Anisotropic Stress Conditions Research Articles

On the stress-dependent tight-rock permeability under anisotropic stress conditions

Permeability is a key parameter for characterizing an unconventional tight-rock reservoir and predicting hydrocarbon production from the reservoir. Because of the technical difficulty in accurately measuring extremely low tight-rock permeability, the permeability measurements have been commonly made in laboratory under hydrostatic (or isotropic stress) conditions. For unconventional reservoirs, stress distributions, however, are generally anisotropic. This paper presents a theoretical and experimental study on stress-dependent tight-rock permeability under anisotropic stress conditions. The theoretical development is based on the concept of effective stress and expresses rock permeability as an exponential function of the effective stress defined in this paper. The laboratory permeability data obtained under anisotropic stress conditions support the usefulness of the theoretical model for the stress-dependent permeability and demonstrate the importance of stress anisotropy in determining rock permeability. Considering that the effective stress is the only independent variable for determining the relationship between rock permeability and stress, we further propose a workflow to convert tight-rock permeability data collected under hydrostatic stress conditions to those for anisotropic stress conditions that are more realistic for field applications. A theoretical relation for upscaling a parameter characterizing the impact of stress anisotropy on local-scale permeability is also discussed as the first step to address this important upscaling issue.

Small Strain Shear Modulus of the Ljubljana Marsh Soil Measured with Resonant Column and Bender Elements under Isotropic and Anisotropic Stress Conditions

The increasing use of finite element analysis in modern infrastructure design emphasizes the importance of determining soil stiffness at small strains. This is usually represented by the normalized shear modulus degradation curve, which is crucial for accurate design. In the absence of specific measurements on the local soil, engineers often rely on empirical correlations and assume comparable behavior of soils with similar intrinsic properties. However, the application of this approach leads to uncertainties, especially for unique geological formations such as the soft cohesive soils of the Ljubljana Marsh. The main objective of this study was to determine the small strain shear modulus of Ljubljana Marsh soil with a plasticity index between 11 and 35%. Isotropic and anisotropic stress conditions were investigated as part of an extensive laboratory test program that included 45 bender element and 89 resonant column tests on 20 soil samples. By emphasizing the importance of measuring soil stiffness at small strains, this study not only provides reliable data for the development of the built environment in the Ljubljana Marsh and similar areas, but also underlines its necessity.

Undrained shear behavior of silty sand with a constant state parameter considering initial stress anisotropy effect

Field observations in sedimentation and erosion-prone areas indicate that most natural sand deposits may contain a certain amount of non-plastic fines and are often under anisotropic stress conditions. A series of triaxial compression tests were performed on clean and silty sand with fines content fc ranging from 0 to 20% at an initial mean effective stress of p0′ = 100 kPa and varying consolidation conditions to understand the impact of initial stress anisotropy on undrained shear behavior. The results indicate that the state parameter ψ is a superior predictor for characterizing the responses of sand-fines mixtures compared to the global void ratio and relative density. A comparison of the behavior of clean and silty sand with a constant ψ (= − 0.03) confirms that the sample with 10% fc exhibits the strongest dilation and greatest shear resistance, irrespective of the consolidation conditions. It is also demonstrated that the initial stress anisotropy with a comparably higher static stress ratio ηs typically diminishes the shear strength of mixtures. However, the influence of initial stress anisotropy on soil stiffness is not unilateral. The sample consolidated to a negative ηs is stiffer than that under isotropic consolidation, while the presence of a positive ηs leads to a decrease in the secant Young's modulus.

