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  • 1.
    Duarte, Margarida Taborda
    et al.
    Luleå tekniska universitet.
    Lindqvist, Per-Arne
    Kou, S.Q.
    Luleå tekniska universitet.
    Miskovsky, Karel
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering.
    Quantitative characterization of rock material for modelling of microstructure2003In: Konferens i mineralteknik / [ed] Marianne Thomaeus; Eric Forssberg, Föreningen Mineralteknisk Forskning / Swedish Mineral Processing Research Association , 2003Conference paper (Other academic)
  • 2.
    Duarte, Margarida Taborda
    et al.
    Geomaterials Research, Cnh da Figueira.
    Liu, H.Y.
    Luleå tekniska universitet.
    Kou, S.Q.
    Luleå tekniska universitet.
    Lindqvist, Per-Arne
    Miskovsky, Karel
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering.
    Microstructural modeling approach applied to rock material2005In: Journal of materials engineering and performance (Print), ISSN 1059-9495, E-ISSN 1544-1024, Vol. 14, no 1, p. 104-111Article in journal (Refereed)
    Abstract [en]

    The importance of the microstructural parameters in rock mechanical behavior has been investigated by several authors. Moreover, the Weibull statistical model has been used to characterize the heterogeneity of several materials on the basis of the concept that the microscopic defects within the material determine their mechanical strength. The modeling of different rocks is a topic that is fundamental for the prediction of rock fragmentation. In this article, the analysis of rock microstructure is performed using the microstructural modeling approach, which consists of the simplification, quantification, and modeling of the main properties of rock microstructure. The grain size, grain shape, and microcracks are modeled by means of statistical density functions, namely, Cauchy, chi-squared, exponential, extreme value, gamma, Laplace, normal, uniform, and Weibull. It is found that the Weibull distribution is the most appropriate statistical model of the grain size and grain shape, when compared with the other eight statistical models. Regarding microcracks, the results show that the gamma distribution is the most appropriate model. The Weibull and gamma distributions are then used to analyze the heterogeneity of the microstructure. This is done by comparison of the statistical models of each microstructural property evaluated in several thin sections of the same rock. It is found that with respect to grain size and grain shape, the rock is homogeneous, while the size distribution of the microcracks shows a clear trend toward less homogeneity. The microstructural modeling approach is important for modeling, characterizing, and analyzing the microstructure of rock material. Among other applications, it can be used to explain differences in the mechanical behavior obtained in testing several specimens.

  • 3.
    Hai-Hui, Lai
    et al.
    Luleå tekniska universitet.
    Lindqvist, Per-Arne
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Rånman, Karl-Erik
    Luleå tekniska universitet.
    Microscopic observations of the fragmentation in rock cutting1980Report (Other academic)
  • 4. Hai-Hui, Lai
    et al.
    Lindqvist, Per-Arne
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Rånman, Karl-Erik
    Luleå tekniska universitet.
    Reconsolidation of crushed rock fragments under a button indenter1980Report (Other academic)
  • 5.
    Johansson, Bernt
    et al.
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Structural and Construction Engineering.
    Axelsson, Kennet B. E.
    Högskolan i Luleå, Luleå tekniska universitet, Luleå University of Technology.
    Grennberg, Torsten
    Luleå tekniska universitet.
    Almgren, Gunnar
    Luleå tekniska universitet.
    Lindqvist, Per-Arne
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Stillborg, Bengt
    Luleå tekniska universitet, Swedish Mineral Research Foundation, Sweden.
    Klisinski, Marek
    Luleå tekniska universitet, Luleå University of Technology, Polish Academy of Sciences, Institute of Fundamental Technological Researeh, Chalmers University of Technology, Department of Structural Mechanics.
    Elfgren, Lennart
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Structural and Fire Engineering.
    Institutionen för Väg- och Vattenbýggnad. Årsberättelse 1993/94 - !994/951994Report (Other (popular science, discussion, etc.))
  • 6.
    Johansson, Bernt
    et al.
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Structural and Construction Engineering.
    Axelsson, Kennet B. E.
    Högskolan i Luleå, Luleå tekniska universitet, Luleå University of Technology.
    Klisinski, Marek
    Luleå tekniska universitet, Luleå University of Technology, Polish Academy of Sciences, Institute of Fundamental Technological Researeh.
    Grennberg, Torsten
    Luleå tekniska universitet.
    Almgren, Gunnar
    Luleå tekniska universitet.
    Lindqvist, Per-Arne
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Stillborg, Bengt
    Luleå tekniska universitet, Swedish Mineral Research Foundation, Sweden.
    Elfgren, Lennart
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Structural and Fire Engineering.
    Institutionen för Väg- och Vattenbyggnad. Verksamhetsberättelse 1992/93 - 1993/941993Report (Other (popular science, discussion, etc.))
  • 7.
    Johansson, Bernt
    et al.
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Structural and Construction Engineering.
    Grennberg, Torsten
    Luleå tekniska universitet.
    Almgren, Gunnar
    Luleå tekniska universitet.
    Lindqvist, Per-Arne
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Stillborg, Bengt
    Luleå tekniska universitet, Swedish Mineral Research Foundation, Sweden.
    Axelsson, Kennet B. E.
    Högskolan i Luleå, Luleå tekniska universitet, Luleå University of Technology.
    Klisinski, Marek
    Luleå tekniska universitet, Luleå University of Technology, Polish Academy of Sciences, Institute of Fundamental Technological Researeh.
    Vikström, Lars
    Luleå tekniska universitet.
    Forsman, Bo
    Luleå tekniska universitet.
    Elfgren, Lennart
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Structural and Fire Engineering.
    Department of Civil and Mining Engineering. Annual Report 1994-951995Report (Other (popular science, discussion, etc.))
  • 8. Johansson, Eva
    et al.
    Lindqvist, Per-Arne
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Sammanställning av metoder för beskrivning, provning och klassificering av berg2003Report (Other academic)
  • 9.
    Kou, S. Q.
    et al.
    Luleå University of Technology.
    Lindqvist, Per-Arne
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Tang, C. A.
    Northeastern University, Shenyang.
    Possible effects of heterogeneity on rock fragmentation1999In: Rock Fragmentation by Blasting: proceedings of the Sixth International Symposium for Rock Fragmentation by Blasting-FRAGBLAST-6, Johannesburg, South Africa, 8-12 August, 1999, Johannesburg: South African Institute of Mining and Metallurgy, 1999, p. 351-357Conference paper (Refereed)
  • 10.
    Kou, Shaoquan
    et al.
    Luleå University of Technology.
    Huang, Yi
    Luleå tekniska universitet.
    Tan, Xiangchun
    Luleå University of Technology.
    Lindqvist, Per-Arne
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Identification of the governing parameters related to rock indentation depth by using similarity analysis1998In: Engineering Geology, ISSN 0013-7952, E-ISSN 1872-6917, Vol. 49, no 3, p. 261-269Article in journal (Refereed)
    Abstract [en]

