Principal Stress Tensor Research Articles

Azimuthal pore pressure response to teleseismic waves: effects of damage and stress anisotropy

SUMMARY Pore pressure oscillations induced by stress variations, including propagating seismic waves from remote earthquakes, have been widely observed in various groundwater systems. The monitored pressure change in wells shows significant water-level oscillations to volumetric strain as well as to S and Love waves. Recent observations demonstrated azimuthal dependence of the pore pressure oscillations with respect to stress indicators and fault zone orientation. Within the fault zone, damage-induced anisotropy is the result of the alignment and orientation of cracks and other internal flaws within the rock. In this work, we provide a complete quantitative description of the pore pressure changes induced by passing seismic waves associated with different orientations and values of principal stress and damage tensor components. The model quantifies the azimuthal dependence of the pore pressure response by a non-dimensional ratio defined as the amplitude of the pressure oscillations induced by a shear strain normalized to the volumetric strain. Three angles and two values are needed to calculate the azimuthal dependence of the pore pressure response: the angle between the directions of the maximum horizontal stress and the seismic event; fault zone orientation; microcrack orientation within the fault zone; and damage and stress values. The model predicts that maximum pore pressure response occurs when microcracks and maximum horizontal stress are in the same orientation, high damage and high stress anisotropy. By adjusting these quantities, we recalculate results of recent seismological studies in the Arbuckle disposal well, Osage County, Oklahoma. The presented model successfully predicts the observed azimuthal dependence in wave-induced fluid pressure response and relates the anisotropic response to tectonic indicators such as the orientations of the maximum horizontal stress, fault zone, and microfractures.

Mechanistic driving force for martensite decay in rolling contact fatigue

Martensite decay due to large scale microstructural alterations is the main fatigue process which occurs during extensive rolling contact fatigue in bearing applications. Despite its practical and scientific importance, the full description of the controlling phenomena is still incomplete. Here, we demonstrate that the main mechanistic driving force for martensite decay comes from the positive components of the principal subsurface stress tensor. Such a conclusion is derived using the concept of Continuum Damage Mechanics where the damage rate is controlled by the elastic energy release and plastic strain range. Modeling results are compared with experiments and a good quantitative agreement is obtained. The analysis presented here illuminates the mechanistic reasons on why the fastest material decay occurs at the depth corresponding to the so-called maximum orthogonal shear stress.

Characteristic parameters of soil failure criteria for plane strain conditions – experimental and semi-theoretical study

Abstract The paper concerns the characteristic parameters of the selected isotropic failure criteria, i.e. Mohr–Coulomb, Drucker–Prager, Matsuoka–Nakai and Lade–Duncan. The parameters are determined directly from the failure criteria and stress measurements or by semi-theoretical approach, assuming that the soil obeys the associated flow rule and using the plane strain condition. In the latter case, the parameters can be expressed as functions of the plane strain internal friction angle, which is determined from measurements. The principal stress tensor components, corresponding to the soil peak strength and necessary to obtain the failure criteria parameters, are measured in a series of true triaxial, plane strain tests, on coarse Skarpa sand samples of different initial relative density, subjected to various confining pressures.

OPTIMAL MESH CRITERIA IN FINITE ELEMENT MODELING OF HUMAN FOOT: THE DEPENDENCE FOR MULTIPLE MODEL OUTPUTS ON MESH DENSITY AND LOADING BOUNDARY CONDITIONS

