Particle Dynamics Investigations of Geologic Materials Lecture 1: Granular Materials One Geologists

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Particle Dynamics Investigations of Geologic
Materials Lecture 1 Granular Materials - One
Geologists Perspective
Julia K. Morgan Rice University Collaborators
Maria Ask Luleå Institute of Technology
Deformation and Failure of Geomaterials,
Brindisi, Italy (June 14-19, 2009)
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Outline

• Background, Motivation, Geologic Examples
  Methodology
• Applications Fault Zones, Fault Gouge, Particle
  Size Evolution Effects
• Applications Gravitationally Driven Deformation
• Landsliding
• Gravity Spreading
• Salt Tectonics
• Applications Tectonically Driven Deformation
• Contractional Tectonics
• Extensional Tectonics

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Representative Geologic Materials

• Granular
• Sediments
• Debris avalanches/flows
• Fault gouge
• Cohesive but brittle, subject to fracture flow
• Crustal rocks - low T-P
• Other geologic materials, approximated as
  granular?
• Salt, magma w/ crystal mush, etc. - correct
  rheology?

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Common Characteristics

• Frictional brittle materials, that can be
  approximated as granular at some scale
• Heterogeneous range of grain / contact scale
  properties
• Particle size, size distribution, shape, elastic
  properties
• Variable packing - porosity, contact
  distributions
• Interparticle cohesion, friction, t, T, P,
  x-dependence
• Complicates ability to define single unifying
  rheologic model to represent full range of
  behaviors.
• Need to define in terms of heterogeneities - can
  we construct similarly complex aggregate model?

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Landslides and Debris Flows/Avalanches
Slump in clay
Slump in clay slope

• Questions
• Why did slope fail - what triggered?
• What were the properties/preconditions?
• How did they evolve?
• Once failure occurs, how far, fast, and big?
• Answers (Raise new questions)
• Mechanical properties (How to determine?)
• Rheology (How to determine?)
• Transient processes (How to track?)
• pore pressures
• dynamic waves

Rock-fall in Eolianite
Rockfall in eolinite cliff (sand, silt)
(Courtesy of O. Katz)
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How to Answer Questions ( Questions)

• Field
• Make observations, infer processes and drivers
• Laboratory
• Test inferences, constrain responses, charaterize
  props
• Numerical continuum, discontinuum
• Replicate inferred conditions, explore detailed
  process and controls
• Particularly at scales / magnitudes smaller than
  possible in field or lab microphysics /
  micromechanics that control behavior (e.g., at
  particle, fracture scale)

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Convergent Margins
Sediments
Rocks
Tsunamigenic Slip
Aseismic Slip
Coseismic Slip
Seismogenic Zone
(Modified from Langseth and Moore, 1990)

• Plate boundary mega-thrust -gt Great earthquakes!

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Drilling and Survey Locations
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Nankai Accretionary Prism
NANKAI TROUGH
NANKAI PRISM
PROTO-THRUST ZONE
Frontal thrusts
Proto- thrusts
Deformation front
Depth (m)
1 km
turbidites
hemipelagic sediments
Proto-decollement
Decollement
Ocean Crust
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Accretionary Sediments
Semi-lithified silty-claystones, cut by tectonic
fractures
smectite-rich
illite-rich
(Morgan et al., 2007)
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Décollement
Intense fracturing Clay polish on surface
(Ujiie et al., 2003)
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Underthrust Section

• Occasional normal faults, and rare dewatering
  structure.
• Underthrust sediments are remarkably undeformed.

Brecciation
No tectonic deformation.
Ch. 5, Fig 23
(Morgan et al., 2007)
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Porosities vs. Effective Stress
(Morgan et al., 2007)
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What controls underthrust sediment properties?

• And how does this controlling property change
  down dip, with what implications?

• Origin of porosity step below décollement

• Lower horizontal (non-tectonic) stresses?

• Underconsolidation, i.e., overpressures?

• Enhanced strength in underthrust sediments?

