Anisotropic Rock Research Articles

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.

Time-dependent analytical solutions for tunnels excavated in anisotropic rheological rock masses

The anisotropy combined with the time-dependency of rock mass is commonly observed in tunnel construction. In this study, a comprehensive analytical investigation is performed on analysing time-dependent ground responses induced by tunnel excavation in an anisotropic rheological rock mass.An innovative analytical solution for the anisotropic viscoelastic problems is first proposed, which can be applied to the general cases that the rheological behaviours in anisotropic principal directions are independent and arbitrary. Using the generalized corresponding principle, the analytical model, which can precisely and rapidly address the problem, is then presented for the deformation and stresses around tunnels in transversely isotropic viscoelastic rock mass, considering different viscoelastic characteristics, different anisotropic angles, and circular/elliptical tunnel shapes. The analytical solutions agree very well with the numerical predictions for the consistent models, and can also be reduced to the isotropic viscoelastic case. Furthermore, the application of analytical solutions in practical engineering is validated by the good agreements between analytical solutions and field measurements. A parametric analysis is then performed to investigate the time-dependency of stress, and the effects of anisotropy ratios and anisotropy angles on displacements and stresses.The proposed analytical solution has a valuable contribution to the field of rock rheological mechanics, as it offers a benchmark for anisotropic viscoelastic problems, insights into the complex behaviour of anisotropic rock masses and provides a more accurate prediction of the ground response that may be useful to optimize the design of tunnel excavation in anisotropic rock masses.

Physical model test and application of 3D printing rock-like specimens to laminated rock tunnels

Weak structural plane deformation is responsible for the non-uniform large deformation disasters in layered rock tunnels, resulting in steel arch distortion and secondary lining cracking. In this study, a servo biaxial testing system was employed to conduct physical modeling tests on layered rock tunnels with bedding planes of varying dip angles. The influence of structural anisotropy in layered rocks on the micro displacement and strain field of surrounding rocks was analyzed using digital image correlation (DIC) technology. The spatiotemporal evolution of non-uniform deformation of surrounding rocks was investigated, and numerical simulation was performed to verify the experimental results. The findings indicate that the displacement and strain field of the surrounding layered rocks are all maximized at the horizontal bedding planes and decrease linearly with the increasing dip angle. The failure of the layered surrounding rock with different dip angles occurs and extends along the bedding planes. Compressive strain failure occurs after excavation under high horizontal stress. This study provides significant theoretical support for the analysis, prediction, and control of non-uniform deformation of tunnel surrounding rocks.

Analytical poro‐elastic solution of deep lined tunnels in anisotropic rock with consideration of tunnel face advance

AbstractThis paper aims at deriving a closed‐form solution for deep lined tunnels within a saturated anisotropic poro‐elastic medium. The derivation of the solution is carried out with the assumption of plane strain conditions along the tunnel axis, an isotropic elastic liner, a steady‐state flow, and perfect contact between the liner and rock. For this purpose, the complex potential function approach pioneered by Lekhnitskii for the anisotropic elastic body was used to develop the mechanical response of the rock mass. A complex hydraulic potential function is also introduced to solve the steady state fluid flow. Then the well‐known Biot theory is chosen to describe the hydro‐mechanical coupling of the anisotropic saturated rock. The stress and displacement solutions of both the liner and the surrounding rock, considering the tunnel face advance with respect to the considered section, are derived based on the principle of the convergence‐confining method. Comparisons with previous closed‐form solutions for isotropic case and finite element solution for anisotropic case were made to show the accuracy of the current closed form solution. Sensitivity analysis is performed based on this analytical solution to highlight the effect of some rock parameters on the stress and displacement of the liner.

