Showing papers on "Stress field published in 2001"

The role of T-stress in brittle fracture for linear elastic materials under mixed-mode loading

Abstract: The purpose of this paper is to revisit the maximum tensile stress (MTS) criterion to predict brittle fracture for mixed mode conditions. Earlier experimental results for brittle fracture of polymethylmethacrylate (PMMA) using angled cracked plates are also re-examined. The role of the T-stress in brittle fracture for linear elastic materials is emphasized. The generalized MTS criterion is described in terms of mode I and II stress intensity factors, K I and K II and the T-stress (the stress parallel to the crack), and a fracture process zone, r c . The generalized MTS criterion is then compared with the earlier experimental results for PMMA subjected to mixed mode conditions. It is shown that brittle fracture can be controlled by a combination of singular stresses (characterized by K) or non-singular stress (T-stress). The T-stress is also shown to have an influence on brittle fracture when the singular stress field is a result of mode II loading.

Crustal stress field in southern California and its implications for fault mechanics

Abstract: We present a new, high spatial resolution image of stress orientation in southern California based on the inversion of earthquake focal mechanisms. We use this image to study the mechanics of faulting in the plate boundary region. The stress field contains significant spatial heterogeneity, which in some cases appears to be a result of the complexity of faulting and in other cases appears to be a cause. Temporal changes in the stress field are also observed, primarily related to major earthquakes. The observed 15° (±10°) rotation of the stress axes due to the 1992 M7.3 Landers mainshock implies that the deviatoric stress magnitude in the crust is low, of the order of 10 MPa. This suggests that active faults in southern California are weak. The maximum principal stress axis near the San Andreas Fault is often at ∼50° to the fault strike, indicating that the shear stress on the fault is comparable to the deviatoric stress. The San Andreas in southern California may therefore be a weak fault in a low-strength crust.

Fault interaction by elastic stress changes: New clues from earthquake sequences

Abstract: Publisher Summary This chapter discusses the recent developments in understanding how earthquakes interact with each other. The new theoretical framework for earthquake cycles is based on calculating the stress changes caused by one event and assessing where and what mechanism of earthquakes these changes may promote. For studying such stress interaction, the computation of the stress field outside a rupturing fault is analyzed. This is different from investigating the dynamic rupture growth requiring the reconstruction of the spatiotemporal evolution of the stress on the fault plane. The chapter discusses the theoretical background of earthquake sequences and reviews some of the simple examples that allowed stress coupling concepts to be accepted. The success of simple stress modeling led to the introduction of several modifications, adaptations, and refinements of the ideas.

Dynamics of the India-Eurasia collision zone

Abstract: We present simple new dynamic calculations of a vertically averaged deviatoric stress field (over a depth average of 100 km) for Asia from geodetic, geologic, topographic, and seismic data. A first estimate of the minimum absolute magnitudes and directions of vertically averaged deviatoric stress is obtained by solving force balance equations for deviatoric stresses associated with gravitational potential energy differences within the lithosphere plus a first-order contribution of deviatoric stresses associated with stress boundary conditions. This initial estimate of the vertically averaged deviatoric stress field is obtained independent of assumptions about the rheology of the lithosphere. Absolute magnitudes of vertically averaged deviatoric stresses vary between 5 and 40 MPa. Assuming bulk viscous behavior for the lithosphere, the magnitudes of deviatoric stresses, together with the magnitudes of strain rates inferred from Quaternary fault slip rate and GPS data, yield vertically averaged effective viscosities for Tibet of 0.5–5×1022 Pa s, compared with 1–2.5×1023 Pa s in more rigid areas elsewhere in the region. A forward modeling method that solves force balance equations using velocity boundary conditions allows us to refine our estimates of the vertically averaged effective viscosity distribution and deviatoric stress field. The total vertically averaged deviatoric stress and effective viscosity field are consistent with a weak lower crust in Tibet; they are consistent with some eastward motion of Tibet and south China lithosphere relative to Eurasia; and they confirm that gravitational potential energy differences have a profound effect on the spatially varying style and magnitude of strain rate around the Tibetan Plateau. Our results for the vertically averaged deviatoric stress argue for a large portion of the strength of the lithosphere to reside within the seismogenic upper crust to get deviatoric stress magnitudes there to be as high as 100–300 MPa (in accord with laboratory and theoretical friction experiments indicating that stress drops in earthquakes are small fractions of the total deviatoric stress).

