James R Rice | Harvard University (original) (raw)
Papers by James R Rice
Journal of Applied Mechanics, 1982
BOOK REVIEW problems by various methods. An appendix discusses finite element methods. The chapte... more BOOK REVIEW problems by various methods. An appendix discusses finite element methods. The chapter on applications in classical mechanics and elasticity is almost too comprehensive. He discusses least action, Hamilton's principle, as well as all of the standard variational principles of infinitesimal elastostatics, elastodynamics, and finite elastostatics. Several examples are given. The chapter on heat conduction is likewise very complete. He discusses the stationary equations, both linear and nonlinear, the nonstationary linear equations, both the standard parabolic equations and the hyperbolic equations, and finally several results for nonstationary nonlinear theory. The chapter on coupled thermoelasticity skims over several variational principles from the recent literature. This set of notes could easily form a text for a graduate engineering course, as the presentation is very concise and thorough. Instabilities and Catastrophes in Science and Engineering.
Journal of the Mechanics and Physics of Solids, 2001
It has been shown recently that steady frictional sliding along an interface between dissimilar e... more It has been shown recently that steady frictional sliding along an interface between dissimilar elastic solids with Coulomb friction acting at the interface is ill-posed for a wide range of material parameters and friction coefficients. The ill-posedness is manifest in the unstable growth of interfacial disturbances of all wavelengths, with growth rate inversely proportional to the wavelength. We first establish the connection between the ill-posedness and the existence of a certain interfacial wave in frictionless contact, called the generalized Rayleigh wave. Precisely, it is shown that for material combinations where the generalized Rayleigh wave exists, steady sliding with Coulomb friction is ill-posed for arbitrarily small values of friction. In addition, intersonic unstable modes and supersonic steady-state modes exist for sufficiently large values of the friction coefficient. Secondly, regularization of the problem by an experimentally motivated friction law is studied. We show that a friction law with no instantaneous dependence on normal stress but a simple fading memory of prior history of normal stress makes the problem well-posed.
Journal of Geophysical Research, Jul 20, 2010
Glaciological observations of under-flooding suggest that fluid-induced hydraulic fracture of an ... more Glaciological observations of under-flooding suggest that fluid-induced hydraulic fracture of an ice sheet from its bed sometimes occurs quickly, possibly driven by turbulently flowing water in a broad sheet flow. Taking the approximation of a fully turbulent flow into an elastic ice medium with small fracture toughness, we derive an approximate expression for the crack-tip speed, opening displacement and pressure profile. We accomplish this by first showing that a Manning-Strickler channel model for resistance to turbulent flow leads to a mathematical structure somewhat similar to that for resistance to laminar flow of a power law viscous fluid. We then adapt the plane-strain asymptotic crack solution of Desroches et al. (1994) and the power law self-similar solution of Adachi and Detournay (2002) for that case to calculate the desired quantities. The speed of crack growth is shown to scale as the overpressure (in excess of ice overburden) to the power 7/6, inversely as ice elastic modulus to the power 2/3, and as the ratio of crack length to wall roughness scale to the power 1/6. We tentatively apply our model by choosing parameter values thought appropriate for a basal crack driven by the rapid drainage of a surface meltwater lake near the margin of the Greenland Ice Sheet. Making various approximations perhaps relevant to this setting, we estimate fluid inflow rate to the basal fracture and vertical and horizontal surface displacements and find order-of-magnitude agreement with observations by Das et al. (2008) associated with lake drainage. Finally, we discuss how these preliminary estimates could be improved.
As preparation for a workshop on "The Dynamics of Fault Zones" (95 th Dahlem Workshop, ... more As preparation for a workshop on "The Dynamics of Fault Zones" (95 th Dahlem Workshop, Berlin, January 2005), specifically on the sub-topic "Rheology of Fault Rocks and Their Surroundings", we addressed critical research issues for understanding the seismic response of fault zones in terms of the constitutive response of fault materials. That requires new concepts and a host of new observations and experiments to document material response, to understand the shear localization process and the inception of earthquake instability, and especially to understand the mechanisms of fault weakening and dynamics of rupture tip propagation and arrest during rapid, possibly large, slip in natural events. We examine in turn the geological structure of fault zones and its relation to earthquake dynamics, the description of rate and state friction at slow rates appropriate to the interseismic period and earthquake nucleation, and the dynamics of fault weakening during rapid sl...
