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At least 19 records

A phoenics model for the triaxial loading of an initially cylindrical mass of rate-type material with provisions for bulging and yield

This work traces the response of a granular material via the Ten Coefficient Truesdell rate-type constituitive model into the simplest meaningful loading: the triaxial test configuration. A functional relation has been posed for computing the rather peculiar relation between average applied stress and average porosity. Using that relation an attack has been mounted on the dilemma that exists between dynamic and constitutive use of the pressure variable; that is relating dynamic pressure, thermodynamic pressure, stress deviator and higher stress invariants. The resolution was as a linear superposition with a one-way feedback, in that while the dynamic component could not effect the constituitive component, the converse was not true since density appears in the momentum transport relation.

French, K. W., Jr.↗

Stress and Strain Heterogeneity and Persistence in Uniaxially‐ and Triaxially‐Loaded Sandstone

Two critical questions in brittle rock mechanics are how rocks developed localized strains and to what extent internal stress heterogeneity controls this localization and subsequent macroscopic failure. Definitive answers have not yet been found, but would provide insight into rock fracture mechanics as relevant to hydrocarbon extraction and sequestration. Here, we use synchrotron X‐ray tomography (XRT) and 3D X‐ray diffraction (3DXRD) during uniaxial and triaxial tests on Nugget and Bentheimer sandstones to examine strain and stress localization prior to mechanical failure. 3DXRD was used to measure intra‐granular lattice strains which were used to compute elastic stress tensors of each grain. Digital volume correlation (DVC) was applied to XRT images to determine the strain field in the sample. Both samples featured marked spatial heterogeneity, localization, and temporal persistence of elevated stresses and strains during their mechanical deformation toward failure. Both samples featured a majority of grains with at least one principal stress component that was tensile, a signature of the influence of heterogeneity on stress transmission. Measurements further revealed that compressive stress orientations and statistics evolved in a similar manner to those of inter‐particle forces in loose granular materials, with triaxially‐compressed rock exhibiting enhanced grain stress heterogeneity compared to uniaxially‐compressed rock. Our results complement recent work by others who employed XRT and scanning 3DXRD to study triaxially‐compressed sandstone, but extend those results to uniaxial compression, sandstones of varied porosity, and grain stress measurements throughout the 3D full extent of the samples rather than in a single layer examined with scanning 3DXRD.

58 GEOSCIENCES↗

Coupled Thermo-Hydrological-Mechanical-Chemical Behavior of Anisotropic Granite for Geologic Disposal of High-Level Radioactive Waste: A Core-Scale Laboratory Investigation

The coupled thermo-hydrological-mechanical-chemical (THMC) behavior of rock within an Excavation Damaged Zone (EDZ) is critical for the safety and long-term performance of a geological repository for high-level radioactive wastes. While many laboratory experiments have been conducted to investigate EDZ rocks, the flow and deformation characteristics resulting from anisotropic rock textures and microcrack distribution under triaxial loading and elevated temperatures remain poorly understood. Particularly, cracks at various scales serve as fast paths for fluid flow and solute transport and present as focal points of mechanical weakness, which complicate the coupled THMC processes in anisotropic EDZ rocks and challenge modeling predictions. Here, in this study, a series of core-scale experiments was conducted on three granite samples under repository-relevant conditions. These rock samples were obtained from the Grimsel Underground Research Laboratory (URL), featured by anisotropic minerals (represented by bedding layers) and microcrack distributions and coarse cm-scale grain sizes. During the experiments, samples were subjected to an elevated temperature at 90 °C and different triaxial loading conditions either by radial (normal to bedding layers) or axial (parallel to bedding layers) compaction. Water was injected into the samples, and the rock permeability evolutions and effluent water chemistry were monitored closely. For intact samples, thermal expansion of minerals at 90 °C resulted in a large, 75% irreversible permeability reduction and rock strengthening under radial compaction, while thermal impact was limited to a 15% permeability reduction under axial compaction. In contrast, for a sample containing open cracks, the growth of fractures during the experiment resulted in an abrupt permeability increase and fast failure at 90 °C. The effluent water chemistry indicates much more considerable mineral dissolution from large shear sliding than that in rocks dominated by mechanical compaction. These results helped better understand the coupled THMC processes in anisotropic rocks containing cracks, evaluate the behaviors of EDZ rocks, and predict the long-term evolution of EDZ for the performance of the repositories.

