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A thermal pressurization model for the spontaneous ...: 2. Traction evolution and dynamic parameters
Language
English
Status
Published
JCR Journal
JCR Journal
Peer review journal
Yes
Title of the book
Issue/vol(year)
/ 111 (2006)
Publisher
Agu
Pages (printed)
B05304
Issued date
2006
Keywords
Abstract
We investigate the dynamic traction evolution during the spontaneous propagation of
a 3-D earthquake rupture governed by slip-weakening or rate- and state-dependent
constitutive laws and accounting for thermal pressurization effects. The analytical
solutions as well as temperature and pore pressure evolutions are discussed in the
companion paper by Bizzarri and Cocco. Our numerical experiments reveal that frictional
heating and thermal pressurization modify traction evolution. The breakdown stress drop,
the characteristic slip-weakening distance, and the fracture energy depend on the slipping
zone thickness (2w) and hydraulic diffusivity (w). Thermally activated pore pressure
changes caused by frictional heating yield temporal variations of the effective normal
stress acting on the fault plane. In the framework of rate- and state-dependent friction,
these thermal perturbations modify both the effective normal stress and the friction
coefficient. Breakdown stress drop, slip-weakening distance, and specific fracture energy
(J/m2) increase for decreasing values of hydraulic diffusivity and slipping zone thickness.
We propose scaling relations to evaluate the effect of w and w on these physical
parameters. We have also investigated the effects of choosing different evolution laws for
the state variable. We have performed simulations accounting for the porosity evolution
during the breakdown time. Our results point out that thermal pressurization modifies
the shape of the slip-weakening curves. For particular configurations, the traction versus
slip curves display a gradual and continuous weakening for increasing slip: in these cases,
the definitions of a minimum residual stress and the slip-weakening distance become
meaningless.
a 3-D earthquake rupture governed by slip-weakening or rate- and state-dependent
constitutive laws and accounting for thermal pressurization effects. The analytical
solutions as well as temperature and pore pressure evolutions are discussed in the
companion paper by Bizzarri and Cocco. Our numerical experiments reveal that frictional
heating and thermal pressurization modify traction evolution. The breakdown stress drop,
the characteristic slip-weakening distance, and the fracture energy depend on the slipping
zone thickness (2w) and hydraulic diffusivity (w). Thermally activated pore pressure
changes caused by frictional heating yield temporal variations of the effective normal
stress acting on the fault plane. In the framework of rate- and state-dependent friction,
these thermal perturbations modify both the effective normal stress and the friction
coefficient. Breakdown stress drop, slip-weakening distance, and specific fracture energy
(J/m2) increase for decreasing values of hydraulic diffusivity and slipping zone thickness.
We propose scaling relations to evaluate the effect of w and w on these physical
parameters. We have also investigated the effects of choosing different evolution laws for
the state variable. We have performed simulations accounting for the porosity evolution
during the breakdown time. Our results point out that thermal pressurization modifies
the shape of the slip-weakening curves. For particular configurations, the traction versus
slip curves display a gradual and continuous weakening for increasing slip: in these cases,
the definitions of a minimum residual stress and the slip-weakening distance become
meaningless.
References
Abercrombie, R. E., and J. R. Rice (2005), Can observations of earthquake
scaling constrain slip weakening?, Geophys. J. Int., 162, 406–424.
Andrews, D. J. (1976), Rupture propagation with finite stress in antiplane
strain, J. Geophys. Res., 81, 3575– 3582.
Andrews, D. J. (2002), A fault constitutive relation accounting for thermal
pressurization of pore fluid, J. Geophys. Res., 107(B12), 2363,
doi:10.1029/2002JB001942.
Beeler, N. M., T. E. Tullis, and J. D. Weeks (1994), The roles of time and
displacement in the evolution effect in rock friction, Geophys. Res. Lett.,
21, 1987–1990.
Bizzarri, A., and M. Cocco (2003), Slip-weakening behavior during the
propagation of dynamic ruptures obeying rate- and state-dependent friction
laws, J. Geophys. Res., 108(B8), 2373, doi:10.1029/2002JB002198.
Bizzarri, A., and M. Cocco (2005), 3-D dynamic simulations of spontaneous
rupture propagation governed by different constitutive laws with
oblique initial stress direction, Ann. Geophys., 48, 277– 299.
Bizzarri, A., and M. Cocco (2006), A thermal pressurization model for the
spontaneous dynamic rupture propagation on a three-dimensional fault: 1.
Methodological approach, J. Geophys. Res., 111, B05303, doi:10.1029/
2005JB003862.