We examine, and find evidence to support, the hypothesis that the width of Siple Coast ice stream... more We examine, and find evidence to support, the hypothesis that the width of Siple Coast ice streams in West Antarctica is set by the development of significant internal melting (i.e., development of temperate ice conditions) within the ice sheet at the margins. We first illustrate, from published ice sheet deformation data and from simple 1-D thermal modeling based on temperature-dependent flow and conduction properties, that most existing Siple Coast ice stream margins are in a state of partial melt, with temperate ice being present over a substantial fraction of the sheet thickness. We show that, although the margins sustain high lateral strain rates, they can support (and hence transmit to the cold ridges) notably less lateral shear stress than would the somewhat less rapidly deforming ice located inboard, away from the ridge. We then propose, and quantify approximately, a possible related mechanism of margin formation, that is, of locking the sheet to the bed at the margin. Shear...
Journal of Geophysical Research: Earth Surface, 2018
Antarctic mass balance and contribution to sea level rise are dominated by the flow of ice throug... more Antarctic mass balance and contribution to sea level rise are dominated by the flow of ice through narrow conduits called ice streams. These regions of relatively fast flow drain over 90% of the ice sheet and generate significant amounts of frictional heat at the ice stream margins where there is a transition to slow flow in the ridge. This heat can generate temperate ice and a sharp transition in flow speed between the stream and the ridge. Within zones of temperate ice, meltwater is produced and drains to the bed. Here we model the downstream development of a temperate zone along an ice stream shear margin and the flow of meltwater through temperate ice into a subglacial hydrologic system. The hydrology sets the basal effective pressure, defined as the difference between ice overburden and water pressure. Using the southern shear margin of Bindschadler Ice Stream as a case study, our model results indicate an abrupt transition from a distributed to channelized hydrologic system wi...
Journal of Geophysical Research: Solid Earth, 2018
Injection‐induced seismicity is thought to be due primarily to increase in fluid pore pressure, w... more Injection‐induced seismicity is thought to be due primarily to increase in fluid pore pressure, which reduces the shear strength of a nearby fault. We address the modeling and prediction of the hydromechanical response due to fluid injection, mainly as wastewater disposal. We consider the full poroelastic effects, including the changes in porosity and permeability of the medium due to changes in local volumetric strains. Our results consider effects of the fault architecture (low‐permeability fault core and anisotropic high‐permeability damage zones) on the pressure diffusion and the fault poroelastic response. We show that the high‐permeable damage zone, the poroelastic response, and the permeability evolution can accelerate the pore pressure diffusion process during and after wastewater injection. By studying a geologically based model of the Guy‐Greenbrier fault and of the earthquake sequence induced along it in Arkansas, United States, from October 2010 to July 2011, we show tha...
Journal of Applied Mechanics, 2015
A 2008 report by Das et al. documented the rapid drainage during summer 2006 of a supraglacial la... more A 2008 report by Das et al. documented the rapid drainage during summer 2006 of a supraglacial lake, of approximately 44×106 m3, into the Greenland ice sheet over a time scale moderately longer than 1 hr. The lake had been instrumented to record the time-dependent fall of water level and the uplift of the ice nearby. Liquid water, denser than ice, was presumed to have descended through the sheet along a crevasse system and spread along the bed as a hydraulic facture. The event led two of the present authors to initiate modeling studies on such natural hydraulic fractures. Building on results of those studies, we attempt to better explain the time evolution of such a drainage event. We find that the estimated time has a strong dependence on how much a pre-existing crack/crevasse system, acting as a feeder channel to the bed, has opened by slow creep prior to the time at which a basal hydraulic fracture nucleates. We quantify the process and identify appropriate parameter ranges, part...
Science, 1976
We report on the experimental observation of spontaneously nucleated ruptures occurring on fricti... more We report on the experimental observation of spontaneously nucleated ruptures occurring on frictionally held bimaterial interfaces with small amounts of wave speed mismatch. Rupture is always found to be asymmetric bilateral. In one direction, rupture always propagates at the generalized Rayleigh wave speed, whereas in the opposite direction it is subshear or it transitions to supershear. The lack of a preferred rupture direction and the conditions leading to supershear are discussed in relation to existing theory and to the earthquake sequence in Parkfield, California, and in North Anatolia.
