1. CAPTURING PHYSICAL PHENOMENA IN PARTICLE DYNAMICS SIMULATIONS OF GRANULAR GOUGE Effects of Contact Laws, Particle Size Distribution, and the 3 rd Dimension Julia K. Morgan Department of Earth Science Rice University (http://terra.rice.edu/department/faculty/~morganj)

2. MOTIVATION Complicated macroscale processes (e.g., fault slip) commonly require phenomenological descriptions. Particle dynamics (PD) models, e.g., DEM, allow us to explore fundamental physics of the system - source of phenomenology. Controlled lab experiments provide intermediate validation points, bridging gap between PD models and whole earth simulations.

3. FAULT MECHANICS EXPERIMENTS Byerlee’s Law Rocks fracture and create gouge Slip localizes -> dynamic instabilities Rate-state friction – phenomenological, not physics-based. We still can’t predict earthquakes Fault structure

4. DISCRETE ELEMENT METHOD (Cundall and Strack, 1979) Advantages of DEM: -Allows heterogeneous and discontinuous deformation. System can evolve through time and space. - Can correlate behavior with physical properties and mechanical state. -Constitutive behavior is a result, not an assumption. Use DEM simulations to explore fundamental mechanics of fault gouge

5. PARTICLE SIZE DISTRIBUTION (Sammis et al., 1986, 1987) Greater relative abundance of small particles ---> Experimental Configurations

6. PSD EFFECTS ON STRENGTH Greater relative abundance of small particles ---> Strength drops to D=1.6 -> Slip weakening mechanism. No means for shear strength recovery.

7. WHY ARE SHEAR STRENGTHS LOW? Ease of particle rolling in 2D. PSD changes during granular shear result in second order decreases in strength, providing a means for slip weakening along fault zones. Rolling of particles in 2D system yields unreliable strength estimates.

8. EFFECT OF PARTICLE ROLLING Numerically damp or restrict particle rolling At high interparticle friction, rolling still dominates in 2D. Must fully restrict particle rolling ~ interlocking angular particles.

9. PARTICLE FRACTURE (Lang, Sparks, and Aharanov, in prep)

10. PSD’s for several run pairs, at 18 MPa (black) and 27 MPa (red), at 3 different strains. Systems shown by red-black pairs have experienced the same number of breakage events (25, 50 or 95). PSD is basically the same for all systems with the same amount of damage, although they have been subjected to different stresses, and significantly different strains.

11. RATE-STATE FRICTION (e.g., Dieterich, 1979) Fault friction depends on sliding velocity, V, and system “state”,  (t, D c ). CPU intensive calculation.

12. TIME-DEPENDENT CONTACT STRENGTHENING (e.g., Dieterich, 1972; Beeler et al., 1994; Marone, 1998). Friction depends on duration of contact, t, during static holds; drops to dynamic value upon slip. Simpler to implement numerically, and may reproduce rate-state phenomenology.

13. DEM MODELS W/ CONTACT HEALING Velocity-strengthening - steady-state friction. Log(time) strengthening - during holds. Instantaneous (direct) change in friction. Evolution with strain (e.g., D c ). Velocity-stepping and slide-hold-slide tests. Insight into the micromechanics of gouge that enable these phenomena. Simple, one-variable dependence produces:

14. Initial Configuration

15. Lower Velocity; No Contact Healing Largely distributed shear

16. Lower Velocity; w/ Contact Healing Distributed shear w/ persistent slip planes

17. Higher Velocity; No Contact Healing Largely distributed shear

18. Higher Velocity; w/ Contact Healing Persistent localized shear strain

19. Velocity = 1E-3  m/s Stick-Slip Deformation Mode: Cyclic Elastic Loading, Plastic Yield, and Failure. Gradual Dilation -> Rapid Contraction. Contact healing results in higher friction, higher elastic modulus.

20. Velocity = 1E-1  m/s Contact healing results in higher friction, greater stress drop. Oscillating Deformation Mode: ~Symmetric loading and unloading. Undulating volume strain.

21. STEADY-STATE RESPONSE Friction, dilation, and percentage of interparticle sliding increase with sliding velocity. -> Velocity strengthening. Implies stable sliding.

22. HOLD – 100% Strain Peak strength and stress drop show negative dependence on velocity. Peak strength is enhanced. Volume strain is suppressed. Friction, sliding contacts, and volume trends are ~ uncorrelated by 108% strain.

23. HOLD – 138% Strain Peak strength shows positive dependence on velocity. Peak strength is enhanced. Volume strain is suppressed. Friction, sliding contacts, and volume trends are ~ uncorrelated by 143% strain.

24. Velocity Step-up: 1E-3->1E-2 µm/s 1E-3->1E-1 µm/s Direct increase in friction and % sliding contacts. Gradual decay in direct effect, to higher steady state values. -> Velocity Strengthening

25. Velocity Step-down: 1E-1->1E-2 µm/s 1E-1->1E-3 µm/s Direct decrease in friction and % sliding contacts. Gradual rise in direct effect, to lower steady- state values. -> Velocity Strengthening

26. SUMMARY Using a simple log-time dependent contact healing law, we are able to reproduce many aspects of observed rate-state friction response. Most interesting is that our contacts are purely elastico-frictional – All “plasticity” is contained within granular interactions. What is “state” – geometry and particle packing?

27. Now for the – ANIMATIONS (http://terra.rice.edu/department/faculty/~morganj)