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Distributed Fiber Optics Measurements of Rock Deformation and Failure in Triaxial Tests
The implementation of distributed strain measurement methods in triaxial and uniaxial tests have demonstrated the development of strain localization, even at early stages. This implies that single point measurement methods are location dependent. The use of distributed methods is required not only to improve the interpreted constitutive parameters obtained from triaxial tests, but also to understand the implications of strain localization in the failure process. Here, this work uses optical fibers in triaxial tests. The developed distributed measurement method was implemented on granite, gabbro, and sandstone samples and tested under different confining pressures, reaching 200 MPa on the granite sample. Using a temporal resolution of 0.25 Hz and 5 mm of spatial resolution, the strain evolution at over 300 locations at the sample surface was measured during testing. When compared to point sensing methods, the use of optical fiber greatly increases the number of measurements at the surface of the sample, and their interpolation provides the entire deformation of the sample surface. In all the tests performed, strain localizations were revealed before failure. A three-dimensional interpretation of a test, combining an optical scan of the sample and the distributed measurements, show good correlation between the fractures and the strain localization.
Deep Learning Predicts Stress–Strain Relations of Granular Materials Based on Triaxial Testing Data
This study presents an AI-based constitutive modelling framework wherein the prediction model directly learns from triaxial testing data by combining discrete element modelling (DEM) and deep learning. A constitutive learning strategy is proposed based on the generally accepted frame-indifference assumption in constructing material constitutive models. The low-dimensional principal stress-strain sequence pairs, measured from discrete element modelling of triaxial testing, are used to train recurrent neural networks, and then the predicted principal stress sequence is augmented to other high-dimensional or general stress tensor via coordinate transformation. Through detailed hyperparameter investigations, it is found that long short-term memory (LSTM) and gated recurrent unit (GRU) networks have similar prediction performance in constitutive modelling problems, and both satisfactorily predict the stress responses of granular materials subjected to a given unseen strain path. Furthermore, the unique merits and ongoing challenges of data-driven constitutive models for granular materials are discussed.
Identifying fatigue damage of mudded intercalations based on dynamic triaxial test
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Geomechanical characterization of Rock Valley carbonates
In Rock Valley, Nevada, the USA, past earthquake sequences and shallow faulting in Paleozoic carbonates remain poorly understood. Carbonates are typically more ductile rocks that do not experience large stress drops or fracture coalescence, which contradicts previous observations in the region. As part of the Source Physics Experiment, an effort has been made to experimentally characterize the petrophysical and geomechanical properties of carbonates from Rock Valley. Well core and outcrop samples were used to determine the difference between shallow-buried Tertiary limestones and deeply buried Paleozoic limestones and dolostones. The carbonates possessed porosities between 3 and 9%, with V P and V S in the Tertiary carbonates around 2700 and 1800 m/s, respectively, and 6000 and 3100 m/s, respectively, in the Paleozoic carbonates. Microstructural characterization revealed that the Paleozoic carbonates contained significantly more pre-existing damage and alteration than the Tertiary carbonates, though the deformation varies from localized to diffuse. Unconfined Brazilian tests and triaxial tests with confining pressures between 0 and 50 MPa showed that, although samples all experienced failure, the dolostones typically failed at greater stresses and possessed greater E/ν ratios than the limestones. Furthermore, the Hoek–Brown failure criterion was used to construct failure envelopes with the compressive and tensile failure tests. Velocity, density, and porosity measurements were used to construct a hypothetical velocity-depth profile and compare the results with the theoretical petrophysical measurements. Using brittleness analysis, the likely failure conditions were determined to be low-porosity dolomitic rock for fault nucleation in the Paleozoic basement.
Water-Weakening and Time-Dependent Deformation of Organic-Rich Chalks
Abstract The Ghareb Formation is a shallowly buried porous chalk in southern Israel that is being considered as a host rock for a geologic nuclear waste repository. Setup and operation of a repository will induce significant mechanical, hydrological and chemical perturbations in the Ghareb. Developing a secure repository requires careful characterization of the rock behavior to different loads. To characterize hydromechanical behavior of the Ghareb, several short- and long-term deformation experiments were conducted. Hydrostatic loading tests were conducted both dry and water-saturated, using different setups to measure elastic properties, time-dependent behavior, and permeability. A set of triaxial tests were conducted to measure the elastic properties and rock strength under differential loading at dry and water-saturated conditions. The hydrostatic tests showed the Ghareb began to deform inelastically around 12–15 MPa, a relatively low effective pressure. Long-term permeability measurements demonstrated that permeability declined with increasing effective pressure and was permanently reduced by ~ 1 order of magnitude after unloading pressure. Triaxial tests showed that water saturation significantly degrades the rock properties of the Ghareb, indicating water-weakening is a significant risk during repository operation. Time-dependent deformation is observed during hold periods of both the hydrostatic and triaxial tests, with deformation being primarily visco-plastic. The rate of deformation and permeability loss is strongly controlled by the effective pressure as well. Additionally, during holds of both hydrostatic and triaxial tests, it is observed that when water-saturated, radial strain surpassed axial strain when above effective pressures of 13–20 MPa. Thus, deformation anisotropy may occur in situ during operations even if the stress conditions are hydrostatic when above this pressure range.