Mechanics of Materials, 1984
A general formulation of two-dimensional elastic-perfectly-plastic anti-plane straining is presen... more A general formulation of two-dimensional elastic-perfectly-plastic anti-plane straining is presented for materials with arbitrary anisotropic convex yield surfaces. Stress and strain distributions in plastic regions adjoining portions of the boundary are obtained directly in terms of the yield surface geometry. When specialized to the classical torsion problem, results lead directly to a generalization of the well-known plastic roof construction for limit loads. Examples of the determination of fully plastic stress distributions and corresponding limit torques are given for circular and rectangular shafts with various yield conditions. Another specialization is made to the contained plastic deformation created by longitudinal shearing of a body containing a sharp edge notch. Here the determination of the elastic-plastic boundary and strain distribution is reduced to a potential theory problem for a region in the stress plane bounded by straight line segments and a portion of the yield surface, and a membrane analogy is presented which allows effective visualization of the solution. A solution valid for small scale yielding near a crack is given in terms of a conformal transformation of the yield surface to a unit circle, and some specific examples are worked. Particular attention is given to single crystal type yield surfaces made up of straight line segments corresponding to discrete slip planes.
Journal of the Mechanics and Physics of Solids, 1985
AESTRACT CRACKS in ductile single crystals are analyzed here for geometries and orientations such... more AESTRACT CRACKS in ductile single crystals are analyzed here for geometries and orientations such that twodimensional states of anti-plane shear constitute possible deformation fields. The crystals are modelled as ideally plastic and yield according to critical resolved shear stresses on their slip systems. Restrictions on the asymptotic forms of stress and deformation fields at crack tips are established for anti-plane loading of stationary and quasistatically growing cracks, and solutions are presented for several specific orientations in f.c.c. and b.c.c. crystals. The asymptotic solutions are complemented by complete elastic-plastic solutions for stationary and growing cracks under small scale yielding, based on previous work by RICE (1967,1984) and FREUND (1979). Remarkably, the plastic zone at a stationary crack tip collapses into discrete planes of displacement and stress discontinuity emanating from the tip; plastic flow consists of concentrated shear on the displacement discontinuities. For the growing crack these same planes, if not coincident with the crack plane, constitute collapsed plastic zones in which velocity and plastic strain discontinuities occur, but across which the stresses and anti-plane displacement are fully continuous. The planes of discontinuity are in several cases coincident with crystal slip planes but it is shown that this need not be the case, e.g., for orientations in which anti-plane yielding occurs by multi-slip, or for special orientations in which the crack tip and the discontinuity planes are perpendicular to the activated slip plane.
Journal of the Mechanics and Physics of Solids, 1994
A HALF-PLANE CRACK propagates dynamically, nominally in the x direction. along the plane _V = 0 i... more A HALF-PLANE CRACK propagates dynamically, nominally in the x direction. along the plane _V = 0 in an unbounded solid subjected to remote loading equivalent to a static stress intensity factor K*. The crack front at time t lies along the arc x = c,,t+a_/'(z, t) where a,) is a constant velocity, J'(z, t) is an arbitrary
Journal of the Mechanics and Physics of Solids, 2001
We study the stability of steady sliding between elastically deformable continua using rate and s... more We study the stability of steady sliding between elastically deformable continua using rate and state dependent friction laws. That is done for both elastically identical and elastically dissimilar solids. The focus is on linearized response to perturbations of steady-state sliding, and on studying how the positive direct e ect (instantaneous increase or decrease of shear strength in response to a respective instantaneous increase or decrease of slip rate) of those laws allows the existence of a quasi-static range of response to perturbations at su ciently low slip rate. We discuss the physical basis of rate and state laws, including the likely basis for the direct e ect in thermally activated processes allowing creep slippage at asperity contacts, and estimate activation parameters for quartzite and granite. Also, a class of rate and state laws suitable for variable normal stress is presented. As part of the work, we show that compromises from the rate and state framework for describing velocity-weakening friction lead to paradoxical results, like supersonic propagation of slip perturbations, or to ill-posedness, when applied to sliding between elastically deformable solids. The case of sliding between elastically dissimilar solids has the inherently destabilizing feature that spatially inhomogeneous slip leads to an alteration of normal stress, hence of frictional resistance. We show that the rate and state friction laws nevertheless lead to stability of response to su ciently short wavelength perturbations, at very slow slip rates. Further, for slow sliding between dissimilar solids, we show that there is a critical amplitude of velocity-strengthening above which there is stability to perturbations of all wavelengths.