Yielding evaluation of cement-treated soft clay under isotropic and anisotropic stress states using continuous Gmax measurements

Yielding evaluation of cement-treated soft clay under isotropic and anisotropic stress states using continuous Gmax measurements

Impact dynamics of granular debris flows based on a small-scale physical model

AbstractThe peak pressure of a granular debris flow at low Froude conditions can be calculated with knowledge of the stress anisotropy and the bulk density as well as the run-up height at impact. Based on a small-scale physical model, measurements of stress anisotropy and flow density values at impact are presented and applied to existing run-up prediction models, and further compared with back-calculated run-up coefficients from measured maximum impact pressures. For this purpose, we conducted 17 experiments with impact measurements and six experiments without impact measurements at Froude numbers, ranging from 0.84 to 2.41. Our results indicate that run-up heights are best reproduced by predictive models, either based on energy or mass and moment conservation, when anisotropic stress conditions, found in this study to range from 1.2 to 5.0, and bulk density variations due to impact, ranging in this study from 0.8 to 2.3, are considered. The influence of stress anisotropy and density variation on the run-up prediction differs, depending on the modelling approach. For the calculation of run-up heights based on the energy conservation concept, the influence of stress anisotropy becomes more significant with increasing Froude number, whereas for models based on mass and momentum conservation, bulk density variations have a greater influence on the estimation of the potential run-up.

Mechanical Response of a Circular Tunnel under Anisotropic Stress Conditions Using the Hoek–Brown Strain-Softening Model

Mechanical Response of a Circular Tunnel under Anisotropic Stress Conditions Using the Hoek–Brown Strain-Softening Model

Borehole stability in naturally fractured rocks with drilling mud intrusion and associated fracture strength weakening: A coupled DFN-DEM approach

Borehole instability in naturally fractured rocks poses significant challenges to drilling. Drilling mud invades the surrounding formations through natural fractures under the difference between the wellbore pressure (Pw) and pore pressure (Pp) during drilling, which may cause wellbore instability. However, the weakening of fracture strength due to mud intrusion is not considered in most existing borehole stability analyses, which may yield significant errors and misleading predictions. In addition, only limited factors were analyzed, and the fracture distribution was oversimplified. In this paper, the impacts of mud intrusion and associated fracture strength weakening on borehole stability in fractured rocks under both isotropic and anisotropic stress states are investigated using a coupled DEM (distinct element method) and DFN (discrete fracture network) method. It provides estimates of the effect of fracture strength weakening, wellbore pressure, in situ stresses, and sealing efficiency on borehole stability. The results show that mud intrusion and weakening of fracture strength can damage the borehole. This is demonstrated by the large displacement around the borehole, shear displacement on natural fractures, and the generation of fracture at shear limit. Mud intrusion reduces the shear strength of the fracture surface and leads to shear failure, which explains that the increase in mud weight may worsen borehole stability during overbalanced drilling in fractured formations. A higher in situ stress anisotropy exerts a significant influence on the mechanism of shear failure distribution around the wellbore. Moreover, the effect of sealing natural fractures on maintaining borehole stability is verified in this study, and the increase in sealing efficiency reduces the radial invasion distance of drilling mud. This study provides a directly quantitative prediction method of borehole instability in naturally fractured formations, which can consider the discrete fracture network, mud intrusion, and associated weakening of fracture strength. The information provided by the numerical approach (e.g. displacement around the borehole, shear displacement on fracture, and fracture at shear limit) is helpful for managing wellbore stability and designing wellbore-strengthening operations.

Crack tip plastic zone shape for anisotropic material subjected to mode -I loading

This paper discusses the effect of anisotropy in terms of anisotropy ratio on ductile materials subjected to mode-I type of loading. Thin plate with plane stress condition is considered for this work. σ3 is taken as zero. For considering the effect of Poisson’s ratio, σ3 = ν (σ1 + σ2) is considered. Isotropic plane strain and anisotropic plane stress condition is considered to develop mathematical relations for stress triaxiality and plastic zone around the crack tip by using Hill – von Mises’s yield criterion. The effect of poisons ratio, anisotropy ratio and stress triaxiality is shown on the size of plastic zone around the crack tip. The results were generated and are compared in the form of polar plot for plane strain condition at different Poisson’s ratio. In addition to this, the effect of anisotropy ratio on stress triaxiality is also investigated. It was observed that increase in Poisson’s ratio causes significant reduction in the size of plastic zone around the crack tip. The increase in anisotropy ratio also shows the same trend, especially for its higher values. It is observed that anisotropy plane stress problem of fracture is almost equivalent to isotropic fracture in plane strain condition.

