Effect Of Stress Anisotropy Research Articles

Development of a dynamic hollow cylinder apparatus for investigating the cyclic response of unsaturated soils subjected to stress anisotropy

The construction of most geo-structures like earthfill dams, roads, highways, embankments, and airport runways deals with the compaction of unsaturated soils under anisotropic cyclic/dynamic loadings. Many of these partially saturated geo-structures also experience three-dimensional dynamic loadings during service life. This paper presents a new hollow cylinder apparatus developed for the investigation of the cyclic response of unsaturated soils subjected to stress anisotropy. The device is unique as it enables, for the first time, studying the combined effects of stress anisotropy (effects of both parameters α and b) and the degree of saturation on the dynamic properties of unsaturated soils, the aspects that cannot be thoroughly captured using existing soil laboratory testing equipment. It allows independent control of the magnitudes and rotations of the principal stresses and measuring strains as well as control/measurement of pore water and pore air pressures in the unsaturated soil samples. The paper describes the main challenges and the adopted solutions for the development of the hollow cylinder apparatus, including the complexities associated with the non-uniformity of water content in the sample height and the measurement of the sample volume change. The relations for determining the effective stresses and strains in the unsaturated soil samples are also derived. The results of several dynamic tests on unsaturated sand over a wide range of shear strains are presented to demonstrate the capabilities of the apparatus.

Effect of stress anisotropy on deformation and particle breakage of silica sand at high-pressure compression tests

The effect of stress anisotropy on the compression behavior and particle breakage of silica sands was investigated by comparing the results from a series of high-pressure compression tests with different stress ratios (confining stress/axial stress). It was found that the stress at the yield point reduces with decreasing stress ratio, indicating that the onset of particle breakage occurs at lower mean stress for specimens with a lower stress ratio. Stress anisotropy results in more particle breakage on account of the existence of deviatoric stress. A good prediction of the relative breakage was proposed considering the influences of stress level and stress path. The relative breakage shows a linear relationship with the volumetric strain regardless of the stress path. The fractal dimension increases nonlinearly with increasing normalized mean stress/relative breakage. The parallel study on the micro-mechanical behavior of silica sands was performed using a novel miniature triaxial apparatus and X-ray micro-computed tomography (μCT). It was observed that particle breakage results in a fractal condition in silica sands with a radius below 0.4 mm. The high-pressure compression tests obtained a linear relationship between the fractal dimension and particle content for particle radius less than 0.4 mm. A hyperbolic model was also proposed to describe the relationship between the relative breakage and input work per unit volume regardless of stress path.

Effect of Stress Anisotropy on the Efficiency of Large-Scale Destress Blasting

Large-scale panel destressing is a rockburst control technique that is used to create a stress shadow in the ore pillar to be mined. The technique aims to reduce the pillar burst proneness by deviating the major induced principal stresses away from the concerned zone of interest. The destress panels, situated in the pillar hanging wall, are choke-blasted with high explosive energy density, and the blast-induced damage in the panel is accompanied by stress dissipation and stiffness reduction due to fragmentation in the panel. These two effects are traditionally modeled holistically with stiffness and stress reduction factors α and β, respectively, applied to the destressed zone. This paper focuses on the interpretation of Phase 3 destress blasting results at Copper Cliff Mine (CCM) where a stress increase (rather than decrease) was detected in the ore pillar crown, while a stress decrease was recorded in the ore pillar sill (as expected). It is hypothesized that high mining-induced stress anisotropy in the pillar crown caused blast-induced fractures to propagate in the orientation of the major principal stress, a condition that would hinder the destressing effect in that orientation. To verify the hypothesis, a series of panel anisotropic rock fragmentation and stress dissipation factors are iteratively tested in a 3-dimensional back analysis of the Phase 3 destress blast. The analysis takes into consideration the stope extraction schedule per the mine plan to better replicate the mining-induced stress condition in the panel and the ore pillar. The results show good agreement with stress measurements taken in situ using borehole stress cells installed in the ore pillar prior to destressing. The paper discusses the implications of preferential fracture propagation orientation and how it might affect the efficiency of destress blasting.

Experimental study of stress anisotropy and noncoaxiality of dense sand subjected to monotonic and cyclic loading

Abstract The noncoaxiality of the principal stress direction and plastic principal strain increment has been broadly recognized as an influencing parameter for design of soil structures. Here we performed a series of systematic hollow cylinder experiments to study the effects of stress anisotropy on the noncoaxiality of dense Babolsar and Toyoura sands. A total of 25 undrained torsional shear tests were carried out under constant mean confining pressure, and fixed principal stress directions, α. We investigated the stress-strain behavior of dense sands for different α-directions, and cyclic stress ratio, CSR, under monotonic and cyclic loading conditions. The results show that the noncoaxiality value depends on the CSR, the level of plastic strain, and α-direction. Independent of the principal stress direction, maximum noncoaxiality value was observed at peak shear strength when there is most interlock between sand particles. Minimum noncoaxiality was recorded in α = 45° tests, in which the direction of maximum shear stress coincided with the horizontal bedding plane direction (weakest plane).

