Showing papers on "Stress field published in 2004"

Calculation of stress in atomistic simulation

Abstract: Atomistic simulation is a useful method for studying material science phenomena Examination of the state of a simulated material and the determination of its mechanical properties is accomplished by inspecting the stress field within the material However, stress is inherently a continuum concept and has been proven difficult to define in a physically reasonable manner at the atomic scale In this paper, an expression for continuum mechanical stress in atomistic systems derived by Hardy is compared with the expression for atomic stress taken from the virial theorem Hardy's stress expression is evaluated at a fixed spatial point and uses a localization function to dictate how nearby atoms contribute to the stress at that point; thereby performing a local spatial averaging For systems subjected to deformation, finite temperature, or both, the Hardy description of stress as a function of increasing characteristic volume displays a quicker convergence to values expected from continuum theory than volume averages of the local virial stress Results are presented on extending Hardy's spatial averaging technique to include temporal averaging for finite temperature systems Finally, the behaviour of Hardy's expression near a free surface is examined, and is found to be consistent with the mechanical definition for stress

Stress orientations and magnitudes in the SAFOD pilot hole

Abstract: [1] Borehole breakouts and drilling-induced tensile fractures in the 2.2-km-deep SAFOD pilot hole at Parkfield, CA, indicate significant local variations in the direction of the maximum horizontal compressive stress, S Hmax , but show a generalized increase in the angle between S Hmax and the San Andreas Fault with depth. This angle ranges from a minimum of 25 ± 10° at 1000-1150 m to a maximum of 69 ± 14° at 2050-2200 m. The simultaneous occurrence of tensile fractures and borehole breakouts indicates a transitional strike-slip to reverse faulting stress regime with high horizontal differential stress, although there is considerable uncertainty in our estimates of horizontal stress magnitudes. If stress observations near the bottom of the pilot hole are representative of stresses acting at greater depth, then they are consistent with regional stress field indicators and an anomalously weak San Andreas Fault in an otherwise strong crust.

Nonlinear rock physics model for estimation of 3D subsurface stress in anisotropic formations: Theory and laboratory verification

Abstract: We develop a rock physics model based on nonlinear elasticity that describes the dependence of the effective stiffness tensor as a function of a 3D stress field in intrinsically anisotropic formations. This model predicts the seismic velocity of both P- and S-waves in any direction for an arbitrary 3D stress state. Therefore, the model overcomes the limitations of existing empirical velocity-stress models that link P-wave velocity in isotropic rocks to uniaxial or hydrostatic stress. To validate this model, we analyze ultrasonic velocity measurements on stressed anisotropic samples of shale and sandstone. With only three nonlinear constants, we are able to predict the stress dependence of all five elastic medium parameters comprising the transversely isotropic stiffness tensor. We also show that the horizontal stress affects vertical S-wave velocity with the same order of magnitude as vertical stress does. We develop a weakanisotropy approximation that directly links commonly measured anisotropic Thomsen parameters to the principal stresses. Each Thomsen parameter is simply a sum of corresponding background intrinsic anisotropy and stressinduced contribution. The stress-induced part is controlled by the difference between horizontal and vertical stresses and coefficients depending on nonlinear constants. Thus, isotropic rock stays isotropic under varying but hydrostatic load, whereas transversely isotropic rock retains the same values of dimensionless Thomsen parameters. Only unequal horizontal and vertical stresses alter anisotropy. Since Thomsen parameters conveniently describe seismic signatures, such as normal-moveout velocities and amplitudevariation-with-offset gradients, this approximation is suitable for designing new methods for the estimation of 3D subsurface stress from multicomponent seismic data.

