Quantitative Structural Analysis: Where does it start?

David D. Pollard, Stanford University Stephen J. Martel, Univ. of Hawaii

Structural Geology and Tectonics ForumGolden, CO – June 16 to 18, 2014

Objectives

• Introduce a new way to teach undergraduate structural geology– Make the foundational concepts accessible– Integrate teaching, research and practice– Unite all aspects of structural geology– Prepare students for professional work

• Recruit help for testing the new textbook

There are many good textbooks

Change may not be easy…

Why is a new book needed?

• Suppose you asked your students this after completing the structure course :

What are the foundational concepts that underlie all tectonic processes and their structural products?

• Would truly meaningful answers emerge?

A meaningful answer• Identifies the glue to integrate field work, lab

testing, modeling, and theory• Connects geometry, kinematics, constitutive

laws, stress states, and boundary conditions• Informs students how to study the natural

complexity of rock deformation• Ties structural geology to related disciplines

(e.g. geophysics, rock mechanics, engineering geology, civil engineering)

Foundational concepts

• Conservation of – mass – momentum – energy

The conservation laws underlie all tectonic processes and their structural products.

Here, we focus on mass and momentum

Cauchy’s first law of motion• Quantifies conservation of mass & momentum

• This law plays a central role in field work, lab experiments, and modeling

• Tectonic processes are conservative

• The only equation of this talk…

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Independent variables: Coordinates

Referential Descriptions of motion Spatial

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Independent variable: TimeD

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Relative age Geochronology Rate

Dependent variables: Velocity, Stress

• Stress analysis and kinematic analysis do not stand alone, but are inextricably linked by the equation of motion

• These variables are associated as the ‘effect’ and ‘cause’ of deformation

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Accommodates the natural complexity of geologic structures

• Deformation varies spatially

• Deformation varies temporally

• Partial derivatives are essential

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Boundary conditions at the outcrop

Photo of Dave and Steve, Bear Creek,Balloon overhead with Cauchy’s eq.

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It looks like these curved faultsopened when they slipped.

We should use ‘contact’boundary conditions.

Universal value

• All relevant constitutive properties of rock– brittle elastic, ductile plastic, viscous, …

• All relevant rates of deformation – quasi-static to dynamic

• All relevant magnitudes of strain– infinitesimal to finite

• All relevant length scales– nm to crustal

• All relevant time scales– ms to Ma

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Putting the equations of motion to use

• Too many dependent variables…

vi (3) sij (6)

• Choose a constitutive law and reduce the number of variables

• Choose the appropriate kinematic relations

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Example 1

• Hooke’s Law for linear elasticity and small strain kinematics

• Navier’s equations of motion for solid mechanics

• Applications: fractures, faults, dikes…– Elastic brittle deformation

Sheeting joints

Martel , S.J., 2011, Geophys. Res. Ltrs., v. 38, p. L20303 (photo by Greg Stock)

Example 2

• Stoke’s Law for linear viscosity and rate of deformation kinematics

• Navier-Stokes equations of motion for fluid mechanics

• Applications: folding, magmatic intrusions, salt tectonics…

Buckle folds

Hudleston, P.J. & Treagus, S.H., 2010, J. Structural Geology, v. 32, p. 2042

Example 3

• Von Mises yield criterion• FEM analysis for elasto-plasticity• Applications: folding, shear zones, fabrics…

– elastic-ductile deformation

Nevitt, J.M., Pollard, D.D., & Warren, J.M., 2014, J. Structural Geology, v. 60, p. 55-69

Localized mylonitic foliation

Summary

• Cauchy’s equations of motion provide a much needed universal and foundational concept for undergrad students of structural geology.

• Teaching from this foundation builds on the pre-requisite courses in the undergrad curriculum, particularly calculus and physics.

Summary

• Teaching from this foundation makes it clear why one should choose a constitutive law and not divorce kinematic and dynamic variables.

• Teaching from this foundation makes it clear that deformation varies in space and time, and provides the tools (partial derivatives) for analyzing the relevant field quantities.

Will you help us?

• If you would like to be a member of the testing team for the new book, please contact:

dpollard@stanford.edu

Testing constitutive laws

Nevitt, J.M., PhD Thesis, 2014

Testing constitutive laws

Nevitt, J.M., PhD Thesis, 2014

Von Mises Drucker-Prager

Power-law creep Constrained viscoplastic

Viscoplastic w/ relaxation Viscoplastic w/ more relaxation

Earthquake faulting

Maerten, F., et. al., 2005, B.S.S.A., v. 95, p. 1654

InSAR data Elastic model

1999 Hector mine earthquake (Mw 7.1), southern California

Volcanic eruption

Curtain of fire, Kilauea