    This paper focuses on the indentation depth in rocks caused by a hemispherical indenter. The problem is approached by a combination of similarity methods with an artificial neural network. The similarity methods offer a profound understanding of the physical problem and help to identify the most important governing parameters or factors that reflect the essence of the rock indentation events, thus simplifying the target problem. The artificial neural network provides an advanced computing model, which allows more factors to be involved. The predictions obtained using this combined approach are in better agreement with the experimental results than predictions using other methods.

  • 11.
    Kou, Shaoquan
    et al.
    Luleå University of Technology.
    Kiu, Hongyuan
    Luleå University of Technology.
    Lindqvist, Per-Arne
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Tang, C.A.
    Center for Rock Instability & Seismicity Research, Northeastern University, Shenyang.
    Rock fragmentation mechanisms induced by a drill bit2004In: International Journal of Rock Mechanics And Mining Sciences, ISSN 1365-1609, E-ISSN 1873-4545, Vol. 41, no Suppl. 1, p. 527-532Article in journal (Refereed)
    Abstract [en]

    In most of the mechanical excavation methods the fundamental process is indentation of the rock by a bit. The present paper focuses on discussing how the rock is fragmented under the action of a drill bit. The discussions are mainly based on numerical modelling using the rock and tool interaction code (R-T2D) and taking rock heterogeneity into consideration. The simulated results concerning rock penetrations with one, two and multiple indenters are, however, compared with experiments available from the literature. The emphasis is put on discussion of the formation of side-cracks and crushed zones that constitute the major rock removal fractures. The agreement between numerical simulation and experimental observations are reasonably good. This reveals the mechanisms of crack initiation, propagation and coalescence induced by the action of button bits to form the rock fragmentation in a drilling process. The investigation can contribute not only to improving percussive drilling but also to understanding other rock fragmentation and comminution methods and equipment since indentation is also the fundamental process for them.

  • 12.
    Kou, Shaoquan
    et al.
    Luleå University of Technology.
    Lindqvist, Per-Arne
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Tan, Xiangchun
    Luleå University of Technology.
    Analytical and experimental investigation of rock indentation fracture1995In: Proceedings: 8. International Congress on Rock Mechanics : Tokyo, Japan, 1995 = Comptes-rendus / 8. Congrès International de Mécanique des Roches = Berichte / 8. Internationaler Kongress über Felsmechanik / International Society for Rock Mechanics / [ed] Toshio Fujii, Rotterdam: Balkema Publishers, A.A. / Taylor & Francis The Netherlands , 1995, Vol. 1, p. 181-184Conference paper (Refereed)
  • 13.
    Kou, Shaoquan
    et al.
    Luleå University of Technology.
    Lindqvist, Per-Arne
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Tang, C.A.
    Centre for Rockbursts and Induced Seismicity Research, Northeastern University, Shenyang, Liaoning.
    Xu, X. H.
    Centre for Rockbursts and Induced Seismicity Research, Northeastern University, Shenyang, Liaoning.
    Numerical simulation of the cutting of inhomogeneous rocks1999In: International Journal of Rock Mechanics And Mining Sciences, ISSN 1365-1609, E-ISSN 1873-4545, Vol. 36, no 5, p. 711-717Article in journal (Refereed)
    Abstract [en]

    In this study, the possible modes of crack initiation and propagation leading to chip formation in rock cutting are studied numerically by using a rock failure process analysis code referred to as RFPA. By using this approach, additional information is obtained on the tool-rock interaction and the failure mechanisms of rock under mechanical tools.

  • 14.
    Kou, Shaoquan
    et al.
    Luleå University of Technology.
    Liu, Hongyuan
    Luleå University of Technology.
    Lindqvist, Per-Arne
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Tang, C. A.
    Center for Rock Instability & Seismicity Research, Northeastern University, Shenyang.
    Xu, X. H.
    National Key Laboratory of Nonlinear Mechanics, Chinese Academy of Sciences, Beijing.
    Numerical investigation of particle breakage as applied to mechanical crushing: Part 2: Interparticle breakage2001In: International Journal of Rock Mechanics And Mining Sciences, ISSN 1365-1609, E-ISSN 1873-4545, Vol. 38, no 8, p. 1163-1172Article in journal (Refereed)
    Abstract [en]

    A numerical approach to interparticle breakage is applied using the rock failure process analysis code, RFPA2D. A 2D particle assembly in a container is first numerically simulated to obtain the fringe patterns of stress fields that resemble the photoelastic test. Then, in addition, the interparticle breakage of the particle assembly in a chamber is conducted. The chamber consists of a steel container and a steel platen for transferring the load, and contains 15 particles of arbitrary sizes and irregular shapes. A plane strain condition is assumed. The particle bed is loaded under form conditions, in which the size reduction and the applied force are a function of the displacement. The numerical results indicate that, during the crushing process, three principal regimes appear: (i) the elastic deformation regime, where each particle deforms elastically; (ii) the fragmentation regime, where the particle assembly is crushed in a particle-by-particle fashion; and (iii) the assembly hardening regime, where the densified assembly recovers a significant stiffness. The dominant mode of failure is at first splitting, which is more or less parallel to the loading direction, and then progressive crushing, which mainly depends on the confinement from the chamber walls. The analysis of the load–displacement curves of the assembly obtained from the simulations reveals a high undulating load plateau, which suggests a macro-ductile behaviour.

