATA ANALYSIS An Introduction, John Wiley & Son 1988

%1001

1 =

n p n = number of test results [2.1]

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2. PARAMETER DISTRIBUTION Alumn Shale

32

0

20

40

60

80

100

0 20 40 60 80 100

BWI

C u m u

l a t i v e p e r c e n

t a g e

0

20

40

60

80

100

0 20 40 60 80 100

DRI

C u m u


t a g e

No. 4

Low 5925 % 61

Median 66

75 % 72

High 77

No. 4

Low 4

25 % 11

Median 13

75 % 13

High 14

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2. PARAMETER DISTRIBUTION Amphibolite

33

No. 79

Low 1725 % 31

Median 39

75 % 50

High 80

No. 78

Low 12

25 % 25

Median 34

75 % 45

High 65

0

20

40

60

80

100

0 20 40 60 80 100

BWI

C u m u


t a g e

0

20

40

60

80

100

0 20 40 60 80 100

DRI

C u m u


t a g e

No. 26

Low 7.8

25 % 13.3

Median 18

75 % 23

High 57

0

20

40

60

80

100

0 20 40 60 80 100

CLI

C u m u


t a g e

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3. USE OF DATA 3.1 Parameter Distributions

95

3.1 PARAMETER DISTRIBUTIONS

When the drillability indices in the BORBAR database are to be used in planning,contracts, risk assessment, etc., one may use the distribution plots (see pages 27 - 80)directly, or one may fit the data to a mathematical function. There are variousstatistical distributions that may be suitable to approximate to the existing data.

Normal Lognormal Weibull Beta Exponential Gamma Linear

Of the distributions listed above, the normal, lognormal and Weibull distributionshave been found to give the best approximations to the cumulative distributions of the

parameters and indices in the BORBAR database.

For rock types with few test results, a linear curve fit may be the most convenient touse.

The Figures 3.1 - 3.4 show some examples of cumulative distributions fitted to theBORBAR data. The equations of the various distribution functions are not givenhere. It is recommended to use the statistical tools of spreadsheet program to fit adistribution to the BORBAR data directly.

The shape of the cumulative curve indicates how the variation of a parameter appearsfor the rock mass as a whole. Still, variation within a specific rock type or a givenlocation may follow a different distribution. The variation of the CLI value for thetotal database is best described by a lognormal or a Weibull distribution. For a givenrock type of a specific project, the CLI value may still have a normal distribution.

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96

Figure 3.1 A normal distribution fitted to the DRI values of the total BORBAR

database. = 47.63 and = 14.815.

Figure 3.2 A lognormal distribution fitted to the CLI values of the total BORBAR

database. = 2.5 and = 1.0.

0

20

40

60

80

100

0 10 20 30 40 50 60 70 80 90 100

DRI

C u m u


t a g e

BORBAR databaseNormal distribution

0

20

40

60

80

100

0 20 40 60 80 100 120 140 160 180 200

CLI

C u m u


t a g e

BORBAR databaseLognormal distribution

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97

Figure 3.3 A Weibull distribution fitted to the AV values of the total BORBAR

database. = 1.2 and = 23.75.

Figure 3.4 A linear distribution fitted to the DRI values of siltstone in the BORBAR

database. y = 1.6x -34.

0

20

40

60

80

100

0 20 40 60 80 100

DRI

C u m u l a t

i v e p e r c e n

t a g e

BORBAR databaseLinear fitted curve

0

20

40

60

80

100

0 20 40 60 80 100 120

AV

C u m u


t a g e

BORBAR databaseWeibull distribution

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98

Table 3.1 summarises the fitted cumulative distributions of the laboratory tested

parameters and the drillability indices of the total BORBAR database.

Parameter Best Fit Mean Standard Deviation Reference

S 20 Normal 46.1 11.94 Figure 2.1

SJ Lognormal 2.40 1.23 Figure 2.2

AV Lognormal 2.45 1.39 Figure 2.3Figure 3.3

AVS Lognormal 1 2.49 1.28 Figure 2.4

Quartz content Normal 26.3 17.5 Figure 2.5

DRI Normal 47.6 14.82 Figure 3.1

BWI Normal 39.1 18.5 Figure 2.7

CLI Lognormal 2.5 1.0 Figure 3.2

Table 3.1 Cumulative distribution of drillability parameters. Lognormal distributionuses the natural logarithm. (The mean and standard deviation for the lognormaldistributions are the computed values. For some of the parameters, slightly different values

of the mean and standard deviation give a better fit for parts of the distribution curve.) 1 A Weibull distribution with = 1.2 and = 20 gives a better fit for parts of thedistribution curve.

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3. USE OF DATA 3.2 Generating Distributions

99

3.2 GENERATING DISTRIBUTIONS

The way the distribution plots for small numbers of test results are generated willhave a significant influence on the percentiles and other information derived from the

plots.

