Rheology and the Lithosphere
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1 Rheology and the Lithosphere Processes in Structural Geology & Tectonics Ben van der Pluijm WW Norton+Authors, unless noted otherwise 3/8/ :51
2 We Discuss Rheology and the Lithosphere What is rheology? Insights from rock deformation experiments Characteristic stress-strain behaviors General creep curve Composite elastic and viscous rheologies Time-dependent rock behavior Maxwell relaxation time Non-linear rheologies Plastic flow stresses Crust and (upper) mantle strength curve(s) Defining lithosphere and asthenosphere Lithologic vs rheologic layering The Lithosphere PSG&T 2
3 Rheology is... the study of deformation (flow) of materials. Associated concepts: Stress Strain, Strain rate Elasticity Viscosity Failure and Friction Plasticity Malaspina Glacier, AK (NASA) The Lithosphere PSG&T 3
4 Earth s Layering The Lithosphere PSG&T 4
5 Insights from Rock Experiments Triaxial deformation apparatus Brittle Plastic Compression and extension experiments The Lithosphere PSG&T 5
6 Confining Pressure Suppresses fracturing Promotes ductility (distributed strain) Increases strength (maximum stress) The Lithosphere PSG&T 6
7 Temperature Suppresses fracturing Promotes ductility Reduces strength The Lithosphere PSG&T 7
8 Fluid Pressure P f P c Inverse form P c : P f P eff = P c - P f ~ 1/P c The Lithosphere PSG&T 8
9 Strain rate ė = 10-6 /sec is 30% change in 4 days ė = /sec is 30% change in 1 million years Fast ~100 MPa Slow ~10 MPa Small ė (significantly) reduces rock strength The Lithosphere PSG&T 9
10 Summary of Rock Responses to P c, P f, T, ė Low Pc, high Pf, low T, (high ė): promotes fracturing High Pc, low Pf, high T, (low ė): promotes viscous flow = upper crust = lower crust, mantle The Lithosphere PSG&T 10
11 Characteristic Stress-Strain Behaviors Representative stress-strain curves. (A) Elastic behavior followed by failure. (B) Small viscous (permanent) strain before failure. (C) Significant viscous (permanent) strain before failure. Yield stress marks stress at change from elastic (recoverable) to viscous (permanent) strain; Failure stress is stress at fracturing. Work hardening/softening. (D) No elastic component and requiring lower stresses to deform: work softening. (E) Elastic-plastic behavior, with permanent strain accumulation at constant stress. (F) Elastic-plastic behavior, requiring increasingly higher stresses to deform: work hardening. The Lithosphere PSG&T 11
12 Strength and Competency Rock strength is maximum stress a material can support before failure. Competency is relative strength term that compares resistance of rocks to deformation. Rock competency scale: Low-grade: rock salt < shale < limestone < greywacke < sandstone < dolomite High-grade: schist < marble < quartzite < gneiss < granite < basalt The Lithosphere PSG&T 12
13 Rock Experiments: the General Creep Curve Creep: I. Elastic, II. Viscous, III. Accelerated viscous. a) Under continued stress a material will fail. b) If we remove stress before failure, material relaxes (elastic component) while permanent (viscous) strain remains. The Lithosphere PSG&T 13
14 Rheologic Models: Elastic and Viscous Behavior Elastic behavior rubber band s = E. e (s s = G. g); Pa Viscous behavior water, syringe s =. ė ; t-dependent; Pa.s s dt = s.t Matching the general creep curve with elastic and viscous rheologies The Lithosphere PSG&T 15
15 Elastic+Viscous Rheologies: Visco-elastic General creep curve (strain time) Visco-elastic behavior water-soaked sponge, memory foam The Lithosphere PSG&T 16
16 Elastic+Viscous Rheologies: Elastico-viscous General creep curve (strain time) Visco-elastic behavior water-soaked sponge, memory foam Elastico-viscous behavior mayonnaise, toothpaste The Lithosphere PSG&T 17
17 Elastic+Viscous Rheologies: General Linear Behavior General creep curve (strain time) Visco-elastic behavior water-soaked sponge, memory foam Elastico-viscous behavior mayonnaise, silly putty General Linear behavior ~natural rock The Lithosphere PSG&T 18
18 Summary: Linear Rheologic Models Elastic behavior rubber band s = E. e (s s = G. g) Viscous behavior water s =. ė ; s dt = s.t Visco-elastic behavior water-soaked sponge, memory foam Elastico-viscous behavior mayonnaise, silly putty General Linear behavior ~rock The Lithosphere PSG&T 19
19 Time-dependent Rock Behavior Rock is like silly putty : elastic or break (fast) or viscous (slow) as f ion of time (strain rate). For example, both earthquakes and mantle plumes in Earth. Crust Mantle Maxwell Relaxation Time: t M = /G is dominance of viscosity ( ) over elasticity (G) Unit: t M = (s/(e/t)) / s/e = time The Lithosphere PSG&T 20
20 Maxwell relaxation time, t M Viscosity (strain rate) is temperature-dependent, so t M (= /G) is T-dependent. t M range plotted in t-t space. Crust Mantle Elasticity dominates on seismic timescales (failure). Viscosity dominates on tectonic timescales (flow). The Lithosphere PSG&T 21
21 Elastic and Viscous Earth Elastic Earth: Mantle viscosity of Pa s, rigidity of Pa (olivine-dominated mantle) t M = s that is, order of 1000 years (e.g., Earth s fast glacial rebound). Viscous Earth: Mantle viscous flow stress: s =. ė = = 10 7 Pa = 10MPa The Lithosphere PSG&T 22
22 Linear vs. Non-linear Rheologies General linear behavior (from analogues) Non-linear (or elastic-plastic) behavior (from experiments) The Lithosphere PSG&T 23
23 Linear vs. Non-linear Viscous Behavior Effective viscosity: Linear rheology ( fluid ) Non-linear rheology ( solid ) ė = 1/. s A = proportionality constant E = activation energy ( kj/mol) R = gas constant (8.3 J/K.mol) T = temperature (K) n = stress exponent (2-5) The Lithosphere PSG&T 24
24 Quantification from Rock Experiments Brittle Plastic Triaxial deformation apparatus The Lithosphere PSG&T 25
25 Plastic Flow Stresses Salt Quartzite Anorthosite Dunite solve for σ The Lithosphere PSG&T 26
26 Friction vs. Plasticity (strength curves) Salt Quartzite Anorthosite Friction: s = 2s n. m [s = 2s s ] Flow: Dunite The Lithosphere PSG&T 27
27 Composite Strength Curves Salt Quartzite Anorthosite Dunite Stacked sandwich lithosphere model (deluxe peanut butter-jelly sandwich) Qz: Strong Qz: Weak Fsp: Strong Fsp: Weak Ol: Strong The Lithosphere PSG&T 28
28 Earth s Lithosphere Lithologic layering Rheologic layering The Lithosphere PSG&T 29
29 Lithospheric Deformation Regimes Frictional Regime Pressure (P l and P f ) dependent (frictional laws) temperature and strain insensitive shear stress is primarily function of normal stress: s s f(s n ) P l /s d T( o C) Rock Regime Plastic Regime Pressure (P l and P f ) insensitive temperature and strain rate dependent (flow laws) shear stress is primarily function of temperature and strain rate: s s f(t,ė) The Lithosphere PSG&T 30
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