The physics of desiccation cracks 1: Ductile fracturing and dependence on relative humidity
Ductile deformation is ubiquitously found in the shrinkage of geomaterials. The existence of ductility requires elastoplastic mechanics when analyzing the structure deformation under external stress. Here, in this work, we explore the physics of ductile fracturing based on the results from desiccation experiments and triaxial tests. By using the digital image correlation (DIC) method to generate the strain maps of samples undergoing desiccation cracking under different relative humidities, we obtain results showing the previously postulated Cnoidal Wave ductile failure patterns propagating under atmospheric condition-controlled crack velocities. We then correlate these observations with rate-dependent plasticity models calibrated through triaxial tests undergoing several unloading–reloading cycles and velocity stepping. This work demonstrates the necessity to consider ductility in soil cracking, indicating that the formation of crack patterns in soil desiccation is a slow and predictable process.
Geodyn Material Library: Pseudocap models for dry porous tocks
This report describes the second edition of the Pseudocap Strength models for porous rocks implemented in GEODYN material library. The first model was developed in 2007 and calibrated for concrete. Then, the model parameters were calibrated based on triaxial tests reported for limestones and sandstones of various porosities. In these models some key parameters were chosen as functions of the reference porosity,Φ. Since then multiple modifications were implemented in the model, therefore, it has been recalibrated for some common porous materials such as limestones, sandstones, alluvium, tuffs and granite. Two types of models are described in this repot. The first type (called Pseudocap Model or PM) is for rocks from a specific location. Parameters were calibrated for several specific geologic materials. The second type (called Generic Pseudocap Model or GPM) is useful for the sites where only basic information (rock type, porosity) is available. Generic models include built-in correlations between porosities and other mechanical properties observed for certain rock types. The models of both types were validated by comparing not only to quasi-static triaxial tests for these materials but also to shock Hugoniot data and spherical explosion data for some materials. All models were derived in the frame of isotropic plasticity. They are designed to be used in explicit finite element/difference codes. Tangent stiffness tensor is not provided but can be calculated numerically for the model to be used in implicit finite element codes. For an isotropic material the stress can be decomposed into volumetric and deviatoric parts. The volumetric part is modeled using an Equation of state (EOS) which calculates the pressure and the bulk sound speed as functions of the internal specific energy and density. Here a simple, Mie-Gruneisen EOS is presented, but tabulated EOS (LEOS) provided by the library can be used as well. The stress is limited by the yield surface which depends on three invariants of the stress tensor and specific internal energy. In addition, to capture the strain-rate dependence a simple multiplier is used for the yield surface which depends on the equivalent plastic strain rate. The failure surface (the ultimate yield, Y f , defined later) is chosen in the Hoek-Brown form, commonly used in rock mechanics. It includes measurable parameters such as Unconfined Compressive Strength (UCS) as well as scale parameters characterizing the quality of the rock such as GSI (Geologic Strength Index). Thus, even though the model is calibrated for small samples it offers a way to extrapolate the strength to the field scale using geological characterization of the rock mass. The model captures effects of brittle-ductile transition in rocks by introducing a cap multiplier to the yield function. The rate of dilatancy (bulking) is proportional to the slope of the yield surface affected by the cap. Therefore, it takes place only at low confinements when the pressure is less than the brittle-ductile transition pressure, P BD . On the contrary, the porous compaction takes place at pressures higher than P BD . The cap moves as the porosity is compacted or new porosity is generated due to dilatancy. The porous compaction is modeled using an evolution equation which includes deviatoric stress so that the onset of compaction corresponds to the cap surface. The model captures effects of shear-enhanced compaction which is an important for porous rocks. Section 2 describes the modeling framework and Section 3 presents the model calibration procedure. Section 4 compares experimental data for various rocks versus model predictions. The model parameters used for this comparison are given in Appendix. The files with material constants are available with the latest GEODYN material library distribution.
