• Expected prior knowledge: Lectures: Introduction to Mathematical Analysis, Statics and Strength of Materials.
  
  
• Study Goal: Presentation of foundations of Theory of Elasticity and its application in Rock and Soil Mechanics (The lecture will be delivered in index notation). Introduction of fundamental concepts of rock and soil mechanics and their application in surface and underground mining.
  
  
• Course contents: 
  Theory of Rock Mechanics
  1. Frame of axes Cartesian coordinates. Einstein summation convention. Kroecker delta. Permutation symbol. Relationship e – δ.
  2. State of strain. Material and space coordinate. Green, Almansy and Couchy strain tensors. Gradient matrix. Geometric interpretation of infinitesimal strain components.
  3. Spherical and deviatoric tensors of state of strain. Principal strains and principal axes of strain tensor. Strain tensor invariants. Tensor of principal axes. Capability equations.
  4. State of stress. Stress vector and stress tensor. Couchy formula. Coordinate transformations for stresses. Formal definition of a tensor. Hydrostatic and stress deviation tensor.
  5. Normal and shear stresses. Principal stresses and principal axes of stress tensors and stress deviation tensors. Invariants of stress and stress deviation tensors. Octahedral stresses. Intensity of stress tensor. Mohr circle of stress components.
  6. Linear elasticity. General Hooke law. Hooke law for Isotropic materials. Stress – strain deviatoric relationship. Hydrostatic stress versus dilatation formula. Relationship between different elastic module.
  7. Elastic strain energy expressed by stress and strain tensor components. Solving theory of elasticity boundary problems using displacement approach. Navier-Stoke’s equation.
  8. Classical strength criteria. Effective stresses.
  9. Coulomb- Mohr strength criterion. Safety factor.
  10. Plane stress and plane strain problems of theory of elasticity. Solving theory of elasticity boundary problems using stress approach. Airy function. Biharmonic polynomials. Airy function In polar coordinate. General form of Airy function.
  11. Introduction to Finite Element Method.
  12. Description of Phases code interface.
  13. Simple example FEM calculation.

Theory of Soil Mechanics
1. Soil classification.
2. Modeling of soil and rock behaviour.
3. Effective stresses.
4. Water flow.
5. Bearing capacity of foundation.
6. Atteberg Limits and compaction characteristic of soil.

Practice of Rock Mechanics
1. Rock mass properties.
2. Rock mass classification.
3. In-situ stresses.
4. Methods for stress analysis.
5. Rock mass discontinuities and their strength.
6. Slope stability problems and rock fall hazard.
7. Rock bolts and cables in rock engineering.
8. Pillar strength and its importance in room-and-pillar mining.
9. Floor strata behavior in room-and-pillar mining.
10. Interaction of roof, pillar and floor.
11. Surface subsidence due to underground mining.
12. Structures resistance against earthquake and mining related motion.
13. Pillar strength and its importance in room-and-pillar mining.
14. Structures resistance against earthquake and mining related motion.
15. Application of Geomechanics in underground mining.

• Expected prior knowledge: Mathematical Statistics, Fundamentals of Geology and Mineral Deposits.
  
  
• Study Goals: Developing basic skills in computer modelling of 3-D objects. Introduction of the principles of digital modelling of typical geological structures. Introduction to the methods of deposit parameters estimation and resources evaluation.
  
  
• Course Contents: 
  1. Methods of creating, editing, managing and presenting of 3-D objects for the needs of modelling geological structures.
  2. Building of digital 3-D models of geological structures on the basis of geological interpretation. Analysis of developed models.
  3. Introduction to estimation methods of deposit parameters.
  4. Principles of geostatistics. Kriging estimators.
  5. Geostatistical modelling of the selected deposit parameters.
  6. Resources evaluation.
  
  The modelling is supported by the specialized, three-dimensional software (Datamine or Geovariances) which provides the suitable software environment. The final project is presented both in the form of 3-D models and reports.

• Expected prior knowledge: Probability and statistical models. Standard office applications for Windows.
   
• Study Goals: The course combines two groups of topics: basics of mineral economics and financial management and introduction to project management.

  Part A: The purpose of the course is to introduce the concept of time value of money and present the methods used to evaluate investment projects. Different techniques are illustrated by examples and case studies. The range of application as well as the advantages and disadvantages of each method are discussed. The issues of inflation and risk analysis are included.
  Part B: Introduction to project management basic concepts, methods and tools. Presentation of given project management areas: Project scope management, Project time management, Project cost management, Project risk management. Project planning, scheduling and control using Microsoft Project. Presentation of the issues of effective communication in project teams, group behaviour and leadership.

