Showing papers on "Stress field published in 1982"

Stress orientations from borehole wall fractures with examples from Colorado, east Texas, and northern Canada

Abstract: Azimuthally aligned breakouts in oil wells are explained as shear fractures in the zone of amplified stress difference near the borehole, in a stress field having unequal horizontal principal stres...

Dynamic faulting studied by a finite difference method

Abstract: We have developed a finite difference method that is especially adapted to the study of dynamic shear cracks. We studied a number of simple earthquake source models in two and three dimensions with special emphasis on the modeling of the stress field. We compared our numerical results for semi-infinite and self-similar shear cracks with the few exact solutions that are available in the literature. We then studied spontaneous rupture propagation with the help of a maximum stress criterion. From dimensional arguments and a few simple examples, we showed that the maximum stress criterion depended on the physical dimensions of the fault. For a given maximum stress intensity, the finer the numerical mesh, the higher the maximum stress that had to be adopted. A study of in-plane cracks showed that at high rupture velocities, the numerical results did not resolve the stress concentration due to the rupture front from the stress peak associated with the shear wave propagating in front of the crack. We suggest that this is the reason why transonic rupture velocities are found in the numerical solutions of in-plane faulting when the rupture resistance is rather low. Finally, we studied the spontaneous propagation of an initially circular rupture. Two distinct modes of nucleation of the rupture were studied. In the first, a plane circular shear crack was formed instantaneously in a uniformly prestressed medium. After a while, once stress concentrations had developed around the crack edge, the rupture started to grow. In the second type of nucleation, a preexisting circular crack became unstable at time t = 0 and started to grow. The latter model appeared to us as a more realistic simulation of earthquake triggering. In this case, the initial stress was nonuniform and was the static field of the preexisting fault.

Is there a genetic relationship between selected regional joints and contemporary stress within the lithosphere of North America

Abstract: On the Appalachian Plateau of New York, ENE striking joints parallel the mid-continent contemporary stress field and do not correlate with other structures. Joints within Ohio, Indiana, Michigan, and West Virginia also parallel the mid-continent maximum horizontal compression as indicated by hydraulic fracture measurements. In northern Indiana, where the contemporary stress field deviates significantly from the orientation of the mid-continent stress, the attitude of the joints deviates accordingly. In addition to joints, structures on several scales from subcontinent size fracture systems to microfabrics in shales apparently parallel the mid-continent stress field. From this I conclude that these joints are mode I cracks whose orientation corresponds to the contemporary tectonic stress field. In itself, the formation of these structures constitutes a tectonic event that has often been overlooked in favor of tectonic events that produce the more spectacular but less pervasive faults and folds.

Implications of an Elastic Analysis of In Situ Stress Measurements Near the San Andreas Fault

Abstract: Twenty-nine measurements of in situ stress obtained with the hydraulic fracturing technique near Palmdale, California, are the basis of an elastic analysis of the state of stress in the Mojave Desert adjacent to the San Andreas fault. The measurements were made at depths extending from 80 to 849 m and at distances from the fault between 2 and 34 km. The elastic solution indicates a state of deviatoric stress typical for continents in that the inferred depth gradient of the maximum shear stress is about 7.9 MPa/km. Extrapolation yields an average shear stress in the upper 14 km of the crust of about 56 MPa, a result that is higher than estimates of the average shear stress on the San Andreas fault based on the analysis of heat flow data. This finding is consistent, however, with estimates of fault strength based on laboratory determinations of the coefficient of friction for samples of San Andreas fault gouge if the regional state of deviatoric stress is limited by the strength of the fault zone. If so, then the coefficient of friction of the San Andreas fault zone inferred from the stress field results is about 0.45. The state of stress does not appear to vary systematically with distance from the San Andreas fault although considerable localized variation is observed. The observations suggest an upper bound of about 0.1 MPa/km for the horizontal gradient of the maximum shear stress in the direction perpendicular to the San Andreas fault, a result that implies a corresponding limit of about 1.4 MPa on the shear traction applied to the base of the seismogenic layer. Finally, we demonstrate the potential application of in situ stress data to the direct assessment of accumulated slip, which could be released in a large earthquake. We show that on the basis of a model involving a locked fault, extending to about 22 km, the total fault slip below the locked portion is less than 13 m. A more comprehensive set of stress data could permit the estimation of an even lower bound.