As described in the Sections 2.1, 2.2 and 2.3, there are various approaches to how thedistribution curve may be generated. In the following, we will make a brief discussionof how one may generate the distribution functions when few data are available.

The following three possible approaches will be treated:

Siegel (see page 26) EXCEL (see page 81) Centre of interval, COI (described below)

COI means that each test result represents the centres of equally large intervals on thecumulative axis of the plot. The 7 DRI values of siltstone in the BORBAR databasewill represent an interval of 14.286 % on the cumulative axis. The percentile of each

DRI value is found by:

Table 3.2 shows the percentiles calculated according to the three models. Figure 3.5shows the same data plotted as cumulative percentages.

i 1 2 3 4 5 6 7

DRI 32 38 50 57 63 75 86

Percentile Siegel 14.286 28.571 42.857 57.143 71.429 85.714 100

Percentile EXCEL 0 16.667 33.333 50 66.667 83.333 100

Percentile COI 7.143 21.429 35.714 50 64.286 78.571 92.857

Table 3.2 Sorted DRI values of siltstone and corresponding percentiles of three

cumulative plot models.

ni

n p i

100)1(

2/100

+= for i = 1 to n [3.1]

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100

Figure 3.5 Cumulative plots of DRI values of siltstone for three cumulative models.7 test results.

Depending on the cumulative model one uses, it is obvious from Figure 3.5 that thederived percentiles, etc. will vary. Table 3.3 shows some typical percentiles for thethree cumulative models.

Percentile 10 25 50 75 90

Siegel - 37 54 66 78

EXCEL 36 44 57 69 79

COI 33 41 57 72 84

Table 3.3 Percentiles of the distribution curves for siltstone.

Figure 3.5 and Table 3.3 shows the following:

The Siegel model gives the most conservative interpretation of the test results with

regard to DRI, CLI, S 20 and SJ. It also gives the most optimistic interpretationwith regard to AV, AVS, quartz content and BWI.

0

20

40

60

80

100

20 30 40 50 60 70 80 90 100

DRI

C u m u


t a g e

SiegelEXCEL

COI

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101

The EXCEL model gives the most optimistic interpretation of the test results less

than the median, which is the unfavourable side of the median with regard to DRI,CLI, S 20 and SJ.

The COI model gives the most optimistic interpretation of the test results largerthan the median, which is the unfavourable side of the median with regard to AV,AVS, quartz content and BWI.

When the number of samples increases, the difference between the cumulative modelsdecreases. Figure 3.6 shows the Siegel and EXCEL cumulative distributions for theDRI values of granodiorite in the BORBAR database.

Figure 3.6 Cumulative plots of DRI values of granodiorite for two cumulativemodels. 33 test results.

All the cumulative plots in this report are made using the Siegel model. This must beconsidered when using the plots in contracts or similar situations.

0

20

40

60

80

100

20 30 40 50 60 70 80

DRI

C u m u


t a g e

SiegelEXCEL

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3. USE OF DATA 3.3 Extreme Values

102

3.3 EXTREME VALUES

OutliersOutliers are test results that may be characterised as extreme, having a relative largedeviation from the centre of the distribution. Outliers may influence the use ofcumulative plots, percentiles, mean values, etc.

To get more robust results, especially for small data sets, Siegel recommends thatoutliers should be removed before the data are treated statistically or used in otherways.

An outlier may be found by estimating the lower and upper outlier thresholds basedon the interquartile range. Siegel recommends the following thresholds:

TO = threshold of outliersq25 = lower quartile of the dataq75 = upper quartile of the data

The BORBAR database contains 10 CLI results for diabase. Figure 3.7 shows at leastone extreme CLI value for diabase. The test results in the database are shown below.

Rank 1 2 3 4 5 6 7 8 9 10CLI 10.3 10.5 13.4 14.8 15.8 16.5 19.0 30.8 53.5 138.1

Table 3.4 Sorted CLI results of diabase in the BORBAR database.

Using the EXCEL cumulative distribution method and the equations [3.2] and [3.3],the outlier thresholds are found to be:

)(5.1 257525 qqqTO low = [3.2]

)(5.1 257575 qqqTO high += [3.3]

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103

TO low < 0

TO high = 49.1

Accordingly, the test results with rank 9 and 10 should be removed from the data set.The EXCEL cumulative distribution will then have the characteristics shown in Table3.5.

Figure 3.7 Cumulative distribution plot of CLI values of diabase in the BORBAR database.

In Chapter 2, all distribution plots and tables of distribution characteristics include alldata.

The outlier method may be used both for skewed and symmetrical distributions.

Trimmed Data SetA trimmed data set means that an equal number of the largest and smallest data values

are deleted from an ordered data set. Siegel recommends to use a 10 % trimmed

0

20

40

60

80

100

0 20 40 60 80 100 120 140

CLI

C u m u


t a g e

Total databaseWithout outliers

Outlier

Outlier

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104

data set, meaning that a total of 20 % of the data values is removed. For the diabase

example, this would result in deleting one test value at each end of the ordered testresults.

