Effects of Jointing on Fragmentation Design and Influence of Joints in Small Scale Testing
Jonas Hyldahl
Civil Engineering, master's level (120 credits) 2018
Luleå University of Technology Department of Civil, Environmental and Natural Resources Engineering
Abstract
This thesis has been conducted for the Luleå University of Technology (LTU), Sweden as part of an inter-university collaboration between LTU and the Montanuniversität Leoben (MUL), Austria.
The project has included three master thesis works, all investigating some aspects of the effects of jointing on fragmentation through small scale tests.
The topic of this thesis has been to develop a method for representing/introducing artificial joint planes into concrete blocks and subsequently manufacture a number of specimens with different joint sets for testing, using block dimensions previously used at MUL. The method for manufacturing the jointed test specimens, developed by the author at LTU, has been evaluated through blasting and fragmentation analysis. Comparison of the different produced joint sets has been done to assess the influence of jointing on fragmentation.
A total of 10 magnetic concrete blocks were produced and evaluated. The 10 blocks had an average density of 2485 ± 41 kg/m3 (mean ± standard deviation). Eight of the 10 blocks contained joint sets (JS) with different characteristics, while two blocks were un-jointed reference blocks. A total of four different joint sets were developed.
The four joint sets had the following properties; JS1: joint spacing 95 mm, strike/dip equal to 0/90°, JS2: joint spacing 47.5 mm, strike/dip equal to 0/90°, JS3: joint spacing 47.5 mm, strike/dip equal to 60°/90° and JS4: joint spacing 89 mm, strike/dip equal to 0/70°.
The produced joints have proven to behave as desired, i.e. being able to reflect incident waves and to stop some incident cracks.
It has been found that there is a strong indication of jointed blocks producing a finer median fragmentation size (x50) than that of the reference blocks. This means that by introducing joint sets into the test specimens the degree of fragmentation by blasting has been increased. This was predicted by the Kuz-Ram model.
Each of the 28 blasted rows has been sieved and analysed. All the data has been fitted to the three parameter Swebrec function, producing an average coefficient of determination (an R- square value) of 0.9946 ± 0.0064.
i
Preface
The mining industry has always fascinated something in me, perhaps the size of the equipment, or the sheer amount of materials moved, but mostly, I think, it is the childish fascination of searching for something in the ground; the feeling of going into the earth, to see and to stand where humanity has never stood before. I fully understand people who, for instance, hate going underground into a tunnel or a mine, but for me, there is something deeply exciting about having hundreds or even thousands of metres of (more or less) solid rock above my head. And thus I have chosen to take, on top of my bachelor degree in civil engineering, a master degree in civil engineering with specialization in mining.
So here, 7 years later, this thesis marks the eclipse of my educational journey, a journey which has taken me from Greenland in North to Australia in South, and though this work might mark the end of my academic career, it doesn’t mean that I’m done learning.
I would like to thank Nikolaos Petropoulos, my supervisor, and Assistant Professor and Director of Swebrec Daniel Johansson for all their help and support, physically as well as mentally, during my work. Thank you so very much!
Also, I would like to thank my fellow students and good friends, especially Patrik Hagström. I doubt, I would have made it through my studies without them. I know it hasn’t always been easy, but thank you for listening and letting me use you for brainstorming and testing ideas as well as a vent for the occasional frustration.
Finally, my deepest gratitude to my family and my girlfriend for all their support and love, and for keeping up with me, having lived and studied in four different countries on three different continents, not always being as easy to get a hold of, or see, as they might have preferred.
Jonas Hyldahl, September 2015
iii
Acknowledgement
The author would like to thank Atlas Copco for supplying the financial foundation on which the work for this thesis was build. This was done through the Rock Engineering Price awarded to Professor Finn Ouchterlony. Likewise the author would like to thank Luleå University of Technology (LTU) and Montanuniversität Leoben (MUL) for support and access to facilities.
This work was carried out as a joint thesis project between the two universities and, besides the author, also included the two master thesis students Orhan Altürk and Ilke Alp Özer, both writing their theses for Montanuniversität Leoben. The author acknowledges their work with blasting and sieving all the remaining samples after a collective start-up, along with performing P- and S-wave measurements.
The author also would like to acknowledge the considerable help from Gerold “Geri” Wölfler, the blast technician at Montanuniversität Leoben, for all his work at the blasting site, as well as Radoslava Ivanova and Peter Schimek for their help and guidance in the early stages of the work with blasting and sieving.
Finally the author would like to thank Professor Finn Ouchterlony of the Montanuniversität Leoben for making the project a collaboration between the two universities, thereby making it possible for the author to work with this topic.
v
List of content
Abstract...... i
Preface ...... iii
Acknowledgement ...... v
1 Introduction ...... 1
2 Literature study ...... 3
2.1 Geology; Joints and Rock Mass Qualification ...... 3
2.2 Fragmentation mechanics ...... 5
2.3 Evaluation of fragmentation ...... 7 2.3.1 The Kuz-Ram model ...... 7
2.3.2 The Swebrec function ...... 11
2.4 Previous work; modelling joints in small scale testing ...... 13
3 Small scale testing ...... 16
3.1 Model development and preparation ...... 16
3.2 Cubes ...... 17 3.2.1 Pull-out times ...... 19
3.3 Magnetic Concrete Blocks...... 20 3.3.1 Reference block design ...... 22
3.3.2 Joint set 1 (JS1) ...... 24
3.3.3 Joint set 2 (JS2) ...... 25
3.3.4 Joint set 3 (JS3) ...... 26
3.3.5 Joint set 4 (JS4) ...... 28
3.3.6 Joints ...... 29
3.3.7 Potential failures and difficulties ...... 33
3.4 Magnetic concrete ...... 35 3.4.1 Recipe ...... 35
3.4.2 Density ...... 36
3.4.3 Wave velocity ...... 37
3.5 Expected rock factor (A) according to the Kuz-Ram-model...... 41
vii 3.6 Quick guide for making blocks containing joint sets ...... 43
3.7 Blasting ...... 44 3.7.1 Test site Erzberg ...... 44
3.7.2 Explosives ...... 45
3.7.3 Delay ...... 46
3.7.4 Initiation pattern ...... 47
3.8 Sieving ...... 48
4 Results ...... 50
4.1 Compiled sieving data – Cylinders ...... 50
4.2 Compiled sieving data – Blocks ...... 51 4.2.1 Coefficient of uniformity ...... 58
4.3 Swebrec function fits ...... 61
5 Discussion ...... 63
5.1 Block manufacturing ...... 63
5.2 Fragmentation results ...... 64
6 Conclusion ...... 73
7 Future work ...... 74
8 References ...... 75
Appendices ...... 77
Appendix 1: Reference 2 ...... 79
Appendix 2: Reference 3 ...... 83
Appendix 3: JS1 Alpha ...... 87
Appendix 4: JS1 Beta ...... 91
Appendix 5: JS1 Gamma ...... 93
Appendix 6: JS2 Beta ...... 97
Appendix 7: JS3 Alpha ...... 101
Appendix 8: JS3 Beta ...... 105
Appendix 9: JS4 Alpha ...... 107
Appendix 10: JS4 Beta ...... 111
viii List of Figures
Figure 1: Geometrical terms for joint description (Nilsen and Thidemann, 1993) ...... 4 Figure 2: Tensile fracture (Morhard, 1987)...... 5 Figure 3: Fracturing by stress wave and gas expansion (Morhard, 1987)...... 6 Figure 4: Example of model bench made from sandstone slabs (Singh and Sarma, 1983). .... 13 Figure 5: Left: Weakness planes parallel to the face. Right: Weakness planes parallel and perpendicular to the face (Yang and Rustan, 1983)...... 14 Figure 6: Production of test specimens with stress fields. (a) depicts an ordinary specimen, (b)-(d) shows the creation of a specimen with an inclined joint plane (Mostyn and Bagheripour, 1995)...... 15 Figure 7: 200×200×200 mm cube with four plastic sheets suspended in steel wires...... 17 Figure 8: Markings on the joint plane surface from the holes poked in the plastic sheet...... 18 Figure 9: View through a smooth blast hole created using a plastic stick...... 21 Figure 10: Reference block, top view...... 22 Figure 11: Reference block, front view...... 22 Figure 12: Reference block, side view...... 23 Figure 13: Reference 3 with the second row charged for blasting...... 23 Figure 14: Joint set 1, top view. Strike/dip = 0/90°, joint spacing = 95 mm...... 24 Figure 15: Joint set 1, front view...... 24 Figure 16: Joint set 1, side view. The hatched area represents the joint plane...... 25 Figure 17: Joint set 2, top view. Strike/dip = 0/90°, joint spacing = 47.5 mm...... 26 Figure 18: Joint set 3, top view. Strike/dip = 60°/90°, joint spacing = 47.5 mm...... 27 Figure 19: Left: JS3 mould ready for casting. Right: JS3 block cast and lid mounted...... 27 Figure 20: Joint set 4, top view. Strike/dip = 0/70°, joint spacing = 89 mm...... 28 Figure 21: Joint set 4, front view...... 28 Figure 22: Mirrored JS4s. Left: JS4 Alpha Row 1. Right: JS4 Beta Row 1...... 29 Figure 23: Makeshift devise for similar placement of rows and holes on each sheet...... 30 Figure 24: Cut-off hole edges and finished joint sheets...... 30 Figure 25: Schematics for joint installation. Left: vertical joints. Right: dipping joints...... 31 Figure 26: Installation and control of plastic sheets in a JS1 mould...... 31 Figure 27: Installed joints in moulds. Left: JS2. Right: JS4...... 32 Figure 28: Example of two plastic sheets that lost their corners, JS2 Alpha...... 33 Figure 29: JS2 Alpha with unremoved plastic sheets...... 34
ix Figure 30: Cavity generated in the bottom of a JS3 block...... 34 Figure 31: Jointed test cube with points for wave velocity measurements indicated...... 38 Figure 32: Box-and-whisker plot of P-wave velocities in magnetic concrete cubes...... 39 Figure 33: Box-and-whisker plot of S-wave velocities in magnetic concrete cubes...... 40 Figure 34: 20 steps on how to prepare concrete blocks containing joint sets...... 43 Figure 35: Fence enclosed yoke...... 44 Figure 36: Yoke and fence covered in blankets, ready for blasting...... 45 Figure 37: Blastholes charged and delay cord in place, Reference 2 row 1...... 46 Figure 38: Fragment size distribution for cylinders...... 50 Figure 39: Fragment size distribution for the Reference blocks...... 51 Figure 40: Fragment size distribution for JS1...... 52 Figure 41: Fragment size distribution for JS4...... 53 Figure 42: Fragment size distribution for JS2...... 53 Figure 43: Fragment size distribution for JS3 ...... 54 Figure 44: Extensive back breakage in row 2 of JS3 Beta...... 54
Figure 45: Box-and-whisker plot of the x30, x50 and x80 percentiles against row number...... 56
Figure 46: x50 plotted against joint spacing for row 1 blasts...... 56
Figure 47: x50 plotted against joint spacing for row 2 blasts...... 57
Figure 48: x50 plotted against joint spacing for row 3 blasts...... 58
Figure 49: Coefficient of uniformity; x30 and x80 plotted against fragment size for row 1...... 59
Figure 50: Coefficient of uniformity; x30 and x80 plotted against fragment size for row 2...... 60
Figure 51: Coefficient of uniformity; x30 and x80 plotted against fragment size for row 3...... 60 Figure 52: The Swebrec function fitted to JS1 Gamma row 1...... 62 Figure 53: New face after row 1 blast on JS1 Alpha (top), JS1 Beta and JS1 Gamma (bottom)...... 65 Figure 54: New face after row 1 blast on JS3 Alpha (top) and JS3 Beta...... 67 Figure 55: New face after row 2 blast on JS4 Alpha (left) and JS4 Beta...... 67 Figure 56: New face after row 3 blasts on JS4 Alpha (left) and JS4 Beta...... 67 Figure 57: Large fragment from JS1 Beta row 1...... 69
Figure 58: x30 plotted against joint spacing for row 1 blasts...... 69 Figure 59: Fragment size distribution; Reference 1...... 72
x List of Tables
Table 1: Produced blocks and associated cylinders ...... 20
Table 2: The recipe for magnetic concrete...... 35
Table 3: Density data for the 10 blasted magnetic concrete blocks...... 36
Table 4: P- and S-wave velocities in magnetic concrete cubes...... 38
Table 5: Properties of the magnetic concrete (Johansson, 2008)...... 40
Table 6: Rock factor values according to the Kuz-Ram formula...... 41
Table 7: Measured delay times...... 47
Table 8: Percentile sizes x30, x50 and x80 for cylinders...... 50
Table 9: Percentile sizes x30, x50 and x80 for all rows...... 55
Table 10: Coefficients of uniformity based on average x30 and x80 percentiles...... 59
Table 11: Swebrec function parameters...... 61
Table 12: Difference between measured and expected breakage by mass...... 64
xi
1 Introduction
The improvement and optimization of blasting, in all areas of the field, is an ongoing process, but full scale tests are both expensive, time consuming and often difficult to conduct. Furthermore, because of geological settings, results tend to be, if not uncertain, then at least to some degree site specific.
Small scale testing provides a much less expensive way of investigating certain phenomena or trends in a much more controlled environment, especially with regards to sample description, and thus provides the option for only changing or altering one parameter at a time.
This master thesis project is proposed by the Lehrstuhl für Bergbaukunde, Bergtechnik und Bergwirtschaft at Montanuniversität Leoben (MUL) and involves three separate thesis works, with different foci, but all centred around the same sample material, i.e. the test specimens.
Overall the purpose of the project is to investigate the effects of jointing on fragmentation. This will be done through a series of small scale blasts performed on magnetic concrete blocks.
The two other thesis works will specifically focus on:
Bench surface roughness analysis using Blast Matrix (BMX) modelling.
Crack detection, characterization and grouping.
The topic of this thesis can be split into two main parts. Firstly to develop a method for representing/introducing artificial joint planes into concrete blocks, using the same block dimensions as previously used at MUL, and then manufacture a number of different joint sets for testing. Secondly the method for manufacturing the jointed test specimens will be evaluated through blasting, fragmentation analysis and comparison of the different produced joint sets to assess the influence of jointing on fragmentation.
1 The work presented in this thesis describes the characteristics and manufacturing process of four different joint sets (JS), along with reference samples, incorporated into magnetic concrete blocks, named JS1, JS2, JS3 and JS4 accordingly.
The testing philosophy being to start with the simplest joint configuration conceivable, while adhere to a small set of assumptions relating to limitations in the nature of the testing method, and then expand the degree of complexity, while maintaining some relationship between the sets.
It is, however, outside the scope of this thesis to investigate the actual properties of the manufactured joints, the intent only being to construct joints with limited bridging (areas where concrete from the joint walls connect) and the ability to act partly or fully as wave stoppers.
This thesis is composed of four main sections: a literature study with relevant background information, the description of the development process of the test samples, obtained fragmentation results and finally an evaluation and discussion of the obtained results.
2 2 Literature study
2.1 Geology; Joints and Rock Mass Qualification Working with rock for any purpose will to some extent always be site specific. Due to this fact, a large discipline has evolved around the description of rock. For engineering purposes, unlike in geology, the composition and history of rock is mostly relevant to the extent that it can provide clues to the physical and mechanical properties associated with the rock type.
With regards to properties it is important to distinguish between rock and rock mass. Intact rock is a part of the rock mass, but rock mass means the whole in-situ material including joints and other discontinuities (Nilsen and Thidemann, 1993).
This distinction becomes especially relevant when talking about scale. There are many reasons why full scale tests are less desirable or less often performed, e.g. impractical to handle, time and machinery constraints, man power usage etc. This means the properties of a rock mass are much more difficult to investigate than the properties of the intact rock. This becomes obvious in a laboratory setting, where the specimens often are on the scale of centimetres compared to a bench blast that can be several hundreds of metres wide.
As stated by Jaeger and Cook (1976), joints are by far the most common type of geological structures. Price (as cited in Jaeger and Cook, 1976) defines joints as “cracks or fractures in rock along which there has been little or no displacement”.
Joints may be isolated or occur solitary, called random joints (though this could be due to the scale at which the rock mass is viewed), but often joints occur as parallel planes. Parallel joints make up a joint set; several joint sets make up a joint system or joint pattern (Nilsen and Thidemann, 1993 and McLean and Gribble, 1979).
McLean and Gribble (1979) point out that joints will have a “considerable effect on the properties of a rock mass”, while Nilsen and Thidemann (1993) states “the properties of the in-situ rock mass will largely be governed by the properties of its joints”. An important part of any site investigation will therefore be joint mapping. This process consists of field measurements of the joint characteristics: orientation, spacing, length, width/openness and roughness (Nilsen and Thidemann, 1993).
To describe the orientation of a joint plane the two characteristic attributes strike and dip are used. The term dip direction is also sometimes used. Figure 1 shows the relationship between these three orientation terms.