Stress field variations in the Swiss Alps and the northern Alpine foreland derived from inversion of fault plane solutions

Abstract: [1] This study is devoted to a systematic analysis of the state of stress of the central European Alps and northern Alpine foreland in Switzerland based on focal mechanisms of 138 earthquakes with magnitudes between 1 and 5. The most robust feature of the results is that the azimuth of the minimum compressive stress, S3, is generally well constrained for all data subsets and always lies in the NE quadrant. However, within this quadrant, the orientation of S3 changes systematically both along the structural strike of the Alpine chain and across it. The variation in stress along the mountain belt from NE to SW involves a progressive, counterclockwise rotation of S3 and is most clear in the foreland, where it amounts to 45°–50°. This pattern of rotation is compatible with the disturbance to the stress field expected from the indentation of the Adriatic Block into the central European Plate, possibly together with buoyancy forces arising from the strongly arcuate structure of the Moho to the immediate west of our study area. Across the Alps, the variation in azimuth of S3 is defined by a progressive, counterclockwise rotation of about 45° from the foreland in the north across the Helvetic domain to the Penninic nappes in the south and is accompanied by a change from a slight predominance of strike-slip mechanisms in the foreland to a strong predominance of normal faulting in the high parts of the Alps. The observed rotation can be explained by the perturbation of the large-scale regional stress by a local uniaxial deviatoric tension with a magnitude similar to that of the regional differential stress and with an orientation perpendicular to the strike of the Alpine belt. The tensile nature and orientation of this stress is consistent with the “spreading” stress expected from lateral density changes due to a crustal root beneath the Alps.

Stress buildup in the Himalaya

Abstract: The seismic cycle on a major fault involves long periods of elastic strain and stress accumulation, driven by aseismic ductile deformation at depth, ultimately released by sudden fault slip events. Coseismic slip distributions are generally heterogeneous with most of the energy being released in the rupture of asperities. Since, on the long term, the fault's walls generally do not accumulate any significant permanent deformation, interseismic deformation might be heterogeneous, revealing zones of focused stress buildup. The pattern of current deformation along the Himalayan arc, which is known to produce recurring devastating earthquakes, and where several seismic gaps have long been recognized, might accordingly show significant lateral variations, providing a possible explanation for the uneven microseismic activity along the Himalayan arc. By contrast, the geodetic measurements show a rather uniform pattern of interseismic strain, oriented consistently with long-term geological deformation, as indicated from stretching lineation. We show that the geodetic data and seismicity distribution are reconciled from a model in which microseismicity is interpreted as driven by stress buildup increase in the interseismic period. The uneven seismicity pattern is shown to reflect the impact of the topography on the stress field, indicating low deviatoric stresses (<35 MPa) and a low friction (<0.3) on the Main Himalayan Thrust. Arc-normal thrusting along the Himalayan front and east-west extension in southern Tibet are quantitatively reconciled by the model.

Origin of the in situ stress field in south-eastern Australia

Abstract: The in situ stress field of south‐eastern Australia inferred from earthquake focal mechanisms and bore‐hole breakouts is unusual in that it is characterised by large obliquity between the maximum horizontal compressive stress orientation (SHmax) and the absolute plate motion azimuth. The evolution of the neotectonic strain field deduced from historical seismicity and both onshore and offshore faulting records is used to address the origin of this unusual stress field. Strain rates derived from estimates of the seismic moment release rate (up to ∼10−16 s−1) are compatible with Quaternary fault–slip rates. The record of more or less continuous tectonic activity extends back to the terminal Miocene or early Pliocene (10–5 Ma). Terminal Miocene tectonic activity was characterised by regional‐scale tilting and local uplift and erosion, now best preserved by unconformities in offshore basins. Plate‐scale stress modelling suggests the in situ stress field reflects increased coupling of the Australian and Pacific Plate boundary in the late Miocene, associated with the formation of the Southern Alps in New Zealand.

