Heterogeneous Stress Field Research Articles

Stress field reconstruction in an active mudslide

Meso-scale structures from gravitational slope deformation observed in landslides and deep-seated gravitational slope failures are very similar to those of endogenous ones. Therefore we applied palaeostress analysis of fault-slip data for reconstructing the stress field of an active mudslide in Pechgraben, Austria. This complex compound landslide has developed in clayey colluvium and shale and was activated after a certain period of dormancy in June 2013. During the active motion on June 12, 2013, 73 fault-slip traces at 9 locations were measured within the landslide body. The heterogeneous fault-slip data were processed in term of palaeostresses, the reconstructed palaeostress tensor being characterized by the orientations of the three principal stress axes and the stress ratio (which provides the shape of the stress ellipsoid). The results of the palaeostress analysis were compared to airborne laser scan digital terrain models that revealed dynamics and superficial displacements of the moving mass prior and after our survey. The results were generally in good agreement with the observed landslide displacement pattern and with the anticipated stress regime according to Mohr-Coulomb failure criteria and Anderson's theory. The compressional regime was mostly registered at the toe in areas, where a compressional stress field is expected during previous mass-movement stages, or at margins loaded by subsequent landslide bodies from above. On the other hand, extension regimes were identified at the head scarps of secondary slides, subsequently on bulged ridges at the toe and in the zone of horst-and-graben structures in the lower central part of the main landslide body, where the basal slip surface probably had locally convex character. Strike-slip regimes, as well as oblique normal or oblique reverse regimes were observed at the lateral margins of the landslide bodies. The directions of principal stresses could be used as markers of landslide movement directions. Although the multiphase strain indicators were, in general, relatively poorly preserved, the palaeostress analysis revealed several different deformation phases at some landslide parts related to different evolution episodes of the complex landslide. Palaeostress analysis based on the multiple inversion method is an affordable approach for reconstructing stress fields within landslides in soft material. This method is an inexpensive and objective tool for stress field reconstruction even in heterogeneous stress field conditions where the distinction of different faults generations may be impossible.

A New View of Incipient Plastic Instability during Nanoindentation**Supported by the Key Program of the National Natural Science Foundation of China under Grant Nos 11132006 and 11302115.

Whether the dislocation nucleation or the sudden dislocation multiplication dominates the incipient plastic instability during the nanoindentation of initial defect-free single crystal still remains unclear. In this work, the dislocation mechanism corresponding to the incipient plastic instability is numerically investigated by coupling discrete dislocation dynamics with the finite element method. The coupling model naturally introduces the dislocation nucleation and accurately captures the heterogeneous stress field during nanoindentation. The simulation results show that the first dislocation nucleation induces the initial pop-in event when the indenter is small, while for larger indenters, the incipient plastic instability is ascribed to the cooperation between dislocation nucleation and multiplication. Interestingly, the local dislocation densities for both cases are almost the same when the sudden load drop occurs. Thus it is inferred that the adequate dislocations generated by either nucleation or multiplication, or both, are the requirement for the trigger of incipient plastic instability. A unified dislocation-based mechanism is proposed to interpret the precipitate incipient plastic instability.

Fully Coupled Hydromechanical Simulation of Hydraulic Fracturing in 3D Discrete-Fracture Networks