3
Figure 1: Geometrical terms for joint description (Nilsen and Thidemann, 1993)
The strike of a plane is measured as the trace of the plane’s intersection with any horizontal surface relative to North. A horizontal line drawn on the surface of a joint plane will have the same strike direction as the joint plane itself (notice that this means any plane will have two strike directions). The dip is the joint’s inclination relative to horizontal. This value is typically given according to the right hand rule, an arbitrary standard specifying, not only the dip, but also which strike direction to use. The rule states that when the palm of the right hand rests against the plane surface, with fingers pointing downwards, the thumb will be towards the strike direction.
Two very common empirical ways of systematically rate the rock mass quality, are the RMR (Rock Mass Rating) and the Q-method (Tunnelling Quality Index). Common for both methods are that joint description parameters dominate in each system (Waltham, 2009).
For example, the Q-method establishes a numerical value in the range of 0.001 to 1000 divided into 9 quality classes from exceptionally poor to exceptionally good (Nilsen and Thidemann, 1993). Equation [1] shows how three sets of parameters are multiplied to obtain the Q-value. For definitions and value ranges, see e.g. Waltham (2009).
RQD J J Q r w [1] Jna J SRF whereRQD Rock Quality Designation Relative block size Jn Joint set number
Jr Joint roughness number Relative frictional strength Ja Joint alteration number
Jw Joint water reduction factor Active stress SRF Strees Reduction Factor
4 2.2 Fragmentation mechanics The purpose of blasting rock is to fracture it, either for general removal or further processing. A number of blasting theories, i.e. the breakage mechanisms manifesting when blasting is performed, exist, and are consistently being modified and updated as more data and new analysis methods become available.
The two basic theories of fragmentation mechanisms by blasting are those of reflection theory and gas expansion theory, and both have a number of variations. In reality the most wholesome theories are probably the ones that combine both.
Figure 2 shows the basic concept of reflection theory. This simple theory it based on the fact that the tension strength of rock is always smaller than the compression strength (Morhard, 1987).
Figure 2: Tensile fracture (Morhard, 1987).
When the explosive charge is detonated, an outgoing compressive wave is generated. When this compressive wave reaches a free surface, it is reflected back into the rock as a tensile wave. In this simple theory, the high-pressure, expanding gases are not attributed any significant responsibility for the fracturing (Morhard, 1987).
5 Figure 3 shows the combined induced fracturing by stress wave and gas expansion around a borehole in three stages (Morhard, 1987). In the first stage (a) high pressure shatters the rock around the borehole and the outgoing shock wave creates radial cracks (tangential stress). In the second stage (b) the positive pressure from the outgoing shock wave drops on reaching the free surface and a tensile wave is reflected back into the rock. The tensile stress pulls apart the rock, creating primary failure cracks. However, it has been calculated that the explosive load must be approximately eight times the normal load for the reflected shock wave to cause failure alone; for most explosives, the shock wave energy only accounts for 5-15 % of the total explosive energy (Morhard, 1987). In stage 3 (c) the actual breakage takes place as a “slower” reaction caused by the expanding gases wherein the radial cracks are rapidly enlarged. Once the mass in front of the borehole yields the high compressive stress within the rock unloads and induces high tensile stress that completes the breakage processes started in stage 2 (Morhard, 1987).
Figure 3: Fracturing by stress wave and gas expansion (Morhard, 1987).
This means, that in this theory, the shock wave is not directly responsible for any significant rock breakage, but rather the basic conditioner for the last stage of the breakage process (Morhard, 1987).
6 2.3 Evaluation of fragmentation Fragmentation models describe fragmentation caused by blasting; the final goal is to predict the fragment size distribution. A very common way of evaluating fragmentation is by investigating the median fragment size. Therefore, many models also share some of the same parameters, but they can differ in the total number of included parameters or the underlying distribution equation. Two examples of fragmentation models are the Kuz-Ram model and the Swebrec function, both described below.
2.3.1 The Kuz-Ram model First published by Cunningham (1983), the Kuz-Ram model has since then become the most used method for estimating fragmentation by blasting (Cunningham, 2005).
There are three key equations to the Kuz-Ram model (Cunningham, 2005): the adapted Kuznetsov equation [2], the adapted Rosin-Rammler equation [6] and the uniformity equation [7].
The adapted Kuznetsov equation is used for estimating the median fragmentation size from a given blast as, Equation [2]:
19/30 1/6115 0.8 x50 A Q q , [2] sANFO
wherex50 median fragment size [cm] A rock factor Q charge weight, per hole [kg]
sANFO explosive's weight strength relative to ANFO [%], with 115 being the relative weight strength of TNT q specific charge [kg/m3 ].
In the original paper, the rock factor (A) was a simple numerical value of either 7, 10 or 13 for medium rocks, hard and highly fissured rocks or hard and weakly fissured rocks, respectively, (Cunningham, 1983), but in Cunningham (1987) the definition of the rock factor was altered and considerably expanded to include the joint descriptors spacing and plane angle, along with density and strength factors.
7 In Cunningham (2005) the way to derive the rock factor was again updated, leading to Equation [3]: A0.06 RMD RDI HF , [3] whereRMD rock mass description powder/friable 10 vertically jointed JF massive formation 50 (here the ter massive formation simply implies jointsm further apart than the bl as tholes)
RDI rock density influence 0.025
HF hardness factor If E 50, HF E / 3 If E 50, HF UCS / 5 , where is the rock density [kg/m3 ], E is the Young's Modulus [GPa] and UCS is the uniaxial compressive strength [MPa].
The derived joint factor (JF), from the RMD, is governed by three factors, Equation [4]:
JF JCF JPS JPA , [4] whereJCF joint condition factor Tight jointsJCF 1 Relaxed jointsJCF 1.5 Gouge-filled jointsJCF 2
JPS joint plane spacing factor joint spacing < 0.1 mJPS 10 joint spacing = 0.1-0.3 m JPS 20 joint spacing = 0.3 m to 95% of P JPS 80 joint spacing > P JPS 50
where P , the reduced pattern, is given as P Burden Spacing
JPA joint plane angle factor Dip out of faceJPA 40 Strike out of faceJPA 30 Dip into face JPA 20.
8 According to Cunningham (2005), the rock factor (A) varies between 0.8 and 22, though if it becomes apparent that the algorithm produces too small or too big values, for instance through preliminary tests, a correction factor, Equation [5], can be applied:
CAAA '/ , [5] where A ' is the back calculated rock factor. The size order of the correction factor should fall within 0.5CA 2 (Cunningham, 2005).
The adapted Rosin-Rammler equation reads, Equation [6]:
n x Rx exp 0.693 [6] x 50 whereR x mass fraction retained on screen opening x
n uniformity index, usually in the range 0.7 2.
The uniformity index (n) is defined as, Equation [7] (Cunningham, 2005):
0.1 14B 1 S / B W BCL CCL L n 2.2 1 0.1 , [7] d 2 B L H whereB burden [m] S spacing [m] d hole diameter [mm] W standard deviation of drilling precision [m]
L charge length [m] BCL bottom charge length [m] CCL column charge length [m] H bench height [m].
Though in the same publication, Cunningham (2005), the expression for the uniformity index was updated to, Equation [8]:
0.3 30BSBWL 1 / nns 2 1 , [8] d 2 B H
where the only new parameter (ns) is the uniformity factor.
9 The uniformity factor is governed by the scatter ratio (Rs), to address the effect on the fragmentation curve from timing scatter in the blast initiation. The scatter ratio is defined as, Equation [9] (Cunningham, 2005):
Tr t Rs 6 , [9] TTxx
where Rs scatter ratio T range of delay scatter for initiation system [ms] r Tx desired delay between holes [ms]
t standard deviation of initiation system [ms].
The uniformity factor (ns) is given as Equation [10], to include the expected effect on fragmentation from precision in blast initiation (Cunningham, 2005):
0.8 Rs ns 0.206 1 . [10] 4
The effect of an increased scatter ratio is a less uniform fragmentation curve (Cunningham, 2005).
The Kuz-Ram model does not include any maximum fragment size (xmax), meaning that it is technically open ended (no upper limit). Furthermore, the model’s biggest drawback, partly originating in the Rosin-Rammler equation, is its lacking capability in estimating the fines adequately (Cunningham, 2005).
10 2.3.2 The Swebrec function
The standard Swebrec function has three parameters; x50, xmax and b as given by the expression in Equation [11] (Ouchterlony, 2005):
1 b xx Px1 lnmax / ln max . [11] xx50
Given that 0 xxmax , the cumulative distributions function, P x 1, R x in Equation [11] will produce values in the range 0-1. Equation [11] is in fact an extension of the form, Equation [12]:
1 P x 1 f x , [12]
where f xmax 0 and f x 50 1 , resulting in the attributes of x max and x 50 being fixed curve points, with P xmax 1 and P x 50 0.5 , respectively.
The Swebrec function differs from the Kuz-Ram model in the addition of the upper limit to the fragment size (xmax), and a different curve undulating exponent (b), given in Equation [13]:
x bn2 ln2 lnmax , [13] x 50 where n is given by Equation [7] (Ouchterlony, 2005).
It should be noted that Equation [13] is valid only under the condition that the slope value at x50 for a Rosin-Rammler function and a Swebrec function, based on the same x50-value are the same. This, in essence, makes it possible to use Equation [2] with the Swebrec function (Ouchterlony, 2005).
Ouchterlony (as stated in Ouchterlony and Moser, 2006) found that for model-scale blasts, the undulating parameter (b) could be expressed as, Equation [14]:
x bx1.0 0.25 ln max 50 [14] x50
11 Equation [15] gives the relationship to produce a fragment size corresponding to a percentage passing (Pp) as (Ouchterlony, 2009):
1/b 1/Pp 1 [15] xp / xmax x 50 / x max .
The Swebrec function has been fitted to a large amount of sieving data from many different sources. This includes full and model scale blasts in different geological and constructed materials, with different geometries and using different explosives. The fittings have been good-to-excellent, with coefficients of determination (r2) bigger than 0.995, in more than 95 % of the cases (Ouchterlony, 2005).
Ouchterlony (2005) states that “the maximum fragment size (xmax), will be physically related to the block size in situ in blasting; however, as a fitting parameter it varies widely” and continues, that the undulating parameter (b) normally is in the range of 1-4.
There is also a five parameter version of the Swebrec function, Equation [16]:
1 bc x x x x P x1ln a max /ln max 1 a max 1/ max 1 , [16] extended x x50 x x 50 with the additional parameters a and c. These parameters increase the precision of the fit for the fines part of the Swebrec fragmentation curve. This five parameter version will not be given any more notice in this work.
The three parameter Swebrec function will, later in this work, be the fragmentation model applied to the fragment size distributions, obtained from model-scale blasts, because of its accuracy and its parameter’s physical meaning.
12 2.4 Previous work; modelling joints in small scale testing Blasting in model-scale testing has been around for decades, and the concept of testing the effects of jointing on fragmentation in model-scale is not new. Therefore, it is somewhat remarkable that the literature is almost solely focused on single, or sometimes two, hole blasts when it comes to jointed test specimens, when blasting in reality predominantly is done in rows of multiple holes, whether it is for mining or landscaping purposes.
Fourney, Baker and Holloway (1983) made extensive experiments with regards to the effects of flaws present in the fragmentation process. Their tests were mainly conducted in plastic models (Homalite 100), but their findings showed reproducibility in granite. They were able to identify a failure mechanism called joint initiated fracturing and concluded that, besides borehole cracking, the outgoing wave system could initiate fractures at remote flaws (Fourney, Baker and Hollaway, 1983).
Singh and Sarma (1983) conducted a model-scale study of single hole blasts in constructed test specimens with different burdens and joint orientations. They constructed bench shaped models of 25 mm thick sandstone slabs bound together by the adhesive Fevicol. The models were 450 × 375 × 150 mm with a bench height of 50 mm. Six different joint orientations were investigated; that of 0°, 30°, 60°, 90°, 120°, and 150° relative to the floor of the bench rotating anti-clockwise. Figure 4 shows an example of a designed model bench (30° rotated joints).
Figure 4: Example of model bench made from sandstone slabs (Singh and Sarma, 1983).
It was found that the degree of fragmentation at a particular point in the model was dependant on the distance to the charge and the number of joints between the point and the charge (Singh and Sarma, 1983). It should be noted, that Singh and Sarma (1983) in their conclusion regarding degree of fragmentation in a point, do not differentiate regarding placement of said point relative to both charge and face (i.e. if the point is in front of or behind the charge).
13 Yang and Rustan (1983) performed 40 one-hole blasts on model-scale specimens (blocks: 100 × 200 × 350 mm), made from magnetite concrete (cement 13 %, magnetite 74 % and water 13 % by weight). Besides reference blocks, three types of models were constructed: one with weakness planes parallel to the face, one with weakness planes parallel and perpendicular to the face and one type with short weakness planes in three or more directions randomly distributed.
The cast blocks were partly sawn into plates and reassembled with different filling materials: cement, glue or epoxy. Figure 5 shows the two first types of models with joints.
Figure 5: Left: Weakness planes parallel to the face. Right: Weakness planes parallel and perpendicular to the face (Yang and Rustan, 1983).
Yang and Rustan (1983) concluded, among other things, that “weakness planes can, depending on direction and property, attenuate the stress wave and growing radial cracks during blasting” and continued to state that “they (weakness planes) usually decrease the strength of the rock and make it difficult for cracks to pass across them”.
Another conclusion was that with increased jointing it became more difficult to change the median fragment size, by changing the charge concentration, compared to less jointed models.
Finally, Yang and Rustan (1983) also concluded that “if a weakness plane is open and filled with air it has a very strong influence on the fragmentation compared to, if the weakness plane is filled by solid material”.
14 The most common way of creating joints in test specimens so far seems to be by gluing together slabs of either cast or natural homogenous materials. One method that more closely resembles what was developed for this thesis, specifically in the way that it did not glue together materials to create joints, but incorporated joints into the mould in the casting process, is the work by Mostyn and Bagheripour (1995).
Mostyn and Bagheripour (1995) developed a new artificial rock-like material with properties similar to that of intact soft sedimentary rock. In their work, they cast their specimens in cylinders and compacted them to generate a stress field. In some specimens they incorporated finite sized joints in the form of ordinary tea bags placed inside the cylindrical moulds. By using an inclined rammer on a half full mould (instead of a flat one) they could also produce inclined joint planes, see Figure 6.
Figure 6: Production of test specimens with stress fields. (a) depicts an ordinary specimen, (b)-(d) shows the creation of a specimen with an inclined joint plane (Mostyn and Bagheripour, 1995).
15 3 Small scale testing
3.1 Model development and preparation Because of the nature of the project, it was necessary to come up with some simple design limitations and manufacturing guidelines that simultaneously ensured the test specimens could be handled as well as produce relevant results.
It was decided, that the joints were to be produced by inserting plastic sheets, held in place in tension by steel wires, into the specimen moulds before casting for later removal, thus creating open joints with limited to no bridging (areas where the two joint plane walls are touching).
The design restrictions can be summarized in the following three points:
For handling purposes, a safety margin of at least 25 mm un-jointed concrete should be present on all sides except one (the block surface).
In fear of expanding gases entering directly into the open joints, thereby possibly either escaping without performing useful work or alternatively creating significantly, unwanted breakage and potentially even causing a complete collapse of the test specimen, no joints are allowed to intersect blastholes. This includes horizontal joint planes.
No joints are allowed to run (have a strike) parallel to the face of the test specimens. Such a configuration was deemed unwanted for the investigative scope of this project.
Once the restrictions were in place, preliminary tests were performed.
16 3.2 Cubes A number of 200 × 200 × 200 mm cubes were manufactured to investigate a large number of uncertainties, including:
Determine how to best install plastic sheets using steel wire. The angle on the steel wires for effective suspension of the plastic sheets in tension. If the moulds needed to be filled from a certain side (parallel or perpendicular to the joint planes), and if so which were the optimum. The optimum pull-out time of the plastic sheets after casting.
It was determined, that in order to pull out the plastic sheets, and thereby creating open joints, the plastic sheets should be suspended in wires going through holes in the casting mould’s walls. Then, when the mould was filled with magnetic concrete and the plastic sheets no longer needed to be held in place, the wires could be pulled out through the same holes.
An easy and reliable method for continually maintaining a constant margin of safety in the bottom of the mould turned out to be by installing the plastic sheets with three wires. One close to the bottom, one in the middle and one close to the top. Each time installing (drawing tight) the middle wire first and then tensioning the plastic sheet by angling the top and bottom wires slightly. Figure 7 shows an early test cube with four installed plastic sheets.
Figure 7: 200×200×200 mm cube with four plastic sheets suspended in steel wires.
17 By filling a test cube with very fine grained quartz sand, in an effort to determine if there was an optimum filling direction, the need for stabilizers were recognized. These came to be made from thin plywood sheets mounted on both sides of each plastic sheet. The stabilizers also had the effect of eliminating the need to avoid filling the moulds perpendicular to the joint strike direction. This had previously been observed to cause bulging of the plastic sheets no matter how cautiously the sand was poured into the cube.
Finally, the cubes were used for determining the pull-out time of the plastic sheets. The curing times of the first test cube turned out to be too long and it was only possible to remove one of the four test joints (after 2 hours and 30 minutes of curing time), though this one sheet came to have great influence on the further development of the joints.
