Stress field

About: Stress field is a research topic. Over the lifetime, 11926 publications have been published within this topic receiving 226417 citations.

Static stress changes and the triggering of earthquakes

Abstract: To understand whether the 1992 M = 7.4 Landers earthquake changed the proximity to failure on the San Andreas fault system, we examine the general problem of how one earthquake might trigger another. The tendency of rocks to fail in a brittle manner is thought to be a function of both shear and confining stresses, commonly formulated as the Coulomb failure criterion. Here we explore how changes in Coulomb conditions associated with one or more earthquakes may trigger subsequent events. We first consider a Coulomb criterion appropriate for the production of aftershocks, where faults most likely to slip are those optimally orientated for failure as a result of the prevailing regional stress field and the stress change caused by the mainshock. We find that the distribution of aftershocks for the Landers earthquake, as well as for several other moderate events in its vicinity, can be explained by the Coulomb criterion as follows: aftershocks are abundant where the Coulomb stress on optimally orientated faults rose by more than one-half bar, and aftershocks are sparse where the Coulomb stress dropped by a similar amount. Further, we find that several moderate shocks raised the stress at the future Landers epicenter and along much of the Landers rupture zone by about a bar, advancing the Landers shock by 1 to 3 centuries. The Landers rupture, in turn, raised the stress at site of the future M = 6.5 Big Bear aftershock site by 3 bars. The Coulomb stress change on a specified fault is independent of regional stress but depends on the fault geometry, sense of slip, and the coefficient of friction. We use this method to resolve stress changes on the San Andreas and San Jacinto faults imposed by the Landers sequence. Together the Landers and Big Bear earthquakes raised the stress along the San Bernardino segment of the southern San Andreas fault by 2 to 6 bars, hastening the next great earthquake there by about a decade.

Some basic stress diffusion solutions for fluid-saturated elastic porous media with compressible constituents

Abstract: This is a study of the formulation, some basic solutions, and applications of the Biot linearized quasistatic elasticity theory of fluid-infiltrated porous materials. Whereas most previously solved problems are based on idealizing the fluid and solid constituents as separately incompressible, full account is taken here of constituent compressibility. Previous studies are reviewed and the Biot constitutive equations relating strain and fluid mass content to stress and pore pressure are recast in terms of new material parameters, more directly open to physical interpretation as the Poisson ratio and induced pore pressure coefficient in undrained deformation. Different formulations of the coupled deformation/diffusion field equations and their analogues in coupled thermoelasticity are discussed, and a new formulation with stress and pore pressure as basic variables is presented that leads, for plane problems, to a convenient complex variable representation of solutions. The problems solved include those of the suddenly introduced edge dislocation and concentrated line force and of the suddenly pressurized cylindrical and spherical cavity. The dislocation solution is employed to represent that for quasi-static motions along a shear fault, and a discussion is given, based on fracture mechanics models for fault propagation, of phenomena involving coupled behavior between the rupturing solid and its pore fluid, which could serve to stabilize a fault against rapid spreading. Also, the solution for a pressurized cylindrical cavity leads to a time-dependent stress field near the cavity wall, and its relevance to time effects in the inception of hydraulic fractures from boreholes, or from drilled holes in laboratory specimens, is discussed. Various limiting cases are identified, and numerical values of the controlling porous media elastic parameters are given for several rocks.

First‐ and second‐order patterns of stress in the lithosphere: The World Stress Map Project

