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Unformatted text preview: Mechanics of Earthquakes and Faulting Mechanics of Earthquakes and Faulting • Energy balance for crack propagation • Stress intensity factors • Static & dynamic fracture mechanics • Critical energy release rate • Process zone • Crack models • Failure Criteria 31 Jan. 2007 σ 22 σ 23 σ 21 r r’ G is Energy flow to crack tip per unit new crack area G = 1  h ( ) 2 m g I v ( ) K I 2 + g II v ( ) K II 2 [ ] + 1 2 m g III v ( ) K III 2 G = G critical = 2 g Critical energy release rate ∆ u 2 D u 1 D u 3 ≠ 4 1  h ( ) m r ' 2 p g I v ( ) K I g II v ( ) K II g III v ( ) K III 1  h ( ) G is a material property the “fracture energy” G = K / E = 2 γ , where K is the critical stress intensity factor (also known as the Static vs. dynamic fracture mechanics, relativistic effects ∆ u 2 D u 1 D u 3 ≠ 4 1 h ( ) m r ' 2 p g I v ( ) K I g II v ( ) K II g III v ( ) K III 1 h ( ) g I ( ) = g II ( ) = g III ( ) =1 Static g I v ( ) and = g II v ( ) , as v C R g III v ( ) = 1 1 h 2 / C s 2 , as v C s Dynamic crack propagation σ 22 σ 23 σ 21 v 1 2 r θ r r’ Stress field is singular at the crack tip. • because we assumed perfectly sharp crack • but real materials cannot support infinite stress σ 22 s 21 s 23 tip 1 2 pr K I K II K III K I = pc s Process zone (Irwin) to account for nonlinear zone of plastic flow and cracking • Size of this zone will depend upon crack velocity, material properties and crack geometry • Energy dissipation in the crack tip region helps to limit the stresses there (why?) σ 22 σ 23 σ 21 r r’ Fault tip stresses, process zone Slip. ∆ u x • Boxcar function, assuming infinite material strength • Elastic model (Eshelby) • Dugdale • Smallscale yielding • e.g., depthaveraged coseismic or postseismic slip distribution; geologic data on the relationship between fault slip and fault length Crack tip stress field, real materials σ r • Singular crack (Eshelby)...
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This note was uploaded on 07/23/2008 for the course GEOSC 508 taught by Professor Marone during the Spring '07 term at Penn State.
 Spring '07
 MARONE

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