Effect of Geological Structures on the Subsidence of the Kiirunavaara Hangingwall Field data collection - Numerical analysis

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(1)2009:101. MASTER'S THESIS. Effect of Geological Structures on the Subsidence of the Kiirunavaara Hangingwall Field data collection - Numerical analysis. Shahin Shirzadegan. Luleå University of Technology Master Thesis, Continuation Courses Mining and geotechnical engineering Department of Civil and Environmental Engineering Division of Rock Mechanics 2009:101 - ISSN: 1653-0187 - ISRN: LTU-PB-EX--09/101--SE.

(2) Effect of large-scale geological structures on the subsidence of the Kiirunavaara hangingwall (field data collection-Numerical analysis). By Shahin Shirzadegan Department of Civil, mining and Environmental Engineering Division of Mining and Geotechnical Engineering Luleå University of Technology SE-97187 Luleå SWEDEN. I.

(3) Preface This Master thesis summarizes my work carried out at the division of Mining and Geotechnical Engineering at Luleå University of Technology. The supervisor of this research has been MSc Tomas Villegas. This project is performed as a Master Thesis for the Master of Science Program in Civil Engineering specializing in Mining and Geotechnical Engineering. I would firstly like to thank my supervisor Tomas Villegas for his valuable support and guidance through all my work. I am grateful to Professor Erling Nordlund the head of division for providing me this opportunity and his help with numerical analysis carried out in this research. Special thanks go to Dr. Jonny sjöberg and M.S. Christina Dáhner from LKAB company to review of this work and support during my stay at Kiiruna. And I am also grateful to Professor Håkan Schunnesson my program coordinator and Dr. Jenny Svanberg at the division of Mining Engineering for their valuable support during two years of my stay in Sweden. Finally, Special thanks must go to my parents, Amir and Jamileh and my brother and sister, Mohammad and Marjan who have always supported and greatly encouraged me throughout my academic life.. Shahin Shirzadegan Autumn 2009, Luleå, Sweden. II.

(4) Abstract The current mining method, sublevel, caving at the Kiirunavaara iron ore mine has induced large scale subsidence to the hangingwall. The orebody dips, on average, 60 degrees eastward. Therefore the subsidence is developing toward the city of Kiiruna, the railway and other infrastructure. One of the most important factors which can affect the hangingwall subsidence is the existence of large-scale geological structures in the hangingwall. As a part of ongoing hangingwall subsidence research project, an exploration campaign was carried out to characterize the rock mass and identify the major geological structures using diamond drilling and geophysical methods. Three drill cores (koj1-koj3) were obtained close to the city of Kiiruna along the mine section Y1900. In addition, six drill cores (koj4-koj9) were obtained along the railway as a part of another project related to the deformation of the ground below the railway. All of the 9 drillcores were mapped by the author in January and February 2009. Each drillcore was composed of several core runs. RQD was calculated for all the core runs, point load test was carried out on one core sample at each run, and orientation analysis was carried out on the oriented cores in the field. Later the RQD values were used to estimate the geological strength index (GSI). Finally, GSI values together with the results from point load tests were used as input data in Roclab program to estimate the rock mass strength and deformation modulus. Results indicated to a good quality of rock mass obtained from drillcores koj1 to koj3. Existence of possible geological structures can govern the surface deformation produced by subsidence at this region. Although the carried out core orientation analysis cannot decide the major geological structures orientation, but at least allows the exploration geologists and geophysical engineers to understand the geology of the area and make decision about the future of the site. Results obtained from mapping drillcores koj4 through koj9 along the railway indicated to a poor quality of rock mass in proximity of the railway. Results from this region will be used in further analysis by geologists to identify the possible weak zones at this region and their effects on the subsidence of the railway area. The 2D distinct element method “UDEC” was used in this work to evaluate the effect of geological structures on the hangingwall subsidence. One so called “basic model” was run without any geological structures. Two different structure sets have been analyzed. One structure set had a dip in the interval 50 – 90 degrees to the east, whereas the other set had the dip 60 degrees to the east and 60 degrees to the west, respectively. The failure surface at each mining level was defined for the different models through failure indicators e.g. yielded elements in shear and tension and surface critical vertical displacement. To evaluate the effect of each orientation and structure set on the hangingwall subsidence, the break angle was calculated at each mining level. The results showed that except the structure inclined 90 degrees, the other inclinations had an obvious effect on the extension of the failure surface on the hangingwall. All models with large-scale structures showed a decrease of the break angle compared to the basic model. The structure III.

(5) orientations showed a tendency to govern the direction of shear and tension failure in the models. The results indicate that it is important to identify the dominating structures and their orientation and the structural geological domains. Keywords: Drillcores, Mapping, Rock mass strength, deformation modulus, Numerical analysis, Geological structures, failure surface, Break angle.. IV.

(6) Contents 1 Introduction .......................................................................................................................................... 1 1.1 Background .................................................................................................................................... 1 1.2 Objectives ...................................................................................................................................... 2 2 Engineering geological data collection ................................................................................................. 3 2.1 Introduction ................................................................................................................................... 3 2.2 Structural geological terms ............................................................................................................ 5 2.3 Structural geological data collection ............................................................................................. 7 2.3.1 Mechanical orientation of drill core ....................................................................................... 7 2.3.2 Handling procedure of an oriented core ................................................................................ 9 2.3.3 Measurements on oriented cores ........................................................................................ 10 2.4 Structural geological data presentation and analysis .................................................................. 13 2.4.1 Pole plots .............................................................................................................................. 14 2.4.2 Pole density........................................................................................................................... 16 2.4.3 Great circles .......................................................................................................................... 18 2.5 Rock Quality Designation Index (RQD) ........................................................................................ 20 3 Rock mass characterization, strength and deformation modulus...................................................... 25 3.1 Geological Strength index (GSI) ................................................................................................... 25 3.2 Generalized Hoek-Brown Criterion.............................................................................................. 30 3.3 Deformation modulus.................................................................................................................. 32 3.4 Mohr-Coulomb Criterion ............................................................................................................. 32 4. Effect of large-scale geological structures on the subsidence of the Kiirunavaara hangingwallNumerical Analysis................................................................................................................................. 40 4.1 Introduction ................................................................................................................................ 40 4.2 Section Y1500 .............................................................................................................................. 41 4.3 Model Approach .......................................................................................................................... 42 4.4 Model Properties and stress data................................................................................................ 44 4.4.1 Model properties .................................................................................................................. 44 4.4.2 Stress data ............................................................................................................................ 45 4.5 Interpretation of results .............................................................................................................. 46 4.8 Adding geological structures and limitations .............................................................................. 51 5 Conclusion........................................................................................................................................... 60 6 Future work......................................................................................................................................... 61 Appendix A ................................................................................................................................................ I. V.

(7) A.1 Rock Quality Designation (RQD) ..................................................................................................... I A.2 Joint Frequency (JF) ........................................................................................................................ I A.3 Point Load Test (PLT) ...................................................................................................................... I Appendix B ........................................................................................................................................ XXXIX References ............................................................................................................................................. XL. VI.

(8) 1 Introduction. 1.1 Background The Kiirunavaara iron ore mine is located in Kiiruna, the northern-most city in the Lappland province of Sweden. The orebody at this mine strikes almost north-south with an average dip of 60 ̊ to the east. The current mining method is sublevel caving which has induced a large scale subsidence of the hangingwall. The process of failing and caving of the rock in ore extraction levels is explained as the main reason for the hangingwall subsidence (Villegas & Nordlund, 2008). Additionally, the eastward dipping ore body induces an unwanted subsidence toward the city of Kiruna, the railway and other infrastructure. In order to reach to an accurate prediction of the subsidence rate coming toward the railway, a comprehensive knowledge of the rock mass quality of this area is vital. Depending on the quality of rock mass near the railway, the existence of geological structures can play a major role in subsidence of that area. In the Kiirunavaara mine several lineaments (anomalies in the geophysical studies) have been identified by Magnor and Mattson (1999) which can extend or reduce the surface subsidence (Villegas & Nordlund, 2008). As part of ongoing hangingwall subsidence research project, an exploration campaign was carried out to characterize the rock mass and identify major geological structures using diamond drilling and geophysical methods. Three drill cores were obtained close to the city of Kiiruna along the mine section Y1900. In addition, six drill cores were also obtained along the railway as a part of another project related to the deformation of the ground below the railway. Several researchers have carried out the stability analyses on the hangingwall and footwall with different assumptions. In the stability analysis by Herdocia (1991), Hustrulid (1991) and Dahner-Lindqvist (1992), it was assumed that there is no stabilizing effect from the caved material on the hangingwall and footwall. Lupo (1996) modified Hoek’s limit equilibrium method (Hoek 1974) and considered the traction forces during draw and the interaction between the hangingwall and the footwall in the model. He assumed that when no draw is carried out, the caved rock provides support to the footwall and hangingwall and during draw action, traction forces increase the shear stresses in hangingwall and footwall. Stephansson et al (1978) worked on two-dimensional physical models and the results indicated that the caved rock does not increase the steepness of fracture angles but reduce 1.