Effects of consolidation conditions on the dynamic shear modulus of saturated coral sand over a wide strain range

The utilization of coral sand as a construction material for ports and other infrastructure systems in coral reefs is prevalent, wherein the soil elements within slopes and embankments typically experience an anisotropic stress state. It is imperative to accurately characterize the degradation behavior of the stratigraphic material's stiffness across a wide range of strains. In this study, the maximum and strain-dependent shear modulus (G0 and G) characteristics of saturated coral sand under isotropic and anisotropic consolidations were investigated by performing multi-stage stress-controlled undrained cyclic torsional shear tests with cyclic hollow cylinder shear apparatus. The experimental results indicated that G0 and G generally rose with increasing initial effective consolidation pressure but decreased with increasing inclination of initial major principal stress from the vertical (αc). In contrast, the effect of consolidation stress ratio (kc) on G0 and G was nonmonotonic, and that of kc and αc on the strain-dependent shear modulus reduction (G/G0) curve was slight. By defining anisotropic consolidation indexes δ0 and δr used for quantifying the effect of consolidation-induced anisotropy on the G0 and the G/G0, respectively. A unified formula of G0 obtained by multiplying Hardin's model by δ0, as well as a unique formula of G/G0 obtained by correcting γr in the Davidenkov skeleton curve expression as a linear function of δr were established under various consolidation conditions, respectively. The proposed G formula over a wide strain range is well validated by the experimental data for siliceous sandy soils from the literature.

Multi-dimensional ultrasonic-assisted belt grinding on the surface integrity of Inconel 718

In order to meet the requirements of the isotropic high-performance machining of complex surfaces, this paper proposed three-dimensional ultrasonic assisted belt grinding (3D-UABG) method that integrates the advantages of surface strengthening and isotropic machining, analyzed the motion characteristics and surface formation laws. Then, the influence of ultrasonic vibrations on the surface integrity of Inconel 718 was studied by a self-designed 3D-UABG device. Finally, the surface formation mechanism was revealed combined with the surface integrity and abrasive grain motion characteristic. Results showed that compared with conventional abrasive belt grinding (CABG), the abrasive grain in normal-ultrasonic assisted belt grinding (N-UABG) reduced the height of texture peak formed an intermittent texture, which makes it have smallest surface roughness. At the same time, the high-frequency impact of abrasive grains not only increased the surface plastic deformation, but also realized the impact strengthening. Planar two-dimensional ultrasonic assisted belt grinding (2D-UABG) reduced the directionality difference of surface quality. However, the deflection characteristics of abrasive grains make it have a large surface roughness. The 3D-UABG surface has good comprehensive mechanical properties. The abrasive grains have three-dimensional dynamic characteristics in space, which effectively inhibit anisotropic stress state, promote uniform deformation, and helpful to obtain approximately isotropic surface texture and small surface roughness. On the one hand, the in-plane motion characteristics of planar two-dimensional ultrasonic vibration gave grinding surface more uniform surface integrity. On the other hand, the spatial motion trajectory of abrasive grains driven by three-dimensional ultrasonic vibration made it have a slow increased cutting depth, which avoided the tear damage caused by materials plastic accumulation and the large roughness caused by abrasive deflection under large cutting depth. In 3D-UABG, lower feed speed and amplitude and linear velocity matched to grinding parameters contribute to the improved surface integrity. This study has guiding significance for the development and engineering application of ultrasonic-assisted belt grinding technology.

Solubility of NaCl under anisotropic stress state.