Coupled THMC processes↗

Laboratory investigation of hydraulic fracturing in granitic rocks using active and passive seismic monitoring

SUMMARY Knowledge of the fracturing processes can be important for the optimization of pressurized fluid injection operations in the deep underground rock mass. Active and passive seismic monitoring techniques have been used in the field for tracking or mapping the propagating hydraulic fracture. Although both these monitoring techniques provide valuable information about the generated fracture network, it is difficult for either technique to comprehensibly identify the different processes associated with hydraulic fracturing. The combined active and passive monitoring has the potential for better characterization of the complex hydraulic fracturing phenomena. In this study, laboratory hydraulic fracturing experiments with combined active and passive seismic monitoring were conducted on true triaxially loaded Barre granite cubes with different fluid injection rates. The seismic inelastic fracturing was detected by 16 passive acoustic emission sensors, where 3678 and 2370 seismic source events were detected for the high and low injection rate experiments, respectively. For active monitoring, strong variations in the attributes of signals were observed which were transmitted through four source–receiver pairs, placed both perpendicular and parallel to the generated hydraulic fracture. Positive velocity changes were observed for active sensor pairs with ray paths passing through the generated hydraulic fracture indicating fluid permeation, whereas isolated dry deformation was characterized by a slight but permanent velocity decrease. Compared to velocity, the energy of the active signals was 1–2 orders of magnitude more sensitive to different hydraulic fracturing processes. However, the sensitivity and signatures of the active signal attributes were found to be dependent on the frequency range and direction of ray path with respect to the location of the generated fracture network. Using the coupled evaluation of the active and passive signals we were able to systematically identify various hydraulic fracturing processes including: (1) aseismic deformation, (2) fracture initiation and fluid permeation, (3) pressure build-up, (4) fracture propagation and (5) pressure release and leak-off. The results of this study showed that combining the respective advantages of active and passive seismic techniques and using both of them to monitor the failure processes can facilitate a more comprehensive understanding and better control of the hydraulic stimulations in subsurface operations.

Geochemistry & Geophysics↗

Microseismic Monitoring of Laboratory Hydraulic Fracturing Experiments in Granitic Rocks for Different Fracture Propagation Regimes

While hydraulic fracturing (HF) is a widely employed process, the underlying fracturing processes are still heavily contested. The attributes of the HF generated fracture network can exhibit substantial variation when dealing with specific HF propagation regimes encountered in the field. In this study, HF experiments were performed on true-triaxially loaded Barre granite cubes, with microseismic monitoring, to identify and characterize the fracturing mechanisms associated with different viscosity injection fluids. Utilizing fluids with high (oil/1450 cP) and low (water/1 cP) viscosity represented two key HF propagation regimes: viscosity- and toughness-dominated. The experiments conducted with oil involved higher breakdown pressures, larger fluid volumes, and slower fracture propagation speeds. Furthermore, the frequency–magnitude distribution (b value) for all experiments (1.9–2.3) was similar to those encountered for large-scale operations. Slightly larger b values were encountered during the initiation phase (2.4–2.7) relative to the fracture propagation and post-fracturing phases (1.9–2.2). Techniques such as polarity and moment-tensor inversion were utilized to characterize the source mechanisms. For the HF experiments with oil, tensile fractures were most dominant (92%) in the initiation phase compared to fracture propagation and post-fracturing phases (70–75%). Similar tensile fracturing dominancy was not observed with water, attributable to fluid permeation and leak-off. Regardless of the injection fluid or classification criteria employed, tensile fractures were the dominant type consistently, with fewer occurring in water experiments but the specific ratio of crack types varied with different source mechanism criteria employed.

58 GEOSCIENCES↗

Modelling yield cap evolution in sandstone based on brittle creep experiments

The Zenifim Formation is being considered as a potential disposal formation for a deep borehole nuclear repository concept in Israel. Site selection and repository construction are intended to ensure that waste is separated from circulating groundwater, but long-term deformation of the wellbore could potentially create fluid flow pathways. To understand how time-dependent rock strength could affect wellbore stability, here we conducted creep tests under low to moderate confining pressures on retrieved core from the Zenifim formation. During creep, samples strain slowly as gradual damage accumulation progressively weakens the samples. Failure eventually occurred through the near-instantaneous formation of a shear fracture. Experimental results were used to calibrate a continuum damage poro-elastic model for sandstones. The calibrated damage-poro-elastic model successfully simulates different types of loading experiments including quasi-static and creep. The state of strain in experiments is close to yield during loading as the yield cap continuously evolves with damage accumulation. For creep tests, most damage occurs during triaxial loading. Minor damage accumulation occurs under constant load until the final stage of creep, where damage accelerates and promotes unstable fracturing.