(9) the extent to which existing fractures open. Later, Lupo (1996) indicated to failure of footwall without support of caved rock. The tests also indicated that instabilities would increase with increasing mining depths. Sjöberg (1999) performed numerical simulations using a finite difference code (FLAC) to evaluate footwall failure and effect of caved material. The model showed that lateral support of caved material was significant. Villegas (2008) analyzed the surface subsidence of the hangingwall by conducting numerical analysis of two sections of the Kiirunavaara mine using a finite element method. The caving process was explicitly simulated by adding voids moving up from the extraction level and changing the properties of the material when the void was filled. Subsidence, stresses, shear strain and plasticity were used to assess the hangingwall failure. Based on the estimated failure location on the ground surface, the break angle and the limit angle were calculated for different mining levels. The results indicated that the break angle and the limit angle are almost constant for deeper mining levels. However, the limit angle differs between sections with different rock mass strength.. 1.2 Objectives There were two main objectives in this work, first to characterize the rock mass and estimating the mechanical properties of the rock mass and discontinuities in proximity of the railway located on the Kiirunaavara hangingwall. The results will be used in further analysis of identifying possible weak zones in this area and their effects on the subsidence of the railway area. The second objective was to analyze the impact of major geological structures on the hangingwall deformation by using the discrete element method UDEC (Itasca 2005). A parameter study has been carried out in which the structural geology has been varied. One so called “basic model” was run without any geological structures. Two different structure sets have been analyzed. One structure set had a dip in the interval 50 – 90 degrees to the east, whereas the other set had the dip 60 degrees to the east and 60 degrees to the west, respectively. In chapter 2, the results of orientation analysis on the oriented samples and the rock quality designation “RQD” for each drill core is estimated. In chapter 3, the rock mass is classified using the geological strength index (GSI) and it is used together with point load test results on the samples to estimate the rock mass strength and deformation modulus. In chapter 4, the impact of large structures on the hangingwall deformation is evaluated through numerical analysis. 2.

(10) 2 Engineering geological data collection. 2.1 Introduction After any excavation in rock mass, the behavior of the remaining rock around the excavation is highly dependent on both the characteristics of rock material and the condition of preexisting discontinuities. Rock mass is mostly intersected by the number of discontinuities such as joints, faults, foliations and bedding planes and it is not very common to find an isotropic or homogenous rock mass in all directions. Mechanical properties and the orientation of the discontinuities have significant effect on generally controlling the engineering characteristics of the rock mass, thus it is essential to collect comprehensive description on discontinuities characteristics. Rock mass description can be completed by collecting data on both rock material and discontinuities. The rock mass can be characterized by the terms of color, structure, weathering/alteration, grain size, rock type, structure, and mechanical properties such as compressive strength of intact rock. Characteristics of discontinuities can be described by the terms such as orientation, spacing, persistence, thickness, infilling minerals, and waviness for joint sets. In this work, the obtained drillcores from the hangingwall and close to the railway were used to characterize the rock mass at this region. Drillcores were mapped by the author in order to find information on the quality of the rock mass at each borehole, and finally the mechanical properties of the rock mass was estimated through field conducted point load tests and using rock mass classification systems RQD and GSI. The orientation analysis is also carried out on the oriented samples in order to provide an initial estimation of the geology structure of the area for the geologists. The information on the name, coordinates, drilling angle, and the length of drill cores is presented in Table 2.1 and Figure 2.1.. 3.

(11) 4. * These endcoordinates are found by calculating the horizontal distance of the drillcore (L*cos(40°)).. 512.8. 1685746 7535246 1685674* 7535244*. 506.9. 1685819 7534947 1685788 7534935. KOJ7-8281. KOJ9-8283. 500.3. 1685932 7534665 1685866 7534665. KOJ6-8280. 517.4. 501.8. 1685940 7534306 1685832 7534330. KOJ5-8279. 1685875 7535193 1685758* 7535193*. 298.25. 498.3. 1686200 7534323 1686097 7534321. KOJ4-8278. KOJ8-8282. 307.96. 501.5. 1687012 7534323 1686888 7534331. KOJ3-8277. 134.37. 136,07** * 133,43** * 131.31. 133,095***. 138.65. 130,675***. 135. 126. 146.1. 43.095. 145,9** 149,3**. 44.37. 147.39. 41.31. 43.43. 151.6. 154.06. 48.65. 46.07. 144. 140. 40.675. 45. 36. 99.05. 99.25. 44.7. 98.7. 168.1. 177.75. 171.05. 595.45. 597.75. ***these dips are average between first and last mesurments!. 70.8. 74.55. 32.8. 67.9. 125.7. 117.4. 131.6. 481.7. 483.6. 69.3. 65.5. 30.37. 71.6. 111.6. 133.5. 109.3. 350. 351.3. Dip from Horizontal Vertical Dip Length distance distance horizontal Dip (gon) (degrees) (m) (m) (degrees) (m). ** There are no divergence measurements on 8282 and 8283, so these numbers have not been corrected for any divergence from the planned direction/inclination of the drillhole!. 297,6**. 295,3**. 278.5. 301.89. 315.68. 328.11. 500.2. 1686592 7534313 1686184 7534391. 301.2. KOJ2-8276. Bearing (gon). Z coordinate elevation (m) 503.6. END. KOJ1-8275. X Easting. START. Drillcores name, start and end of drilling coordinates, drilling angle and length.. Y Y X Easting Northing Northing 1686878 7534334 1686499 7534391. Drillcore. Table 2.1.

(12) Koj9 Koj8. City of Kiiruna Koj7. Railway direction. Koj6. Hangingwall. Koj1. Koj4 Koj2. Koj5. Figure 2.1. Koj3. Location and horizontal projections of drill cores are shown with green lines. Red crosses indicate to the start point of drilling. First the drillcores were named by the series (koj1-koj9), but later the names were changed to the series 8275-8283(Mai-Britt M. Jenssen, 2009). In the entire of this work the names koj1-koj9 is used to identify the drillcores.. 2.2 Structural geological terms This section deals with definition of joints pattern, major and minor discontinuities, and structural domain. To understand the joints pattern, it is important to be familiar with the joint orientation. Joints are commonly assumed as 2D planes with a specific orientation. The orientation of each joint plane is defined by the terms of dip-dip direction or dip-strike. For engineering purposes, dip and dip direction terms have a wide usage. In Figure 2.2, definitions of these terms are illustrated.. 5.

(13) Figure 2.2. Definition of dip, dip direction, and strike for a discontinuity (joint) plane.. To define the dip and dip direction in a simple way one can imagine a ball rolling down the line of a plane with maximum inclination, this line can define the dip direction and dip of the plane. The vertical angle of this line (which is measured from a horizontal plane) is the dip definition. If we draw the horizontal projection of the line with maximum inclination then the dip direction is achieved. This angle is measured clockwise from the north. The strike of this plane can be defined as the intersection of a horizontal plane and the surface of discontinuity. For engineering purposes the most useful geometric classification of discontinuities is by scale. Cruden (1977) has divided the size of discontinuities into two groups; 1) major discontinuities and 2) minor discontinuities. Major discontinuities are e.g., faults, dykes, contacts and related features of the same order of magnitude as that of the site to be characterized. The spacing, physical properties and geometrical characteristics are usually established deterministically for each of these major discontinuities. Minor discontinuities are e.g., joints, minor shears and bedding planes which, for practical purposes, represent an infinite population in the area of design. As a result, their geometrical characteristics and physical properties must be estimated by measurements of a representative sampled population. Structural domains are zones of a rock mass in which the geometrical and physical properties of the discontinuities can be treated as being statistically homogeneous.. 6.