The use of finite element models has gained popularity in the field of foot and footwear biomechanics to predict the stress–strain distribution and the treatment effectiveness of therapeutic insoles for pathological foot conditions. However, a comprehensive evaluation of mesh quality is often ignored, meanwhile no golden standard exists for the mesh density and selection of element size at an acceptable accuracy. Here, we make a convergence test and established anatomically-realistic foot models at different mesh densities. The study compared the discrepancy in output variables to the changes of element type and mesh density under barefoot and footwear conditions with compressive and shear loads, which are commonly encountered in foot and footwear biomechanics simulations. For a range of loading conditions simulated in 125 finite element models, the peak plantar pressure consistently converged with optimal mesh size determined at 2.5[Formula: see text]mm. The convergence variable of principal strains and stress tensors, however, varies significantly. The max von-Mises stress showed strong sensitive behavior to the changes of the mesh density. The pattern for contact pressure distribution became less accurate when the element sizes increase to 6.0[Formula: see text]mm; in particular, the locations of the pressure peak do not show remarkable changes, but the size of the area of contact still changes. The current study could offer a general guideline when generating a reasonable accurate finite element models for the analysis of plantar pressure distributions and stress/strain states employed for foot and footwear biomechanics evaluations.

Mechanical analysis of carbon fiber reinforced polymer composite using CATIAV5 R14

High performance plastics and composites have become the substitutes for traditional materials, showing improved performance now-a-days. As compared to conventional materials, polymer matrix composites (PMCs) are well- known for their high strength and stiffness at a lower weight. The aim of this paper is to provide information on mechanical analysis of hydraulic flow pipe created utilizing carbon reinforced composites. The effects of test parameters as deformation, equivalent (von-mises) stress and principal stress tensor are discussed. The 3D model of composite cylindrical flow pipe using carbon fiber reinforced with resin epoxy and polypropylene designed, simulated and analysed using CATIA V5 R14 2017workbench. It has been found that carbon fibre reinforced with resin epoxy has shown the total deformation of 2.4788e-013 m which is lesser as compared to Polypropylene having total deformation of 4.7321e-014. Carbon fiber reinforced with resin epoxy composite sample has higher life cycle due to its less total deformation and high stress bearing capacity.

Tectonics of the Dead Sea Fault Driving the July 2018 Seismic Swarm in the Sea of Galilee (Lake Kinneret), Israel

AbstractNorthern Israel was struck during July 2018 by a ML4.4 earthquake followed by a seismic sequence that lasted about 30 days. This seismic sequence occurred in the center of a temporary seismic network deployed around the Sea of Galilee (Lake Kinneret). The network was installed to investigate the regional kinematics of the Dead Sea Fault, which is a major transform fault running N‐S for more than 1,000 km. The data allowed us to develop a local velocity model for the Sea of Galilee. We relocated more than 600 earthquakes and calculated 27 focal mechanisms pointing out a complex kinematic setting, possibly controlled by fluids at depth. The seismic sequence developed along a NNW‐striking direction and it is bounded to the east by the N‐striking Dead Sea fault. Hypocenter depths range between 6 and 13 km. Directions of the principal stress tensors suggest a transtentional deformation, in agreement with the overall kinematics of the region.We analyze and discuss our data set to investigate mechanisms that potentially triggered the observed seismic swarm, including exacerbated ground water pumping proposed by previous authors. We suggest that the seismic sequence is driven by the dissipation of the elastic load that accumulated in this region.

MATHEMATICAL MODELS SIMULATING THE FORMATION OF THE STRESS-STRAIN STATE OF EPIPLATFORM OROGENS

The sources of the natural stress-strain state (SSS) of epiplatform orogens are investigated by tectonophysical methods based on seismological data. According to the available data, the horizontal axes of the main deviatoric extension are dominant in depressions, while in the ridges of the orogens, the axes of the main deviatorial compression are dominant.Our comparative analysis is focused on SSS of the orogenic crust. It is generally accepted that the sources of such SSS are geodynamic processes, including the pressure on the Eurasian Plate from the Indian Plate, and the small-scale thermogravitational asthenospheric convection. In the mathematical (analytical) simulation technique used in our study, the main criterion for the correctness of models in terms of tectonophysics is the correspondence between the orientation pattern of the principal stress tensor axes in the crust model to the natural data. According to Model I, the lithospheric SSS under lateral compression is less consistent with the sought-for SSS. Model II also gives the results that do not fully correspond to the stress data from tectonophysical reconstructions. However, additional analysis suggests that asthenospheric convection is a more promising (from the point of view of tectonophysics) geodynamic process for explaining epiplatform orogenesis. In our opinion, more complex and probably non-analytical mathematical models should consider this source of loading of the lithosphere as one of the most significant factors in the formation of the orogenic crust SSS in Central Asia.