Triaxial Shear Tests on Simulated Sierra White Fault Gouge & Borehole Simulation in Sierra White Gouge
Laboratory shear tests were conducted on pulverized Sierra White granite (SWG) to investigate slip mechanisms in naturally occurring faults. Synthetic fault geometries were constructed by sandwiching fine grained SWG powder in between steel forcing blocks. For dry experiments, ~3.5 g of SWG powder was poured onto the face of the lower steel forcing block and leveled. For saturated experiments, enough fluid was added to the ~3.5 g of Sierra White granite powder to form a slurry. This slurry was applied to the lower forcing block and leveled. Inclined forcing blocks with 25.4 mm diameter and 35° faces, which were machined from ground steel rods with fine teeth on the faces, help to hold the gouge in place and prevent delamination at the interface. The top forcing block had a 2.03 mm centered hole to allow pore fluid access to the gouge. A fine steel mesh prevented back flow of the gouge into pore fluid lines. Samples were isolated from the confining medium using three layers of heat shrink polyolefin, as shown in Figure 1. The outer layer was shrunk over the o-rings on the end caps to form an impermeable seal, which was reinforced with steel tie wires on both sides of the o-rings. Hardened steel spacers and copper shim stock was placed between the steel forcing blocks and the end caps to preserve the parallelism of the Hastelloy wetted parts. For dry samples, the end caps were plugged, while the end caps for the saturated samples were connected to pore lines.
Evolution of anisotropy with saturation and its implications for the elastoplastic responses of clay rocks
Many clay rocks have distinct bedding planes. Experimental studies have shown that their mechanical properties evolve with the degree of saturation (DOS), often with higher stiffness and strength after drying. For transversely isotropic rocks, the effects of saturation can differ between the bed-normal (BN) and bed-parallel (BP) directions, which gives rise to saturation-dependent stiffness and strength anisotropy. Accurate prediction of the mechanical behavior of clay rocks under partially saturated conditions requires numerical models that can capture the evolving elastic and plastic anisotropy with DOS. In this study, we present an anisotropy framework for coupled solid deformation-fluid flow in unsaturated elastoplastic media. Here we incorporate saturation-dependent strength anisotropy into an anisotropic modified Cam-Clay (MCC) model and consider the evolving anisotropy in both the elastic and plastic responses. The model was calibrated using experimental data from triaxial tests to demonstrate its capability in capturing strength anisotropy at various levels of saturation. Through numerical simulations, we demonstrate the role of evolving stiffness and strength anisotropy in the mechanical behavior of clay rocks. Plane strain simulations of triaxial compression tests were also conducted to demonstrate the impacts of material anisotropy and DOS on the mechanical and fluid flow responses.
Determination of fundamental mechanical properties of biomass using the cubical triaxial tester to model biomass flow
The flowability of biomass is an indicator of how amenable biomass is to handling. The flowability measurements are often determined with empirical or tertiary experiments. This status quo impedes employing engineering principles to advance the design and operation of biomass handling systems. It is imperative to establish an experimental protocol minimizing empirical aspects of flowability characterization to account for the variability of biomass. This study demonstrates the operational principles of the large chamber cubical triaxial tester and the procedure of triaxial tests to quantify bulk flow behaviors of two milled biomass feedstocks, namely corn stover 2 mm (CS) and Douglas fir 1 mm (DF). The Mohr-Coulomb (MC), Drucker-Prager (DP) and modified Cam Clay (mCC) models are calibrated for both biomasses. Analysis indicates that CS will exhibit a cohesive flow with a larger cohesion coefficient of MC (3.8 ± 3.5 kPa) than DF (0.42 ± 0.9 kPa) and a larger d value of DP (6.9 kPa) than DF (0.0 kPa), respectively. CS exhibits a higher spring-back index of mCC (0.39 ± 0.05) than DF (0.27 ± 0.05) also suggesting handling issues, which agrees with the experiences in the industry. This study demonstrates the capability of a CTT in a quantitative investigation of biomass handling characteristics.