(14) 2.3 Structural geological data collection The recovery of core by diamond drilling allows information to be obtained from volumes of a rock mass which cannot be observed directly. Due to no direct access or any exposure of the rock mass around the area of study (in this case the railway area), using this method has helped to provide valuable information about the condition of rock mass in that region. Mechanically oriented samples were used to determine the joints orientation. Some of the core samples are shown in Figure 2.3. The orientation of fractures is calculated by measuring two angles with respect to the mark of reference line, then data are transferred to real dip and dip direction by using the computer program DIPS (Rocscience, 2003). In the following sections of this chapter, the core orienting process, handling procedures of oriented cores, core orientation measurements, and finally calculated results are presented.. Figure 2.3. Drill cores on the core logging table of LKAB Kiruna.. 2.3.1 Mechanical orientation of drill core. To make the cores mechanically oriented, first the bottom of the drill core must be specified. There are two ways to find the core bottom, the first and simplest method is to use heavy steel spears to make a percussion mark on the top surface of the drill core. The marked point will represent the bottom of the surface. The problem with this method is that after the device impact, the spear point can slide sideways down the core (Figure 2.4).. 7.

(15) Figure 2.4. Using a spear to make a core oriented. The spear lowers down the borehole and makes an impression core surface to clear the bottom of the hole (Marjoribanks, 1997).. The second method is to make a template of the core stub surface. The exploration campaign in Kiruna mine has used this method to draw orientation marks on drill cores. The device which is used in this technique consists of spring-loaded steel pins that orients in the hole by means of a weight. The device is lowered on to the top of the core stub and records an impression by pressing against the end of core. After drilling the core and pulling out from ground, the core end and impression of the steel pins will match together. The problem with this method is that it does not work well when the end of the core is smooth and normal to the core axis (Figure 2.5). After specifying the bottom of hole (BOH) at the end of a core run, a reference line can be drawn along the entire length of the run and also on the adjacent runs that can be joined to it. For drawing the reference line, the BOH must be transferred to the top of the ho le (TOH). To transfer the (BOH) orientation mark to the top of the core, we can use both a circumferential protractor or done by eye with enough accuracy (Marjoribanks, 1997).. 8.

(16) Figure 2.5. Mechanical orientation of drill core using a core-end template device. The template tool descends inside the core barrel (Marjoribanks, 1997).. 2.3.2 Handling procedure of an oriented core. Some additional handling procedures are required for oriented cores. Broken pieces of the core must be re-assembled in up and down the hole from the driller’s orientation mark. This procedure is necessary for all cores, but it is essential for oriented cores. The removed pieces of core from the tray are matched together on a length of V shape channel. The channel must be three meters in length (length of a standard drill run) and the property must be from metal or wood. While we are re-assembling the broken cores, broken ends must be carefully joined together to make sure that all pieces are in their original orientation. If in a core run, pieces are not fit together, or some pieces are lost, then the orientation measurements are not possible for that run. The other important procedure for handling drillcores is to specify the top of core surface. This point is diametrically opposite the driller’s on the lower surface (BOH) of the core. By using a long straight edge and a felt-tip pen, the trace of the vertical plane on the upper surface can be drawn. The third handling procedure is to use an ink marker to mark arrows on the core every 25 cm, at least one arrow for each piece of core must be considered. These arrows are to provide orientation direction for each piece of core (necessary when the piece of core is 9.

(17) taken out from the tray due to tests or measuring structure). The other advantage of arrows is for the time of further cutting of the core for assay by giving guide to the responsible person working with samples which half of the core is to be retained (Figure 2.6).. Figure 2.6. Marking out oriented core. Broken pieces are removed from core tray and reassembled, run by run, in a V-section channel. Each core piece is marked with a down hole orientation arrow. The arrows are placed on the half to be retained after sampling (Marjoribanks, 1997).. 2.3.3 Measurements on oriented cores. 1. Dip of the plane; The shape of a discontinuity looks elliptical when it is intersected by the surface of the cylindrical drill core. If we label the lower point of this ellipse as E, and the upper point as E′, then line E-E′ located within the vertical reference plane, can result in that the hole is drilled at 90 ̊ to the strike of the surface. Here the angle between the core axis and the axis of the intersection ellipse after considering the inclination of the hole will be the dip of the plane of discontinuity. Measuring this angle (dip) can be done by using a semicircular transparent plastic protractor or goniometer held against the piece of core. To complete the definition of the discontinuity plane, it is also required to measure the dip direction. The dip direcTon can be either the similar to the azimuth of the hole or the reciprocal (180 ̊ +) of the azimuth (Figure 2.7).. 10.

(18) Figure 2.7. Measuring orientation of a planar structure intersected in oriented drill core. Two angles of α and β must be measured. α is the angle between ellipse axis (EE′) and the core axis. β is the angle between bottom of the hole (BOH) and point E on the ellipse. (Marjoribanks 1997). The orientation of a plane of discontinuity in a drill core can be found by one of these three methods: 1- Measuring the angle between the structure and the reference plane of the core, and then finding the attitude graphically by using a stereo net. 2- Measuring the angle between the structure and the reference plane of the core, and then finding attitude mathematically by manually calculations or using computer software. 3- Finding orientation of the core in a core frame and using a geological compass to measure the structure.. 2. Angle from top of the core; This is the angle measured from the reference line to the top of the core. It is measured clockwise looking down the core direction. (Figure 2.8). 11.

(19) Figure 2.8. The angle measured from the reference line to the top of the core (Rocsince 2003).. 3. Drilling angle; This is the inclination of the borehole axis from the zenith. If a borehole is oriented vertically upward then the value will be zero and if the borehole is oriented vertically downward, then the value will be 180. (Figure 2.9). Figure 2.9. Inclination of borehole from azimuth axis (Rocsience 2003).. 4. Azimuth; This value is measured from true north. To find the azimuth of a vertical borehole, one can use the clockwise angle from true north to the reference line, looking along the direction of borehole advance. (Figure 2.10). 12.

(20) Figure 2.10. Azimuth value measured from true north (DIPS 2003).. Core samples from koj1 and koj2 were mechanically oriented by the Kiruna hangingwall subsidence exploration campaign. It was intended to get a section with three oriented cores that could be correlated with seismic reflection. In each drill core the upper 200 m was mechanically oriented. Information on oriented cores and their related borehole are summarized in Table 2.2. This information is used as input data to the DIPS computer program to determine the real dip and dip direction of joint sets.. Table 2.1 Drilling location. Information on length and drilling angle of core oriented samples Total length Oriented (m) core length. Angle from top of the core. Drilling angle. Azimuth. koj1(8275). 600.50. 202.09. 180. 126. 271. koj2(8276). 597.30. 200.65. 180. 135. 270. 2.4 Structural geological data presentation and analysis In this work, the angles between the plane of structures and the reference plane of the core are measured, and the attitudes are determined mathematically using the computer software DIPS (Rocscience, 2003). The analysis of data gained from oriented cores is divided into a three stage process as following: 1- Plotting poles of the planes to depict the orientation of all discontinuities. 2- Contouring the poles to find the major discontinuity sets. 3- Plotting great circles for discontinuity sets and determining their related orientation. 13.

(21) 2.4.1 Pole plots. A pole plot is constructed from a large number of single points. Each single point represents one plane of discontinuity on this plot. The pole to a plane is 90 degrees away from every point on the great circle that represents the plane. Using this plot makes it is possible to examine the orientation of large number of discontinuities. Pole plots generally give a good view of pole concentrations which are representative of joint sets orientation. Different symbols in this type of plot can be used to make it easier to differentiate between various types of discontinuities. If enough information on the type of discontinuity sets from the geological mapping data is available, the data can also be plotted with the symbols such as F, J, etc. indicating to foliations and/or joints, for instance. The pole plots from boreholes koj1 and koj2 generated by the computer program DIPS are shown in Figures 2.11 and 2.12. These figures show lower hemisphere, equal angle projection of 482 poles for the borehole koj1 and 558 poles for the borehole koj2. The poles from any type of discontinuities are shown by black squares to make it possible to see the concentration of poles on the plot. This is the most basic representation of the orientation data (i.e. the orientation data pairs in the first two columns of a Dips file).. 14.

(22) Figure 2.11. Scatter plot of 482 poles for borehole koj1 shown on an equal angle lower hemisphere projection.. Figure 2.12. Scatter plot of 558 poles for borehole koj2 shown on an equal angle lower hemisphere projection. 15.