Review of the creep constitutive models for rocks and the application of creep analysis in geomechanics

AbstractThe creep behavior of rocks has been broadly researched because of its extensive application in geomechanics. Since the time-dependent stability of underground constructions is a critical aspect of geotechnical engineering, a comprehensive understanding of the creep behavior of rocks plays a pivotal role in ensuring the safety of such structures. Various factors, including stress level, temperature, rock damage, water content, rock anisotropy, etc., can influence rocks’ creep characteristics. One of the main topics in the creep analysis of rocks is the constitutive models, which can be categorized into empirical, component, and mechanism-based models. In this research, the previously proposed creep models were reviewed, and their main characteristics were discussed. The effectiveness of the models in simulating the accelerated phase of rock creep was evaluated by comparing their performance with the creep test results of different types of rocks. The application of rock’s creep analysis in different engineering projects and adopting appropriate creep properties for rock mass were also examined. The primary limitation associated with empirical and classical component models lies in their challenges when it comes to modeling the tertiary phase of rock creep. The mechanism-based models have demonstrated success in effectively simulating the complete creep phases; nevertheless, additional validation is crucial to establish their broader applicability. However, further investigation is still required to develop creep models specific to rock mass. In this paper, we attempted to review and discuss the most recent studies in creep analysis of rocks that can be used by researchers conducting creep analysis in geomechanics.

The description of octahedral crystals using five parameters.

The shape of a flat-faceted octahedral crystal can be uniquely defined by the measured distances between pairs of its parallel facets and the length of one of its false edges. In total, only five numerical values are involved in this approach. Some interdependencies of parameters that allow one to control the correctness of measurements were derived. The proposed method is suitable for describing the shape as full-faceted, or as incomplete octahedral crystals (e.g. diamond) with unequally developed facets. This so-called `real crystal form' can be considered as one of the typomorphic features of minerals, connecting the dissymmetry to the anisotropy of the host rock. The measurement results can be used in crystallo-morphological analysis, restoration of the lost crystal shape in the case of man-made damage and in the practice of diamond prospecting.

Effect of Water-Induced Rock Softening on Rock Anisotropy During Drilling Process

Effect of Water-Induced Rock Softening on Rock Anisotropy During Drilling Process

Scattering of SH waves by elliptical cavity and type-III crack in deep anisotropic geology

Most of the underground rock formations are anisotropic, and the study of the dynamic response of anisotropic geology containing internal defects is necessary for the development of underground tunnels or caverns. In this paper, the wave function expansion method, the complex function method, and the Green's function method are used to solve the problem of scattering of SH waves in anisotropic rock in the presence of elliptical cavity and type-III crack. Boundary conditions for solving the problem are given using the conformal transformation method, and crack in the medium is constructed using the "crack cutting" technique. The scattered wave field generated by the crack is constructed based on the Green function method, and the displacement and stress fields in the model are obtained by the wave field superposition principle in the case of SH wave incidence. The dynamic stress concentration factor (DSCF) on the boundary of the elliptical cavity and the dynamic stress intensity factor (DSIF) at the crack tip are derived. The correctness of the method is verified by degenerating it to a classical analytic solution. Finally, the effects of the anisotropic strength of the rock mass, the dimensions of the cavern, and the incidence angle and wave number of the SH wave on the DSCF and DSIF are analyzed by numerical calculations in both the frequency and time domains. The results show that the anisotropy of the rock mass, the shape of the cavern and the defects of the surrounding medium have a great influence on the dynamic response of the underground structures, which should be given enough attention in the development and design of deep underground caverns or tunnels.

Investigating the causes of permeability anisotropy in heterogeneous conglomeratic sandstone using multiscale digital rock

Heterogeneous conglomeratic sandstone exhibits anisotropic physical properties, rendering a comprehensive analysis of its physical processes challenging with experimental measurements. Digital rock technology provides a visual and intuitive analysis of the microphysical processes in rocks, thereby aiding in scientific inquiry. Nevertheless, the multiscale characteristics of conglomeratic sandstone cannot be fully captured by a single-scale digital rock, thus limiting its ability to characterize the pore structure. Our work introduces a proposed workflow that uses multiscale digital rock fusion to investigate permeability anisotropy in heterogeneous rock. We use a cycle-consistent generative adversarial network to fuse computed tomography scan data of different resolutions, creating a large-scale and high-precision digital rock that comprehensively represents the conglomeratic sandstone pore structure. Subsequently, the digital rock is partitioned into multiple blocks, and the permeability of each block is simulated using a pore network. Finally, the total permeability of the sample is calculated by conducting an upscaling numerical simulation using the Darcy-Stokes equation. This process facilitates the analysis of the pore structure in conglomeratic sandstone and provides a step-by-step solution for permeability. From a multiscale perspective, this approach reveals that the anisotropy of permeability in conglomeratic sandstone stems from the layered distribution of grain sizes and differences in grain arrangement across different directions.

