Anisotropic Stress Conditions Research Articles

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.

On shape forming by contractile filaments in the surface of growing tissues.

Growing tissues are highly dynamic, and flow on sufficiently long timescales due to cell proliferation, migration, and tissue remodeling. As a consequence, growing tissues can often be approximated as viscous fluids. This means that the shape of microtissues growing in vitro is governed by their surface stress state, as in fluid droplets. Recent work showed that cells in the near-surface region of fibroblastic or osteoblastic microtissues contract with highly oriented actin filaments, thus making the surface properties highly anisotropic, in contrast to what is expected for an isotropic fluid. Here, we develop a model that includes mechanical anisotropy of the surface generated by contractile fibers and we show that mechanical equilibrium requires contractile filaments to follow geodesic lines on the surface. Constant pressure in the fluid forces these contractile filaments to be along geodesics with a constant normal curvature. We then take this into account to determine equilibrium shapes of rotationally symmetric bodies subjected to anisotropic surface stress states and derive a family of surfaces of revolution. A comparison with recently published shapes of microtissues shows that this theory accurately predicts both the surface shape and the direction of the actin filaments on the surface.

A coupled CFD-DEM investigation into suffusion of gap-graded soil considering anisotropic stress conditions and flow directions

A coupled CFD-DEM investigation into suffusion of gap-graded soil considering anisotropic stress conditions and flow directions

Effects of initial stress anisotropy on the onset of undrained instability for Guamo sand

Undrained instability is a failure mode that has been observed in many sandy slopes. However, the highly anisotropic stress states caused by the geometry of the slope have not been duly considered from the experimental point of view. This article studies the influence of the initial stress anisotropy of laboratory samples on the static undrained instability of the Colombian reference sand. Forty-five consolidated undrained triaxial tests were performed, prescribing combinations of different initial void ratios, mean confining pressure, and initial stress ratios. Experimental results allow concluding that: a. the size of the instability zone on the p′ − q plane becomes smaller for larger initial anisotropic stress ratios; b. a novel undrained instability plane can be proposed in the p′ − q − e space to set a boundary between stable and unstable undrained loading conditions; c. mean confining pressure plays a vital role in the estimation of undrained instability for Guamo sand samples under low and medium confining stresses; d. despite multiple factors that influence the onset of undrained instability, a relation can be derived between the undrained instability susceptibility of sandy slopes and the initial stress ratio η0.

Femtosecond laser micromachining for stress-based figure correction of thin mirrors

The fabrication of a large number of high-resolution thin-shell mirrors for future space telescopes remains challenging, especially for revolutionary mission concepts such as NASA’s Lynx X-ray Surveyor. It is generally harder to fabricate thin mirrors to the exact shape than thicker ones, and the coatings deposited onto mirror surfaces to increase the reflectivity typically have high intrinsic stress that deforms the mirrors further. Since the rapid development of femtosecond laser technologies over the last few decades has triggered wide applications in materials processing, we have developed a mirror figure correction and stress compensation method using a femtosecond laser micromachining technique for stress-based surface shaping of thin-shell x-ray optics. We employ a femtosecond laser to selectively remove regions of a stressed film that is grown onto the back surface of the mirror, to modify the stress states of the mirror. In this paper, we present experimental results to create both isotropic and anisotropic stress states on thin flat silicon mirrors with thermal oxide ( S i O 2 ) films using femtosecond lasers. We show that equibiaxial stress can be generated through uniformly micromachined holes, while non-equibiaxial stress arises from the ablation of equally spaced troughs. We also present results from strength tests to show how this process minimally affects the strength of mirrors. These developments are beneficial to the high-throughput correction of thin-shell mirrors for future space-based x-ray telescopes.