A micromechanical study on the stress rotation in granular materials due to fabric evolution

In the present study, the non-coaxiality between the axes of principal stress and strain rate tensors is investigated from micromechanical point of view. Based on the so called stress–force–fabric (SFF) relationship, which describes the macro–micro relation, an expression is derived for the principal direction of stress tensor in terms of micromechanical parameters of the fabric. In general, the rotation of principal stress axis and accordingly, the non-coaxiality angle, are influenced by both the anisotropy coefficients and directions of anisotropy of the fabric characteristics. The derived macro–micro relationship was evaluated by performing DEM simulations of 2D specimens of aggregates. It was shown that the principal directions of anisotropy parameters are almost coincident for the assemblies containing circular particles or elongated angular particles with random distribution. In such case, the principal direction of stress tensor can be regarded as the average principal direction of anisotropy. However, when the aggregate with elongated particles has inherently-anisotropic fabric, a correct estimation of the stress angle rotation requires considering all the anisotropy parameters including both anisotropy coefficients and directions.

A transmissivity model for deformation zones in fractured crystalline rock and its possible correlation to in situ stress at the proposed high-level nuclear waste repository site at Forsmark, Sweden

The Forsmark site was recently proposed by the Svensk Karnbranslehantering AB (SKB) to serve as the potential site for construction of a future geological repository for spent high-level nuclear fuel at about 470 m depth in fractured crystalline rock. The considerations included, among other things, distance from regionally significant deformation zones with highly strained rock, lithological homogeneity, low hydraulic conductivity, groundwater salinity with an acceptable range, and lack of potential mineral resources. This report describes the calculation of transmissivity of deduced deformation zones at Forsmark and the transmissivity model used in the regional groundwater flow modeling carried out in support of the integrated site description. Besides significant decrease with increasing depth (more than four orders of magnitude over a depth of about 1 km), the calculated transmissivity values also reveal considerable spatial variability along the strikes of the zones, i.e. lateral heterogeneity (more than two orders of magnitude). A hydro-mechanical coupling is discussed, based on presented models for the tectonic evolution and the principal stress tensor. Tentatively, laboratory-scale relationships developed from normal stress experiments on a single fracture in crystalline rock can be used to estimate the maximum values of transmissivity of deduced deformation zones at Forsmark.

Bonding pathways of high-pressure chemical transformations

A three-stage bonding pathway towards high-pressure chemical transformations from molecular precursors or intermediate states has been identified by first-principles simulations. With the evolution of principal stress tensor components in the response of chemical bonding to compressive loading, the three stages can be defined as the van der Waals bonding destruction, a bond breaking and forming reaction, and equilibrium of new bonds. The three-stage bonding pathway leads to the establishment of a fundamental principle of chemical bonding under compression. It reveals that during high-pressure chemical transformation, electrons moving away from functional groups follow anti-addition, collision-free paths to form new bonds in counteracting the local stress confinement. In applying this principle, a large number of molecular precursors were identified for high-pressure chemical transformations, resulting in new materials.

An Assessment of the Seismicity of the Bursa Region from a Temporary Seismic Network