SummaryWe developed a hydraulic-fracturing simulator that implicitly couples fluid flow with the stresses induced by fracture deformation in large, complex, 3D discrete-fracture networks (DFNs). The code is efficient enough to perform field-scale simulations of hydraulic fracturing in DFNs containing thousands of fractures, without relying on distributed-memory parallelization. The simulator can describe propagation of hydraulic fractures and opening and shear stimulation of natural fractures. Fracture elements can open or slide, depending on their stress state, fluid pressure, and mechanical properties. Fracture sliding occurs in the direction of maximum resolved shear stress. Nonlinear empirical equations are used to relate normal stress, fracture opening, and fracture sliding to fracture aperture and transmissivity. Fluid leakoff is treated with a semianalytical 1D leakoff model that accounts for changing pressure in the fracture over time. Fracture propagation is modeled with linear-elastic fracture mechanics. The Forchheimer equation (Forchheimer 1901) is used to simulate non-Darcy pressure drop in the fractures because of high flow rate. A crossing criterion is implemented that predicts whether propagating hydraulic fractures will cross natural fractures or terminate against them, depending on orientation and stress anisotropy. Height containment of propagating hydraulic fractures between bedding layers can be modeled with a vertically heterogeneous stress field or by explicitly imposing hydraulic-fracture-height containment as a model assumption. Limitations of the model are that all fractures must be vertical; the mechanical calculations assume a linearly elastic and homogeneous medium; proppant transport is not included; and the locations of potentially forming hydraulic fractures must be specified in advance. Simulations were performed of a single propagating hydraulic fracture with and without leakoff to validate the code against classical analytical solutions. Field-scale simulations were performed of hydraulic fracturing in a densely naturally fractured formation. The simulations demonstrate how interaction with natural fractures in the formation can help explain the high net pressures, relatively short fracture lengths, and broad regions of microseismicity that are often observed in the field during stimulation in low-permeability formations, and that are not predicted by classical hydraulic-fracturing models. Depending on input parameters, our simulations predicted a variety of stimulation behaviors, from long hydraulic fractures with minimal leakoff into surrounding fractures to broad regions of dense fracturing with a branching network of many natural and newly formed fractures.

Tectonic evolution of a Laramide transverse structural zone: Sweetwater Arch, south central Wyoming

AbstractStructural, anisotropy of magnetic susceptibility (AMS), and paleomagnetic data record patterns of layer‐parallel shortening (LPS), vertical‐axis rotation, and regional fault‐fold evolution across the Sweetwater Arch, a major west to WNW trending, basement‐cored Laramide uplift in Wyoming. The southern arch flank is bounded by a WNW striking reverse fault zone that imbricated basement and cover rocks, the northern flank is bounded by a west striking fault zone with a component of strike‐slip and NW trending en echelon folds, and the eastern plunge transitions into an area of multiple‐trending faults and folds. Synorogenic strata record major arch uplift from Maastrichtian to Early Eocene time, followed by arch collapse. LPS, with development of systematic minor fault sets and AMS lineations, preceded large‐scale folding. LPS directions, estimated from both minor fault and AMS data, were oriented WSW along the northern flank, subparallel to Laramide regional shortening, but were refracted to the SSW along the southern flank, and to the west along the eastern arch plunge. Additional minor faults developed along steep fold limbs during continued shortening, with directions remaining SSW along the southern flank but becoming more variable along the eastern plunge where an increasingly heterogeneous stress field developed as additional faults were activated along basement heterogeneities. Vertical‐axis rotation was limited along the arch flanks, whereas the eastern plunge underwent counterclockwise rotation. Deflections in shortening directions were partly related to basement heterogeneities, including weak supracrustal belts on the arch flanks, a strong granitic core, and local reactivation of Precambrian shear zones.

Initialization of highly heterogeneous virgin stress fields within the numerical modeling of large-scale mines

The objective of the present paper is to propose a methodology to numerically simulate (i.e., initialize) the pre-mining stress field in complex but rather frequent situations in which the classical overburden-weight assumption and existing stress measurements are in disagreement and where the stresses strongly vary from one zone to another, even at constant depth. This methodology is illustrated by the case of a deep mine in France that exploits a 10°-dipping coal seam, in which numerous stress measurements were carried out. Virgin principal stresses in this mine have been shown to be highly heterogeneous and anisotropic. To correctly reproduce such a challenging initial stress state in a numerical model and to be able to later calculate mining-induced stresses, five distinct methods (M#1 to M#5) are successively presented and compared, along with their advantages and drawbacks. All of them are based on “fixed” boundary conditions, with null normal displacements on all lateral boundaries except on the top one, which is considered as a free surface of the Earth coinciding with the natural flat topography. The initial conditions of the model assume that the pre-mining stress components linearly depend on the Cartesian coordinates x, y and z (depth), and the Simplex Method is used to calculate the linear coefficients by minimizing the squared difference between the measured stresses and their simulated values. We show that the use of 3D stress gradients produces more realistic results than a 1D vertical stress gradient.