Figure 8 shows how the holes poked in the plastic sheet for “sewing” the wires through have left clear markings in the otherwise smooth joint plane surface. These markings, in the form of long parallel grooves, arose when the sheet was pulled out. The grooves were created by bulging edges around the holes. These edges were a by-product of poking the holes in the plastic.
Figure 8: Markings on the joint plane surface from the holes poked in the plastic sheet.
The way to remove these grooves, that were judged to possibly influence the fragmentation in an unwanted way, was simple yet time consuming. The bulging rim around every poked hole was carefully cut off with a sharp knife.
The test casting also revealed the need for further greasing of the joint planes to ease the pull- out process.
18 3.2.1 Pull-out times The optimum pull-out time was determined to be between 1 hour and 45 minutes and 2 hours measured from the beginning of the casting; continuously the “aimed for”-time was that of 1 hour and 45 minutes.
This time was reached based on a cube where four test joints were pulled out after: 1 hour 15 min, 1 hour 40 min, 2 hours 5 min and 2 hours 30 min, respectively.
Based on a desire for joints with some resemblance to natural joints, meaning not completely open, but still open to such a degree that effects would be expected, the joint surface should have the properties (Ouchterlony, 2015a):
Being able to reflect the incident waves. To stop at least some of the incident cracks.
Therefore, the bridging in the earliest pull-out time was deemed too extensive. The joint created by the longest pull-out time had strange markings on the upper half and furthermore looked too open. Thus a desired pull-out time was established to be between 1 hour 40 min and 2 hours 5 min, but closer to 1 hour 45 min to ensure a little healing (bridging) (Ouchterlony, 2015a).
It should be noted by now that any mentioning of joints, relating to test specimens, is a general reference to the slices made in the concrete by the plastic sheets inserted before casting.
19 3.3 Magnetic Concrete Blocks A total of 13 magnetic concrete blocks were cast in 8 casting sessions (one session equals one concrete batch). No more than two blocks were cast at a time and experience showed, especially for the more complex joint sets, that it was a job requiring at least two individuals. Table 1 summarizes the produced blocks with their different fabricated characteristics and the number of blasted rows for each block. Originally, the intent was to cast and blast one concrete cylinder per concrete batch, to check for coherency in fragmentation, but due to surface errors on a large number of cylinders only four were blasted. Table 1 includes the four cylinders and their associated batches.
One block (JS3 -) was discarded upon inspection coming out of the mould and one block (JS2 Alpha) was not blasted due to low priority and time constraints (see Section 3.3.7), meaning a total of 11 blocks were blasted. Of those 11 blocks only 10 will be included in the main analysis of this thesis because of an error associated with the mould in which Reference 1 was cast. A short analysis of Reference 1 will be included in Section 5.2.
Table 1: Produced blocks and associated cylinders
Name Batch Joint spacing Strike/dip Rows blasted Reference 1 1 0 - NA Reference 2 1 0 - 3 Reference 3 7 0 - 3 JS1 Alpha 2 95 mm 0/90° 3 JS1 Beta 2 95 mm 0/90° 2 JS1 Gamma 7 95 mm 0/90° 3 JS2 Alpha 3 47.5 mm 0/90° NA JS2 Beta 5 47.5 mm 0/90° 3 JS3 - 3 47.5 mm 60°/90° NA JS3 Alpha 6 47.5 mm 60°/90° 3 JS3 Beta 8 47.5 mm 60°/90° 2 JS4 Alpha 4 89 mm 0/70° 3 JS4 Beta 5 89 mm 0/70° 3 C1 8 Cylinder - C2 7 Cylinder - C3 5 Cylinder - C4 3 Cylinder NA
Table 1 shows that the discarded JS3 and the not blasted JS2 Alpha came from the same batch (batch 3). Because of this, that batch will be disregarded. Cylinder 4 came from batch 3 and will therefore not be included in the cylinder analysis in Section 4.1.
20 All blocks were allowed at least 28 days of curing time before they were blasted. The block design was that of length, height and width (L × H × W) equal to 660 mm, 210 mm and 280 mm, respectively, giving a nominal volume of 0.0388 m3. Each block contained 21 blastholes distributed in 3 rows of 7 holes. The burden (B) of each row was 70 mm and the inter-row blasthole spacing (S) was 95 mm resulting in an S/B-ratio of 1.36.
This setup has previously been used at Montanuniversität Leoben (Schimek, Ouchterlony and Moser, 2012 and Morros, 2013) and is a variation on the setup developed by Johansson (2011), who used blocks of a similar design, but with slightly different dimensions and only two rows of blastholes. At MUL they have chosen to switch the width and height (essentially laying the blocks down), allowing for an extra row of blast holes (Ouchterlony, 2015b).
The blast holes were, according to established LTU practise (Johansson, 2008, 2011 and Petropoulos, 2011), made by installing plastic sticks with a 10.5 mm diameter in the moulds, according to the drill pattern. This method has the advantage of fixed end points for the blast holes, only allowing marginal, if any, blast hole deviation, see Figure 9.
Figure 9: View through a smooth blast hole created using a plastic stick.
Furthermore, the sticks were used to help the concrete disperse and settle, when poured into the moulds, by shaking them and rotating them in circles, while making sure the lower end of the sticks stayed in cut-outs made in the bottom of each mould. The plastic sticks were allowed to cure with the blocks for 7-8 hours before they were removed.
The following sections describe in detail the different block designs and the process of manufacturing a mould with plastic sheets to emulate joints.
21 3.3.1 Reference block design The reference blocks use the MUL design. Figure 10, Figure 11 and Figure 12 show the schematics of the top, front and side view, respectively, of the reference block layout.
Figure 10: Reference block, top view.
For practical reasons, the schematics of blocks with joint sets only contain measurements specific to that design, but all blocks are based on the overall reference layout.
Figure 11: Reference block, front view.
22
Figure 12: Reference block, side view.
When comparing the reference layout to that of the other layouts, it is obvious that the reference blocks are the least advanced and easiest to produce.
Figure 13 shows the Reference 3 block after the first row has been blasted and the second row has been charged. T-connections were used to connect the two types of PETN detonating- cords.
Figure 13: Reference 3 with the second row charged for blasting.
23 3.3.2 Joint set 1 (JS1) Joint set 1, abbreviated JS1, is the simplest layout produced. It contains 6 vertical joints with a strike direction perpendicular to the face of the block, and can thus be written as strike/dip equal to 0/90°. The joint spacing is equal to that of the blasthole spacing (95 mm), but the joint placement is shifted half a blasthole spacing to the side, parallel to the block face, placing the joints right in between the blastholes.
Figure 14, Figure 15 and Figure 16 show the schematics of the top, front and side view, respectively, of the JS1 block layout.
Figure 14: Joint set 1, top view. Strike/dip = 0/90°, joint spacing = 95 mm.
Figure 15: Joint set 1, front view.
24
Figure 16: Joint set 1, side view. The hatched area represents the joint plane.
3.3.3 Joint set 2 (JS2) Joint set 2 (JS2) is the next stage in the design complexity development. JS2 contains 12 joints, with a strike/dip equal to 0/90°, but compared to JS1, the joint spacing has been halved to 47.5 mm. Because of the 25 mm safety margin requirement, the inclusion of joints on the outside of the outermost blastholes was rejected. The joints effectively divide the block into slabs where only every other slab contains blastholes, see Figure 17. From a manufacturing standpoint, the difficulty is more than doubled from JS1 to JS2 even though the joint spacing is only halved.
The produced JS2 Alpha cured too long before the plastic sheets were attempted to be removed, causing only two sheets to be removable. This happened because of two things: firstly, filling of the moulds took very long (the batch also contained the discarded JS3 block; this was the first time either joint set were produced) and secondly, difficulties arose when attempting to fit the lids on top of the moulds, meaning further delays. Figure 28 and Figure 29, in Section 3.3.7, show the two removed plastic sheets and JS2 Alpha with the remaining sheets still in the block.
25
Figure 17: Joint set 2, top view. Strike/dip = 0/90°, joint spacing = 47.5 mm.
3.3.4 Joint set 3 (JS3) Joint set 3 (JS3) was by far the most advanced set to cast. Compared to JS1 and JS2, joint set 3 still has vertical joints, but the strike direction of the joints is changed to 60°, giving a strike/dip equal to 60°/90°. JS3 blocks contain 10 joints compared to the 6 joints in JS1 and 12 in JS2.
By using a strike of 60°, the joint distance becomes 47.5 mm, the same as JS2, and the distance between the joints on the face of the block becomes 95 mm, the same as JS1. This characteristic could be interesting from a crack development and BMX modelling standpoint (the topics of the two other thesis works associated with the project), though these topics are outside the scope of this thesis.
The 9 slabs created by the joint planes (excluding the corner pieces) contain 1-3 blastholes. The five middle slabs contain 3 blastholes each, irregularly distributed within each slab, but in a similar way for all five, thus providing good symmetry within the block. Figure 18 shows the schematic of the top view of the JS3 block layout.
The 10 joints are of five different lengths. The joint lengths are; 460 mm, 417.5 mm, 308 mm, 198 mm and 88.5 mm from longest to shortest, respectively.
26
Figure 18: Joint set 3, top view. Strike/dip = 60°/90°, joint spacing = 47.5 mm.
It is worth noticing that on a row by row basis, the blastholes are displaced; first to the right, then centred, and for the third row to the left within the slabs. This will in principle make the first and third row identical (but mirrored), but in reality this will not be the case due to the joint, the virgin state of the first row and the safety margin which makes the first row not fully jointed.
Figure 19 shows a JS3 mould before and after casting. It was found that by cutting the lid into three pieces, the mounting process became much easier and faster.
Figure 19: Left: JS3 mould ready for casting. Right: JS3 block cast and lid mounted.
27 3.3.5 Joint set 4 (JS4) Joint set 4 (JS4) differs from the three other sets because it is the only set with dipping joints. JS4 has 6 joints like JS1, and like JS1 and JS2 the strike direction is perpendicular to the face. The joint spacing is 89 mm (though measured on the surface, the horizontal distance is 95 mm). While adhering to the design restrictions, the joint planes do not intersect the blastholes. The joint planes dip 70°, giving a strike/dip equal to 0/70°. Figure 20 and Figure 21 show schematics of the top and front view of the JS4 block layout.
Figure 20: Joint set 4, top view. Strike/dip = 0/70°, joint spacing = 89 mm.
Figure 21: Joint set 4, front view.
28 Notice that, unlike the other joint sets, JS4 has a different layout depending on how it is placed in the yoke. If the block is placed as depicted in Figure 21, the strike/dip is 0/70°. If the block is turned 180 degrees before installation (making the front view in Figure 21 facing into the yoke), the strike/dip will be 180°/70°. Figure 22 shows that this case of mirrored layouts happened for the two JS4 blocks in this project.
Figure 22: Mirrored JS4s. Left: JS4 Alpha Row 1. Right: JS4 Beta Row 1.
Since the initiation direction was kept constant, this could lead to a difference in fragmentation because the joint plane / shock wave interaction will happen differently. Any signs that this was the case will be discussed in Section 5.2.
3.3.6 Joints The joints were produced using 0.2 mm thick construction quality plastic that was cut according to measurements on a paper cutting board for optimum precision. Afterwards, the plastic sheets were placed, one at a time, in a makeshift apparatus, see Figure 23. With this, holes were poked using the same setup each time. The holes were poked using the pointed end of an ordinary drawing compass that proved to produce holes of a suitable size.
In Figure 23, three lines cross the white plate (indicated with arrows). These lines mark the placement of the bottom edge of the plastic sheet used to get the desired placement of the three rows of 9 holes. Also marked, are indicators for even hole distribution. The outer holes were placed 7 mm from the edge and the 9 holes were spaced with 27 mm between them. This spacing was attempted maintained for JS3 joints as well.
29
Figure 23: Makeshift devise for similar placement of rows and holes on each sheet.
After the holes were poked, the edge created around each hole was cut off with a knife and steel wire was sewn through the holes, see Figure 24. Figure 25 shows the two schematics of the wire placement in the moulds for vertical (JS1, JS2 and JS3) and dipping (JS4) joints, respectively.
Figure 24: Cut-off hole edges and finished joint sheets.
Figure 25 (left) shows the schematic for vertical joint installation. No blastholes are shown. Red indicates wires, blue and hatched indicate plastic sheet. The holes for the wires in the plastic sheet are also indicated. Distances to the left are related to the sheet; its dimensions and placement in the mould. Distances to the right are related to mould dimensions regarding the holes for the wires.
30
Figure 25: Schematics for joint installation. Left: vertical joints. Right: dipping joints.
Figure 25 (right) shows the schematic of a dipping joint installation. The plastic sheet’s placement relative to the blastholes is indicated, but the blastholes are not fully drawn. Distances to the right of the joint are related to the sheet; its dimensions and placement in the mould (distances between wires (red circles), total length of plastic in the mould (blue) and safety margin). Distances to the left of the joint are related to hole placement in the casting mould wall (green stars). For the middle hole, the circle and star coincide.
Initially, the sheets were covered with molybdenum grease to ease the pull-out, but it was found that the ordinary oil, used for greasing the moulds, was just as effective and much easier and quicker to work with. Figure 26 and Figure 27 show installed joints in different joint sets.
Figure 26: Installation and control of plastic sheets in a JS1 mould.
31
Figure 27: Installed joints in moulds. Left: JS2. Right: JS4.
Figure 27 (left) shows the final installation method for vertical joints. The only thing missing, for the shown mould to be ready, is for the plastic sticks to be placed in the mould. The installation method consists of a central plastic sheet (the joint) suspended 25 mm above the bottom of the mould in three steel wires (the plastic sheet that extend above the others in the figure). On both sides, the joint sheet is stabilized by thin plywood sheets that rest on the bottom of the mould. The plywood sheets are, like the joint sheets, oiled. Each plywood sheet then has, on the side facing away from the joint sheet, an additional plastic sheet that likewise is covered in oil.
After a mould was filled with magnetic concrete, the plywood sheets were carefully removed. Then, if they did not come out with the plywood sheets, the outer plastic sheets were removed and the mould was topped off with additional concrete.
Figure 27 (right) shows installed dipping joints (JS4). The mould depicted is almost ready, only an extra plastic sheet, on top of each of the plywood sheets, is missing.
JS4 separates itself from the other systems by the fact that the joint sheets are not removed after casting. The plastic sheets are allowed to stay in for the duration of the curing. This was deemed necessary because of the inclination. It was feared that, because of the early pull-out, the overlaying concrete would simply close the joints completely if the plastic was removed.
JS4 only uses one plywood sheet per joint. The plywood pieces rest on the bottom of the mould, against the plastic sticks, and against a thick piece of steel wire at the top of the mould. After filling a JS4 mould, the plywood sheets were carefully removed (very often simultaneously with the extra plastic sheet), allowing the overlaying concrete to settle on the now, from beneath, concrete supported joint sheet.
32 3.3.7 Potential failures and difficulties As with all iterative processes, there were errors, some more serious than others, and lessons were learnt during the development process of casting the blocks containing joint sets. Several pointers are worth noticing along with a couple of the errors that were made.
A small, but important, lesson was that the sides of the moulds should not be exactly the same height as the finished block height, but instead be slightly higher. This was solved using small extension pieces.
Another important lesson was the need for steel wire, and not copper or other softer metal substitutes, as was discovered when some wires broke, both during sheet installation (when suspending the sheets in the mould), but also during casting and when the wires were to be removed. In those cases, there were no other options than to leave the wire in place. That also meant those sheets could not be removed. As it happened, the blocks where copper wire was used, were among the ones not being considered in the analysis of this thesis.
A couple of times some sheets were seriously strained during removal and for one of the blasted blocks, some plastic were left inside, though the amount was deemed insignificant. The plastic left was that of three corners, from two sheets, ripped off at the lower wire placement, approximately three cm2 in total. Figure 28 shows two plastic sheets from the unblasted JS2 Alpha where corners were ripped off at the middle wire placement. These damages were the most severe experienced; except for cases where sheets simply broke off at the block surface. This was not the case on any of the blasted blocks.
Figure 28: Example of two plastic sheets that lost their corners, JS2 Alpha.
Figure 29 shows JS2 Alpha with 10 out of 12 plastic sheets still in place. The block was not blasted since it was deemed a low priority due to this. A considerable strain had also been put
33 on the remaining sheets, in an effort to pull them out, further adding to the uncertainty regarding how the block would have fragmented, had it been blasted.
Figure 29: JS2 Alpha with unremoved plastic sheets.
Figure 30 shows a collage of the discarded JS3 specimen. A big cavity was generated in the bottom of the block. It is theorised that the cavity was generated as a result of concrete sticking to either the stabilizers or the joint sheets when these were pulled out, and then never properly settled back afterwards.
Figure 30: Cavity generated in the bottom of a JS3 block.
34 3.4 Magnetic concrete
3.4.1 Recipe The recipe used for the concrete was the same as previously used by Johansson (2008) and Petropoulos (2011). Though, for supply reasons no Tributylphosfate (TBP) was used. This change was deemed irrelevant for the physical properties of the finished concrete. The recipe (including the TBP percentile) is shown in Table 2. The relating mass of each component is also shown for a nominal block volume of 0.0388 m3 and a nominal density of 2500 kg/m3.
Table 2: The recipe for magnetic concrete.
