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Rate and State friction law

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Chaitanya Raval

In this presentation i have given basic fault study and the important rate and state friction law. The presentation walks through the elastic rebound theory also. Thus the basic idea of why earthquake occurs, how this rate and state law came into the picture is crystal clear.

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Study on fault basics and Rate and state friction law Presented By:- RAVAL CHAITANYA IU1751210010 Guided By:- Assistant Professor Vasudeo Chaudhari
Objective Understanding rate and state friction law of motion to get dynamic analysis of particular earthquake 2
Introduction Fault is a fracture/zone of fracture between two blocks of rock In a simple way, fault is the movement of rock on either side Faults are the boundaries of huge plates that make up earths crust If the rock movement is sudden, it causes earthquake If the rock movement is slow, it is called creep, an aseismic process Faults can be horizontal, vertical or oblique Angle of fault with respect to surface (dip) and direction of slip along fault are defined to classify faults 3
Types of fault Faults which move along the direction of dip plane are dip-slip faults (in vertical direction) If hanging wall moves downward, it is called Normal fault slip If hanging wall moves upward, it is called Reverse (Thrust) fault slip Faults which move horizontally are called strike-slip fault If the far block on either side moves in left, it is called left lateral strike-slip If the far block on either side moves in right, it is called right lateral strike-slip Sometimes fault doesnt come up to the surface, it is known as Blinded fault 4
Dip-slip fault 5 Figure 1: Normal fault slip Figure 2: Reverse( thrust ) fault slip
Strike-slip fault 6 Figure 4: Right lateral strike-slipFigure 3: Left lateral strike-slip
What is an earthquake? Earthquake is the energy released due to sudden movement of rocks in form of seismic waves Causes of earthquake : 1 Surface causes 2 Volcanic causes 3 Tectonic causes 7
Elastic rebound theory Elastic rebound theory represents the occurrence of tectonic earthquake Considering an earthquake has just occurred in a block, which causes co-seismic deformation After certain time many after-shocks will cause post-seismic deformation Considering time t = 0, when all energy is dissipated Slow accumulation of stress between the blocks will start from t = 0 Pre-seismic deformation may occur between blocks in few centimeters for many years 8
Conti 9 Figure 5: Elastic Rebound
Conti The stress accumulated in the blocks are not uniformly distributed, it is localized stress at different portion Localized stresses are concentrated in a narrow band in width around the fault Once the deformation around the fault is such that the stresses are greater than the frictional resistance of blocks, earthquake is triggered At t = 0, sudden release of accumulated slip on fault occurs, which causes slip on the fault, known as elastic rebound Earthquake is a cyclic process, not necessarily periodic 10
Nucleation procedure Fault rupture causes an earthquake The point at which the earthquake is triggered is known as Nucleation, rupture than propagate in all direction from the nucleation point Fault rupture may have only one or many ruptures on the fault plane Many times earthquake triggered at one point causes perturbation on nearer fault, which leads the other fault earthquake having an earthquake, called induced vibration 11