  • 15.
    Li, L
    et al.
    Center for Rock Instability & Seismicity Research, Northeastern University, Shenyang.
    Tang, C.
    School of Civil and Hydraulic Engineering, Dalian University of Technology.
    Tang, S.
    School of Civil and Hydraulic Engineering, Dalian University of Technology.
    Lindqvist, Per-Arne
    Damage coupled thermo-mechanical model for rock failure process and applications2006In: Acta Mechanica Sinica, ISSN 0567-7718, E-ISSN 0459-1879, Vol. 38, no 4, p. 505-513Article in journal (Refereed)
    Abstract [en]

    Based on the heterogeneous characteristics of rock at mesoscopic level, the thermo-mechanical (TM) coupled behavior during the failure process of rock subjected to thermal stress is analyzed with elastic damage mechanics and thermo-elastic theory. A mesoscopic TM coupling model, implemented in rock fracture process analysis (RFPA), is proposed, which can be used to study the damage and failure process, as well as elastic stress for the coupled TM rock problem. With the numerical model, the damage and associated mechanical properties evolution of mesoscopic structure in rocks subjected to TM loading can be analyzed. Numerical simulation is carried out to investigate the stability of the rock pillar in a hard rock laboratory. The numerically obtained stress field, failure pattern of pillar rock and associated acoustic emission (AE) events all agree well with the in-situ data, which shows that the proposed model is reasonable and effective, and may provide guides for the experiment design and associated applications

  • 16.
    Li, Lianchong
    et al.
    Research Center for Numerical Tests on Material Failure, Dalian University.
    Tang, Chunan
    Center for Rock Instability & Seismicity Research, Northeastern University, Shenyang.
    Lindqvist, Per-Arne
    Fracture Behavior in a Rock Pillar Subjected to Coupled Thermo-Mechanical Loading2006In: Key Engineering Materials, ISSN 1013-9826, E-ISSN 1662-9795, Vol. 324/325, p. 443-446Article in journal (Refereed)
    Abstract [en]

    Using RFPA code, analyses have been carried out to investigate the stability of a rock pillar in a experiment for nuclear waste repositories, the numerically obtained stress field, temperature distribution, failure pattern of the pillar rock and associated AE events are all agree well with the in-situ data. Minor fracture initiation may take place in the vicinity of the boreholes after heating. Heating induces minor spalling at central pillar wall for 0.5 m sections below the tunnel floor, but the area of spalling is found to be limited. The core of the pillar remains intact for stress conditions corresponding to 120 days of heating which not only prove that the proposed technique provides a powerfully alternative and effective approach for the study on thermal-mechanical-damage coupling mechanism but also provide meaningful guides for the experiment design and associated applications.

  • 17. Lindqvist, Per-Arne
    Belastningscykel hos dieseldrivna fordon under jord för renare avgaser: Delrapport 1: Dieseldrivna fordon i svenska gruvor1977Report (Other academic)
  • 18. Lindqvist, Per-Arne
    Belastningscykel hos dieseldrivna fordon under jord för renare avgaser: Delrapport 2: Lastmaskinernas användning1978Report (Other academic)
  • 19.
    Lindqvist, Per-Arne
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Energy consumption in disc cutting of hard rock1982In: Tunnelling '82: papers presented at the third international symposium, organized by the Institution of Mining and Metallurgy ... / [ed] M.J. Jones, London: The Institution of Mining and Metallurgy , 1982, p. 189-196Conference paper (Other academic)
  • 20. Lindqvist, Per-Arne
    FoU bergmaskiner: en kartläggning av forsknings- och utvecklingsbehov inom området bergmaskiner med huvudvikt på arbetsmiljö1976Report (Other academic)
  • 21.
    Lindqvist, Per-Arne
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Malmkännedom1987Report (Other academic)
  • 22.
    Lindqvist, Per-Arne
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Möjliga vägar att utveckla vibrationsanalys: slutrapport från UTC-projektet "Larmnivåer och felorsaker vid vibrationsövervakning"1998Report (Other academic)
  • 23.
    Lindqvist, Per-Arne
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Rock fragmentation by indentation and disc cutting: some theoretical and experimental studies1982Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    The main objective of the thesis is to increase the understanding of failure mechanisms of rock drilling and rock cutting methods in general, and rock boring by disc cutters in particular. The thesis consists of five separate papers. Paper A presents the theoretical elastic stress field of indexed indenters and some laboratory observations. A fracture mechanics calculation of crack length from disc cutters is described for the first time. Paper B deals with the behavior of crushed material beneath a penetrating tool. A laboratory investigation of the strength of crushed rock is made and the reconsolidation of crushed rock is evaluated. Paper C reports on in-situ indentation test in a scanning electron microscope. The continuous development of cracks is studied. Paper D presents a new theoretical model for side chipping, assuming tensile failure of the rock. The model is tested in the laboratory by full scale disc cutting tests. Paper E deals with energy-absorbing processes in disc cutting. A classification of energy forms is submitted and first order energy forms measured in a full scale disc cutting experiment. The thesis outlines the essential features of the elastic stress field of indexed indenters. Laboratory investigations have verified the existence of subsurface cracks predicted by stress fields. The evolution of such cracks is qualitatively understood. The tensile side chipping model was tested with satisfactory results. In disc cutting practice the process of groove formation should be separated from side chipping. This will result in less formation of unnecessary long cracks, lower energy consumption, better utilization of available torque and thrust, and decreasing vibrations. Future development of cutters should take advantage of long subsurface cracks, possibly resulting in a dramatic increase in capacity.

