Subsurface Stress Field Research Articles

Leveraging the ETAS model to forecast mining microseismicity

SUMMARY Mining operations result in changes of the subsurface stress field that can lead to the occurrence of microseismic events. The development of strategies for forecasting and avoidance of significant events is crucial for safe and efficient operations of mines. One such example, discussed here is the observed induced microseismicity in soft rock potash mines. It is primarily driven by the rock excavations but can also be triggered by preceding events or can result from the delayed effects of plastic creep of soft rocks. Therefore, it is important from seismic hazard assessment and risk mitigation points of view to understand the statistical aspects of microseismicity in potash or other types of mines. In this study, the temporal evolution of the induced microseismicity from a potash mine in Saskatchewan is analysed and modelled. Specifically, the epidemic type aftershock sequence model is used to approximate the occurrence rate of the induced mining microseismicity. The estimated parameters signify that the microseismicity displays swarm-type characteristics with limited inter-event triggering. Moreover, the Bayesian predictive framework is used to compute the probabilities of the occurrences of the largest expected events above a certain magnitude for prescribed forecasting time intervals during the evolution of the sequence. This approach for computing the probabilities allows one to incorporate fully the uncertainties of the model parameters. The Markov Chain Monte Carlo sampling of the posterior distribution are used to generate parameter chains to quantify their variability. Furthermore, several statistical tests are conducted to assess the credibility of the obtained retrospective forecasts compared to the observed microseismicity. The obtained results show that the developed approach can accurately forecast the number of events and intensity of the sequence. It also provides a framework for computing the probabilities for the largest expected events.

The effect of highly elongated micro-contacts on rolling contact stress field

This study presents a boundary element model to analyze contact pressure distribution and the subsurface stress field in rough rolling elements. The methodology is demonstrated by the stress field of the backup roll and work roll in the cold/temper rolling process and characterized by a parallel orientation of roughness lay with rolling direction, resulting in a cluster of highly elongated elliptical micro-contacts. The numerical outcomes revealed that the amplitude of in-plane and out-of-plane shear stress components are strongly dependent on the ellipticity of the micro-contacts. Comparison with experimental results shows that the crack plane is oriented transversal to the rolling direction and the crack initiation location corresponds to the location where the shear stress components are maximum.

Smith–Watson–Topper Parameter in Partial Slip Bimodal Oscillations of Axisymmetric Elastic Contacts of Similar Materials: Influence of Load Protocol and Profile Geometry

Based on a very fast numerical procedure for the determination of the subsurface stress field beneath frictional contacts of axisymmetric elastic bodies under arbitrary 2D oblique loading, the contact mechanical influences of loading parameters and contact profile geometry on the Smith–Watson–Topper (SWT) fatigue crack initiation parameter in elastic fretting contacts with superimposed normal and tangential oscillations are studied in detail. The efficiency of the stress calculation allows for a comprehensive physical analysis of the multi-dimensional parameter space of influencing variables. It is found that a superimposed normal oscillation of the contact can significantly increase or decrease the SWT parameter, depending on the initial phase difference and frequency ratio between the normal and tangential oscillation. Written in proper non-dimensional variables, the rounded flat punch always exhibits smaller values of the SWT parameter, compared to a full paraboloid with the same curvature, while the truncated paraboloid exhibits larger values. A small superimposed profile waviness also significantly increased or decreased the SWT parameter, depending on the amplitude and wave length of the waviness. While both the load protocol and the profile geometry can significantly alter the SWT parameter, the coupling between both influencing factors is weak.

Elastic Stress Field beneath a Sticking Circular Contact under Tangential Load

Based on a potential theoretical approach, the subsurface stress field is calculated for an elastic half-space which is subject to normal and uniaxial tangential surface tractions that—in the case of elastic decoupling—correspond to rigid normal and tangential translations of a circular surface domain. The stress fields are obtained explicitly and in closed form as the imaginary parts of compact complex-valued expressions. The stress state in the surface and on the central axis are considered in detail. As, within specific approximations that have been discussed at length in the literature, any tangential contact problem with friction can be understood as a certain incremental series of such rigid translations, the solutions presented here can serve as the basis of very fast superposition algorithms for the analysis of subsurface stress fields in general tangential contact problems with friction. This idea is demonstrated by means of the frictional tangential contact between an elastic half-space and a rigid cylindrical flat punch with rounded corners.