Dislocation‐free zone model of fracture comparison with experiments

Abstract: The dislocation‐free zone (DFZ) model of fracture has been extended to study the relationship between the stress intensity factor, extent of plastic deformation, and crack tip geometry of an elastic‐plastic crack as a function of applied stress. The results show that the stress intensity factor K decreases from the elastic value at first slowly, then goes rapidly to zero as the number of dislocations in the plastic zone increases. The crack with a zero stress intensity factor has its crack tip stress field completely relaxed by plastic deformation and hence is called a plastic crack. Between the elastic and plastic cracks, a wide range of elastic‐plastic cracks having both a stress singularity and a plastic zone are possible. These elastic‐plastic cracks with a DFZ are predicted if there is a critical stress intensity factor Kg required for the generation of dislocations at the crack tip. The expression for Kg is obtained from the crack tip dislocation nucleation model of Rice and Thomson. In most metals,...

Assessing the Permeability Characteristics of Fractured Rock

Abstract: The geometric and hydraulic characteristics of fractures and fractured rock masses are reviewed to assess the current state and future direction of fracture hydrology research. Laboratory data suggest that the parallel-plate analogy for flow through a single fracture is valid. Fracture-flux is a function of the cube of the fracture aperture. Flow through fractures is a function of normal stress, shear stress, and fracture surface characteristics such as roughness. Flow through fractured rock masses is determined by fracture orientation, spacing, fracture interconnection, and the stress field. These factors must be considered in assessing the directional permeabilities of fractured rocks. Consideration of these factors and the structural characteristics of fractured rock leads to the formulation of a conceptual framework for flow in fractured rock masses that is a form of coupled discrete-fractured porous media model. In this conceptual framework, the shear zones and fracture zones are described as discrete hydrogeologic features; individual fractures (joints) are defined as discrete features near zones of interest, such as underground excavations; and the fractured rock mass in general is described as a form of equivalent fractured porous medium. It is proposed that the properties of the equivalent continuous porous medium must be developed from discretemore » fracture properties, reflecting the dependence of fracture permeability on the stress tensor, fracture geometry, distribution of fracture apertures, and degree of fracture interconnection.« less

The effect of thin hard coatings on the Hertzian stress field

Abstract: In this paper the effect of thin rigid coatings on the stress field generated by a Spherical indentation on a flat halfspace is investigated using a finite-element program. It is shown that thin hard coatings can have a significant effect on the radial and circumferential stresses. Of particular interest is the reduction in the maximum (radial) tensile stresses, since this indicates that hard coatings can be used to protect brittle materials against elastic contact damage. The stress reduction increases with the Young's modulus and thickness of the coating. The reduction in the substrate stresses is, however, accompanied by an increase in the maximum tensile stresses in the coating itself.

The interface crack with a contact zone (an analytical treatment)

Abstract: An analytical treatment is made of the problem of an interface crack with a contact zone. It is shown that the unrealistic oscillatory singularities are removed independent of the contact zone size. The model of Comninou [1, 2, 3, 4] leads to an equation for the contact zone length with possibly an infinity of solutions. However, only the largest of these appears to satisfy all the subsidiary conditions of the problem posed i.e. that of a single contact region. The singular shear stress field at the crack tip is effectively independent of the precise (small) contact zone length. An alternative model, illustrated in Fig. 3, is suggested. Each of these models leads to the same energy release rate.