Campillo, M., and I. R. Ionescu (1997), Initiation of antiplane shear instability
under slip dependent friction, J. Geophys. Res., 102, 20,363–
20,371.
Cocco, M., and A. Bizzarri (2002), On the slip-weakening behavior of rateand
state dependent constitutive laws, Geophys. Res. Lett., 29(11), 1516,
doi:10.1029/2001GL013999.
Dalguer, L. A., K. Irikura, W. Zhang, and J. D. Riera (2002), Distribution of
dynamic and static stress changes during 2000 Tottori (Japan) earthquake:
Brief interpretation of the earthquake sequences; foreshocks, mainshock
and aftershocks, Geophys. Res. Lett., 29(16), 1758, doi:10.1029/
2001GL014333.
Das, S., and K. Aki (1977a), A numerical study of two-dimensional
spontaneous rupture propagation, Geophys. J. R. Astron. Soc., 50,
643–668.
Das, S., and K. Aki (1977b), Fault plane with barriers: A versatile earthquake
model, J. Geophys. Res., 82, 5658–5670.
Fialko, Y. (2004), Temperature fields generated by the elastodynamic propagation
of shear cracks in the Earth, J. Geophys. Res., 109, B01303,
doi:10.1029/2003JB002497.
Kanamori, H., and T. H. Heaton (2000), Microscopic and macroscopic
physics of earthquakes, GeoComplexity and the Physics of Earthquakes,
Geophys. Monogr. Ser., vol. 120, edited by J. B. Rundle, D. L. Turcotte,
and W. Klein, pp. 147–163, AGU, Washington, D. C.
Lachenbruch, A. H. (1980), Frictional heating, fluid pressure, and the resistance
to fault motion, J. Geophys. Res., 85, 6097– 6122.
Linker, M. F., and J. H. Dieterich (1992), Effects of variable normal stress
on rock friction: Observations and constitutive equations, J. Geophys.
Res., 97, 4923–4940.
Mair, K., and C. Marone (1999), Friction of simulated fault gauge for a
wide range of slip velocities and normal stresses, J. Geophys. Res., 104,
28,899–28,914.
Manning, C. E., and S. E. Ingebritsen (1999), Permeability of the continental
crust: Implications of geothermal data and metamorphic systems,
Rev. Geophys., 37, 127–150.
McGarr, A., J. B. Fletcher, and N. M. Beeler (2004), Attempting to bridge
the gap between laboratory and seismic estimates of fracture energy,
Geophys. Res. Lett., 31, L14606, doi:10.1029/2004GL020091.
Miller, S. A. (2002), Properties of large ruptures and the dynamical influence
of fluids on earthquakes and faulting, J. Geophys. Res., 107(B9),
2182, doi:10.1029/2000JB000032.
Nakatani, M. (1998), A new mechanism of slip weakening and strength
recovery of friction associated with the mechanical consolidation of
gouge, J. Geophys. Res., 103, 27,239–27,256.
Noda, H., and T. Shimamoto (2005), Thermal pressurization and slip-weakening
distance of a fault: An example of the Hanaore Fault, Southwest
Japan, Bull. Seismol. Soc. Am., 95(4), 1224 – 1233, doi:10.1785/
0120040089.
Ohnaka, M. (2003), A constitutive scaling law and a unified comprehension
for frictional slip failure, shear fracture of intact rock, and earthquake
rupture, J. Geophys. Res., 108(B2), 2080, doi:10.1029/2000JB000123.
Ohnaka, M., Y. Kuwahara, and K. Yamamoto (1987), Constitutive relations
between dynamic physical parameters near a tip of the propagating slip
zone during stick-slip shear failure, Tectonophysics, 144, 109– 125.
Okubo, P. G., and J. H. Dieterich (1984), Effects of physical fault properties
on frictional instabilities produced on simulated faults, J. Geophys. Res.,
89, 5817– 5827.
Palmer, A. C., and J. R. Rice (1973), The growth of slip surfaces in the
progressive failure of overconsolidated clay, Proc. R. Soc. London, Ser. A,
332, 527– 548.
Scholz, C. H., N. H. Dawers, J.-Z. Yu, M. H. Anders, and P. A. Cowie
(1993), Fault growth and fault scaling laws: Preliminary results, J. Geophys.
Res., 98, 21,951–21,961.
Segall, P., and J. R. Rice (1995), Dilatancy, compaction, and slip instability
of a fluid-infiltrated fault, J. Geophys. Res., 100, 22,155–22,171.