Microscopic investigation of the influence of complex stress states on internal erosion and its impacts on critical hydraulic gradients

AbstractInternal erosion involves the loss of fine particles within the matrix of coarse particles under seepage flow, posing a severe threat to hydraulic structures. This paper focuses on internal erosion considering anisotropic stress conditions. The influence of the anisotropic stress state, represented by vertical stress equal to, bigger than, or smaller than horizontal stress, was investigated using coupled computational fluid dynamics (CFD) and the discrete element method (DEM). Results show that the loss of fine particle specimens under anisotropic stress conditions is greater than that for samples under isotropic stress states, as the loss of fine particles leads to an evolution of anisotropy into isotropy, with local contact force chains gradually forming spatially isotropic structures. The strong force chains of specimens under triaxial compression were also found to develop a dominant orientation in the vertical direction, leading to clogging in the upward migration of fine particles and increasing the critical hydraulic gradient. In addition, the evolution of void ratio, hydraulic drag force, connectivity, and coordination number has also been analyzed to exhibit the influence of stress anisotropy on internal erosion.

Modeling anisotropic ductile fracture of AA7075-T6 sheet for sheet metal forming considering anisotropic stress state

Anisotropic ductile fracture is one of the critical issues in the precision plastic forming of lightweight sheet metals. In this work, a new anisotropic ductile fracture model is developed by introducing the anisotropic stress triaxiality into the weight equation of the shear-controlled ductile fracture criterion. In an attempt to consider the effect of material anisotropy on stress state, the proposed fracture model is constructed in the anisotropic stress state form. The proposed anisotropic fracture model is used to characterize the anisotropic ductile fracture behavior of the AA7075-T6 sheet with a thickness of 2.0 mm under various stress states at room temperature. A series of uniaxial tensile tests are conducted using the in-plane shear specimen, the specimen with a central hole, and the plane strain grooved specimen to experimentally investigate the ductile fracture of AA7075-T6 along rolling, diagonal, and transverse directions. The proposed fracture model is calibrated by fracture strains determined from the hybrid experimental–numerical approach. With the calibrated fracture model, the anisotropic ductile fracture behaviors of AA7075-T6 over a wide range of stress states are predicted and compared with experimental measurements. The results show that the proposed fracture model successfully captures the anisotropic ductile fracture behavior of AA7075-T6 under various stress states at room temperature. Furthermore, to further illustrate the fracture predictive capability of the proposed fracture model, the predicted anisotropic fracture forming limit diagram is compared with the experimental forming limit strains obtained from the literature. Reasonable agreement is shown between literature data points and predicted fracture forming limit diagram. Accordingly, the proposed model has a great advantage in quantitative characterizing the anisotropic ductile fracture of high-strength aluminum alloy sheets under various loading conditions.

Unified state boundary surface model for clay and sand under saturated and unsaturated conditions

A unified state boundary surface that defines the upper limit of the specific volume of saturated clay and sand is first derived. It is extended to unsaturated soils by applying Bishop’s effective stress and using the effective degree of saturation as an independent state variable. Then, a critical state model for unsaturated clay and sand is formulated based on the unified state boundary surface. The model combines a rational soil–water characteristic curve incorporating packing density and hydraulic hysteresis. The model is validated by comparing the calculated results and results of extensive experiments, including one-dimensional and isotropic compression tests, triaxial shearing tests, and soaking-collapse tests under isotropic and anisotropic stress conditions on sand, clay, and mixed soil under saturated and unsaturated conditions. The proposed unified soil model presents a noble and universal framework for the rational description of broad soils’ behavior, in which the state boundary surface plays a central role. The model accurately predicts the compression, shearing, and soaking-induced collapse behaviors of various soil types in saturated and unsaturated conditions.