A temporary earthquake station network of 11 seismological recorders was operated in the Bursa region, south of the Marmara Sea in the northwest of Turkey, which is located at the southern strand of the North Anatolian Fault Zone (NAFZ). We located 384 earthquakes out of a total of 582 recorded events that span the study area between 28.50–30.00°E longitudes and 39.75–40.75°N latitudes. The depth of most events was found to be less than 29 km, and the magnitude interval ranges were between 0.3 ≤ ML ≤ 5.4, with RMS less than or equal to 0.2. Seismic activities were concentrated southeast of Uludag Mountain (UM), in the Kestel-Igdir area and along the Gemlik Fault (GF). In the study, we computed 10 focal mechanisms from temporary and permanents networks. The predominant feature of the computed focal mechanisms is the relatively widespread near horizontal northwest-southeast (NW–SE) T-axis orientation. These fault planes have been used to obtain the orientation and shape factor (R, magnitude stress ratio) of the principal stress tensors (σ1, σ2, σ3). The resulting stress tensors reveal σ1 closer to the vertical (oriented NE–SW) and σ2, σ3 horizontal with R = 0.5. These results confirm that Bursa and its vicinity could be defined by an extensional regime showing a primarily normal to oblique-slip motion character. It differs from what might be expected from the stress tensor inversion for the NAFZ. Different fault patterns related to structural heterogeneity from the north to the south in the study area caused a change in the stress regime from strike-slip to normal faulting.

Field evidences of secondary surface ruptures occurred during the 20 February 1956 Eskişehir earthquake in the NW Anatolia

Surface rupture and source fault of the 20 February 1956 Eskişehir earthquake have been a matter of debate that potentially contributes towards the understanding of the active deformation and seismic risk in the highly populated NW Anatolia. Field observations on the two fault segments (namely Kavacık and Uludere faults) in the north of the Eskişehir graben revealed evidences of co-seismic surface rupture and mass movements during the Eskişehir earthquake. Surface rupture was observed as a 2.5m wide, a 100m long and ca. 20 cm deep asymmetric depression in the Gümüşlü valley, 2 km east of the Uludere village. A trench dug on this depression confirms a prominent high-angle south dipping fault (dominantly left lateral strike slip) and two faint north-dipping antithetics as clear noticeable shear zones in organic-rich thick soil. Mass failures are particularly observed in spring depressions filled with loose torrent and carbonaceous material in front of the fault scarp. Some rock slides of several tens of meters in size that obviously require significantly high ground shaking were also developed on steep fault scarps. The orientation of the principal stress tensor as deduced from the surface rupture of the Eskişehir earthquake displays clear inconsistency with the geometry of prominent faults in the area. We concluded that this disagreement may be explained by a curved surface rupture. The western and eastern tips of this rupture are EW trending and the probable NW-running part in the middle would correspond to the bounding zone between two right-stepping faults.

Glyph based representation of principal stress tensors in virtual reality environments

This article describes a new visualization method for an illustrative visualization of physical values in immersive workspaces. Through the newly developed visualization pipeline, FEM results such as stress, temperature and resulting deformation, as well as the underlying constraints can be visualized in virtual and augmented reality (AR) applications. Special features are the use of 3D glyphs for mapping stress direction and gradient as well as data preparation and the resulting data format, which was especially developed for use with virtual reality (VR) systems. This article demonstrates the current state of VR developments, which were done at the Institute for Machine Tools and Production Processes, for improving the analysis of complex FE datasets, and gives an outlook to future research activities.

Types of focal mechanism solutions and parameter consistency of the sub-blocks in Sichuan and Yunnan Provinces

Based on P-and S-wave amplitudes and some clear initial P-wave motion data, we calculated focal mechanism solutions of 928 M≥2.5 earthquakes (1994–2005) in four sub-blocks of Sichuan and Yunnan Provinces, namely Sichuan-Qinghai, Yajiang, Central Sichuan and Central Yunnan blocks. Combining these calculation results with those of the focal mechanism solutions of moderately strong earthquakes, we analyzed the stress field characteristics and dislocation types of seismogenic faults that are distributed in the four sub-blocks. The orientation of principal compressive stress for each block is: EW in Sichuan-Qinghai, ESE or SE in Yajiang, Central Sichuan and Central Yunnan blocks. Based on a great deal of focal mechanism data, we designed a program and calculated the directions of the principal stress tensors, σ1, σ2 and σ3, for the four blocks. Meanwhile, we estimated the difference (also referred to as consistency parameter $$\bar \theta $$ ) between the force axis direction of focal mechanism solution and the direction of the mean stress tensor of each block. Then we further analyzed the variation of $$\bar \theta $$ versus time and the dislocation types of seismogenic faults. Through determination of focal mechanism solutions for each block, we present information on the variation in $$\bar \theta $$ value and dislocation types of seismogenic faults.

