Download FRICTION PROBLEMS IN EARTHQUAKE SOURCE MECHANICS

FRICTION PROBLEMS IN EARTHQUAKE
SOURCE MECHANICS
by
George P. Mavroeidis
Department of Civil Engineering
The Catholic University of America
NSF Workshop on Friction
Montreux, Switzerland
March 13-16, 2008
Introduction
•
Definition: Engineering Seismology is that part of seismology dealing
with earthquakes close enough to the causative source where ground
motion is strong enough to pose a threat to engineering structures.
•
Objective: Estimation of strength, frequency content, duration and
spatial variability of the most destructive ground shaking that is likely to
occur at a site.
•
Approach: Combination of deterministic and stochastic ground motion
simulation techniques, taking into account source, path and site effects.
•
Outcome: Seismic input in various formats (e.g., time histories, response
spectra, peak ground motion parameters or spectral values) for
engineering analysis and design.
Earthquake Source Mechanics
• Objective: Understanding of the earthquake generation process.
(a) Exploration of physical phenomena underlying fracture and friction.
(b) Development of physical models for the qualitative and quantitative
description of inhomogeneous faulting and the prediction of strong
ground motion.
• Special Features:
(a) Large-scale nature of frictional interactions.
(b) Role of lubrication (solid-fluid-solid interaction) in controlling
earthquake faulting.
(c) Until recently, researchers could neither experiment with nor directly
observe the earthquake focal region.
NSF EarthScope Program –
San Andreas Fault Observatory at Depth (SAFOD)
An ambitious scientific initiative that
aims at providing answers to several
issues:
(a) Composition, physical properties,
and mechanical behavior of rocks in
an active fault zone.
(b) Nature of stresses responsible for
earthquakes.
(c) Physics of earthquake nucleation,
rupture and friction, propagation and
arrest.
A deep hole was drilled to install
geophysical instruments (~2-3 km
beneath the Earth’s surface) within the
San Andreas Fault zone in Parkfield,
CA, for long-term monitoring.
(http://earthquake.usgs.gov/research/parkfield/)
(d) Role of lubrication in controlling
fault strength and earthquake
recurrence.
NSF EarthScope Program –
San Andreas Fault Observatory at Depth (SAFOD)
Preliminary Results (Hickman et al., 2007):
Stress orientation and magnitude is consistent with a weak San Andreas
fault in an otherwise strong crust.
• Low friction (µ<0.2) along the fault and high friction elsewhere.
• Pore pressure confined to the fault zone (e.g., Rice, 1992).
•
Laboratory Earthquakes
• Objective: Provide insight into the mutual interactions of frictional
shear failure, heat production, and fluid or melt lubrication.
• Challenges:
(a) How to develop experimental setups that accurately emulate
field conditions?
(b) How to upscale the laboratory results to the field scale?
• Progress: New very high slip-rate friction experiments have
displayed phenomena strikingly similar to field observation despite
the huge reduction in scale.
Further progress requires active cross-disciplinary collaborations
of rock physics experimentalists and theoreticians with geologists,
seismologists, and other field scale geoscientists.
Laboratory Earthquakes
Laboratory
investigation of subRayleigh-tosupershear rupture
transition by
spontaneously
nucleated dynamic
rupture event in
frictional interfaces
held together by farfield tectonic loads
(Xia, Rosakis, and
Kanamori, 2004).
Fault Lubrication (Solid-Fluid-Solid Interface)
Physical Problem
• Fluids exert a strong influence on the sliding behavior of faults through both
mechanical and chemical effects.
• An elevated fluid pressure is generated in a thin film of viscous fluid that is
sheared between nearly parallel surfaces.
• The lubrication pressure supports part of the load, therefore reducing the
normal stress and the associated friction across the gap.
Modeling
• The fluid motion between two subparallel planes is described by the NavierStokes equation assuming a flow through a thin and rough gap (i.e., small
Reynolds number).
• According to Brodsky and Kanamori (2001), the lubrication model can be
parameterized using Sommerfeld number (i.e., measure of the lubrication
pressure normalized by the lithostatic load).
• Key parameters: fluid viscosity, slip zone thickness, fault velocity and
displacement, lithostatic load.
• Lubrication pressure reduces the frictional stress during an earthquake by as
much as 30% relative to hydrostatic value or 50% relative to the dry rock
friction.
Fault Lubrication (Solid-Fluid-Solid Interface)
Difference in lubrication
as S increases
(Kanamori, 2004)
•
•
S = PL / P0 = (6 η U L) / (d2 P0) (Sommerfeld Number)
As S increases, friction decreases and the speed of fault motion increases.
The wall is flattened by elastic deformation and the gap is widened because
of increased lubrication pressure. Excitation of high-frequency energy due to
collision of asperities is then suppressed.
Other Issues
• Role of frictional heating and thermal pressurization of pore fluids on
earthquake rupture and friction.
• Role of frictional heating and melting on earthquake rupture and friction.
