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On the transient behavior of frictional melt during seismic slip
Author(s)
Language
English
Obiettivo Specifico
3.1. Fisica dei terremoti
Status
Published
JCR Journal
JCR Journal
Peer review journal
Yes
Title of the book
Issue/vol(year)
/115 (2010)
Publisher
American Geophysical Union
Pages (printed)
B10301
Issued date
June 1, 2010
Abstract
In a recent work on the problem of sliding surfaces under the presence
of frictional melt (applying in particular to earthquake fault dynamics),
we derived from first principles an expression for the steady state
friction compatible with experimental observations. Building on the
expressions of heat and mass balance obtained in the above study for
this particular case of Stefan problem (phase transition with a migrating
boundary) we propose here an extension providing the full time-dependent
solution (including the weakening transient after pervasive melting
has started, the effect of eventual steps in velocity and the final
decelerating phase). A system of coupled equations is derived and
solved numerically. The resulting transient friction and wear evolution
yield a satisfactory fit (1) with experiments performed under variable
sliding velocities (0.9-2 m/s) and different normal stresses (0.5-20
MPa) for various rock types and (2) with estimates of slip weakening
obtained from observations on ancient seismogenic faults that host
pseudotachylite (solidified melt). The model allows to extrapolate
the experimentally observed frictional behavior to large normal stresses
representative of the seismogenic Earth crust (up to 200 MPa), high
slip rates (up to 9 m/s) and cases where melt extrusion is negligible.
Though weakening distance and peak stress vary widely, the net breakdown
energy appears to be essentially independent of either slip velocity
and normal stress. In addition, the response to earthquake-like slip
can be simulated, showing a rapid friction recovery when slip rate
drops. We discuss the properties of energy dissipation, transient
duration, velocity weakening, restrengthening in the decelerating
final slip phase and the implications for earthquake source dynamics.
of frictional melt (applying in particular to earthquake fault dynamics),
we derived from first principles an expression for the steady state
friction compatible with experimental observations. Building on the
expressions of heat and mass balance obtained in the above study for
this particular case of Stefan problem (phase transition with a migrating
boundary) we propose here an extension providing the full time-dependent
solution (including the weakening transient after pervasive melting
has started, the effect of eventual steps in velocity and the final
decelerating phase). A system of coupled equations is derived and
solved numerically. The resulting transient friction and wear evolution
yield a satisfactory fit (1) with experiments performed under variable
sliding velocities (0.9-2 m/s) and different normal stresses (0.5-20
MPa) for various rock types and (2) with estimates of slip weakening
obtained from observations on ancient seismogenic faults that host
pseudotachylite (solidified melt). The model allows to extrapolate
the experimentally observed frictional behavior to large normal stresses
representative of the seismogenic Earth crust (up to 200 MPa), high
slip rates (up to 9 m/s) and cases where melt extrusion is negligible.
Though weakening distance and peak stress vary widely, the net breakdown
energy appears to be essentially independent of either slip velocity
and normal stress. In addition, the response to earthquake-like slip
can be simulated, showing a rapid friction recovery when slip rate
drops. We discuss the properties of energy dissipation, transient
duration, velocity weakening, restrengthening in the decelerating
final slip phase and the implications for earthquake source dynamics.
Sponsors
S.N. and G.D.T. were supported by a European Research Council Starting
Grant Project (acronym USEMS) and by a Progetti di Eccellenza Fondazione
Cassa di Risparmio di Padova e Rovigo. We are grateful to Nick Beeler
(and to an anonymous referee) for their constructive reviews and their
help to improve the clarity of the manuscript.
Grant Project (acronym USEMS) and by a Progetti di Eccellenza Fondazione
Cassa di Risparmio di Padova e Rovigo. We are grateful to Nick Beeler
(and to an anonymous referee) for their constructive reviews and their
help to improve the clarity of the manuscript.
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170, edited by R.~Abercombie, A.~McGarr, H.~Kanamori, and G.~D. Toro,
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basis of fault strength due to flash heating, \textit{J. Geophys. Res.},
\textit{113}(B1), B01,401, {doi:10.1029/2007JB004988}, 2008.
\bibitem[{\textit{Bizzarri and Cocco}(2006)}]{bizzarri:2006}
Bizzarri, A., and M.~Cocco, A thermal pressurization model for the spontaneous
dynamic rupture propagation on a three-dimensional fault: 1. methodological
approach, \textit{J. Geophys. Res.}, \textit{111}, B05,303, 2006.