Dynamic modeling of the 1992 Landers earthquake

Abstract: We have used observed band-pass filtered accelerograms and a previously determined slip distribution to invert for the dynamic rupture propagation of the 1992 Landers earthquake. In our simulations, dynamic rupture grows under the simultaneous control of initial stress and rupture resistance by friction, which we modeled using a simple slip-weakening law. We used a simplified Landers fault model where the fault segments were combined into a single vertical, planar fault. By trial and error we modified an initial stress field, inferred from the kinematic slip distribution proposed by Wald and Heaton [1994], until dynamic rupture generated a rupture history and final slip distribution that approximately matched those determined by the kinematic inversion. We found that rupture propagation was extremely sensitive to small changes in the distribution of prestress and that a delicate balance with energy release rate controls the average rupture speed. For the inversion we generated synthetic 0.5 Hz ground displacements using an efficient Green's function propagator method (AXITRA). This method enables us to propagate the radiation generated by the dynamic rupture to distances greater than those feasible using the finite difference method. The dynamic model built by trial-and-error inversion provides a very satisfactory fit between synthetics and strong motion data. We validated this model using records from stations used in the slip inversion as well as some which were not included. We also inverted for a complementary model that fits the data just as well but in which the initial stress was perfectly uniform while rupture resistance was heterogeneous. This demonstrates that inversion of ground motion is nonunique.

Localized failure modes in a compactant porous rock

Abstract: Since dilatancy is generally observed as a precursor to brittle faulting and the development of shear localization, attention has focused on how localized failure develops in a dilatant rock. However, recent geologic observations and reassessment of bifurcation theory have indicated that strain localization may be pervasive in a compactant porous rock. The localized bands can be in shear or in compaction, and oriented at relatively high angles (up to 90°) to the maximum compression direction. Here we report microstructural characterization of the spatial distribution of damage in failed samples which confirms that compaction bands and high-angle conjugate shears can develop in sandstones with porosities ranging from 13% to 28%. These failure modes are generally associated with stress states in the transitional regime from brittle faulting to cataclastic ductile flow. The laboratory results suggest that these complex localized features can be pervasive in sandstone formations, not just limited to aeolian sandstone in which they were first documented. They may significantly impact the stress field, strain partitioning and fluid transport in sedimentary formations and accretionary prisms. While bifuraction theory provides an useful framework for analyzing the inception of localization, our data rule out a constitutive model that does not account for the activation of multiple damage mechanisms in the transitional regime.

Observations of Earthquake Source Parameters at 2 km Depth in the Long Valley Caldera, Eastern California

Abstract: To investigate seismic source parameter scaling and seismic efficiency in the Long Valley caldera, California, we measured source parameters for 41 earthquakes ( M 0.5 to M 5) recorded at 2 km depth in the Long Valley Exploratory Well. Borehole recordings provide a wide frequency bandwidth, typically 1 to 200–300 Hz, and greatly reduce seismic noise and path effects compared to surface recordings. We calculated source parameters in both the time and frequency domains for P and S waves. At frequencies above the corner frequency, spectra decay faster than ω3, indicating that attenuation plays an important role in shaping the spectra (path averaged Q p = 100–400, Q s = 200–800). Source parameters are corrected for attenuation and radiation pattern. Both static stress drops and apparent stresses range from approximately 0.01 to 30 MPa. Although static stress drops do not vary with seismic moment for these data, our analyses are consistent with apparent stress increasing with increasing moment. To estimate tectonic driving stress and seismic efficiencies in the region, we combined source parameter measurements with knowledge of the stress field and a Coulomb failure criterion to infer a driving stress of 40–70 MPa. Subsequent seismic efficiencies are consistent with McGarr's (1999) hypothesis of a maximum seismic efficiency of 6%.