Characteristics, causes and significance of subsurface stress field of Beijing earth fissures group

The development of earth fissures in a certain area often has certain genetic correlations, which is called ‘group-developing phenomenon’ of earth fissures. So far, 41 earth fissures have developed in the Beijing area in the North China Plain. Surveys and exploration studies have shown that these earth fissures have a good correspondence relationship with the activities of the adjacent control faults. Accordingly, they can be divided into 9 zones. The mechanical analysis of these fissures groups reveals that they are roughly formed through 3 models, namely, ‘contemporaneous model’ (dip-slipping movement), ‘secondary model’ (strike-slipping movement) and ‘companion model’ (basin extension movement). The characteristics of this type (fault-controlled) earth fissures in combination with their distribution regularities in the area can be used to indicate that the distribution of subsurface tectonic stress fields is as a whole an extension of the NW-SE-trending, which is not completely consistent with the near E-W-trending extension of deep material migration. These analyses show that under the background of extensional deformation of the basin, the subsurface stress field characteristics of superficial formations are more complex, which not only embodies the movement form (unity) of the deep structure in whole, but also partially reflects the adjustability of the regional tectonic stress field.

Multi-objective optimization of the subsurface residual stress field of TC4 alloy in machine hammer peening

Machine hammer peening (MHP) is a surface strengthening process by introducing residual compressive stress at the part's surface. Many indicators of residual stress, such as the surface residual compressive stress and depth of residual compressive stress, significantly impact the fatigue performance of parts and thus need to be optimized. The present study focuses on two main problems in multi-objective optimization of the subsurface residual stress field induced by MHP: the relationship between a specific residual stress field and a combination of impact velocity and indentation distribution and how to implement the MHP process that could produce such a combination. The latter problem was first addressed by a kinematic model of the MHP device, which can optimize the MHP device input parameters to achieve the target axial impact velocity. For the former problem, a finite element model was first established to simulate the residual stress field induced by MHP. Then, the response surface method was used to optimize the simulated residual stress field with multiple objectives. Based on the above two models, we can obtain the appropriate MHP parameters to induce a target subsurface residual stress field. A verification experiment was carried out, and the residual stress field obtained was relatively close to the theoretical one, with a deviation of 1.7 % for the depth of residual compressive stress and 13.8 % for the surface residual compressive stress.

Numerical method for quasi-static adhesive elastic contact subjected to tangential loading

This paper presents a three-dimensional (3D) numerical model for simulating the adhesive contact with linear isotropic elasticity considering the interaction between normal and tangential loads. The model is based on the Boussinesq-Cerruti integral equations for elasticity, the Maugis-Dugdale (MD) model for adhesion, and the friction/adhesion interaction theory in the McMeeking model; it uses the Coulomb's law of friction to identify the occurrence of local microslip. Efficient and accurate determination of the contact behavior, together with adhesive and stick/slip regions, uses the iterative conjugate gradient method (CGM) and the discrete convolution and fast Fourier transform (DC-FFT) algorithm. The model analyzes adhesive-contact pressure, shear traction, and subsurface stress fields. It is used to study the effects of increasing tangential loading on the variations of stick/slip zones and adhesive-energy dissipation, as well as the influence of sinusoidal roughness on surface adhesion behavior. Compared with most theoretical models, the proposed numerical model has no restrictions on surface geometry and roughness of contact bodies, and it should have a wider range of applications.