58 GEOSCIENCES↗

Cubic-meter scale laboratory fault re-activation experiments to improve the understanding of induced seismicity risks

Abstract To understand fluid induced seismicity, we have designed a large-scale laboratory experiment consisting of a one-cubic-meter sandstone with an artificial fault cut and fluid-injection boreholes. The sandstone block is assembled in a true triaxial loading frame and equipped with 38 piezoelectric sensors to locate and characterise acoustic emission events. The differential stress on the artificial fault is increased in stages to bring it towards a critically stressed state. After each stage of differential stress increase, fluids are injected at low pressures through boreholes to test the potential of fault re-activation. In addition, a high-pressure injection was conducted that created a hydraulic fracture from the injection borehole towards the artificial fault. The newly generated fluid pathway resulted in an activation of the complete block through a stick–slip movement. We compare acoustic emission measurements from the laboratory experiment with seismicity observations from the field-scale CO 2 injection at Decatur, Illinois, U.S., and conclude that the existence of fluid pathways plays a decisive role for the potential of induced seismicity.

47 OTHER INSTRUMENTATION↗

Time dependent deformation of a basalt at low differential stress

A detailed study of linear elastic deformation in Ralston basalt during triaxial loading has been made as a function of strain rate (8 x 10 to the -8th per sec to 5 x 10 to the -5th per sec) and moisture content under constant confining pressure (500 bars) and temperature (20 C). Young's modulus was found to be constant and independent of moisture content and strain rate; however, Poisson's ratio decreased 5.7 plus or minus 1.6% and 6.7 plus or minus 1.6% per order of magnitude increase in strain rate for two suites of dry samples and 1.4 plus or minus 1.2% per equivalent change in strain rate for one suite of wet rocks. Lateral expansion in dry rocks is therefore a more sensitive function of strain rate than it is in wet rocks. It is suggested that this strain-rate dependence is related to microcracking.

Brodsky, N.↗

Experiment Evaluation of Bifurcation in Sands

The basic principles of bifurcation analysis have been established by several investigators, however several issues remain unresolved, specifically how do stress level, grain size distribution, and boundary conditions affect general bifurcation phenomena in pressure sensitive and dilatant materials. General geometrical and kinematics conditions for moving surfaces of discontinuity was derived and applied to problems of instability of solids. In 1962, the theoretical framework of bifurcation by studying the acceleration waves in elasto-plastic (J2) solids were presented. Bifurcation analysis for more specific forms of constitutive behavior was examined by studying localization in pressure-sensitive, dilatant materials, however, analyses were restricted to plane deformation states only. Bifurcation analyses were presented and applied to predict shear band formations in sand under plane strain condition. The properties of discontinuous bifurcation solutions for elastic-plastic solids under axisymmetric and plane strain loading conditions were studied. The study focused on theory, but also references and comparisons to experiments were made. The current paper includes a presentation of a summary of bifurcation analyses for biaxial and triaxial (axisymmetric) loading conditions. The Coulomb model is implemented using incremental piecewise scheme to predict the constitutive relations and shear band inclination angles. Then, a comprehensive evaluation of bifurcation phenomena is presented based on data from triaxial experiments performed under microgravity conditions aboard the Space Shuttle under very low effective confining pressure (0.05 to 1.30 kPa), in which very high peak friction angles (47 to 75 degrees) and dilatancy angles (30 to 31 degrees) were measured. The evaluation will be extended to include biaxial experiments performed on the same material under low (10 kPa) and moderate (100 kPa) confining pressures. A comparison between the behavior under biaxial and triaxial loading conditions will be presented, and related issues concerning influence of confining pressure will be discussed.

Alshibi, Khalid A.↗

Characterization of Damage in Triaxial Braid Composites Under Tensile Loading

Carbon fiber composites utilizing flattened, large tow yarns in woven or braided forms are being used in many aerospace applications. Their complex fiber architecture and large unit cell size present challenges in both understanding deformation processes and measuring reliable material properties. This report examines composites made using flattened 12k and 24k standard modulus carbon fiber yarns in a 0 /+60 /-60 triaxial braid architecture. Standard straight-sided tensile coupons are tested with the 0 axial braid fibers either parallel with or perpendicular to the applied tensile load (axial or transverse tensile test, respectively). Nonuniform surface strain resulting from the triaxial braid architecture is examined using photogrammetry. Local regions of high strain concentration are examined to identify where failure initiates and to determine the local strain at the time of initiation. Splitting within fiber bundles is the first failure mode observed at low to intermediate strains. For axial tensile tests splitting is primarily in the 60 bias fibers, which were oriented 60 to the applied load. At higher strains, out-of-plane deformation associated with localized delamination between fiber bundles or damage within fiber bundles is observed. For transverse tensile tests, the splitting is primarily in the 0 axial fibers, which were oriented transverse to the applied load. The initiation and accumulation of local damage causes the global transverse stress-strain curves to become nonlinear and causes failure to occur at a reduced ultimate strain. Extensive delamination at the specimen edges is also observed.