Stress, pore pressure, and dynamically constrained hydrocarbon columns in the South Eugene Island 330 field, northern Gulf of Mexico

Abstract: Hydrocarbon phase pressures at the peak of two severely overpressured reservoirs in the South Eugene Island 330 field, Gulf of Mexico, converge on the minimum principal stress of the top seal. We interpret that the system is dynamically constrained by the stress field present through either fault slip or hydraulic fracturing. In two fault blocks of a shallower, moderately overpressured reservoir sand, hydrocarbon phase pressures are within a range of critical pore pressure values for slip to occur on the bounding growth faults. We interpret that pore pressures in this system are also dynamically controlled. We introduce a dynamic capacity model to describe a critical reservoir pore pressure value that corresponds to either the sealing capacity of the fault against which the sand abuts or the pressure required to hydraulically fracture the overlying shale or fault. This critical pore pressure is a function of the state of stress in the overlying shale and the pore pressure in the sand. We require that the reservoir pore pressure at the top of the structure be greater than in the overlying shale. The four remaining reservoirs studied in the field exhibit reservoir pressures well below critical values for dynamic failure and are, therefore, considered static. All reservoirs that are dynamically constrained are characterized by short oil columns, whereas the reservoirs having static conditions have very long gas and oil columns.

Accelerating seismicity and stress accumulation before large earthquakes

Abstract: The stress field that existed before a large earth- quake can be calculated based on the known source parame- ters of the event. This stress field can be used to define a region that shows greater seismic moment rate changes prior to the event than arbitrarily shaped regions, allowing us to link two previously unrelated subjects: Coulomb stress interactions and accelerating seismicity before large earthquakes. As an example, we have examined all M≥6.5 earthquakes in California since 1950. While we illustrate the model using seismicity in California, the technique i s general and can be applied to any tectonically active re- gion. We show that where sufficient knowledge of the re- gional tectonics exists, this method can be used to aug- ment current techniques for seismic hazard estimation.

Homogenization method for a discrete-continuum simulation of dislocation dynamics

Abstract: The question of the description of the elastic fields of dislocations and of the plastic strains generated by their motion is central to the connection between dislocation-based and continuum approaches of plasticity. In the present work, the homogenization of the elementary shears produced by dislocations is discussed within the frame of a discrete-continuum numerical model. In the latter, a dislocation dynamics simulation is substituted for the constitutive form traditionally used in finite element calculations. As an illustrative example of the discrete-continuum model, the stress field of single dislocations is obtained as a solution of the boundary value problem. The hybrid code is also shown to account for size effects originating from line tension effects and from stress concentrations at the tip of dislocation pile-ups.

Scale dependence, correlations, and fluctuations of stresses in rapid granular flows

Abstract: It is shown that, unlike in simple molecular fluids, the stress field in granular fluids may be strongly scale, or resolution, dependent. This is a result of the intrinsic lack of scale separation in these fluids. Another consequence of the lack of scale separation in granular fluids is that microscopic stress fluctuations, whose origin (like in molecular fluids) is the underlying discreteness of the system, may appear as observables in macroscopic measurements; the correlation (or decay) time of the stress fluctuations is of the order of the mean-free time, which is also a macroscopic time. All of these properties are intrinsic to granular fluids and not (for example) results of the practical lack of scale separation that is dictated by the fact that grains are of macroscopic dimensions or the limited statistics in simulations. Numerical evidence, based on molecular-dynamic simulations of shear flows of smooth disks in a two-dimensional enclosure, serves to demonstrate the above phenomena.

Effects of volcano loading on dike propagation in an elastic half‐space

Abstract: We use laboratory experiments and numerical models to examine the effects of volcano loading on the propagation of buoyant dikes in a two-dimensional elastic half-space. In laboratory experiments we simulate the propagation of buoyant dikes in an isotropic regional stress field by injecting air into tanks of solidified gelatin. A weight resting on the surface of the gelatin represents a volcanic load. A numerical model is used to simulate these experiments. Both experiments and numerical simulations show that as a dike ascends, it begins to curve toward the load in response to the local stress field imposed by the load. The lateral distance over which dikes curve to the load increases with the ratio of average pressure at the base of the load to the dike driving pressure. For realistic volcano and dike dimensions this pressure ratio is going to be large, suggesting that dikes can converge to a volcano over lateral distances several times the load width. Numerical calculations involving an anisotropic regional stress field, however, predict that the lateral extent of dike attraction shrinks as the regional horizontal compressive stress decreases relative to the vertical compressive stress. Dike focusing will be substantial if the regional differential stresses are less than the average pressure at the base of the load. If this is the case, then our models predict a positive feedback between the size of volcanoes and the area of dike attraction. This feedback may promote the development of large discrete volcanoes and also predicts a positive correlation between the spacing and sizes of adjacent volcanoes. To test this prediction, we examine nearest-neighbor pairs of the 21 largest volcanoes in the Cascade Range. The 14 pairs examined show a large range in volcano spacing (6–115 km) and a statistically significant correlation between spacing and average volcano height. This result is consistent with our model results and suggests that the local compressive stress induced by these volcanoes may be an important factor in controlling magma transport in the lithosphere.