Hydromechanical coupling in unsaturated clayey rocks with double porosity based on a multiscale homogenization procedure

Shales and clay rocks are porous media with multiscale microstructures used in many engineering applications. Intact clay rocks often exhibit a bimodal pore size distribution in which the nanopores are related to the interlayer spacing in the clay platelet and the micropores are related to the interparticle pores between clay particles. The double-porosity microstructure has significant implications for the hydromechanical behavior of these rocks especially in unsaturated conditions. In this study, we develop a double-porosity hydromechanical framework incorporating a homogenization scheme to simulate fluid flow and elastic deformation in anisotropic clay rocks. The homogenization scheme provides an enriched description of the elastic behavior of clay rocks during changes in the degree of saturation by bridging the nano, micro, and macroscale characterizations. We also model the nanopores and micropores as two independent pore networks with distinct fluid flow mechanisms and permeabilities. The proposed framework is cast into a three-field mixed finite element formulation for solving fully coupled flow and deformation problems. Numerical examples of free and confined swelling in Opalinus clay samples are presented to demonstrate the impacts of a multiscale microstructure on wetting processes in clay rocks.

An anisotropic rock physics modeling for the coalbed methane reservoirs and its applications in anisotropy parameter prediction

The elastic properties and anisotropy of coalbed methane reservoirs are still poorly understood due to the complicated pore structure and the existing state of the coalbed methane. Therefore, an anisotropic rock physics model for the coalbed methane reservoirs is proposed based on the related effective medium theories, which focuses on the equivalent calculation of the elastic properties for adsorbed coalbed methane and the characterization of the multiple pore structure. Many factors related to the elastic properties of coal are considered, including the composition, pore structure, adsorbed gas content and pore fluid. The measured ultrasonic and well-logging data demonstrate that the proposed physics model is effective in predicting the elastic constants and velocity anisotropy parameters. The results suggest that the elastic constants increase with the increase of adsorbed gas content to some extent, and the effect of porosity on the elastic constants is much more obvious than that of adsorbed gas content. The velocity anisotropy parameters increase with the aligned fracture porosity and the fracture aspect ratio, and the P-wave anisotropy is more sensitive to these two factors. With increasing organic matter and clay content and porosity, Young's modulus and brittleness index decrease while the Poisson's ratio increases, and the impact of the porosity on the brittleness index is more significant than that of organic matter and clay content. The results are helpful in establishing the relationship between reservoir physics parameters and seismic response and can provide a basis for coalbed methane reservoir prediction and hydraulic fracturing.

Multiscale modeling of gas-induced fracturing in anisotropic clayey rocks

In the context of repositories for nuclear waste, understanding the behavior of gas migration through clayey rocks with inherent anisotropy is crucial for assessing the safety of geological disposal facilities. The primary mechanism for gas breakthrough is the opening of micro-fractures due to high gas pressure. This occurs at gas pressures lower than the combined strength of the rock and its minimum principal stress under external loading conditions. To investigate the mechanism of microscale mode-I ruptures, it is essential to incorporate a multiscale approach that includes subcritical microcracks in the modeling framework. In this contribution, we derive the model from microstructures that contain periodically distributed microcracks within a porous material. The damage evolution law is coupled with the macroscopic poroelastic system by employing the asymptotic homogenization method and considering the inherent hydro-mechanical (HM) anisotropy at the microscale. The resulting permeability change induced by fracture opening is implicitly integrated into the gas flow equation. Verification examples are presented to validate the developed model step by step. An analysis of local macroscopic response is undertaken to underscore the influence of factors such as strain rate, initial damage, and applied stress, on the gas migration process. Numerical examples of direct tension tests are used to demonstrate the model's efficacy in describing localized failure characteristics. Finally, the simulation results for preferential gas flow reveal the robustness of the two-scale model in explicitly depicting gas-induced fracturing in anisotropic clayey rocks. The model successfully captures the common behaviors observed in laboratory experiments, such as a sudden drop in gas injection pressure, rapid build-up of downstream gas pressure, and steady-state gas flow following gas breakthrough.