Origin of the lithospheric stress field

Abstract: [1] An understanding of the tectonic stress field is geologically important because it is the agent that preserves in the crust a memory of dynamical processes. In an effort to elucidate the origin of the present state of stress of the lithosphere we use a finite element model of the Earth's lithosphere to calculate stresses induced by mantle flow, crustal heterogeneity, and topography and compare these to observations of intraplate stresses as given by the World Stress Map. We explore two models of lithospheric heterogeneity, one based directly on seismic and other observational constraints (Crust 2.0), and another that assumes isostatic compensation. Mantle tractions are computed from two models of mantle density heterogeneity: a model based on the history of subduction of the last 180 Myr, which has proved successful at accurately reproducing the present-day geoid and Cenozoic plate velocities, and a model inferred from seismic tomography. We explore the effects of varying assumptions for the viscosity structure of the mantle, and the effects of lateral variations in viscosity in the form of weak plate boundaries. We find that a combined model that includes both mantle and lithospheric sources of stress yields the best match to the observed stress field (∼60% variance reduction), although there are many regions where agreement between observed and predicted stresses is poor. The stress field produced by mantle tractions alone shows a greater degree of long-wavelength structure than is apparent in the stress observations but agrees very well with observations in some areas where radial mantle tractions are particularly strong such as in southeast Asia and the western Pacific. The stress field produced by lithospheric heterogeneity alone depends strongly on the assumed crustal model: Whereas the isostatically compensated model yields very poor agreement with observations, the model based on Crust 2.0 matches the observations about as well as mantle tractions alone and matches very well in certain areas where the influence of high topography is very important (e.g., Andes, East Africa). A possible interpretation of our results is that the stress field is significantly influenced by lateral variations in the viscosity of the mantle, which leads to variable amounts of decoupling between lithosphere and mantle, allowing the mantle signature to dominate in some areas and the crustal signature to dominate in others. The poor fit between the isostatically compensated crustal model and observations and the large differences between the two crustal models point toward the importance of dynamic topography and remaining uncertainties in crustal structure and rheology. We also consider the possibility that observations of stress from the shallow crust may not reflect the state of stress of the entire plate; stresses in the upper plate may be at least partially decoupled from broader-scale plate driving forces by lateral and vertical variations in lithospheric rheology.

Influence of Heterogeneity of Mechanical Properties on Hydraulic Fracturing in Permeable Rocks

Abstract: Numerical simulations of circular holes under internal hydraulic pressure are carried out to investigate the hydraulic fracture initiation, propagation and breakdown behavior in rocks. The hydraulic pressure increases at a constant rate. The heterogeneity of the rocks is taken into account in the study by varying the homogeneity index. In addition, the permeability is varied with the states of stress and fracture. The simulations are conducted by using a finite element code, F-RFPA2D, which couples the flow, stress and damage analyses. The simulation results suggest that the fracture initiation and propagation, the roughness of the fracture path and the breakdown pressure are influenced considerably by the heterogeneity of rocks. The hole diameter elongation and the stress field evolution around the fracture tip during the fracture propagation can also provide useful information for the interpretation of the hydraulic fracturing behaviour.

Conditions for static bubbles in viscoplastic fluids

Abstract: We consider the slow motion of a gas bubble in a cylindrical column filled with a viscoplastic fluid, modeled here as a Herschel–Bulkley fluid. Because of the yield stress of the fluid, it is possible that a bubble will remain trapped in the fluid indefinitely. We adapt Prager’s two variational principles to our problem. From these variational principles we develop two general stopping conditions, i.e., for a given bubble we can calculate a critical Bingham number above which the bubble will not move. The first condition is derived by bounding the velocity field and the second condition by bounding the stress field. We illustrate these conditions by considering specific bubble shapes, e.g., axisymmetric bubbles. We also develop a condition for bubble motion.

Earthquake Triggering along the Xianshuihe Fault Zone of Western Sichuan, China

Abstract: Western Sichuan is among the most seismically active regions in southwestern China and is characterized by frequent strong (M ≥ 6.5) earthquakes, mainly along the Xianshuihe fault zone. Historical and instrumental seismicity show a temporal pattern of active periods separated by inactive ones, while in space a remarkable epicenter migration has been observed. During the last active period starting in 1893, the sinistral strike–slip Xianshuihe fault of 350 km total length, was entirely broken with the epicenters of successive strong earthquakes migrating along its strike. This pattern is investigated by resolving changes of Coulomb failure function (ΔCFF) since 1893 and hence the evolution of the stress field in the area during the last 110 years. Coulomb stress changes were calculated assuming that earthquakes can be modeled as static dislocations in an elastic halfspace, and taking into account both the coseismic slip in strong (M ≥ 6.5) earthquakes and the slow tectonic stress buildup associated with major fault segments. The stress change calculations were performed for faults of strike, dip, and rake appropriate to the strong events. We evaluate whether these stress changes brought a given strong earthquake closer to, or sent it farther from, failure. It was found that all strong earthquakes, and moreover, the majority of smaller events for which reliable fault plane solutions are available, have occurred on stress–enhanced fault segments providing a convincing case in which Coulomb stress modeling gives insight into the temporal and spatial manifestation of seismic activity. We extend the stress calculations to the year 2025 and provide an assessment for future seismic hazard by identifying the fault segments that are possible sites of future strong earthquakes.