Journal of Geophysical Research, 2010
Journal of Geophysical Research, 2011
Material juxtapositions across mature faults are a common occurrence. Previous work has found tha... more Material juxtapositions across mature faults are a common occurrence. Previous work has found that this elastic mismatch results in a rupture that will preferentially propagate in the direction of slip displacement on the more compliant side of the fault, with more off-fault damage in the stiffer material. This result has implications for inferring preferred rupture directions based on observations of damage zone asymmetry. We perform a complete numerical investigation of the role of the stress state on the distribution of plastic deformation and the direction of preferred rupture propagation. We show that there are important factors, in addition to the elastic mismatch, which control the preferred direction of propagation as well as the side of the fault in which damage predominately accumulates. The orientation of the most compressive principal stress is the controlling factor in determining the location of plastic deformation. For different orientations, plastic deformation can accumulate in either the stiffer or the more compliant material. For high angles of most compressive stress, the aforementioned preferred rupture direction prediction holds true. However, the off-fault plastic response can reverse that direction for low angles of most compressive stress so that rupture will preferentially propagate in the direction of slip displacement in the stiffer material.
Journal of Geophysical Research: Solid Earth, 2009
We analyze the nucleation and propagation of shear cracks along nonplanar, kinked, and branched f... more We analyze the nucleation and propagation of shear cracks along nonplanar, kinked, and branched fault paths corresponding to the configurations used in recent laboratory fracture studies by Rousseau and Rosakis (2003, 2009). The aim is to reproduce numerically those shear rupture experiments and from that provide an insight into processes which are active when a crack, initially propagating in mode II along a straight path, interacts with a bend in the fault or a branching junction. The experiments involved impact loading of thin Homalite‐100 (a photoelastic polymer) plates, which had been cut along bent or branched paths and weakly glued back together everywhere except along a starter notch near the impact site. Strain gage recordings and high‐speed photography of isochromatic lines provided characterization of the transient deformation fields associated with the impact and fracture propagation. We found that dynamic explicit 2‐D plane‐stress finite element analyses with a simple l...
Journal of Geophysical Research: Solid Earth, 2000
Faults often separate materials with different elastic properties. Nonuniform slip on such faults... more Faults often separate materials with different elastic properties. Nonuniform slip on such faults induces a change in normal stress. That suggests the possibility of self‐sustained slip pulses [Weertman, 1980] propagating at the generalized Rayleigh wave speed even with a Coulomb constitutive law (i.e., with a constant coefficient of friction) and a remote driving shear stress that is arbitrarily less than the corresponding frictional strength. Following Andrews and Ben‐Zion [1997] (ABZ), we study numerically, with a two‐dimensional (2‐D) plane strain geometry, the propagation of ruptures along such a dissimilar material interface. However, this problem has been shown to be ill‐posed for a wide range of elastic material contrasts [Renardy, 1992; Martins and Simões, 1995; Adams, 1995]. Ranjith and Rice [2000] (RR) showed that when the generalized Rayleigh speed exists, as is the case for the material contrast studied by ABZ, the problem is ill‐posed for all values of the coefficient ...
Journal of Geophysical Research: Solid Earth, 2000
What are the origins of earthquake complexity? The possibility that some aspects of the complexit... more What are the origins of earthquake complexity? The possibility that some aspects of the complexity displayed by earthquakes might be explained by stress heterogeneities developed through the self‐organization of repeated ruptures has been suggested by some simple self‐organizing models. The question of whether or not even these simple self‐organizing models require at least some degree of material heterogeneity to maintain complex sequences of events has been the subject of some controversy. In one class of elastodynamic models, previous work has described complexity as arising on a model fault with completely uniform material properties. Questions were raised, however, regarding the role of discreteness, the relevance of the nucleation mechanism, and special parameter choices, in generating the complexity that has been reported. In this paper, we examine the question of whether or not continuum complexity is achieved under the stringent conditions of continuous loading, and whether...
Journal of Geophysical Research: Solid Earth, 2002
On the basis of elastodynamic stress fields for singular crack and nonsingular slip‐weakening mod... more On the basis of elastodynamic stress fields for singular crack and nonsingular slip‐weakening models of propagating rupture, we develop preliminary answers to such questions as follows: If a rupturing fault is intersected by another, providing a possible bend in the failure path, when will stressing be consistent with rupture along the bend? What secondary fault locations and orientations, in a damaged region bordering a major fault, will be stressed to failure by the main rupture? Stresses that could initiate rupture on a bend are shown to increase dramatically with crack speed, especially near the limiting speed (Rayleigh for mode II, shear for mode III). Whether a bend path, once begun, can be continued to larger scales depends on principal stress directions and ratios in the prestress field. Conditions should often be met in mode II for which bend paths encouraged by stressing very near the rupture tip are discouraged by the larger‐scale stressing, a basis for intermittent ruptu...