Salt solubility is generally determined under isotropic stress conditions. Yet, in the context of salt weathering of porous media, mechanical constraints on the in-pore growth of salt crystals are likely to be orientation-dependent, resulting in an anisotropic stress state on the crystal. In this paper, we determine by molecular simulation the solubility of NaCl in water when the crystal is subjected to anisotropic stress. Such anisotropy causes the chemical potential of the crystal to be orientation-dependent, and proper thermodynamic formulation requires describing the chemical potential as a tensor. The solute and crystal chemical potentials are computed from free energy calculations using Hamiltonian thermodynamic integration, and the usual condition of solubility is reformulated to account for the tensorial nature of the crystal chemical potential. We investigate in detail how the uniaxial compression of the crystal affects its solubility. The molecular simulation results led to revisiting the Correns law under anisotropic stress. Regarding the solute, the non-ideal behavior of the liquid phase is captured using Pitzer's ion interaction approach up to high concentrations of interest for in-pore crystallization and beyond the concentrations addressed in the existing literature. Regarding NaCl crystals, the validity of the generalized Gibbs-Duhem equation for a tensorial chemical potential is carefully verified, and it is found that crystallization progresses almost orthogonally to the crystal surface even under high shear stresses. Comparing uniaxial and isotropic compression highlights the major differences in solubility caused by stress anisotropy, and the revisited Correns law offers an appropriate framework to capture this phenomenon.

Deformation characteristics on anisotropic consolidated methane hydrate clayey-silty sediments of the South China Sea under heat injection

Natural gas hydrate is a new energy source with huge reserves, and the carbon content of hydrates is twice the carbon content of all proven fossil fuels combined, but the natural gas hydrate exploitation involves solid-liquid-gas phases change, which could induce a potential geological and environmental risk. Accurate description of the deformation behavior of sediments during hydrate dissociation is the key to predict the long-term stability of hydrate reservoirs. Nowadays, related studies mainly focus on the deformation behavior of hydrate-bearing sediment without dissociation. In this study, the deformation behaviors of remolded cores during thermal dissociation under anisotropy stress states were studied. The results show that 1) hydrate dissociation can lead to sediment deformation, the deformation rate of the sediments during the process of hydrate dissociation is 3 orders of magnitude larger than that before the dissociation. 2) the sediments under larger effective confining pressure (burial depth) present less deformation. 3) the sediments under isotropic stress conditions exhibit smaller deformation than that under anisotropic stress conditions. 4) dynamic permeability evolution during hydrate dissociation process can lead to effective confining pressure changes of the sediment, which can exacerbate the deformation.

A novel elastoplastic model for Yunnan sandstone under poly-axial loading

The lack of understanding of plastic hardening (softening) laws, especially under anisotropic stress conditions, results in inappropriate geotechnical management. Most of the yielding envelopes do not consider the effect of intermediate principal stress and the influence of Lode’s angle. In addition, the application of plastic flow rules regarding yielding surfaces compromises the softening of rock internal friction as well as the influence of Lode’s angle on the plastic potential. Moreover, the ductility to brittleness transition in the intermediate principal stress direction still requires a theoretical foundation. In this study, based on poly-axial testing results of Yunnan sandstone, we adopted a failure criterion with the intermediate principal stress proposed by Menétrey and Willam. The proposed new failure envelope was applied to capture the plastic evolution of rock samples. A plastic hardening-softening model is constructed, based on the framework of the plastic theory. The softening envelope is modified to better present the stress drop and considers the deterioration of rock internal friction in the post-peak stage of poly-axial loading. The differential of plastic potential according to the principal stresses is also modified, considering the rotation of Lode’s angle in the poly-axial loading tests. The model results were compared with laboratory testing results, which showed great consistency across 9 different loading tests (5 under triaxial stress and 4 under poly-axial stress with 22 stress-strain curves in total). The induced brittleness by the intermediate principal stress is also well captured by the proposed model.

The generalized Clapeyron equation and its application to confined ice growth

AbstractMost theoretical descriptions of stresses induced by freezing are rooted in the (generalized) Clapeyron equation, which predicts the pressure that a solid can exert as it cools below its melting temperature. This equation is central for topics ranging beyond glaciology to geomorphology, civil engineering, food storage and cryopreservation. However, it has inherent limitations, requiring isotropic solid stresses and conditions near bulk equilibrium. Here, we examine when the Clapeyron equation is applicable by providing a rigorous derivation that details all assumptions. We demonstrate the natural extension for anisotropic stress states, and we show how the temperature and pressure ranges for validity depend on well-defined material properties. Finally, we demonstrate how the range of applicability of the (linear) Clapeyron equation can be extended by adding higher-order terms, yielding results that are in good agreement with experimental data for the pressure melting of ice.