Heterogeneous stress field in the source area of the 2003 M6.4 Northern Miyagi Prefecture, NE Japan, earthquake

Heterogeneous stress field in the source area of the 2003 M6.4 Northern Miyagi Prefecture, NE Japan, earthquake

A structural finite element model for lamellar unit of aortic media indicates heterogeneous stress field after collagen recruitment

Incorporation of collagen structural information into the study of biomechanical behavior of ascending thoracic aortic (ATA) wall tissue should provide better insight into the pathophysiology of ATA. Structurally motivated constitutive models that include fiber dispersion and recruitment can successfully capture overall mechanical response of the arterial wall tissue. However, these models cannot examine local microarchitectural features of the collagen network, such as the effect of fiber disruptions and interaction between fibrous and non-fibrous components, which may influence emergent biomechanical properties of the tissue. Motivated by this need, we developed a finite element based three-dimensional structural model of the lamellar units of the ATA media that directly incorporates the collagen fiber microarchitecture. The fiber architecture was computer generated utilizing network features, namely fiber orientation distribution, intersection density and areal concentration, obtained from image analysis of multiphoton microscopy images taken from human aneurysmal ascending thoracic aortic media specimens with bicuspid aortic valve (BAV) phenotype. Our model reproduces the typical J-shaped constitutive response of the aortic wall tissue. We found that the stress state in the non-fibrous matrix was homogeneous until the collagen fibers were recruited, but became highly heterogeneous after that event. The degree of heterogeneity was dependent upon local network architecture with high stresses observed near disrupted fibers. The magnitude of non-fibrous matrix stress at higher stretch levels was negatively correlated with local fiber density. The localized stress concentrations, elucidated by this model, may be a factor in the degenerative changes in aneurysmal ATA tissue.

Quantitative mapping of stress heterogeneity in polycrystalline alumina using hyperspectral fluorescence microscopy

The microstructurally-induced heterogeneous stress fields arising in a series of Cr-doped polycrystalline alumina materials are mapped with sub-micrometer sub-grain size resolution using fluorescence microscopy. Analysis of the hyperspectral data sets generated during imaging enabled both the amplitude and position of the characteristic Cr R1 fluorescence peak to be determined at every pixel in an image. The peak amplitude information was used to segment the images into individual grains and grain boundary regions. The peak position information, in conjunction with measurements on single-crystal controls, was used to quantify overall stress distributions in the materials and provide stress scales for maps. The combined information enabled spatial variations in the stress fields in crystallographic axes to be mapped and compared directly with microstructural features such as grains and grain boundaries. The mean c-axis stresses in these materials were approximately 200 MPa with stress distribution widths of about 70 MPa, both increasing with average grain size. Greatest variations in stress were observed at grain junctions; no trend in the stress for individual grains with grain size was observed.

Rock Physics Modeling of Unconsolidated Sands: Accounting for Partial Friction Grain Contacts and Heterogeneous Stress Field

A partial friction heterogeneity model of a random-compacted granular pack can be formulated using two parameters ([Formula: see text],[Formula: see text] to account for (1) macroscopic stress heterogeneity distribution of grain packs and (2) microscopic partial friction on the area of grain contact. This proposed partial friction heterogeneity model indicates that surface friction between grain contact is nonignorable, which results in tangential loading path being irreversible. Meanwhile, the tangential stress causes partial sliding on grain contact surface. Macroscopically, the effective shear modulus increases when either fraction of partial slip grain contacts or micro-friction on the area of grain contacts increases.

