Anisotropic Rock Research Articles

Quantitative Risk Assessment of Wellbore Collapse of Inclined Wells in Formations with Anisotropic Rock Strengths

Quantitative Risk Assessment of Wellbore Collapse of Inclined Wells in Formations with Anisotropic Rock Strengths

Investigation on the transmission of Love waves due to an impulsive line source in a heterogeneous double porous rock structure.

The region around the reservoir sometimes encounters the seismic response of ground. The phenomena of Love waves propagation also caused by seismic activity which can further significantly influenced by an impulsive line source present in the rock structures of ground. The current study elucidates the propagation behavior of Love waves induced by an impulsive line source within the anisotropic layered heterogeneous double porous rock structures commonly found in proximity to the reservoir areas. The expression of the dispersion relation for the Love waves propagation due to an impulsive line source has been derived by using the Fourier transformation and Green's function technique. The above-mentioned rock composite structure is consisted of two different portions: upper transversely isotropic double porous (TIDP) layer medium and lower heterogeneous isotropic double porous half-space (IDP) medium. In the aforesaid half-space medium, both types of heterogeneities viz. linear and quadratic have been considered. The impacts of heterogeneity parameters associated with the lower heterogeneous IDP half-space, porosity parameter (corresponds to both upper TIDP layer and lower IDP half-space) and anisotropic parameter of TIDP layer on Love waves phase velocity have also been studied. Some special outlines have also been depicted graphically.

Anisotropic induced polarization modeling with neural networks and effective medium theory

Interpreting three-dimensional induced polarization (IP) data requires rock physics models that reflect the omnipresent anisotropy of the Earth’s crust. The Generalized Effective Medium Theory of Induced Polarization (GEMTIP) can model the IP signatures of rocks with polarizable mineral inclusions. However, it is computationally demanding because it requires numerically solving the depolarization tensors of each inclusion. We aim to streamline GEMTIP simulations by (1) integrating anisotropic background conductivity and triaxial ellipsoidal inclusions in the model and (2) estimating the depolarization tensors with a neural network. We validate the neural network predictions against known solutions for spherical and spheroidal inclusions, and we test our method using data from an actual rock sample. The neural network shows a relative sensitivity of 56% to inclusion shape and 44% to host rock anisotropy and is up to 100,000 times faster than numerical integration. We release the pre-trained neural network implementation as an open-source Python package, thereby providing a new method to interpret the IP signatures of anisotropic rocks.

Research on orthotropic anisotropy characteristics of thick bedded limestone based on in situ deformation tests

The orthotropic anisotropy of sedimentary rocks has a significant impact on the force and deformation behavior of the project. In this paper, radial pressurization tests were carried out in the borehole in a typical northern karst area to obtain the deformation properties and orthotropic anisotropy of the rock masses. The test results showed that the deformation modulus and elastic modulus of the limestone rocks in the dam site area obeyed normal distribution. The deformation modulus was basically larger than the proposed deformation modulus of Class II rocks (10 GPa). The deformation behavior and anisotropy degree of the limestone showed a weak correlation with the elevation, but a strong correlation with the development density of the rock joints. The larger development density of the rock in the right bank test section leads to a larger degree of orthotropic anisotropy and frequency of occurrence.

TESTING OF ROCK SAMPLES FROM OIL AND GAS FIELDS TO DETERMINE THEIR PHYSICAL AND MECHANICAL CHARACTERISTICS

Determination of the physical and mechanical properties of anisotropic limestone rocks is an important and urgent task, since carbonate deposits are very often found in oil and gas fields of the Mangistau region. The data show that limestone creates from 70% to 90% of all problems related to the stability of wells, which is due to the peculiarities of their physical and mechanical properties. Experimental studies of the physical and mechanical properties of limestone have features both in terms of monolith selection and in terms of preparation of samples for research, and in the methods of conducting and processing experiments. These features are due to extremely low permeability, anisotropy of elastic and strength properties due to their layered structure. The experience of testing core samples of layered limestone is considered, tests are carried out on equipment under the program of consolidated-undrained loading in accordance with the standards. As a result of experiments on core samples cut at an angle, along and across the layering, the anisotropic elastic properties of rocks, as well as their dependencies on geophysical parameters, were studied. The anisotropy of elastic properties has a significant effect both on the stress-strain state when solving specific problems of continuum mechanics and on the design values of the initial stress field as a whole. Taking into account the anisotropy parameters obtained in this paper will make it possible to solve Geomechanics problems in relation to layered limestones of the Sarmatian stage.