Influence of residual stress on elastic modulus and hardness of soda-lime glass measured by nanoindentation

Abstract: The influence of stress on the elastic modulus E and hardness H in soda-lime glass was studied in the Vickers residual stress field by nanoindentation. The Oliver–Pharr method of analysis first gave higher values of E and H, but after correcting for the pileup contact areas around the nanoindents, results consistent with literature values were obtained at regions in the stress field where the stresses were either low or close to zero. Determination of the pileup contact areas was made possible by the use of the atomic force microscope, which has facility for generating cross-section images of the indents. The elastic modulus was found to decrease with stress, which is explained with reference to the influence of applied stresses on the Si–O–Si bond angle. The hardness on the other hand did not depend on the stresses except in the region very close to the edge of the Vickers indent where the stresses are high.

Sensitivity of static stress calculations to the earthquake slip distribution

Abstract: [1] The apparent strong correlation between Coulomb stress changes and the spatial distribution of aftershocks suggests the possibility of making near-real-time estimations of areas at risk of experiencing off-fault aftershocks. In order to do this in practice a number of issues must first be addressed, including the extent to which the main shock slip must be known in detail before a meaningful stress map can be constructed. Here we investigate this issue by constructing a time-ordered sequence of slip solutions for the Landers earthquake, computing Coulomb stress changes for each solution, and quantitatively comparing the stress field with the observed aftershocks by (1) resolving the Coulomb stress change onto the aftershock nodal planes and calculating the percentage of events consistent with triggering and (2) constructing a two-dimensional map of Coulomb stress and computing the correlation coefficient between the positive and negative areas and the locations of the aftershocks. We find that slip solutions based on empirical relations and either focal mechanism or moment tensor data produce stress fields inconsistent with the observed spatial distribution of aftershocks, whereas slip solutions incorporating the correct rupture geometry but greatly simplified slip produce stress fields consistent with the aftershock distribution when very near-fault events are excluded. We further find that resolving stress perturbations onto earthquake nodal planes and computing the percentage of events experiencing positive Coulomb stress provides a poor measure of success because of the limited range of structures on which events occur and the compatibility of the main shock stress field with these structures. Our results support the hypothesis that Coulomb stress changes affect the spatial distribution of aftershocks and suggest that meaningful calculations of Coulomb stress can be made as soon as an earthquake's rupture geometry is well constrained.

Second-order theory for the effective behavior and field fluctuations in viscoplastic polycrystals

Abstract: A recently developed “second-order” homogenization procedure (Ponte Castaneda (J. Mech. Phys. Solids 50 (2002a, b) 737, 759)) is extended to viscoplastic polycrystals and applied to compute the effective response of a certain special class of isotropic polycrystals. The method itself reduces to a simple expression requiring the computation of the averages of the stress field and the covariances of its fluctuations over the various grain orientations in an optimally selected “linear comparison polycrystal”. Therefore, the method not only allows the determination of the effective behavior of the polycrystal, but as a byproduct also yields information on the heterogeneity of the stress and strain-rate fields within the polycrystal. An application is given for a model 2-dimensional, isotropic polycrystal with power-law behavior for the constituent grains. The resulting predictions for the effective behavior are found to satisfy sharp bounds available from the literature and to be consistent with the results of recent numerical simulations. The associated averages and fluctuations of the stresses and strain rates are found to depend strongly on the strain-rate sensitivity (i.e., nonlinearity) and grain anisotropy. In particular, the stress and strain-rate fluctuations were found to grow and become strongly anisotropic with increasing values of the nonlinearity and grain anisotropy parameters.