Spatially heterogeneous stress field in the source area of the 2011 Mw 6.6 Fukushima-Hamadori earthquake, NE Japan, probably caused by static stress change

In order to know whether principal stress orientations in the source area rotated after the 2011 April 11 Mw 6.6 Fukushima-Hamadori earthquake in NE Japan, we investigated detailed spatial distributions of stress orientations for both the pre- and post-main shock periods using a large amount of focal mechanism data. We applied stress tensor inversions to focal mechanism data from Japan's National Research Institute for Earth Science and Disaster Prevention's F-net broadband seismic network and the Japan Meteorological Agency (JMA). The σ3-axes estimated for the pre-main shock period are predominantly oriented WSW–ENE, and are relatively homogeneously in space. In contrast, the orientations of the σ3-axes show a significantly heterogeneous distribution in space for the post-main shock period. In the northern subarea of the focal region, the σ3-axes are oriented NW–SE. In the east and west portions of the central subarea, they are oriented NNW–SSE and WNW–ESE, respectively, almost perpendicular to each other. In the southern subarea, the σ3-axes are oriented WSW–ENE. On the whole, the σ3-axis orientations show concentric circle-like distribution surrounding the large slip area of the MwMw 6.6 main shock rupture. The change of principal stress axis orientations after the earthquake is not significant because of the sparse data set for the pre-main shock period. We calculated static stress changes from the Mw 6.6 main shock and three Mw > 5.5 earthquakes to compare with the observed stress axis orientations in the post-main shock period. The σ3-axis orientations of the calculated total static stress change show a concentric circle-like distribution surrounding the large slip area of the main shock, similar to that noted above. This observation strongly suggests that the spatially heterogeneous stress orientations in the post-main shock period were caused by the static stress change from the Mw 6.6 main shock and other large earthquakes. In order to estimate the differential stress magnitude in the focal area, we calculated deviatoric stress tensors in the post-main shock period by assuming that they are the sum of the deviatoric stress tensors in the pre-main shock period and the static stress changes. Comparison of the calculated and observed stress tensors revealed differential stress magnitudes of 2–30 MPa that explain the observed stress orientations, considering the probable range of estimated stress ratios in the pre-main shock period.

Determination of the First Stress Tensor Invariant of a Complex Steel Sheet Structure from Thermoelastic Stress Analysis

The determination of welded steel sheet assemblies high cycle fatigue properties is a prior concern of the automotive industry. Such assemblies are designed as high-safety parts, for which any fatigue failure is supposed to be prevented. Thus, the determination of complex structures stress field is necessary to design them. Even though finite element models are more and more accurate, experimental methods for the stress field tensors measurement under cyclic loadings are useful to validate those models. The purpose of this work is the experimental determination of the first stress tensor invariant amplitude at the surface of a complex structure under cyclic loading, a car wishbone, with a method based on thermal measurements, the Thermoelastic Stress Analysis (TSA). Parameters which have an influence on the measured temperature at the surface of the structure are studied, including the non-adiabatic behaviour of specimens due to a heterogeneous stress field and the influence of the paint used to measure the temperature with an infra-red camera. All these parameters are taken into account to determine successfully the wishbone stress tensor amplitude during a cyclic test.

Bioinjection treatment: Effects of post-injection residual stress on left ventricular wall stress

Injection of biomaterials into diseased myocardium has been associated with decreased myofiber stress, restored left ventricular (LV) geometry and improved LV function. However, its exact mechanism(s) of action remained unclear. In this work, we present the first patient-specific computational model of biomaterial injection that accounts for the possibility of residual strain and stress introduced by this treatment. We show that the presence of residual stress can create more heterogeneous regional myofiber stress and strain fields. Our simulation results show that the treatment generates low stress and stretch areas between injection sites, and high stress and stretch areas between the injections and both the endocardium and epicardium. Globally, these local changes are translated into an increase in average myofiber stress and its standard deviation (from 6.9±4.6 to 11.2±48.8kPa and 30±15 to 35.1±50.9kPa at end-diastole and end-systole, respectively). We also show that the myofiber stress field is sensitive to the void-to-size ratio. For a constant void size, the myofiber stress field became less heterogeneous with decreasing injection volume. These results suggest that the residual stress and strain possibly generated by biomaterial injection treatment can have large effects on the regional myocardial stress and strain fields, which may be important in the remodeling process.