(23) 2.4.2 Pole density. Scatters in a pole plot are due to the variation in orientation of discontinuities. If a plot contains poles from a large number of discontinuity sets, then it will be difficult to distinguish between the poles from the different sets and the average orientation of each set. By contouring a pole plot it will become more convenient to identify different highly concentrated areas of poles. In this work the computer program DIPS was used to provide contours. It is also possible (but time consuming) to carry out contouring by hand using the techniques described by Hoek and Bray (1981). Figure 2.13 shows the contour plot from the poles plotted in Fig. 2.11. The pole plot in figure 2.11 showed that the orientation of the discontinuity planes has little scatter; the contour plot of these poles has a maximum concentration of 6.42%. Figure 2.14 shows the contour plot of the poles plotted in Figure 2.12. Maximum concentration of these poles are equal to 7.43%. In a pole plot and where the discontinuities orientation show more scatter, it will be more difficult to find discontinuity sets. In Figures 2.13 and 2.14 the different pole concentrations are shown by symbols for each 1% contour interval. The percentage concentration refers to the number of poles in each 1% area of the surface of the lower hemisphere.. 16.

(24) Figure 2.13. Pole density contour plot for the scatter plot illustrated in Figure 2.11 (Borehole koj1).. Figure 2.14. Pole density contour plot for the scatter plot illustrated in Figure 2.12 (Borehole koj2). 17.

(25) 2.4.3 Great circles. After plotting the contours, and by finding the highest pole density in different locations of stereo net, it is possible to find the average dip and dip direction for each joint set. In pole plots, high pole density locations are easy to determine by eye, but when the scatter of poles is very high, it is not that easy to find the average dip and dip direction visually, and to determine the contours, one can use statistical techniques. The DIPS program is suitable for various contouring procedures to help to determine the high pole density points. By applying these contouring procedures we will be able to get the great circle plot in Figures 2.15 and 2.16. These plots are defining the average dip and dip direction of major bedding planes, joints and other geological structures in the rock mass. These types of information are also useful for analyzing the structural stability and estimating the support design of underground excavations. Usually it is only possible to have a maximum of about six great circles on a plot, because with greater numbers, it will be difficult to identify all the intersection points of the circles. Four great circles indicating to four joint sets are obtained from density contour plot of borehole koj1. In the borehole koj2, 3 great circles are observed. The orientation of set number 2 and set number 3 in koj1 and koj2 are quite similar together. Equal angle method is used to find these great circles. Determined orientation of geological structures from major joint sets in koj1 and koj2 are summarized in Table 2.3:. Table 2.2. Summary of joint sets orientation in koj1 and koj2. These values are not related to mine north. koj1. koj2. Joint set. Dip. Dip direction. Joint set. Dip. Dip direction. 1. 69. 122. 1. 87. 86. 2. 81. 88. 2. 9. 86. 3. 64. 55. 3. 61. 48. 4. 29. 96. -------. -------. -------. These great great circles do not determine the original aspect of joints or faults, but at least allows the exploration geologists and geophysical engineers to understand the geology of the area and make decision about the future of the site.. 18.

(26) Figure 2.15. Poles and corresponding great circles for the average dip and dip direction of 4 discontinuity sets represented by the contour plots shown in Figure 2.13.. Figure 2.16. Poles and corresponding great circles for the average dip and dip direction of 3 discontinuity sets represented by the contour plots shown in Fig. 2.14. 19.

(27) 2.5 Rock Quality Designation Index (RQD) To provide a quantitative estimation of rock mass quality from drill core logs, the rock quality designation index (RQD) was developed by Deere (Deere et al., 1967) and is defined as the percentage of intact core pieces longer than 100 mm (4 inches) in the total length core. The core should be at least 2.15 inches in diameter and should be drilled with a double-tube core barrel. The correct procedures for measurement of the length of core pieces and the calculation of RQD are summarized in Figure 2.17.. Figure 2.17. Procedure of calculation of RQD (Deere, 1967).. The problem of estimating the RQD from mapping drillcores is that RQD is a directionally dependent parameter and there is a possibility of a change in RQD value by changing the borehole orientation. RQD is taken to represent the in situ quality of the rock mass. Hence, during logging drill cores, care must be taken to ensure that fractures which have been caused by handling or drilling processes or mechanical breaks are identified and they must be ignored when estimating the value of RQD.. 20.

(28) Each one of obtained drillcores were composed of several core runs, thus to estimate the quality of rock along the drill cores, the RQD value for each run was calculated, and for the core runs with similar value of RQD and in the vicinity of each other, one value of RQD was estimated by averaging. Different colors are assigned to the estimated value of RQD depending on the range which involved the estimation. A detailed RQD result for each run is shown in Appendix A. The results are illustrated graphically in two sections, section A-A from West to East and Section B-B from north to south. Section A-A involves drillcores koj1 through koj5 and section B-B involves drillcores koj4 through koj9. In Figure 2.18, a plan view of these sections is illustrated.. SECTION B-B. Koj9. Koj8. Koj7. Koj6. Koj5. Koj4. Koj3. Koj2 Koj1. SECTION A-A. Figure 2.18. Section A-A and section B-B, provided to show the RQD along the drillcores koj1 through koj9.. In Figure 2.19, the RQD values for different parts of drill cores section A-A are shown. Different colors are used to show the quality of rock in each level. The quality of rock changes to a better condition from red to blue. In this section, koj1, koj2 and koj3 (long drillcores) has shown better quality compare to the short drill cores koj4 through koj9 in this section and also in section B-B.. 21.

(29) In koj1, most of the most of the core runs are in the range of 75-100%. Small intervals of range 50-75% are scattered along this drill core. In koj2, the range of 50-75% is more extended. The range of 75-100% is located mostly in the middle and upper sections of this drill core. One small range of 0-25% can be observed in the middle of this drill core. In koj4 and koj5, which are located along the railway, the quality of rock has decreased. The range of RQD in koj4 is mostly between 25-50%. In the upper parts of this drill core the range of 50-75% is visible. In koj5, the range is mostly between 0-25% which indicates to the poor quality of rock mass at this borehole.. Figure 2.19. RQD value in section A-A, drill cores koj1 through koj5. Decrease of quality from west to east can be seen in this figure.. 22.

(30) The RQD value for the drill cores koj5 to koj9 is illustrated in Figure 2.20. In koj6 the most parts of the core is in the range of 0-25%. In koj7, koj8 and koj9 the quality looks better in comparison with two other drill cores in this section. The red color is less scattered in these 3 drill cores and the range between 50-75% is more visible. In Figure 2.21 the value of RQD is illustrated using rectangular graphs.. Figure 2.20. RQD value in section B-B. The quality of rock changes to a better condition from south to north. 23.

(31) RQD% -Koj1. 66%. 92%. 85%. 82%. 86% 63%. 58%. 83%. 80% 77% 73% 69%. 79%. 47%. 42%. 425 457. 534 557. 10% 23. 0. 54. 106. 85. 196. RQD%-Koj2. 91%. 257 284. 334 352 365 397. 91%. 66%. 82%. 78%. 71%. 67%. Depth (m) 600.5. 81% 64% 57%. 43% 15% 0. 99. 148 178 203. 236. 284. 327 350. 421. Depth (m). 488. 522. 597. RQD%-Koj3. 91% 70%. 63% 36%. 47%. 44%. 57% 20%. 76 94 104. 145. 20% 168. Depth (m). 0 13 28 45. Depth (m). 64% 28%. 74%. 68%. 0. RQD%-Koj9. RQD%-Koj6. 51. Depth (m). 21%. 22%. 15%. RQD%-Koj5. 39%. 177.85. RQD%-Koj8. 79. 0. 0. 27%. 37%. 55%. Depth (m). 153 173. 31% 49% 35% 60% 30% 43% 20%. RQD%-Koj4 33% 60% 12%. 89 109. RQD%-Koj7 23% 60% 30%. 0. 25 35. 58%. 87. 100. 58%. 32% 20%. 16%. Depth (m) 0. Figure 2.21. 82. 0 15. 100. RQD value in boreholes koj1 through koj9.. 24. Depth (m). 47 63 77 100. Depth (m).