Time‐lapse VSP integration and calibration of subsurface stress field utilizing machine learning approaches: A case study of the morrow B formation, FWU

AbstractThis study aims to develop a methodology for calibrating subsurface stress changes through time‐lapse vertical seismic profiling (VSP) integration. The selected study site is a region around the injector well located within Farnsworth field unit (FWU), where there is an ongoing CO2‐enhanced oil recovery (EOR) operation. In our study, a site‐specific rock physics model was created from extensive geological, geophysical, and geomechanical characterization through 3D seismic data, well logs, and core assessed as part of the 1D MEM conducted on the characterization well within the study area. The Biot‐Gassmann workflow was utilized to combine the rock physics and reservoir simulation outputs to determine the seismic velocity change due to fluid substitution. Modeled seismic velocities attributed to mean effective stress were determined from the geomechanical simulation outputs, and the stress‐velocity relationship developed from ultrasonic seismic velocity measurements. A machine learning‐assisted workflow comprised of an artificial neural network and a particle swarm optimizer (PSO) was utilized to minimize a penalty function created between the modeled seismic velocities and the observed time‐lapse VSP dataset. The successful execution of this workflow has affirmed the suitability of acoustic time‐lapse measurements for 4D‐VSP geomechanical stress calibration pending measurable stress sensitivities within the anticipated effective stress changes and the availability of suitable and reliable datasets for petroelastic modeling. © 2023 Society of Chemical Industry and John Wiley & Sons, Ltd.

The origin of microstructural alterations in M50 bearing steel undergoing rolling contact fatigue

M50 bearing steel designed for aerospace applications exhibits unique microstructural alterations at the subsurface during rolling contact fatigue (RCF). In this work, three types of microstructural alterations, light etching region (LER), white etching band (WEB) and white etching area (WEA) are systematically studied. A hardness profile at the subsurface is obtained by microindentation with material softening being detected. It is found that the material softening is associated with the formation of WEBs. The microstructural nature of the three types of microstructural alterations is revealed by detailed characterisation using focused ion beam milling and transmission electron microscopy. It is found that LERs, WEBs and WEAs are a manifestation of the decay of the parent martensite and all consist of dislocation cells or fine grains, indicative of plastic deformation. Through subsurface stress field analysis, LER, WEBs and WEAs are found to be caused by different stress components. The similarities and differences of the microstructural alterations in M50 and in widely studied 100Cr6 are discussed where the stability of carbides is believed to play a key role. The difference in material response in the microstructural alterations in M50 is further analysed and modelled based on Kocks and Mecking theory, with different types of activated dislocation slip systems found to be the root cause for such difference. Based on the material response analysis for WEBs, a material softening model for M50 during RCF is established by considering residual plastic strain accumulation, yielding prediction results in agreement with experimental measurement.

Numerical modelling of microstructure inhomogeneity to reproduce experimentally observed scatter in fretting fatigue lifetimes

Experimental fretting fatigue lives exhibit large degree of scatter. One of the aspects behind this is the microstructural inhomogeneity which affects the stresses in the material. Variance in stress values can greatly impact crack initiation speed, leading to changes in fretting fatigue lifetimes, as well as the crack propagation behaviour. This research aims to study this issue in more detail and recreate the experimentally observed scatter using numerical modelling. In this work, Voronoi tessellation is used to simulate microstructural topologies of low carbon steel, where each grain is assigned elasto-plastic properties at random, from a predetermined range. In total, 60 finite element models are created and the effect of microstructural inhomogeneity on fretting fatigue lifetime dispersion is evaluated using a Continuum Damage Mechanics approach. Additionally, crack propagation is studied with XFEM combined with Smith-Watson-Topper fatigue parameter to determine crack path under multiaxial, non-proportional loading conditions. For both crack initiation and propagation investigation, the Theory of Critical Distances is applied to overcome the effect of high stress gradients. Simulation results show that microstructural inhomogeneity has significant impact on the contact stress distributions and subsurface stress and strain fields. Scatter observed in the predicted lifetimes matches well with that observed in practical experiments and is used to propose a design curve for the studied material. The applied crack path prediction approach captures the variance in crack paths originating from microstructural inhomogeneity and shows good correlation with reference experimental results at low bulk stress levels.