Littell, Justin D.↗

EGS Collab Experiment 2: 4100 Foot Level Elastic Property Data

Static and dynamic elastic properties (Young's modulus, Shear Modulus, P-wave Modulus, and Poisson's Ratio) of amphibolites and rhyolites from the TV4100 and TH4100 boreholes at the Sanford Underground Research Laboratory (SURF). Elastic properties include Young's modulus, Poisson's ratio, shear modulus, and p-wave modulus. Raw data from the experiments and slides describing the experimental procedure and a summary of results are included, along with a readme file with additional definitions and information.

15 GEOTHERMAL ENERGY↗

Characterization and Analysis of Triaxially Braided Polymer Composites under Static and Impact Loads

In order to design impact resistant aerospace components made of triaxially-braided polymer matrix composite materials, a need exists to have reliable impact simulation methods and a detailed understanding of the material behavior. Traditional test methods and specimen designs have yielded unrealistic material property data due to material mechanisms such as edge damage. To overcome these deficiencies, various alternative testing geometries such as notched flat coupons have been examined to alleviate difficulties observed with standard test methods. The results from the coupon level tests have been used to characterize and validate a macro level finite element-based model which can be used to simulate the mechanical and impact response of the braided composites. In the analytical model, the triaxial braid unit cell is approximated by using four parallel laminated composites, each with a different fiber layup, which roughly simulates the braid architecture. In the analysis, each of these laminated composites is modeled as a shell element. Currently, each shell element is considered to be a smeared homogeneous material. Simplified micromechanics techniques and lamination theory are used to determine the equivalent stiffness properties of each shell element, and results from the coupon level tests on the braided composite are used to back out the strength properties of each shell element. Recent improvements to the model include the incorporation of strain rate effects into the model. Simulations of ballistic impact tests have been carried out to investigate and verify the analysis approach.

Goldberg, Robert K.↗

Mechanical Response of Castlegate Sandstone under Hydrostatic Cyclic Loading

The stress history of rocks in the subsurface affects their mechanical and petrophysical properties. Rocks can often experience repeated cycles of loading and unloading due to fluid pressure fluctuations, which will lead to different mechanical behavior from static conditions. This is of importance for several geophysical and industrial applications, for example, wastewater injection and reservoir storage wells, which generate repeated stress perturbations. Laboratory experiments were conducted with Castlegate sandstone to observe the effects of different cyclic pressure loading conditions on a common reservoir analogue. Each sample was hydrostatically loaded in a triaxial cell to a low effective confining pressure, and either pore pressure or confining pressure was cycled at different rates over the course of a few weeks. Fluid permeability was measured during initial loading and periodically between stress cycles. Samples that undergo cyclic loading experience significantly more inelastic (nonrecoverable) strain compared to samples tested without cyclic hydrostatic loading. Permeability decreases rapidly for all tests during the first few days of testing, but the decrease and variability of permeability after this depend upon the loading conditions of each test. Cycling conditions do affect the mechanical behavior; the elastic moduli decrease with the increasing loading rate and stress cycling. The degree of volumetric strain induced by stress cycles is the major control on permeability change in the sandstones, with less compaction leading to more variation from measurement to measurement. The data indicate that cyclic loading degrades permeability and porosity more than static conditions over a similar period, but the petrophysical properties are dictated more by the hydrostatic loading rate rather than the total length of time stress cycling is imposed.

58 GEOSCIENCES↗

Hyperelastic nature of the Hoek–Brown criterion

In this article, we propose a nonlinear elasto-plastic model, for which a specific class of hyperbolic elasticity arises as a straight consequence of the yield criterion invariance on the plasticity level. We superimpose this nonlinear elastic (or hyperelastic) behavior with plasticity obeying the associated flow rule. Interestingly, we find that a linear yield criterion on the thermodynamical force associated with plasticity results in a quadratic yield criterion in the stress space. This suggests a specific hyperelastic connection between Mohr–Coulomb and Hoek–Brown (or alternatively between Drucker–Prager and Pan–Hudson) yield criteria. We compare the elasto-plastic responses of standard tests for the Drucker–Prager yield criterion using either linear or the suggested hyperbolic elasticity. Notably, the nonlinear case stands out due to dilatancy saturation observed during cyclic loading in the triaxial compression test. We conclude this study with structural finite element simulations that clearly demonstrate the numerical applicability of the proposed model.

