MSc Geoscience for Sustainable Energy / Course details

Year of entry: 2022

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Course unit details:
Subsurfance Mechanics and GeoEngineering

Unit code EART60572
Credit rating 15
Unit level FHEQ level 7 – master's degree or fourth year of an integrated master's degree
Teaching period(s) Semester 2
Offered by Department of Earth and Environmental Sciences
Available as a free choice unit? No


The stress analysis techniques explored in this unit are delivered via a suite of paper-based practical exercises. All necessary mathematics is taught within the unit although an understanding of matrix manipulation will help. After introducing some foundational material on matrix manipulation, we consider what the “state of stress” actually means and use both graphical and matrix manipulation methods to evaluate that state of stress from measurements of normal stress and shear stress on a plane or from measurements of principal stresses. We examine how stress analyses may be carried out in geographical coordinate systems and, as a by-product of this, show how operations commonly done with a stereonet may be done instead by manipulating vectors. We then turn to examine stresses in thrust sheets and develop that approach into slope stability applications. We conclude the first half of the unit by examining the mechanical consequences of fluids within porous rocks

In the second half of the course we use the techniques learned to date to deduce the stresses required for brittle failure in contractional, extensional and strike-slip tectonic settings, and then use this analysis to constrain the magnitude of horizontal stresses in down-borehole settings. We conclude the unit by looking at stress with depth in the lithosphere, extending our primarily upper crust/brittle regime analyses into deeper lithosphere/plastic deformation regimes

The practical classes are supplemented in the first half of the course with lectures describing how the mechanical properties of rocks are determined, and providing an overview of the deformation responses of rocks and soils with particular emphasis on elastic and brittle behaviour. The lecture content will not feature heavily in the assessment but rather is there to provide context for the techniques taught in the practicals


The aim of this unit is to provide a dominantly practical introduction to graphical and mathematical techniques that are widely used within the rock mechanics and geotechnical industries to evaluate states of stress in the subsurface. The techniques are applied to estimate stresses in structural geology (stresses on faults, strength with depth), engineering geology (slope stability) and down-borehole settings. As such the unit provides a strong foundation for students with a grounding in applied geomechanics required to pursue a career within any parts of the energy, mineral resource and environmental sectors that have an interest in the strength and potential for brittle failure of the rocks that they encounter in their operations.


This is unit is critical for diverse applications such as near-well performance during CO2 injection, caprock mechanics for sealing the CO2 stroage, well pressure management.

Learning outcomes


On the successful completion of the course, students will be able to:




explain what is meant by the state of stress at a point, and be able to distinguish different types of stress / pressure states




add and multiply vectors and matrices, be able to evaluate eigenvalues and eigenvectors of matrices, be able to use logarithms, and be able to carry out elementary dimensional analysis




use matrix manipulation and graphical (Mohr circle) techniques to solve for the normal stress and shear stress on a plane from the principal stresses (or vice versa), and be able to include pore fluids in the analysis




carry out stereonet operations by vector manipulation, thereby establishing a basis for carrying out stress analyses in geographical coordinate systems




apply stress analysis techniques to assess the possibility of mechanical failure in down-borehole settings




assess the likely deformation response in any tectonic setting (contractional, extensional, strike-slip) from constitutive equations for elastic deformation, brittle failure and creep




1.      Lecture: Experimental approaches for examining rock deformation processes

Practical: Some exercises on matrices and how to manipulate them; dummy suffix notation

2.      Lecture: Elasticity

Practical: Revision of graphical methods to analyse stress (Mohr’s circle); analysing stress using    matrices; introduction to stress transformations (3d stress analysis)

3.      Lecture: Plastic deformation

Practical: 3d stress analysis in geographical coordinates (manipulating vectors)

4.      Lecture: Brittle deformation – fracturing

Practical: Stresses in blocks: thrust sheets; slope stability

5.      Lecture: Brittle deformation – frictional sliding and brittle failure of high porosity rocks

Practical: Dimensional analysis; porosity and permeability; flow through fractures