The physics of desiccation cracks 2: Modeling and prediction of the crack patterns
Here, this paper extends the experimental results of our companion paper by modeling and predicting the onset and pattern formation of desiccation cracks in geomaterials (Ruoyu et al., 2023). Thin-layer silt samples in controlled atmospheric conditions were tested to obtain the surface strain maps with the digital image correlation (DIC) method during dehydration. Support experiments, including consolidation and displacement-controlled triaxial tests, were conducted for the properties of geomaterials. These experimental results were used to validate a viscoplastic theoretical model by comparing cracks and singularities locations that distribute following the Cnoidal wave pattern. A critical value exists in the viscoplastic model that determines the number of singularities, which accurately predicts the number of cracks in the experiment. The critical values contain two crucial parameters: rate sensitivity and λ. Rate sensitivity describes the rate-dependent stress–strain relation, while λ shows the ability of pore pressure redistribution under the external mechanical loading rate. These results provide a new view to analyze the desiccation cracks considering the rate-dependent viscoplasticity.
Accurate Effective Stress Measures: Predicting Creep Life for 3D Stresses Using 2D and 1D Creep Rupture Simulations and Data
Operating structural components experience complex loading conditions resulting in 3D stress states. Current design practice estimates multiaxial creep rupture life by mapping a general state of stress to a uniaxial creep rupture correlation using effective stress measures. The data supporting the development of effective stress measures are nearly always only uniaxial and biaxial, as 3D creep rupture tests are not widely available. This limitation means current effective stress measures must extrapolate from 2D to 3D stress states, potentially introducing extrapolation error. In this work, we use a physics-based, crystal plasticity finite element model to simulate uniaxial, biaxial, and triaxial creep rupture. Here, we use the virtual dataset to assess the accuracy of current and novel effective stress measures in extrapolating from 2D to 3D stresses and also explore how the predictive accuracy of the effective stress measures might change if experimental 3D rupture data was available. We confirm these conclusions, based on simulation data, against multiaxial creep rupture experimental data for several materials, drawn from the literature. The results of the virtual experiments show that calibrating effective stress measures using triaxial test data would significantly improve accuracy and that some effective stress measures are more accurate than others, particularly for highly triaxial stress states. Results obtained using experimental data confirm the numerical findings and suggest that a unified effective stress measure should include an explicit dependence on the first stress invariant, the maximum tensile principal stress, and the von Mises stress.
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.
HFTS-1 Natural Joint Data and Engineering Summary
This report provides an analysis of engineering and geologic data collected from the Hydraulic Fracturing Test Site #1 (HTSF-1) project in the southern Midland Basin, Reagan County, Texas. The site is being studied as part of the Science-informed Machine Learning for Accelerating Real-Time Decisions in Subsurface Applications (SMART) Initiative at the National Energy Technology Laboratory (NETL). The data collected is intended to provide a basis of understanding of the site and to construct simulation models. This report provides a summary analysis of the engineering and geologic data collected from the project to provide a basis of understanding of the site and to construct simulation models. The report examines various possible correlations in engineering properties based on natural fracture data from the program, which consisted of 11 horizontal wells, one vertical well, and one slant well. The horizontal wells are in two horizons: 1) Upper and 2) Middle Wolfcamp formations. Program data include: fracture frequency and fracture orientation data from four core runs in a slant well; fracture spacing and orientation from a vertical pilot well; laboratory triaxial testing and mineralogical determinations; and porosity results from magnetic resonance analyses from various wells, together with observations based on the data collection. In addition, available references were reviewed on the site for additional insights. As the focus of the report is on the natural system, hydraulic fracture data from the site were not examined in detail in this report. Data variability is the chief observation in examination of the database. Fracture frequency in the slant well can range from sections with values as high as five fractures per ft to sections up to 100+ ft in length with no natural observed fractures. Fracture spacing across is typically less than 10 ft, but can range up to hundreds of feet. Apparent fracturing shows the trends in two predominate orientations, E-SW and WNW-ESE, but minor variations exist. The rock units vary across the site from siliceous mudstones to calcareous mudstones, showing a general layering with depth. The laboratory properties such as strength and modulus show no apparent trend with depth, but appear to correlate with rock mineralogy with high strength and modulus values where calcium content is high. In addition, an attempt to examine variability and mineralogy on a larger scale was made using a color-coded system based on gamma ray measurements. A staged colored approach was adopted, presuming that lower gamma ray values indicate higher value of calcium content (blue scale) and that higher gamma ray values indicate higher clay mineral content (orange scale). As provided in report appendices, the system correlated well with visual examination of the slant core and the petrofabric analyses of the vertical pilot well. The results showed large variability in mineral content along the horizontal plane across the site. The change in mineral content was also rapid, on a scale less than that of the average hydraulic fracture stage length of about 180 ft.