97 MATHEMATICS AND COMPUTING↗

Geophysical Signatures of Crack Network Coalescence in Rocks at Multiple Length Scales

The main goal of the research project was to identify the geophysical signatures of fracture growth in natural rocks by utilizing novel geophysical techniques. The research objectives were to (a) investigate the potential for geophysical methods to determine when cracks initiate, the types and locations of propagated cracks, and the coalescence of networks of cracks in natural rocks at multiple scales, (b) determine how damage at the microscale evolved into damage at the macroscale and then link the microscopic and macroscopic observations, (c) quantify crack coalescence in rocks under realistic stress conditions using coupled mechanical-geophysical-optical visualization, and (d) identify the precursors in geophysical signals to crack coalescence. The following research thrusts were explored to achieve the research objectives: (1) uniaxial compression testing of rock specimens with and without a set of pre‐existing flaws and (2) triaxial compression testing of natural rock specimens. These thrusts allowed for exploring fracturing in rocks under realistic in situ environments and at multiple scales. This project provided educational opportunities for nine graduate and undergraduate students and resulted in 27 peer-reviewed publications. This first research thrust focused on investigating the micromechanics of fractures in rocks through uniaxial compression testing combined with advanced geophysical and imaging techniques, specifically acoustic emission (AE) monitoring, ultrasonic imaging, and 2-dimensional Digital Image Correlation (2D-DIC). By examining damage processes under time-independent and time-dependent loading conditions, insights into damage localization, crack initiation, and fracturing mechanisms were gained. It was observed that the AE signals and the strain-based measurements directly reflect the state of damage in the rock specimen and could be used to identify the cracking levels, such as the crack initiation (CI) and crack damage (CD), and the mode of deformation. A novel calibration apparatus was developed to enhance the accuracy of AE sensors, allowing for the estimation of key parameters such as magnitude, source dimension, stress drop, and radiated seismic energy associated with the fractures. The findings highlighted significant variations in the temporal evolution of AE source parameters during the primary, secondary, and tertiary stages of creep, identifying tensile cracking as the primary deformation mode. The second research thrust focused on enhancing the understanding of fracturing processes in natural rocks through triaxial compression testing, real-time AE monitoring, and ultrasonic monitoring. We investigated the impact of various factors such as fracture propagation regimes, injection parameters, rock types, and pre-existing conditions on the hydraulic fracture (HF) behavior using scaled true-triaxially loaded specimens of Barre granite and Lyons sandstone. Custom sensor housing facilitated concurrent active and passive monitoring to analyze hydro-mechanical responses and microseismicity associated with different HF scenarios. A coupled investigation of passive microseismicity and active signal attributes permitted a detailed comprehension of the various HF processes (aseismic deformation, fracture initiation and propagation, fluid permeation, and leak-off) and their dependence on the specific rock type. The findings of this research demonstrated the effectiveness of AE monitoring techniques in providing valuable insights into the impact of various factors on the behavior and dynamics of HF processes. The advancements in monitoring techniques, offering a more thorough and precise approach, represent a significant step towards optimizing HF practices and ensuring sustainable resource extraction.

58 GEOSCIENCES↗

A real time neural net estimator of fatigue life

A neural net architecture is proposed to estimate, in real-time, the fatigue life of mechanical components, as part of the Intelligent Control System for Reusable Rocket Engines. Arbitrary component loading values were used as input to train a two hidden-layer feedforward neural net to estimate component fatigue damage. The ability of the net to learn, based on a local strain approach, the mapping between load sequence and fatigue damage has been demonstrated for a uniaxial specimen. Because of its demonstrated performance, the neural computation may be extended to complex cases where the loads are biaxial or triaxial, and the geometry of the component is complex (e.g., turbopump blades). The generality of the approach is such that load/damage mappings can be directly extracted from experimental data without requiring any knowledge of the stress/strain profile of the component. In addition, the parallel network architecture allows real-time life calculations even for high frequency vibrations. Owing to its distributed nature, the neural implementation will be robust and reliable, enabling its use in hostile environments such as rocket engines. This neural net estimator of fatigue life is seen as the enabling technology to achieve component life prognosis, and therefore would be an important part of life extending control for reusable rocket engines.

Troudet, T.↗