Understanding the effects of pore pressure–induced crack deformation on the acoustic anisotropy of rocks with aligned cracks

AbstractCracks are extensively existing in rocks and play a significant role in the acoustic anisotropy of cracked rocks. Rocks in nature are affected by pore pressure, whereas the crack deformation with pore pressure and the impacts of the crack deformation on the anisotropic acoustic properties remain little known. Combining the theoretical model with the laboratory measurements of the anisotropic velocities of artificial sandstone samples with and without aligned penny‐shaped cracks, we invert for the crack parameters that characterize the crack deformation as a function of pore pressure and theoretically simulate the impacts of pore pressure–induced variation in the crack parameters on the anisotropic velocities. The results show that with increasing pore pressure, the inverted crack porosity increases exponentially, whereas the inverted crack aspect ratio decreases exponentially and the two crack parameters are linearly correlated. Moreover, model calculation demonstrates that the anisotropic velocities exhibit distinct reductions with the variation in the crack parameters caused by increasing pore pressure. In particular, the reduction in the velocity of the shear wave travelling parallel to the crack plane with polarization perpendicular to the crack plane is the most pronounced. We also demonstrate that the effects of the pore pressure–induced increasing crack porosity on the anisotropic velocities are more pronounced than the impacts of the decreasing crack aspect ratio. The findings not only reveal the variation of the crack geometry with pore pressure and the effects of the crack deformation on the anisotropic velocities of the cracked rocks but also can provide theoretical support for improving the characterization of the cracks through seismic survey.

Phase-field approach for precise fracture tracking in anisotropic rocks: Integrating orthotropy-based energy decomposition and two-fold symmetric fracture toughness

Rock formations are known to exhibit material anisotropy, both in terms of elastic and fracture properties. This means that the fracture path in such formations is not a priori known but rather a complex unknown that requires robust numerical techniques to predict accurately. In this context, the phase-field model is considered particularly effective, provided that certain physical considerations are carefully adjusted to align with the physics of the problem. While addressing elastic anisotropy is well-established, the tension–compression asymmetry necessary to inhibit crack interpenetration in phase-field fracture models needs to account for the specific material anisotropy. Additionally, to accurately capture crack propagation, it is critical to simultaneously account for orientation-dependent fracture toughness in such materials. To address this, the present study employs an anisotropic phase-field model that integrates the generalized spectral decomposition proposed in the literature for orthotropic materials with a two-fold symmetric fracture toughness, to predict the fracture trajectories in rock-type samples under fixed mixed-mode loading ratios. While each of the two aspects has primarily been applied to model orthotropic plates under simple tensile and shearing loading conditions in the literature, here we study their applicability in complex loading scenarios. To this end, the experimental data from notched semi-circular specimens of Grimsel Granite undergoing complex mixed-mode loading obtained in our previous work is considered. We focus on two given mode-mixity ratios and perform numerical studies. Our results emphasize the importance of considering this generalized decomposition for phase-field modeling of fracturing in rock-type materials, particularly under loading conditions where the crack might otherwise be unrealistically driven into the compressive region. Although certain features are well captured by considering anisotropy in elasticity alone, our findings demonstrate that incorporating a two-fold symmetric fracture toughness proves to be advantageous for more precise tracking of the fracture path.

Determination of elastic modulus and anisotropy for rocks using digital drilling method

The main purpose of this study is to provide a digital drilling-based method for determining rock elastic modulus and evaluating the anisotropy. By considering a concept of crushed zone, the drilling response was characterized as the function of specific energy and drilling strength. On this basis, an equivalent elastic modulus was proposed to evaluate the rock elastic modulus. Moreover, an anisotropy index was proposed according to the difference in specific energy under different borehole directions. Digital drilling experiments were conducted for three lithologies at drilling directions namely 0, 60, and 120° (Based on vertical orientation), revealing the anisotropic effect exhibited in the rock. To validate the measurement of rock elastic modulus and its anisotropy, the compressive tests under same conditions were carried out. The results suggested that the proposed indicator provided an accurate evaluation for the rock's elastic modulus, with an error margin of less than 10%. Drilling-based anisotropy is identified in the drilling response, especially the critical state between cutting and friction. The statical indicator CoV (coefficient of variation) was utilized to characterize the anisotropy along the borehole. This research's innovation lies in providing an approach to evaluating rock anisotropy and determining its elastic modulus by considering the drilling response.