Journal of Applied Mechanics, 1982
BOOK REVIEW problems by various methods. An appendix discusses finite element methods. The chapte... more BOOK REVIEW problems by various methods. An appendix discusses finite element methods. The chapter on applications in classical mechanics and elasticity is almost too comprehensive. He discusses least action, Hamilton's principle, as well as all of the standard variational principles of infinitesimal elastostatics, elastodynamics, and finite elastostatics. Several examples are given. The chapter on heat conduction is likewise very complete. He discusses the stationary equations, both linear and nonlinear, the nonstationary linear equations, both the standard parabolic equations and the hyperbolic equations, and finally several results for nonstationary nonlinear theory. The chapter on coupled thermoelasticity skims over several variational principles from the recent literature. This set of notes could easily form a text for a graduate engineering course, as the presentation is very concise and thorough. Instabilities and Catastrophes in Science and Engineering.
Journal of the Mechanics and Physics of Solids, 2001
It has been shown recently that steady frictional sliding along an interface between dissimilar e... more It has been shown recently that steady frictional sliding along an interface between dissimilar elastic solids with Coulomb friction acting at the interface is ill-posed for a wide range of material parameters and friction coefficients. The ill-posedness is manifest in the unstable growth of interfacial disturbances of all wavelengths, with growth rate inversely proportional to the wavelength. We first establish the connection between the ill-posedness and the existence of a certain interfacial wave in frictionless contact, called the generalized Rayleigh wave. Precisely, it is shown that for material combinations where the generalized Rayleigh wave exists, steady sliding with Coulomb friction is ill-posed for arbitrarily small values of friction. In addition, intersonic unstable modes and supersonic steady-state modes exist for sufficiently large values of the friction coefficient. Secondly, regularization of the problem by an experimentally motivated friction law is studied. We show that a friction law with no instantaneous dependence on normal stress but a simple fading memory of prior history of normal stress makes the problem well-posed.
Journal of Geophysical Research, Jul 20, 2010
Glaciological observations of under-flooding suggest that fluid-induced hydraulic fracture of an ... more Glaciological observations of under-flooding suggest that fluid-induced hydraulic fracture of an ice sheet from its bed sometimes occurs quickly, possibly driven by turbulently flowing water in a broad sheet flow. Taking the approximation of a fully turbulent flow into an elastic ice medium with small fracture toughness, we derive an approximate expression for the crack-tip speed, opening displacement and pressure profile. We accomplish this by first showing that a Manning-Strickler channel model for resistance to turbulent flow leads to a mathematical structure somewhat similar to that for resistance to laminar flow of a power law viscous fluid. We then adapt the plane-strain asymptotic crack solution of Desroches et al. (1994) and the power law self-similar solution of Adachi and Detournay (2002) for that case to calculate the desired quantities. The speed of crack growth is shown to scale as the overpressure (in excess of ice overburden) to the power 7/6, inversely as ice elastic modulus to the power 2/3, and as the ratio of crack length to wall roughness scale to the power 1/6. We tentatively apply our model by choosing parameter values thought appropriate for a basal crack driven by the rapid drainage of a surface meltwater lake near the margin of the Greenland Ice Sheet. Making various approximations perhaps relevant to this setting, we estimate fluid inflow rate to the basal fracture and vertical and horizontal surface displacements and find order-of-magnitude agreement with observations by Das et al. (2008) associated with lake drainage. Finally, we discuss how these preliminary estimates could be improved.
As preparation for a workshop on "The Dynamics of Fault Zones" (95 th Dahlem Workshop, ... more As preparation for a workshop on "The Dynamics of Fault Zones" (95 th Dahlem Workshop, Berlin, January 2005), specifically on the sub-topic "Rheology of Fault Rocks and Their Surroundings", we addressed critical research issues for understanding the seismic response of fault zones in terms of the constitutive response of fault materials. That requires new concepts and a host of new observations and experiments to document material response, to understand the shear localization process and the inception of earthquake instability, and especially to understand the mechanisms of fault weakening and dynamics of rupture tip propagation and arrest during rapid, possibly large, slip in natural events. We examine in turn the geological structure of fault zones and its relation to earthquake dynamics, the description of rate and state friction at slow rates appropriate to the interseismic period and earthquake nucleation, and the dynamics of fault weakening during rapid sl...