Parametric study of fracture interference effects on fracture geometry for wellbore strengthening

ABSTRACT As one of the most widely used preventive treatment of lost circulation, wellbore strengthening techniques need to be further investigated to improve its efficiency. It is crucial to accurately predict the dynamic propagation of fractures for wellbore strengthening, while most of the numerical simulations neglect the distortion of fracture trajectory affected by fracture interference. Thus, a fully coupled poroelastic model is established by using the extended finite element method (XFEM) – based cohesive zone method (CZM) to investigate the effect of fracture interference. The rock deformation, seepage flow of pore fluid, fluid flow of fracture and leak-off of drilling fluid are coupled by the model. The sensitivity analysis is studied by capturing the change of fracture length, width and deviation angle. The results show that the distortion of the fracture trajectory and the closure extent of fracture surface after bridging can be controlled more easily with lower injection rate and larger spacing. A proper viscosity can balance between the distortion of the fracture trajectory and the tendency of fracture reopening after bridging. The anisotropic stress mainly affects the wellbore strengthening by influencing the propagation direction. Adjusting the inclination and azimuth of the wellbore to increase the effect of stress anisotropy can reduce the effect of stress shadow.

Exploring the influence of rock inherent heterogeneity and grain size on hydraulic fracturing using discrete element modeling

The effects of rock inherent heterogeneity and grain size on hydraulic fracture initiation and propagation for different propagation regimes are investigated through two dimensional discrete element modeling. Random particle assembly is used to mimic rock inherent heterogeneity in the numerical model while regular particle assembly is used as the reference. The rock inherent heterogeneity mainly affects the hydraulic fracture net pressure in the viscosity dominated regime and the effect is more profound in the toughness dominated regime. In the toughness dominated regime, in addition to the increase of net pressure relative to the regular particle sample, the hydraulic fracture profiles in the random particle sample also show larger tortuosity and asymmetry caused by the local heterogeneity, and the fracture growth of one of the wings can be temporarily arrested. Numerical simulations show that the effective toughness of the random particle sample is larger than that of the regular particle sample. This is caused by tortuosity, in which case the net pressure in the random particle sample is also affected by the local geometrical arrangements of the particles. Also, the apparent toughness is influenced by the magnitude of initial stress, which comes in addition to the tensile strength of the contact bond and the particle radius. The effect of stress anisotropy has limited effect on the hydraulic fracture propagation for both the viscosity and toughness dominated regimes.

An implicit joint-continuum model for the hydro-mechanical analysis of fractured rock masses

Fractures control the hydro-mechanical behavior of rock masses. Explicit numerical analyses require detailed information on fracture properties, spacing, and orientation. This paper advances an implicit joint-continuum model for the coupled hydro-mechanical analysis of regularly spaced-persistent fractured rock masses. The stiffness tensor combines the compliance of each fracture set and the intact rock; similarly, the permeability tensor adds the fluid transport through fractures and the matrix. The fully coupled hydro-mechanical analysis incorporates the rock mass stiffness and permeability tensors, and satisfies force equilibrium and macroscopic fluid mass balance. We implement the implicit joint-continuum model within a finite element framework and verify the numerical simulator against closed-form solutions for simple boundary conditions. The application of the code to the hydraulic stimulation of a fractured rock mass shows the effect of stress anisotropy and fracture orientation on the development of open-mode discontinuities (i.e., hydraulic fracture) and hydro-shearing. The implicit joint-continuum model can be readily extended to more complex coupled processes, including thermal and chemical phenomena.

Experimental study of the effect of stress anisotropy on fracture propagation in Eagle Ford shale under water imbibition

Hydration swelling due to the rock-water reaction may create induced fractures to enhance hydrocarbon recovery in shale reservoirs. This paper investigates the effects of anisotropic stress and hydration swelling on fracture generation and propagation in Eagle Ford shale. To explore whether fractures can be induced by hydration under anisotropic stress conditions, sequential imbibition tests and water imbibition tests were conducted. CT scanning was used to obtain cross-sectional images of shale cores with different axial and confining pressures. The sequential imbibition tests indicated that hydration swelling might induce fractures, and more fractures were generated under water imbibition than oil imbibition. This finding shows that hydration swelling is beneficial to fracture generation under anisotropic compressive stress, which challenges the believe that hydration swelling may cause formation damage. Experiments also show that more induced fractures were generated in the samples under anisotropic stress conditions than under isotropic conditions. The greater the stress anisotropy, the larger the induced fracture geometry is. Beddings and natural fractures can facilitate fracture initiation and propagation.

