Stress field

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

Use of focal mechanisms to determine stress: A control study

Abstract: To allow focal mechanisms to be inverted for the stress field requires a different inversion algorithm than for slickenside data because focal mechanisms do not represent fault slip data unless one can decide which nodal plane is the fault plane. If one can decide which nodal plane is the fault plane, then the focal mechanisms can be inverted with the slickenside inversion algorithm. This decision cannot always be made, so algorithms for inverting focal mechanisms for the stress field are studied. These algorithms either use both of the possible fault planes or attempt to choose the correct fault plane while determining the stress tensor. Simulated focal mechanisms are made from slickenside data and used to provide a control study for the focal mechanism inversion algorithms. The results of this control study show that focal mechanisms can be inverted to find the best stress tensor, but the resolution is decreased unless the fault planes can be picked a priori. The resolution can also be increased by including constraints on the magnitude of the tangential traction on the fault plane. Therefore, using focal mechanisms to study small variations in the stress field requires that other data (e.g., studies of the hypocenters, surface faulting, or structural information concerning the region) be introduced to pick which of the nodal planes is the fault plane. This study also introduces the method of bootstrap resampling to the statistics of this problem. The non-Gaussian nature of the data makes the nonparametric formulation of the bootstrap approach ideal for this problem.

Quantum-mechanical theory of stress and force.

Abstract: The stress theorem presented previously by the present authors is derived in detail and is related to the virial and force theorems. Stress fields are considered in two alternative forms, both of which give the same macroscopic stress and forces on nuclei when integrated over appropriate surfaces. A crucial concept is interactions that ``cross'' surfaces. Explicit forms of the stress field within the local-density approximation are given, together with a generalization of the approximate Liberman form for pressure. Reciprocal-space expressions and ab initio calculations are considered in detail in an accompanying paper.

Slip-tendency analysis and fault reactivation

Abstract: Slip-tendency analysis is a new technique that permits rapid assessment of stress states and related potential fault activity. The tendency of a surface to undergo slip in a given stress field depends on its frictional characteristics (primarily controlled by rock type) and the ratio of shear to normal stress acting on the surface, here defined as slip tendency (determined by orientation of the surface within the stress field). An interactive computer tool displays the stress tensor in terms of its associated slip-tendency distribution and the relative likelihood and direction of slip on surfaces of all orientations. The technique provides easy visualization and rapid evaluation of stress in terms of its potential for causing slip on individual faults or fault populations for use in seismic-risk and fault-rupture–risk assessment, exploration for high-risk and earthquake-prone blind faults, selection of likely earthquake focal mechanism solutions, and for use in analysis of compatibility of geologic structures.

A new look at the atomic level virial stress: on continuum-molecular system equivalence

Abstract: The virial stress is the most commonly used definition of stress in discrete particle systems. This quantity includes two parts. The first part depends on the mass and velocity (or, in some versions, the fluctuation part of the velocity) of atomic particles, reflecting an assertion that mass transfer causes mechanical stress to be applied on stationary spatial surfaces external to an atomic‐particle system. The second part depends on interatomic forces and atomic positions, providing a continuum measure for the internal mechanical interactions between particles. Historic derivations of the virial stress include generalization from the virial theorem of Clausius (1870) for gas pressure and solution of the spatial equation of balance of momentum. The virial stress is stress‐like a measure for momentum change in space. This paper shows that, contrary to the generally accepted view, the virial stress is not a measure for mechanical force between material points and cannot be regarded as a measure for mechanical stress in any sense. The lack of physical significance is both at the individual atom level in a time‐resolved sense and at the system level in a statistical sense. It is demonstrated that the interatomic force term alone is a valid stress measure and can be identified with the Cauchy stress. The proof in this paper consists of two parts. First, for the simple conditions of rigid translation, uniform tension and tension with thermal oscillations, the virial stress yields clearly erroneous interpretations of stress. Second, the conceptual flaw in the generalization from the virial theorem for gas pressure to stress and the confusion over spatial and material equations of balance of momentum in theoretical derivations of the virial stress that led to its erroneous acceptance as the Cauchy stress are pointed out. Interpretation of the virial stress as a measure for mechanical force violates balance of momentum and is inconsistent with the basic definition of stress. The versions of the virial‐stress formula that involve total particle velocity and the thermal fluctuation part of the velocity are demonstrated to be measures of spatial momentum flow relative to, respectively, a fixed reference frame and a moving frame with a velocity equal to the part of particle velocity not included in the virial formula. To further illustrate the irrelevance of mass transfer to the evaluation of stress, an equivalent continuum (EC) for dynamically deforming atomistic particle systems is defined. The equivalence of the continuum to discrete atomic systems includes (i) preservation of linear and angular momenta, (ii) conservation of internal, external and inertial work rates, and (iii) conservation of mass. This equivalence allows fields of work‐ and momentum‐preserving Cauchy stress, surface traction, body force and deformation to be determined. The resulting stress field depends only on interatomic forces, providing an independent proof that as a measure for internal material interaction stress is independent of kinetic energy or mass transfer.

State of Stress in the Earth's Crust

Abstract: Measurements ofthe stress field within the crust can provide perhaps the most useful information concerning the forces responsible for various tectonic processes, such as earthquakes Advances in knowledge of the state of stress at mid-crustal depths are essential if further progress is to be made toward solving a broad class of problems in geodynamics Most stress measurements have been, and will continue to be, motivated by engineering needs rather than the needs of geologists engaged in fundamental research Knowledge of the state of stress is critical to the design of underground excavations for mining and for nuclear waste disposal (eg Jaeger & Cook 1969, pp 435-64) The massive hydraulic fracturing of formations in oil and gas fields to stimulate production is another application for which knowledge of the stress field at depth is very important and, in fact, many of the deeper stress determinations have been by-products of these "hydrofrac" operations (eg Howard & Fast 1970) A recent and exciting application of hydraulic fracturing is the Hot-Dry-Rock Geothermal Energy Program (Aamodt 1977) Heat is extracted from the rock by circulating fluid down a pipe into hot rock and then up through a second pipe A large fracture connecting the two pipes serves as the heat exchanger Knowing the state of stress is critical in the solution to the problem of creating and maintaining such a crack There is little argument about the applicability of information on the state of stress to these and many other engineering problems The application of stress measurements to the solution of problems in tectonics is not so straightforward as in engineering design Whereas the engineer is concerned with the stress field affecting the rock, the geologist attempts to deduce the processes that might have caused the stresses Before the measured stress field can be related