Effect of stress-induced anisotropy on shear modulus response of compacted coal ash under small-strain dynamic loading conditions

Un-utilized coal ash is commonly used as fill material for the construction of highway and railway embankment, which experiences different anisotropic stress conditions under different types of loading conditions. This study investigated the shear modulus of compacted coal ash under different anisotropic stress conditions simulating highway and railway embankment stress states. The small-strain shear modulus was obtained by performing the bender element tests under consolidation and shearing stages of consolidated undrained (CU) triaxial testing. The effect of different consolidation stress paths on the small-strain shear modulus of coal ash was evaluated using experimental data obtained from a bender element system affiliated with a stress-path controlled advanced triaxial setup. The small-strain shear modulus of coal ash at different ranges of mean effective stresses (at the end of consolidation) was also determined under various anisotropic stress conditions. The measured shear modulus (Gmax) of compacted coal ash under small-strain dynamic loading conditions was determined to be the function of mean effective stresses and deviatoric stress. At the later stage of shearing, the shear modulus was observed to attain a constant value subjected to large strain levels.

Strength, Deformation, and Particle Breakage Behavior of Calcareous Sand: Role of Anisotropic Consolidation

The effect of an anisotropic stress state on the monotonic behavior of calcareous sand has been rarely investigated, although calcareous sands in the field mainly experience anisotropic consolidation rather than isotropic consolidation. This study provides a laboratory study of the undrained and drained behaviors of dense calcareous sand consolidated anisotropically under various initial mean effective stresses (p0′) and anisotropic stress ratios (Kc), where significant effects of p0′ and Kc on the strength-deformation-degradation characteristics of calcareous sand can be observed. For undrained tests, higher deviatoric stress can be reached under a lower p0′. This could be due to the buildup of negative excess pore-water pressure (u) induced by sample dilatancy. As Kc increased, the negative u accumulated more distinctly, whereas the maximum and minimum u decreased. For drained tests, the maximum deviatoric stress decreased as Kc increased, even though more dilatancy occurred. Undrained loading generally resulted in a higher extent of particle breakage due to the buildup of negative u that increased the mean effective stress. A unique critical-state line was observed in both isotropic and anisotropic samples regardless of the loading condition. However, unlike quartz sand, a pseudosteady state that defined the transition from a dilatancy-dominant nonflow response to breakage-dominant stress degradation was observed in calcareous sand before reaching the critical state. Results also reveal the negligible effect of Kc on the peak-state stress ratio at undrained conditions. However, Kc had significant effect on stress ratio at peak or phase-transformation state in experiments under drained conditions, which can be well represented by using the concept of state dependence. Moreover, Kc had an adverse effect on the initial secant modulus.

Effect of Overburden Depth and Stress Anisotropy on a Ground Reaction Caused by Advancing Excavation of a Circular Tunnel

The assumption of the Convergence–Confinement Method (CCM) is the analysis of the interaction behavior of the support and ground of a deep circular tunnel under an isotropic stress field. Aiming to improve this method, this paper proposes a discussion on the influence of the overburden depth and stress anisotropy. To consider the influence of the overburden effect, the ground reaction in different depths due to tunnel advancing excavation is investigated. Under anisotropic stress conditions, the analytical solutions of the stress/displacement in the plastic and elastic regions of this ground reaction can also be suitable for theoretical analysis in a consistent manner. The key factor in this study is the use of confinement loss, which can not only describe the simulation of tunnel advancing effects but also become a superimposed value of the incremental procedure. In addition, the calculation spreadsheets can be used to estimate and implement the theoretical analytical solutions into executable computational solutions. To check the validity of the analytical solution, finite element analysis is used to examine the distribution of stress/displacement around the tunnel, especially the distribution along the overburden pressure line in the circular tunnel cross-section. Comparing the analytical solution calculated by the incremental procedure with the result of the numerical analysis shows a consistent trend.