Experimental study on the mechanical and failure behaviors of deep rock subjected to true triaxial stress: A review

It has become an inevitable trend of human development to seek resources from the deep underground. However, rock encountered in deep underground engineering is usually in an anisotropic stress state ( σ 1 > σ > σ 3 ) due to the influences of geological structures and engineering disturbances. It is therefore essential to study the mechanical, seepage, and dynamic disaster behaviors of deep rock under true triaxial stress to ensure the safe operation of deep rock engineering and the efficient exploitation of deep resources. In recent years, experimental techniques and research on true triaxial rock mechanics have achieved fruitful results that have promoted the rapid development of deep rock mechanics; thus, it is necessary to systematically review and summarize these developments. This work first introduced several typical true triaxial testing apparatus and then reviewed the corresponding research progress on rock deformation, strength, failure mode, brittleness, and energy as well as the 3D volumetric fracturing (dynamic disaster) properties of deep rocks under true triaxial stress. Then, several commonly used true triaxial rock strength criteria and their applicability, the permeability characteristics and mathematical models of deep reservoir rocks, and the disaster-causing processes and mechanisms of disturbed volumetric fracturing (rockburst, compound dynamic disasters) in deep rock engineering were described. This work may provide an essential reference for addressing the true triaxial rock mechanics issues involved in deep rock engineering, especially regarding the stability of surrounding rock at depth, disaster prevention and control, and oil and gas exploitation.

Cyclic resistance of fly ash influenced by anisotropic stress condition, sand contents, and gravel content

A series of cyclic triaxial tests were performed to study the effect of anisotropic stress, sand content (in a fly ash-sand mixture), and addition of gravel on the cyclic resistance of fly ash. The results indicated that the failure mode of pure fly ash in the presence of isotropic stress was cyclic mobility and that the cyclic resistance of pure fly ash was significantly lower than that of clean Nakdong River sand for given test conditions. The cyclic resistance of pure fly ash decreased when the effective confining stress increased from 100 to 200 kPa, as expected. The failure of pure fly ash conducted in the absence of stress reversal was due to the initial axial strain accumulation and subsequent sudden runaway deformation, and this failure mode differed dramatically from that of fly ash conducted under symmetrical stress reversal. An increase in the anisotropic ratio resulted in a decrease in the cyclic resistance of pure fly ash. Nakdong River sand and gravels were added to pure fly ash and it was examined whether the cyclic resistance of fly ash increased. Addition of sand was observed to decrease the cyclic resistance for 10% and 20% sand content by volume, regardless of the amount of increase in the dry density of the samples. Furthermore, the cyclic resistance of fly ash-gravel mixtures was greater than that of pure fly ash by approximately 17%.

Macro- and Micromechanical Assessment of the Influence of Non-Plastic Fines and Stress Anisotropy on the Dynamic Shear Modulus of Binary Mixtures

Resonant column tests were carried out on Hostun sand mixed with 5%, 10% and 20% non-plastic fines (defined as grains smaller than 0.075 mm) in order to quantify the combined influence of the void ratio (e), anisotropic stress state (defined as σv′/σh′) and fines content (fc) on the maximum small-strain shear modulus Gmax. A significant reduction in the Gmax with increasing fc was observed. Using the empirical model forwarded by Roesler, the influence of e and σv′/σh′ on Gmax was captured, although the model was unable to capture the influence of varying fines content using a single equation. From the micro-CT images, a qualitative observation of the initial skeletal structure of the ‘fines-in-sand’ grains was performed and the equivalent granular void ratio e* was determined. The e was henceforth replaced by e* in Roesler’s equation in order to capture the variation in fc. The new modification was quantified in terms of the mean square error R2. Furthermore, the Gmax of Hostun sand–fine mixtures was predicted with good accuracy by replacing e with e*. Additionally, a micromechanical interpretation based on the experimental observation was developed.

Effect of microwave radiation on mechanical behaviors of tight fine sandstone subjected to true triaxial stress

