Showing papers on "Stress field published in 2005"

Coefficient of Earth Pressure at Rest

Abstract: The widely used Jaky coefficient of earth pressure at rest, K0 , is revisited. It is demonstrated that this coefficient was derived from an analysis of the stress state in a sand prism that yields an unrealistic stress field. It is also surprising that the at rest stress state is represented as a function of the limit state parameter (internal friction angle). Consequently, one arrives at the conclusion that reasonable predictions made by classical K0 are somewhat coincidental. Jaky’s solution to K0 is discussed in view of more recent research on the stress fields in prismatic mounds of sand.

Detecting fluid signals in seismicity data through statistical earthquake modeling

Abstract: [1] According to the well-known Coulomb failure criterion the variation of either stress or pore pressure can result in earthquake rupture. Aftershock sequences characterized by the Omori law are often assumed to be the consequence of varying stress, whereas earthquake swarms are thought to be triggered by fluid intrusions. The role of stress triggering can be analyzed by modeling solely three-dimensional (3-D) elastic stress changes in the crust, but fluid flows which initiate seismicity cannot be investigated without considering complex seismicity patterns resulting from both pore pressure variations and earthquake-connected stress field changes. We show that the epidemic-type aftershock sequence (ETAS) model is an appropriate tool to extract the primary fluid signal from such complex seismicity patterns. We analyze a large earthquake swarm that occurred in 2000 in Vogtland/NW Bohemia, central Europe. By fitting the stochastic ETAS model, we find that stress triggering is dominant in creating the observed seismicity patterns and explains the observed fractal interevent time distribution. External forcing, identified with pore pressure changes due to fluid intrusion, is found to directly trigger only a few percent of the total activity. However, temporal deconvolution indicates that a pronounced fluid signal initiated the swarm. These results are confirmed by our analogous investigation of model simulations in which earthquakes are triggered by fluid intrusion as well as stress transfers on a fault plane embedded in a 3-D elastic half-space. The deconvolution procedure based on the ETAS model is able to reveal the underlying pore pressure variations.

Eshelby formalism for nano-inhomogeneities

Abstract: The Eshelby formalism for inclusion/inhomogeneity problems is extended to the nano-scale at which surface/interface effects become important. The interior and exterior Eshelby tensors for a spherical inhomogeneous inclusion with the interface stress effect subjected to an arbitrary uniform eigenstrain embedded in an infinite alien matrix, and the stress concentration tensors for a spherical inhomogeneity subjected to an arbitrary remote uniform stress field are obtained. Unlike their counterparts at the macro-scale, the Eshelby and stress concentration tensors are, in general, not uniform inside the inhomogeneity but are position-dependent. They have the property of radial transverse isotropy. It is also shown that the size-dependence of the Eshelby tensors and the stress concentration tensors follow very simple scaling laws. Finally, the Eshelby formula to calculate the strain energy in the presence of the interface effect is given.

Detecting fluid signals in seismicity data through statistical earthquake modeling : Stress transfer, earthquake triggering, and time-dependent seismic hazard

Abstract: [1] According to the well-known Coulomb failure criterion the variation of either stress or pore pressure can result in earthquake rupture. Aftershock sequences characterized by the Omori law are often assumed to be the consequence of varying stress, whereas earthquake swarms are thought to be triggered by fluid intrusions. The role of stress triggering can be analyzed by modeling solely three-dimensional (3-D) elastic stress changes in the crust, but fluid flows which initiate seismicity cannot be investigated without considering complex seismicity patterns resulting from both pore pressure variations and earthquake-connected stress field changes. We show that the epidemic-type aftershock sequence (ETAS) model is an appropriate tool to extract the primary fluid signal from such complex seismicity patterns. We analyze a large earthquake swarm that occurred in 2000 in Vogtland/NW Bohemia, central Europe. By fitting the stochastic ETAS model, we find that stress triggering is dominant in creating the observed seismicity patterns and explains the observed fractal interevent time distribution. External forcing, identified with pore pressure changes due to fluid intrusion, is found to directly trigger only a few percent of the total activity. However, temporal deconvolution indicates that a pronounced fluid signal initiated the swarm. These results are confirmed by our analogous investigation of model simulations in which earthquakes are triggered by fluid intrusion as well as stress transfers on a fault plane embedded in a 3-D elastic half-space. The deconvolution procedure based on the ETAS model is able to reveal the underlying pore pressure variations.