A Cohesive-Zone-Based Contact Mechanics Analysis of Delamination in Homogeneous and Layered Half-Spaces Subjected to Normal and Shear Surface Tractions

AbstractA contact mechanics analysis of interfacial delamination in elastic and elastic-plastic homogeneous and layered half-spaces due to normal and shear surface tractions induced by indentation and sliding was performed using the finite element method. Surface separation at the delamination interface was controlled by a surface-based cohesive zone constitutive law. The instigation of interfacial delamination was determined by the critical separation distance of interface node pairs in mixed-mode loading based on a damage initiation criterion exemplified by a quadratic relation of the interfacial normal and shear tractions. Stiffness degradation was characterized by a linear relation of the interface cohesive strength and a scalar degradation parameter, which depended on the effective separation distances corresponding to the critical effective cohesive strength and the fully degraded stiffness, defined by a mixed-mode loading critical fracture energy criterion. Numerical solutions of the delamination profiles, the subsurface stress field, and the development of plasticity illuminated the effects of indentation depth and sliding distance on interfacial delamination in half-spaces with different elastic-plastic properties, interfacial cohesive strength, and layer thickness. Simulations yielded insight into the layer and substrate material property mismatch on interfacial delamination. A notable contribution of the present study is the establishment of a computational mechanics methodology for developing plasticity-induced cumulative damage models for multilayered structures.

Explicit Analytic Solutions for the Subsurface Stress Field in Single Plane Contacts of Elastically Similar Truncated Cylinders or Wedges

As has been pointed out recently, a possible solution strategy to the wear–fatigue dilemma in fretting, operating on the level of contact mechanics and profile geometries, can be the introduction of “soft” sharp edges to the contact profiles, for example, by truncating an originally smooth profile. In that regard, analysis of possible mechanical failure of a structure, due to the contact interaction, requires the knowledge of the full subsurface stress state resulting from the contact loading. In the present manuscript, a closed-form exact solution for the subsurface stress state is given for the frictional contact of elastically similar truncated cylinders or wedges, within the framework of the half-plane approximation and a local-global Amontons–Coulomb friction law. Moreover, a fast and robust semi-analytical method, based on the appropriate superposition of solutions for parabolic contact, is proposed for the determination of the subsurface stress fields in frictional plane contacts with more complex profile geometries, and compared with the exact solution. Based on the analytical solution, periodic tangential loading of a truncated cylinder is considered in detail, and important scalar characteristics of the stress state, like the von-Mises equivalent stress, maximum shear stress, and the largest principal stress, are determined. Positive (i.e., tensile) principal stresses only exist in the vicinity of the contact edge, away from the pressure singularity at the edge of the profile, and away from the maxima of the von-Mises equivalent stress, or the maximum shear stress. Therefore, the fretting contact should not be prone to fatigue crack initiation.

Surface smoothening and strengthening combined effect of mechanical hammer peening on inconel 718 superalloy

ABSTRACT In this study, the surface strengthening and smoothening combined effect of the mechanical hammer peening (MHP) treatment is demonstrated. On a IN718 nickel-based superalloy workpiece surface, the MHP treatment introduced a subsurface residual stress field featured with a maximum stress around −1.4 GPa and a penetration depth exceeding 1 mm, and an increase of the micro-hardness from 286.43 HV to 426.27 HV. Simultaneously, it produced a significantly smoothened surface (Ra 27 nm) compared with the untreated sample (Ra 555 nm). Moreover, applying an electric pulse of 100 A would further reduce the surface roughness, without deteriorating the surface strengthening effect. The surface strengthening effect of MHP treatment mainly originates from the increase of dislocation density, grain misorientation and refinement, which are caused by impacts of the punching head; while the surface smoothening effect is the result of precisely controlled and regularly aligned punching indents. Utilizing MHP in the manufacturing process chain of aircraft parts could combine the surface strengthening and smoothening processes into one single process, which substantially improves both the production efficiency and enhances the surface finish. Especially, the working principle of MHP makes it suitable for arbitrary or complicated surfaces, that is, aeroengine blades.