Ingredient Mass % kg Quartz sand (≤ 0.2 mm) 31.71 30.77 Magnetite powder 29.65 28.77 Portland cement 25.62 24.86 Water 12.64 12.26 Glenium 51 (plasticizer) 0.25 0.243 Tributylphosfate (defoamer) 0.13 0.126
Upon the casting of blocks with joint sets, it became apparent that the recipe was not developed for moulds with limited space for pouring and steering; the moulds were filled with plastic, wires and plywood sheets. The viscosity of the concrete made filling the moulds containing joint sets very complicated and time consuming compared to the “empty” reference moulds.
Due to this fact more Glenium was generally added to the mix in order to improve the viscosity of the concrete. The nominal amount of Glenium in one block should be 0.243 kg, but the average amount added was 0.291 ± 0.075 kg (mean ± standard deviation).
One cylinder was produced for each concrete batch. This was done to assess the coherency in fragmentation; thereby ensuring potential differences in fragmentation between different joint sets were not caused by inconsistencies in the concrete. However, surface errors in some cylinders resulted in only four being blasted, and with one batch being irrelevant, only three cylinders are included in the analysis in Section 4.1. The three cylinders still covers each of the five different block types produced, see Table 1.
Another way of assessing the similarity between blocks produced from different batches of concrete is to compare the block densities. This was the method used by Johansson (2008).
35 3.4.2 Density Table 3 shows the calculated densities for all the blasted blocks. The average density and the standard deviation are also shown. The average density of the 10 blocks was 2485 ± 41 kg/m3.
Table 3: Density data for the 10 blasted magnetic concrete blocks.
Density Name [kg/m3]
Reference 2 2487 Reference 3 2471
JS1 Alpha 2543 JS1 Beta 2426 JS1 Gamma 2477
JS2 Beta 2459
JS3 Alpha 2555 JS3 Beta 2517
JS4 Alpha 2453 JS4 Beta 2460
Average 2485 Std. deviation 41.4
Even though the 10 blocks were cast in seven different sessions, and the casting process was made complicated by repeatedly changing the joint sets (resulting in the casting process itself being an iterative process), and the simple fact that each block was close to a 100 kg in materials, the standard deviation shows that the method is well suited for repeatability.
An average density of 2485 ± 41 kg/m3 falls within the same range as the obtained densities by Johansson (2008), 2510 ± 25 kg/m3 and Petropoulos (2011), 2459 ± 10 kg/m3, but is above the 2380 ± 10 kg/m3 associated with the magnetic concrete previously used at MUL (Schimek, Ouchterlony and Moser, 2012). This difference is attributed to the fact that at MUL, for some of their concrete components, they are using ingredients with different characteristics; noticeably a generally courser sand and especially a different type of magnetite powder, than the magnetite powder supplied to LTU by LKAB.
36 The geometry of the blocks, and thus the specific charge, is different compared to previous LTU tests, and the magnetite powder and quartz sand in the concrete are different compared to previous MUL tests. The quartz sand used for the blocks in this work had a grain size of ≤0.2 mm, compared to the quartz sand used at MUL with a grain size of 0.1-0.5 mm (Schimek, Ouchterlony and Moser, 2012). The magnetite powder in the blocks used in this work was pure magnetite, whereas the powder used at MUL is a composite product, Ferroxon 618 (Schimek, Ouchterlony and Moser, 2012). Due to this, the MUL concrete is not very magnetic, but instead has a distinct visual difference. The MUL concrete is almost black compared to the blue-tinted, pale grey blocks described in this work.
Since the block setup is from MUL (block dimensions, number of blast holes and specific charge), but the concrete recipe is from LTU, comparison of fragmentation results between the work presented here and previous tests, whether from MUL or LTU, will not be done. Furthermore, considering the scope of this work, incorporating joints into the specimens, comparison of fragmentation results with previous tests makes little sense.
3.4.3 Wave velocity Wave velocity measurements were performed at MUL on three test cubes manufactured for the purpose and the data made available to the author. The cubes were similar to the ones used to develop the joint installation method and determine the optimum pull-out time. The cubes were made using the same recipe as the blocks, though because of the limited amount of concrete needed (nominal 24 L total), the concrete was mixed using a hand mixer and a bucket instead of the ROJO 75LC mixer used for producing the batches for the blocks.
One cube was made as a reference, without joints, and two cubes were made with joints similar to the ones used in the blocks. Like in the original test cubes, four joint sheets with a spacing of 40 mm were installed vertically in the cube moulds. In one cube, the plastic sheets were left in and in the other they were removed.
Figure 31 shows an isometric drawing of a jointed cube with two measuring points marked on each side. The measurements were taken halfway down the sides of the cubes, one third width in from either side. Two measurements were taken in each point. The measurements were performed on a Geotron-Elektronik system, using UP-SW sensors. During the secondary wave measurements, in order to clearly identify the S-wave onset, one sensor was turned 180°, thereby applying a phase lag to the emitted polarised shear wave.
37
Figure 31: Jointed test cube with points for wave velocity measurements indicated.
Table 4 shows the measured P- and S-wave velocities for the three cubes. For cube 2 and cube 3, measurements were done both perpendicular and parallel to the joints.
Table 4: P- and S-wave velocities in magnetic concrete cubes.
Cube Wave Velocity [m/s] Description # type Measurements Avg. Std Dev P-wave 3091.0 3295.0 3263.0 3346.0 3249 111 1 Reference S-wave 2252.0 2181.0 2278.0 2121.0 2208 71 P-wave 3322.0 3091.0 3101.0 3295.0 3202 123 2 Perpendicular to joints S-wave 1908.0 1892.0 2024.0 2045.0 1967 78 P-wave 3277.0 3231.0 3630.0 2946.0 3271 281 2 Parallel to joints S-wave 2014.0 2230.0 2384.0 1992.0 2155 187
Perpendicular to joints P-wave 3063.0 2967.0 3328.0 3077.0 3109 154 3 (through plastic) S-wave 2051.0 2055.0 2055.0 2043.0 2051 6
Parallel to joints P-wave 3221.0 3215.0 2894.0 2941.0 3068 175 3 (between plastic) S-wave 2019.0 1901.0 1908.0 2026.0 1964 68
38 Figure 32 shows the P-wave velocities from Table 4 in a box-and-whisker plot. The whiskers in the plot represent the minimum and maximum measured values.
P-wave measurements 3700
3600
3500
3400
3300
3200
3100 Velocity [m/s] Velocity 3000
2900
2800
2700 Reference Perpendicular to Parallel to joints Perpendicular to Parallel to joints joints joints (w. plastic) (w. plastic)
Figure 32: Box-and-whisker plot of P-wave velocities in magnetic concrete cubes.
Based on Figure 32 it appears that the joints, with or without the plastic sheets, do not have a significant influence on the P-wave velocity. The average measurements on the third cube do seem to be lower than for the two other cubes, but not statistically significant.
All the P-wave measurements are however significantly lower than the 3808 m/s stated by Johansson (2008) for the LTU concrete, and the 3865 m/s stated by Khormali (as cited by Schimek, Ouchterlony and Moser, 2012) for the MUL concrete. The reason for this difference is unknown. Johansson (2008) performed his velocity measurements on Ø42 mm cores.
Figure 33 shows the S-wave velocities from Table 4 in a box-and-whisker plot. The whiskers in the plot represent the minimum and maximum measured values.
Based on Figure 33 there do appear to be a difference in S-wave velocities parallel and perpendicular to the joints; especially between the reference cube and the measurements perpendicular to the joints, which is in accordance with the desired properties.
39 S-wave measurements 2500
2400
2300
2200
2100
Velocity [m/s] Velocity 2000
1900
1800
1700 Reference Perpendicular to Parallel to joints Perpendicular to Parallel to joints joints joints (w. plastic) (w. plastic)
Figure 33: Box-and-whisker plot of S-wave velocities in magnetic concrete cubes.
No other mechanical properties were measured for the work associated with this thesis, but Johansson (2008) performed several tests, including uniaxial compression test and Brazilian test, to determine the properties of the magnetic concrete (mortar). His results are summarized in Table 5.
Table 5: Properties of the magnetic concrete (Johansson, 2008).
Average obtained value Properties ± std dev (if any given)
Uniaxial compressive strength, σc 50.7 ± 4.8 MPa
Tensile strength, σBt 5.23 ± 0.34 MPa Young's Modulus, E 21.9 GPa Poisson's ratio, ν 0.22
P-wave velocity, vP 3808 ± 73 m/s Density 2511 ± 25 kg/m3
40 3.5 Expected rock factor (A) according to the Kuz-Ram-model Based on the layout of the magnetic concrete blocks, it is possible to estimate the expected rock factor (the A-value) from the Kuz-Ram formula (see Equation [2]). Table 6 shows the rock factor for each block type along with the values for each parameter leading to that A-value (from Equation [3]).
Table 6: Rock factor values according to the Kuz-Ram formula.
Block Joint JF A RMD RDI HF type spacing JCF JPS JPA Ref 0 4.17 50 - - - 12.125 7.3 JS1 95 5.97 80 1 50 30 12.125 7.3 JS2 47.5 3.57 40 1 10 30 12.125 7.3 JS3 47.5 3.57 40 1 10 30 12.125 7.3 JS4 89 5.97 80 1 50 30 12.125 7.3
For blocks containing joints the joint condition factor (JCF) is assumed to be equal to 1 (tight joints). With regards to the joint plane spacing (JPS), it could be argued that all the joint spacings are smaller than 0.1 m and thus should be set to 10, but for JS1 and JS4 the reduced pattern (P) is smaller than the joint spacing and thus JPS has been set to 50. The joint plane angle factor (JPA) has been set to 30 for all joint-containing block types because of the strike directions. The rock density influence (RDI) and hardness factor (HF) has been set to 12.125 and 7.3, respectively, for all the blocks, based on the average measured density, as well as the compressive strength and the Young’s Modulus stated by Johansson (2008).
The A-values presented in Table 6 falls within the range stated by Cunningham (2005). Because of the way the parameters for the rock factor is defined, and even though the designs of the jointed blocks appear different in nature, Table 6 shows only two different A-values for the jointed blocks, and they all have the same joint plane angle factor.
Since all parameters in the Kuz-Ram formula, except the rock factor, are kept constant in this thesis, and all the blocks have the same base geometry and all rows were blasted with the same delay, the rock factor will be proportional to the expected median fragment size. This proportionality should, as a minimum, be valid for rows of the same type, e.g. first rows or second rows, since it seems valid to assume preconditioning will significantly alter the fragmentation results between rows.
41 The groups of A-values in Table 6 thus indicate that JS1 and JS4 should have similar expected median fragment sizes and the same goes for JS2 and JS3. It can be seen in Table 6 that the A-value for the reference blocks falls in-between the A-value for the JS1 and JS4 blocks and the A-value for the JS2 and JS3 blocks:
JS1 & JS4 > Reference > JS2 & JS3.
Because of this, it follows that the expected median fragment size for the reference blocks should fall in-between the median fragmentation of JS1 & JS4 and JS2 & JS3. Choosing a JCF of 1.5 would not have changed this expected distribution; JS1 and JS4 would instead have had a rock factor of 7.47 and JS2 and JS3 would instead have had a rock factor of 3.87.
The A-values presented in Table 6 are theoretical and heavily empirical, and, especially with regards to the chosen JPS for JS1 and JS4, and hence the expected median fragment size relative to the expected reference value, will be subject of discussion later on.
42 3.6 Quick guide for making blocks containing joint sets Figure 34 is a step-by-step description of the procedure for preparing and making concrete blocks containing joint sets. The guide is not joint set specific.
Figure 34: 20 steps on how to prepare concrete blocks containing joint sets.
43 3.7 Blasting All blasting was done in Austria. Blasting took place at the blasting test site in the open pit, iron ore mine Erzberg situated approximately 20 km northwest of Leoben.
3.7.1 Test site Erzberg At the Erzberg mine, a testing site has been built to facilitate research. At the site, a blast chamber (situated in the entrance of an old drift) and a large concrete structure, a yoke, for the blasting of concrete blocks, are available.
A yoke can be described as a bench-like structure in which the test specimen sits. By inserting a test block into a yoke, the yoke offers the possibility of performing tests under semi enclosed circumstances replicating the effects of bench blasting. In this type of blasting, waves are transmitted to the surrounding rock, i.e. the yoke, leaving only two exposed surfaces to act as wave reflectors: the top and the front (face) of the block.
The blocks were placed into the yoke and grouted into place with fast hardening cement and allowed to harden at least over night before being blasted. Figure 35 shows the fence enclosed yoke along with a heavy rubber mat that was placed directly in front of the block before blasting. The last slab of a test block has been filled in with fast hardening cement for stabilizing and recovery. Figure 36 shows the entire test structure covered in thick blankets to retain all fragments for easy collection. After each blast, the blanket was emptied and beaten to remove and collect any and all fragments for analysis.
Figure 35: Fence enclosed yoke.
44
Figure 36: Yoke and fence covered in blankets, ready for blasting.
Due to the work associated with one of the other theses in the project, the part of the blocks left in the yoke, after the third rows had been blasted (the last 70 mm of the 280 mm wide blocks), needed to be grouted into place, again using fast hardening cement. This was done to ensure structural safe recovery and in order to preserve the integrity of the now heavily preconditioned magnetic concrete for crack detection at a later time. The fast hardening cement was again allowed to cure for at least one day.
The crack detection work is also the reason behind the red colouring on the top surface of the blocks displayed in figures throughout this report. The colouring is used for easier crack detection. Crack detection is not a part of the scope of this thesis.
Including installation and afterwards removal of the blocks from the yoke, a single block took no less than three days to test. Though typically, the installation of a new block in the yoke was done at the same time as the removal of the previous block.
3.7.2 Explosives The used explosive source was a decoupled, high explosive PETN detonating-cord, Detonex 20, from Austin Powder, with a grain load of 20 g/m. With the used block design, that results in a specific charge per row equal to 3.03 kg/m3. Equation [17] shows the general formula for specific charge (q):
Q q , [17] BSH where Q is the total charge [kg], B is burden [m], S is spacing [m] and H is height [m].
45 3.7.3 Delay Similar to the work done by Morros (2013), the nominal delay time used was 73 μs. This was achieved by running a fixed length of trunk (firing) line of 5 g/m PETN detonating-cord with a known velocity of detonation (VOD) between the blastholes, see Figure 37.
Figure 37: Blastholes charged and delay cord in place, Reference 2 row 1.
The delay times were measured for each blast to ensure similarity between the planned delay and the actual delay. In Figure 37 the wiring used for measuring the delay times can be seen. The system works by interruption of a circuit at the moment of detonation; this is registered by an oscilloscope.
Table 7 shows the measured delay times. An issue with data registration occurred for some rows resulting in missing data, but the data available generally points to a method well suited for generating repeatable results.
The blocks with missing data are: Reference 3 (no data), JS1 Alpha (only row 3 was registered) and JS4 Beta (row 3 was not registered).
46 Table 7: Measured delay times.
Rows Row # Delay [μs] Block name blasted measured 1 2 3 4 5 6 1 75.0 70.0 74.0 73.0 72.5 74.0 Reference 2 3 2 75.0 72.5 74.0 72.5 73.0 72.5 3 71.5 73.5 72.0 73.0 71.5 73.0 JS1 Alpha 3 3 72.0 74.0 73.5 74.0 73.0 72.5 1 72.5 72.0 72.5 72.0 72.5 73.0 JS1 Beta 2 2 72.5 72.0 72.5 73.5 71.0 74.5 1 73.0 72.0 72.5 74.0 85.0 61.0 JS1 Gamma 3 2 72.5 72.0 73.5 73.5 72.5 72.5 3 74.0 72.5 72.0 74.0 71.5 73.5 1 73.0 72.5 74.5 73.0 73.0 72.0 JS2 Beta 3 2 73.0 71.0 74.5 72.0 74.0 72.0 3 72.5 72.5 74.0 73.5 72.5 75.0 1 73.0 73.0 73.5 74.5 70.5 74.0 JS3 Alpha 3 2 73.0 72.5 72.0 73.0 73.5 70.5 3 73.0 73.5 73.0 72.0 73.0 72.5 1 73.0 72.5 73.0 73.5 72.5 73.5 JS3 Beta 2 2 73.5 72.5 75.0 72.0 74.5 73.5 1 71.5 73.0 73.0 72.0 73.0 72.5 JS4 Alpha 3 2 72.0 72.5 73.0 72.5 73.0 73.5 3 72.5 73.0 73.5 72.0 72.5 72.0 1 74.0 72.5 73.0 73.0 73.0 73.5 JS4 Beta 3 2 73.5 72.5 75.0 73.0 72.0 71.5
The average delay time is 72.88 ± 1.75 μs for all the measured delays. Table 7 shows that an error occurred when the trunk line was connected to the explosive cord in hole 6 of JS1 Gamma row 1. This resulted in a longer delay between hole 5 and 6 and a similarly shorter delay between hole 6 and 7. In the fragmentation analysis it will be argued that this error did not influence the degree of fragmentation, see Section 5.2. The error does not affect the average delay time, but the standard deviation is affected. Therefore, if these two measurements are omitted, instead an average of 72.88 ± 0.94 μs is achieved.