We examine, and find evidence to support, the hypothesis that the width of Siple Coast ice stream... more We examine, and find evidence to support, the hypothesis that the width of Siple Coast ice streams in West Antarctica is set by the development of significant internal melting (i.e., development of temperate ice conditions) within the ice sheet at the margins. We first illustrate, from published ice sheet deformation data and from simple 1-D thermal modeling based on temperature-dependent flow and conduction properties, that most existing Siple Coast ice stream margins are in a state of partial melt, with temperate ice being present over a substantial fraction of the sheet thickness. We show that, although the margins sustain high lateral strain rates, they can support (and hence transmit to the cold ridges) notably less lateral shear stress than would the somewhat less rapidly deforming ice located inboard, away from the ridge. We then propose, and quantify approximately, a possible related mechanism of margin formation, that is, of locking the sheet to the bed at the margin. Shear...
Journal of Geophysical Research: Earth Surface, 2018
Antarctic mass balance and contribution to sea level rise are dominated by the flow of ice throug... more Antarctic mass balance and contribution to sea level rise are dominated by the flow of ice through narrow conduits called ice streams. These regions of relatively fast flow drain over 90% of the ice sheet and generate significant amounts of frictional heat at the ice stream margins where there is a transition to slow flow in the ridge. This heat can generate temperate ice and a sharp transition in flow speed between the stream and the ridge. Within zones of temperate ice, meltwater is produced and drains to the bed. Here we model the downstream development of a temperate zone along an ice stream shear margin and the flow of meltwater through temperate ice into a subglacial hydrologic system. The hydrology sets the basal effective pressure, defined as the difference between ice overburden and water pressure. Using the southern shear margin of Bindschadler Ice Stream as a case study, our model results indicate an abrupt transition from a distributed to channelized hydrologic system wi...
Journal of Geophysical Research: Solid Earth, 2018
Injection‐induced seismicity is thought to be due primarily to increase in fluid pore pressure, w... more Injection‐induced seismicity is thought to be due primarily to increase in fluid pore pressure, which reduces the shear strength of a nearby fault. We address the modeling and prediction of the hydromechanical response due to fluid injection, mainly as wastewater disposal. We consider the full poroelastic effects, including the changes in porosity and permeability of the medium due to changes in local volumetric strains. Our results consider effects of the fault architecture (low‐permeability fault core and anisotropic high‐permeability damage zones) on the pressure diffusion and the fault poroelastic response. We show that the high‐permeable damage zone, the poroelastic response, and the permeability evolution can accelerate the pore pressure diffusion process during and after wastewater injection. By studying a geologically based model of the Guy‐Greenbrier fault and of the earthquake sequence induced along it in Arkansas, United States, from October 2010 to July 2011, we show tha...
Journal of Applied Mechanics, 2015
A 2008 report by Das et al. documented the rapid drainage during summer 2006 of a supraglacial la... more A 2008 report by Das et al. documented the rapid drainage during summer 2006 of a supraglacial lake, of approximately 44×106 m3, into the Greenland ice sheet over a time scale moderately longer than 1 hr. The lake had been instrumented to record the time-dependent fall of water level and the uplift of the ice nearby. Liquid water, denser than ice, was presumed to have descended through the sheet along a crevasse system and spread along the bed as a hydraulic facture. The event led two of the present authors to initiate modeling studies on such natural hydraulic fractures. Building on results of those studies, we attempt to better explain the time evolution of such a drainage event. We find that the estimated time has a strong dependence on how much a pre-existing crack/crevasse system, acting as a feeder channel to the bed, has opened by slow creep prior to the time at which a basal hydraulic fracture nucleates. We quantify the process and identify appropriate parameter ranges, part...
Science, 1976
We report on the experimental observation of spontaneously nucleated ruptures occurring on fricti... more We report on the experimental observation of spontaneously nucleated ruptures occurring on frictionally held bimaterial interfaces with small amounts of wave speed mismatch. Rupture is always found to be asymmetric bilateral. In one direction, rupture always propagates at the generalized Rayleigh wave speed, whereas in the opposite direction it is subshear or it transitions to supershear. The lack of a preferred rupture direction and the conditions leading to supershear are discussed in relation to existing theory and to the earthquake sequence in Parkfield, California, and in North Anatolia.
