Anisotropic Stress Conditions Research Articles

Characterization and modeling of biaxial plastic anisotropy in metallic sheets

The anisotropic behavior of cold-rolled sheet metals has been extensively studied, typically characterized by uniaxial loading tests in different directions to determine yield strengths and plastic flow (Lankford r-values). However, biaxial principal stress states often focus solely on yield loci in the RD/TD (rolling/transverse) directions, with limited studies on other loading directions. This study analyzes the relationship between the principal stress yield loci and the material principal anisotropic stress directions based on the Hill48 yield function. Biaxial tensile tests are conducted on DP590 high-strength steel using cruciform specimens cut in various directions different from the sheet RD/TD directions. The evolution of the anisotropic yield locus and plastic flow of DP590 under biaxial tensile directions beyond the traditional RD/TD anisotropic directions is revealed. Furthermore, a modified Hill48 model that considers any principal stress direction of loading is proposed, accurately describing the continuous evolution of equi-biaxial tension stress, near-plane strain stress, and plastic flow direction for different principal stress directions of loading. The issues of failing to predict plastic flow under biaxial loadings in the original Hill48 model, and the degraded representation of existing constitutive models when accounting for out-of-plane anisotropy are addressed by decoupling the relationship between anisotropic parameters and stress state. In addition, the proposed calibration strategy of anisotropic parameters, using experimental data from various principal stress directions of loading, effectively captures the anisotropic evolution caused by changes in principal stress directions. Comprehensive evaluation and verification of the plasticity model should consider yield locus for any principal stress directions of loading, and also the normal and shear planes.

Integrating 1D and 3D geomechanical modeling to ensure safe hydrogen storage in bedded salt caverns: A comprehensive case study in canning salt, Western Australia

The viability of hydrogen storage in bedded salt caverns hinges on understanding the geomechanical challenges posed by the anisotropic stress states and complex geology of such environments. This study presents a comprehensive geomechanical analysis focusing on a proposed cavern within the Carribuddy Formation in Western Australia, characterized by its interbedded salt layers. This paper introduces a new geomechanical workflow, encompassing 1D and 3D modeling techniques to provide detailed changes of mechanical properties and stress state in interbedded salt formation allowing to identify the initial optimal operational pressures for underground hydrogen storage. Initial 1D models evaluated mechanical properties and in-situ stresses, while subsequent 3D simulations, enriched by data from neighboring wells, detailed the stress, strain, and displacement responses of the cavern walls to internal pressure changes. The analysis pinpointed an initial safe gas pressure range between 3000 and 4000 psi, attributing this margin to the robust characterization of the mechanical and in-situ stress of the formation. Our findings underscore the significance of high-resolution geomechanical modeling in identifying initial optimal operational pressures for hydrogen storage in salt caverns, ensuring both safety and structural integrity.

Wellbore breakouts in heavily fractured rocks: A coupled discrete fracture network-distinct element method analysis

Wellbore breakout is one of the critical issues in drilling due to the fact that the related problems result in additional costs and impact the drilling scheme severely. However, the majority of such wellbore breakout analyses were based on continuum mechanics. In addition to failure in intact rocks, wellbore breakouts can also be initiated along natural discontinuities, e.g. weak planes and fractures. Furthermore, the conventional models in wellbore breakouts with uniform distribution fractures could not reflect the real drilling situation. This paper presents a fully coupled hydro-mechanical model of the SB-X well in the Tarim Basin, China for evaluating wellbore breakouts in heavily fractured rocks under anisotropic stress states using the distinct element method (DEM) and the discrete fracture network (DFN). The developed model was validated against caliper log measurement, and its stability study was carried out by stress and displacement analyses. A parametric study was performed to investigate the effects of the characteristics of fracture distribution (orientation and length) on borehole stability by sensitivity studies. Simulation results demonstrate that the increase of the standard deviation of orientation when the fracture direction aligns parallel or perpendicular to the principal stress direction aggravates borehole instability. Moreover, an elevation in the average fracture length causes the borehole failure to change from the direction of the minimum in-situ horizontal principal stress (i.e. the direction of wellbore breakouts) towards alternative directions, ultimately leading to the whole wellbore failure. These findings provide theoretical insights for predicting wellbore breakouts in heavily fractured rocks.