(32) 3 Rock mass characterization, strength and deformation modulus. 3.1 Geological Strength index (GSI) Two necessary input data to numerical analysis to study rock mass behavior are rock mass strength and deformation modulus. Due to various parameters affecting the strength and deformation modulus it is very difficult to determine the global mechanical properties of a jointed rock mass and define a general law to predict these parameters. Some traditional methods used to determine these parameters are plate loading test for deformation modulus and in-situ block shear tests for strength parameters. The performance of these tests is possible when the exploration audits are excavated, but the costs of conducting insitu tests are high. To solve these problems, characterization of jointed rock mass was developed to classify the jointed rock mass. One of these classification systems is GSI which was originally developed by Hoek (1994). In this classification system the properties of intact rock and joints condition are used to determine the rock mass strength and deformation modulus. In addition, it is not necessary to have direct access to underground rock mass. The GSI system concentrates on the description of two factors, structure and block surface conditions. Among all classification systems, GSI is the only system which generates information on Hoek-Brown parameters (mb and s) and Mohr-Coulomb parameters (cohesion, friction angle and tensile strength). To find the GSI value in for each drill core, the guideline table presented in Figure 3.1 is used. In this guideline two parameters are required to be estimated to determine GSI value; structure condition and surface condition. According to Henry (2001), very low RQD values (< 30%) on the RQD log in Kiruna mine corresponds to mapped bad conditions. In addition, based on the mapping of drill cores koj1 through koj9, intervals with high value of RQD (>75%) were mostly rock types in a good quality condition. Thus, based on these observations, it was decided to estimate a correlation between structures condition and RQD value in which, the RQD value 75-100% is assigned to the “Blocky” structure condition, RQD of 50-75% is assigned to the “Very Blocky” condition. “Blocky/Disturbed” is in the RQD range of 25-50% and “Disintegrated” condition locates within range 0-25%. Estimation of surface condition changes mostly within the range good to poor according to the core mapping results.. 25.

(33) Range of surface condition observed during mapping the cores.. Figure3. 1 Characterization of rock mass on the basis of block structure and structure condition (Hoek and Brown 1998 adjusted from Hoek 1994).. 26.

(34) In Figures 3.2 and 3.3 the GSI values for drill cores from sections A-A and B-B are illustrated. In these figures the changes of GSI value is indicated by changing colors from red to blue. Low values of GSI are scaled with red (10-20) and yellow (20-40) colors and high values of GSI are scaled by dark blue (60-70) and light blue (70-80) colors. In this color spectrum, green indicates moderate values (40-60). In Figure 3.2 and in boreholes koj1 and koj2 the values of GSI are relatively high and mostly within the range of 60-70. In borehole koj2 the range of 40-60 is more extended compared to the borehole koj1. In koj3, the range 40-60 can be seen in most sections of this core run. Two small sections in ranges of 20-40 and 70-80 are also visible. In boreholes koj4 and koj5 the value of GSI is decreased compared to the eastern drill cores. In koj4, range of values is mostly between 20-40 and 40-60. Some small sections of 10-20 are visible in the borehole koj4. In the borehole koj5 the majority of core run have GSI value in the range of 20-40.. Figure3. 2. GSI value along drill cores koj1 through koj5 in section A-A.. 27.

(35) In Figure 3.2 it can be seen that drill cores koj6, koj7, koj8 and koj9 have relatively similar GSI ranges and the range 20-40 and 40-60 are most common in these core runs. In Figure 3.4 the value of GSI is illustrated using rectangular graphs.. Figure3. 3. GSI value along drill cores koj5 through koj9 in section B-B.. 28.

(36) GSI –Koj 1. 70. 75. 70. 50. 70 65. 65. 50. 70. 70 55. 50. 65 45. 45. 20. 23. GSI –Koj 2. 0. 54. 85. 106. 334 352 365 397 425 443 457. 257. 196. 75. 75 50. 65. 65. 55. 534 557. 600.5. Depth (m). 65 50. 50. 50. 35 20 99. GSI –Koj 3. 0. 236. 284. 327 350. 421. 50. 488. 522. 597. Depth (m). 30. 109. 50. 50 40 35. 15. 20. 40 30. 0. 30. 51. Depth (m). 0 13 28 45. Depth (m) 76 94 105 145 154 169. 0. 50. Figure3. 4. Depth (m). 35. 30. 25 35. 87 100. GSI value in boreholes koj1 through koj9 29. Depth (m). 50. 50 35. 0 15. 100. Depth (m). 55. 50. 30. 35. 82. 35. 30. 50. 40. 50. 20 177.85. 25. Depth (m). 40. 40. 79. GSI –Koj 5. 0. 35. 173. GSI –Koj 8. 60. 153. GSI –Koj 7. 89. GSI –Koj 9. GSI –Koj 4. 203. 75. 35. GSI –Koj 6. 178. 55. 0. 0. 148. 30. 25. 47 63 77 100. Depth (m).

(37) GSI values are used to estimate the Mohr-Coulomb and Hoek-Brown strength parameters and deformation modulus. Weighted averaging mean was used to determine one GSI value for each drill core. In this method, instead of the GSI values shown in a core length (Figures 3.2 and 3.3) contributing equally to the final average, some data points (with longer length of similar value of GSI) contribute more than others. This method is used to avoid smoothing the data and missing portions with poor and/or good rock. For short drill cores koj4 to koj9 and long drill core koj3 (173 m length), one value of GSI is estimated for entire length of the core and for long drillcores koj1 and koj2, depending on variation of GSI along the core run, different GSI values is estimated. A summary of GSI value in each drill core is presented in Table 3.1 and 3.2.. Table3. 1. Estimated GSI value in drill cores koj1 through koj3. koj1. Drill core core length 0-105 m position GSI. Table3. 2. koj2. koj3. 105-333 m. 333-600 m. 0-282m. 282-347m. 347-600m. 70. 64. 59. 20. 58. 48. 50. Estimated GSI value in short drill cores koj4 through koj9.. Drill core. koj4. koj5. koj6. koj7. koj8. koj9. GSI. 35. 32. 34. 36. 45. 39. 3.2 Generalized Hoek-Brown Criterion To estimate the rock mass strength in this work the generalized Hoek-Brown criterion is applied. According to this criterion and to calculate the strength of a jointed rock mass, it is required to estimate both the intact rock uniaxial strength and the joint condition. The generalized Hoek-Brown criterion is: σ'1 =σ'3 + σci (mb. σ' 3 σci. a. + s). (3.1). In equation (3.1): σ'1 and σ'3 are the major and minor effective principal stresses at failure, 30.

(38) σci is the uniaxial compressive strength of the intact rock, mb is the reduced value of material constant mi : mb = mi exp(. GSI-10 28-14D. ). (3.2). s and a are the material constants which can be calculated from equation (3.3) and (3.4): s= exp (. GSI-100 ) 9-3D. 1. 1. 2. 6. a= +. ). (3.3). e 15 -e 3 -GSI. -20. (3.4). In equations (3.2) and (3.3), D is the disturbance factor which is considered to estimate the degree of disturbance of rock mass after blasting and stress relaxation. The value of D varies between 0 and 1. Value of 0 indicates to an undisturbed in situ rock mass and value of 1 indicates to a very disturbed rock mass. In Appendix B a guideline for estimating the D factor is presented. The uniaxial compressive strength can be calculated from equation (3.1) and by setting σ'3 =0 . σc =σci .sa. (3.5). And by setting σ'1 =σ'3 = σt to calculate the tensile strength the equation (3.6) will be derived which represents a biaxial tension condition: σt = -. s.σi. (3.6). mb. For brittle materials, Hoek (1968) showed that the uniaxial tensile strength is equal to biaxial tensile strength. In this criterion, the presence of Geological strength index (GSI) is to account for the joint condition of the rock mass under study. The introduction of the (GSI) is done by Hoek, Wood and Shah (1992), Hoek (1994) and Hoek, Kaiser and Bawden (1995). The GSI values for different drilling points from Kiruna city and the railway are illustrated in figures 3.2 and 3.3. Estimated values of GSI are presented in tables 3.1 to 3.2 for drilling points koj1 through koj9. One of the common methods to determine the intact rock uniaxial compressive strength is uniaxial testing. In this case, the value of σc is determined indirectly through point load 31.

(39) index. The detailed value of point load tests, and its conversion to uniaxial compressive strength is shown in Appendix A.. 3.3 Deformation modulus The simplified Hoek and Diederiches equation was used to calculate the rock mass modulus (Hoek and Diederichs (2006)). In this equation GSI and D (Disturbance factor) are required as input parameters. The modulus is calculated in GPa: Em = 100. . 1-D/2 75+25D-GSI/11. 1+e. (GPa). (3.7). 3.4 Mohr-Coulomb Criterion In terms of minor and major principal stresses, σ1 and σ3 , the Mohr-Coulomb failure criterion can be expressed as: σ1 =. 2c cos ∅ 1- sin ∅. +. 1+ sin ∅ 1- sin ∅. .σ3. (3.8). In equation (3.8), C and ∅ are the cohesive strength and friction angle of the rock mass, respectively. These can be determined from the Hoek-Brown envelope by fitting an average linear relationship to the curve generated by solving equation (3.1) for a range of minor principal stress σt <σ3 <σ3max , as illustrated in figure 1. In the fitting process it is important to balance the area above and below the Mohr-Coulomb plot. This will result in equations (3.9) and (3.10) for the angle of friction and cohesive strength:. ∅= sin-1 c=. 6amb s+mb σ3n a-1. 2 1+a 2+a +6amb s+mb σ3n a-1.