Mechanics of Materials, 1984
A general formulation of two-dimensional elastic-perfectly-plastic anti-plane straining is presen... more A general formulation of two-dimensional elastic-perfectly-plastic anti-plane straining is presented for materials with arbitrary anisotropic convex yield surfaces. Stress and strain distributions in plastic regions adjoining portions of the boundary are obtained directly in terms of the yield surface geometry. When specialized to the classical torsion problem, results lead directly to a generalization of the well-known plastic roof construction for limit loads. Examples of the determination of fully plastic stress distributions and corresponding limit torques are given for circular and rectangular shafts with various yield conditions. Another specialization is made to the contained plastic deformation created by longitudinal shearing of a body containing a sharp edge notch. Here the determination of the elastic-plastic boundary and strain distribution is reduced to a potential theory problem for a region in the stress plane bounded by straight line segments and a portion of the yield surface, and a membrane analogy is presented which allows effective visualization of the solution. A solution valid for small scale yielding near a crack is given in terms of a conformal transformation of the yield surface to a unit circle, and some specific examples are worked. Particular attention is given to single crystal type yield surfaces made up of straight line segments corresponding to discrete slip planes.
Journal of the Mechanics and Physics of Solids, 1985
AESTRACT CRACKS in ductile single crystals are analyzed here for geometries and orientations such... more AESTRACT CRACKS in ductile single crystals are analyzed here for geometries and orientations such that twodimensional states of anti-plane shear constitute possible deformation fields. The crystals are modelled as ideally plastic and yield according to critical resolved shear stresses on their slip systems. Restrictions on the asymptotic forms of stress and deformation fields at crack tips are established for anti-plane loading of stationary and quasistatically growing cracks, and solutions are presented for several specific orientations in f.c.c. and b.c.c. crystals. The asymptotic solutions are complemented by complete elastic-plastic solutions for stationary and growing cracks under small scale yielding, based on previous work by RICE (1967,1984) and FREUND (1979). Remarkably, the plastic zone at a stationary crack tip collapses into discrete planes of displacement and stress discontinuity emanating from the tip; plastic flow consists of concentrated shear on the displacement discontinuities. For the growing crack these same planes, if not coincident with the crack plane, constitute collapsed plastic zones in which velocity and plastic strain discontinuities occur, but across which the stresses and anti-plane displacement are fully continuous. The planes of discontinuity are in several cases coincident with crystal slip planes but it is shown that this need not be the case, e.g., for orientations in which anti-plane yielding occurs by multi-slip, or for special orientations in which the crack tip and the discontinuity planes are perpendicular to the activated slip plane.
Journal of the Mechanics and Physics of Solids, 1994
A HALF-PLANE CRACK propagates dynamically, nominally in the x direction. along the plane _V = 0 i... more A HALF-PLANE CRACK propagates dynamically, nominally in the x direction. along the plane _V = 0 in an unbounded solid subjected to remote loading equivalent to a static stress intensity factor K*. The crack front at time t lies along the arc x = c,,t+a_/'(z, t) where a,) is a constant velocity, J'(z, t) is an arbitrary
Journal of the Mechanics and Physics of Solids, 2001
We study the stability of steady sliding between elastically deformable continua using rate and s... more We study the stability of steady sliding between elastically deformable continua using rate and state dependent friction laws. That is done for both elastically identical and elastically dissimilar solids. The focus is on linearized response to perturbations of steady-state sliding, and on studying how the positive direct e ect (instantaneous increase or decrease of shear strength in response to a respective instantaneous increase or decrease of slip rate) of those laws allows the existence of a quasi-static range of response to perturbations at su ciently low slip rate. We discuss the physical basis of rate and state laws, including the likely basis for the direct e ect in thermally activated processes allowing creep slippage at asperity contacts, and estimate activation parameters for quartzite and granite. Also, a class of rate and state laws suitable for variable normal stress is presented. As part of the work, we show that compromises from the rate and state framework for describing velocity-weakening friction lead to paradoxical results, like supersonic propagation of slip perturbations, or to ill-posedness, when applied to sliding between elastically deformable solids. The case of sliding between elastically dissimilar solids has the inherently destabilizing feature that spatially inhomogeneous slip leads to an alteration of normal stress, hence of frictional resistance. We show that the rate and state friction laws nevertheless lead to stability of response to su ciently short wavelength perturbations, at very slow slip rates. Further, for slow sliding between dissimilar solids, we show that there is a critical amplitude of velocity-strengthening above which there is stability to perturbations of all wavelengths.