  • 24.
    Lindqvist, Per-Arne
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Some comments on the standardization of boreability and cuttability tests1983Report (Other academic)
  • 25.
    Lindqvist, Per-Arne
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Spår- och brytrulle för fullborrning1983Report (Other academic)
  • 26.
    Lindqvist, Per-Arne
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Stress fields and subsurface crack propagation of single and multiple rock indentation and disc cutting1984In: Rock Mechanics and Rock Engineering, ISSN 0723-2632, E-ISSN 1434-453X, Vol. 17, no 2, p. 97-112Article in journal (Refereed)
    Abstract [en]

    Indentation stress fields of one- and two-point loads applied on an ideal elastic half-space are presented. Laboratory observations, although few, are in surprisingly good agreement with long median and cone-type tensile cracks predicted by normal principal stresses. Results indicate that simultaneous loading by multiple indenters offers a possibility partly to control the direction and length of such cracks. This suggests the development of new cutter configurations with a possible increase in efficiency, as compared with present rock boring and rock cutting practice. A simple fracture mechanics calculation of the length of subsurface cracks is performed by applying indentation fracture studies of ceramics. Results demonstrate the influence of material parameters such as fracture surface energy, hardness and elastic constants.

  • 27. Lindqvist, Per-Arne
    et al.
    Johansson, Eva
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Bergets inverkan på praktisk produktionsoptimering2005Report (Other academic)
  • 28. Lindqvist, Per-Arne
    et al.
    Johansson, Eva
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Kartläggning av produktionsoptimering: studiebesök och fallstudier2004Report (Other academic)
  • 29. Lindqvist, Per-Arne
    et al.
    Johansson, Eva
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Metoder för design och simulering vid produktionsoptimering2005Report (Other academic)
  • 30. Lindqvist, Per-Arne
    et al.
    Kou, Shao-Quan
    Luleå tekniska universitet.
    Tre indikatorer för praktisk produktionsoptimering: litteraturstudie och förslag till forskningsprogram2005Report (Other academic)
  • 31.
    Lindqvist, Per-Arne
    et al.
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Lai, Hai-Hui
    Institute of Mining and Metallurgy, Changsha.
    Behaviour of the crushed zone in rock indentation1983In: Rock Mechanics and Rock Engineering, ISSN 0723-2632, E-ISSN 1434-453X, Vol. 16, no 3, p. 199-207Article in journal (Refereed)
    Abstract [en]

    Micro hardness tests of compressed crushed rock indicate that the plastic behavior of powder of ductile rocks, in this case a marble, resembles that of intact rock, irrespective of the deformation history of the crushed material. The inelastic deformation of such rocks under a bit can then be treated by plasticity theory. The deformation properties of crushed material of granite and sandstone are of a brittle nature.

  • 32.
    Lindqvist, Per-Arne
    et al.
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Lai, Hai-Hui
    Central South Institute of Mining and Metallurgy, Changsha, Hunan.
    Alm, Ove
    Luleå University of Technology.
    Indentation fracture development in rock continuously observed with scanning electron microscope1984In: International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, ISSN 0148-9062, E-ISSN 1879-2073, Vol. 21, no 4, p. 165-182Article in journal (Refereed)
    Abstract [en]

    Indentation tests observed in a scanning electron microscope (SEM) using a sharp and a truncated wedge in three different rocks are reported. By indenting at the edge of one surface and scanning the neighboring surface perpendicular to the direction of loading, it was possible to study the continuous development of cracks throughout the tests. Cracks initiated mainly at the edge and corners of wedges but initiation in the interior of the rock was also observed. Crack initiation and crack paths observed in all rocks are in good agreement with assumed theoretical elastic stress fields, although the nature of the fractures is greatly influenced by different material properties such as grain size, cleavage planes and grain bonding. Recorded force-displacement curves allowed distinction between different fracture processes.

  • 33.
    Lindqvist, Per-Arne
    et al.
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Magnusson, Leif
    Luleå tekniska universitet.
    Byggteknik i berg: byggdesign och byggmetoder för djupförvar av använt kärnbränsle1994Report (Other academic)
  • 34.
    Lindqvist, Per-Arne
    et al.
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Magnusson, Leif
    Luleå tekniska universitet.
    Deep geological disposal of spent nuclear fuel: state of knowledge prior to selection of repositiory site summary, conclusions and assessments1994Report (Other academic)
  • 35.
    Lindqvist, Per-Arne
    et al.
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Magnusson, Leif
    Luleå tekniska universitet.
    Djupförvaring av använt kärnbränsle: kunskapsläget inför val av lokaliseringsort1994Report (Other academic)
  • 36.
    Lindqvist, Per-Arne
    et al.
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Rånman, Karl-Erik
    Luleå tekniska universitet.
    Mechanical rock fragmentation: chipping under a disc cutter1980Report (Other academic)
  • 37.
    Liu, H. Y.
    et al.
    Luleå University of Technology.
    Kou, S. Q.
    Luleå University of Technology.
    Lindqvist, Per-Arne
    Tang, C. A.
    Dalian University of Technology.
    Numerical modelling of the heterogeneous rock fracture process using various test techniques2007In: Rock Mechanics and Rock Engineering, ISSN 0723-2632, E-ISSN 1434-453X, Vol. 40, no 2, p. 107-144Article in journal (Refereed)
    Abstract [en]

