
This course introduces students to the mathematical foundation and rock mechanics background needed to understand the deformation behaviour of the crust and mantle at the macroscopic, mesoscopic and microscopic scales. The course is primarily designed for students interested in structural geology, geophysics, crust/lithosphere/mantle and Earth materials studies, or planning to embark on the Master Programme in Earth Structure and Dynamics. However, it will also be valuable to students interested in transport, flow and/or Earth material properties in the context of geochemistry, sedimentology, petroleum geology, geotechnical engineering, hydrogeology, meteorology and oceanography.
The course aims to provide students with:

The fundamentals and definitions of stress and (incremental) strain(rate)

A basis in the physical equations describing the mechanics of continuous media (fluids, solids), including the laws of conservation of mass and momentum

An understanding of how the mechanical behaviour of materials can be specified phenomenologically in terms of stressstrain(rate) relations or constitutive equations, and how these can be used to describe elastic deformation, viscous flow and solid state flow.

A quantitative understanding of the mechanical behaviour (constitutive equations and failure criteria) of real rock materials in the crust and mantle, and of the processes that control this behaviour.

The ability to attach physical meaning to geological structures and to formulate hypotheses about the responsible processes.

The ability to apply the principles learned to modelling simple problems in tectonics, geodynamics and crustal geomechanics (e.g. enhanced hydrocarbons production and CO2 storage), and to report (team) results in a systematic manner.



The course introduces students to the mathematical foundation and rock mechanics background needed to understand the deformation behaviour of the crust and upper mantle at the macroscopic, mesoscopic and microscopic scales.
Topics include:
Part 1 (Spakman 50%):
 Stress and deformation: mathematical basis, tensorial description, equilibrium equation, symmetry of stress tensor representations of stress (principal stress, stress ellipsoid, Mohr’s circle)
 Deformation, displacement gradient tensor, strain and rotation tensor. Conservation laws: material derivatives, mass balance (continuity equation), momentum conservation
 Intro to constitutive equations; linear elasticity for isotropic media, elastodynamic equation for seismic waves
 Hydrostatic fluids, linear viscosity, NavierStokes equation; Course summary
This part will be thought in Dutch if no foreign students are in the class.
Part 2 (Spiers 50%):
 Rheology and deformation processes in rocks  rock behavior in nature and experiment, relationship with continuum mechanics.
 Elastic behaviour of rock: atomic scale basis, elastic constants, iso vs. anisotropic behaviour, poroelasticity of reservoir rocks.
 Brittle/frictional behaviour: fracture, faulting and mechanical effects of pore fluid pressure.
 Ductile Deformation: crystal defects, plastic and diffusional flow, constitutive equations, deformation maps, recrystallization, generalising 1D flow laws to 3D
Mechanical behaviour of the crust and upper mantle: lithosphere strength profiles for continental, oceanic and fault zone scenarios.
Development of Transferable Skills
 Leadership and ability to work in a team: Students will complete miniprojects and assignments in teams of two and are encouraged to interact with other teams to discuss the problems investigated. Within this structure, students must distribute tasks and organize their workflow and time planning.
 Written communication: Each miniproject or practical assignment results in a written product (or report) that must be completed and handed in by a strict deadline.
 Problem solving: The miniprojects, practicals and homework exercises present challenging problems that require creativity and imagination to find solutions. Besides mathematical challenges, students learn to create conceptual models and describe them quantitatively.
 Verbal communication skills: Students are strongly encouraged to participate in actively answering questions posed by the lecturers in class.
 Work ethic. The deadlines for completing miniproject/practical and homework exercises are extremely strict so that worked answers can be distributed to all students, but only when all students have submitted a given product. Failure to be professional in meeting these deadlines results in disqualification from the course.
 Initiative and analytical / quantitative skills: The miniprojects/practicals and homework exercises involve breaking challenging mathematical and conceptual problems down into their component parts. Mathematical exercises must be solved by mastering the principles of continuum mechanics. The conceptual components must be systematically described using suitable equations and parameter values, introduced in the lectures, to arrive at quantitative answers.
 Flexibility and adaptability: Students must deal with both mathematical concepts and the application of these concepts to solve realistic problems relating to the rheology of the lithosphere.
 Technical skills: In several of the assignments, students practice basic mathematical skills, as well as spreadsheet and graphing skills.
Grading:
 The final grade for the course is calculated as follows. Mid term exam Spakman (Continuum 50%) + end term exam Spiers (Rheology 50%) = 100% of final grade (both parts count equally towards the final grade).
 Practicals/tutorials/homework: Continuously assessed on a pass/fail basis.
 All Practicals/tutorials & homeworks must be completed with a “pass” to complete the course.
 The minimum pass grade (average of Part 1 Spakman and Part 2 Spiers) for the course is 5.5 out of 10, with all assignments completed. Grades between 5.50 and 5.99 are rounded up to 6.0. A grade of 5.49 or less is a fail. The right to a repair examination is granted only if the unrounded average grade for Parts 1 and 2 lies between 4.00 and 5.49 and if the student has completed and obtained a pass for all assignments. A grade of 3.99 does not entitle a student to a repair examination. Repair exams may address Part 1 (Continuum) or Part 2 (Rheology) – students may choose which they prefer to resit (one only). After the repair exam, the final course grade is calculated as the average of the grades obtained for Parts 1 and 2, with the repaired grade updated. If the course grade obtained is 5.50 or above it will be set at 6.0, i.e. no final scores higher than 6.0 are given following a repair exam. If the final grade is < 5.49, the result is a fail and entire course has be redone, if a pass is sought.
 The right to a repair exam is not automatic if ill. Deregistering for an exam or test due to illness does not automatically entitle students to take a repair test or exam. After recovery, the student must supply a doctor’s note certifying that the student was ill on the day of the test/exam. Without this, students have no right to a repair exam.