Trimming the data set is best suited for symmetrical distributions.

Data Set No. of Tests Low 25 % Median 75 % High

All Tests 10 10.3 13.8 16.1 27.9 138.1

Without Outliers 8 10.3 12.7 15.3 17.1 30.8

10 % Trimmed 8 10.5 14.5 16.1 22.0 53.5

Table 3.5 Distribution characteristics of CLI results of diabase in the BORBAR database with extreme values removed from the data set.

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3. USE OF DATA 3.4 Planning and Contracts

105

3.4 PLANNING AND CONTRACTS

The drillability properties of the rock mass have a great influence on the timeconsumption and excavation costs for various project types in rock. The variability ifthe rock mass properties influences the uncertainty or the risk of the project. Thegreatest influence probably occurs in projects involving mechanical excavation.

Planning

In the planning phase of a project, one has to rely on general knowledge supplied withinformation from field mapping, borehole logging and rock samples.

Depending on the amount of information one has, use of the distribution curves of thedrillability indices will vary somewhat.

At early planning stages, only general information of the rock mass may be available.A reasonable approach will be to use the median parameter values of the given rocktype as expected rock conditions. If the rock type in the area is known to generally

belong to one of the categories in Table 3.6, the rock conditions may be evaluated asthe percentile in the middle of the intervals shown in the table.

Category Cumulative Percentage of Total Number of Samples

Extremely low 0 5

Very low 5 15

Low 15 35

Medium 35 65

High 65 85

Very high 85 95

Extremely high 95 100

Table 3.6 Cumulative percentage for category intervals of drillability indices.From Project Report 1A-98 DRILLABILITY Test Methods .For the indices DRI and CLI, "Poor drillability" corresponds to a "Low" index value. Forthe index BWI, "Poor drillability" corresponds to a "High" index value.

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106

Evaluating risk or uncertainty should be based on using percentiles rather than using a

percentage variation in the parameter value itself. This approach is most important forskewed distributions. It is recommended to use a span of at least 20 percentileswhen estimating risk or uncertainty for a project with no rock samples tested.

If representative rock samples have been tested, one may use the laboratory testresults directly, but there is always a risk that one or more samples are not asrepresentative as intended. The specific test results should be evaluated taking generalknowledge and parameter distribution curves into consideration as well.

When the laboratory test results of one or more rock samples are known, the span in a

risk or uncertainty estimation may be reduced to e.g. 15 percentiles.

Use in Contracts

The contract of a project should accept that it is practically impossible to present precise information about the conditions of the complete rock mass to be excavated.

Such information will only be available when the excavation is completed. Thecontract should contain tools to handle variation in the rock mass properties withregard to time consumption and excavation costs.

Figure 3.8 outlines how a predetermined rate of compensation may be established in acontract. "Rock properties" may be valid for one or more rock mass parameters usedas basis to estimate e.g. the penetration rate or the cutter wear for a TBM project.Preferably, "rock properties" should express the combined effect of all rock mass

parameters used in the estimations.

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107

Figure 3.8 Example of predetermined rate of compensation for variation in the rockmass conditions.

0.6

0.8

1

1.2

1.4

1.6

+50 +40 +30 +20 +10 0 -10 -20 -30 -40 -50

Percent Change in Rock Properties

F a c t o r o f

E c o n o m

i c C o m p e n s a t

i o n

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APPENDIX A. Previous Editions

108

A. PREVIOUS EDITIONS

A similar treatment of drillability indices as given in this report, has not been published before as far as we know. The Catalogue of Drillability Indices, on whichthis report is based, has been published in several editions over the years. Previouseditions of the Drillability Report including project group members are listed below:

6-75 THE DRILLING RATE INDEX DRI(Norwegian edition)

Bjrn KiellandHalvdan Ousdal

O. Torgeir BlindheimOdd Johannessen

8-79 DRILLABILITY Catalogue of Drillability Indices(Norwegian and English editions)

O. Torgeir BlindheimErik Dahl JohansenArne LislerudOdd Johannessen

4-88 DRILLABILITY Catalogue of Drillability Indices(Norwegian edition)

Amund BrulandSigurd EriksenAstrid M. MyranRune RakeOdd Johannessen

13-90 DRILLABILITY Catalogue of Drillability Indices(Norwegian and English editions)

Amund BrulandSigurd EriksenAstrid M. MyranOdd Johannessen

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APPENDIX B. Research Partners

109

B. RESEARCH PARTNERS

The following external research partners have supported the project:

Statkraft anlegg as Norwegian Public Roads Administration Statsbygg Scandinavian Rock Group AS NCC Eeg-Henriksen Anlegg AS Veidekke ASA Andersen Mek. Verksted AS DYNO Nobel Atlas Copco Rock Drills AB Tamrock OY The Research Council of Norway

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