Probabilistic analysis of dual circular tunnels in rock masses considering rotated anisotropic random fields

Considering the spatial variability of rock masses in tunnelling analysis is a challenge in geotechnical engineering. This paper focuses on predicting collapse loads and probabilities of design failure for dual circular tunnels constructed in anisotropic rock masses. This study employs the random adaptive finite element limit analysis method, which incorporates rotated anisotropic random fields, to model uncertainties in rock mass properties. The generalised Hoek–Brown constitutive model is employed to define the yield failure criteria of a rock mass. The adaptive finite element limit analysis is first validated against a previous study, demonstrating good agreement. Then, the probability of design failure for dual circular tunnels is comprehensively investigated. This study emphasises the importance of considering both geometric parameters and rotated anisotropic random fields in comprehensive probabilistic analyses. The results provide insights into the mean and coefficient of variation of the stability numbers, as well as the probability of design failure for different geometric configurations and rotated anisotropic random fields. In conclusion, the variation in failure probability for practical applications is presented, highlighting the significance of accounting for spatial variability, rotation angle and anisotropy in rock mass properties in tunnelling.

Deformation microstructures of blueschists in Alpine Corsica, France, and implications for seismic anisotropy and the low-velocity layer in subducting oceanic crust

Understanding the deformation microstructures and seismic properties of blueschists is important for interpreting the seismic anisotropy at the top of subducting oceanic crust. The deformation microstructures and seismic properties of epidote blueschist, epidote-lawsonite blueschist, and lawsonite blueschist from Alpine Corsica, France, were studied using electron backscatter diffraction mapping and transmission electron microscopy. The crystal-preferred orientations (CPOs) of glaucophane show a strong maximum of the [001] axes aligned sub-parallel to the lineation. The maximum of the (010) poles of epidote is aligned sub-parallel to the lineation. The [001] axes of lawsonite are strongly aligned sub-normal to the foliation. Intracrystalline misorientation, dislocation, and occasional fragmentation of glaucophane indicate that glaucophane CPO was developed mainly by dislocation creep. The intracrystalline deformation features of epidote, such as subgrain boundaries and dislocations, indicate that the CPO of the epidote was formed by dislocation creep. In contrast, our data indicate that lawsonite CPO was developed by a combination of rigid-body rotation and dislocation creep with a minor effect of twinning. The P-wave anisotropy (AVp) and maximum S-wave anisotropy (max.AVs) of epidote blueschists (AVp = 12.3–16.9% and max.AVs = 6.53–11.75%) are higher than those of lawsonite blueschists. The seismic velocities of the blueschists are lower than those of mantle peridotites. The coexistence of epidote and lawsonite in the blueschist results in variations in seismic anisotropy and P-wave velocity in the whole rock, depending on the modal content of epidote and lawsonite. A high content ratio of epidote to lawsonite in blueschist produces strong P- and S-wave anisotropies of blueschist when the glaucophane content is more than ∼50%. The P-wave velocity of blueschist decreases proportionally with increasing epidote content. Our results indicate that the seismic properties of deformed blueschists contribute to the seismic anisotropy and the low-velocity layer in subducting oceanic crusts in subduction zones.

Anisotropic dynamic permeability model for porous media

Based on the tortuous capillary network model, the relationship between anisotropic permeability and rock normal strain, namely the anisotropic dynamic permeability model (ADPM), was derived and established. The model was verified using pore-scale flow simulation. The uniaxial strain process was calculated and the main factors affecting permeability changes in different directions in the deformation process were analyzed. In the process of uniaxial strain during the exploitation of layered oil and gas reservoirs, the effect of effective surface porosity on the permeability in all directions is consistent. With the decrease of effective surface porosity, the sensitivity of permeability to strain increases. The sensitivity of the permeability perpendicular to the direction of compression to the strain decreases with the increase of the tortuosity, while the sensitivity of the permeability in the direction of compression to the strain increases with the increase of the tortuosity. For layered reservoirs with the same initial tortuosity in all directions, the tortuosity plays a decisive role in the relative relationship between the variations of permeability in all directions during pressure drop. When the tortuosity is less than 1.6, the decrease rate of horizontal permeability is higher than that of vertical permeability, while the opposite is true when the tortuosity is greater than 1.6. This phenomenon cannot be represented by traditional dynamic permeability model. After the verification by experimental data of pore-scale simulation, the new model has high fitting accuracy and can effectively characterize the effects of deformation in different directions on the permeability in all directions.