During the exploitation of deep resources, rock masses are under three-dimensional anisotropic stress conditions owing to tectonic conditions and engineering disturbances. Owing to the advantages of high heating efficiency and selective volume heating, microwaves have broad application prospects in fields such as unconventional low-permeability reservoir fracturing. Therefore, it is of great significance to study the mechanical behavior of rocks under true triaxial stress after microwave irradiation. In this study, true triaxial tests of sandstone under different microwave irradiation conditions were conducted. The results showed that the strength of the irradiated sandstone first increased and then decreased. The strength of the irradiated sandstone was significantly lower than that of the unirradiated sandstone. The pre-peak brittleness of the sandstone gradually increased with an increase in σ₂. The brittleness of the irradiated samples was lower than that of the unirradiated samples. For the post-peak brittleness index of the sandstone, with the increase of σ₂, the microwave irradiated and unirradiated sandstone both gradually decreased first and then slowly increased. The residual strength of the unirradiated sandstone showed a trend of first increasing and then stabilizing, while the residual strength of the irradiated sample showed a greater dispersion and fluctuation. And, the residual strength of sandstone first increased and then decreased with the increase of microwave duration. In addition, a new double logarithmic linear strength model was proposed, which is in good agreement with the experimental results. The true triaxial stress induced anisotropic damage and deformation of sandstone are critical to rock fracture. The stress difference induced by water vapor expansion and mineral thermal expansion is the main factor for microwave breaking water-bearing sandstone. This work is of great significance to the research and application of microwave assisted breaking hard rock and fracturing deep low-permeability reservoir rocks.

Mechanism of wetting–induced deformation and failure of unsaturated soils

AbstractThe mechanisms of hydraulic collapse (wetting‐induced deformation) are studied through a series of simulations using a model for unsaturated soils. The model is a critical state soil model extended for unsaturated soils using Bishop's effective stress tensor, the state boundary surface (SBS) moving with the change in the degree of saturation, and a rational soil‐water characteristic curve that takes account of density and hydraulic hysteresis. Comparisons with published experimental data validate the proposed model. The simulation results show that the model adequately captures the hydraulic collapse behavior under both isotropic and anisotropic stress conditions. The effects of density, mean net stress, and deviatoric stress on the hydraulic collapse behavior are further investigated through a parametric calculation, and the mechanics of the wetting–induced instability are discussed. The effects of suction history, namely repeated wetting and drying cycles, on the deformation and failure, are also presented. The proposed model provides a validated method for modeling hydromechanical collapse in unsaturated soil and provides a better understanding of the mechanisms involved.

Creep behaviour of structured clays in triaxial stress space: theory and experimental investigation

ABSTRACT This paper investigates the time-dependent behaviour of structured clays in triaxial stress space both theoretically and experimentally. A range of existing theoretical frameworks and phenomenological equations are reviewed and discussed in their ability to interpret the creep behaviour at different states in stress space. New experimental results are presented for two structured clays subjected to complex loading conditions. Each test consists of a defined stress path with intermediate stages of creep. Considerable creep deformations were observed at all anisotropic effective stress conditions. Measured viscous deformations were observed to be related to the stress state, approaching stress path and degree of structure present in the soil. The incremental strain ratio, , measured during constant stress was found to rotate counter-clockwise as a result of drained shearing towards failure for all tests. The experiments also show that for very small stress increments, phenomenological and empirical relations incorrectly predict the development of creep strains with time.

Small-strain shear modulus of calcareous sand under anisotropic consolidation

In this study, the small-strain shear modulus of a calcareous sand was investigated by conducting bender element tests on both horizontal and vertical planes. The effects of sample preparation method, stress path and stress history on the developing of void ratio, the parameters in the modified Hardin Equation, and the stiffness anisotropy were examined. The test results show that the moist tamping samples have the least void ratio variation among the five samples. The void ratio recovery in effective horizontal stress [Formula: see text] = 100 kPa tests is higher than that in the effective vertical stress [Formula: see text] = 100 kPa tests. The samples prepared in the dry state have lower stiffness than those prepared in the moisture state, which is not influenced by the anisotropic stress state. The stiffness anisotropy induced by the sample preparation method is significant under anisotropic consolidation. In [Formula: see text] = 100 kPa tests, the stiffness ratios at the end of the unloading stage are lower than the initial values at the loading stage, which is not found in the [Formula: see text] = 100 kPa tests, meaning that the stress history and stress path could affect the stiffness anisotropy and eliminate the impact of fabric anisotropy.