• Course Contents:
  Mineral Economics and Financial Management
  1. Supply and demand, equilibrium price, changes in demand and supply.
  2. Stock and commodity markets used by mineral industries.
  3. Costs in economics and in accounting. Cost and money outflow. Relevant cost, incremental cost, marginal cost, alternative cost. Short-term decision making in mining.
  4. Costs as the subject of cost accounting, different systems of cost accounting Different methods of cost data presentation (by types, divided into direct and indirect costs). Cost allocation.
  5. Variable and fixed costs. Break even point. Cost-volume –profit analysis.
  6. Basics of financial accounting. Income statement and cash flow statement. Balance sheet. Working capital. Examples of financial statements of mining companies.
  7. Financial ratio analysis. Liquidity, profitability, activity and debt ratios. Calculation and analysis of financial ratios of mining companies. Financial and operating leverage.
  8. The concept of time value of money. Computation of future and present value of money by means of spreadsheet functions.
  9. Basics of capital budgeting. Evaluation of different methods. Computation by means of Excel-functions.
  10. Examples of mineral projects evaluation.
  11. The concept of risk and return. Quantification of risk.
  12. Risk analysis in project evaluation: sensitivity analysis, scenario analysis, other methods.
  

Project management
1. Basic concepts (process, project, project management, management by projects, critical factors for project success, competences).
2. Preparing and initiation of the project. Project analysis (project environment, stakeholders, project objectives).
3. Planning and estimating of the project.
4. Project phases and life cycle.
5. Project organization.
6. Project scope management.
7. Planning of activities, resources and costs.
8. Project risk management.
9. Project monitoring.
10. Quality management. Change control.
11. Project communications. Project closing.
12. Project management methodologies.

Communication and Leadership in Project Management
1. Issues of understanding communication. Definitions. Models (Schramm model, Berlo’s SMCR (source, message, channel, receiver) model, McCroskey model, Reusch and Bateson model, Westley-MacLean model).
2. Conflict.Sources of conflicts.Kilmann and Thomas classification of conflict. Kilmann and Thomas test. Different styles of conflict solving. Roles of conflict in group development.
3. Team roles.Team roles Belbin perspective. Discussion group roles. Effective managerial behaviour in the context of team roles.
4. Leadership.Hersey and Blanchard theory. Black and Mouton approach to leadership. Fiedler theory and his Least Preferred Coworker Scale. Situational leadership self-assessment.
5. Summary.Effective managerial behaviour from the different contexts.

• Expected prior knowledge:
  Knowledge of physics to a level which is necessary to understand and describe phenomena and physical fields occurring in the geosphere.
  Knowledge of mathematic analysis and algebra to a level necessary for the understanding of mathematical issues in engineering.
  Knowledge of basic issues related to soil mechanics.
  Knowledge of basic issues related to rock mechanics.
  Knowledge of basic issues related to mining and mining technology.
  Knowledge of basic issues related to mineral deposit geology occurring in the lithosphere of the Earth.
  Knowledge of issues related to the identification and exploration of mineral deposits occurring in the lithosphere of the Earth.
  Knowledge of basic physical and mechanical properties of rocks.
  
  
• Study Goal:
  To introduce students with the nature and subject matter of descriptive and applied geophysics studies and also the basic physical properties of rocks, phenomena and physical fields occurring in the geosphere.
  To introduce students to the physical and geological basics of methods of applied geophysics.
  To introduce students to surface and hole geophysical methods used to identify and search for mineral deposits.
  To familiarise students with apparatus, equipment and methodology of field research in surface seismic, gravimetric, electrometric, radiometry and magnetometry.
  To familiarise students with issues and problems associated with geophysical measurements and apparatus in boreholes.
  To familiarise students with the basics of descriptive seismology, aero-geophysics, marine geophysics and satellite techniques in geophysics.
  To introduce students to the issues and problems associated with geophysical methods used in underground and open-pit mining in order to monitor both natural and mining hazards.
  To familiarise students with methods of processing and interpretation based on geophysical field research.
  To be skilled in carrying out tests using the magnetometer method.
  To be skilled in processing and interpreting, at a basic level, results of geophysical field research.
  