Asperity, slip, recurrence time, slip-rate Whenever two plates collide, there is chance that one plate sub-duct the other one At one point, the sub-ducting plate and the upper plate get locked as they both move towards each other The locked area is known as Asperity of fault Whenever earthquake occurs, the relative displacement occurs between two plates, it is known as Slip The duration between two major events is called recurrence time interval Suppose major event of earthquake occurs every 1000 years and average slip per major event is 3 meters, then the average creep of 3000/1000 = 3 mm/year occurs, called slip rate 12
Stick-slip motion Any variation in frictional resistance during sliding causes dynamic instability, a sudden movement occurs due to stress drop In repetitions, the sliding occurs when stress is recharged, followed by another instability Essentially, in such systems where sliding occurs due to instability, such frictional behavior is called regular stick-slip. 13
Conti 14 Figure 11: Force-displacement diagram Figure 10: Block slider model
Conti Condition for instability, > K Coulomb proposed that the static friction coefficient must exceed the dynamic coefficient of friction for the unstable sliding Robanowicz said if two surfaces are kept stationary, given the load for time t, the static friction coefficient increases with log t Robanowicz proposed Critical distance Dc, when friction value is changed from one value to other, the instability is given by, 袖 袖 > K 15
Rate and state friction Time and velocity both are important aspects for friction An increase of 袖 upon the initiation of sliding, followed by previous decay of steady- state value, the effect is called healing As Deiterich-Ruina stated that friction depends on instantaneous sliding velocity V and time-dependent variable 慮 袖 = 袖 (V, 慮) = 袖0 + a* ln 0 + b* ln 0 where, = 1 - 16
Conti 17 Figure 12(A): Static-dynamic model Figure 12(B): Slip weakening Figure 12(C): Deiterich-Ruina friction model
Conti (A) for shear stress, = 袖*, where 袖 is coefficient of friction and is normal stress (B) shear stress is the decreasing function of slip un to 倹 and then remain at constant stress, most common way is piece-wise linear Alternative law is Stribeck-curve, depending on a single quantity yet pure velocity dependence fails to give the stress drop at particular point Aging law for healing and slip law for rapid change in slip are combined for proper result 18
Conti The friction at steady state velocity, 袖 = 袖0 + (a-b) * ln 0 if 袖 is defined as 袖 at velocity V, then 袖 ln = a-b In the static case when 慮 = t, so for long hold times 袖 (ln ) = b the friction jump of the direct effect is given by 袖 = a* ln 2 1 19
A and B parameters Seismogenic layer If a > b, rate strengthening If a < b, rate weakening 20 Figure 13: Parameters A and B effect in generation of earthquake
References STICK-SLIP INSTABILITIES AND SHEAR STRAIN LOCALIZATION IN AMORPHOUS MATERIALS EG Daub, JM Carlson - Physical Review E, 2009 AFTERSLIP AND AFTERSHOCKS IN THE RATEANDSTATE FRICTION LAW A Helmstetter, BE Shaw - Journal of Geophysical Research: Solid Earth, 2009 SOURCE SCALING PROPERTIES FROM FINITE-FAULT-RUPTURE MODELS PM Mai, GC Beroza - Bulletin of the Seismological Society of America, 2000 THE DYNAMIC ANALYSIS OF STICK-SLIP MOTION C Gao, D Kuhlmann-Wilsdorf, DD Makel - Wear, 1994 [HTML] TOWARDS A UNIVERSAL RULE ON THE RECURRENCE INTERVAL SCALING OF REPEATING EARTHQUAKES? KH Chen, RM Nadeau, RJ Rau - Geophysical Research Letters, 2007 [PDF] SEMINAR ON B-VALUE O Kulhanek - Dept. of Geophysics, Charles University, Prague, 2005 21
References NONLINEAR STRAIN BUILDUP AND THE EARTHQUAKE CYCLE ON THE SAN ANDREAS FAULT W Thatcher - Journal of Geophysical Research: Solid Earth, 1983 THEORETICAL AND QUANTITATIVE ANALYSES OF THE FAULT SLIP RATE UNCERTAINTIES FROM SINGLE EVENT AND EROSION OF THE ACCUMULATED OFFSET Z Ren, Z Zhang, T Chen, W Wang - Island Arc, 2013 ON THE VARIATION OF B-VALUES WITH EARTHQUAKE SIZE EA Okal, BA Romanowicz - Physics of the Earth and Planetary Interiors, 1994 SOURCE MECHANISMS OF EARTHQUAKES: THEORY AND PRACTICE A Ud鱈as, R Madariaga, E Buforn - 2014 THE MECHANICS OF EARTHQUAKES AND FAULTING- BY CHRISTOPHER H. SCHOLZ RA Harris - Seismological Research Letters, 2003 22