(40). σci 1+2a s+1-amb σ3n s+mb σ3n a-1. 1+a 2+a 1+6amb s+mb σ3n a-1 / 1+a 2+a . Where σ3n = σ3max /σci.. 32. (3.9) (3.10).

(41) Figure3. 5. Relationship between major and minor principal stresses for Hoek Brown and equivalent Mohr Coulomb criteria (Roclab 2007).. In this work an upper limit of confining stress σ3max is determined, for the related GSI and in each drilling point. To determineσ3max , the ‘slopes method’ in Roclab (calculating factor of safety and the shape and location of the failure surface) was selected. Using Bishop’s circular failure analysis for a wide range of slope geometries and rock mass properties, gives (Roclab, Rocscience, 2007): σ3max σcm. =0.72 . . σcm -0.91 γH. (3.11). In equation (3.11), H is the height of the slope, is rock mass density and is the rock mass strength which can be calculated from equation (3.12): σcm = σci. a-1 m mb +4s-amb -8s b +s 4. 2 1+a 2+a. (3.12). The RocLab computer program (Rocscience 2007) was used to calculate strength and deformability of rock mass at drilling locations koj1 to koj9 through equations 3.1 to 3.12. The intact rock density was estimated to 2700 kg/m3 and mi=18 (Villegas, 2008). The uniaxial 33.

(42) compressive strength for each drill core was calculated from point load test results which in turn were obtained from breaking samples in every interval of drill cores. For the intervals with similar GSI value, a uniaxial compressive strength was estimated through average weighting method. The detailed results of point load test and uniaxial compressive strength of each interval are presented in appendix A. In Tables 3.3 and 3.4 the estimated value of uniaxial compressive strength for long drill cores and short drill cores is shown.. Table3. 3 Drillcore core position UCSi. Table 3.4. Estimated value of uniaxial compressive strength for long drill cores. koj1. koj2. 0-105 m 105-333 m 333-600 m 0-282m 136. 237. 236. 221. koj3. 282-347m. 347-600m. 117. 196. 107. Estimated value of uniaxial compressive strength for short drill cores. Drill core. koj4. koj5. koj6. koj7. koj8. koj9. UCSi. 145. 65. 102. 90. 174. 96. The low value of uniaxial compressive strength in koj5 is due to several heavily fractured sections within this drill core in which the point load test was not possible on most of them. Calculations are repeated for disturbance factors 0.5 and 1. Disturbance factor equal to 1 gives high values of strength parameters which cannot be a good representative for a large scale rock mass; thus, in this work, the strength parameters calculated through D=0.5 are assumed as the peak strength parameters. Based on back calculation analysis by Lupo (1996), residual values of rock mass strength is very close to the values obtained from D=0, thus, by setting this factor to zero, it is assumed that the achieved rock mass parameters indicate to residual strength parameters. A guideline table of disturbance factor is shown in Appendix B. The limits of confining stress over which the relationship between the HoekBrown and the Mohr-Coulomb criteria were considered is 0<σ3 <15.5. The upper limit of confinement is determined assuming rock slopes of 300,500 and 800 m heights (Villegas, 2008). Results are presented in Tables 3.5 – 3.31.. 34.

(43) Table 3.5. Parameters of Hoek-Brown criterion for borehole Koj1 (0-105 m) with GSI= 48.. D. mb. s. a. Em (GPa). σcm (MPa). σtm (MPa). 0.5. 1.513. 0.0010. 0.507. 2.01. 4.057. 0.088. 1. 0.439. 0.0002. 0.507. 0.44. 1.686. 0.053. Table 3.6 D 0.5 1. Table 3.7. Mohr Coulomb fit for borehole koj1 (0-105m) based on data from Table 3.5. σ3 =0-6.5 MPa C (MPa) ∅ ° 43.67 2.088 33.45 1.340. σ3 =0-10 MPa C (MPa) ∅ ° 39.80 2.843 29.64 1.812. σ3 =0-15.5 Mpa C (MPa) ∅ ° 36.19 3.785 26.25 2.390. Parameters of Hoek-Brown criterion for borehole Koj1 (105-333m) with GSI=70. D. mb. s. a. Em (GPa). σcm (MPa). σtm (MPa). 0.5. 4.314. 0.0183. 0.501. 12.69. 31.901. 1.006. 1. 2.112. 0.0067. 0.501. 3.07. 19.323. 0.756. Table 3.8 D 0.5 1. Table 3.9 D 0.5 1. Table 3.10 D 0.5 1. Mohr Coulomb fit for borehole koj1 (105-333m) based on data from Table 3.7 σ3 =0-6.5 MPa C (MPa) ∅ ° 54.88 5.240 49.83 3.879. σ3 =0-10 MPa C (MPa) ∅ ° 51.71 6.426 46.35 4.840. σ3 =0-15.5 Mpa C (MPa) ∅ ° 48.54 7.998 42.96 6.093. Parameters of Hoek-Brown criterion for borehole Koj1 (333-600m) with GSI=64. mb 3.242 1.376. s 0.0082 0.0025. a 0.502 0.502. Em (GPa) 7.92 1.83. σcm (MPa) 21.192 11.601. σtm (MPa) 0.599 0.425. Mohr Coulomb fit for borehole koj1 (333-600m) based on data from Table 3.9. σ3 =0-6.5 MPa C (MPa) ∅ ° 53.17 4.139 46.79 2.958. σ3 =0-10 MPa C (MPa) ∅ ° 49.78 5.276 43.10 3.825. 35. σ3 =0-15.5 Mpa C (MPa) ∅ ° 46.45 6.752 39.57 4.931.

(44) Table 3.11 D 0.5 1. Table 3.12 D 0.5 1. Table 3.13. Parameters of Hoek-Brown criterion for borehole Koj2 (0-282m) with GSI=59 mb 2.555 0.963. s 0.0042 0.0011. a 0.503 0.503. Em (GPa) 5.23 1.17. σcm (MPa) 14.128 7.104. σtm (MPa) 0.365 0.247. Mohr Coulomb fit for borehole koj2 (0-282m) based on data from Table 3.11. σ3 =0-6.5 MPa. ∅ °. 51.16 43.60. C (MPa) 3.402 2.364. σ3 =0-10 MPa C (MPa) ∅ ° 47.60 4.459 39.77 3.127. σ3 =0-15.5 Mpa. ∅ °. 44.15 36.18. C (MPa) 5.811 4.086. Parameters of Hoek-Brown criterion for borehole Koj2 (282-347m) with GSI=20. D. mb. s. a. Em (GPa). σcm (MPa). σtm (MPa). 0.5. 0.399. 2.33e-5. 0.544. 0.16. 0.354. 0.007. 1. 0.059. 1.62e-6. 0.544. 0.03. 0.083. 0.003. Table 3.14 D 0.5 1. Table 3.15. Mohr Coulomb fit for borehole koj2 (282-347m) based on data from Table 3.13 σ3 =0-6.5 MPa C (MPa) ∅ ° 29.85 0.938 15.58 0.414. σ3 =0-10 MPa C (MPa) ∅ ° 26.43 1.290 13.24 0.556. σ3 =0-15.5 Mpa. ∅ °. 23.42 11.33. C (MPa) 1.723 0.725. Parameters of Hoek-Brown criterion for borehole Koj2 (347-600m) with GSI=54.. D. mb. s. a. Em (GPa). σcm (MPa). σtm (MPa). 0.5. 2.014. 0.0022. 0.504. 3.41. 8.889. 2.014. 1. 0.673. 0.0005. 0.504. 0.75. 4.102. 0.136. Table 3.16 D 0.5 1. Mohr Coulomb fit for borehole koj2 (347-600m) based on data from Table 3.15. σ3 =0-6.5 MPa C (MPa) ∅ ° 48.61 2.803 39.82 1.888. σ3 =0-10 MPa C (MPa) ∅ ° 44.89 3.753 35.93 2.534. 36. σ3 =0-15.5 Mpa C (MPa) ∅ ° 41.35 4.954 32.35 3.337.