3.7.4 Initiation pattern The initiation pattern for all the blocks was sequential, beginning with the blasthole furthest to the right hand side when facing the front of the block in the yoke.
47 3.8 Sieving Sieving took place at the laboratory facilities of the Department of Mineral Resources and Petroleum Engineering at MUL. Before any blasting was done the test site was cleaned, then after each blast all the debris was collected and the site cleaned before the next blast took place. The debris was collected in buckets which were marked with the date and the specific block information and then transported to MUL where the sieving was performed.
At MUL the debris was passed through a number of sieves decreasing in size in accordance with the established protocol for this at MUL. The screen (mesh) sizes that the debris was passed through were: 125, 100, 80, 63, 50, 40, 31.5, 25, 20, 14, 12.5, 10, 6.3, 4, 2, 1, 0.5 mm, and, because of the smaller maximum grain size of the utilized quartz sand, an additional mesh size of 0.25 mm was added.
The sieving was performed by hand to achieve high accuracy and minimize secondary breakage. Down to and including the 14 mm mesh, all the debris was manually fed through the screens. If the amount of material passing the 14 mm mesh exceeded 3 kg (which were the case for all the rows from all the blocks), it was split to facilitate easier handling during passing of the smaller mesh sizes. No magnetic separation was done, but throughout the sieving both an optical sorting and sorting using a hand held magnet was performed on the debris to separate the magnetic concrete from non-magnetic components. This included the fast hardening cement used for grouting the block into the yoke, organic matter from the blast site and pieces of wiring.
The retained mass from each mesh was measured and weighted against the total mass of the debris to facilitate the construction of fragment size distribution curves for all the blasted rows. Equation 18-23 describes the mathematical procedure of calculating the passing percentages and any losses.
The needed information, besides the individually retained masses by each sieve, msieve includes:
the total mass, mtotal,
the total mass smaller than 14 mm, mtotal, <14mm,
the total screenfed mass smaller than 14 mm, mtotal, <14 (screenfed)
the total sieved mass smaller than 14 mm, mtotal, <14 (sieved)
the total sieved mass bigger than or equal to 14 mm, mtotal, ≥14mm (sieved)
the mass of the removed material, mwaste.
48
Equation [18] shows the standard equation for calculating the retained mass on each sieve.
msieve %mretained 100% [18] mtotal
For the work performed here, due to the splitting of all the samples, for fractions ≥14 mm, Equation [18] could be rewritten as Equation [19].
msieve %mretained, 14 mm 100% [19] mmtotal, 14 mm sieved total, 14 mm
For the fractions in the range <14 mm, Equation [20] shows the formula for calculating the retained mass percentage in each sieve.
msieve %mretained,14 mm / m total ,14() mm sieved m total ,14 mm 100% mtotal, 14 mm ( sieved ) [20] mtotal, 14 mm
Once either Equation [19] or [20] has been applied to all the retained masses, calculating the cumulative mass percentage retained by a given mesh size is simply done by summing all the individual retained mass percentages from the sieves above and down to the mesh size, x in question, Equation [21]. This is the practical equivalent to the theoretical (empirical) R(x) in Equation [6].
R()% x mretained x [21]
And finally, the retained mass percentages by a given mesh size can be easily calculated, Equation [22].
P( x )passing 1 R x [22]
The loss in any given sieving campaign can be calculated as, Equation [23].
mloss m total m total,14() mm sieved m total ,14 mm m waste m total ,14( screenfed ) m total ,14, mm sieved [23]
49 4 Results
All blasted rows of each block have undergone sieving analysis and a number of sieving curves have been produced. Furthermore, all data has been fitted with the Swebrec function, see the Appendices for all the individual Swebrec graphs.
One method of analysis used at MUL is the calculation of the percentile sizes x30, x50 and x80. Together with the compiled sieving curves for each block type, these three parameters will be presented in the next sections.
4.1 Compiled sieving data – Cylinders As mentioned in Section 3.4.1, a number of concrete cylinders were blasted in order to access the coherency in fragmentation, see Table 1. Figure 38 shows the compiled fragment size distribution curves for the three cylinders.
Cylinders 100 90
80 70 60 50 40 30 Mass Passing Passing [%] Mass 20 10 0 0.1 1 10 100 Mesh size [mm] C1 C2 C3
Figure 38: Fragment size distribution for cylinders.
Table 8 shows the percentile sizes x30, x50 and x80. The values correspond to the cumulative mass passing 30 %, 50 % and 80 %, respectively, based on linear interpolation between the two nearest fragment sizes in the size distribution graph.
Table 8: Percentile sizes x30, x50 and x80 for cylinders.
Cylinders C1 C2 C3 Avg.
x30 11.91 12.74 11.10 11.9
x50 18.74 18.86 17.54 18.4 [mm]
Fraction Fraction x80 29.52 27.50 27.37 28.1
50 The relative change in fragment size for each cylinder (as a decrease in size from x80 to x30) is 59.7 %, 53.7 % and 59.3 % for C1, C2 and C3, respectively. The difference between the biggest and smallest x30 percentile value is 1.6 mm or 13.8 %. For x50 and x80 the differences are 1.3 mm or 7.3 % and 2.1 mm or 7.6 %, respectively. This, like the comparison of densities for the concrete blocks, shows a method well suited for producing repeatable results.
For comparison purpose, the standard deviation of the x50 percentile is 0.73 mm, i.e. x50 = 18.4 ± 0.73 mm. Johansson (2008) blasted 15 cylinders made with the same recipe and got an x50 equal to 15.3 ± 1.1 mm.
4.2 Compiled sieving data – Blocks In the following, the fragment size distributions for the jointed blocks are presented in order of decreasing joint spacing. Figure 39 shows the fragment size distribution for the two Reference blocks. The figure clearly shows how the fragmentation becomes finer with each row blasted. It also shows how the size distributions of the second rows (R2) and the third rows (R3) each fall close together. The size distributions of the two first rows do not look alike, though this is not uncommon. This is attributed to the unconditioned (virgin) state of the material and results in a dust and boulder effect, producing fewer, larger fragments and a fines tale, as discussed by Johansson and Ouchterlony (2012).
Reference blocks 100 90 80
70 60 50 40
Mass Passing Passing Mass [%] 30 20 10 0 0.1 1 10 100 Mesh size [mm]
Reference 2 R1 Reference 2 R2 Reference 2 R3 Reference 3 R1 Reference 3 R2 Reference 3 R3
Figure 39: Fragment size distribution for the Reference blocks.
51 Figure 40 shows the fragment size distribution for the three JS1 blocks. The size distribution for each block adhere to getting finer with each blasted row. Though, the first row of JS1 Alpha has a finer fragmentation than the second row of JS1 Gamma for the courser ~55 % of the fragmented material. Likewise, JS1 Alpha row 2 has a finer fragmentation than JS1 Gamma row 3 for the finer ~58 % of the fragmented material. It is obvious that the general trends of the curves are less steep for the JS1s than for the Reference blocks. Only Row 1 and Row 2 were shot from JS1 Beta because of a faulty third row burden.
JS1 100 90 80
70 60 50 40
Mass Passing Passing Mass [%] 30 20 10 0 0.1 1 10 100 Mesh size [mm]
JS1 A R1 JS1 A R2 JS1 A R3 JS1 B R1 JS1 B R2 JS1 G R1 JS1 G R2 JS1 G R3
Figure 40: Fragment size distribution for JS1.
Figure 41 shows the fragment size distribution for the two JS4 blocks. The overall trend regarding curve position is still present. However, the first rows are much less varied and follow the other rows more closely than what was the case for the reference blocks and the JS1 blocks. Overall there is very little scatter, and even though the JS4 Beta row 2 curve falls below both of the JS4 row 1 curves (for the coarser part of ~60 % of the material, combined with no trace of the dust and boulder effect), these two rows appear more directly comparable to the second rows than the case were for the reference blocks and the JS1 blocks.
52 JS4 100 90 80
70 60 50 40
Mass Passing Passing Mass [%] 30 20 10 0 0.1 1 10 100 Mesh size [mm] JS4 A R1 JS4 A R2 JS4 A R3 JS4 B R1 JS4 B R2 JS4 B R3
Figure 41: Fragment size distribution for JS4.
Only one JS2 block was blasted, which provides no option for directly establishing a sense of quality for the data. Figure 42 shows the fragment size distribution for the single JS2 block.
JS2 100 90 80
70 60 50 40
Mass Passing Passing Mass [%] 30 20 10 0 0.1 1 10 100 Mesh size [mm]
JS2 B R1 JS2 B R2 JS2 B R3
Figure 42: Fragment size distribution for JS2.
53 The available fragmentation data for JS2 adhere to finer size distribution with increased row number. The distribution curve for the second row dips towards the first row around the midsection, but stays between the first and third row. The first row, like the first rows of JS4, displays little to no scatter and appears very smooth.
Figure 43 shows the fragment size distribution for the two JS3 blocks. The degree of fragmentation increases with row number, and for JS3 Alpha row 2 and 3 look very similar. Because of extensive back breakage in JS3 Beta after blasting row 2, no row 3 was blasted, see Figure 44. Due to the back breakage, data from row 2 of JS3 Beta will not be used beyond Figure 43 and Table 9. The quality of that data set will be discussed in Section 5.2.
JS3 100 90 80
70 60 50 40
Mass Passing Passing [%] Mass 30 20 10 0 0.1 1 10 100 Mesh size [mm]
JS3 A R1 JS3 A R2 JS3 A R3 JS3 B R1 JS3 B R2
Figure 43: Fragment size distribution for JS3
Figure 44: Extensive back breakage in row 2 of JS3 Beta.
54 Table 9 shows the percentile sizes x30, x50 and x80 for each row blasted.
Table 9: Percentile sizes x30, x50 and x80 for all rows.
Block type Reference JS1 JS4 JS2 JS3 Joint spacing [mm] 0 95 89 47.5 Name Ref 2 Ref 3 JS1 A JS1 B JS1 G JS4 A JS4 B JS2 B JS3 A JS3 B Row 1 30.3 37.5 17.2 25.9 22.0 25.5 20.9 22.1 18.1 23.0 average 33.9 21.7 23.2 - 20.6 Row 2 16.3 17.6 9.3 11.5 15.2 17.4 19.8 18.0 11.2 16.8 x30 average 16.9 12.0 18.6 - 14.0 Row 3 14.3 12.6 8.8 - 11.3 14.0 12.6 13.2 9.7 - average 13.5 10.0 13.3 - - Row 1 64.2 91.7 30.9 65.8 39.9 38.0 37.0 37.3 35.6 42.2 average 77.9 45.5 37.5 - 38.9 Row 2 37.6 40.3 19.2 21.3 36.4 30.9 39.9 35.1 20.2 30.0 x50 average 39.0 25.6 35.4 - 25.1 Row 3 29.5 25.0 16.4 - 20.9 24.3 23.0 24.3 18.0 - average 27.3 18.7 23.7 - - Row 1 91.6 123.3 56.5 91.3 83.1 68.9 61.9 59.8 70.9 83.5 average 107.4 77.0 65.4 - 77.2 Row 2 85.2 74.0 51.6 50.7 69.5 60.0 72.8 55.2 38.2 67.9 x 80 average 79.6 57.3 66.4 - 53.0 Row 3 56.2 50.4 33.1 - 45.2 46.7 48.0 46.8 35.5 - average 53.3 39.2 47.4 - -
Table 9 shows that the median fragment size for JS1 Beta row 1 seems much larger than the x50-values for row 1 of JS1 Alpha and JS1 Gamma. This will be discussed in Section 5.2.
Figure 45 shows a box-and-whisker plot, using the x30, x50 and x80 percentiles combined into single data sets, for each percentile, for row 1, row 2 and row 3 across all blocks. The whiskers in the plot represent the minimum and maximum measured values. It is clear that the overall fragment size decreases with increasing row number (row 1 produces a coarser material than row 2, which produces a coarser material than row 3). Besides the increased (finer) fragmentation by row, the effect of preconditioning is also visible through how the spread (scatter) of each percentile narrows (the fragmentation becomes more uniform) with increasing row number. Figure 45 does not consider joint spacing.
55 x30, x50 & x80 box plot comparison 140
120
100
80
60
Fragment[mm] size 40
20
0 x30 x50 x80 x30 x50 x80 x30 x50 x80
Row 1 Row 2 Row 3
Figure 45: Box-and-whisker plot of the x30, x50 and x80 percentiles against row number.
The following three figures, Figure 46, Figure 47 and Figure 48 show the interpolated x50 percentile values plotted against joint spacing for row 1, row 2 and row 3, respectively, for all block types.
Row 1: x50 vs joint spacing 100 90 80 70 60 50 40
Fragmentation[mm] 30 20 0 20 40 60 80 100 Joint spacing [mm]
Reference JS1 JS2 JS3 JS4
Figure 46: x50 plotted against joint spacing for row 1 blasts.
56 In Figure 46 the overall impression is a tendency for the jointed blocks, regardless of joint set type, to have a smaller median fragment size than that of the reference blocks. The median fragment sizes of the block types JS2, JS3 and JS4 all fall closely together. The three median fragment sizes produced by JS1 blocks are more scattered, but two points resemble the values of the other three block types and one is bigger, overlapping with the smallest of the reference values. This will be discussed further in Section 5.2. The combined average median fragment size across the eight jointed first rows is 40.8 ± 10.6 mm. The average x50 reference value for row 1 is 77.9 mm.
Row 2: x50 vs joint spacing
50
40
30
20
10 Fragmentation[mm] 0 0 20 40 60 80 100 Joint spacing [mm]
Reference JS1 JS2 JS3 JS4
Figure 47: x50 plotted against joint spacing for row 2 blasts.
Figure 47 shows a similar trend as Figure 46 with lower, though much less pronounced, x50- values for the jointed blocks compared to the reference values. Only one median fragment size, produced by a JS4 block, overlaps with the lowest reference value. JS2 produces a courser fragmentation, approximately 54 %, than JS3, though they have the same joint spacing. The median fragment size value for JS2 falls between the two JS4 values, meaning they produce a similar degree of fragmentation though they have very different joint sets. One JS1 value is much larger than the two other JS1 values, approximately 57 %, but the higher value comes from a different block than the one that produced the higher value in row 1. The two smaller JS1 values resemble the one JS4 value, while the higher JS1 value resembles the one JS2 value. The combined average median fragment size across the seven jointed second rows is 29.10 ± 8.6 mm. The average x50 reference value for row 2 is 39.0 mm.
57 Figure 48 reinforces the tendency from Figure 46 and Figure 47. No median fragment size from a jointed block is bigger than a reference value in Figure 48. JS2 produces an approximately 30 % courser fragmentation than JS3 for the third row. The fragmentation of JS2 and JS4 are still close, though the JS2 median fragment size now coincides with the highest JS4 value. The two JS1 values cover a range that includes the one JS3 value. The combined average median fragment size across the six jointed third rows is 21.2 ± 3.3 mm.
The average x50 reference value for row 3 is 27.3 mm.
Row 3: x50 vs joint spacing
35
30
25
20
15 Fragmentation[mm] 10 0 20 40 60 80 100 Joint spacing [mm]
Reference JS1 JS2 JS3 JS4
Figure 48: x50 plotted against joint spacing for row 3 blasts.
4.2.1 Coefficient of uniformity At MUL the analysis of the fragment size distribution also includes the calculation of the “coefficient of uniformity” (CoU), a value very similar to the geotechnical term by the same name used in grain size distribution analyses. The CoU is calculated as the x80/x30-ratio. A higher value indicates a flatter curve with more varied fragment size content; likewise, a lower value indicates a steeper curve with a smaller variation in fragment size content. Table 10 shows the calculated coefficients of uniformity for each block type and row.
Table 10 shows that for row ones the reference CoU is smaller than JS1 and JS3 and bigger than JS2 and JS4. For the second rows the reference value falls close to the JS1 value, but JS2, JS3 and JS4 all have lower CoUs. The third rows have very similar CoU values, but the reference value is the biggest. The CoU value for JS2 is continually the smallest or tied for the spot. JS3 produces CoUs that are very similar for all three rows.
58 Table 10: Coefficients of uniformity based on average x30 and x80 percentiles.
Block type Reference JS1 JS4 JS2 JS3 Joint spacing [mm] 0 95 89 47.5 47.5
x30 33.9 21.7 23.2 22.1 20.6
x 107.4 77.0 65.4 59.8 77.2 Row 1 80 x80/x30 3.2 3.5 2.8 2.7 3.8
x30 16.9 12.0 18.6 18.0 11.2
Row 2 x80 79.6 57.3 66.4 55.2 38.2
only one value available) value one only
s x80/x30 4.7 4.8 3.6 3.1 3.4
erage percentiles 13.5 10.0 13.3 13.2 9.7
indicate x30
Av
Row 3 x80 53.3 39.2 47.4 46.8 35.5
italic ( x80/x30 4.0 3.9 3.6 3.6 3.6
Figure 49, Figure 50 and Figure 51 show the x30 and x80 percentiles plotted against fragment size to demonstrate the curvature associated with the CoUs shown in Table 10.