Temporal and Spatial Variation of Local Stress Fields before and after the 1992 Eruptions of Crater Peak Vent, Mount Spurr Volcano, Alaska

Abstract: We searched for changes in local stress-field orientation at Mount Spurr volcano, Alaska, between August 1991 and December 2001. This study focuses on the stress-field orientation beneath Crater Peak vent, the site of three eruptions in 1992, and beneath the summit of Mount Spurr. Local stress tensors were calculated by inverting subsets of 140 fault-plane solutions for earthquakes beneath Crater Peak and 96 fault-plane solutions for earthquakes beneath Mount Spurr. We also calculated an upper-crustal regional stress tensor by inverting fault-plane solutions for 66 intraplate earthquakes located near Mount Spurr during 1991–2001. Prior to the 1992 eruptions, and for 11 months beginning with a posteruption seismic swarm, the axis of maximum compressive stress beneath Crater Peak was subhorizontal and oriented N67–76° E, approximately perpendicular to the regional axis of maximum compressive stress (N43° W). The strong temporal correlation between this horizontal stress-field rotation (change in position of the σ 1 / σ 3 axes relative to regional stress) and magmatic activity indicates that the rotation was related to magmatic activity, and we suggest that the Crater Peak stress-field rotation resulted from pressurization of a network of dikes. During the entire study period, the stress field beneath the summit of Mount Spurr also differed from the regional stress tensor and was characterized by a vertical axis of maximum compressive stress. We suggest that slip beneath Mount Spurr’s summit occurs primarily on a major normal fault in response to a combination of gravitational loading, hydrothermal circulation, and magmatic processes beneath Crater Peak. Online material : Regional and local fault-plane solutions.

Three-dimensional linear elastic distributions of stress and strain energy density ahead of V-shaped notches in plates of arbitrary thickness

Abstract: This paper presents an analytical solution, substantiated by extensive finite element calculations, for the stress field at a notch root in a plate of arbitrary thickness. The present approach builds on two recently developed analysis methods for the in-plane stresses at notch root under plane-stress or plane strain conditions, and the out-of-plane stresses at a three-dimensional notch root. The former solution (Filippi et al., 2002) considered the plane problem and gave the in-plane stress distributions in the vicinity of a V-shaped notch with a circular tip. The latter solution by Kotousov and Wang (2002a), which extended the generalized plane-strain theory by Kane and Mindlin to notches, provided an expression for the out-of-plane constraint factor based on some modified Bessel functions. By combining these two solutions, both valid under linear elastic conditions, closed form expressions are obtained for stresses and strain energy density in the neighborhood of the V-notch tip. To demonstrate the accuracy of the newly developed solutions, a significant number of fully three-dimensional finite element analyses have been performed to determine the influences of plate thickness, notch tip radius, and opening angle on the variability of stress distributions, out-of-plane stress constraint factor and strain energy density. The results of the comprehensive finite element calculations confirmed that the in-plane stress concentration factor has only a very weak variability with plate thickness, and that the present analytical solutions provide very satisfactory correlation for the out-of-plane stress concentration factor and the strain constraint factor.

Regional division of the recent tectonic stress field in china and adjacent areas

Abstract: On the basis of the "Basic database of crustal stress environment in China", this paper summarizes the basic characteristics of recent tectonic stress field in China and adjacent areas, proposes the principle of dividing the tectonic stress districts. The recent tectonic stress field of China and adjacent areas is classified into four classes: The characteristic of the first order tectonic stress district shows uniformity and stability in large areas and long time. This stress field is mostly controlled by the geometry character of plate boundary and the force acting on plate boundary. The stress action of second order tectonic stress district shows coherence in a relatively large area. This stress field is controlled by regional block interaction. The stress regime of the third order tectonic stress district shows comparability in finite areas. This stress field is mostly influenced by interior block interaction inside the areas. The stress character (direction, intensity, structure, etc) of the forth order stress district shows better coherence. This stress field is mostly controlled by block and fault interaction. The paper preliminarily analyzes the dynamic environment which controlled the recent tectonic stress field in China and adjacent areas.

Fracture analysis in the conventional theory of mechanism-based strain gradient (CMSG) plasticity

Abstract: In a remarkable series of experiments, Elssner et al. (1994) and Korn et al. (2002) observed cleavage cracking along a bimaterial interface between Nb and sapphire. The stress required for cleavage cracking is around the theoretical strength of the material. Classical plasticity models fall short to reach such a high stress level. We use the conventional theory of mechanism-based strain gradient plasticity (Huang et al., 2004) to investigate the stress field around the tip of an interface crack between Nb and sapphire. The tensile stress at a distance of 0.1 μm to the interface crack tip reaches 13.3σY, where σY is the yield stress of Nb. This stress is nearly 4 times of that predicted by classical plasticity theory (3.6σY) at the same distance to the crack tip, and is high enough to trigger cleavage cracking in materials and interfaces. This is consistent with Elssner et al.'s (1994) and Korn et al.'s (2002) experimental observations.