Estimating Eddy Stresses by Fitting Dynamics to Observations Using a Residual-Mean Ocean Circulation Model and Its Adjoint

Abstract: A global ocean circulation model is formulated in terms of the “residual mean” and used to study eddy–mean flow interaction Adjoint techniques are used to compute the three-dimensional eddy stress field that minimizes the departure of the coarse-resolution model from climatological observations of temperature The resulting 3D maps of eddy stress and residual-mean circulation yield a wealth of information about the role of eddies in large-scale ocean circulation In eddy-rich regions such as the Southern Ocean, the Kuroshio, and the Gulf Stream, eddy stresses have an amplitude comparable to the wind stress, of order 02 N m � 2 , and carry momentum from the surface down to the bottom, where they are balanced

Stress and crustal anisotropy in Marlborough, New Zealand: evidence for low fault strength and structure‐controlled anisotropy

Abstract: SUMMARY The major strike-slip faults in the greater Marlborough region, central New Zealand, are of both scientific and societal interest as they accommodate relative plate motion in the upper plate of an oblique subduction zone and pose a high seismic risk to central New Zealand. Studies in California suggest that some plate-bounding strike-slip faults are frictionally weak and that crustal anisotropy is controlled by the ambient stress. Whether these observations are more generally applicable to major strike-slip faults has yet to be determined. We have used inversions of focal mechanism and first motion data to calculate the principal stress directions in Marlborough and related them to the geometry of the major faults. The average angle between the axis of maximum horizontal compressive stress (S Hmax) and the average strike of the major faults is 60 ◦ ; this is substantially higher than the ∼30 ◦ expected for reactivation of av ertical strike-slip fault given Byerlee friction and hydrostatic fluid pressure. This geometry can be explained, however, by the faults having a moderately low friction coefficient (∼0.35), a moderately high fluid pressure (∼0.7 × lithostatic) or some combination of the two. This observation substantiates the hypothesis that the San Andreas fault is not unique in being frictionally weak. We have also conducted shear-wave splitting analysis on local S phases to determine the directions of crustal anisotropy and investigated their orientations with respect to the geological fabric and the principal stress directions. The anisotropy determined using shallow earthquakes reveals that the fast direction is 65 ± 50 ◦ and is generally aligned with the NE‐SW-striking faults, and we therefore conclude that crustal anisotropy in Marlborough is controlled more by the geological structures than by the prevailing stress field.

Lower bound limit analysis with adaptive remeshing

Abstract: The objective of this work is to present an adaptive remeshing procedure for lower bound limit analysis with application to soil mechanics. Unlike conventional finite element meshes, a lower bound grid incorporates statically admissible stress discontinuities between adjacent elements. These discontinuities permit large stress jumps over an infinitesimal distance and reduce the number of elements needed to predict the collapse load accurately. In general, the role of the discontinuities is crucial as their arrangement and distribution has a dramatic influence on the accuracy of the lower bound solution (Limit Analysis and Soil Plasticity, 1975). To ensure that the discontinuities are positioned in an optimal manner requires an error estimator and mesh adaptation strategy which accounts for the presence of stress singularities in the computed stress field. Recently, Borges et al. (Int. J. Solids Struct. 2001; 38:1707–1720) presented an anisotropic mesh adaptation strategy for a mixed limit analysis formulation which used a directional error estimator. In the present work, this strategy has been tailored to suit a discontinuous lower bound formulation which employs the stresses and body forces as primary unknowns. The adapted mesh has a maximum density of discontinuities in the direction of the maximum rate of change in the stress field. For problems involving strong stress singularities in the boundary conditions (e.g. a strip footing), the automatic generation of discontinuity fans, centred on the singular points, has been implemented. The efficiency of the proposed technique is demonstrated by analysis of two classical soil mechanics problems; namely the bearing capacity of a rigid strip footing and the collapse of a vertical cut. Copyright © 2005 John Wiley & Sons, Ltd.