Analysis of states of stress between provinces of constant stress

Abstract: Recent studies have indicated the existence of crustal provinces or domains within which the state of stress shows little apparent horizontal variation. Between provinces the state of stress may undergo substantial changes, often over remarkably short distances. As analyzed here, the transition in stress state between adjacent domains is caused by shear tractions acting on the base of the elastic-brittle layer and is mediated by a stress field within a zone between the provinces that can be determined by solving the equations of force equilibrium and stress compatibility. The component of horizontal stress oriented perpendicular to the provincial boundary changes smoothly across the transition zone from one province to the other, whereas the horizontal stress oriented parallel to the boundary shows smaller but discontinuous changes. The horizontal component of shear stress is unlikely to change from one province to another because of the implausible nature of the required basal traction; thus, in this regard, states of stress in adjacent domains appear to be coupled. The coincidence of a number of stress transition zones with boundaries defined by heat flow suggests that in many cases the basal tractions are the result of thermally induced mass transport below the elastic-brittle layer in the direction of increasing horizontal compressive stress. This analysis provides a quantitative relationship between changes in the stress field measured in the upper portion of the crust and shear stresses acting on the base of the elastic-brittle layer.

Modeling and detecting interactions between earth tides and earthquakes with application to an aftershock sequence in the Pyrenees

Abstract: Assuming that earthquakes are governed by solid friction and that the fault plane solutions are known, a simplified model of correlation between the seismicity and a specified component of the tidal stress is proposed. In the case of an earthquake sequence with a uniform time distribution and with a prevailing focal mechanism, a test of statistical significance is derived from a binomial probability distribution. This interaction model is checked over the aftershock sequence of a magnitude 5 earthquake which occurred within a seismic array in the Pyrenees on 29 February 1980. The tidal stress field, including the ocean tide effect, is computed for this area. The global time decrease of the seismicity is taken into account by a time transformation. In order to deal with the time and space complexity of the stress field, a moving window analysis is used. It is shown that during one 7-day period out of a total of 30 days, a positive correlation appears between earth tides and seismicity, in agreement with the proposed model.

Screw dislocation in a two‐phase isotropic thin film

Abstract: By using the complex potential and conformal mapping techniques, the stress field of a straight screw dislocation lying parallel to the surface of a two‐phase isotropic thin film of equal thickness in each phase and a welded interface is analyzed. The solution, when reduced to a single‐phase thin film, is in agreement with that derived by Liebfried and Dietze using an infinite array of image dislocations. The presence of a second phase is found to increase the magnitude of the stress components for the screw dislocation except for τxz near the interface where the effect is the reverse. The image force on the dislocation near the interface can be attractive or repulsive depending upon whether the dislocation is situated in the hard or soft phase. In the case where the dislocation is situated in the soft phase, the total image force tends to drive the screw dislocation to the surface. Furthermore, the screw dislocation is found to be unstable at the interface. The elastic solution for an interfacial disloca...

Stress-relief buckles in the McFarland quarry, Ottawa

Abstract: Six quarry-floor buckles in a west-end Ottawa bedrock quarry are described and a semi-quantitative estimate of the stress field is inferred from them. The maximum principal stress component is hori...

A distributed dislocation stress analysis for crazes and plastic zones at crack tips

Abstract: A distributed dislocation method is developed to obtain analytically the applied stress as well as the surface stress profile along narrow plastic zones at the tip of a crack in a homogeneous tensile stress field. Replacing the plastic zone by a continuous array of mathematical dislocations, the stress field solution of this mixed boundary value problem (the displacement profile of the plastic zone is fixed while the tensile stresses are zero across the crack) can be solved. A computer program based on this stress field solution has been constructed and tested using the analytical results of the Dugdale model. The method is then applied to determining the surface stress profiles of crazes and plane-stress plastic deformation zones grown from electron microprobe cracks in polystyrene and polycarbonate respectively. The necessary craze and zone surface displacement profiles are determined by quantitative analysis of transmission electron micrographs. The surface stress profiles, which show small stress concentrations at the craze or zone tip falling to an approximately constant value which is maintained to the crack tip, are compared with those previously computed using an approximate Fourier transform method involving estimation of the displacement profile in the crack. The agreement between the approximate method and the exact distributed dislocation method is satisfactory.