Sibson, R. H. (1977), Kinetic shear resistance, fluid pressures and radiation
efficiency during seismic faulting, Pure Appl. Geophys., 115, 387– 400.
Sibson, R. H. (2003), Thickness of the seismic slip zone, Bull. Seismol. Soc.
Am., 93, 1169– 1178.
Sleep, N. H. (1995a), Frictional heating and the stability of rate and state
dependent frictional sliding, Geophys. Res. Lett., 22, 2785–2788.
Sleep, N. H. (1995b), Ductile creep, compaction, and rate and state dependent
friction within major fault zones, J. Geophys. Res., 100, 13,065–
13,080.
Sleep, N. H. (1997), Application of a unified rate and state friction theory to
the mechanics of fault zones with strain localization, J. Geophys. Res.,
102, 2875– 2895.
Sleep, N. H. (1999), Rate- and state-dependent friction of intact rock and
gouge, J. Geophys. Res., 104, 17,847–17,855.
Tinti, E., A. Bizzarri, A. Piatanesi, and M. Cocco (2004), Estimates of slip
weakening distance for different dynamic rupture models, Geophys. Res.
Lett., 31, L02611, doi:10.1029/2003GL018811.
Tinti, E., P. Spudich, and M. Cocco (2005), Earthquake fracture energy
inferred from kinematic rupture models on extended faults, J. Geophys.
Res., 110, B12303, doi:10.1029/2005JB003644.
Wibberley, C. A. J., and T. Shimamoto (2003), Internal structure and permeability
of major strike-slip fault zones: The Median Tectonic Line in
mid prefecture, southwest Japan, J. Struct. Geol., 25, 59–78.
scaling constrain slip weakening?, Geophys. J. Int., 162, 406–424.
Andrews, D. J. (1976), Rupture propagation with finite stress in antiplane
strain, J. Geophys. Res., 81, 3575– 3582.
Andrews, D. J. (2002), A fault constitutive relation accounting for thermal
pressurization of pore fluid, J. Geophys. Res., 107(B12), 2363,
doi:10.1029/2002JB001942.
Beeler, N. M., T. E. Tullis, and J. D. Weeks (1994), The roles of time and
displacement in the evolution effect in rock friction, Geophys. Res. Lett.,
21, 1987–1990.
Bizzarri, A., and M. Cocco (2003), Slip-weakening behavior during the
propagation of dynamic ruptures obeying rate- and state-dependent friction
laws, J. Geophys. Res., 108(B8), 2373, doi:10.1029/2002JB002198.
Bizzarri, A., and M. Cocco (2005), 3-D dynamic simulations of spontaneous
rupture propagation governed by different constitutive laws with
oblique initial stress direction, Ann. Geophys., 48, 277– 299.
Bizzarri, A., and M. Cocco (2006), A thermal pressurization model for the
spontaneous dynamic rupture propagation on a three-dimensional fault: 1.
Methodological approach, J. Geophys. Res., 111, B05303, doi:10.1029/
2005JB003862.
Campillo, M., and I. R. Ionescu (1997), Initiation of antiplane shear instability
under slip dependent friction, J. Geophys. Res., 102, 20,363–
20,371.
Cocco, M., and A. Bizzarri (2002), On the slip-weakening behavior of rateand
state dependent constitutive laws, Geophys. Res. Lett., 29(11), 1516,
doi:10.1029/2001GL013999.
Dalguer, L. A., K. Irikura, W. Zhang, and J. D. Riera (2002), Distribution of
dynamic and static stress changes during 2000 Tottori (Japan) earthquake:
Brief interpretation of the earthquake sequences; foreshocks, mainshock
and aftershocks, Geophys. Res. Lett., 29(16), 1758, doi:10.1029/
2001GL014333.
Das, S., and K. Aki (1977a), A numerical study of two-dimensional
spontaneous rupture propagation, Geophys. J. R. Astron. Soc., 50,
643–668.
Das, S., and K. Aki (1977b), Fault plane with barriers: A versatile earthquake
model, J. Geophys. Res., 82, 5658–5670.
Fialko, Y. (2004), Temperature fields generated by the elastodynamic propagation
of shear cracks in the Earth, J. Geophys. Res., 109, B01303,
doi:10.1029/2003JB002497.
Kanamori, H., and T. H. Heaton (2000), Microscopic and macroscopic
physics of earthquakes, GeoComplexity and the Physics of Earthquakes,
Geophys. Monogr. Ser., vol. 120, edited by J. B. Rundle, D. L. Turcotte,
and W. Klein, pp. 147–163, AGU, Washington, D. C.