    A series of numerical tests including both rock mechanics and fracture mechanics tests are conducted by the rock and tool (R-T2D) interaction code coupled with a heterogeneous masterial model to obtain the physical-mechanical properties and fracture toughness, as well as to simulate the crack initiation and propagation, and the fracture progressive process. The simulated results not only predict relatively accurate physical-mechanical parameters and fracture toughness, but also visually reproduce the fracture progressive process compared with the experimental and theoretical results. The detailed stress distribution and redistribution, crack nucleation and initiation, stable and unstable crack propagation, interaction and coalescence, and corresponding load-displacement curves can be proposed as benchmarks for experimental study and theoretical research on crack propagation. It is concluded that the heterogeneous material model is reasonable and the R-T2D code is stable, repeatable and a valuable numerical tool for research on the rock fracture process.

  • 38.
    Liu, H.I.
    et al.
    School of Engineering, University of Tasmania.
    Lindqvist, Per-Arne
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Åkesson, U.
    CBI Swedish Cement and Concrete Institute, Borås.
    Kou, S.Q.
    Institute of Mechanics, Chinese Academy of Sciences, Beijing.
    Lindqvist, J.E.
    CBI Swedish Cement and Concrete Institute, Borås.
    Characterization of rock properties using texture-based modelling: a geometallurgical approach2011In: Conference in Mineral Engineering: Luleå, 8-9 February 2011 / [ed] Johanna Alatalo, Luleå: Luleå tekniska universitet, 2011Conference paper (Other academic)
  • 39.
    Liu, Hongyuan
    et al.
    Luleå University of Technology.
    Kou, Shaoquan
    Luleå University of Technology.
    Lindqvist, Per-Arne
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Numerical simulation of the fracture process in cutting heterogeneous brittle material2002In: International journal for numerical and analytical methods in geomechanics (Print), ISSN 0363-9061, E-ISSN 1096-9853, Vol. 26, no 13, p. 1253-1278Article in journal (Refereed)
    Abstract [en]

    The process of cutting homogeneous soft material has been investigated extensively. However, there are not so many studies on cutting heterogeneous brittle material. In this paper, R-T2D (Rock and Tool interaction), based on the rock failure process analysis model, is developed to simulate the fracture process in cutting heterogeneous brittle material. The simulated results reproduce the process involved in the fragmentation of rock or rock-like material under mechanical tools: the build-up of the stress field, the formation of the crushed zone, surface chipping, and the formation of the crater and subsurface cracks. Due to the inclusion of heterogeneity in the model, some new features in cutting brittle material are revealed. Firstly, macroscopic cracks sprout at the two edges of the cutter in a tensile mode. Then with the tensile cracks releasing the confining pressure, the rock in the initially high confining pressure zone is compressed into failure and the crushed zone gradually comes into being. The cracked zone near the crushed zone is always available, which makes the boundary of the crushed zone vague. Some cracks propagate to form chipping cracks and some dip into the rock to form subsurface cracks. The chipping cracks are mainly driven to propagate in a tensile mode or a mixed tensile and shear mode, following curvilinear paths, and finally intersect with the free surface to form chips. According to the simulated results, some qualitative and quantitative analyses are performed. It is found that the back rake angle of the cutter has an important effect on the cutting efficiency. Although the quantitative analysis needs more research work, it is not difficult to see the promise that the numerical method holds. It can be utilized to improve our understanding of tool-rock interaction and rock failure mechanisms under the action of mechanical tools, which, in turn, will be useful in assisting the design of fragmentation equipment and fragmentation operations.

  • 40.
    Liu, Hongyuan
    et al.
    Luleå University of Technology.
    Kou, Shaoquan
    Luleå University of Technology.
    Lindqvist, Per-Arne
    Numerical studies on the inter-particle breakage of a confined particle assembly in rock crushing2005In: Mechanics of materials (Print), ISSN 0167-6636, E-ISSN 1872-7743, Vol. 37, no 9, p. 935-954Article in journal (Refereed)
    Abstract [en]

    Understanding rock crushing mechanisms may provide an efficient key to better fragmentation efficiency. In this paper, firstly the fracture processes of a rock specimen under uniaxial and triaxial compressions are simulated using the rock and tool interaction (R–T2D) code and compared with the results from experimental observations in literatures. It is found that, with increasing confinement, the fracture process is more progressive and the failure mechanism gradually changes from axial splitting to shear fracture. Then the inter-particle breakage process in a particle bed under confined conditions is numerically investigated from a mechanics point of view. The results show that when the particle breaks depends on the strength criterion, how it is broken depends on the stress distribution and redistribution, and where it is broken depends on the heterogeneous distribution in the particle. It is found that, irrespective of the particle shape or particle bed arrangement, the fragmentation starts from the particles which are loaded in quasi-uniaxial compression. The resulting fragmentation is usually axial splitting between the two highest stressed loading points. After that, the particles which are loaded at first in quasi-triaxial compression, because of the confinement from the neighbouring particles, the loading plate or the container wall, fail progressively. Depending on the location of the loading points, small fragments are torn off at the loading points with a large piece preserved. In the final stage, the local crushing at the highest stressed contact points becomes an important failure mechanism. Through this study, it is concluded that the R–T2D code can capture the features of the inter-particle breakage process, and a better qualitative understanding of the physics and mechanics of deformation and breakage is gained.