On the correction of residual stress measurements obtained using the centre-hole method

Abstract: Significant errors in interpreting the results of the centre-hole technique may arise where test conditions deviate from a uniform uniaxial low-level stress field. This paper demonstrates that where the stress field varies linearly with depth, the as-measured stress represents the stress at one-quarter hole depth. In cases where surface preparation for strain gauging has induced residual stress or where stress levels are sufficiently high to induce plasticity during hole forming, simple formulae are proposed to correct for these effects.

Boundary-layer effects in composite laminates. I - Free-edge stress singularities. II - Free-edge stress solutions and basic characteristics

Abstract: The fundamental nature of the boundary-layer effect in fiber-reinforced composite laminates is formulated in terms of the theory of anisotropic elasticity. The basic structure of the boundary-layer field solution is obtained by using Lekhnitskii's stress potentials (1963). The boundary-layer stress field is found to be singular at composite laminate edges, and the exact order or strength of the boundary layer stress singularity is determined using an eigenfunction expansion method. A complete solution to the boundary-layer problem is then derived, and the convergence and accuracy of the solution are analyzed, comparing results with existing approximate numerical solutions. The solution method is demonstrated for a symmetric graphite-epoxy composite.

Hybrid stress finite element analysis of bending of a plate with a through flaw

Abstract: A hybrid stress finite element procedure for the solution of bending stress intensity factors of a plate with a through-the-thickness crack is presented. Reissner's sixth-order plate theory including the effects of transverse shear deformation is used. The dominant singular crack tip stress field is embedded in the crack tip singular elements and only regular polynomial functions are assumed in the far field elements. The stress intensity factors can be calculated directly from the crack tip singular stress solution functions. The effects of the plate thickness, the ratio between the crack size and the inplane dimension of the plate, and the singular element size on the stress intensity factor solution are investigated. The effects of the explicit enforcement of traction-free conditions along crack surfaces, which are the natural boundary conditions in the present hybrid stress finite element model, are also investigated. The numerical results of bending of a plate with a straight central crack compare favourably with analytical solutions. It is also found that the explicit enforcement of traction-free conditions along crack surfaces is mandatory to obtain meaningful results for the Mode I type of bending stress intensity factor.

The quasi-static stress field around a fractured well bore

Abstract: Multiple fractures created around a well bore can enhance the oil and gas productivity of the fractured well. Recent analyses have shown that if the rate of pressure loading used to induce fracture is sufficiently high, the resulting plastic flow and elastic rebound can set up a “cage” of highly compressive residual stress around the borehole which effectively prohibits crack growth into the formation. The present analysis considers the lower end of the loading rate spectrum and shows that for pressure loading rates sufficiently low so that quasi-static conditions prevail, an initial crack opening under pressure creates highly compressive circumferential stresses around the well bore and the clamping effect of these stresses prohibits additional crack initiation. The existence of these theoretical upper and lower bounds on loading rates to create multiple fractures in well boreholes has been experimentally demonstrated for at least one geologic formation.

Characteristics of plastic deformation under the action of ultrasound

Abstract: The process of plastic deformation under the action of ultrasound differs in a number of ways from deformation under static loading; a computer simulation has shown that these differences are attributable to the specific characteristics of the operation of a source of dislocations for a periodic law of variation of the stresses. Among the most significant features of the ultimate dislocation structure are the saturation of the density of defects (attainment of limiting states) and the formation of stable dislocation clusters, which do not produce stress fields.

Stress relaxation in the earth and seismic activity

Abstract: Consideration of the models described in the preceding pages shows that a sound theoretical basis exists for a physical understanding of post-seismic ground deformations and several other phenomena associated with the asthenosphere relaxation. Since the asthenosphere seems to be involved in a direct way in the seismic mechanism, the knowledge of its rheological properties becomes an essential point to understand the seismic mechanism too. Once a reasonable knowledge of the asthenosphere behaviour is achieved, the models can tell us how the system lithosphere-asthenosphere will evolve after an earthquake or a similar perturbation of the stress field. It will be necessary to compute the stress pattern not only at the Earth surface, but also at the depth where the faults lay. By knowing how stress changes in space and time through the lithosphere, one might predict, for instance, the arrival of a stress wave on a seismogenetic structure: this wave might trigger an earthquake in this zone, if favourable conditions are found.