(45) Table 3.17 D 0.5 1. Table 3.18 D 0.5 1. Table 3.19 D 0.5 1. Table 3.20 D 0.5 1. Table 3.21 D 0.5 1. Table 3.22 D 0.5 1. Parameters of Hoek-Brown criterion for borehole Koj3 GSI=58. mb 2.436 0.896. s 0.0037 0.0009. a 0.503 0.503. Em (GPa) 4.80 1.07. σcm (MPa) 6.388 3.158. σtm (MPa) 0.162 0.109. Mohr Coulomb fit for borehole koj3 based on data from Table 3.17. σ3 =0-6.5 MPa C (MPa) ∅ ° 45.68 2.375 37.55 1.656. σ3 =0-10 MPa C (MPa) ∅ ° 41.85 3.192 33.65 2.225. σ3 =0-15.5 Mpa C (MPa) ∅ ° 38.25 4.219 30.12 2.929. Parameters of Hoek-Brown criterion for borehole Koj4 with GSI=35. mb 0.815 0.173. s 0.0002 1.97e-5. a 0.516 0.516. Em (GPa) 0.63 0.14. σcm (MPa) 1.657 0.542. σtm (MPa) 0.031 0.017. Mohr Coulomb fit for borehole koj4 based on data from Table 3.19. σ3 =0-6.5 MPa C (MPa) ∅ ° 38.76 1.591 26.01 0.892. σ3 =0-10 MPa C (MPa) ∅ ° 34.91 2.185 22.59 1.206. σ3 =0-15.5 Mpa C (MPa) ∅ ° 31.41 2.919 19.67 1.584. Parameters of Hoek-Brown criterion for borehole Koj5 with GSI=32. mb 0.706 0.140. s 0.0001 1.2e-5. a 0.520 0.520. Em (GPa) 0.48 0.10. σcm (MPa) 0.585 0.180. σtm (MPa) 0.011 0.006. Mohr Coulomb fit for borehole koj5 based on data from Table 3.21. σ3 =0-6.5 MPa C (MPa) ∅ ° 31.44 1.088 19.14 0.571. σ3 =0-10 MPa C (MPa) ∅ ° 27.77 1.488 16.31 0.764. 37. σ3 =0-15.5 Mpa C (MPa) ∅ ° 24.55 1.975 13.96 0.995.

(46) Table 3.23. Parameters of Hoek-Brown criterion for borehole Koj6 with GSI=34.. D. mb. s. a. Em (GPa). σcm (MPa). σtm (MPa). 0.5. 0.777. 0.0002. 0.517. 0.57. 1.078. 0.020. 1. 0.161. 1.67e-5. 0.517. 0.12. 0.346. 0.011. Table 3.24 D 0.5 1. Table 3.25 D 0.5 1. Table 3.26 D 0.5 1. Table 3.27 D 0.5 1. Table 3.28 D 0.5 1. Mohr Coulomb fit for borehole koj6 based on data from Table 3.23 σ3 =0-6.5 MPa C (MPa) ∅ ° 35.67 1.359 23.05 0.744. σ3 =0-10 MPa C (MPa) ∅ ° 31.86 1.864 19.85 1.002. σ3 =0-15.5 Mpa C (MPa) ∅ ° 28.45 2.484 17.15 1.312. Parameters of Hoek-Brown criterion for borehole Koj7 with GSI =36. mb 0.854 0.021. s 0.0002 2.33e-5. a 0.515 0.515. Em (GPa) 0.69 0.15. σcm (MPa) 1.112 0.371. σtm (MPa) 0.021 0.011. Mohr Coulomb fit for borehole koj7 based on data from Table 3.25. σ3 =0-6.5 MPa C (MPa) ∅ ° 35.59 1.360 23.38 0.761. σ3 =0-10 MPa C (MPa) ∅ ° 31.77 1.863 20.15 1.025. σ3 =0-15.5 Mpa C (MPa) ∅ ° 28.35 2.482 17.41 1.341. Parameters of Hoek-Brown criterion for borehole Koj8 with GSI =45. mb 1.312 0.354. s 0.0007 0.0001. a 0.508 0.508. Em (GPa) 1.54 0.33. σcm (MPa) 4.192 1.651. σtm (MPa) 0.087 0.051. Mohr Coulomb fit for borehole koj8 based on data from Table 3.27. σ3 =0-6.5 MPa C (MPa) ∅ ° 44.33 2.153 33.49 1.347. σ3 =0-10 MPa C (MPa) ∅ ° 40.48 2.936 29.69 1.824. 38. σ3 =0-15.5 Mpa C (MPa) ∅ ° 36.88 3.914 26.30 2.408.

(47) Table 3.29. Parameters of Hoek-Brown criterion for borehole Koj9 with GSI= 39.. D. mb. s. a. Em (GPa). σcm (MPa). σtm (MPa). 0.5 1. 0.986 0.231. 0.0003 3.84e-5. 0.512 0.512. 0.9 0.19. 1.490 0.526. 0.029 0.016. Table 3.30 D 0.5 1. Mohr Coulomb fit for borehole koj9 based on data from Table 3.29. σ3 =0-6.5 MPa C (MPa) ∅ ° 37.36 1.494 25.56 0.868. σ3 =0-10 MPa C (MPa) ∅ ° 33.49 2.047 22.15 1.171. 39. σ3 =0-15.5 Mpa C (MPa) ∅ ° 30.00 2.727 19.23 1.536.

(48) 4. Effect of large-scale geological structures on the subsidence of the Kiirunavaara hangingwall-Numerical Analysis 4.1 Introduction Many computer programs based upon a continuum mechanics formulation (e.g., finite element and Lagrangian finite-difference programs) can simulate the variability in material types and nonlinear constitutive behavior typically associated with a rock mass, but the explicit representation of discontinuities requires a discontinuum-based formulation. There are several finite element, boundary element and finite difference programs available which have interface elements or “slide lines” that enable them to model a discontinuous material to some extent. However, their formulation is usually restricted in one or more of the following ways. First, the logic may break down when many intersecting interfaces are used; second, there may not be an automatic scheme for recognizing new contacts; and, third, the formulation may be limited to small displacements and/or rotation. For these reasons, continuum codes with interface elements are restrictive in their applicability for analysis of underground excavations in jointed rock (UDEC, Itasca 2004). Distinct element program UDEC (Itasca 2004) is used to evaluate the effect of major geological structures orientation on the break angle in the hangingwall of kiirunavaara mine. UDEC is a distinct element numerical method, which locates within the classification of discontinuoum methods. The existence of contacts between the discrete bodies distinguishes this discontinuous medium from a continuous one. In this discontinuous numerical model, mechanical behavior of both discontinuities and solid material is represented. UDEC can simulate both deformation and rigid bodies separated by discontinuities. This code can be used for both static and dynamic calculations.. 40.

(49) 4.2 Section Y1500 Section Y1500 from Kiirunavaara hangingwall was chosen to carry out the numerical analysis. At this section the rock mass is heavily jointed and has been assumed homogeneous and isotropic. High caveability and chimneys, which fail a few months after creation is the other characteristic for this section (Villegas, 2008). The location of this section is in the northern part of the Kiirunavaara mine where the hangingwall is closer to the city and the footwall is close to the mine installations and buildings (Figure 4.1). The open pit is filled with crushed rock from underground mining. According to Stephansson et al (1978), the failure mode in this section is a combination of toppling and shear failure. Limit equilibrium analyses have previously been performed to analyze the hangingwall stability by Herdocia (1991), Hustrulid (1991), Lupo (1996) to estimate the break angle at this section.. Luossojarvi. kiiruna. Y1000 Y1500 Y2000 Footwall Y3000. Hangingwall Y4000. Y5000. Figure 4.1. Mine Section Y-1500.. 41.

(50) 4.3 Model Approach A rectangular model was created with the size of 6000˟2370 m (width˟depth). The top boundary is located at the ground surface. Fictious joints are used to model the orebody at each mining stage (Figure 4.2). In UDEC “joints” represent both the physically real geologic structures and the boundaries of man-made structures or the materials that will be removed or changed during the subsequent stages of the analysis, thus, the presence of fictious joints should not influence the model results. High values of shear and normal stiffness (10e10 Pa/m) are assigned to these fictious joints to behave as artificial boundaries. The inclination of the orebody is almost 60 degrees. The orebody is divided into blocks of 80˟25 m width and height, respectively, which are removed in different mining stages. Blocks are zoned to behave deformable. In the vicinity of the orebody the edge size is decreased to increase the resolution in that region. A Mohr-Coulomb constitutive material was assigned to the model, and global damping was used to provide an equilibrium solution for gravity loading of the elastic system. Boundary and initial stress conditions were set to bring to the model to an initial equilibrium state. Two lateral vertical external boundaries were fixed in x-direction and the lower horizontal boundary was fixed in y direction. The upper boundary was assumed as the free surface. The initial state of stress was selected according to section 4.4.2. The rounding length of the model was 0.50 m. JOB TITLE : Basic Model. (*10^3). UDEC (Version 4.00) 1.500. LEGEND 3-Sep-09 3:23 cycle 4430 block plot boundary plot x-boundary condition: S - Stress (force) B - Boundary Element V - Viscous F - Fixed velocity P - Pore pressure boundary plot y-boundary condition: S - Stress (force) B - Boundary Element V - Viscous F - Fixed velocity P - Pore pressure. Ground surface Z=0. 0.500. F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF F F F. Mining level Z=-1000 m. -0.500. -1.500. -2.500. -3.500. LTU lulea uinversity of technology 0.500. 1.500. 2.500. 3.500 (*10^3). Figure 4.2. Basic Model.. 42. 4.500. 5.500.