  
• Course contents:
  Lecture
  The scope of the lecture, condition of crediting and literature. Subject matter and scope of research of general and applied geophysics. The physical properties of rocks. Overview of geophysical methods and their physical basics and applications. Comprehensive geophysical research. Methodology of geophysical measurements.
  Gravimetry. Physical basics. Apparatus and equipment. Methods of field research. Interpretation. Prospective effectiveness and application.
  Magnetometry. Physical basics. Apparatus and equipment. Methods of field research. Interpretation. Prospective effectiveness and application.
  Electric and electromagnetic methods. Physical basics. Apparatus and equipment. Methods of field research. Interpretation. Prospective effectiveness and application.
  Surface seismic methods. Reflective seismics (2D and 3D technique). Refractive seismics. Physical basics. Apparatus and equipment. Methods of field research. Interpretation. Prospective effectiveness and application.
  Well logging (drilling). Subject matter of research. Technical conditions of borehole profiling. A borehole considered as a testing center. Geophysical measuring equipment. Organization of field works.
  Basic well logging methods. Physical grounds. Apparatus and equipment. Methods of field research. Interpretation. Prospective effectiveness and application.
  Mine Geophysics. Seismology. Seismoacoustics. Active seismic tomography. Passive seismic tomography. Microgravimetry.
  

  Project
  Gravimetry. Gravimetric anomalies. Interpretation.
  Refractive seimics. Reflective seismics. Interpretation. Static corrections.
  Magnetometry. Magnetometer. Methodology of field works.
  Interpretation of magnetic field measurements.

• Expected prior knowledge: Introduction to Rock Mechanics.
  
  
• Study Goals: Fundamental understanding of integrated analysis of deformations using the combination of monitoring and numerical modelling of deformations, what is essential for studying the processes occurring in engineering structures and in rock mass at the construction and post-construction stages.
  To understand the fully automated monitoring principles, data collection, and processing.
  
  
• Course Contents: Integrated analysis of deformations; rock mass and earth mass material characteristics; determination of in-situ rock mass parameters; deterministic modeling of rock mass behavior; FEM; geodetic and geotechnical monitoring of deformations; deterministic modeling, Deformation Monitoring Surveys, design and implementation of geodetic deformation monitoring system. Short review of monitoring requirements and available monitoring techniques. Deformation measurements using the total station in the manual mode and in the fully automated way. Automation of monitoring surveys by using the ALERT-DDS deformation detection software.
  Principle of integrated analysis of deformations; analysis based on system theory; analysis based on continuum mechanics; approximate methods for solving continuum problems; Finite Element Method (FEM); large scale problems in rock mechanics; deformation modelling of underground mining and tunnelling problems (empirical and deterministic); deformation modelling of open pit mining problems (empirical and deterministic); deformation modelling of earth dam and steep embankment problems. Geodetic and geotechnical monitoring of deformations. New monitoring geodetic techniques: Robotic Total Stations (RTS), Global Positioning System (GPS), Pseudolites, InSAR, Ground Based Radar Interferometry, laser scanners, continuous and fully automated monitoring system ALERT-DDS, challenges of geodetic monitoring systems. Geotechnical monitoring techniques, new geotechnical instrumentation (MEMS, fibre optics). FEM analysis using Geostudio software. Case studies: oil fields (Venezuela), McKenzie natural gas project (Kanada), slope stability in open pit Chuquicamata copper mine in Chile, Highland Valley copper mine in Canada, Barrick Gold mine in Nevada. Hydro-electric projects: integrated analysis of large earth dams and concrete face rock fill dams (CFRD) in Canada, USA, and China.
  

  Laboratory class: Review of monitoring requirements and available monitoring techniques. Design and implementation of geodetic deformation monitoring system. Deformation measurements using the total station in the manual mode and in the fully automated way. Automation of monitoring surveys by using the ALERT-DDS deformation detection software. Integration of multi-sensor observations (GPS, total station) for high accuracy measurements, stability check of control points, identification and separation of various causes of deformation.
  Laboratory exercise: A total station is used to measure the relative position of points with respect to the position of the robotic total station (RTS) with automated target recognition (ATR). Small targets are placed in the areas of interest throughout the object being monitored; the RTS is programmed to point to these targets and make precise measurements. The measurements are performed in the predefined pattern and schedule. The raw data are collected by RTS and then processed by the software to determine the final coordinates, displacements, displacements velocities of all the target points. Verification of the results. Optional: Multi-sensor observations (GPS, total station) for high accuracy and stability check.
  Mining example: excavated areas in open pit mines require stability monitoring to guide production and safety (steeper walls mean more efficient use of resources, but may be more prone to failure) application accurate displacement monitoring system.