Investigation of Indirect Shear Strength of Black Shale for Urban Deep Excavation

This study thoroughly investigated the compressive and tensile strength characteristics of black shale using both experimental and analytical approaches. Uniaxial compression tests were conducted to determine the elastic constants of black shale modeled as idealized, linear elastic, homogeneous, and transversely isotropic. Additionally, Brazilian tests were carried out on shale, considering it a transversely isotropic material. Strain measurements were recorded at the center of disc specimens subjected to diametric loading. By placing strain gages at the disc centers, the five elastic constants were accurately estimated. The effects of experimental methods and diametric loading on the elastic constant determination were evaluated and analyzed, and the indirect shear strength of the black shale, considering anisotropy, was determined using the estimated stress concentration coefficient. This study revealed that the indirect tensile strength of black shale is significantly influenced by the angle between the anisotropic planes and the diametric loading direction. Moreover, it was revealed that the stress concentration coefficients for anisotropic rocks vary from those of isotropic rocks, depending on the inclination angle of the bedding planes. This study confirms that the shear (tensile) strength of anisotropic black shale is not constant but varies with the orientation of the anisotropic planes in relation to the applied load.

A Stress‐Driven Double‐Phase–Field Framework for Tensile Fracturing Processes in Transversely Isotropic Rocks

ABSTRACTWe present a double‐phase–field framework for tensile fracturing processes in transversely isotropic rocks. Two distinct phase‐field variables are introduced to represent smeared approximations of tensile fractures along the weak bedding planes and through the anisotropic rock matrix, respectively. Driving forces that control fracture propagation in the phase‐field framework are constructed as a stress‐based formula with a recently developed tensile failure criterion that distinguishes the two failure modes in transversely isotropic rocks. For numerical implementation, we adopt a staggered integration scheme and decouple the governing equations so that the displacement field and phase‐field variables can be updated in sequence for a given loading step. The finite element formulation of the proposed framework is introduced in detail in this paper and is implemented in an in‐house finite element code. The numerical implementation is then validated by reproducing the uniaxial tension test results of Lyons sandstone. After that, we conduct simulations on a pre‐notched square plate loaded in tension to demonstrate the features of the proposed framework. Finally, we conduct simulations of three‐point bending tests of Pengshui shale and show that the proposed model can reproduce the force–displacement curves and failure patterns of specimens with different bedding plane orientations observed in laboratory experiments.

Optimized gradient boosting models and reliability analysis for rock stiffness [formula omitted]

The Extreme gradient boosting algorithm XGBoost has been confirmed to be an accurate method for predicting rock stiffnesses and anisotropic parameters from basic input features such as rock porosity, density, vertical compression stress, pore pressure and burial depth (Nguyen-Sy, T., To, Q.D., Vu, M.N., Nguyen, T.D. and Nguyen, T.T., 2020. Study the elastic properties and the anisotropy of rocks using different machine learning methods. Geophysical Prospecting, 68(8), 2557–2578). This study has the following contributions: reducing the R2-error score (that is, 1-R2) by 35 %, RMSE by 21 % and MAE by 16 % comparing to the previous study by considering an advanced CatXG hybrid boosting model in combination with the optimizer Optuna for predicting C13 (the most difficult stiffness to accurately predict); 2-conduct a reliability analysis for the predicted stiffness C13 with respect to the randomness of the input features. We also discuss the use of C11 or C33 as additional input features for accurately predicting C13 as well as the prediction of the related anisotropic parameter δ. This significant improvement of predicted stiffness C13 is extremely important because it encourages petrophysical engineers to use machine learning for predicting the elastic stiffnesses of rocks.