An effective stress-based DSC model for predicting hydromechanical shear behavior of unsaturated collapsible soils subjected to initial shear stress

Evaluation of hydromechanical shear behavior of unsaturated soils is still a challenging issue. The time and cost needed for conducting precise experimental investigation on shear behavior of unsaturated soils have encouraged several investigators to develop analytical, empirical, or semi-empirical models for predicting the shear behavior of unsaturated soils. However, most of the previously proposed models are for specimens subjected to the isotropic state of stress, without considering the effect of initial shear stress. In this study, a hydromechanical constitutive model is proposed for unsaturated collapsible soils during shearing, with consideration of the effect of the initial shear stress. The model implements an effective stress-based disturbed state concept (DSC) to predict the stress-strain behavior of the soil. Accordingly, material/state variables were defined for both the start of the shearing stage and the critical state of the soil. A series of laboratory tests was performed using a fully automated unsaturated triaxial device to verify the proposed model. The experimental program included 23 suction-controlled unsaturated triaxial shear tests on reconstituted specimens of Gorgan clayey loess wetted to different levels of suctions under both isotropic and anisotropic stress states. The results show excellent agreement between the prediction by the proposed model and the experimental results.

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.

A fully automated unsaturated triaxial device for testing of soils under complicated hydromechanical stress paths

A fully-automated unsaturated triaxial device is developed at the Advanced Soil Mechanic Laboratory of the Sharif University of Technology (SUT) to investigate the hydromechanical behavior of unsaturated soils under any complicated path. The main improvements of the developed device are (1) the ability to continuously measure accurately different stress/strain variables during long duration of unsaturated tests. This is of great importance in capturing the sudden deformations of the specimen, under wetting (2) providing a user-friendly controller software enabling the definition of any desired stress/strain variable and stress/strain paths under either stress-controlled or strain-controlled conditions. Finally, to evaluate the performance of the developed apparatus, two wetting tests were carried out to study the effect of initial shear stress on the hydromechanical behavior of unsaturated reconstituted specimens of Gorgan loess. In these wetting tests, the specimens were wetted under isotropic and anisotropic stress states by stepwise reduction of suction to approach to the saturated condition. The obtained results showed the excellent performance of the developed device to accurately follow the defined stress path along with the continuous measurement of stress/strain variables. The tested collapsible soil specimen that was wetted under the effect of initial shear stress exhibited a larger volume decrease accompanied by a larger degree of saturation compared to those of the specimen wetted under the isotropic stress state with the same initial mean net stress.

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

The 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.

Influence of Anisotropic Stress Conditions on Tunnel Deformation and Sequential Excavation Performance in Rock Mass

Abstract This study looks at how anisotropic stress conditions affect the mechanical response of circular tunnels in rock mass using a finite element plane strain model. The deformation response and evolution of the yield zone are evaluated using a non-linear Hoek-Brown failure criterion. The results show that predictions made under the widely employed assumption of isotropic stress conditions significantly underestimate the deformations for in-situ stress ratios greater than 1.0 and overestimate the values for in-situ stress ratios less than 1 under full-face excavation. The pattern of the yield zone changes noticeably as the in-situ stress ratio changes. With stress anisotropy, the yield zone becomes asymmetric. When the in-situ stress ratio is less than 1.0, the yield zone concentrates on the sidewalls and transitions to the crown when the in-situ stress ratio assumes values greater than 1.0. Also, the effect of anisotropic stress conditions on the performance of two commonly used excavation support schemes is studied. The results emphasize the importance of consideration of the in-situ stress ratio for prediction of tunnel deformation and selection of sequential excavation schemes.

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.