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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.