  • 41.
    Liu, Hongyuan
    et al.
    Luleå tekniska universitet.
    Kou, Shaoquan
    Luleå tekniska universitet.
    Lindqvist, Per-Arne
    Lindqvist, Jan Erik
    Åkesson, Urban
    Microscope rock texture characterization and simulation of rock aggregate properties2005Report (Other academic)
    Abstract [en]

    The literature review on the relationship between the textural properties and mechanical properties of rock aggregates indicates that most studies investigated the relationship in two separate processes, i.e. microscope observations and mechanical tests, and then correlate the mechanical properties with one of textural properties indirectly using various regression models.Samples of three granites with similar mineral content but varying mechanical properties are investigated by microscope texture quantification including image analysis followed by rock mechanics testing and rock aggregate testing in the laboratory. Computer simulation of rock mechanics properties, of strength of single aggregate particles and fracture of multiple particles in a cylindrical chamber (DSC test) is then made. Finally computer simulations are compared of with tumbling mill tests (LA test) through results from previous research.This study uses numerical modelling as a main tool to directly investigate the relationships, i.e. from the physical mechanisms' point of view and taking major textural properties into consideration. Two main modelling methods, i.e. microstructural modelling and micromechanical modelling are implemented. In the microstructural modelling, the numerical simulation model is built on the basis of rock microstructure. In the micromechanical modelling, the model is constructed on the basis of the Weibull theory.The modelled results from single particle tests of three granites, i.e. Ävja, LEP and Vändle under BTS, point-to-point, plane-to-plane, point-to-plane and multiple-point loading conditions using microstructural modelling and micromechanical modelling show that Ävja is weaker than LEP and Vändle in terms of the aggregate tensile strength and applied work. The microstructural modelling also reveals that LEP is weaker than Vändle but the micromechanical modelling indicates that LEP and Vändle have similar mechanical properties.From this work it is concluded that microscope texture quantification and computer simulation is a promising approach to analyse mechanical properties of rock aggregates. Numerical modelling of the DSC test shows the potential to simulate multi particle chamber compression tests for assessment of rock aggregate quality. In general, the texture properties work together to influence the mechanical properties of rock aggregates. Computer simulation using a heterogeneous material model provides a valuable tool to investigate the relationship between the textural properties and mechanical properties of rock aggregates by taking main textural properties into consideration. In particular, for the three rocks in this study, micro crack size distribution, grain perimeter and grain size show strong correlations with the mechanical properties, e.g. for DSC strength: cracks and grain size negatively affect the mechanical properties but the perimeter positively influences the mechanical properties.

  • 42.
    Liu, Hongyuan
    et al.
    Luleå University of Technology.
    Kou, Shaoquan
    Luleå University of Technology.
    Lindqvist, Per-Arne
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Tang, C. A.
    Luleå University of Technology.
    Numerical simulation of the rock fragmentation process induced by indenters2002In: International Journal of Rock Mechanics And Mining Sciences, ISSN 1365-1609, E-ISSN 1873-4545, Vol. 39, no 4, p. 491-505Article in journal (Refereed)
    Abstract [en]

    Rock fragmentation processes induced by single and double indenters were examined by a numerical method. The simulated results reproduce the progressive process of rock fragmentation in indentation. Rock deforms elastically at the initial loading stage. Then tensile cracks are initiated around the two corners of the truncated indenter and propagate in the well-known conical Hertzian manner. The rocks immediately under the indenter are in a highly tri-axial stress state, and some of them fail in the ductile cataclastic mode with the stress satisfying the ductile failure surface of the double elliptic strength criterion. With the tensile cone cracks and ductile cataclastic failure releasing the confining pressure, the rocks under the indenter are compressed into failure and the crushed zone gradually comes into being. With increasing loading displacement, the re-compaction behaviour of the crushed zone occurs. Side cracks initiated from the crushed zone or bifurcated from cone cracks are driven by tensile stress associated with the crushed zone to propagate in a curvilinear path and finally intersect with the free surface to form chips. It is pointed out that the curvilinear path is caused by heterogeneity. The simulated force-penetration curve is in fact the indication of the propagation of cracks, the crushing of microstructural grains and the formation of chips. It is found that the confining pressure has an important influence on the indentation results. With decreasing confining pressure, there is a decrease in the indentation strength and a change in the rock failure process from the formation of rock chips to a vertically axially splitting failure. The simulated fragmentation process in the double indenter test reproduces the side cracks, which are induced by two indenters, propagate, interact and finally coalesce, chipping the rock between the indenters. The line spacing is an important factor that affects the fragmentation efficiency in multiple indenter tests. It is pointed out that simultaneous loading with multiple indenters with an appropriate line spacing seems to provide a possibility of forming larger rock chips, controlling the direction of subsurface cracks and consuming a minimum total specific energy. According to the simulated results, it is believed that the numerical simulation method will contribute to an improved knowledge of rock fragmentation in indentation, which will in turn help to enhance mining and drilling efficiency through the improved design of mining tools and equipment.

  • 43.
    Liu, Hongyuan
    et al.
    Luleå University of Technology.
    Kou, Shaoquan
    Luleå University of Technology.
    Lindqvist, Per-Arne
    Tang, C.A.
    Center for Rock Instability & Seismicity Research, Northeastern University, Shenyang.
    Numerical simulation of shear fracture (mode II) in heterogeneous brittle rock2004In: International Journal of Rock Mechanics And Mining Sciences, ISSN 1365-1609, E-ISSN 1873-4545, Vol. 41, no Suppl. 1, p. 14-19Article in journal (Refereed)
    Abstract [en]

    The fracture process of a heterogeneous brittle rock in the shear-box test is numerically investigated by means of the rock and tool interaction code (R-T2D). On the basis of the simulated results, the mode II fracture toughness is calculated, which is KIIC =7.72MPa root m, and the influence of heterogeneity and confinement on the formation and characteristics of shear fracture is discussed. It is found that with the confinement increasing, the fracture mechanisms in the shear-box test of heterogeneous brittle rock change from mixed tensile and shear failure but are dominated with tensile failure to dominant shear failure. It is concluded that the shear-box test under a confined condition is favourable for creating a condition for mode II fracture and a suitable method for measuring the mode II fracture toughness.