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Rate and State friction law

  • 1. Study on fault basics and Rate and state friction law Presented By:- RAVAL CHAITANYA IU1751210010 Guided By:- Assistant Professor Vasudeo Chaudhari
  • 2. Objective Understanding rate and state friction law of motion to get dynamic analysis of particular earthquake 2
  • 3. Introduction Fault is a fracture/zone of fracture between two blocks of rock In a simple way, fault is the movement of rock on either side Faults are the boundaries of huge plates that make up earths crust If the rock movement is sudden, it causes earthquake If the rock movement is slow, it is called creep, an aseismic process Faults can be horizontal, vertical or oblique Angle of fault with respect to surface (dip) and direction of slip along fault are defined to classify faults 3
  • 4. Types of fault Faults which move along the direction of dip plane are dip-slip faults (in vertical direction) If hanging wall moves downward, it is called Normal fault slip If hanging wall moves upward, it is called Reverse (Thrust) fault slip Faults which move horizontally are called strike-slip fault If the far block on either side moves in left, it is called left lateral strike-slip If the far block on either side moves in right, it is called right lateral strike-slip Sometimes fault doesnt come up to the surface, it is known as Blinded fault 4
  • 5. Dip-slip fault 5 Figure 1: Normal fault slip Figure 2: Reverse( thrust ) fault slip
  • 6. Strike-slip fault 6 Figure 4: Right lateral strike-slipFigure 3: Left lateral strike-slip
  • 7. What is an earthquake? Earthquake is the energy released due to sudden movement of rocks in form of seismic waves Causes of earthquake : 1 Surface causes 2 Volcanic causes 3 Tectonic causes 7
  • 8. Elastic rebound theory Elastic rebound theory represents the occurrence of tectonic earthquake Considering an earthquake has just occurred in a block, which causes co-seismic deformation After certain time many after-shocks will cause post-seismic deformation Considering time t = 0, when all energy is dissipated Slow accumulation of stress between the blocks will start from t = 0 Pre-seismic deformation may occur between blocks in few centimeters for many years 8
  • 9. Conti 9 Figure 5: Elastic Rebound
  • 10. Conti The stress accumulated in the blocks are not uniformly distributed, it is localized stress at different portion Localized stresses are concentrated in a narrow band in width around the fault Once the deformation around the fault is such that the stresses are greater than the frictional resistance of blocks, earthquake is triggered At t = 0, sudden release of accumulated slip on fault occurs, which causes slip on the fault, known as elastic rebound Earthquake is a cyclic process, not necessarily periodic 10
  • 11. Nucleation procedure Fault rupture causes an earthquake The point at which the earthquake is triggered is known as Nucleation, rupture than propagate in all direction from the nucleation point Fault rupture may have only one or many ruptures on the fault plane Many times earthquake triggered at one point causes perturbation on nearer fault, which leads the other fault earthquake having an earthquake, called induced vibration 11
  • 12. Asperity, slip, recurrence time, slip-rate Whenever two plates collide, there is chance that one plate sub-duct the other one At one point, the sub-ducting plate and the upper plate get locked as they both move towards each other The locked area is known as Asperity of fault Whenever earthquake occurs, the relative displacement occurs between two plates, it is known as Slip The duration between two major events is called recurrence time interval Suppose major event of earthquake occurs every 1000 years and average slip per major event is 3 meters, then the average creep of 3000/1000 = 3 mm/year occurs, called slip rate 12