Kinematic Source Models
In the absence of detailed physical descriptions of a scale-dependent process,
we are forced to use classical continuum mechanics and a phenomenological
approach to describe fault weakening and rupture propagation on a virtual
mathematical plane of zero thickness.
Recorded Data
–
–
–
–
Strong Motion
Teleseismic
Geodetic / GPS
Tsunami
Crustal Model
– P- and S-wave velocities
– Density
Source Parameters
Kinematic
Source Model
+
Inversion
Algorithm
– Slip
– Rise Time
– Rupture Velocity
Fault Geometry
– Length, Width
– Strike, Dip
Source parameters are not necessarily related through a constitutive law and
should be considered as macroscopic parameters (i.e., not directly associated
with the processes occurring at smaller scales).
Dynamic Source Models
Recorded Data
–
–
–
–
Strong Motion
Teleseismic
Geodetic / GPS
Tsunami
Crustal Model
– P- and S-wave velocities
– Density
Source Parameters
Dynamic
Source Model
+
Inversion
Algorithm
– Slip
– Rise Time
– Rupture Velocity
Fault Geometry
– Length, Width
– Strike, Dip
•
Dynamic source models require source parameters to obey certain physical
laws of elastodynamics and a prescribed friction criterion.
•
There are uncertainties regarding the nature of the frictional law and the
state of stress on the fault prior the earthquake (initial conditions).
•
The stress drop is frequently specified as a spatial random field consistent
with the statistical properties of the slip heterogeneity found in finite-source
models of past earthquakes.
Fracture and Friction
Fracture is dominant in deformation of rocks without preexisting macroscopic
failure zones => Coulomb criteria and Mohr circle analysis.
Friction is dominant in situations with preexisting sliding surfaces.
(Ohnaka, 2003)
•
•
•
The constitutive law for shear rupture needs to be formulated in terms of observable
quantities.
The shear stress acting on both walls of the fault zone thickness is commonly used
for the constitutive formulation.
The shear stress acting on individual asperities, gauge fragments, and cracks
contained in the fault zone or the shear stress acting on the real, macroscopic rupture
surfaces formed in the fault zone are not observable.
Fracture and Friction
•
•
•
Fault motion does not occur smoothly, but rather in a stop-and-go fashion, called
stick-slip frictional instability. The earthquake is the “slip” and the interseismic
period of elastic strain accumulation is the “stick”.
Friction changes as a function of slip, velocity and history of sliding surface. An
earthquake can occur, if friction decreases rapidly with slip.
Several forms of rate- and state-dependent friction models [e.g., Dietrich, 1979,
1981; Ruina, 1983] have been used to model laboratory observations. They provide
a conceptual framework incorporating the main stages of an earthquake cycle and is
widely used in seismology.
Suddenly imposed increase
and the decrease in sliding
velocity (after Scholz, 1998).
Forward Simulation Analysis:
Kinematic and Dynamic Source Models
Source Parameters
– Slip
– Rise Time
– Rupture Velocity
Fault Geometry
– Length, Width
– Strike, Dip
Kinematic or
Dynamic
Source Models
Synthetic Data
– Time Histories
– Response Spectra
Crustal Model
– P- and S-wave velocities
– Density
•
Actual Earthquakes: Source parameters are obtained from inversion
analysis of recorded data (i.e., strong motion, teleseismic, geodetic, etc) for
the specific seismic event.
•
Hypothetical Earthquakes: Source parameters are obtained from statistical
processing of results of finite-source models of past earthquakes and
development of correlated spatial distributions of source parameters.
Characterization of Surface Rupture and Asperities
Heterogeneous rupture during the 1966
Parkfield, California, earthquake
(modified from Aki, 1979).
Specific Barrier Model
(Papageorgiou and Aki, 1983)
•
The “Specific Barrier Model” is a physical model of the earthquake source for the quantitative
description of inhomogeneous faulting and the prediction of strong ground motion.
•
The model consists of circular cracks of equal diameter (2ρ0) (referred to as the “barrier
interval”), filling up a rectangular fault of length L and width W.
•
As the rupture front sweeps the fault plane with the “sweeping velocity” V, a stress drop (Δσ)
(referred to as the “local stress drop”) takes place in each crack starting from its center and
spreading with a “spreading velocity” υ.
•
The model is described by five (5) parameters: L, W, V (= υ), 2ρ0 and Δσ.
Summary
•
Earthquake source mechanics is a research area characterized by the
interaction between solid-solid interfaces and lubrication flows.
•
The characterization of surface roughness and asperities with a view to
predicting system response is a critical issue.
•
The development of a full frictional law that takes into account several
earthquake phenomena (i.e., seismogenesis and seismic coupling, pre- and
post-seismic phenomena, effect of stress transients, lubrication, thermal
pressurization, melting, etc) is a challenging issue.
•
Field investigations (e.g., NSF EarthScope Program) and laboratory
experiments are anticipated to shed light into several open issues including:
(a) physical properties of rocks,
(b) nature of stresses responsible for earthquakes,
(c) physics of earthquake nucleation, rupture and friction, propagation and
arrest, and
(d) role of lubrication in controlling fault strength and earthquake
recurrence.