See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/226235830 Local and Spatial Joint Frequency Uncertainty and its Application to Rock Mass Characterisation Article in Rock Mechanics and Rock Engineering · August 2009 DOI: 10.1007/s00603-008-0009-x CITATIONS READS 24 300 2 authors: Steinar L. Ellefmo Jo Eidsvik Norwegian University of Science and Technology Norwegian University of Science and Technology 31 PUBLICATIONS 178 CITATIONS 60 PUBLICATIONS 1,024 CITATIONS SEE PROFILE SEE PROFILE Some of the authors of this publication are also working on these related projects: Ethical aspects of deep-sea mining View project MarMine - Exploitation technologies for marine minerals on the extended Norwegian continental shelf View project All content following this page was uploaded by Jo Eidsvik on 30 May 2014. The user has requested enhancement of the downloaded file. Local- and spatial joint frequency uncertainty and its application to rock mass characterisation Steinar L. Ellefmo*1, Jo Eidsvik2 1 Department of Geology and Mineral Resources Engineering, Norwegian University of Science and Technology (NTNU), Sem Saelands vei 1, N-7491 Trondheim, Norway 2 Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU), Alfred Getz vei 1, N-7491 Trondheim, Norway Summary Stability is a key issue in any mining or tunnelling activity. Joint frequency constitutes an important input into stability analyses. Three techniques are used herein to quantify the local- and spatial joint frequency uncertainty, or possible joint frequencies given joint frequency data, at unsampled locations. Rock Quality Designation is estimated from the predicted joint frequencies. The first method is based on kriging with subsequent Poisson sampling. The second method transforms the data to near-Gaussian variables and uses the Turning Band Method to generate a range of possible joint frequencies. Method three assumes that the data are Poisson distributed and models the log-intensity of these data with a spatially smooth Gaussian prior distribution. Intensities are obtained and Poisson variables are generated to examine the expected joint frequency and associated variability. The joint frequency data is from an iron ore in the Northern part of Norway. The methods are tested at unsampled locations and validated at sampled locations. All three methods perform quite well when predicting sampled points. The probability that the joint frequency exceeds five joints per meter is also estimated to illustrate a more realistic utilisation. The obtained probability map highlights zones in the ore where stability problems have occurred. It is therefore concluded that the methods work and that more emphasis should have been put on these kinds of analyses Page: 1 of 35 when the mine was planned. By using simulation instead of estimation, it is possible to get a clear picture of possible joint frequency values or ranges, i.e. the uncertainty. Keywords: Joint frequency, rock mass classification, geostatistics, iron ore *Corresponding author: Tel.: +47 73 59 48 56. Fax: +47 73 59 48 14; E-mail address: [email protected] Page: 2 of 35 1. Introduction Focus on stability is crucial in any type of underground workings like underground mining or tunneling. In mining ore grade and stability are two decisive parameters. If it is not possible to produce ore above cut-off at stable conditions, the ore is sterilized until the mining face is stabilized. Unexpected instability incidents are expensive. They require additional expensive efforts and they are time consuming. In mining it is important to produce according to schedule to avoid loosing too much income. Tunneling projects must often be finalized within a rather strict time frame. Unexpected delays due to instabilities must therefore be avoided. Preliminary investigations in mining and tunneling are in principle similar, but typically very different when it comes to extent. Mining projects need to perform extensive drilling campaigns to characterize and delineate the ore body. If the boreholes are logged also for geotechnical information like joint frequency and joint characteristics, they can, used along with suitable quantification techniques, provide valuable input into stability analyses. Boreholes drilled to characterize the grade distributions in the ore, might not be suitable if one also wants to collect geotechnical data. For example, in order to assess at what rate the joint frequency decline with increasing distance from a fault, it would be best to drill perpendicular to the fault plane. Mining companies have to the authors’ knowledge acknowledged this and perform separate drilling campaigns to collect geotechnical data. Once data is collected these must be processed and analyzed to give meaningful interpretation and decisions. Herein we present techniques based Page: 3 of 35 on geostatistics to predict the expected joint frequency and associated local- and spatial variability (uncertainty) at unsampled locations. The methods are validated by also predicting the joint frequency at sampled locations. The joint frequencies