Coefficient of Uniformity, Row 1 90
80 70 60 50 40 Mass Passing Passing Mass [%] 30 20 0.0 20.0 40.0 60.0 80.0 100.0 120.0 Fragment size [mm]
Reference JS1 JS2 JS3 JS4
Figure 49: Coefficient of uniformity; x30 and x80 plotted against fragment size for row 1.
59 Coefficient of Uniformity, Row 2 90
80 70 60 50 40 Mass Passing Passing Mass [%] 30 20 0.0 20.0 40.0 60.0 80.0 100.0 120.0 Fragment size [mm]
Reference JS1 JS2 JS3 JS4
Figure 50: Coefficient of uniformity; x30 and x80 plotted against fragment size for row 2.
Coefficient of Uniformity, Row 3 90
80 70 60 50 40 Mass Passing Passing Mass [%] 30 20 0.0 20.0 40.0 60.0 80.0 100.0 120.0 Fragment size [mm]
Reference JS1 JS2 JS3 JS4
Figure 51: Coefficient of uniformity; x30 and x80 plotted against fragment size for row 3.
It is clear that the overall CoU decreases with increasing row number, meaning the variation in fragment size distribution gets smaller as more rows get blasted. This is contributed to the dust and boulder effect getting less and less pronounced as the material gets more and more preconditioned by each consecutive blast.
60 4.3 Swebrec function fits All fragment size distribution data was run through the curve fitting software “Table Curve 2D” at LTU and fitted to the three parameter Swebrec function. Table 11 shows the fitted Swebrec parameters for each row. The linear interpolated x50 percentiles are also shown. The mean R-square value (r2) is 0.9945 ± 0.0066.
Table 11: Swebrec function parameters.
Interpolated Swebrec 2 Block Row # xmax b r x50 x50 Row 1 64.19 59.07 125.00 1.520 0.9930 Reference 2 Row 2 37.61 38.60 155.13 2.011 0.9854 Row 3 29.50 28.31 178.01 2.910 0.9985
Row 1 91.70 83.49 162.24 1.326 0.9747 Reference 3 Row 2 40.33 38.23 198.32 2.507 0.9926 Row 3 25.02 25.32 125.11 2.517 0.9981
Row 1 30.86 29.73 185.20 3.215 0.9987 JS1 Alpha Row 2 19.21 20.03 155.00 2.701 0.9965 Row 3 16.43 16.18 125.11 3.224 0.9992
Row 1 65.79 57.57 125.01 1.467 0.9797 JS1 Beta Row 2 21.29 22.12 136.68 2.841 0.9967
Row 1 39.87 42.21 208.39 2.674 0.9966 JS1 Gamma Row 2 36.35 35.80 128.70 1.930 0.9909 Row 3 20.89 21.32 125.11 2.834 0.9983
Row 1 37.25 36.27 128.70 2.656 0.9993 JS2 Beta Row 2 35.14 32.11 125.02 2.596 0.9946 Row 3 24.31 23.88 125.01 2.839 0.9967
Row 1 35.64 34.41 289.00 3.456 0.9983 JS3 Alpha Row 2 20.23 19.94 125.00 3.172 0.9995 Row 3 18.02 17.98 609.14 4.628 0.9808
JS3 Beta Row 1 42.23 42.70 184.64 2.579 0.9978
Row 1 38.04 39.35 126.98 2.535 0.9973 JS4 Alpha Row 2 30.86 31.21 187.55 3.119 0.9987 Row 3 24.34 24.62 125.00 3.032 0.9986
Row 1 37.02 35.94 125.03 2.474 0.9982 JS4 Beta Row 2 39.86 40.24 129.34 2.083 0.9957 Row 3 23.03 24.97 125.11 2.477 0.9971
61 Based on Table 11, the overall similarity between linear interpolated (measured) median fragment sizes and the curve fitted fragment sizes are good. The average interpolated x50 is
35.0 ± 16.6 mm and the average Swebrec x50 is 34.1 ± 14.6 mm or a difference across all 27 comparisons of 2.5 %. The biggest difference between the interpolated x50 and the Swebrec x50 occurs for JS1 Beta row 1 and is 13.3 %.
Figure 52 shows an example of curve fitting with the Swebrec function to sieving data from JS1 Gamma row 1.
JS1 Gamma row 1 Eqn 8001 (a,b,c) r^2=0.99662132 DF Adj r^2=0.99589732 FitStdErr=1.9710887 Fstat=2212.3019 a=2.6738538 b=4.9374617 c=208.39362 5 5 3 3 1 1
-1 -1 Residuals [5] Residuals -3 -3 [5] Residuals
10 10
1 1
Mass passing,% Mass passing,% Mass
0.1 0.1 0.1 1 10 100 1000 Mesh size, mm
Figure 52: The Swebrec function fitted to JS1 Gamma row 1.
In Figure 52 a number of statistical parameters relating to the curve fitting are presented. The important parameters for this work are the r2-value and the a-, b- and c-values. The a-, b- and c-parameters are related to the Swebrec function in the following way:
Parameter ab the Swebrec function's undulation curve parameter
Parameter b the Swebrec function's xmax / x 50 Parameter cx the Swebrec function's . max
Thus the Swebrec x50-value are obtained by dividing the c-parameter value with the b-parameter value.
62 5 Discussion
5.1 Block manufacturing The method for manufacturing the joint sets in the magnetic concrete blocks was continually developed, changed and improved a number of times, but despite that, the overall method still proved robust enough to produce 10 blocks with an average density of 2485 ± 41 kg/m3. However, the method of manufacturing could still be improved. As described in Figure 34, manufacturing and preparing the blocks contain many time consuming steps. For instance, the realisation that ordinary oil was just as effective as the cumbersome molybdenum grease increased the effectiveness by which the joints sheets could be greased and mounted into the moulds significantly.
One thing that would improve and ease the joint manufacturing would be the ability to cut or punch out the wire holes instead of poking them. This would remove the need for the very time consuming and meticulously cutting of the plastic edges around each and every hole. A tool for this purpose could however prove difficult to find and it might have to be manufacturing in order to have the right diameter. With regards to the edges, before it was decided they needed to be cut off, it was attempted to even them out by using a heat gun. The heat gun, however, proved ineffective at low heat and even on slightly higher heat settings caused damage in the form of big wrinkles to the surrounding plastic.
The magnetite concrete was a continuous challenge to work with because of its high viscosity and the amount of obstacles the concrete had to disperse around. It is believed that an increase in the added amount of plasticizer could meet this challenge, making it considerably easier and quicker to fill the moulds. The amount would have to be beyond the additionally added plasticizer in this project, and that would require new strength testing to ensure continuous reproducible strength results similar to previous blocks. Likewise, new timed pull-out tests would be needed to ensure joints with similar characteristics.
An added workability in the form of a lower viscosity would also have the side effect of easing the top off of the moulds ensuring a more even surface and possibly produce better (sharper) joint openings after the joint pull-outs.
63 5.2 Fragmentation results Table 12 shows the collected mass for each blasted row (shaded grey) along with the total mass. To the left are the mass and density for each block specified. To the right is the expected mass for one and for all blasted rows indicated. For simple comparison, the expected mass assumes a clean cut when blasting (i.e. one row is a quarter of the block). The percentage difference from the expected one row mass is indicated below the collected masses in parentheses. Furthest to the right, the difference between the collected total mass and the total expected mass is shown.
Table 12: Difference between measured and expected breakage by mass.
At the bottom of Table 12, the average collected mass and the standard deviation are stated for each row. JS3 Beta row 2 is not included in the row 2 average. The percentage-values stated in parentheses below the masses in the columns “Total mass”, “Expected; one row” and “Expected; all rows” are of the total block mass.
64 Table 12 shows a clear tendency for the blasted row masses to be bigger than expected. This can mainly be attributed to the very simple assumption of blasts producing clean cuts perpendicular to the block face. Such a cut would normally only result from the refined technique smooth blasting, specially intended for the purpose. Table 12 can be used to see trends and unusual variations. Figure 53 shows the three JS1 blocks over one another after the first row blast. Table 12 showed a 6 percentage points difference between the row with the smallest and largest difference between collected and expected breakage, but Figure 53 shows that all three block faces look as expected. It is concluded that a difference of up to +10 % is not indicative of any unusual or severe back breakage for the JS1 layout. The same conclusion is drawn for JS2, which produced a very similar looking face.
Figure 53: New face after row 1 blast on JS1 Alpha (top), JS1 Beta and JS1 Gamma (bottom).
65 Two holes in the first row of JS1 Gamma were blasted with wrong delay times. By comparing the data for the first row blasts of the JS1 blocks in Table 9 and Table 12, and looking at Figure 53; there is no indication that the delay time error evident in Table 7 had a significant influence on the fragmentation of JS1 Gamma row 1.
The two JS3 blocks show a difference between collected and expected breakage of +16.0 % and +15.1 % for JS3 Alpha row 1 and JS3 Beta row 1, respectively. This could be indicative of more severe back breakage, but Figure 54 shows that this is not the case. Wedge formations into the face between the boreholes can be seen on both blocks, but the face still appear whole. JS3 Alpha furthermore generally produced very similar looking faces after the second and third row blasts. The face after the third blast looked more disturbed, but not severe. It is concluded that this layout probably will produce more back breakage than JS1 and JS2, but that around +15 % difference between collected and expected breakage is still acceptable. The author was not present for the blasting of JS3 Beta, but from the supplied photo material it appears that from the third blasthole a crack cut perpendicular to the joints into the block at a strike of 330° (relative to the joint orientation), passing three joints (slightly side shifting during the second pass) and clean through the fourth blasthole in the third row before ending in a joint end towards the back of the block, see Figure 44. This resulted in a large wedge shaped crater into and beyond the third row. The wedge came out as one big piece. Table 12 shows that the material collected after the second row blast of JS3 Beta was measured to 30.7 kg, which is more than 26 % heavier than expected and by far the biggest measured deviation. Combined with the fact that 12.7 % of the mass from the second row did not pass the biggest mess size during sieving (For JS3 Alpha row 2 100 % passed the 80 mm sieve, see
Figure 43) is seen as the reason why x50 for JS3 Beta row 2 is approximately 40 % larger than x50 for JS3 Alpha row 2. The difference is thus the result of the influence from the back breakage and not natural variation. Because of this, it was decided not to include JS3 Beta row 2 in the fragmentation analysis.
As mentioned previously, the two JS4 blocks were placed differently in the yoke, as mirror images of each other. Though the values in Table 9 show similar percentile sizes for row 1 for both x30, x50 and x80 between the two blocks, they were visually different on the face and surface, see Figure 22. This is supported by the numbers in Table 12; showing a difference in collected and expected row mass of +10.0 % and +3.7 % for JS4 Alpha and JS4 Beta, respectively. This could potentially be caused by the shock wave interacting differently with the differently orientated joints, though it is more likely that it is simple variation, especially since the two blocks looked much more identical after the second rows had been blasted, see Figure 55.
66
Figure 54: New face after row 1 blast on JS3 Alpha (top) and JS3 Beta.
Figure 55: New face after row 2 blast on JS4 Alpha (left) and JS4 Beta.
Figure 56: New face after row 3 blasts on JS4 Alpha (left) and JS4 Beta.
67 The numbers in Table 12 show that the difference between collected and expected mass for row 2 is +8.5 % and +15.3 % for JS4 Alpha and JS4 Beta, respectively. Because more material was blasted of the surface of JS4 Alpha in the row 1 blast, the lower difference in row 2 could simply be a result of this (i.e. the back breakage could be worse than the number indicates, but because some material was already missing from the row the result will be skewed). Figure 56 shows that for both JS4 blocks the third row blast took out large parts of the remaining row. What should be noted is that JS4 still had plastic sheets in the joints, meaning no bridging at all happened. This can explain some of the damages shown in Figure 22, Figure 55 and Figure 56. It is not clear if the mirrored joint sets had an effect on the fragmentation. All three rows produced similar median fragment sizes, see Table 9. What is clear is that though similar, the fragmentation results from JS4 should be viewed with caution because of the back breakage. Further investigation is needed to clarify if mirroring the joint set has an effect on fragmentation.
It was noted that some rows appeared to have had their top surface damaged from the blasting of the previous row. This could lead to a systematic error when material from different rows gets mixed without a way to separate it again. It is difficult to say how much of it was actually caused by back breakage, but some is partly deemed a consequence of the way blasting is performed at Erzberg, with the explosive cord being too close to the surface of the test specimens. It is not deemed to have had a major influence on the fragmentation results, but could be avoided in future work by using a different blasting cord setup and by protecting the top of the blastholes more.
Figure 46, Figure 47 and Figure 48 all showed a tendency for jointed rows to produce smaller median fragment sizes than the un-jointed reference rows. Figure 46 furthermore showed very little variation in produced x50-values among jointed rows no matter the joint spacing. The median fragment size for seven out of eight jointed first rows fell within a range of
~11 mm; all seven smaller than the reference values. Only one x50 was noticeably off; that of JS1 Beta. Since Table 12 does not indicate any unusual deviation for that row, the reason is attributed to an extreme case of the dust and boulder effect. The first row of JS1 Beta broke into several large pieces upon detonation; the biggest is shown in Figure 57.
68
Figure 57: Large fragment from JS1 Beta row 1.
The piece is 95 mm wide (the same as the joint spacing for JS1) and roughly half the height of the block. On the fragment, the safety margin and part of a smooth joint plane surface can be seen. The average median fragment size was 40.8 ± 10.6 mm for all the jointed first rows. This is a smaller variation than the average median fragment size for the second rows (29.10 ± 8.6 mm). If JS1 Beta row 1 is viewed as an exception to the tendency of jointed rows to produce finer fragment sizes than un-jointed rows, the average x50 for the other seven rows is 37.3 ± 3.6 mm. That is a smaller variation in average x50 for the unconditioned first rows than the heavily conditioned third rows (21.2 ± 3.3 mm). If instead of the median fragment size the x30 percentile is looked at, the trend is very clearly backed up. It is clear all jointed rows produced a finer fragmentation for the finest 30 % of the collected material.
Row 1; x30 vs joint spacing 40.0 35.0 30.0 25.0 20.0 15.0 10.0
Fragmentation[mm] 5.0 0.0 0 20 40 60 80 100 Joint spacing [mm]
Reference JS1 JS2 JS3 JS4
Figure 58: x30 plotted against joint spacing for row 1 blasts.
69 It is theorised that the small variation in first row median fragment sizes is caused by all the rows only being partly jointed because of the 25 mm safety margin. This means all first rows are only 64 % jointed, or that they share a 36 % un-jointed layout, resulting in smaller variation. The safety margin means that the reference blocks are the only ones with truly unconditioned first rows. The joint endings work as remote flaws from where the shockwave, running along the joint plane, could initiate failures from. One support for this claim is the
CoU-values shown in Figure 49. Compared to Figure 50 and Figure 51, where all x30-values group up, the average reference x30 percentile in Figure 49 is much higher than any of the values from jointed rows. The small variation could alternatively indicate that for unconditioned cases, the virgin state has a bigger influence on the median fragment sizes than the differences in joint set layouts. The available data here is very limited and further investigations should be conducted to investigate these two divergent explanations.
The reference x50-values are closer to the jointed x50-values for second and third row blasts, see Figure 47 and Figure 48, but the jointed x50-values also vary more. JS1 roughly produces x50-values equivalent to those of JS3, though the joint spacing of JS3 is half the joint spacing of JS1. The distance between the joints on the face of the blocks are however the same, which means that might be more important than the actual joint distance. JS2 and JS3 both have
47.5 mm joint spacing’s, but the x50-values for the two block types vary with 14.9 mm (54 %) and 6.3 mm (30 %) for the second and third rows, respectively. The reasoning for this is due to how the joints divide the blocks into slabs. For JS3, all slabs contain blastholes, whereas for JS2, only every other slab contains blastholes. This creates a situation where the explosive force has a reduced influence on some parts of the blocks due to the characteristics of the joints. This means the slabs without blastholes will have a courser fragmentation producing an overall courser fragmentation for JS2 compared to JS3. JS4 seems to produce x50-values roughly equivalent to or a little below those of JS2.
These fragmentation results were not expected based on the Kuz-Ram rock factor (A). The theory suggested that two of the blocks, JS1 and JS4, should group and produce median fragment sizes larger than the median reference size, when utilizing the reduced pattern P, and the remaining blocks, JS2 and JS3, should group and produce smaller median fragment sizes. Cunningham (2005) states that the formula can give strange results when both the joint spacing and the reduced pattern are smaller than 0.3 m, or if the reduced pattern is less than 1 m, all of which are the case for these small scale tests.
70 For sake of comparison, the dimensions of the test specimens are scaled up to something resembling a real bench and the fragmentation results are presumed directly translatable. Using a factor of 72 a bench height of ~15 m is achieved. The other dimensions roughly become: bench length of 48 m, bench width of 20 m, burden of 5 m, spacing of 6.6 m and a reduced pattern of 5.8 m. The joint spacing’s become: 6.6 m (95 mm), 6.0 m (89 mm) and 3.3 m (47.5 mm). For the different joint sets the JPS become: 50 (JS1), 80 (JS2), 80 (JS3) and 50 (JS4); which results in the following rock factors when keeping the other parameters the same: 5.97 (JS1), 7.77 (JS2), 7.77 (JS3), 5.97 (JS4) and 4.17 (Reference). The up-scaled rock factors correctly sort the reference value as the one to produce the smallest median fragment size, but it also fails to group the median fragments according to the observations. Therefore it seems reasonable to conclude that it would have been better to simply use a JPS of 10 for all the blocks (joint spacing < 0.1 m).