Effect of plasticity on elastic modulus measurements

Abstract: [1] Recent developments in high-pressure X-ray studies enable the measurement of the elastic strain anisotropy induced by a macroscopic differential stress in an aggregate sample. Such data are commonly used to constrain the single-crystal elastic moduli under the assumptions of the Reuss-Voigt state. We find this procedure is valid only for samples that have not been plastically deformed. Measured elastic strain anisotropy for MgO at stress levels below the yield point agree well with the Reuss elastic model. Plastic deformation effects a change in the stress field for subpopulations of grains that represent different crystallographic orientations with respect to the applied stress field. Our data for the plastically deformed sample are consistent with the predictions of a self-consistent aggregate model for deforming polycrystals. Such models may be useful as a guide to define the elastic properties in light of the active slip systems. INDEX TERMS: 3902 Mineral Physics: Creep and deformation; 3909 Mineral Physics: Elasticity and anelasticity; 3924 Mineral Physics: High-pressure behavior; 3954 Mineral Physics: X ray, neutron, and electron spectroscopy and diffraction; 3994 Mineral Physics: Instruments and techniques. Citation: Weidner, D. J., L. Li, M. Davis, and J. Chen (2004), Effect of plasticity on elastic modulus measurements, Geophys. Res. Lett., 31, L06621, doi:10.1029/ 2003GL019090.

Inverse Kinematic and Forward Dynamic Models of the 2002 Denali Fault Earthquake, Alaska

Abstract: We perform inverse kinematic and forward dynamic models of the M 7.9 2002 Denali fault, Alaska, earthquake to shed light on the rupture process and dynamics of this event, which took place on a geometrically complex fault system in central Alaska. We use a combination of local seismic and Global Positioning System (gps) data for our kinematic inversion and find that the slip distribution of this event is characterized by three major asperities on the Denali fault. The rupture nucleated on the Susitna Glacier thrust fault, and after a pause, propagated onto the strike-slip Denali fault. Approximately 216 km to the east, the rupture abandoned the Denali fault in favor of the more southwesterly directed Totschunda fault. Three-dimensional dynamic models of this event indicate that the abandonment of the Denali fault for the Totschunda fault can be explained by the Totschunda fault’s more favorable orientation with respect to the local stress field. However, a uniform tectonic stress field cannot explain the complex slip pattern in this event. We also find that our dynamic models predict discontinuous rupture from the Denali to Totschunda fault segments. Such discontinuous rupture helps to qualitatively improve our kinematic inverse models. Two principal implications of our study are (1) a combination of inverse and forward modeling can bring insight into earthquake processes that are not possible with either technique alone, and (2) the stress field on geometrically complex fault systems is most likely not due to a uniform tectonic stress field that is resolved onto fault segments of different orientations; rather, other forms of stress heterogeneity must be invoked to explain the observed slip patterns.

Comparison of stress field forming methods for vibro-acoustography

Abstract: Vibro-acoustography is a method that produces images of the acoustic response of a material to a localized harmonic motion generated by ultrasound radiation force. The low-frequency, oscillatory radiation force (e.g., 10 kHz) is produced by amplitude modulating a single ultrasound beam, or by interfering two beams of slightly different frequencies. Proper beam forming for the stress field of the probing ultrasound is very important because it determines the resolution of the imaging system. Three beam-forming geometries are studied: amplitude modulation, confocal, and x-focal. The amplitude of radiation force on a unit point target is calculated from the ultrasound energy density averaged over a short period of time. The profiles of radiation stress amplitude oil the focal plane and on the beam axis are derived. The theory is validated by experiments using a small sphere as a point target. A laser vibrometer is used to measure the velocity of the sphere, which is proportional to the radiation stress exerted on the target as the transducer is scanned over the focal plane or along the beam axis. The measured velocity profiles match the theory. The theory and experimental technique may be useful in future transducer design for vibro-acoustography.