Dynamic Rupture Modeling of the Transition from Thrust to Strike-Slip Motion in the 2002 Denali Fault Earthquake, Alaska

We use three-dimensional dynamic (spontaneous) rupture models to investigate the nearly simultaneous ruptures of the Susitna Glacier thrust fault and the Denali strike-slip fault. With the 1957 M_w 8.3 Gobi-Altay, Mongolia, earthquake as the only other well-documented case of significant, nearly simultaneous rupture of both thrust and strike-slip faults, this feature of the 2002 Denali fault earthquake provides a unique opportunity to investigate the mechanisms responsible for development of these large, complex events. We find that the geometry of the faults and the orientation of the regional stress field caused slip on the Susitna Glacier fault to load the Denali fault. Several different stress orientations with oblique right-lateral motion on the Susitna Glacier fault replicate the triggering of rupture on the Denali fault about 10 sec after the rupture nucleates on the Susitna Glacier fault. However, generating slip directions compatible with measured surface offsets and kinematic source inversions requires perturbing the stress orientation from that determined with focal mechanisms of regional events. Adjusting the vertical component of the principal stress tensor for the regional stress field so that it is more consistent with a mixture of strike-slip and reverse faulting significantly improves the fit of the slip-rake angles to the data. Rotating the maximum horizontal compressive stress direction westward appears to improve the fit even further.

Failure criteria of anisotropically damaged materials based on the critical plane concept

AbstractThe damage state of a cracked material is assumed to be specified by crack density distribution on physical planes. The critical plane approach is used with account for damaged and intact area fractions on the plane. The maximum of failure function is specified for all potential failure planes and the critical plane orientation is determined. The resulting failure condition is applied to study strength evolution for triaxially compressed specimens with varying orientation of principal stress and damage tensor axes. Both Coulomb and non‐linear failure conditions of Mohr type are applied to specify the representative critical plane. A general stress state is considered and the failure condition is specified for different relative orientations of orthotropy and principal stress axes. Copyright © 2002 John Wiley & Sons, Ltd.

Earthquake focal mechanisms and stress field in Sichuan-Yunnan area determined using P wave polarity and short period P and S waveform data

Based on waveform data, several methods to determine focal mechanisms of small earthquakes were developed since 1980. Kisslinger (1980) and Julian, Foulger (1996) proposed an approach to determine solution by using amplitude ratio of P and S wave. Schwartz (1995) devised a method to determine solutions by the use of polarity data and amplitudes of seismogram envelopes. Amplitudes of short period seismic waves propagating in an inhomogene-ous medium are sensitive to the variation in velocity and Q structure. Nakamura, et al (1999) took medium inhomo-geneity into account in determining focal mechanisms of small earthquakes using waveform data. If the locations of small earthquakes are concentrated in a small region, we can assume that the raypaths from the events to a given station are almost the same. So P and S wave attenuations are independent of event locations. In this case it is con-venient to determine focal mechanisms of these events by using short period P and S wave dataj. Focal mechanism solutions of small earthquakes in 5 regions, i.e., Rongchang, Mabian-Muchuan, Ya￠an, Baoxing and Mianzhu, which are covered by the Chengdu Telemetered Network, are obtained by analyzing the P polarity and short body wave amplitude data recorded in the network since 1992. According to the method proposed by Gephart and Forsyth (1984), based on well determined focal mechanism solutions in 15 sub-zones of Sichuan and Yunnan area, three principal stress tensors s1, s2, and s3, instead of averages of P, B, and T axis of the solutions, are determined to represent the regional stress field distribution.