Elastic fields in a polyhedral inclusion with uniform eigenstrains and related problems

Abstract: In this paper, the elastic field in an infinite elastic body containing a polyhedral inclusion with uniform eigenstrains is investigated. Exact solutions are obtained for the stress field in and around a fully general polyhedron, i.e., an arbitrary bounded region of three-dimensional space with a piecewise planner boundary. Numerical results are presented for the stress field and the strain energy for several major polyhedra and the effective stiffness of a composite with regular polyhedral inhomogeneities. It is found that the stresses at the center of a polyhedral inclusion with uniaxial eigenstrain do not coincide with those for a spherical inclusion (Eshelby's solution) except for dodecahedron and icosahedron which belong to icosidodeca family, i.e., highly symmetrical structure.

Stress fields around defects and fibers in a polymer using carbon nanotubes as sensors

Abstract: Raman spectroscopy was used to map the stress distribution in the vicinity of discontinuities in a polymer using single-wall nanotubes seeded in the specimen. In the case of a hole in a polymer matrix subjected to unidirectional stress, the experimental stress field compared well with the classical linear elasticity solution. For a single glass fiber embedded in a polymer, the tangential thermal residual stress in the vicinity of the fiber was picked up by Raman spectroscopy and is in satisfactory agreement with a standard two-phase concentric cylinder model.

Stress Orientations Obtained from Earthquake Focal Mechanisms: What Are Appropriate Uncertainty Estimates?

Abstract: Crustal stress orientations provide important information about the mechanics of regional deformation. Numerous methods exist for inverting earthquake focal mechanisms for stress orientation, and the more widely used methods usually obtain similar results for similar data sets. However, error estimates are highly variable, complicating the interpretation of results. The southern California stress field, for example, contains much statistically significant spatial and temporal variability according to the error estimates of one method (Michael, 1984, 1987b), but very little according to those of another (Gephart and Forsyth, 1984). To resolve whether the southern California stress field is generally homogeneous or heterogeneous, we must determine which of the error estimates best reflects the true inversion uncertainty. To do this, we tested both methods on a suite of synthetic focal mechanism data sets containing random errors. The method of Gephart and Forsyth (1984) usually provides more accurate estimates of stress orientation, especially for high-quality data sets, but its confidence regions are in most cases too large. The method of Michael (1984, 1987b) is more accurate for very noisy data sets and provides a more appropriate estimate of uncertainty, implying that the stress field in southern California is probably heterogeneous.

Disturbed stress field model for reinforced concrete: implementation

Abstract: The Disturbed Stress Field Model (DSFM) is a smeared delayed-rotating-crack model, proposed recently as an alternative to fully fixed or fully rotating crack models, for representing the behavior of cracked reinforced concrete. It is an extension of the modified compression field theory; advancements relate to the inclusion of crack shear slip in the element compatibility relations, the decoupling of principal stress and principal strain directions, and a revised look at compression softening and tension stiffening mechanisms. This paper describes a procedure for implementing the formulations of the DSFM into a nonlinear finite-element algorithm. The procedure is based on a total-load secant-stiffness approach, wherein the crack slip displacements are treated as offset strains. Computational aspects of the formulation are shown to be simple and numerically robust. The hybrid crack slip formulation used is found to accurately model the divergence of stress and strain directions, providing an improved representation of behavior. Predictions of shear strength and failure mode are significantly influenced in some cases.

Analyses of the stress field in southeastern France from earthquake focal mechanisms