Analytical solution for tunnels not aligned with geostatic principal stress directions

It is well-known that rock masses may present marked stress anisotropy. However, most of the tunnel analyses (numerical and analytical) assume the tunnel axis aligned with one of the principal stress directions. When this is not the case, axial shear stresses appear, which then are neglected, as it is done in all analytical solutions available for tunnel analysis. Existing solutions may consider advanced nonlinear ground behavior (i.e. elastic-brittle-plastic with e.g. Hoek and Brown failure criteria), linear-elastic ground with transversely anisotropic properties, seismic loading, groundwater and support, etc., but all consider that the axis of the tunnel aligns with one of the principal far-field stresses. This is also what is generally assumed when conducting more sophisticated, three dimensional numerical analyses. In this paper, an analytical solution to calculate the stresses and displacements induced by far-field axial shear stresses is presented. Solutions for supported and unsupported tunnels are provided. The proposed analytical solution can be combined with the classical Kirsch and Einstein-Schwartz solutions to determine the complete stress and displacement fields around the tunnel. Further, the effects of stress anisotropy are discussed.

Localized stress field modelling around fractures using three-dimensional discrete element method

Understanding of field stress condition in fractured rock mass is required to investigate stability of underground excavations. To analyze stress perturbation in fractured rock mass, a regional model is generated using a DEM based code, 3DEC.Three major steep faults were considered in the model. The regional model then was used to estimate stresses on the boundaries of smaller descriptive model termed as the base model. Stresses were observed to vary in magnitude at the intersection of discontinuity sets and stress drop was observed at the discontinuity. In addition, stress tensors in the model were observed to rotate parallel to the discontinuity. A vertical borehole in base model revealed that high stresses concentrated along discontinuities may result in forming yield zones around the borehole. Furthermore, the base mode was subjected to strength and stress anisotropy analysis. Effect of stress anisotropy on stress perturbation was significant, whereas, stress values slightly changed by strength anisotropy. In both cases, due to the effect of discontinuities the induced stress field was non-linear and fluctuating. Effect of stress anisotropy on stress perturbation found to be more significant for the maximum principal stress as compare with the minimum principal stress.

Thermal shale fracturing simulation using the Cohesive Zone Method (CZM)

Extensive research has been conducted over the past two decades to improve hydraulic fracturing methods used for hydrocarbon recovery from tight reservoir rocks such as shales. Our focus in this paper is on thermal fracturing of such tight rocks to enhance hydraulic fracturing efficiency. Thermal fracturing is effective in generating small fractures in the near-wellbore zone - or in the vicinity of natural or induced fractures - that may act as initiation points for larger fractures. Previous analytical and numerical results indicate that thermal fracturing in tight rock significantly enhances rock permeability, thereby enhancing hydrocarbon recovery. Here, we present a more powerful way of simulating the initiation and propagation of thermally induced fractures in tight formations using the Cohesive Zone Method (CZM). The advantages of CZM are: 1) CZM simulation is fast compared to similar models which are based on the spring-mass particle method or Discrete Element Method (DEM); 2) unlike DEM, rock material complexities such as scale-dependent failure behavior can be incorporated in a CZM simulation; 3) CZM is capable of predicting the extent of fracture propagation in rock, which is more difficult to determine in a classic finite element approach. We demonstrate that CZM delivers results for the challenging fracture propagation problem of similar accuracy to the eXtended Finite Element Method (XFEM) while reducing complexity and computational effort. Simulation results for thermal fracturing in the near-wellbore zone show the effect of stress anisotropy in fracture propagation in the direction of the maximum horizontal stress. It is shown that CZM can be used to readily obtain the extent and the pattern of induced thermal fractures.