  • 44.
    Liu, Hongyuan
    et al.
    School of Engineering, University of Tasmania.
    Lindqvist, Per-Arne
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Åkesson, Urban
    CBI Swedish Cement and Concrete Institute, Borås.
    Kou, Shaoquan
    Institute of Mechanics, Chinese Academy of Sciences, Beijing.
    Lindqvist, Jan-Erik
    CBI Swedish Cement and Concrete Institute, Borås.
    Characterisation of rock aggregate breakage properties using realistic texture-based modelling2012In: International journal for numerical and analytical methods in geomechanics (Print), ISSN 0363-9061, E-ISSN 1096-9853, Vol. 36, no 10, p. 1280-1302Article in journal (Refereed)
    Abstract [en]

    Realistic texture-based modelling methods, that is microstructural modelling and micromechanical modelling, are developed to simulate the rock aggregate breakage properties on the basis of the rock actual microstructure obtained using microscopic observations and image analysis. The breakage properties of three types of rocks, that is Avja, LEP and Vandle taken from three quarries in Sweden, in single aggregate breakage tests and in inter-aggregate breakage tests are then modelled using the proposed methods. The microstructural modelling directly integrates the microscopic observation, image analysis and numerical simulation together and provides a valuable tool to investigate the mechanical properties of rock aggregates on the basis of their microstructure properties. The micromechanical modelling takes the most important microstructure properties of rock aggregates into consideration and can model the major mechanical properties. Throughout this study, it is concluded that in general, the microstructure properties of rock aggregate work together to affect their mechanical properties, and it is difficult to correlate a single microstructure property with the mechanical properties of rock aggregates. In particular, for the three types of rock Avja, LEP and Vandle in this study, crack size distribution, grain size and grain perimeter (i.e. grain shape and spatial arrangement) show good correlations with the mechanical properties. The crack length and the grain size negatively affect the mechanical properties of Avja, LEP and Vandle, but the perimeter positively influences the mechanical properties. Besides, the modelled rock aggregate breakage properties in both single aggregate and inter-aggregate tests reveal that the aggregate microstructure, aggregate shape and loading conditions influence the breakage process of rock aggregate in service. For the rock aggregate with the same microstructure, the quadratic shape and good packing dramatically improve its mechanical properties. During services, the aggregate is easiest to be fragmented under point-to-point loading condition, and then in the sequence of multiple-point, point-to-plane and plane-to-plane loading conditions

  • 45.
    Liu, Hongyuan
    et al.
    Luleå University of Technology.
    Roquete, Margarida
    Luleå University of Technology.
    Kou, Shaoquan
    Luleå University of Technology.
    Lindqvist, Per-Arne
    Characterization of rock heterogeneity and numerical verification2004In: Engineering Geology, ISSN 0013-7952, E-ISSN 1872-6917, Vol. 72, no 1, p. 89-119Article in journal (Refereed)
    Abstract [en]

    On the basis of microstructure analysis and image analysis, rock heterogeneity is modelled by the rock and tool (R-T2D) interaction code according to homogenisation theory. The simulated results predict very well the non-linear stress–strain behaviour and the progressive fracture process of heterogeneous rock material. It is found that the weak parts and subsequent fractures before localization represent an obvious statistically uniform characteristic. Therefore, a statistical method is used to model rock heterogeneity. The results from the statistical modelling are in surprisingly good agreement with those from the homogenisation modelling. Considering the research scale, the rock heterogeneity is characterized better by the Weibull statistical method as a few characteristic parameters: the homogeneous index and the elemental seed parameters of the R-T2D finite element network. Finally, a series of numerical experiments are conducted to validate that the characterization of rock heterogeneity is reasonable and feasible, and that the R-T2D code is stable, repeatable and a valuable tool to research the fracture process of heterogeneous material.

  • 46.
    Liu, H.Y.
    et al.
    University of Sydney.
    Kou, S.O.
    Luleå tekniska universitet.
    Lindqvist, Per-Arne
    Numerical studies on bit-rock fragmentation mechanisms2008In: International Journal of Geomechanics, ISSN 1532-3641, E-ISSN 1943-5622, Vol. 8, no 1, p. 45-67Article in journal (Refereed)
    Abstract [en]

    The rock fragmentation process induced by a single button-bit, two neighboring button-bits, and multiple button-bits are numerically studied using the rock and tool interaction code (R-T2D). Through this study, a better understanding of the bit-rock fragmentation mechanisms is gained. It is found that side crack is initiated from the crushed zone or bifurcated from Hertzian crack to propagate approximately parallel to the free rock surface but in a curvilinear path driven by the tensile stress associated with the expansion of the crushed zone during the loading process. In the crushed zone, the mechanism of side crack is mixed tensile and shear failure, but outside the crushed zone, the dominant mechanism of side crack is tensile failure. A semiempirical and semitheoretical relationship among the side crack length, the drilled rock property, and the drilling force is formulated to approximately predict the side crack length. In the simultaneous loading, the interaction and coalescence of side cracks induced by the neighboring button-bits with an optimum line spacing enable formation of largest rock chips, control of the direction of subsurface cracks and a minimum total specific energy consumption. A formula is derived to determine the optimum line spacing on the basis of the drilled rock properties, the diameter and shape of the button-bit, and the drilling conditions. In the rock fragmentation by multiple button-bits, most of the rock between the neighboring button-bits is chipped as a result of the coalescence of side cracks. In the remaining rock, the intensely crushed zones and significant extensional cracks are observed adjacent to the sidewall and the inside of the borehole. Fragment side distribution shows more than 80% of the fragments are fines in the crushed zones as well as the cracked zones, the large fragments be indeed observed, which are the big chips caused by the coalescence of side cracks.