Optimal mine pitwall profiles in jointed anisotropic rock masses

ABSTRACT A new methodology based on the limit analysis upper bound method for the topological optimisation of slopes is presented, to determine geotechnically optimal slope profiles in anisotropic jointed rock masses. The methodology accounts for the effects of discontinuities such as joints, bedding planes, and tension cracks. We applied this methodology to the context of open pit mines, with the goal of achieving geotechnically optimal pitwall profiles. The optimal profiles maximise the Overall Slope Angle (OSA) while maintaining a prescribed Factor of Safety (FoS) and satisfying the geometric constraints imposed by benches and ramps. The method, implemented in the software OptimalSlope, utilises direction-dependent cohesion and internal friction angle parameters to replicate the effect of joints on slope stability. Key inputs include joint orientation, non-persistence, and probability of occurrence. We tested the methodology on a Mexican open pit mine to be excavated into Cretaceous siltstone featuring eight different joint sets and a primary bedding plane. Optimal pitwall profiles were determined for various combinations of bedding dip angles (0°, 15°, 30°, 45°, 60°, 75°, 90°) and mine pitwall orientations (hanging wall, footwall, side walls), considering the three-dimensional kinematics of the joints through anisotropic functions of cohesion and friction angle. Results indicate that the optimal pitwall profiles generally exhibit higher OSA compared to planar profiles with the same FoS, except in one bedding dip direction. Additionally, stability analyses performed using Rocscience Slide2 independently verified the FoS values of the optimal profiles.

Analysis of tensile failure mechanism in intact, foliated, and cracked rocks using distinct element method: Influence of anisotropy

A thorough numerical analysis was conducted to understand the failure mechanisms and behaviour in intact rocks, foliated rocks and rocks with pre-existing cracks using the Brazilian tensile strength tests. The dominant anisotropy in rocks, especially foliated rocks like phyllites, slates and schists, as well as sedimentary rocks like sandstone, limestones and shale, leads to complex failure mechanism. The presence of cracks leads to anisotropy causing different mechanisms of failure and variation in tensile strengths of rock mass. Numerical simulations were conducted based on experimental studies of foliated phyllite and dolomitic limestone from the Tejam Group, Lesser Himalaya. The variations in failure behaviour and strength of foliated rocks were studied for samples at different foliation angle using the particle distinct element model. The simulation results show that with increase in foliation angle to the loading direction (from 0° to 90°), the peak tensile strength of rocks remains almost same for specimens with θ = 0° to 30° and then increases linearly till 90°. The influence of cracks as anisotropy was also studied by changing crack length (from 5 mm to 30 mm) and angle (from 0° to 90°). The development of failure patterns in rocks with pre-existing cracks leads to a better understanding of the failure modes and makes it possible to interpret failure behavior, pattern, and strength parameters. With increase in crack length, the tensile strength of rocks decreases. Overall, this study depicts the influence of anisotropy and microparameters on failure modes and behavior in Brazilian tensile strength tests on foliated and pre-cracked rocks.

Wave velocities and anisotropy of rocks: Implication for origin of low velocity zone of the Qinling Orogenic Belt, China

Structure and composition of Earth is of fundamental importance in exploring the dynamic evolution of the crust and mantle. The Qinling Orogenic Belt (QOB) is located between the North China plate and the South China Plate, and is one of the main orogenic belts in China. To explore the composition and origin of anisotropy and the low wave velocity zone of the QOB, ten rock samples (gneiss and schist) were collected from the five sites of the QOB and the P- and S-wave velocities of these samples were measured under 0.6 to 2.0 GPa and 100 to 550 °C. The wave velocities increase with increasing pressure and decreasing temperature. The VP and VS of the schist and gneiss match the velocity of the middle and lower crust of the QOB, indicating that schist and gneiss are important component of the QOB. All the schist and gneiss samples exhibit obvious seismic anisotropy with 1.64%–17.42% for VS and 2.93%–14.78% for VP under conditions of crust and upper mantle. The CPO/LPO and layering distribution of mica in rock samples are the main reasons for this anisotropy. The VS structures below the five sampled sites from seismic ambient noise tomography were built to explore the effect of schist and gneiss on the composition and structure of the QOB. The results indicate that orientation-arranged gneiss and schist driven by the tectonic stresses might be a new origin of the character of VP/VS, seismic anisotropy, and the low velocity zone in the QOB.