Principal tectonic stress tensor in the region of the Kroupnic fault from seismic and geodetic data

Principal tectonic stress tensor in the region of the Kroupnic fault from seismic and geodetic data

Mechanical Signals in Plant Development: A New Method for Single Cell Studies

Cell division, which is critical to plant development and morphology, requires the orchestration of hundreds of intracellular processes. In the end, however, cells must make critical decisions, based on a discrete set of mechanical signals such as stress, strain, and shear, to divide in such a way that they will survive the mechanical loads generated by turgor pressure and cell enlargement within the growing tissues. Here we report on a method whereby tobacco protoplasts swirled into a 1.5% agarose entrapment medium will survive and divide. The application of a controlled mechanical load to agarose blocks containing protoplasts orients the primary division plane of the embedded cells. Photoelastic analysis of the agarose entrapment medium can identify the lines of principal stress within the agarose, confirming the hypothesis that cells divide either parallel or perpendicular to the principal stress tensors. The coincidence between the orientation of the new division wall and the orientation of the principal stress tensors suggests that the perception of mechanical stress is a characteristic of individual plant cells. The ability of a cell to determine a shear-free orientation for a new partition wall may be related to the applied load through the deformation of the matrix material. In an isotropic matrix a uniaxial load will produce a rotationally symmetric strain field, which will define a shear-free plane. Where high stress intensities combine with the loading geometry to produce multiaxial loads there will be no axis of rotational symmetry and hence no shear free plane. This suggests that two mechanisms may be orienting the division plane, one a mechanism that works in rotationally symmetrical fields, yielding divisions perpendicular to the compressive tensor, parallel to the long axis of the cell, and one in asymmetric fields, yielding divisions parallel to the short axis of the cell and the compressive tensor.

Stress orientation determined from fault slip data in Hampel Wash Area, Nevada, and its relation to contemporary regional stress field

Fault‐slip data were collected from an area of relatively young faulting in a seismically active part of the Nevada Test Site 12 km NW of Mercury, Nevada. The data come primarily from intensely faulted Miocene tuffaceous sedimentary rocks in Hampel Wash, which is bounded on the north by the Quaternary ENE trending Rock Valley fault and on the south by a parallel unnamed fault. Data from faults with known sense of displacement exhibit a bimodal distribution of slip angles (rakes). Faults exhibiting steep rakes (typically 75° to 90°) cluster about a N30°–35°E strike; most dip 65° to 80°. Faults having shallow rakes (generally less than 20°) exhibit a wide range of strikes (from N6°W to N80°E) and mostly dip between 80° and 90°. The predominant N30°–35°E strike of the steep‐rake faults and the quasi‐conjugate nature of a consistent subset of the shallowrake faults suggest a maximum horizontal stress orientation of about N30°–35°E and a least horizontal principal stress direction of N55°–60°W. Analysis of the data using a least squares iterative inversion to determine a mean deviatoric principal stress tensor indicates a normal‐faulting stress regime (S1 vertical) with principal stress axes in approximately horizontal and vertical directions (S1, trend = N 19°E and plunge = 82°N; S2, N30°E and 8°S; and S3, N60°W and 2°E). The maximum horizontal stress, S2, was found to be nearly intermediate in magnitude between S1 and S3. The N60°W least horizontal principal stress orientation obtained from the fault‐slip inversion agrees with our geometric analysis of the data and is consistent with a modern least horizontal principal stress orientation of N50°–70°W inferred from earthquake focal mechanisms, well bore breakouts, and hydraulic fracturing measurements in the vicinity of the Nevada Test Site. This solution fits all the data well, except for a subset of strike‐slip faults that strike N30°–45°E, subparallel to the normal faults of the data set. Nearly pure dip‐slip and pure strike‐slip movement on similarly oriented faults, however, cannot be accommodated in a single stress regime. Superposed sets of striae observed on some faults suggest temporal rotations of the regional stress field or local rotations within the region of the fault zone.