(Morgan and Ask, JGR, 2004)
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Porosities vs. Effective Stress
(Morgan et al., 2007)
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Porosities vs. Effective Stress
(Morgan et al., 2007)
Preconsolidation Stress
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Porosities vs. Effective Stress
(Morgan et al., 2007)
Preconsolidation Stress
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Question

• Can we distinguish between high pore fluid
  pressures (low effective stress) and enhanced
  sediment strength (cementation)?
• Direct measurements of in-situ stress and pore
  pressure (Not imminent)
• Laboratory deformation experiments

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How to Answer Questions ( Questions)

• Field
• Make observations, infer processes and drivers
• Laboratory
• Test inferences, constrain responses, charaterize
  props
• Numerical continuum, discontinuum
• Replicate inferred conditions, explore detailed
  process and controls
• Particularly at scales / magnitudes smaller than
  possible in field or lab microphysics /
  micromechanics that control behavior (e.g., at
  particle, fracture scale)

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Uniaxial Reconsolidation Tests
Maria Ask
View of Karigs lab
Data acquisition
Sample chamber
Sample column
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Sample Locations

• Four samples from the underthrust section.
• Depths of 40-80 m below décollement.

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Sediment Reconsoli-dation
(Morgan et al., 2007)
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Sediment Reconsoli-dation
(Morgan et al., 2007)
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Experimental Results
(Morgan and Ask, 2004)
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Experimental Results
(Morgan and Ask, 2004)
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Experimental Results
(Morgan and Ask, 2004)
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Underthrust Sediments

• High apparent preconsolidation strengths!!
• Step up in porosities below décollement.
• Sharp decoupling at base of fault.
• Lack of décollement downcutting in frontal
  region.
• Evidence for cementation of underthrust unit
• Contrasting mineralogy above and below fault.
• Preserved large (secondary) pore spaces.
• Cement authigenic illite at grain contacts?
• Note, not what was initially predicted!

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Implications Sub-Decollement Strength

• Enhanced yield strength of underthrust sediments
  in excess of predicted sigma-v
• Can support vertical load without excess pore
  pressures.
• Can maintain high pore volumes to depth.
• Excess strength increases down-dip.
• Sediments become increasingly sensitive
  down-dip - subject to triggered failure during
  earthquakes.

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Sediment Stability

• Sensitivity
• S peak strength/consolidation stress

• High S can lead to rapid, unstable, and complete
  matrix collapse.
• Sudden loss of shear strength.
• Rapid increase in pore fluid pressures.
• Pore fluid expulsion and porosity reduction.
• Low effective stresses and failure.
• gt e.g., slope failure and debris flows.

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Enhanced Sediment Strength
(Morgan et al., 2007)
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Deformation Paths Down-Dip Processes
(Morgan et al., 2007)
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Conclusions Hypotheses to Test

• Underthrust sediments are significantly stronger
  than tectonically remolded accreted sediments,
  and prevent décollement downcutting.
• This enhanced strength is thought to result from
  post-consolidation diagenesis, i.e., structuring,
  and increases downdip, w/ longer exposure to
  diagenetic conditions
• Downdip loss of strength may cause rapid
  consolidation, generation of high pore pressures,
  and décollement downcutting - and may account for
  changes in fault slip behavior.
• gt NEED EFFICIENT WAY TO TEST HYPOTHESES

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How to Answer Questions ( Questions)

• Field
• Make observations, infer processes and drivers
• Laboratory
• Test inferences, constrain responses, charaterize
  props
• Numerical
• Replicate inferred conditions, explore detailed
  process and controls
• Particularly at scales / magnitudes smaller than
  possible in field or lab microphysics /
  micromechanics that control behavior (e.g., at
  particle, fracture scale)

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Numerical Granular Mechanics

• Granular - frictional, dilatant,
  pressure-dependent
• Brittle - in some cases
• Cohesive, undergoes fracture (comminution, when
  evolves into granular)
• Characterized by inhomogeneities, contrasting
  properties / strengths, leading to discontinuous
  deformation - stress concentrations, faults,
  fractures, localized slip and deformation.
• Seek method that captures natural variability
  under range of loading conditions
• gtgtgt PARTICLE DYNAMICS METHODS ltltlt

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Particle Dynamics Method

• Construct geologic medium as assemblage of simple
  particles (e.g., disk or spheres) captures
  natural heterogeneity (packing density,
  pre-existing slip surfaces), and can impose
  additional heterogeneities (contrasting
  properties, geometry)
• Track particle interaction and, apply simple
  physics
• Contact friction, elastic particle deformation
• Interparticle bonds, normal, shear, and rotation
• Pairwise interactions, no long-range interactions
• Resolve forces onto particles, track resultant
  motion
• Driven by prescribed (e.g., boundary)
  displacements

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Discrete Element Method(Cundall and Strack, 1979)