Experimental study of compaction localization in carbonate rock and constitutive modeling of mechanical anisotropy
Abstract Sedimentary rocks are inherently anisotropic and prone to strain localization. While the influence of rock anisotropy on the brittle/dilative regime has been studied extensively, its influence on the ductile/compactive regime is much less explored. This paper discusses the anisotropic behavior of a high‐porosity carbonate rock from central Europe (the Maastricht Tuffeau). A set of triaxial tests with concurrent x‐ray tomography has been performed at different confining pressures. The anisotropic characteristics of this rock have been investigated by testing samples cored at different inclinations of the bedding, thus revealing non‐negligible effects of the coring direction on yielding and compaction behavior. Specifically, samples cored perpendicular to bedding display higher strength and longer stages of post‐yielding deformation before manifesting re‐hardening. Despite such alterations of the inelastic response, Digital Image Correlation has revealed that the strain localization mode is independent of the coring direction, thus being primarily affected by the confinement level. To capture the observed interaction between material anisotropy and compaction behavior at the continuum‐scale, an elastoplastic constitutive law has been proposed. For this purpose, a set of tensorial bases has been introduced to replicate how the oriented rock fabric modulates the yielding and plastic flow characteristics of the material. The analyses show that the impact of the coring direction on yield function and plastic flow rule is fundamentally different, thus requiring the use of distinct projection strategies (a strategy here defined heterotopic mapping). The performance of the model, studied through parametric analyses and by calibrating the experimental results, illustrates the improved capability of the proposed constitutive approach when applied to strongly anisotropic porous rocks.
Role of crystallographic orientation on intragranular void growth in polycrystalline FCC materials
In this study, we study the effect of crystallographic orientation and applied triaxiality on the growth of intragranular voids. Two 3D full-field micromechanics methods are used, the dilatational visco-plastic fast-Fourier transform (DVP-FFT) and the crystal plasticity Finite Elements (CP-FE), both of which incorporate a combination of crystalline plasticity and dilatational plasticity. We demonstrate with several select cases that predictions of void growth from both formulations agree qualitatively. With the more computationally efficient DVP-FFT, additional effects of polycrystalline microstructure and the influence of nearest neighborhood are investigated. Crystals bearing a single intracrystalline void are studied in three types of 3D microstructural environments: isolated single crystals, individual equal-sized grains within a regular polycrystal, and individual variable sized grains within a polycrystal with grains and voids randomly located. We show that loading type plays a significant role. In strain-rate controlled conditions, voids in the hardest [111]-crystals grow the fastest in time, whereas in stress-controlled conditions, voids in the softest [100]-crystal grow the fastest in time. The analysis reveals that on average void growth is slower for the same starting orientation in the polycrystal than in the single crystal. We find that at the highest triaxiality tested that the correlation between crystal orientation and void growth rate in the polycrystal strengthens, drawing closer to that seen in the isolated single crystals. These results and model can help guide the microstructural design of polycrystalline materials with high strength and damage-tolerance in high-rate deformation.
Integrating Experiments and Well Logs to Predict Caney Shale Static Mechanical Properties During Production with Supervised Machine Learning
Caney shale is one of the emerging oil reservoirs in Oklahoma. Understanding the impact of effective stress on its mechanical properties is critical for predicting hydraulic fracture geometry and overall hydrocarbon production. The objective of our study is to evaluate the impact of effective stress on the dynamic Young’s modulus using ultrasonic velocity measurements for Caney shale samples. A triaxial cell was utilized to measure ultrasonic (P-wave and S-wave) velocities for ten downhole Caney shale samples under various effective stresses to indirectly assess the impact of pore pressure change. The dynamic Young’s moduli estimated from these measurements were integrated with available conventional well logs (excluding sonic logs) and triaxial test results from Benge et al. (2021) to predict the static Young’s modulus using Random Forest (RF) and Extreme Gradient Boosting (XGBoost) models. The results showed that the estimated dynamic Young’s moduli from ultrasonic measurements were higher than the corresponding static Young’s modulus of cores from the same vertical well at similar depths. With increasing effective stress, the dynamic Young’s modulus increased for all samples. The estimated dynamic-to-static correction factor tended to be higher in zones of high neutron porosity (PHIN) and low density compared to other zones. Finally, SHapley Additive exPlanations (SHAP) for RF and XGBoost models identified depth, gamma ray (GR), and PHIN as key features for predicting the static Young’s modulus. This study enhances our understanding of the dynamic and static Young’s moduli for the Caney shale interval, as a function of effective stress and conventional well logs. The findings from this study can improve predictions of production throughout the well's lifespan by offering insights into the mechanical property degradation resulting from pore pressure depletion.