Multicycle dynamics of nonplanar strike-slip faults

Abstract: [1] We perform two-dimensional dynamic models of strike-slip faults with a change in strike (a bend) over multiple earthquake cycles to examine the long-term effects of nonplanar fault geometry. A viscoelastic model (a proxy for off-fault deformation and tectonic loading) is introduced for the interseismic process to avoid pathological stress buildup around the bend. A finite element method with an elastodynamic model is used to simulate dynamic earthquake ruptures. We find that stresses near the bend differ strongly from the regional stress field and that the fault develops a relatively steady state in which the stress level and the event pattern on the fault are stable. Reduced normal stress on the dilatational side and increased normal stress on the compressive side of the bend during dynamic ruptures result in the bend serving as an initiation and/or a termination point(s) for rupture. Typical events on such a fault consist of two classes: unilateral events that rupture only the favorable segment and bilateral events that rupture the favorable segment and part of or the entire unfavorable segment. In the latter class of events, a time delay in rupture around the bend results from a high yield stress on the compressive side of the bend. Other effects of the bent fault geometry include higher displacement on the inward wall than on the outward wall, higher slip on the more favorable segment than on the less favorable segment, and a large slip velocity on the compressive side of the bend.

Flaw Tolerance in a Thin Strip Under Tension

Abstract: Recent studies on hard and tough biological materials have led to a concept called flaw tolerance which is defined as a state of material in which pre-existing cracks do not propagate even as the material is stretched to failure near its limiting strength. In this process, the material around the crack fails not by crack propagation, but by uniform rupture at the limiting strength. At the failure point, the classical singular stress field is replaced by a uniform stress distribution with no stress concentration near the crack tip. This concept provide an important analogy between the known phenomena and concepts in fracture mechanics, such as notch insensitivity, fracture size effects and large scale yielding or bridging, and new studies on failure mechanisms in nanostructures and biological systems. In this paper, we discuss the essential concept for the model problem of an interior center crack and two symmetric edge cracks in a thin strip under tension. A simple analysis based on the Griffith model and the Dugdale-Barenblatt model is used to show that flaw tolerance is achieved when the dimensionless number A n =ΓE/(S 2 H) is on the order of 1, where r is the fracture energy, E is the Young s modulus, S is the strength, and H is the characteristic size of the material. The concept of flaw tolerance emphasizes the capability of a material to tolerate cracklike flaws of all sizes.

Characterization of Acoustic Emission Sources in a Rock Salt Specimen under Triaxial Compression

Abstract: This study presents the application of an automated moment tensor analysis procedure on microcracks, which were generated during a triaxial compression test of a cylindrical rock salt specimen (diameter 150 mm, length 300 mm). The acoustic emission signals were detected in a frequency range between 20 kHz and 1 MHz using 12 acoustic emission sensors mounted on the surface of the specimen cylinder. The moment tensor analysis was applied to about 30,000 events, which were precisely located using at least 16 P - and S -wave arrival times. For more than 40% of these events, approximately 12,500 events, stable moment tensor solutions could be evaluated using the first motion of the P -wave radiation patterns. Most of the evaluated events showed significant isotropic source components, which is in good agreement with dilatation of the rock during compressional loading. The majority of the events were caused by tensile opening leading to dilatation of the rock. The tension ( T ) axes, which are normal to the crack plane of these tensile microcracks, were predominantly oriented radially in the cylindrical specimen, perpendicular to the maximum principal stress, which is oriented axially. The direction of the tensile opening calculated by the moment tensor evaluation coincides very well with the direction of the minimum principal stress. The applied collapsing method discovers cellular structures with a cell size in the range of a few centimetres. However, it seems that the events occur only in zones where the cell interfaces are favourably orientated in the stress field. These events are attributed to cracking at grain interfaces which occurs in rock salt under very slow creep loading above the dilatancy boundary.