Journal of Geophysical Research, 2010
Journal of Geophysical Research, 2011
Material juxtapositions across mature faults are a common occurrence. Previous work has found tha... more Material juxtapositions across mature faults are a common occurrence. Previous work has found that this elastic mismatch results in a rupture that will preferentially propagate in the direction of slip displacement on the more compliant side of the fault, with more off-fault damage in the stiffer material. This result has implications for inferring preferred rupture directions based on observations of damage zone asymmetry. We perform a complete numerical investigation of the role of the stress state on the distribution of plastic deformation and the direction of preferred rupture propagation. We show that there are important factors, in addition to the elastic mismatch, which control the preferred direction of propagation as well as the side of the fault in which damage predominately accumulates. The orientation of the most compressive principal stress is the controlling factor in determining the location of plastic deformation. For different orientations, plastic deformation can accumulate in either the stiffer or the more compliant material. For high angles of most compressive stress, the aforementioned preferred rupture direction prediction holds true. However, the off-fault plastic response can reverse that direction for low angles of most compressive stress so that rupture will preferentially propagate in the direction of slip displacement in the stiffer material.
Journal of Geophysical Research: Solid Earth, 2009
We analyze the nucleation and propagation of shear cracks along nonplanar, kinked, and branched f... more We analyze the nucleation and propagation of shear cracks along nonplanar, kinked, and branched fault paths corresponding to the configurations used in recent laboratory fracture studies by Rousseau and Rosakis (2003, 2009). The aim is to reproduce numerically those shear rupture experiments and from that provide an insight into processes which are active when a crack, initially propagating in mode II along a straight path, interacts with a bend in the fault or a branching junction. The experiments involved impact loading of thin Homalite‐100 (a photoelastic polymer) plates, which had been cut along bent or branched paths and weakly glued back together everywhere except along a starter notch near the impact site. Strain gage recordings and high‐speed photography of isochromatic lines provided characterization of the transient deformation fields associated with the impact and fracture propagation. We found that dynamic explicit 2‐D plane‐stress finite element analyses with a simple l...
Journal of Geophysical Research: Solid Earth, 2000
Faults often separate materials with different elastic properties. Nonuniform slip on such faults... more Faults often separate materials with different elastic properties. Nonuniform slip on such faults induces a change in normal stress. That suggests the possibility of self‐sustained slip pulses [Weertman, 1980] propagating at the generalized Rayleigh wave speed even with a Coulomb constitutive law (i.e., with a constant coefficient of friction) and a remote driving shear stress that is arbitrarily less than the corresponding frictional strength. Following Andrews and Ben‐Zion [1997] (ABZ), we study numerically, with a two‐dimensional (2‐D) plane strain geometry, the propagation of ruptures along such a dissimilar material interface. However, this problem has been shown to be ill‐posed for a wide range of elastic material contrasts [Renardy, 1992; Martins and Simões, 1995; Adams, 1995]. Ranjith and Rice [2000] (RR) showed that when the generalized Rayleigh speed exists, as is the case for the material contrast studied by ABZ, the problem is ill‐posed for all values of the coefficient ...
Journal of Geophysical Research: Solid Earth, 2000
What are the origins of earthquake complexity? The possibility that some aspects of the complexit... more What are the origins of earthquake complexity? The possibility that some aspects of the complexity displayed by earthquakes might be explained by stress heterogeneities developed through the self‐organization of repeated ruptures has been suggested by some simple self‐organizing models. The question of whether or not even these simple self‐organizing models require at least some degree of material heterogeneity to maintain complex sequences of events has been the subject of some controversy. In one class of elastodynamic models, previous work has described complexity as arising on a model fault with completely uniform material properties. Questions were raised, however, regarding the role of discreteness, the relevance of the nucleation mechanism, and special parameter choices, in generating the complexity that has been reported. In this paper, we examine the question of whether or not continuum complexity is achieved under the stringent conditions of continuous loading, and whether...
Journal of Geophysical Research: Solid Earth, 2002
On the basis of elastodynamic stress fields for singular crack and nonsingular slip‐weakening mod... more On the basis of elastodynamic stress fields for singular crack and nonsingular slip‐weakening models of propagating rupture, we develop preliminary answers to such questions as follows: If a rupturing fault is intersected by another, providing a possible bend in the failure path, when will stressing be consistent with rupture along the bend? What secondary fault locations and orientations, in a damaged region bordering a major fault, will be stressed to failure by the main rupture? Stresses that could initiate rupture on a bend are shown to increase dramatically with crack speed, especially near the limiting speed (Rayleigh for mode II, shear for mode III). Whether a bend path, once begun, can be continued to larger scales depends on principal stress directions and ratios in the prestress field. Conditions should often be met in mode II for which bend paths encouraged by stressing very near the rupture tip are discouraged by the larger‐scale stressing, a basis for intermittent ruptu...