Discrete element analysis of hydraulic stimulation in a slate geothermal reservoir using the ubiquitous foliation model

This study employs the discrete element method for a series of coupled hydro-mechanical analyses aimed at investigating the hydraulic stimulation effect on a slate geothermal reservoir. Initially, a ubiquitous foliation model (UFM) is devised to characterize the mechanical properties of slate. The UFM consists of a foliation model for near-field discontinuity features and a ubiquitous model for far-field anisotropic rock behavior. The devised model undergoes validation through an established benchmark analysis considering isotropic conditions. The analysis is subsequently extended to investigate anisotropic shear response influenced by the foliation. In cases where the anisotropic angle equals 90°, new fractures initiate along the foliation, which leads to a concentrated and severe damage pattern. In contrast, models with the anisotropic angle of 45° and 135° exhibit minor failures due to foliation orientation hindering fracture propagation. Lastly, an anisotropic hydraulic-mechanical analysis is undertaken to assess the hydraulic stimulation influence and its consequential effects on a slate geothermal reservoir. The results indicate that higher injection rates amplify damage to the rock matrix and the propagation of fractures, which are concentrated between open fractures and adjacent foliations.

Predicting the Critical Grout Pressure in Anisotropic Rocks Based on the Maximum Energy Release Rate Criterion

Predicting the Critical Grout Pressure in Anisotropic Rocks Based on the Maximum Energy Release Rate Criterion

Fracture initiation pressure prediction of hydraulic fracturing for layered reservoirs considering borehole deformation

Accurately predicting fracture initiation pressure is crucial for successfully applying hydraulic fracturing technology in layered reservoirs. However, existing models overlook the effects of rock anisotropy and borehole deformation. In this study, we simplified the layered reservoir to a transversely isotropic medium and developed a model to estimate borehole deformation precisely. Based on this estimated deformation, we created a model to predict fracture initiation pressure in hydraulic fracturing. By comparing previous models and experimental data, we validated the effectiveness of these proposed models. We examined the impacts of various factors on borehole deformation, fracture initiation pressure, and initiation angle. The results revealed that circular boreholes in layered reservoirs deform into elliptical boreholes under in situ stress, with the major axis not aligning with the principal stress direction, which highlights the significant impact of rock anisotropy on borehole deformation. Furthermore, the fracture initiation pressure of hydraulic fracturing either increases or decreases following borehole deformation, depending on specific geological parameters. The calculated initiation angle after borehole deformation is within 10°, closer to previous experimental results, underscoring the notable effect of borehole deformation on hydraulic fracturing. Our research indicates that the impact of borehole deformation on hydraulic fracturing is significant and should not be overlooked. This finding will offer fresh avenues for further study in the field of hydraulic fracturing.

An experimental study of tensile stress and deformation in an anisotropic rock

Anisotropy is a very common condition in rock mass; it can be due to different factors and directly affects the failure mechanisms affecting the rock mass. For example, metamorphic rocks that are foliated, sedimentary rocks that are stratified or volcanic formations with alternating layers. Despite the existence of several studies related to anisotropy those specifically addressing the tensile strength of anisotropic rocks are quite limited. The present study is focused on the determination of the deformability, compressive and tensile strength of anisotropic rocks. It must be highlighted that the mechanical behavior of the anisotropic rock mass is dependent on the angle between the inclination of planes of weakness (e.g. foliation) and the direction of the load. Assuming a vertical load, the two extremes of tensile strength are 0°(horizontal) and 90° (vertical). A series of laboratory tests has been done in anisotropic sandstone (lithic arkose), from Burgos (Spain), including uniaxial compressive strength tests, direct tensile strength tests, and diametric compression (Brazilian tests). The tests were carried out with strain gauges that allowed estimating the elastic modulus. To determine the anisotropic direction, ultrasonic pulse wave velocity tests were also performed. The variation of strength and deformability as a function of anisotropy is analyzed, as well as the variation of elastic behavior in tensile and compressive.

The Influence of Rock Anisotropy on the Plan of Constructions

The Influence of Rock Anisotropy on the Plan of Constructions