Analytical solutions of noncircular tunnels in transversely isotropic rheological rock masses

In the field of tunnelling applications, it is often found that the rock masses exhibit anisotropy and rheological properties. To optimize the utilization of underground space, the use of noncircular tunnels is often preferred. However, it is important to note that these noncircular tunnels can lead to high-stress concentrations and significant displacements.This article presents a thorough analytical study on the time-dependent ground responses induced by the excavation of noncircular tunnels in transversely isotropic viscoelastic rock masses. The study considers a comprehensive set of engineering factors, including the viscoelastic characteristics of the surrounding rock, any anisotropic angle, and arbitrary tunnel shapes.Using the generalized corresponding principle of anisotropic elasticity and anisotropic viscoelasticity, an analytical model is introduced. This model can accurately and swiftly address the problem of deformation and stresses around noncircular tunnels in anisotropic rheological rock masses. The analytical solutions are verified by their good agreement with the Finite Element Method (FEM) results under identical assumptions. Moreover, the qualitative agreement between the analytical solutions and field data further validates the practical application of the analytical solution.A parametric analysis is then performed to investigate the effects of anisotropy ratio, anisotropy angle, and coefficient of lateral pressure on stresses and displacements.The proposed analytical solutions can help reveal the particular mechanical mechanism of the time-dependent ground responses due to the combination of rock anisotropy and rheology. Furthermore, they can provide a more accurate prediction of the ground response, which may be useful to optimize the design of tunnel excavation in anisotropic rheological rock masses.

Reconstruction of large-scale anisotropic 3D digital rocks from 2D shale images using generative adversarial network

Digital rock technology has played a significant role in unconventional oil and gas exploration and development. Current techniques face challenges such as high cost or low efficiency when reconstructing 3D pore structures at the nanoscale, which limit the study of rock physical properties in reservoirs. To address these issues, this work proposes an efficient generative adversarial network workflow for generating large-scale anisotropic 3D digital rocks from 2D images. Instead of relying on 3D data, the model is trained using only 2D images. During training, rock images taken from various angles can be utilized to construct anisotropic 3D digital rocks. Moreover, a novel method for generating large-scale 3D data is devised, where the input random noise is divided with overlap to generate small-scale digital rocks and concatenated into a larger-scale 3D digital rock. The similarity between the 3D reconstructed data and the training images was assessed separately, as well as the pore structure of the 3D reconstructed data, and the feasibility of the proposed method was verified using the simulation of absolute permeability. The digital rock modeling process presented in this study enables rapid and accurate 2D-to-3D large-scale digital rock modeling, providing an effective representation of the anisotropy present in shale oil reservoirs.

Response of semicircular canyons and movable cylindrical cavities to SH waves in anisotropic half-space geology

The development of tunnels or the laying of underground pipelines are essential engineering projects in modern society, and in canyon tunnels and underground pipeline projects, the surface motion and cavity edge motion have been topics of concern in ground vibration problems. We investigate the wave scattering problem in an elastic half-space anisotropic medium containing a semicircular canyon and a subsurface movable cylindrical cavity by using the wave function expansion method, the complex function method, and the mirror method. By deriving the governing equation and transforming it into the standard form of the Helmholtz equation satisfying the zero-stress boundary condition, we solve the corresponding displacement functions. Introducing a position correction coefficient, the scattered wavefield in a half-space anisotropic medium is constructed by the mirror method, which improves the problem of scattered wave source singularity in anisotropic half-space media. Then, combining the free boundary conditions with a Fourier series expansion method, we solve the unknown coefficients in the equations. The correctness of the method is verified by degenerating it to a classical analytic solution. Finally, using frequency- and time-domain analysis, we investigate the effects of the relevant parameters on the surface motion [Formula: see text], the dynamic stress concentration factor, and the displacement amplitude [Formula: see text]. The results indicate that rock anisotropy and the presence of semicircular canyons have a significant effect on the dynamic response of subsurface structures. This not only provides a theoretical basis for practical unlined tunnels or pipeline projects but also can provide a basis for seismic design of underground structures.