Contact Analyses for Bodies With Frictional Heating and Plastic Behavior

Abstract: The stress field within machine components is an important indicator for contact failures. Since both thermal stresses due to frictional heating and plasticity are significant in engineering application, it is critical to predict the total stress field. In this work, the steady-state thermal effect is considered and a thermo-elastic-plastic contact model is developed. The model is applicable for rolling and/or sliding contact problem, as far as small equivalent plastic strain hypothesis is respected. Influence coefficients for surface normal displacement, temperature, and strain and stress tensors are used with the discrete convolution and fast Fourier transform algorithm. The single-loop conjugate gradient iteration scheme is also applied to achieve fast convergence speed. Simulations are presented for several academic examples ranging from elastic to thermo-elastic-plastic. The thermo-elastic-plastic analyses show that the heat factor in a contact situation has significant effect not only on the critical Hertzian pressure and on the pressure distribution, but also on the magnitude and depth of the maximum von Mises stress during loading and the residual ones found after unloading.

Present-day stress orientation in Brunei: a snapshot of ‘prograding tectonics’ in a Tertiary delta

Abstract: The Baram Delta province of NW Borneo is unusual when compared with most other Tertiary deltas, as it has built up upon an active margin. Hence, structures observed in the Baram Delta province are the result of both margin-parallel gravity-driven deltaic tectonics and approximately margin-normal transpressive tectonics associated with the active margin. Image and dipmeter logs have been examined for breakouts and drilling-induced tensile fractures (DITFs) in 47 wells throughout Brunei. Breakouts and DITFs observed in 19 wells suggest that the maximum horizontal stress is oriented margin-normal (NW-SE) in the proximal parts of the basin and margin-parallel (NE-SW) in the outer shelf region. The margin-parallel outer shelf stress field is interpreted as a local 'deltaic' stress field caused by the shape of the clastic wedge. The margin-normal maximum horizontal stress in the inner shelf is interpreted to reflect basement stresses associated with the active margin. However, the maximum horizontal stress in the inner shelf is approximately perpendicular to the strike of Miocene-Pliocene normal growth faults, suggesting that maximum horizontal stress in the inner shelf has rotated from margin-parallel ('deltaic') to margin-normal ('basement-associated') over time. Hence, approximately the same stress rotation has occurred over time in the inner shelf as is currently observed spatially from the outer to inner shelf. The spatial and temporal stress rotations in Brunei are thus interpreted to be the result of 'deltaic' and 'basement-associated' tectonic regimes that are 'prograding' basin-wards. The proximity of the active margin has resulted in progressive uplift and inversion of the hinterland that has 'forced' the delta system to prograde rapidly. The zone of active deltaic growth faulting (and margin-parallel maximum horizontal stress) has shifted basin-wards ('prograded') as the delta system has rapidly prograded across the shelf. After uplift and delta progradation, the old growth faults of the inner shelf ceased being active and have then been successively reactivated by a similarly 'prograding' margin-normal inversion front.

The dynamic behavior of two collinear interface cracks in magneto-electro-elastic materials

Abstract: In this paper, the dynamic behavior of two collinear symmetric interface cracks between two dissimilar magneto-electro-elastic material half planes under the harmonic anti-plane shear waves loading is investigated by Schmidt method. By using the Fourier transform, the problem can be solved with a set of triple integral equations in which the unknown variable is the jump of the displacements across the crack surfaces. To solve the triple integral equations, the jump of the displacements across the crack surface is expanded in a series of Jacobi polynomials. Numerical solutions of the stress intensity factor, the electric displacement intensity factor and the magnetic flux intensity factor are given. The relations among the electric filed, the magnetic flux field and the stress field are obtained.