The role of viscoelasticity on heterogeneous stress fields at frictional interfaces

We investigate the evolution of heterogeneous stress states along frictional interfaces. Using finite-element simulations, we model the occurrence of precursory slip sequences on a deformable-deformable as well as a deformable–rigid interface between two solids. Every interface rupture creates a stress concentration at its arrest position and erases the stress concentrations produced by previous slip events. While the interface is sticking perfectly between two slip events, erased stress concentrations reappear and survive several cycles of ruptures. Such reestablished stress concentrations are smaller than they were before the rupture. We show that the decrease rate of these stress concentrations is exponential with respect to the number of subsequent events and that the bulk viscoelasticity is at the origin of this history effect. During a slip event, the friction tractions at the interface change almost instantaneously, which leads, between two ruptures, to a relaxation-resembling viscous effect that restores the stress concentration. We describe the decrease rate analytically and highlight that it is proportional to the ratio of the viscous over the instantaneous Young’s moduli, and illustrate it by varying the material properties in our simulations.

Effect of coverage and double peening treatments on the fatigue life of a quenched and tempered structural steel

The effects of shot peening treatments comprising different degrees of coverage and also the influence of double treatments applied to a quenched and tempered medium-carbon alloyed steel were analyzed. The latter consisted, in one case, of high intensity peening followed by a lower intensity peening treatment and, in the other, of the removal of the damaged surface layer. Surface roughness, subsurface hardening and the residual stress profiles were determined and compared. Furthermore, the fatigue life corresponding to the different shot peening treatments was assessed on a rotating beam machine under alternative stresses of 50% of the tensile strength of the steel. The full coverage peening treatment gave rise to the best fatigue behavior, as under-coverage produces a heterogeneous surface stress field, while overlong shot peening treatments probably lead to surface damage. On the other hand, double surface treatments are at least partially able to mitigate the surface damage produced by a first high intensity peening treatment. Nevertheless, none of the applied double treatments was able to exceed the fatigue life of the optimal single shot peening.

Residual stress fields analysis in rolled Zircaloy-4 plates: Grazing incidence diffraction and elastoplastic self-consistent model

An experimental and theoretical investigation was carried out to study the in-depth distribution of residual stress after a cold-rolling test in a zirconium alloy. Grazing incidence X-ray diffraction was used to analyze the heterogeneous stress field with regard to different diffraction volumes below the surface of the sample. An interpretation of the intergranular stress analysis based on in-depth stress development has been made using an elastoplastic self-consistent model in order to account for the effect of plastic anisotropy. The contribution and the magnitude of both the first- and second-order residual stresses as a function of the penetration depth has been correctly evaluated using information from the model. The results show the complementarity of the methods used.

Inversion for absolute deviatoric crustal stress using focal mechanisms and coseismic stress changes: The 2011 M9 Tohoku‐oki, Japan, earthquake

AbstractThe absolute magnitude of stress in the crust and the shear strength of faults are poorly known, yet fundamental quantities, in lithospheric dynamics. While stress magnitude cannot be measured directly, deviatoric stress state can be inferred indirectly from focal mechanism solutions collected before and after an earthquake. We extend a standard stress inversion for normalized stresses to invert for the 3‐D spatial distribution of absolute deviatoric stress and variation of fault strength with depth using focal mechanism solutions and coseismic stress changes produced by large earthquakes. We apply the method to the 2011 M9 Tohoku‐oki, Japan, earthquake. The northern Japan fore‐arc crust between 5 and 15 km depths appears to be weak with fault strength of 40–90 MPa, consistent with a coefficient of friction of 0.2–0.5. The M9 Tohoku‐oki coseismic stress change was large enough, relative to the ambient stress, to rotate the principal stress directions typically ~20° in the upper 20 km of the crust. The data from Japan require a heterogeneous ambient deviatoric stress field with short‐wavelength (~20–50 km) fluctuations in principal stress orientations.