Seismic anisotropy of granitic rocks from a fracture stimulation well at Utah FORGE using ultrasonic measurements

For effective fracture stimulation in Enhanced Geothermal Systems (EGS), characterization of subsurface rock elastic properties is essential. Because seismic anisotropy significantly influences hydraulic fracturing, locating and characterizing microseismic events, and forecasting stress trajectories, our research undertakes laboratory experiments to study seismic anisotropy parameters of core samples from the Utah FORGE EGS site. We evaluated two rock samples from well 58–32, at two depths of 2074.16 m (6,805 feet) and 2268.01 m (7,441 feet), respectively. We analyze the mineralogy and classify the shallower rock as syenogranite, and the deeper rock as orthogneiss and monzonite. We cut cylindrical plugs from these two core samples, imaged them by computed tomography (CT) X-ray imaging, and measured their seismic anisotropy using ultrasonic waves at 1 MHz and under varying confining pressures (5–50 MPa) in ambient temperature conditions. With the assumption of the transversely isotropic (TI) medium, we measured three P-wave velocities and two S-wave velocities along different propagation directions to compute the Thomsen anisotropy parameters. Our results showed that the measured seismic velocities of each rock sample increase with increasing effective pressures, a behavior likely caused by closure of microcracks identified in our CT images. We also find that the measured anisotropies are higher at lower effective pressures. The maximum measured anisotropies for P-waves and S-waves are ∼23% and ∼20%, respectively. Therefore, we expect in the field operation that anisotropy should increase with increasing pore pressure caused by injection, which could be valuable in future EGS reservoir management and monitoring.

Characterization of stress‐dependent microcrack compliance and orientation distribution in anisotropic crystalline rocks

AbstractCrystalline rocks in the subsurface are of interest for geothermal energy extraction, nuclear waste storage, and, when weathered or fractured, as aquifers. Compliant discontinuities such as microcracks, cracks and fractures may nucleate and propagate due to changes in pore pressure, stress and temperature. These discontinuities may provide flow pathways for fluids and, if fracturing extends to surrounding rocks, may allow escape of fluids to neighbouring formations. Monitoring such rocks using sonic logs, passive seismic, borehole seismic and surface seismic requires understanding of the propagation of elastic waves in the presence of such discontinuities. These may have an anisotropic orientation distribution as in situ stress may be anisotropic. As crystalline rock may display intrinsic anisotropy due to foliation and the preferential orientation of anisotropic minerals, quantification of the relative importance of intrinsic and microcrack‐induced anisotropy is important. This may be achieved based on the stress sensitivity of elastic wave velocities. A method that allows both the orientation distribution of microcracks and the stress dependence of their normal and shear compliance to be estimated independently of the elastic anisotropy of the background rock is presented. Results are given for anisotropic samples of gneiss from Bukov in the Czech Republic and granite from Grimsel in Switzerland based on the ultrasonic velocity measurements of Aminzadeh et al. The microcrack orientation distribution is approximately transversely isotropic for both samples with a preferred orientation of microcrack normals perpendicular to foliation. This preferred alignment is stronger in the sample of gneiss than in the granite sample, and the normal and shear compliance of the microcracks decreases with increasing compressive stress. This occurs because the contact between opposing faces of the discontinuities grows with increasing compressive stress, and this results in a decrease in elastic anisotropy with increasing compressive stress. At low stress, the ratio of microcrack normal compliance to shear compliance is approximately 0.25 for the granite sample and 0.7 for the sample of gneiss. The normal compliance ZN for both samples decreases faster with increasing compressive stress than the shear compliance ZT, resulting in a decrease in ZN/ZT with increasing compressive stress.

An assumed enhanced strain finite element framework for tensile fracturing processes with dual-mechanism failure in transversely isotropic rocks

We present an assumed enhanced strain finite element framework for the simulation of tensile fracturing processes in transversely isotropic rocks. Fractures along the weak bedding planes and through the anisotropic rock matrix are treated with distinct enrichment, and a recently proposed dual-mechanism tensile failure criterion for transversely isotropic rocks is adopted to determine crack initiation for the two failure modes. The cohesive crack model is adopted to characterize the response of embedded cracks. As for the numerical implementation of the proposed framework, both algorithms for the update of local history variables at Gauss points and of the global finite element system are derived. Four boundary-value problem simulations are carried out with the proposed framework, including uniaxial tension tests of Argillite, pre-notched square loaded in tension, three-point bending tests on Longmaxi shale, and simulations of tensile cracks induced by a strip load around a tunnel in transversely isotropic rocks. Simulation results reveal that the proposed framework can properly capture the tensile strength anisotropy and the anisotropic evolution of tensile cracks in transversely isotropic rocks.