• Normal contact resistance (no attraction)
  dependent on contact area (Hertzian contact)
• Frictional sliding resistance (no cohesion),
  dependent on normal force (Mindlins addition)
• Integrate Newtons equation of motion (linear and
  rotational)
• Dissipate energy by damping velocities or
  contacts (artificial, but necessary - how best)

Contact Laws
Newtons Equation of Motion
(Morgan and Boettcher, 1999)
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Discrete Element Method(Cundall and Strack, 1979)
Good for micromechanics
Bonding Law
Contact Laws
Newtons Equation of Motion
Failure Criteria
(Morgan and Boettcher, 1999 Guo and Morgan,
2007)
tmax Fsmax / A
?max -Fnmax / A M R / I
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Discrete Element Method(Cundall and Strack, 1979)
Contact Laws
Bonding Law

• Normal contact resistance (no attraction),
  dependent on contact area (Hertzian contact)
• Frictional sliding resistance (no cohesion),
  dependent on normal contact force (Mindlins
  addition)
• Integrate Newtons equation of motion (linear and
  rotational)
• Dissipate energy by damping velocities
  (artificial, and necessary - quasi-static)
• However, method works very well, providing
  important insights into structural evolution and
  mechanical controls.

Newtons Equation of Motion
Bond Force - Normal Displacement Relationships
Failure Criteria
(Morgan and Boettcher, 1999 Morgan, in prep)
Good for tectonic systems
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Advantages of Particle Dynamics

• Aggregate response dependent on many parameters,
  which can vary temporally and spatially.
• Emergent features develop naturally, i.e., grain
  reorganizations, force chains, strain
  localizations, etc.
• Can study relationships among microproperties and
  resultant features, through time and space.
• But can also calculate averages - i.e., continuum
  properties, thus analogous to laboratory
  experiments (but with added insights)

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Quantifying Stress
(Morgan and McGovern, 2005)

• Resolution depends on averaging domain
• Multiple particles, smoother field
• Individual particles, force chains

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Quantifying Stress - Landslide Example
particle configuration
weak plane

• Block failure along weak (bedding) plane
• Stresses reveal
• Decoupling across detachment
• Stress chains
• Heterogeneous field
• Red - compressive
• Blue - tensile

vertical stress
horizontal stress
Principal stress vector (scaled by diff stress)
erroneous stress vectors
(Courtesy of O. Katz)
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Quantifying Finite Strain
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Quantifying Finite Strain
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Quantifying Finite Strain

• Resolution depends on averaging domain
• Multiple particles, smoother field, but misses
  details
• Can denote at finer (particle) scale, i.e.,
  discontinuities

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Quantifying Strain - Landslide Example
dh / dx
weak plane
dh / dy

• Block failure along weak (bedding) plane
• Total displacement gradient components reveal
• Block separation
• Block rotation
• Interblock slip
• Red - positive
• Blue - negative

weak plane
dv / dx
weak plane
dv / dy
weak plane
(Courtesy of O. Katz)
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Quantifying Strain - Landslide Example
particle configuration
weak plane
dilation

• Block failure along weak (bedding) plane
• Scalar strain invariants reveal
• Block separation
• Block rotation
• Interblock slip
• Red - dilation right lateral
• Blue - contraction, left-lateral

weak plane
distortion
weak plane
(Courtesy of O. Katz)
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Caveats, However

• Not real material, but virtual one. Can choose
  non-physical properties to yield non-physical
  behavior.
• Must choose reasonable parameters, and calibrate.
  
• Unfortunately, small scale properties poorly
  known.
• Missing or poorly known parameters, e.g.,
• Damping to stabilize system and simulate
  inelastic deformation
• Effects of discretization in space and time,
  e.g.,
• Particle size limits spacing of discontinuities
• Time step influences acoustic velocities
• Missing or incorrect physics and chemistry, e.g.,
• Temperature effects (changes rates of bonding,
  loss of cohesion)
• Time-dependent friction effects - adhesion, rate
  state
• Diagenesis or metamorphism (mineralogic changes)
• Pore fluids, pressure solution, melting

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Philosophy

• Although imperfect - discrete numerical modeling
  can provide extraordinary (and intuitive)
  insights into systems characterized by simple
  rules (and some complex through approximation),
  subject to reasonable caveats against
  overinterpreting the results.
• Allows us to make critical connection between
  smaller scale (Newtonian physics) and assemblage
  scale (rheology and emergent behavior), with many
  potential applications, to solve specific
  problems/questions.
• Examples next time!