Anisotropic failure modes of high-strength aluminium alloy under various stress states

The influence of stress state and plastic anisotropy on the fracture behaviour of a rolled AA7075-T651 aluminium plate under quasi-static loading conditions is studied both experimentally and numerically. Material tests in different directions of the plate were carried out using specimens with various shapes to provide a wide range of stress states. The strain to failure and the failure modes were found to vary strongly with the stress state, but also with the loading direction due to the complex microstructure of the alloy. Finite element simulations adopting an anisotropic plasticity model were used to obtain local values of stresses and strains and to define the strains at fracture for the various stress states. The numerical simulations show that due to the heterogeneous stress and strain fields in the specimens, it is very difficult to accurately locate the point where fracture initiates and thus to determine the local fracture strain as a function of stress state and loading direction.

Effects of mechanical layering on hydrofracture emplacement and fluid transport in reservoirs

Fractures generated by internal fluid pressure, for example, dykes, mineral veins, many joints and man-made hydraulic fractures, are referred to as hydrofractures. Together with shear fractures, they contribute significantly to the permeability of fluid reservoirs such as those of petroleum, geothermal water, and groundwater. Analytical and numerical models show that – in homogeneous host rocks – any significant overpressure in hydrofractures theoretically generates very high crack tip tensile stresses. Consequently, overpressured hydrofractures should propagate and help to form interconnected fracture systems that would then contribute to the permeability of fluid reservoirs. Field observations, however, show that in heterogeneous and anisotropic, e.g., layered, rocks many hydrofractures become arrested or offset at layer contacts and do not form vertically interconnected networks. The most important factors that contribute to hydrofracture arrest are discontinuities (including contacts), stiffness changes between layers, and stress barriers, where the local stress field is unfavourable to hydrofracture propagation. A necessary condition for a hydrofracture to propagate to the surface is that the stress field along its potential path is everywhere favourable to extension-fracture formation so that the probability of hydrofracture arrest is minimised. Mechanical layering and the resulting heterogeneous stress field largely control whether evolving hydrofractures become confined to single layers (strata¬bound frac¬tures) or not (non-stratabound fractures) and, there¬fore, if a vertically intercon¬nec¬ted fracture system forms. Non-stratabound hydrofractures may propagate through many layers and generate interconnected fracture systems. Such systems commonly reach the percolation threshold and largely control the overall permeability of the fluid reservoirs within which they develop.

Mechanical–Electrical Measurements and Relevant Test Structures for Sensing Interconnect Stress Effects in CMOS Technology

For CMOS technology, the increase of interconnects metal density is responsible for heterogeneous mechanical stress fields in active regions of silicon. Coupled mechanical–electrical measurements are performed to evaluate the impact of stress at circuit and device levels. This mismatch originated by interconnects metal lines stress is measured through the use of piezoresistive test structures. Local mechanical stress can thus be monitored in a simple process control compatible approach.

Dynamic Rupture Simulation of the 2008 Mw 7.9 Wenchuan Earthquake with Heterogeneous Initial Stress

The rupture process and tectonic surroundings of the 2008 Wenchuan, China, earthquake are both complex in a way that might be related to the heterogeneous stress field of the Longmen Shan region. In this study, we construct dynamic models with heterogeneous initial stress to reproduce a kinematic inversion result by Wen et al. (2012) and investigate the physical mechanisms of the variable slip pattern and rupture velocity in this event. The results show that, for the 2008 Wenchuan earthquake, (1) the rupture behavior and slip pattern can be explained by heterogeneities in initial stress and (2) the variations of rupture velocity and ground‐motion pattern are strongly affected by both stress drop and fault strength. Our preferred dynamic model agrees with the kinematic model that the 2008 Wenchuan earthquake initiated with a slow velocity in the southwest, sped up in the segment with the largest slip, and then slowed down for the remaining propagation to the northeast.