Reading Week 6 (no classes)

7.      Lecture: Slope Stability

Practical: Test 1 assessment

8.      Lecture:  Hydraulic Fracture

Practical: Mohr circle analysis of the stresses at brittle failure

9.      Lecture:  Geothermal energy and subsurface energy storage

Practical: Stresses in extensional and contractional terrains; an introduction to stress polygons

10.    Lecture:  Geomechanics of Carbon Capture and Storage

Practical: Down-borehole evaluation of porosity, fluid pressure, vertical stress and horizontal stress

11.    Lecture:  Geomechanical considerations of geological disposal of nuclear waste

Practical: Revision Practical

12.    Practical: Test 2 assessment

Teaching and learning methods

The, paper-based exercises practical classes are designed to include

(1)    exercises that can be completed within the duration of the practical class and which contain the fundamental material each student should know to do well in the assessments, plus

(2)    supplementary exercises developing this fundamental material beyond that which will be directly assessed and which can be completed by the interested student between classes

The computer based classes will follow a similar structure with the following:

(1)  an introduction to the Matlab or Python commands we will use.

(2)  the main exercise that is to be completed during the class.

(3)  follow up material to develop understanding.

Within each class, helpful hints on solution strategy or practical demonstrations are given, and staff are on hand in the classes to guide students, one-on-one, through the exercises as they work on them. All necessary mathematics (primarily vector and matrix manipulation) is taught within the classes in the traditional way (with pen-and-paper + calculators). Attention is paid to how graphical techniques that have been introduced in previous course units to solve elementary versions of these types of exercise (e.g., using stereonets, Mohr Circles), follow from the mathematics.

During the practical classes interim solutions are posted on the board in timely fashion. Worked solutions to all exercises (fundamental and supplementary) are posted on Blackboard after each class. In several instances, reviews of these solutions will be given at the start of the following practical class. Students are encouraged to discuss their work with staff during each practical, and this includes not only the exercises that they are solving in that class but also any exercises that they may have completed between classes. It is through these exchanges that most formative feedback is delivered. Students may also arrange to meet staff outside the practical classes to discuss their work if they wish.

At several points during the course, key revision guidance is given both within the class and posted on Blackboard in a folder entitled ‘How to do well in this unit’. This will be underscored prior to each of the two assessments

Assessment methods

Assessment type

% Weighting within unit

Hand out and hand in dates



How, when and what feedback is provided

ILO tested




Teaching Week 7

2.5 hr

No formal feedback will be given beyond a detailed mark breakdown issued within the 15 working day period for return of in-course marks. Students may view their script by arrangement

1, 2, 3, 4




Teaching Week 12

2.5 hr

As an end-of-unit examination, no formal feedback will be given. However, students may view their script, together with a very detailed mark breakdown, after the exam period by arrangement.

2, 3, 5

Recommended reading

  • Zoback MD, 2007, Reservoir Geomechanics, Cambridge University Press [recommended]
  • Jaeger JC, Cook NGW, Zimmerman RW, 2007, Fundamentals of Rock Mechanics (4th edition), Blackwell [recommended]
  • Allmendinger RW, Cardozo N, Fisher DM, 2012, Structural Geology Algorithms: Vectors and Tensors, Cambridge University Press [recommended]
  • Karato S-I, 2008, Deformation of Earth Materials: An Introduction to the Rheology of Solid Earth, Cambridge University Press [recommended]
  • Poirier J-P, 1985, Creep of Crystals: High Temperature Deformation Processes in Metals, Ceramics and Minerals, Cambridge University Press [recommended]
  • Paterson MS, Wong T-F, 2005, Experimental Rock Deformation – The Brittle Field (2nd edition), Springer [recommended]

Study hours

Independent study hours
Independent study 150

Teaching staff

Staff member Role
Julian Mecklenburgh Unit coordinator

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