Stress field

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

Nucleation and growth of faults in brittle rocks

Abstract: We present a model for the nucleation and growth of faults in intact brittle rocks. The model is based on recent experiments that utilize acoustic emission events to monitor faulting processes in Westerly granite. In these experiments a fault initiated at one site without significant preceding damage. The fault propagated in its own plane with a leading zone of intense microcracking. We propose here that faults in granites nucleate and propagate by the interaction of tensile microcracks in the following style. During early loading, tensile microcracking occurs randomly, with no significant crack interaction and with no relation to the location or inclination of the future fault. As the load reaches the ultimate strength, nucleation initiates when a few tensile microcracks interact and enhance the dilation of one another. They create a process zone that is a region with closely spaced microcracks. In highly loaded rock, the stress field associated with microcrack dilation forces crack interaction to spread in an unstable manner and recursive geometry. Thus the process zone propagates unstably into the intact rock. As the process zone lengthens, its central part yields by shear and a fault nucleus forms. The fault nucleus grows in the wake of the propagating process zone. The stress fields associated with shear along the fault further enhance the microcrack dilation in the process zone. The analysis shows that faults should propagate in their own plane, making an angle of 20°–30° with the maximum compression axis. This model provides a physical basis for “internal friction,” the empirical parameter of the Coulomb criterion.

Disturbed Stress Field Model for Reinforced Concrete: Validation

Abstract: The results of analytical investigations are presented supporting the disturbed stress field model as a viable conceptual model for describing the behavior of cracked reinforced concrete elements. ...

Regional patterns of tectonic stress in Europe

Abstract: Nearly 1500 stress orientation determinations are now available for Europe. The data come from earthquake focal mechanisms, overcoring measurements, well bore breakouts, hydraulic fracturing measurements, and young fault slip studies and sample the stress field from the surface to seismogenic depths. Three distinct regional patterns of maximum compressive horizontal stress (SHmax) orientation can be defined from these data: a consistent NW to NNW SHmax stress orientation in western Europe; a WNW-ESE SHmax orientation in Scandinavia, similar to western Europe but with a larger variability of SHmax orientations; and a consistent E-W SHmax orientation and N-S extension in the Aegean Sea and western Anatolia. The different stress fields can be attributed to plate-driving forces acting on the boundaries of the Eurasian plate, locally modified by lithospheric properties in different regions. On average, the orientation of maximum stress in western Europe is subparallel to the direction of relative plate motion between Africa and Europe and is rotated 17° clockwise from the direction of absolute plate motion. The uniformly oriented stress field in western Europe coincides with thin to medium lithospheric thickness (approximately 50–90 km) and high heat flow values (>80 m W/m2). In western Europe a predominance of strike-slip focal mechanisms implies that the intermediate principal stress is vertical. The more irregular horizontal stress orientations in Scandinavia coincide with thick continental lithosphere (110–170 km) and low heat flow (<50 m W/m2). The cold thick lithosphere in this region may result in lower mean stresses associated with far-field tectonic forces and allow the stress field to be more easily perturbed by local effects such as deglaciation flexure and topography. The stress field of the Aegean Sea and western Anatolia is consistent with N-S extension in a back arc setting behind the Hellenic trench subduction zone. The stress field is influenced in places by regional geologic structures, e.g., in the Western Alps, where SHmax directions show a slight tendency toward a radial stress pattern. Not all major geologic structures, however, appear to affect the SHmax orientation, e.g., in the vicinity of the Rhine rift system horizontal stress orientations are continuous.

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

Elastic stress and deformation near a finite spherical magma body: Resolution of the point source paradox

Abstract: Approximate solutions are obtained for the stress and displacement fields due to a pressurized spherical cavity in an elastic half-space. The solutions take the form of series expansions in powers of e = a/d, where a is the cavity radius and d is the depth. The leading-order term in the expression for the surface uplift, which arises at O(e3), recovers the well-known result of Mogi for the response to a point dilatation. The first higher-order correction accounts for a cavity of finite size and thus offers the possibility of fitting leveling data for not only the depth but also the radius and pressure increment. However, this correction is of O(e6) and, consequently, is weak. The result provides a formal explanation for the success of the point dilatation model in representing uplift data even when it is known independently that e is not small. The higher-order correction causes the surface uplift to fall off more rapidly in the radial direction, implying that a fit of the point source solution tends to underestimate the depth d. In contrast to the surface displacement, the stress field near the cavity is affected profoundly by the proximity of the free surface. Three higher-order corrections to the stress field are obtained, which result in a uniformly valid approximation to O(e5). The hoop stress at the cavity exhibits a tensile maximum at the circle of tangency with a cone with its apex at the free surface. This result appears to be consistent with the locus of fractures radiating outward from the magma body inferred by seismic methods in Long Valley, California.