 CompetentiesIngangseisenVoorkennisBasis in classical mechanics (Newton’s laws), differential equations and/or linear algebra (matrixmatrix multiplication, eigenvalues & eigenvectors, coordinate transformation)  Voorkennis kan worden opgedaan metUse of Bachelor Level2 readers and textbooks in physicsoriented and math courses:  Differential equations in Earth Sciences (GEO21301)  Linear algebra and vector analysis ( GEO21201)  Bronnen van zelfstudieSee above sources plus recommended material for this course 
  Verplicht materiaalReaderReader Spakman + Reader Spiers via Print on demand. 

 Aanbevolen materiaalBoek§ Ranalli, G.: Rheology of the Earth, Chapman & Hall, Ottawa, 1995, 2nd Edition. 
 BoekRelevant sections of the following books will also provide useful (noncompulsory) background for troubleshooting: 
 BoekHull and Bacon (1984). Introduction to dislocations. International Series on Materials Science andTechnology, Vol. 37. Pergamon. 
 BoekNye, J.F. (1986). Physical Properties of Crystals, Oxford. 
 BoekPasschier and Trouw (1996). Microtectonics, Springer, Berlin. 
 BoekFossen, H. (2010). Structural Geology, Cambridge Univ Press 
ISBN  :   9780521516648 

 WerkvormenLectures
 Tutorials/Practicals AlgemeenAll Practical/Miniproject/Tutorial and homework assignments must be completed with a “pass” to complete the course. Feedback on assignments will be in the form of worked answers, where appropriate. Voorbereiding bijeenkomstenPractical/Project/Tutorial assignments and homeworks to be completed on a weekly basis or as otherwise sepecified in the yearly course guide or in class. Bijdrage aan groepswerkStudents will be instructed in class on when to complete assignments/homework on an individual basis or in teams of two.

 ToetsenEindresultaatWeging   100 
Minimum cijfer    
BeoordelingMid term exam Spakman (Continuum 50%) + end term exam Spiers (Rheology 50%) = 100% of final grade (both parts count equally towards the final grade). For further explanation check the content on the left.


 