Influence of stress anisotropy on small-strain stiffness of reinforced sand with polypropylene fibres

This paper reports on the small-strain stiffness (Gmax) of a well graded crushed rock reinforced with polypropylene fibres. The experimental study was conducted on twenty-five fully saturated samples subjected to bender element tests. The contents of fibre used were equal to 0%, 0.5%, 1.0%, 1.5% and 2.0%. The bender elements were inserted in a resonant column and a stress path triaxial apparatus accommodating samples of 70 and 50 mm in diameter, respectively, with a ratio of length to diameter equal to 2:1. The samples were initially consolidated isotropically to pressures of 50, 100, 400 and 700 kPa. At a given isotropic pressure, Gmax measurements were conducted increasing the deviatoric compressive stress (q) and keeping a constant mean effective confining pressure (p'). This allowed the study of the effect of stress anisotropy, expressed with the ratio (q/p'), and the role of fibre inclusion and content on Gmax of the reinforced samples under variable mean effective confining pressures. The data were analysed by means of the normalized shear modulus, Gmax,normalized, against the stress ratio, where Gmax,normalized expressed the increase of the small-strain shear modulus under an anisotropic stress state with respect to the corresponding modulus under an isotropic stress state. For a given confining pressure, the results showed a clear increase of Gmax,normalized with increased content of fibres which implied that the sensitivity of modulus to the stress anisotropy became more pronounced for greater contents of fibres. However, this influence of fibre inclusion and content on the small-strain stiffness of the samples was found weaker at greater magnitudes of p'.

A note on influence of stress anisotropy on the Poisson's ratio of dry sand

In this study, extender and bender element tests were conducted investigating the small-strain Poisson's ratio of variable sands, with a focus on the effect of stress anisotropy in order to quantify the sensitivity of Poisson's ratio to the applied deviatoric stress. Four different uniform sands were tested, including a biogenic sand, a crushed rock and two natural sands, covering a wide range of particle shapes. From these sands, eleven samples were prepared in the laboratory and were tested under variable stress paths, maintaining a constant mean effective pressure while increasing the deviatoric compressive load. Under the application of these given stress paths, the data analysis indicated that the sensitivity of Poisson's ratio to the stress ratio was more pronounced for sands with irregularly shaped particles in comparison to sands with fairly rounded and spherical grains. For sands with very irregularly shaped particles, the increase of Poisson's ratio from the isotropic to the anisotropic stress state reached 50%, while this increase for natural sands with fairly rounded particles was in the order of 20%.

Behavior of carbon fiber-reinforced recycled concrete aggregate

The behavior of a uniform recycled concrete aggregate (RCA) reinforced with carbon fibers is examined in the study. Six specimens with percentages of fiber from 0% to 2% were prepared in a triaxial apparatus and tested using bender elements. These specimens followed an anisotropic stress path after their initial consolidation at isotropic pressures of 100 or 500 kPa. Additionally, 19 specimens with fiber content equal to 0%, 1% and 2% were prepared in the triaxial apparatus and their large deformation behavior was quantified. The results indicated that at very small strains, the shear modulus of the fiber-reinforced samples was reduced in comparison to the unreinforced RCA samples. In terms of the effect of stress anisotropy on the shear modulus of the samples, firm conclusions could not be drawn with respect to the role of fiber content from this limited testing series. At larger strains, the reinforced and unreinforced samples showed relatively similar stress–strain response and volumetric behavior, with very similar critical state parameters in terms of (λ) and (Γ). The reinforcement with fibers increased the critical state angle of shear strength from about 33.5 to about 36.0° as the content of fibers increased from 0% to 2%.

Experimental investigation of primary-wave velocities and constrained moduli of quartz sand subjected to extender element tests and stress anisotropy

The measurement of primary wave velocities (Vp) of geo-materials is an essential step for the geophysical and dynamic characterization of sediments. Advances in experimentation have established in recent years the use of the extender element test method in laboratory research and practice. This method is applicable for the measurement of Vp of geo-materials applying a high-frequency pulse excitation, typically between 5 and 20 kHz. In the study, extender elements inserted in a stress path triaxial apparatus were used for the measurement of primary-wave velocities of quartz sands of variable grain morphologies. During the dynamic tests, the samples were subjected to a deviatoric compressive load, which allowed the study of the effect of stress anisotropy, expressed through the stress ratio, on Vp. To overcome difficulties of poor signal output of P-waves, which may occur when the sample is fully saturated, the samples were prepared and tested in a dry state. Measurements of sample volumetric strains were conducted from local strain sensor attached to the sample which captured radial deformations during the isotropic and anisotropic stress paths and a vertically positioned LVDT which captured the axial strains of the samples. Accordingly, based on the measured P-wave velocities and the density of the samples, the constrained modulus (Mmax) was quantified. The results indicated that for a given mean effective confining pressure, the sensitivity of Vp and Mmax to the magnitude of the applied stress ratio was controlled, markedly, by the morphology of the grains; for sands of fairly rounded and spherical grains, this effect was relatively small, but for sands of irregular in shape grains, the stress ratio affected markedly the behavior of the samples.