Using a JPS of 10, however, leads to the peculiar case where the rock factor becomes identical for all four joint sets and then, by extension, the expected median fragment size x50, when all parameters are kept the same. This is certainly a product of the scale, but it is also the case for the jointed first rows (where the joints seemed to have the least impact). Had JPS been set to 10 for all joint sets in Section 3.5, the Kuz-Ram model would correctly have predicted that jointed rows would produce finer fragmentation than un-jointed rows. What the rock factor in the Kuz-Ram model seems to not distinguish well between, are the different joint sets on this scale. It could be argued, that JS4 with the plastic sheets still in place might not appropriately be characterised as having tight joints, but that would have to be further investigated to clarify if another classification would be better.
For the unconditioned cases, the x50-values for the different joint sets might show so little variation that the parameters in practise are irrelevant, but for preconditioned cases, which are by far the norm, it is not suitable. Further blast tests of jointed specimens need to be performed to increase the statistical foundation in order to more accurately determine how the different median fragment sizes of different joint sets relate to each other and how they fit with the Kuz-Ram model.
71 Reference 1 is included in Table 12. The block was not included in any of the analyses in this thesis because it was produced with a wrong burden, which means it would not be comparable to any of the other blocks. Since the block was blasted, the following is a short look at the effect. Row 1 had a burden of 60 mm and row 2 a burden of 80 mm. This means row 1 was 14 % smaller and row 2 14 % bigger than intended. That is why Table 12 shows row 1 produced 2.6 % less material than expected (the only first row with this characteristic) and row 2 produced 12 % more than expected. If instead the actual burdens are used for calculating the expected row masses, the numbers in Table 12 would read: 22.91 kg (+13.6 %), 26.34 kg (-2.0 %) and 25.18 kg (+7.0 %) for row 1, row 2 and row 3, respectively. The new expected numbers can to an extend be explained by the detonating cord being more or less powerful relative to the burden than normal. The third row could have been more preconditioned than intended from the second row blast. Figure 59 show the fragment size distribution for Reference 1. It is clear the wrong burden impacted the fragmentation. The decreased burden of row 1 produced a finer fragmentation than expected. Correspondingly, with the increased burden of row 2, the explosive force was not sufficient to adequately fragment the burden resulting in ~27 % of the material not being able to pass through the biggest mesh (125 mm).
Figure 59: Fragment size distribution; Reference 1.
72 6 Conclusion
Ten (10) magnetic concrete blocks have been produced and a total of 28 rows have been blasted, including 8 blocks wherein joint sets were incorporated. The average density of the blocks was 2485 kg/m3 ± 41 kg/m3.
A method for representing joint planes by suspending plastic sheets in a casting mould, and afterwards pulling the plastic sheets out, has been developed. This method includes a systematic manufacturing guide. A total of 4 different joint sets were developed, designated JS1, JS2, JS3 and JS4, respectively, each set becoming more complex than the previous.
JS1 had a joint spacing of 95 mm and a strike/dip equal to 0/90°. JS2 had a joint spacing of 47.5 mm and a strike/dip equal to 0/90°. JS3 had a joint spacing of 47.5 mm and a strike/dip equal to 60°/90°. JS4 had a joint spacing of 89 mm and a strike/dip equal to 0/70°.
Each blasted row has been the subject of a sieving analysis and all the data has been fitted to the three parameter Swebrec function, producing an average coefficient of determination (an R-square value) of 0.9946 ± 0.0064.
Only a single jointed block (JS3 Beta) experienced extensive failure (back breakage), and not until the second row blast. The JS4 layout showed the most back breakage in general, but this could be the result of the plastic sheets still being in the blocks when blasted. In general the results are seen as proof of the robustness of the joint design and test setup.
There is a strong indication that all the fabricated joint sets produce a finer median fragment size (x50), than the median fragment size obtained from the reference blocks. With the (limited) amount of available data, it is difficult to conclude with any statistical assurance how some of the joint set produced median fragment sizes relate to each other, but there are indications that the order of fragmentation (course to fine) goes as:
Reference > JS2 ≥ JS4 > JS1 ≥ JS3.
It is found that the Kuz-Ram formula could successfully predict a lower median fragment size for jointed rows, but that the formula is less suited to deal with the differences among joint sets on this scale.
73 7 Future work
Some focus points are outlined below for potential future work relating to the same topic. Future investigations could have the scope of:
Investigating the effect of adding more plasticizer to the recipe in order to increase the workability of the magnetic concrete, without affecting the established strength properties significantly.
Produce and blast additionally blocks to increase the statistical foundation of the work presented in this thesis.
Investigate the effect of trunk line placement, and potentially develop a method to avoid influence on breakage from the detonation cord on the surface of the test specimens.
74 8 References
Cunningham, C V B, 1983. The Kuz-Ram Model for Prediction of Fragmentation from Blasting, in Proceedings 1st International Symposium on Rock Fragmentation by Blasting, volume 2, Luleå, Sweden (eds: R Holmberg and A Rustan) pp 439-452 (Luleå University of Technology: Luleå). Cunningham, C V B, 1987. Fragmentation Estimations and the Kuz-Ram Model – Four Years On, in Proceedings 2nd International Symposium on Rock Fragmentation by Blasting, Keystone, Colorado (eds: W L Fourney and R D Dick) pp 475-487 (Society for Experimental Mechanics: Bethel, Connecticut, USA). Cunningham, C V B, 2005. The Kuz-Ram fragmentation model – 20 years on, in Proceedings 3rd EFEE World Conference on Explosives and Blasting, Brighton, United Kingdom (ed: R. Holmberg et al) pp 201-210 (European Federation of Explosives Engineering: UK). Fourney, W L, Barker, D B and Holloway, D C, 1983. Fragmentation in Jointed Rock Material, in Proceedings 1st International Symposium on Rock Fragmentation by Blasting, volume 2, Luleå, Sweden (eds: R Holmberg and A Rustan) pp 505-531 (Luleå University of Technology: Luleå). Jaeger, J C and Cook, N G W, 1976. Fundamentals of Rock Mechanics, 2nd edition, pp 1-8 (Chapman and Hall Ltd: London). Johansson, D, 2008. Fragmentation and waste rock compaction in small-scale confined blasting, Licentiate Thesis, Luleå University of Technology, Division of Mining and Geotechnical Engineering, Luleå. Johansson, D, 2011. Effects of confinement and initiation delay on fragmentation and waste rock composition, Doctorial Thesis, Luleå University of Technology, Division of Mining Engineering and Geotechnical Engineering, Luleå. Johansson, D and Ouchterlony, F, 2012. Shock Wave Interactions in Rock Blasting: the Use of Short Delays to Improve Fragmentation in Model-Scale, Rock Mechanics and Rock Engineering, 46(1): 1-18. McLean, A C and Gribble, C D, 1979. Geology for Civil Engineers, pp 135-139 (George Allen & Unwin: London). Morhard, R C, 1987. Explosives and Rock Blasting, pp 157-203 (Field Technical Operations, Atlas Powder Company: Dallas). Morros, C A, 2013. Model-scale tests on the influence of drillhole deviation on blasting fragmentation, MSc Thesis, Montanuniversität Leoben, Chair of Mining Engineering and Mineral Economics, Leoben. Mostyn, G R and Bagheripour, 1995. A new model material to simulate rock, in Proceedings 2nd International Conference on the Mechanics of Jointed and Faulted Rock – MJFR-2, Vienna, Austria (ed: H-P Rossmanith) pp 225-230 (A.A. Balkema: Rotterdam). Nilsen, B and Thidemann, A, 1993. Rock Engineering, pp 20-24 & pp 79-82 (Norwegian Institute of Technology: Trondheim). Ouchterlony, F and Moser, P, 2006. Likenesses and differences in the fragmentation of full- scale and model-scale blasts, in Proceedings 8h International Symposium of Rock Fragmentation by Blasting – Fragblast 8, Santiago, Chile, pp 207-220 (Editec: Santiago). Ouchterlony, F, 2005. The Swebrec© function: linking fragmentation by blasting and crushing, Mining Technology, 114(1): 29-44. Ouchterlony, F, 2009. Fragmentation characterization; the Swebrec function and its use in blasting engineering, in Proceedings 9th International Symposium on Rock
75 Fragmentation by Blasting – Fragblast 9, Granada, Spain (ed: J A Sanchidrián) pp 3-22 (CRC Press/Balkema, Leiden, The Netherlands). Ouchterlony, F, 2015a. Personal communication, Montanuniversität Leoben, 7th of April. Ouchterlony, F, 2015b. Personal communication, Montanuniversität Leoben, 17th of May. Petropoulos, N, 2011. Influence of confinement on fragmentation and investigation of the burden movement, MSc Thesis, Luleå University of Technology, Division of Mining and Geotechnical Engineering, Luleå. Schimek, P, Ouchterlony, F and Moser, P, 2012. Experimental blast fragmentation in model- scale bench blasts, in Proceedings Measurement and Analysis of Blast Fragmentation, New Delhi, India (eds: J A Sanchidrián and A K Singh) pp 51-60 (CRC Press/Balkema, Leiden, The Netherlands). Singh, D P and Sarma, K S, 1983. Influence of Joints on Rock Blasting – A Model Scale Study, in Proceedings 1st International Symposium on Rock Fragmentation by Blasting, volume 2, Luleå, Sweden (eds: R Holmberg and A Rustan) pp 533-554 (Luleå University of Technology: Luleå). Waltham, T, 2009. Foundations of Engineering Geology, 3rd edition, pp 54-55 & p 86 (Taylor & Francis: Abingdon). Yang, Z G and Rustan, A, 1983. The Influence from Primary Structure on Fragmentation, , in Proceedings 1st International Symposium on Rock Fragmentation by Blasting, volume 2, Luleå, Sweden (eds: R Holmberg and A Rustan) pp 581-603 (Luleå University of Technology: Luleå).
76 Appendices
77
Appendix 1: Reference 2 Row 1
Sieving; Mesh size Mass passing [mm] [%] 125 100.00 100 90.00 80 66.30 63 48.77 50 41.27 40 36.78 31.5 30.63 25 27.15 20 22.80 14 18.32 12.5 15.91 10 13.60 6.3 9.62 4 6.74 2 4.34 1 2.93 0.5 2.19 0.25 1.56 < 0.25 0.00
Reference 2 row 1 Eqn 8001 (a,b,c) r^2=0.99303268 DF Adj r^2=0.99153968 FitStdErr=2.6340206 Fstat=1068.9537 a=1.5195144 b=2.1162012 c=125.00038 4 4 2 2 0 0
-2 -2 Residuals [3] Residuals -4 -4 [3] Residuals
10 10
Mass passing,% Mass passing,% Mass
1 1 0.1 1 10 100 1000 Mesh size, mm
79 Row 2
Sieving; Mesh size Mass passing [mm] [%] 125 100.00 100 100.00 80 73.06 63 67.14 50 58.30 40 51.53 31.5 46.09 25 40.15 20 35.23 14 26.78 12.5 23.75 10 20.24 6.3 14.09 4 9.93 2 6.24 1 4.18 0.5 3.10 0.25 2.28 < 0.25 0.00
Reference 2 row 2 Eqn 8001 (a,b,c) r^2=0.98544621 DF Adj r^2=0.98232754 FitStdErr=4.0719865 Fstat=507.82955 a=2.0112929 b=4.0188364 c=155.12733 7.5 7.5
2.5 2.5
-2.5 -2.5 Residuals [3] Residuals -7.5 -7.5 [3] Residuals
10 10
Mass passing,% Mass passing,% Mass
1 1 0.1 1 10 100 1000 Mesh size, mm
80 Row 3
Sieving; Mesh size Mass passing [mm] [%] 125 100.00 100 93.07 80 93.07 63 86.63 50 73.95 40 64.82 31.5 52.67 25 43.97 20 38.05 14 29.58 12.5 26.19 10 21.76 6.3 14.97 4 10.24 2 6.38 1 4.25 0.5 3.27 0.25 2.45 < 0.25 0.00
Reference 2 row 3 Eqn 8001 (a,b,c) r^2=0.99850049 DF Adj r^2=0.99817917 FitStdErr=1.4334115 Fstat=4994.1437 a=2.910006 b=6.2873181 c=178.00861 3 3
1 1
-1 -1
-3 -3
Residuals [8] Residuals [8] Residuals
10 10
Mass passing,% Mass passing,% Mass
1 1 0.1 1 10 100 1000 Mesh size, mm
81
Appendix 2: Reference 3 Row 1
Sieving; Mesh size Mass passing [mm] [%] 125 81.83 100 54.65 80 43.44 63 38.30 50 33.50 40 30.94 31.5 27.77 25 23.47 20 20.46 14 16.90 12.5 14.60 10 12.73 6.3 8.84 4 6.33 2 4.06 1 2.57 0.5 1.79 0.25 0.95 < 0.25 0.00
Reference 3 row 1 Eqn 8001 (a,b,c) r^2=0.97469782 DF Adj r^2=0.96927593 FitStdErr=3.607803 Fstat=288.91717 a=1.3255905 b=1.9433397 c=162.24336 5 5 2.5 2.5 0 0 -2.5 -2.5
-5 -5
Residuals [3] Residuals [3] Residuals
10 10
1 1
Mass passing,% Mass passing,% Mass
0.1 0.1 0.1 1 10 100 1000 Mesh size, mm