  • 13. Stick-slip motion Any variation in frictional resistance during sliding causes dynamic instability, a sudden movement occurs due to stress drop In repetitions, the sliding occurs when stress is recharged, followed by another instability Essentially, in such systems where sliding occurs due to instability, such frictional behavior is called regular stick-slip. 13
  • 14. Conti 14 Figure 11: Force-displacement diagram Figure 10: Block slider model
  • 15. Conti Condition for instability, > K Coulomb proposed that the static friction coefficient must exceed the dynamic coefficient of friction for the unstable sliding Robanowicz said if two surfaces are kept stationary, given the load for time t, the static friction coefficient increases with log t Robanowicz proposed Critical distance Dc, when friction value is changed from one value to other, the instability is given by, 袖 袖 > K 15
  • 16. Rate and state friction Time and velocity both are important aspects for friction An increase of 袖 upon the initiation of sliding, followed by previous decay of steady- state value, the effect is called healing As Deiterich-Ruina stated that friction depends on instantaneous sliding velocity V and time-dependent variable 慮 袖 = 袖 (V, 慮) = 袖0 + a* ln 0 + b* ln 0 where, = 1 - 16
  • 17. Conti 17 Figure 12(A): Static-dynamic model Figure 12(B): Slip weakening Figure 12(C): Deiterich-Ruina friction model
  • 18. Conti (A) for shear stress, = 袖*, where 袖 is coefficient of friction and is normal stress (B) shear stress is the decreasing function of slip un to 倹 and then remain at constant stress, most common way is piece-wise linear Alternative law is Stribeck-curve, depending on a single quantity yet pure velocity dependence fails to give the stress drop at particular point Aging law for healing and slip law for rapid change in slip are combined for proper result 18
  • 19. Conti The friction at steady state velocity, 袖 = 袖0 + (a-b) * ln 0 if 袖 is defined as 袖 at velocity V, then 袖 ln = a-b In the static case when 慮 = t, so for long hold times 袖 (ln ) = b the friction jump of the direct effect is given by 袖 = a* ln 2 1 19
  • 20. A and B parameters Seismogenic layer If a > b, rate strengthening If a < b, rate weakening 20 Figure 13: Parameters A and B effect in generation of earthquake
  • 21. References STICK-SLIP INSTABILITIES AND SHEAR STRAIN LOCALIZATION IN AMORPHOUS MATERIALS EG Daub, JM Carlson - Physical Review E, 2009 AFTERSLIP AND AFTERSHOCKS IN THE RATEANDSTATE FRICTION LAW A Helmstetter, BE Shaw - Journal of Geophysical Research: Solid Earth, 2009 SOURCE SCALING PROPERTIES FROM FINITE-FAULT-RUPTURE MODELS PM Mai, GC Beroza - Bulletin of the Seismological Society of America, 2000 THE DYNAMIC ANALYSIS OF STICK-SLIP MOTION C Gao, D Kuhlmann-Wilsdorf, DD Makel - Wear, 1994 [HTML] TOWARDS A UNIVERSAL RULE ON THE RECURRENCE INTERVAL SCALING OF REPEATING EARTHQUAKES? KH Chen, RM Nadeau, RJ Rau - Geophysical Research Letters, 2007 [PDF] SEMINAR ON B-VALUE O Kulhanek - Dept. of Geophysics, Charles University, Prague, 2005 21
  • 22. References NONLINEAR STRAIN BUILDUP AND THE EARTHQUAKE CYCLE ON THE SAN ANDREAS FAULT W Thatcher - Journal of Geophysical Research: Solid Earth, 1983 THEORETICAL AND QUANTITATIVE ANALYSES OF THE FAULT SLIP RATE UNCERTAINTIES FROM SINGLE EVENT AND EROSION OF THE ACCUMULATED OFFSET Z Ren, Z Zhang, T Chen, W Wang - Island Arc, 2013 ON THE VARIATION OF B-VALUES WITH EARTHQUAKE SIZE EA Okal, BA Romanowicz - Physics of the Earth and Planetary Interiors, 1994 SOURCE MECHANISMS OF EARTHQUAKES: THEORY AND PRACTICE A Ud鱈as, R Madariaga, E Buforn - 2014 THE MECHANICS OF EARTHQUAKES AND FAULTING- BY CHRISTOPHER H. SCHOLZ RA Harris - Seismological Research Letters, 2003 22