Abstract: To date, more than 7300 in situ stress orientations have been compiled as part of the World Stress Map project. Of these, over 4400 are considered reliable tectonic stress indicators, recording horizontal stress orientations to within <±25°. Remarkably good correlation is observed between stress orientations deduced from in situ stress measurements and geologic observations made in the upper 1–2 km, well bore breakouts extending to 4–5 km depth and earthquake focal mechanisms to depths of ∼20 km. Regionally uniform stress orientations and relative magnitudes permit definition of broad-scale regional stress patterns often extending 20–200 times the approximately 20–25 km thickness of the upper brittle lithosphere. The “first-order” midplate stress fields are believed to be largely the result of compressional forces applied at plate boundaries, primarily ridge push and continental collision. The orientation of the intraplate stress field is thus largely controlled by the geometry of the plate boundaries. There is no evidence of large lateral stress gradients (as evidenced by lateral variations in stress regime) which would be expected across large plates if simple resistive or driving basal drag tractions (parallel or antiparallel to absolute motion) controlled the intraplate stress field. Intraplate areas of active extension are generally associated with regions of high topography: western U.S. Cordillera, high Andes, Tibetan plateau, western Indian Ocean plateau. Buoyancy stresses related to crustal thickening and/or lithospheric thinning in these regions dominate the intraplate compressional stress field due to plate-driving forces. These buoyancy forces are just one of several categories of “second-order” stresses, or local perturbations, that can be identified once the first-order stress patterns are recognized. These second-order stress fields can often be associated with specific geologic or tectonic features, for example, lithospheric flexure, lateral strength contrasts, as well as the lateral density contrasts which give rise to buoyancy forces. These second-order stress patterns typically have wavelengths ranging from 5 to 10+ times the thickness of the brittle upper lithosphere. A two-dimensional analysis of the amount of rotation of regional horizontal stress orientations due to a superimposed local stress constrains the ratio of the magnitude of the horizontal regional stress differences to the local uniaxial stress. For a detectable rotation of 15°, the local horizontal uniaxial stress must be at least twice the magnitude of the regional horizontal stress differences. Examples of local rotations of SHmax orientations include a 75°–85° rotation on the northeastern Canadian continental shelf possibly related to margin-normal extension derived from sediment-loading flexural stresses, a 50°–60° rotation within the East African rift relative to western Africa due to extensional buoyancy forces caused by lithospheric thinning, and an approximately 90° rotation along the northern margin of the Paleozoic Amazonas rift in central Brazil. In this final example, this rotation is hypothesized as being due to deviatoric compression oriented normal to the rift axis resulting from local lithospheric support of a dense mass in the lower crust beneath the rift (“rift pillow”). Estimates of the magnitudes of first-order (plate boundary force-derived) regional stress differences computed from modeling the source of observed local stress rotations magnitudes can be compared with regional stress differences based on the frictional strength of the crust (i.e., “Byerlee's law”) assuming hydrostatic pore pressure. The examples given here are too few to provide a definitive evaluation of the direct applicability of Byerlee's law to the upper brittle part of the lithosphere, particularly in view of uncertainties such as pore pressure and relative magnitude of the intermediate principal stresses. Nonetheless, the observed rotations all indicate that the magnitude of the local horizontal uniaxial stresses must be 1–2.5+ times the magnitude of the regional first-order horizontal stress differences and suggest that careful evaluation of such local rotations may be a powerful technique for constraining the in situ magnitude stress differences in the upper, brittle part of the lithosphere.

A class of mixed assumed strain methods and the method of incompatible modes

Abstract: A three-field mixed formulation in terms of displacements, stresses and an enhanced strain field is presented which encompasses, as a particular case, the classical method of incompatible modes. Within this frame-work, incompatible elements arise as particular ‘compatible’ mixed approximations of the enhanced strain field. The conditions that the stress interpolation contain piece-wise constant functions and be L2-ortho-gonal to the enhanced strain interpolation, ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation. The preceding conditions are formulated in a form particularly convenient for element design. As an illustration of the methodology three new elements are developed and shown to exhibit good performance: a plane 3D elastic/plastic QUAD, an axisymmetric element and a thick plate bending QUAD. The formulation described herein is suitable for non-linear analysis.

Dislocations and Cracks in Anisotropic Elasticity

Abstract: The solution of the elastic equations is considered for the case in which the state of the solid is independent of one of the three Cartesian coordinates. The stresses due to a dislocation, a wall of parallel dislocations, and a crack in an arbitrary non-uniform stress field are obtained. The results hold for the most general anisotropy in which no symmetry elements of the crystal are assumed.