are transformed into Rock Quality Designation (RQD) values. The RQD (Deere and Miller 1966) is a parameter used today in many mining and tunneling projects to describe the degree of jointing in a rock mass. Geostatistics has been used in rock mass characterization. La Pointe (1980) uses geostatistics to indicate the degree of inhomogeneity in the frequencies and orientation of two distinct joint sets. Young (1987) uses indicator kriging to evaluate the local probability distribution of rock joint orientations in geological formations. Hoerger and Young (1987) use local estimates of rock mass conditions obtained through geostatistics as input into geotechnical designs. Yu and Mostyn (1993) review concepts and models used to model the spatial correlation of joint geometric parameters. Syrjänen and Lovén (2003) used geostatistics on estimated Geological Strength Index (Hoek et al. 1995). They conclude that rock mechanical quality parameters from drill cores can be estimated using geostatistical interpolation methods. Einstein (2003) reports the use of geostatistics on RQD values. Liu and Srinivasan (2004) used multiple point statistics to simulate fracture networks. In this paper the joint frequency and its associated variability (uncertainty) is quantified using three different simulation approaches. The simulation approach enables assessment of not only expected RQD-values, but also possible RQD-values, i.e. possible RQD- ranges. As an application, the probability that the joint frequency exceeds five joints per meter is predicted at points covering a part of the Kvannevann Iron Ore in Page: 4 of 35 Northern Norway. In effect this also estimates the probability that the RQD- value is below 90% at unsampled locations. Probability maps are generated to visualize the result. In Chapter 2 the geology, the joint frequency geodata and the Kvannevann Iron Ore mining operation is presented. Chapter 3 presents the objective and previous work performed on the geodata used in this paper. Chapter 4 gives a short introduction to RQD and how it is used in this study. Chapter 5 presents the three techniques applied to quantify the joint frequency and associated variability at unsampled locations. Chapter 6 presents the prediction results and discusses its implications. In Chapter 7 some concluding remarks are made. Two of the simulation approaches are presented in more detail in the Appendix. 2. Background 2.1. Mining operation The applied mining method at the Kvannevann Iron Ore Mine is sublevel stoping. One drill drift is tunnelled in the centre of the planned stope. From this drift production holes of 3 to 4 inches in diameter, are drilled about 30 metres upwards and about 40 metres downwards in vertical fans. Another drift is tunnelled about 70 meter below the drill drift from which the production holes are drilled upwards. Typically, three or four fans are charged and blasted in one round. Blasted ore is loaded onto trucks and transported out to a crusher near the mine entrance. The stopes are about 110 metres high, 40 metres wide and 60 metres long. Figure 1 provides a mine map showing level 250, i.e. 250 meters above sea level. Crushed ore is trammed about 35 kilometres down to Page: 5 of 35 the beneficiation plant. The mine has an annual production at about 1.6 million tonnes of ore. 2.2. Geology The iron ores in Dunderland Valley belong to Rødingfjell Nappe Complex (RNC) which constitutes a part of the uppermost allochthone of the Scandinavian Caledonides. RNC contains rocks of assumed late Pre-Cambrian to Cambrian-Silurian age and consists of the Beiarn Nappe, the Slagfjell Nappe, the Plura Nappe and the Ramnålia Nappe (Søvegjarto et. al., 1989). Two iron-ore-bearing zones are found in Ramnålia Nappe, more specifically in the Dunderland formation. The Dunderland formation consists of dolomite- and calcite marble, mica schist, calcareous mica schist and two iron ore bearing horizons. The economic Kvannevann Iron Ore in the Dunderland formation is a low grade meta-sedimentary iron ore with an average total iron grade around 34%. The ore is highly banded in terms of mineral variations, grain size, grain shape and iron content. Spatially, the ore is steeply dipping. The main minerals in the ore are hematite and magnetite, calcite and dolomite, quartz, garnet, epidote, mica (biotite and muscovite) and amphiboles. 2.3. Joint frequency data A joint is a planar or semi-planar discontinuity in a rock formed through movement perpendicular to the fracture surface (e.g; Park 1989; Braathen and Gabrielsen 2000). There are three joint sets in the area (Nilsen 1979). Table 1 shows the joint strike and the joint dip of these joint sets. The strike angle is given as the Page: 6 of 35 clockwise angle from north and the dip is the angle downwards from the horizontal. Joints represent zones of weakness in the rock mass. Thus, to assess the stability of the rock mass, the spatial joint frequency distribution is an important input. Boreholes from a 1980-drilling campaign have been logged for joint frequency by counting the number of joints pr.