(51) At each mining level, the model was first run with elastic material until reaching to initial equilibrium and then it was changed to the non-linear plastic material for the final state. The material were prevented from yielding during computing the model in elastic condition, but the original properties were restored when the equilibrium was achieved. The mining sequence is shown in Figure 4.3. Firstly the ore block is extracted (a). In the next stage (b) while the mining advance lower levels at the same time the previously mined block is filled with caved material. This mining sequence continues until mining level 1000 m (c). The ore blocks were extracted and filled in blocks of 80˟25 m (width˟height). This sequence was repeated for 40 times until reaching to the mining level 1000 m. During this process the major problem was the contacts overlap especially at the final mining levels. Overlaps were mostly occurred between a caved block and an excavated block. To avoid this problem the value of overlap tolerance was increased.. a). Figure4. 3. b). c). Mining sequence. Black color represents the ore extraction and blue color represents the block filled with caved material.. 43.

(52) 4.4 Model Properties and stress data 4.4.1 Model properties Mechanical properties of rock mass in section Y1500 are obtained from previous analysis carried out by Villegas (2008). The input parameters for the rock mass in the hangingwall and footwall are shown in Tables 4.1 and 4.2. The same material properties are used in orebody, but the density is changed to 4700 kg/m3. The values calculated in chapter 3 are not used because it was intended to compare the results of the analysis in the distinct element method to the results from finite element method carried out by Villegas (2008) under the same material properties and quite similar model dimensions.. Rock mass properties for the mine section Y 1500. Table 4.1. Parameters GSI Density Young's Modulus Poisson's ratio Tensile strength Cohesion Friction angle Dilation angle Residual Cohision Residual friction. Table 4.2. Mine section 1500 62 2700 kg/m3 6.7 GPa 0.22 0.4 MPa 5.8 MPa 44 ̊ 29 ̊ 1 MPa 37 ̊. Mechanical Properties of Caved Rock.. Density. 2000 kg/m3. Young's Modulus. 200 MPa. Poisson's Ratio. 0.25. Friction Angle (peak and residual) Cohesion (peak and residual). 35 ̊. 0. 44.

(53) 4.4.2 Stress data. The applied components of normal stresses are the relations derived by sandström (2003) from regression analyses of overcoring measurements. These equations are valid below 400 m. σew = 0.037z. (5.1). σv = 0.029z. (5.2). σns = 0.028z. (5.3). Where σew = horizontal virgin stress in MPa in the east-west direction. σv = vertical virgin stress in MPa. σns = horizontal virgin stress in MPa in the north-south direction. z. = depth below ground surface in meters.. The relation between the major principal (σew) and the vertical stress is 1.28.. 45.

(54) 4.5 Interpretation of results Because UDEC models a nonlinear system as it evolves in time, the interpretation of results may be more difficult than with a conventional finite element program that produces a “solution” at the end of its calculation phase. There are several indicators that can be used to assess the state of the numerical model for a static analysis (e.g., whether the system is stable, unstable, or is in steady-state plastic flow). Some of the indicators which are used to detect the stability condition of model and locating the failure surface are described in the following. One of the good indicators in UDEC to check the stability condition of the model is by plotting the unbalanced forces history (at each mining stage in this work). In deformable blocks forces accumulate at grid points. In an equilibrium or steady plastic flow state the algebraic sum of these forces must be almost zero. During model computation, the maximum unbalanced force is determined for the whole model. This force was saved as a history and viewed as a graph. In Figure 4.4 the graph of unbalanced forces for mining depth 950 m is shown. In this figure it can be observed that the graph of unbalanced forces is converging to a straight line close to zero indicating that the model has reached equilibrium. For other mining stages similar graphs were observed.. JOB TITLE : .. UDEC (Version 4.00). (e+009) 7.00. LEGEND 28-Sep-09 0:17 cycle 311180 history plot maximum unbalanced force Vs. 1.80E+03<time> 1.87E+03. 6.00. 5.00. 4.00. 3.00. 2.00. 1.00. 0.00. LTU lulea uinversity of technology. Figure 4.4. 1.80. 1.81. 1.82. 1.83. 1.84. 1.85. 1.86. 1.87. 1.88. (e+003). Unbalanced forces in mining level 950 m.. Plots of plastic indicators were used to estimate the failure surface, and then the location of this surface was used to determine the break angle at each mining depth. By using this plot it 46.

(55) was possible to detect how the failure mechanism was developed. The contiguous line of active plastic zones (zones failed in tension and shear) was used to locate the failure surface. For example, the plastic state of the model in mining depth 950 m is shown in Figure 4.5. In this figure the yielded elements with green color indicate yielding in past, which means that initial plastic flow often occurs at the beginning of a simulation, but subsequent stress redistribution unloads the yielding elements so that their stresses no longer satisfy the yield criterion. Only the actively yielding elements (“at yield surface”) which are shown with red color for shear failure and purple color for tension failure are important to the detection of a failure mechanism. If there was no contiguous line or band of active plastic zones between boundaries, two patterns were compared before and after the execution of steps to see if the region of active yield was increasing or decreasing. If it was decreasing, then the system was probably heading for equilibrium and if it was increasing, then ultimate failure could be possible. Vertical velocity contours for the same mining depth shown in Figure 4.6 also indicates to the plastic flow state around the orebody in which the boundary of this state shown with pink color almost coincident with the location of failure surface estimated from plastic plot.. JOB TITLE : plastic state. (*10^3). UDEC (Version 4.00). Failure surface. LEGEND. 0.250. 3-Sep-09 7:12 cycle 311180 block plot no. zones : total 36119 at yield surface (*) 175 yielded in past (X) 11357 tensile failure (o) 892. -0.250. -0.750. -1.250. -1.750. LTU lulea uinversity of technology 2.250. Figure 4.5. 2.750. 3.250 (*10^3). 3.750. 4.250. Failure surface at mining depth 950 m of the ‘basic model’ estimated by detecting active plastic zones. Red colors are indicating to shear failure and purple color is due to failure in tension.. 47.

(56) JOB TITLE : velocity contours. (*10^3). UDEC (Version 4.00). Failure surface. LEGEND 0.000. 3-Sep-09 7:12 cycle 311180 Y velocity contours contour interval= 2.000E-04 -9.800E-03 to -8.000E-03. -0.400. -9.800E-03 -9.600E-03 -9.400E-03 -9.200E-03. -0.800. -9.000E-03 -8.800E-03 -8.600E-03 -8.400E-03 -8.200E-03. -1.200. -8.000E-03. block plot. -1.600. LTU lulea uinversity of technology 2.400. 2.800. 3.200. 3.600. 4.000. 4.400. (*10^3). Figure 4.6. Failure surface confirmed by vertical velocity contours. Based on surveying data of the hangingwall reported by Dahner and Stöckel (2006), Villegas (2008) estimated a critical vertical displacement (CVD) between 0.6 to 0.8 m for mining section Y1500 as the onset of failure. Then he used the failure surface defined by CVD together with other indicators such as yielded elements, maximum shear strain, and stress concentration to locate the failure surface and calculate the break angle in the model. For mining section Y1500 he estimated a constant break angle of 64 degrees after the mining level 800 m. The break angles estimated in this work showed a constant value of 65-66 after mining depth 850 m which could indicate that the failure surface located on plastic plot is well defined, but by monitoring the vertical displacements of one point in UDEC model it was observed that vertical displacements calculated by this code are high, and a CVD value of 1.5 m from the model in UDEC corresponds to a CVD of 0.6 to 0.8 m observed in the field and obtained from finite element analysis by Villegas (2008). The onset of failure equal to 1.5 m was coincident with failure surface defined in plastic plot (see Figure 4.7). The higher values of calculated vertical displacements in UDEC compared to finite element methods maybe because of the dicontinum based formulation of this code. The plot of shear strain contours are also used as another indicator to failure surface (Figure 4.8).. 48.

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