83 Row 2
Sieving; Mesh size Mass passing [mm] [%] 125 100.00 100 86.92 80 86.92 63 67.35 50 57.55 40 49.74 31.5 44.22 25 39.21 20 33.53 14 24.81 12.5 22.27 10 18.03 6.3 12.55 4 8.43 2 5.07 1 3.11 0.5 2.22 0.25 0.97 < 0.25 0.00
Reference 3 row 2 Eqn 8001 (a,b,c) r^2=0.99263599 DF Adj r^2=0.99105799 FitStdErr=2.9178882 Fstat=1010.9674 a=2.5068982 b=5.1874423 c=198.32168 5 5 3 3 1 1
-1 -1 Residuals [5] Residuals -3 -3 [5] Residuals
10 10
1 1
Mass passing,% Mass passing,% Mass
0.1 0.1 0.1 1 10 100 1000 Mesh size, mm
84 Row 3
Sieving; Mesh size Mass passing [mm] [%] 125 100.00 100 100.00 80 100.00 63 88.66 50 79.74 40 68.00 31.5 57.11 25 49.98 20 43.58 14 32.63 12.5 29.72 10 24.95 6.3 16.70 4 10.63 2 7.07 1 4.54 0.5 3.33 0.25 2.32 < 0.25 0.00
Reference 3 row 3 Eqn 8001 (a,b,c) r^2=0.99805649 DF Adj r^2=0.99764002 FitStdErr=1.6994455 Fstat=3851.4916 a=2.5173094 b=4.9407714 c=125.11375 4 4
2 2
0 0
-2 -2
Residuals [3] Residuals [3] Residuals
10 10
Mass passing,% Mass passing,% Mass
1 1 0.1 1 10 100 1000 Mesh size, mm
85
Appendix 3: JS1 Alpha Row 1
Sieving; Mesh size Mass passing [mm] [%] 125 100.00 100 95.76 80 92.51 63 82.30 50 77.68 40 65.56 31.5 50.99 25 40.92 20 34.72 14 24.73 12.5 22.64 10 18.61 6.3 12.78 4 8.65 2 5.47 1 3.61 0.5 2.64 0.25 0.95 < 0.25 0.00
JS1 Alpha row 1 Eqn 8001 (a,b,c) r^2=0.99873681 DF Adj r^2=0.99846613 FitStdErr=1.3489507 Fstat=5929.8543 a=3.214917 b=6.2303313 c=185.2002 4 4
2 2
0 0
-2 -2
Residuals [7] Residuals [7] Residuals
10 10
1 1
Mass passing,% Mass passing,% Mass
0.1 0.1 0.1 1 10 100 1000 Mesh size, mm
87 Row 2
Sieving; Mesh size Mass passing [mm] [%] 125 100.00 100 100.00 80 100.00 63 91.66 50 78.35 40 74.11 31.5 64.73 25 57.83 20 51.25 14 41.75 12.5 37.53 10 31.58 6.3 23.44 4 16.36 2 10.33 1 6.84 0.5 4.76 0.25 1.82 < 0.25 0.00
JS1 Alpha row 2 Eqn 8001 (a,b,c) r^2=0.99653556 DF Adj r^2=0.99579318 FitStdErr=2.2076403 Fstat=2157.3508 a=2.7014801 b=7.7368813 c=154.99555 4 4 2 2 0 0
-2 -2 Residuals [3] Residuals -4 -4 [3] Residuals
10 10
Mass passing,% Mass passing,% Mass
1 1 0.1 1 10 100 1000 Mesh size, mm
88 Row 3
Sieving; Mesh size Mass passing [mm] [%] 125 100.00 100 100.00 80 100.00 63 100.00 50 93.03 40 88.91 31.5 77.95 25 67.27 20 57.71 14 44.74 12.5 39.85 10 33.44 6.3 22.80 4 16.33 2 10.15 1 6.66 0.5 4.91 0.25 3.13 < 0.25 0.00
JS1 Alpha row 3 Eqn 8001 (a,b,c) r^2=0.99922413 DF Adj r^2=0.99905787 FitStdErr=1.119519 Fstat=9659.0788 a=3.2239687 b=7.732599 c=125.10985 3 3 2 2 1 1
0 0 Residuals [4] Residuals -1 -1 [4] Residuals
10 10
Mass passing,% Mass passing,% Mass
1 1 0.1 1 10 100 1000 Mesh size, mm
89
Appendix 4: JS1 Beta Row 1
Sieving; Mesh size Mass passing [mm] [%] 125 100.00 100 93.94 80 62.02 63 46.41 50 45.01 40 40.47 31.5 33.90 25 29.35 20 25.53 14 20.11 12.5 17.57 10 14.58 6.3 10.05 4 6.91 2 4.27 1 2.80 0.5 2.03 0.25 1.40 < 0.25 0.00
JS1 Beta row 1 Eqn 8001 (a,b,c) r^2=0.97971095 DF Adj r^2=0.9753633 FitStdErr=4.5136317 Fstat=362.1576 a=1.4670636 b=2.1713855 c=125.00527 7.5 7.5
2.5 2.5
-2.5 -2.5 Residuals [3] Residuals -7.5 -7.5 [3] Residuals
10 10
Mass passing,% Mass passing,% Mass
1 1 0.1 1 10 100 1000 Mesh size, mm
91 Row 2
Sieving; Mesh size Mass passing [mm] [%] 125 100.00 100 100.00 80 100.00 63 96.35 50 79.14 40 72.59 31.5 64.99 25 56.07 20 47.89 14 35.96 12.5 32.62 10 26.10 6.3 17.63 4 11.76 2 7.34 1 4.72 0.5 3.40 0.25 2.33 < 0.25 0.00
JS1 Beta row 2 Eqn 8001 (a,b,c) r^2=0.99666891 DF Adj r^2=0.9959551 FitStdErr=2.2636758 Fstat=2244.0128 a=2.8409953 b=6.1790522 c=136.68269 5 5 3 3 1 1 -1 -1
-3 -3 Residuals [3] Residuals -5 -5 [3] Residuals
10 10
Mass passing,% Mass passing,% Mass
1 1 0.1 1 10 100 1000 Mesh size, mm
92 Appendix 5: JS1 Gamma Row 1
Sieving; Mesh size Mass passing [mm] [%] 125 100.00 100 88.01 80 78.55 63 64.80 50 58.43 40 50.19 31.5 37.52 25 33.19 20 27.86 14 20.81 12.5 17.67 10 15.01 6.3 10.52 4 6.83 2 4.17 1 2.51 0.5 1.56 0.25 0.68 < 0.25 0.00
JS1 Gamma row 1 Eqn 8001 (a,b,c) r^2=0.99662132 DF Adj r^2=0.99589732 FitStdErr=1.9710887 Fstat=2212.3019 a=2.6738538 b=4.9374617 c=208.39362 5 5 3 3 1 1
-1 -1 Residuals [5] Residuals -3 -3 [5] Residuals
10 10
1 1
Mass passing,% Mass passing,% Mass
0.1 0.1 0.1 1 10 100 1000 Mesh size, mm
93 Row 2
Sieving; Mesh size Mass passing [mm] [%] 125 100.00 100 100.00 80 87.98 63 75.06 50 56.83 40 51.89 31.5 47.48 25 42.26 20 37.04 14 28.24 12.5 25.73 10 21.47 6.3 14.92 4 9.34 2 6.19 1 4.14 0.5 3.07 0.25 2.14 < 0.25 0.00
JS1 Gamma row 2 Eqn 8001 (a,b,c) r^2=0.9908592 DF Adj r^2=0.98890046 FitStdErr=3.3761026 Fstat=812.99728 a=1.9295879 b=3.5951004 c=128.70431 5 5 2.5 2.5 0 0 -2.5 -2.5
-5 -5
Residuals [3] Residuals [3] Residuals
10 10
Mass passing,% Mass passing,% Mass
1 1 0.1 1 10 100 1000 Mesh size, mm
94 Row 3
Sieving; Mesh size Mass passing [mm] [%] 125 100.00 100 100.00 80 100.00 63 97.22 50 85.62 40 73.82 31.5 66.55 25 57.69 20 48.32 14 36.16 12.5 32.67 10 27.16 6.3 18.40 4 11.64 2 7.51 1 5.00 0.5 3.69 0.25 2.47 < 0.25 0.00
JS1 Gamma row 3 Eqn 8001 (a,b,c) r^2=0.9983485 DF Adj r^2=0.99799461 FitStdErr=1.6113156 Fstat=4533.8359 a=2.8341472 b=5.8669373 c=125.10576 3 3
1 1
-1 -1 Residuals [3] Residuals -3 -3 [3] Residuals
10 10
Mass passing,% Mass passing,% Mass
1 1 0.1 1 10 100 1000 Mesh size, mm
95
Appendix 6: JS2 Beta Row 1
Sieving; Mesh size Mass passing [mm] [%] 125 100.00 100 100.00 80 91.00 63 83.43 50 69.58 40 53.89 31.5 41.85 25 34.33 20 26.87 14 19.20 12.5 16.51 10 13.54 6.3 8.96 4 6.08 2 3.72 1 2.41 0.5 1.73 0.25 1.10 < 0.25 0.00
JS2 Beta row 1 Eqn 8001 (a,b,c) r^2=0.99934152 DF Adj r^2=0.99920041 FitStdErr=0.99057271 Fstat=11382.315 a=2.6559393 b=3.5488772 c=128.70459 1 1
0 0
-1 -1 Residuals [5] Residuals -2 -2 [5] Residuals
10 10
Mass passing,% Mass passing,% Mass
1 1 0.1 1 10 100 1000 Mesh size, mm
97 Row 2
Sieving; Mesh size Mass passing [mm] [%] 125 100.00 100 100.00 80 100.00 63 91.56 50 72.28 40 54.99 31.5 46.26 25 39.56 20 32.84 14 24.39 12.5 21.90 10 17.97 6.3 12.21 4 8.16 2 4.99 1 3.16 0.5 2.27 0.25 1.54 < 0.25 0.00
JS2 Beta row 2 Eqn 8001 (a,b,c) r^2=0.9946257 DF Adj r^2=0.99347406 FitStdErr=2.8789346 Fstat=1388.0303 a=2.5958868 b=3.8932088 c=125.02019 7.5 7.5 5 5 2.5 2.5 0 0 -2.5 -2.5
-5 -5
Residuals [3] Residuals [3] Residuals
10 10
Mass passing,% Mass passing,% Mass
1 1 0.1 1 10 100 1000 Mesh size, mm
98 Row 3
Sieving; Mesh size Mass passing [mm] [%] 125 100.00 100 100.00 80 100.00 63 100.00 50 83.77 40 71.96 31.5 59.97 25 51.09 20 43.21 14 31.64 12.5 28.72 10 24.30 6.3 16.31 4 10.99 2 7.19 1 4.71 0.5 3.48 0.25 2.34 < 0.25 0.00
JS2 Beta row 3 Eqn 8001 (a,b,c) r^2=0.99669537 DF Adj r^2=0.99598723 FitStdErr=2.2991438 Fstat=2262.0429 a=2.8388121 b=5.2338782 c=125.0099 10 10 7.5 7.5 5 5 2.5 2.5 0 0
-2.5 -2.5
Residuals [4] Residuals [4] Residuals
10 10
Mass passing,% Mass passing,% Mass
1 1 0.1 1 10 100 1000 Mesh size, mm
99
Appendix 7: JS3 Alpha Row 1
Sieving; Mesh size Mass passing [mm] [%] 125 100.00 100 89.52 80 84.95 63 75.67 50 66.81 40 55.52 31.5 44.76 25 39.32 20 32.92 14 23.71 12.5 21.24 10 16.70 6.3 10.92 4 7.03 2 4.23 1 2.72 0.5 1.97 0.25 1.27 < 0.25 0.00
JS3 Alpha row 1 Eqn 8001 (a,b,c) r^2=0.99831159 DF Adj r^2=0.99794979 FitStdErr=1.46219 Fstat=4434.5522 a=3.4555041 b=8.4000391 c=289.00339 4 4
2 2
0 0
-2 -2
Residuals [5] Residuals [5] Residuals
10 10
Mass passing,% Mass passing,% Mass
1 1 0.1 1 10 100 1000 Mesh size, mm
101 Row 2
Sieving; Mesh size Mass passing [mm] [%] 125 100.00 100 100.00 80 100.00 63 95.91 50 92.28 40 82.62 31.5 70.44 25 58.72 20 49.58 14 36.64 12.5 33.12 10 27.23 6.3 17.95 4 11.60 2 7.23 1 4.81 0.5 3.58 0.25 2.40 < 0.25 0.00
JS3 Alpha row 2 Eqn 8001 (a,b,c) r^2=0.99953163 DF Adj r^2=0.99943127 FitStdErr=0.87868782 Fstat=16005.558 a=3.1715079 b=6.2693812 c=125.00286 2.5 2.5 1.5 1.5 0.5 0.5
-0.5 -0.5 Residuals [4] Residuals -1.5 -1.5 [4] Residuals
10 10
Mass passing,% Mass passing,% Mass
1 1 0.1 1 10 100 1000 Mesh size, mm
102 Row 3
Sieving; Mesh size Mass passing [mm] [%] 125 100.00 100 100.00 80 100.00 63 100.00 50 93.70 40 85.21 31.5 75.30 25 64.41 20 54.42 14 41.06 12.5 36.47 10 30.73 6.3 20.12 4 13.41 2 8.10 1 5.49 0.5 3.99 0.25 2.62 < 0.25 0.00
JS3 Alpha row 3 Eqn 8001 (a,b,c) r^2=0.98083577 DF Adj r^2=0.97672915 FitStdErr=5.6417431 Fstat=383.85417 a=4.6276677 b=33.880839 c=609.14411 15 15 10 10 5 5
0 0
Residuals [2] Residuals [2] Residuals
10 10
Mass passing,% Mass passing,% Mass
1 1 0.1 1 10 100 1000 Mesh size, mm
103
Appendix 8: JS3 Beta Row 1
Sieving; Mesh size Mass passing [mm] [%] 125 100.00 100 91.44 80 77.59 63 69.36 50 55.80 40 48.33 31.5 38.20 25 31.82 20 27.23 14 19.65 12.5 17.19 10 14.15 6.3 9.59 4 5.88 2 3.72 1 2.72 0.5 2.07 0.25 1.19 < 0.25 0.00
JS3 Beta row 1 Eqn 8001 (a,b,c) r^2=0.99781946 DF Adj r^2=0.9973522 FitStdErr=1.6092329 Fstat=3432.0192 a=2.5787856 b=4.3237445 c=184.63704 3 3
1 1
-1 -1 Residuals [5] Residuals -3 -3 [5] Residuals
10 10
Mass passing,% Mass passing,% Mass
1 1 0.1 1 10 100 1000 Mesh size, mm
105 Row 2
Sieving; Mesh size Mass passing [mm] [%] 125 87.31 100 87.31 80 87.31 63 77.08 50 72.61 40 62.36 31.5 51.85 25 43.95 20 34.70 14 25.98 12.5 23.09 10 18.90 6.3 13.24 4 8.53 2 5.43 1 3.70 0.5 2.82 0.25 1.97 < 0.25 0.00
JS3 Beta row 2 Eqn 8001 (a,b,c) r^2=0.99565339 DF Adj r^2=0.99472197 FitStdErr=2.2714315 Fstat=1717.9815 a=4.9955731 b=29.256221 c=876.96862 4 4 2 2 0 0 -2 -2
-4 -4 Residuals [7] Residuals -6 -6 [7] Residuals
10 10
Mass passing,% Mass passing,% Mass
1 1 0.1 1 10 100 1000 Mesh size, mm
106 Appendix 9: JS4 Alpha Row 1
Sieving; Mesh size Mass passing [mm] [%] 125 100.00 100 100.00 80 94.15 63 72.47 50 66.11 40 53.09 31.5 39.65 25 29.25 20 24.19 14 16.72 12.5 14.60 10 12.01 6.3 8.39 4 5.61 2 3.55 1 2.37 0.5 1.81 0.25 1.26 < 0.25 0.00
JS4 Alpha row 1 Eqn 8001 (a,b,c) r^2=0.99727558 DF Adj r^2=0.99669177 FitStdErr=1.9967257 Fstat=2745.377 a=2.5353986 b=3.2271964 c=126.97706 2 2 0 0 -2 -2
-4 -4 Residuals [5] Residuals -6 -6 [5] Residuals
10 10
Mass passing,% Mass passing,% Mass
1 1 0.1 1 10 100 1000 Mesh size, mm
107 Row 2
Sieving; Mesh size Mass passing [mm] [%] 125 100.00 100 100.00 80 88.69 63 82.80 50 70.49 40 61.24 31.5 50.87 25 42.02 20 34.43 14 24.24 12.5 21.26 10 17.51 6.3 11.74 4 7.33 2 4.70 1 3.04 0.5 2.22 0.25 1.46 < 0.25 0.00
JS4 Alpha row 2 Eqn 8001 (a,b,c) r^2=0.99872598 DF Adj r^2=0.99845297 FitStdErr=1.3491866 Fstat=5879.3734 a=3.1194819 b=6.0087925 c=187.54774 4 4
2 2
0 0
-2 -2
Residuals [5] Residuals [5] Residuals
10 10
Mass passing,% Mass passing,% Mass
1 1 0.1 1 10 100 1000 Mesh size, mm
108 Row 3
Sieving; Mesh size Mass passing [mm] [%] 125 100.00 100 100.00 80 100.00 63 97.67 50 83.70 40 72.53 31.5 61.47 25 51.26 20 41.69 14 29.96 12.5 24.76 10 20.26 6.3 14.05 4 9.20 2 5.76 1 3.77 0.5 2.76 0.25 1.82 < 0.25 0.00
JS4 Alpha row 3 Eqn 8001 (a,b,c) r^2=0.9986214 DF Adj r^2=0.99832599 FitStdErr=1.5095987 Fstat=5432.8065 a=3.0321645 b=5.0762706 c=125.00268 4 4
2 2
0 0 Residuals [6] Residuals -2 -2 [6] Residuals
10 10
Mass passing,% Mass passing,% Mass
1 1 0.1 1 10 100 1000 Mesh size, mm
109
Appendix 10: JS4 Beta Row 1
Sieving; Mesh size Mass passing [mm] [%] 125 100.00 100 100.00 80 96.58 63 81.23 50 66.40 40 53.36 31.5 43.79 25 34.99 20 28.93 14 21.29 12.5 18.90 10 16.19 6.3 10.38 4 6.70 2 3.49 1 1.86 0.5 0.99 0.25 0.16 < 0.25 0.00
JS4 Beta row 1 Eqn 8001 (a,b,c) r^2=0.99816999 DF Adj r^2=0.99777785 FitStdErr=1.6500412 Fstat=4090.8468 a=2.4742444 b=3.4791442 c=125.03012 4 4
2 2
0 0
-2 -2
Residuals [3] Residuals [3] Residuals
10 10
1 1
Mass passing,% Mass passing,% Mass
0.1 0.1 0.1 1 10 100 1000 Mesh size, mm
111 Row 2
Sieving; Mesh size Mass passing [mm] [%] 125 100.00 100 100.00 80 86.12 63 71.65 50 56.15 40 50.13 31.5 41.99 25 35.62 20 30.23 14 22.13 12.5 19.56 10 15.90 6.3 10.86 4 6.80 2 4.30 1 2.68 0.5 1.89 0.25 1.28 < 0.25 0.00
JS4 Beta row 2 Eqn 8001 (a,b,c) r^2=0.99565116 DF Adj r^2=0.99471926 FitStdErr=2.3765215 Fstat=1717.0967 a=2.0830935 b=3.2141204 c=129.33901 4 4 2 2 0 0
-2 -2 Residuals [3] Residuals -4 -4 [3] Residuals
10 10
Mass passing,% Mass passing,% Mass
1 1 0.1 1 10 100 1000 Mesh size, mm
112 Row 3
Sieving; Mesh size Mass passing [mm] [%] 125 100.00 100 100.00 80 100.00 63 91.54 50 82.08 40 71.44 31.5 61.11 25 53.40 20 44.79 14 33.86 12.5 29.67 10 25.08 6.3 17.08 4 10.86 2 6.99 1 4.69 0.5 3.43 0.25 2.43 < 0.25 0.00
JS4 Beta row 3 Eqn 8001 (a,b,c) r^2=0.99708759 DF Adj r^2=0.9964635 FitStdErr=2.1091302 Fstat=2567.6834 a=2.476826 b=5.0093605 c=125.10602 4 4
2 2
0 0 Residuals [1] Residuals -2 -2 [1] Residuals
10 10
Mass passing,% Mass passing,% Mass
1 1 0.1 1 10 100 1000 Mesh size, mm
113