  • 47.
    Liu, H.Y.
    et al.
    Luleå tekniska universitet.
    Kou, S.Q.
    Luleå tekniska universitet.
    Lindqvist, Per-Arne
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Tang, C.A.
    Center for Rock Instability & Seismicity Research, Northeastern University, Shenyang.
    Numerical studies on the failure process and associated microseismicity in rock under triaxial compression2004In: Tectonophysics, ISSN 0040-1951, E-ISSN 1879-3266, Vol. 384, no 1-4, p. 149-174Article in journal (Refereed)
    Abstract [en]

    In this paper, firstly the mesoscopic elemental mechanical model for elastic damage is developed and implemented into the rock and tool interaction code (R-T (super 2D) ). Then the failure processes of a heterogeneous rock specimen subjected to a wide variety of confining pressures (0-80 MPa) are numerically investigated using the R-T (super 2D) code. According to the simulated results, on the one hand, the numerical simulation reproduced some of the well-known phenomena observed by previous researchers in triaxial tests. Under uniaxial compression, rock failure is caused by a combination of axial splitting and shearing. Dilatancy and a post-failure stage with a descending load bearing capacity are the prominent characteristics of the failure. As the confining pressure increases, the extension of the failed sites is suppressed, but the individual failure sites become dense and link with each other to form a shear fracture plane. Correspondingly, the peak strength, the residual strength and the shear fracture plane angle increase, but the brittleness decreases. When the confining pressure is high enough, the specimen behaves in a plastic manner and a narrow shear fracture plane leads to its failure. The prominent characteristics are volume condensation, ductile cataclastic failure, and a constant load bearing capacity with increasing strain. On the other hand, the numerical simulation revealed some new phenomena. The highest microseismicity events occur in the post-failure stage instead of the maximal stress, and most of the microseismicity energies are released in the failure localization process. As the confining pressure increases, the microseismicity events in the non-linear deformation stage increase dramatically and the ratio between the energies dissipated at the non-linear deformation stage and those dissipated in the whole loading process increases correspondingly. Therefore, it is concluded that the developed mesoscopic elemental mechanical model for elastic damage is able to reproduce accurately the failure characteristics in loading rock specimens under triaxial conditions, and the numerical modelling can furthermore obtain some new clarifications of the rock fracture process.

  • 48.
    Miskovsky, Karel
    et al.
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering.
    Duarte, M. Taborda
    Luleå tekniska universitet.
    Kou, Shaoquan
    Luleå University of Technology.
    Lindqvist, Per-Arne
    Influence of the mineralogical composition and textural properties on the quality of coarse aggregates2004In: Journal of materials engineering and performance (Print), ISSN 1059-9495, E-ISSN 1544-1024, Vol. 13, no 2, p. 144-150Article in journal (Refereed)
    Abstract [en]

    To evaluate the influence of the petrographic variables on the quality of coarse aggregates consisting of granitoid (granite to tonalite) rocks, 17 samples selected from the Swedish part of the Baltic shield have been studied concerning their petrographic properties, for example, mineral composition, grain size, grain boundaries, and the frequency of micro-cracks. All of the samples selected also have been studied in mechanical tests used to evaluate the quality of aggregates in Sweden. The quality has been determined by means of flakiness, impact value, abrasion value I, and abrasion value II. An analysis of the influence of the mineral composition and textural properties on the aggregate quality has been performed using statistical correlation and linear models. The results indicate that an increasing content of feldspar negatively influences the strength against impact, while an increasing content of mica (tested to 35 vol.%) combined with a diminishing grain size and more irregular grain boundaries has a positive influence on the resistance of granitoids to mechanical impact. Abrasion value II seems to be mainly influenced negatively by an increasing frequency of micro-cracks. The practical implementation of the results is suggested.

  • 49.
    Miskovsky, Karel
    et al.
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering.
    Duarte, Margrida Taborda
    Kou, S.Q
    Luleå tekniska universitet.
    Lindqvist, Per-Arne
    Influence of the mineralogical composition and textural properties on the quality of coarse aggregates2007In: 2007 General Assembly of the European Geosciences Union, Vienna (Austria), 15-20 Apr 2007, European Geosciences Union (EGU), 2007Conference paper (Other academic)
  • 50.
    Rai, P.
    et al.
    Department of Mining Engineering, Indian Institute of Technology (BHU), Varanasi.
    Schunnesson, Håkan
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Mining and Geotechnical Engineering.
    Lindqvist, Per-Arne
    Kumar, Uday
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Operation, Maintenance and Acoustics.
    An Overview on Measurement-While-Drilling Technique and its Scope in Excavation Industry2015In: Journal of The Institution of Engineers (India): Series D, ISSN 2250-2122, Vol. 96, no 1, p. 57-66Article in journal (Refereed)
    Abstract [en]

    Measurement-while-drilling (MWD) aims at collecting accurate, speedy and high resolution information from the production blast hole drills with a target of characterization of highly variable rock masses encountered in sub-surface excavations. The essence of the technique rests on combining the physical drill variables in a manner to yield a fairly accurate description of the sub-surface rock mass much ahead of following downstream operations. In this light, the current paper presents an overview of the MWD by explaining the technique and its set-up, the existing drill–rock mass relationships and numerous on-going researches highlighting the real-time applications. Although the paper acknowledges the importance of concepts of specific energy, rock quality index and a couple of other indices and techniques for rock mass characterization, it must be distinctly borne in mind that the technique of MWD is highly site-specific, which entails derivation of site-specific calibration with utmost care.

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