• Expected prior knowledge:
  Possesses basic knowledge of technologies used in open-pit mines and underground mines.
  Is able to use Microsoft Office environment to prepare documents in Word, multimedia presentations in Power Point and work with Excel spreadsheets.
  Is able to identify harmful, dangerous and nuisance factors in the workplace environment.
  
  
• Study Goal:
  To introduce the principles of occupational risk assessment in accordance with relevant standards.
  To present the principles of occupational risk assessment and the determination of admissibility with the use of STER software and the RISC SCORE method.
  
  
• Course contents: 
  Lecture
  Definition of occupational risk. Legal basics of occupational risk assessment. Risk assessment methods. Course of occupational risk assessment. Information necessary for occupational risk assessment. Identification of harmful, dangerous and nuisance factors in the work environment.
  Estimation of occupational risk assessment and determination of admissibility. Corrective and preventive actions. Familiarising employees with the results of occupational risk assessment. Implementation of agreed corrective and preventive actions. Monitoring the effectiveness of implemented actions. Periodic occupational risk assessment. Harmful factors – identification and assessment of risks.
  Dangerous factors – identification and assessment of risks.
  Nuisance factors in occupational risk assessment: psychological burden, static burden, monotype.
  Methods of occupational risk assessment: STER software, the RISC SCORE method, written test.
  

  Laboratory
  Occupational risk assessment with the use of STER software for two work posts – description of work post, identification of hazards.
  Occupational risk assessment with the use of STER software for two work posts – estimation of occupational risk and determination of admissibility of harmful factors (dust, noise)
  Occupational risk assessment with the use of STER software for two work posts – estimation of occupational risk and determination of admissibility of harmful factors (vibration, chemical agents)
  Occupational risk assessment with the use of STER software for two work posts – estimation of occupational risk and determination of admissibility of dangerous factors (slippery or uneven surfaces, falling elements, moving parts, moving machinery and transported bimi items)
  Occupational risk assessment with the use of STER software for two work posts – estimation of occupational risk and determination of admissibility for nuisance factors (psychological burden, static burden, monotype)
  Occupational risk assessment for a selected work post with the use of the RISC SCORE method, presentation of executed exercises, test.

• Expected prior knowledge: Basic knowledge in the field of inorganic and organic chemistry.
  
  
• Study Goals:
  1 Becoming familiar with the physical and chemical properties of water; chemical composition of natural waters and their contamination; water classification and water quality standards.
  2 Becoming familiar with the physical and chemical processes which influence the content of the trace compounds in the air. Learning methods of mathematical description of the temporal and special variability of substances concentration in the air.
  3 Gaining knowledge in the types of waste, the methods for determination of physico-chemical properties of the waste and the theoretical ways for their treatment.
  
  
• Course Contents:
  Lecture
  Physical and chemical properties of water. Minerals and natural organic compounds in water.
  Classification and water quality standards.
  Physical and chemical parameters of water analysis.
  Tests for determination of organic compounds in water.
  Crediting (part 1).
  Atmosphere, air and trace compounds. Mass balance of species in air and its mathematical description.
  Chemistry of gas phase in the troposphere.
  Chemistry of liquid phase in the troposphere.
  Species removal from the troposphere: wet and dry deposition.
  Crediting (part II).
  Quantitative characteristics of waste. General chemistry: differences between chemical compounds and mixtures, methods of separating components from mixtures as a basis for sieve and morphological analyses.
  Determination and evaluation of fertilizing and calorific properties of waste.
  Organic chemistry: elements, general properties, characteristics of common compounds pointing out the connection with waste (e.g. chlorinated hydrocarbons as solvents, alkenes as raw materials for the production of polyolefins).
  Organic chemistry: carbohydrates, fats, proteins. Decomposition under aerobic and anaerobic conditions (chemical reactions, biocatalysis, quality of end-products).
  Laboratory classes
  Introduction; overview of the scope of the course. Analyses: alkalinity, hardness, calcium and magnesium.
  Analyses: chlorides, ammonium nitrogen, nitrite nitrogen and nitrate nitrogen, sulphates and total dissolved solids.
  Analyses: ferric, chemical oxygen demand (COD-Mn), manganese. Electrolyte balance. Assessment of water quality.
  Temporal variability of species concentration in air as a function of the delivery and removal processes.
  Quantitative analysis of photochemical cycle NO2, NO, O3.
  Modelling of gas phase-liquid phase equilibrium for SO2 in the troposphere.
  Emission sources identification using a receptor model.