Lachenbruch, A. H. (1980), Frictional heating, fluid pressure, and the resistance
to fault motion, J. Geophys. Res., 85, 6097– 6122.
Linker, M. F., and J. H. Dieterich (1992), Effects of variable normal stress
on rock friction: Observations and constitutive equations, J. Geophys.
Res., 97, 4923–4940.
Mair, K., and C. Marone (1999), Friction of simulated fault gauge for a
wide range of slip velocities and normal stresses, J. Geophys. Res., 104,
28,899–28,914.
Manning, C. E., and S. E. Ingebritsen (1999), Permeability of the continental
crust: Implications of geothermal data and metamorphic systems,
Rev. Geophys., 37, 127–150.
McGarr, A., J. B. Fletcher, and N. M. Beeler (2004), Attempting to bridge
the gap between laboratory and seismic estimates of fracture energy,
Geophys. Res. Lett., 31, L14606, doi:10.1029/2004GL020091.
Miller, S. A. (2002), Properties of large ruptures and the dynamical influence
of fluids on earthquakes and faulting, J. Geophys. Res., 107(B9),
2182, doi:10.1029/2000JB000032.
Nakatani, M. (1998), A new mechanism of slip weakening and strength
recovery of friction associated with the mechanical consolidation of
gouge, J. Geophys. Res., 103, 27,239–27,256.
Noda, H., and T. Shimamoto (2005), Thermal pressurization and slip-weakening
distance of a fault: An example of the Hanaore Fault, Southwest
Japan, Bull. Seismol. Soc. Am., 95(4), 1224 – 1233, doi:10.1785/
0120040089.
Ohnaka, M. (2003), A constitutive scaling law and a unified comprehension
for frictional slip failure, shear fracture of intact rock, and earthquake
rupture, J. Geophys. Res., 108(B2), 2080, doi:10.1029/2000JB000123.
Ohnaka, M., Y. Kuwahara, and K. Yamamoto (1987), Constitutive relations
between dynamic physical parameters near a tip of the propagating slip
zone during stick-slip shear failure, Tectonophysics, 144, 109– 125.
Okubo, P. G., and J. H. Dieterich (1984), Effects of physical fault properties
on frictional instabilities produced on simulated faults, J. Geophys. Res.,
89, 5817– 5827.
Palmer, A. C., and J. R. Rice (1973), The growth of slip surfaces in the
progressive failure of overconsolidated clay, Proc. R. Soc. London, Ser. A,
332, 527– 548.
Scholz, C. H., N. H. Dawers, J.-Z. Yu, M. H. Anders, and P. A. Cowie
(1993), Fault growth and fault scaling laws: Preliminary results, J. Geophys.
Res., 98, 21,951–21,961.
Segall, P., and J. R. Rice (1995), Dilatancy, compaction, and slip instability
of a fluid-infiltrated fault, J. Geophys. Res., 100, 22,155–22,171.
Sibson, R. H. (1977), Kinetic shear resistance, fluid pressures and radiation
efficiency during seismic faulting, Pure Appl. Geophys., 115, 387– 400.
Sibson, R. H. (2003), Thickness of the seismic slip zone, Bull. Seismol. Soc.
Am., 93, 1169– 1178.
Sleep, N. H. (1995a), Frictional heating and the stability of rate and state
dependent frictional sliding, Geophys. Res. Lett., 22, 2785–2788.
Sleep, N. H. (1995b), Ductile creep, compaction, and rate and state dependent
friction within major fault zones, J. Geophys. Res., 100, 13,065–
13,080.
Sleep, N. H. (1997), Application of a unified rate and state friction theory to
the mechanics of fault zones with strain localization, J. Geophys. Res.,
102, 2875– 2895.
Sleep, N. H. (1999), Rate- and state-dependent friction of intact rock and
gouge, J. Geophys. Res., 104, 17,847–17,855.
Tinti, E., A. Bizzarri, A. Piatanesi, and M. Cocco (2004), Estimates of slip
weakening distance for different dynamic rupture models, Geophys. Res.
Lett., 31, L02611, doi:10.1029/2003GL018811.
Tinti, E., P. Spudich, and M. Cocco (2005), Earthquake fracture energy
inferred from kinematic rupture models on extended faults, J. Geophys.
Res., 110, B12303, doi:10.1029/2005JB003644.
Wibberley, C. A. J., and T. Shimamoto (2003), Internal structure and permeability
of major strike-slip fault zones: The Median Tectonic Line in
mid prefecture, southwest Japan, J. Struct. Geol., 25, 59–78.
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