Dynamic characterization of a biogenic sand with a resonant column of fixed-partly fixed boundary conditions

The dynamic properties of sands, including the small-strain shear modulus (Gmax) and the small-to-medium strain shear modulus (G) and shear damping (Ds) have been examined extensively in the literature. However, most works published over the past decades have focused on the behavior of soils subjected to isotropic stress paths. In the present study, the dynamic properties of a biogenic sand with origin from Western Australia were examined in the laboratory using a resonant column of fixed-partly fixed boundary conditions. This configuration allows the study of the small-strain shear modulus, the strain-dependent modulus and shear damping of samples subjected to stress anisotropy, which stress conditions may represent more effectively the in-situ state of a soil. For this purpose, proper calibrations of the resonant column were carried out in order to capture the rotational inertia of the apparatus in a wide range of cyclic frequencies covering, in this way, typical resonant frequencies of real soil samples. Basic geotechnical characterization of the biogenic sand was carried out quantifying the shape of the grains and conducting a series of monotonic triaxial tests capturing the peak and critical state friction angles. The dynamic test results indicated a more pronounced effect of the stress anisotropy on Gmax of the biogenic sand in comparison to the corresponding effect on quartz sands reported in the literature. For the limited set of experiments conducted in the study, the effect of stress anisotropy was found less pronounced for the small-to-medium strain shear modulus and shear damping, even though the results indicated a marked drop of shear damping at small strains when the samples were subjected to a deviatoric compressive load.

Ferromagnetic resonance in exchange coupled bilayer films with stress anisotropy

Ferromagnetic resonance frequency and magnetic susceptibility in ferromagnetic/antiferromagnetic bilayer films with stress anisotropy are investigated using a ferromagnetic resonance method. In-plane anisotropy, weak and strong perpendicular anisotropy are taken into account in this theoretical model. The effect of stress anisotropy has been investigated; it was found that the resonance frequencies all increase for in-plane and weak perpendicular anisotropy, as the stress anisotropy field increases. In addition, the stress anisotropy field does not obviously affect the magnetic susceptibility for saturation field.

Effect of stress anisotropy on the pore water pressure generation of loose sand

Effect of stress anisotropy on the pore water pressure generation of loose sand

Assessment of the effect of stress anisotropy on tunnel deformation in the Kaligandaki project in the Nepal Himalaya

Most of the analytical approaches that are available for assessing plastic deformation in tunnels that pass through weak, schistose, and foliated rock masses assume an isostatic stress state. However, in situ stresses are seldom isostatic in a tunnel passing through a varying rock overburden. The work reported here analyzed the effect of stress anisotropy on the magnitude of plastic deformation in the Kaligandaki headrace tunnel in the Nepal Himalaya, where extensive deformation monitoring plans were implemented during tunnel excavation. Recorded tunnel deformation, mapped geological information, lab-tested rock mechanical properties, and an approach reported by Hoek and Marinos (Tunn Tunn Int 32(11):45–51, 2000) were used to estimate rock mass parameters. The convergence confinement method (Carranza-Torres and Fairhurst, Tunn Undergr Space Technol 15(2):187–213, 2000) was used to assess the effective support pressure for the known tunnel deformations of 77 tunnel sections assuming an isostatic stress state. Numerical modeling was carried out to assess the effect of stress anisotropy on tunnel deformation. The analysis indicated that CCM overestimates the magnitude of tunnel deformation. This may be explained by the fact that CCM applies for a circular tunnel in the isostatic stress state, which is seldom the case. Actual measured deformations were calibrated using numerical modeling to develop equations that may be used to estimate the plastic deformation of tunnels that are subjected to stress anisotropy. However, it should be emphasized that the proposed equations are based on the data records for a single tunnel, so further validation will be needed using data records of other well-monitored tunnel projects.

Simulation of yielding and stress–stain behavior of shanghai soft clay

In this paper, a simple bounding surface plasticity model is used to reproduce the yielding and stress–strain behavior of the structured soft clay found at Shanghai of China. A series of undrained triaxial tests and drained stress probe tests under isotropic and anisotropic consolidation modes were performed on undisturbed samples of Shanghai soft clay to study the yielding characteristics. The degradation of the clay structure is modeled with an internal variable that allows the size of the bounding surface to decay with accumulated plastic strain. An anisotropic tensor and rotational hardening law are introduced to reflect the initial anisotropy and the evolution of anisotropy. Combined with the isotropic hardening rule, the rotational hardening rule and the degradation law are incorporated into the bounding surface formulation with an associated flow rule. Validity of the model is verified by the undrained isotropic and anisotropic triaxial test and drained stress probe test results for Shanghai soft clay. The effects of stress anisotropy and loss of structure are well captured by the model.