Non-Newtonian Thermo-Elastohydrodynamics and Sub-Surface Stress Field of High-Performance Racing Spur Gears

Meshing teeth pairs of involute spur gears often form the final drive of high-performance motorsport transmissions. They are subject to high normal and shear loading. Under transient conditions pertaining to a meshing cycle, the contact conditions alter from the onset of teeth pair engagement through to maximum normal loading, followed by contact separation. Sliding motion only ceases instantaneously at the pitch point. The regime of lubrication remains mostly in non-Newtonian thermo-elastohydrodynamic conditions. The results show that a starved inlet boundary is attained throughout most of the meshing cycle which leads to the diminution of the pressure spike at the exit from the contact conjunction. The reversing sub-surface shear stresses are the main source of the onset of any inelastic deformation, which is dominated by the primary pressure peak in compliance with the Hertzian maximum pressure. The shear stress field is supplemented by an induced field due to the presence of the pressure spike. Under starved conditions this secondary stress field is diminished. The combined solution of elastohydrodynamics with a thermal network model, non-Newtonian lubricant traction, and sub-surface stress evaluation provides for a comprehensive solution not hitherto reported in the literature.

Influence of Wear Profile Geometry on Critical Plane Fatigue Crack Initiation Criteria in Plane and Axisymmetric Elastic Fretting Contacts

The subsurface elastic stress fields in plane and axisymmetric contacts with friction under oscillating tangential loading are calculated via a very robust, high-precision method, which operates with appropriate superpositions of analytic solutions for the respective Hertzian contact problems. Based on the stress fields, two critical plane fatigue crack initiation criteria—the Smith-Watson-Topper (SWT) parameter and the Findley parameter—are evaluated for three types of contact profile geometries: (unworn) parabolic contact, the partial slip limiting wear profile of an initially parabolic contact, and truncated parabolic contact. Appropriate scaling laws are introduced to formulate a general solution in terms of non-dimensional variables. The crack initiation criteria are determined in the full subsurface loading plane. It is found that the truncated profile—which may originate from sliding wear—has practically the same local distribution of crack initiation criteria as the unworn profile, despite the (weak) stress singularity at the edge of the flat face. The partial slip limiting wear profile, on the other hand, exhibits a strong edge stress singularity at the boundary of the permanent stick zone, the crack initiation criteria are drastically increased (and theoretically infinite). Also, while for the unworn and truncated profiles high values of the crack initiation criteria are extremely localized around “hotspots” at the surface, for the partial slip limiting wear profile they reach much deeper into the subsurface material. This offers a new explanation for the dominance of fatigue failure in the partial slip regime of fretting. The differences between plane and axisymmetric cases are generally small. The SWT parameter is generally more localized than the Findley parameter.

3D Microseismic Monitoring Using Machine Learning

AbstractMicroseismic source localization is important for inferring the dynamic status of the subsurface stress field during hydraulic fracturing. Traditional deterministic methods for 3D microseismic source localization require either ray tracing or full waveform modeling, thus are computationally expensive. We propose a very efficient (e.g., within 1 s) microseismic source localization method based on machine learning. First, three‐dimensional (3D) ray tracing is performed with hypothetical event locations and realistic acquisition geometry to calculate the theoretical travel‐times. The theoretical travel‐time differences and the spatial locations of the stations are treated as the input features of the training data set, and the corresponding source locations are used as the labels. The manually or automatically picked arrival time differences between different stations and a reference station after a microseismic event and the actual station locations are fed into the well‐trained model for a fast and accurate location prediction. The proposed method is efficient enough to be widely applied for the real‐time monitoring of hydraulic fracturing. The machine learning model is analogous to 3D grid search but performs 3D ray tracings before the actual localization, and needs to be retrained when applied to a new study area. We use several synthetic tests and a real data example from the Weiyuan hydraulic fracturing experiment in Sichuan, China, to demonstrate the effectiveness of the proposed method. The application of the proposed method to earthquake localization is also demonstrated to be straightforward.

Deformation and stress in materials with inhomogeneity/void under contact loading

Materials may have inhomogeneities or inclusions embedded, which can result in stress concentrations, complex deformation, or even cracks, around the interface of inhomogeneity/inclusion and matrix. This paper evaluates the subsurface deformation and stress fields in the vicinity of a solid inhomogeneity, a hollow shell, and a void, or a crack, based on the numerical equivalent inclusion method (NEIM) and fast Fourier Transforms (FFT). A group of numerical simulations is conducted to reveal the displacements around inhomogeneities and cracks, in the forms of single inhomogeneity (solid or void), a layered inhomogeneity (a hollow shell), and an inhomogeneity with void tips. Stress volume integrals are calculated to quantify the influences of material properties, geometry, location, and orientation of inhomogeneities on displacement and stress transmissions across the inhomogeneity-matrix interfaces.