A Cyclic True Triaxial with Rigid-Rigid-Flexible Boundary for Determination of Cross-Anisotropic Nature of Geomaterials

Abstract This paper describes a custom-designed Soil Poly-Axial Test System, SPAX-3000, developed to investigate the cross-anisotropic material properties of geomaterials under varying loading conditions. SPAX-3000, a mixed-boundary type of large-scale cyclic true triaxial apparatus (CTTA), is capable of applying a wide range of principal stress combinations on prismatic specimens of dimensions 152 × 152 × 304 mm. Two vertical and two horizontal load actuators on two opposite faces apply principal major (σ1) and intermediate (σ2) stresses independently to evaluate the performance of pavement structures under anisotropic stress states through resilient modulus (MR) testing. SPAX-3000 is controlled through software (CATS Software, provided by the manufacturer to provide advanced digital servo control of stresses and deformations). In this study, SPAX-3000 capabilities were evaluated through MR testing of both isotropic (urethane rubber) and cross-anisotropic materials (base, subbase, and subgrade) for the development of stress histories. The test results showed that SPAX-3000 is capable of determining MR independently of the anisotropy characteristics of the tested materials. Stress-hardening and stress-softening behaviors were observed for the coarse- and fine-grained geomaterials under different loading conditions. Anisotropy ratios (ratio of horizontal MR [MhR] to the vertical MR [MvR]) were determined for the base, subbase, and subgrade materials. MR test results showed that higher MvR results were obtained than that of MhR regardless of the loading conditions. The anisotropy ratios ranged from 0.08 to 0.21, 0.38 to 0.87, and 0.05 to 0.50 for the base, subbase, and subgrade materials, respectively. The highest MvR values (200–590 MPa) were obtained for the base material, whereas subbase material yielded the highest MhR (35–169 MPa). In general, stress-hardening behavior was observed for the geomaterials tested in both directions except for the stiffness of subgrade and subbase materials in the vertical direction.

Explicit numerical models for the prediction of plastic and weakening rockmass behaviour around a circular tunnel in isotropic and anisotropic stress conditions

The Geological Strength Index, GSI, is an assessment system for rockmass structure conditions (blockiness and discontinuity condition) based on the visual examination of exposed rockmass surfaces. The Generalized Hoek-Brown failure criterion is widely used with GSI to estimate the strength and stiffness of jointed rockmasses in traditional continuum numerical modelling. Modern numerical analysis tools allow networks of discrete structure to be represented with assigned properties based on site investigation data. In this paper, models with defined explicit structure are shown to yield similar results to implicit GSI-based models and provide more detailed information on the spatial variability of tunnel response when reasonable rockmass input parameters are estimated and calibrated. Once plastic explicit models are calibrated to give similar response to plastic implicit GSI-based models, explicit models using weakening joint and intact rock elements are used to determine appropriate post-yield strength and dilation parameters for use in implicit GSI-based modelling.

Bounding surface rotational hardening model for overconsolidated clay accounting for evolving fabric anisotropy

AbstractSoil is inherently anisotropic owing to the sedimentation process under gravity and is generally under anisotropic stress state in the field. To reflect the influence of anisotropic consolidation, rotational hardening (RH) is favorably used in constitutive models, mimicking in‐situ stress conditions. However, most of the existing models do not account for the inherent anisotropy of clays under isotropic stress state as well as the interplay between the fabric and loading direction, and the corresponding initial yield surface is assumed to be oriented along the hydrostatic axis. Furthermore, as the rotational angle is usually deemed as the clayed soil's anisotropy measure, a critical yield surface without rotation appears to contradict the highly anisotropic fabric at critical state. In this study, an anisotropic bounding surface model that incorporates RH and fabric anisotropy is formulated to simulate the behavior of overconsolidated (OC) clay subject to different consolidation histories, while addressing the aforementioned inconsistency issue. During the loading process, both fabric anisotropy and rotational angle evolve continuously based on their respective evolution rules. Fabric anisotropy evolves to the critical state when the rotational angle returns to zero, satisfying the anisotropic critical state theory (ACST). In addition, the model employs an anisotropic elasticity to consider the influence of the initial fabric at a low‐stress level. The predictive capacity of the model can be demonstrated by simulating several compression and extension tests on clay over a wide range of overconsolidation ratios (OCRs) and anisotropic consolidation stress ratios under both drained and undrained conditions.