\bibitem[{\textit{Brantut et~al.}(2008)\textit{Brantut, Schubnel, Rouzaud,
Brunet, and Shimamoto}}]{brantut:2008}
Brantut, N., A.~Schubnel, J.~Rouzaud, F.~Brunet, and T.~Shimamoto, High
velocity frictional properties of a natural clay bearing fault gouge,
\textit{J. Geophys. Res.}, \textit{113}, B10,401, {doi:10.1029/2007JB005551},
2008.
\bibitem[{\textit{Brodsky and Kanamori}(2001)}]{brodsky:2001}
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\bibitem[{\textit{Brune et~al.}(1969)\textit{Brune, Henyey, and
Roy}}]{brune:1969}
Brune, J., T.~Henyey, and R.~Roy, Heat flow, stress, and rate of slip along the
san andreas fault, california, \textit{J. Geophys. Res.}, \textit{74},
3821--3827., 1969.
\bibitem[{\textit{Brune et~al.}(1993)\textit{Brune, Brown, and
Johnson}}]{brune:1993}
Brune, J.~N., S.~Brown, and P.~A. Johnson, Rupture mechanism and interface
separation in foam ruber models of earthquakes: A possible solution to the
heat flow solution and the paradox of large overthrusts,
\textit{Tectonophysics}, \textit{218}, 59--67, 1993.
\bibitem[{\textit{Cardwell et~al.}(1978)\textit{Cardwell, Chinn, Moore, and
Turcotte}}]{cardwell:1978}
Cardwell, R., D.~Chinn, G.~Moore, and D.~Turcotte, Frictional heating on a
fault zone with finite thickness, \textit{Geophys. J. Roy. Astr. Soc.},
\textit{52}, 525--530, 1978.
\bibitem[{\textit{Carslaw and Jaeger}(1959)}]{carslaw:1986}
Carslaw, H.~S., and J.~C. Jaeger, \textit{Conduction of Heat in Solids}, Oxford
University Press, USA, 1959.
\bibitem[{\textit{Cocco and Tinti}(2008)}]{cocco:2008}
Cocco, M., and E.~Tinti, Scale dependence in the dynamics of earthquake
propagation; evidence from seismological and geological observations,
\textit{Earth and Planetary Science Letters}, \textit{273}, 123--131, 2008.
\bibitem[{\textit{Crank and Nicolson}(1947)}]{crank:1947}
Crank, J., and P.~Nicolson, A practical method for numerical evaluation of
solutions of partial differential equations of the heat conduction type,
\textit{Proc. Camb. Phil. Soc.}, \textit{43}, 50--67, 1947.
\bibitem[{\textit{Del~Gaudio et~al.}(2009)\textit{Del~Gaudio, {Di Toro}, Han,
Hirose, Nielsen, Shimamoto, and Cavallo}}]{delgaudio:2009}
Del~Gaudio, P., G.~{Di Toro}, R.~Han, T.~Hirose, S.~Nielsen, T.~Shimamoto, and
A.~Cavallo, Frictional melting of peridotite and seismic slip, \textit{J.
Geophys. Res.}, \textit{114}, B06,306, {doi:10.1029/2008JB005990}, 2009.
\bibitem[{\textit{{Di~Toro} and Pennacchioni}(2004)}]{ditoro:2004}
{Di~Toro}, G., and G.~Pennacchioni, Superheated friction-induced melts in zoned
pseudotachylytes within the adamello tonalites (italian southern alps),
\textit{J. Struct. Geol.}, \textit{26}, 1783--1801, 2004.
\bibitem[{\textit{{Di~Toro} et~al.}(2004)\textit{{Di~Toro}, Goldsby, and
Tullis}}]{ditoro:2004b}
{Di~Toro}, G., D.~Goldsby, and T.~Tullis, Friction falls towards zero in quartz
rock as slip velocity approaches seismic rates, \textit{Nature},
\textit{427}, 436--439, 2004.
\bibitem[{\textit{{Di~Toro} et~al.}(2005)\textit{{Di~Toro}, Pennacchioni, and
Teza}}]{ditoro:2005}
{Di~Toro}, G., G.~Pennacchioni, and G.~Teza, Can {P}seudotachylyte be used to
infer earthquake source parameters? {An} example of limitations in the study
if exhumed faults, \textit{Tectonophysics}, \textit{402}, 3--20,
{doi:10.1016/j.tecto.2004.10.014}, 2005.
\bibitem[{\textit{{Di Toro} et~al.}(2006a)\textit{{Di Toro}, Hirose, Nielsen,
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