Modelling of Non-Newtonian Starved Thermal-elastohydrodynamic Lubrication of Heterogeneous Materials in Impact Motion

This study presents a numerical model for the thermal-elastohydrodynamic lubrication of heterogeneous materials in impact motion, in which a rigid ball bounces on a starved non-Newtonian oil-covered plane surface of an elastic semi-infinite heterogeneous solid with inhomogeneous inclusions. The impact–rebound process and the microscopic response of the subsurface inhomogeneous inclusions are investigated. The inclusions are homogenized according to Eshelby’s equivalent inclusion method. The Elrod algorithm is adopted to determine the lubrication starvation based on the solutions of pressure and film thickness, while the lubricant velocity and shear rate of the non-Newtonian lubricant are derived by using the separation flow method. The dynamic response of the cases subjected to constant impact mass, momentum, and energy is discussed to reveal the influence of the initial drop height on the impact–rebound process. The results imply that the inclusion disturbs the subsurface stress field and affects the dynamic response of the contact system when the surface pressure is high. The impact energy is the decisive factor for the stress peak, maximum hydrodynamic force, and restitution coefficient, while the dynamic response during the early approaching process is controlled by the drop height.

Stress Field Estimation From S‐Wave Anisotropy Observed in Multi‐Azimuth Seismic Survey With Cabled Seafloor Seismometers Above the Nankai Trough Megathrust Zone, Japan

AbstractThe spatial variation of azimuthal S‐wave phase velocity anisotropies caused by differential horizontal stress along the Nankai Trough was analyzed to understand the stress state of the overhung block of the forearc region, off Kii Peninsula, Japan. We conducted controlled‐source seismic surveys along the circumference of a 3 km radius circle centered at each seismometer of a cabled seafloor observatory installed in the Nankai subduction zone. We applied an anisotropy semblance method to estimate the orientation of fast and slow S‐wave velocities of shallow sediments and deep accretionary prism using the multi‐azimuth seismic dataset acquired at each seismometer location. The estimated orientations of fast S‐wave velocity are parallel to the convergent direction of the subducting place beneath the Kumano basin in the deeper accretionary prism while perpendicular to the convergent direction in the shallow sediments inside the Kumano basin. These fast S‐wave polarization orientations in shallow sediments show good agreement with horizontal maximum stress orientations estimated in situ borehole measurements in the observation area. We estimated the differential horizontal stress field in the Nankai Trough region from obtained S‐wave anisotropy using a simple crack model. Using this method, we first suggest the convergent‐parallel horizontal maximum compression in the deeper part of the accretionary prism above the locked portion. Assuming obtained S‐wave anisotropy is attributed to the tectonic loading by the subducting plate, these results suggest that the S‐wave azimuthal anisotropy measurements can be used to monitor the subsurface stress field as a function of time.

Development of white etching bands under accelerated rolling contact fatigue

Bearing steel under severe loading condition undergoes substantial subsurface microstructural alterations known as Dark etching regions and white etching bands. White etching bands (WEBs) develop after hundreds of millions of stress cycles in bearing components and have been reported for several decades but the formation mechanism of white bands is not fully elucidated. Current research presents a systematic rolling contact fatigue (RCF) testing in a rotary tribometer under accelerated conditions, where rolling cycles are simulated in a 4-ball test configuration. The post RCF investigations have been carried out to understand the formation mechanism of WEBs in a ball-on-ball point contact load. WEBs have been characterised with the help of nanoindentation and Energy-dispersive X-ray spectroscopy analysis. The quantitative analysis of WEBs growth with subsurface stress field has revealed that the unique orientations of white bands are governed by the plane of maximum relative normal stress along the contact track. Moreover, the accelerated growth and reversal of WEBs sequence at elevated temperature have revealed that the WEBs formation is dependent on temperature/load combination. The observed growth of lenticular carbides in current research is also compared with dislocation gliding model and the role of carbon diffusion within WEBs is highlighted.