Abstract: SUMMARY Owing to the apparent deformation field heterogeneity, the stress regimes around the Provence block, from the fronts of the Massif Central and Alpine range up to the Ligurian Sea, have not been well defined. To improve the understanding of the SE France stress field, we determine new earthquake focal mechanisms and compute the presentday stress states by inversion of the 89 available focal mechanisms around the Provence domain, including 17 new ones calculated in the current study. This study provides evidence of six distinct deformation domains around the Provence block, with different tectonic regimes. On a regional scale, we identify three zones characterized by significantly different stress regimes: a western one affected by an extensional stress (normal faulting) regime; a southeastern one characterized by a compressional stress (reverse to strike-slip faulting) regime with NNW- to WNW-trending s1; and a northeastern one, namely the Digne nappe front, marked by a NE-trending compression. Note that the Digne nappe back domain is controlled by an extensional regime that is deforming the western Alpine core. This extensional regime could be a response to buoyancy forces related to the Alpine high topography. The stress regimes in the southeast of the Argentera Massif and around the Durance fault are consistent with a coherent NNW-trending s1, implying a left-lateral component of the active reverse oblique slip of the Moyenne Durance Fault. In the Rhone Valley, an E-trending extension characterizes the tectonic regime, implying a normal component of the present-day Noˆmes fault displacement. This study provides evidence for short-scale variation of the stress states, which arises from abrupt changes in the boundary force influences on upper crustal fragments (blocks). These spatial stress changes around the Provence block result from the coeval influence of forces applied at both its extremities, namely in the northeast the Alpine front push, and in the southeast the northward African plate drift. In addition to these boundary forces, the mantle plume under the Massif Central influences the western block boundary.

Theoretical analysis of the velocity field, stress field and vortex sheet of generalized second order fluid with fractional anomalous diffusion

Abstract: The velocity field of generalized second order fluid with fractional anomalous diiusion caused by a plate moving impulsively in its own plane is investigated and the anomalous diffusion problems of the stress field and vortex sheet caused by this process are studied. Many previous and classical results can be considered as particular cases of this paper, such as the solutions of the fractional diffusion equations obtained by Wyss; the classical Rayleigh’s time-space similarity solution; the relationship between stress field and velocity field obtained by Bagley and co-worker and Podlubny’s results on the fractional motion equation of a plate. In addition, a lot of significant results also are obtained. For example, the necessary condition for causing the vortex sheet is that the time fractional diffusion index β must be greater than that of generalized second order fluid α; the establiihment of the vorticity distribution function depends on the time history of the velocity profile at a given point, and the time history can be described by the fractional calculus.

Evolution of the stress field in the northern Aegean Sea (Greece)

Abstract: SUMMARY The evolution of the stress field in the area of the northern Aegean Sea during the 20th century has been studied. The area is dominated by dextral strike-slip faulting and is characterized by frequent strong earthquakes. Coulomb stress changes (DCFF) were calculated assuming that earthquakes can be modelled as static dislocations in an elastic half-space, and taking into account both the coseismic slip in large (Mi7.0) earthquakes and the slow tectonic stress build-up along the major fault segments. The stress change calculations were performed for strike-slip faults of strike, dip, and rake appropriate to the large events. We evaluate whether these stress changes brought a given large earthquake closer to, or farther from, failure. It was found that each of the large events occurred in regions of increased calculated Coulomb stress. Moreover, the majority of smaller events for which reliable fault-plane solutions are available were also located in areas of positive DCFF. By extending the calculations to 2020, and assuming that no additional large (Mi7.0) earthquake occurs between 1999 and 2020, possible sites of future large earthquakes are identified.

A present-day tectonic stress map for eastern Asia region

Abstract: Based on the data of earthquake centroid moment tensor (CMT) solution, P-wave first motion focal mechanism solution and deep hole breakouts, a present-day tectonic stress map for eastern Asia region is compiled. The original stress data are smoothed for every 200 km × 200 km area by taking the average of all stress indicators within each sub-region. The stress map shows the spatial distribution of the orientation of principal stress axes and the stress regimes. An earthquake focal mechanism map for the eastern Asia is also given. The maps of orientation of principal stress axes show that, apart from the strong influence of the collision between the Indian Ocean plate and Eurasian plate, the present-day tectonic stress in eastern Asia is significantly affected by the back-arc extension of the subduction zones. The joint effect of the continental collision at the Himalaya arc and back-arc extension in the Burma arc region may be responsible for the remarkable rotation of the principal stress orientations in southeastern part of the Tibet plateau. The joint action of the collision between the Philippine Sea plate and Eurasian plate at Taiwan Island and the back-arc extension of the Ryukyu arc affect the stress field in eastern part of China. There are no strong earthquakes in the present day in the vast back-arc region of the Java trench subduction zone. The back-arc extension there may create a condition favorable to the southward flow of the lithosphere material in southeastern Asia. In the inner part of the Tibet plateau region, roughly demarcated by the Kunlun mountain, the northern and northeastern part is a broad intracontinental compressive zone, while the southern and southwestern part is generally in a normal-faulting stress state.