Onto what planes should Coulomb stress perturbations be resolved

Abstract: [1] Coulomb stress maps are produced by computing the tensorial stress perturbation due to an earthquake rupture and resolving this tensor onto planes of a particular orientation. It is often assumed that aftershock fault planes are “optimally oriented”; in other words, the regional stress and coseismic stress change are used to compute the orientation of planes most likely to fail and the coseismic stress is resolved onto these orientations. This practice assumes that faults capable of sustaining aftershocks exist at all orientations, an assumption contradicted by the observation that aftershock focal mechanisms have strong preferred orientations consistent with mapped structural trends. Here we systematically investigate the best planes onto which stress should be resolved for the Landers, Hector Mine, Loma Prieta, and Northridge earthquakes by quantitatively comparing observed aftershock distributions with stress maps based on optimally oriented planes (two- and three-dimensional), main shock orientation, and regional structural trend. We find that the best model differs between different tectonic regions but that in all cases, models that incorporate the regional stress field tend to produce stress maps that best fit the observed aftershock distributions, although not all such models do so equally well. Our results suggest that when the regional stress field is poorly defined, or in structurally complex areas, the best model may be to fix the strike of the planes upon which the stress is to be resolved to that of the main shock but allow the dip and rake to vary.

Fault branching and rupture directivity

Abstract: [1] Could the directivity of a complex earthquake be inferred from the ruptured fault branches it created? Typically, branches develop in forward orientation, making acute angles relative to the propagation direction Direct backward branching of the same style as the main rupture (eg, both right lateral) is disallowed by the stress field at the rupture front Here we propose another mechanism of backward branching In that mechanism, rupture stops along one fault strand, radiates stress to a neighboring strand, nucleates there, and develops bilaterally, generating a backward branch Such makes diagnosing directivity of a past earthquake difficult without detailed knowledge of the branching process As a field example, in the Landers 1992 earthquake, rupture stopped at the northern end of the Kickapoo fault, jumped onto the Homestead Valley fault, and developed bilaterally there, NNW to continue the main rupture but also SSE for 4 km forming a backward branch We develop theoretical principles underlying such rupture transitions, partly from elastostatic stress analysis, and then simulate the Landers example numerically using a two-dimensional elastodynamic boundary integral equation formulation incorporating slip-weakening rupture This reproduces the proposed backward branching mechanism based on realistic if simplified fault geometries, prestress orientation corresponding to the region, standard lab friction values for peak strength, and fracture energies characteristic of the Landers event We also show that the seismic S ratio controls the jumpable distance and that curving of a fault toward its compressional side, like locally along the southeastern Homestead Valley fault, induces near-tip increase of compressive normal stress that slows rupture propagation

Deformation of the subducted Indian lithospheric slab in the Burmese arc

Abstract: [1] Stress inversion of focal mechanism data in the Burmese arc region indicates distinct stress fields above and below 90 km along the subducted Indian lithospheric slab. In the upper part, the σ1 and σ3 axes trend NNE and ESE respectively, in conjunction with the ambient stress field of the Indian plate. However, in the lower part of the slab there is no preferred orientation of the σ1 or σ2 axes, but a very well defined σ3 axis is observed, that trends steeply in the down-dip direction. It is inferred that while the upper part is governed by the NNE oriented horizontal plate tectonic forces, the lower part is governed entirely by tensile forces due to gravitational loading on the subducted slab. A model of attempted slab detachment at the base of the lithospheric contact zone is suggested, which is supported by results of high-resolution seismic tomographic studies in this region.

The behavior of a crack in functionally graded piezoelectric/piezomagnetic materials under anti-plane shear loading

Abstract: In this paper, the behavior of a crack in functionally graded piezoelectric/piezomagnetic materials subjected to an anti-plane shear loading is investigated. To make the analysis tractable, it is assumed that the material properties vary exponentially with the coordinate parallel to the crack. By using a Fourier transform, the problem can be solved with the help of a pair of dual integral equations in which the unknown variable is the jump of the displacements across the crack surfaces. These equations are solved using the Schmidt method. The relations among the electric displacement, the magnetic flux and the stress field near the crack tips are obtained. Numerical examples are provided to show the effect of the functionally graded parameter on the stress intensity factors of the crack.