Anisotropic Stress Conditions Research Articles

Effect of Anisotropic Stress State on Elastic Shear Stiffness of Sand–Silt Mixture

Soil stiffness is a critical property in the evaluation of earth structure deformation and its accurate estimation is an essential part of any geotechnical investigation. In this study, the significant contribution of non-plastic silica fines content in the relationship between small-strain shear modulus and stress anisotropy of silty sands is investigated through a comprehensive set of bender element tests. All the samples of the study were created in the laboratory and tested in a stress path triaxial apparatus applying isotropic and anisotropic stress paths. The mixtures had variable contents of sand and a non-plastic silica silt. Data analysis demonstrated that the exclusive effect of fines content on the changing rate of elastic shear modulus due to anisotropic stress state turns out to be considerable and increasing for all the tested parent sands up to a specific silt portion, about 20%, after which this effect becomes negligible. Using the experimental results, the previously proposed expression for the prediction of the small-strain shear modulus under stress anisotropy for granular materials is extended to sand–silt mixtures. A comparison of the measured against the predicted elastic shear moduli under stress anisotropy, demonstrated that the concept of the skeleton (granular) void ratio could not be applied effectively in the evaluation of the dynamic behaviour of sand–silt mixtures.

Discrete element method analysis of small-strain stiffness under anisotropic stress states

This contribution assesses the influence of stress anisotropy on stiffness using discrete element method (DEM) simulations of true-triaxial tests supplemented with analytical studies. The samples considered comprised of normally consolidated random monodisperse samples. The simulations were carried out at four different mean stress levels; at each stress level, various combinations of the three principal stresses were considered. Stiffness was measured using planar wave propagation simulations. Using regression analysis it is shown that density effects can be considered using void ratio correction factors derived for isotropically compressed samples. However, a void ratio correction factor that considers coordination number is seen to be more marginally appropriate than the conventional form used in geotechnical experimental work. Material exponents that quantify the influence of each stress component on the stiffness were then determined. Analytical expressions derived from effective medium theory are less effective than the correction functions following the form used in the current experimental practice.

Particle breakage in triaxial shear of a coral sand

This paper presents a laboratory experimental study to comprehensively investigate the characteristics of particle breakage using numerous triaxial tests on a coral sand. Coral is a highly crushable granular material which fills the gaps between more crushable and less crushable granular materials. The monotonic tests and cyclic tests were terminated at the designated axial strains and the designated cyclic numbers, respectively. The grain size distributions were measured by sieve analyses of the specimens after the triaxial tests were performed. The relative breakage and relative fractal dimension were used to quantify the particle breakage. The cause of particle breakage that increased with increasing isotropic consolidation stress was shown to be isotropic stress. An almost linear increase in particle breakage in relative breakage was found as axial strain increased, whereas the increase in particle breakage in relative fractal dimension showed upward convexity. More particle breakage occurred in denser samples. During consolidation to the identical mean effective stress, the anisotropic stress state played a bigger role in particle breakage than the isotropic stress state, but during shearing particle breakage occurred more sharply in the triaxial tests with the isotropic consolidation to the higher confining pressure. In the cyclic shearing, the particle breakage in relative breakage and relative fractal dimension increased in upward convexity as the cyclic number increased, but in upward concavity with increasing axial strain. A hyperbolic model was proposed to correlate the relative fractal dimension with the relative breakage for use with both monotonic and cyclic tests. In the monotonic tests, a hyperbolic model was proposed to correlate the particle breakage in relative breakage and relative fractal dimension with the plastic work per unit volume. It is proposed that the loading-mode-induced (i.e., monotonic loading and cyclic loading) different mechanism of particle breakage meant that this model could not be applicable in the cyclic tests. The results suggested that the hyperbolic correlation of the particle breakage in relative fractal dimension and the plastic work per unit volume is the most reliable method of interpreting the energy consumption characteristics of particle breakage. This approach takes the fractal nature of soil into consideration. A microscopic view of particle breakage is also effective for observing the evolution of particle breakage.

A hydromechanical approach for anisotropic elasto-viscoplastic geomaterials: Application to underground excavations in sedimentary rocks

To better describe excavation operations in deep geological formations, several aspects should be considered, especially the material anisotropy, time-dependent behavior, and hydromechanical coupling. In the present paper, a hydromechanical model based on the framework of continuous porous media was proposed. The mechanical elasto-viscoplastic constitutive model accounted for the material elastic and non-elastic anisotropies, using a transformation between the real transversely isotropic material and a fictitious isotropic material. Considering the hydraulic behavior, the permeability was expressed as a function of the volumetric viscoplastic strain. The model was applied to a case study of two tunnel excavations in an anisotropic rock under an initial anisotropic stress state. The results of the numerical simulations using a finite element code were in good agreement with the field convergence and permeability data.

Effects of Particle Grading and Stress State on Strain-Nonlinearity of Shear Modulus and Damping Ratio of Sand Evaluated by Resonant-Column Testing

ABSTRACT The effects of particle grading characteristics, pressure level, and anisotropic stress state in triaxial compression on the decrease in the normalized shear modulus and the increase in the damping ratio of sand when the shear strain amplitude increases from 0.001% to 0.1% were evaluated conducting tests with a fixed-partly fixed resonant column. Specimens having different grading characteristics were reconstituted using crushed rock particles. The results show noticeable effects of the coefficient of uniformity, the mean confining pressure and the stress ratio on the shear strain-nonlinearity of shear modulus and damping ratio over the strain range examined.

Energy-Based Approach to Quantify Cyclic Resistance and Pore Pressure Generation in Anisotropically Consolidated Sand

AbstractIn practical engineering, sand fills or deposits are often under an anisotropic stress condition. Thus, these soil elements sustain an initial static shear stress before being acted upon by...

Large-Scale True Triaxial Apparatus for Geophysical Studies in Fractured Rock

The study of fractured rock masses in the laboratory remains challenging because of the large specimen sizes and bulky loading systems that are required. This article presents the design, structural analysis, and operation of a compact and self-reacting true triaxial device for fractured rock. The frame subjects a 50 cm by 50 cm by 50 cm fractured rock specimen to a maximum stress of 3 MPa along three independent axes. Concurrent measurements include long-wavelength P-wave propagation, passive acoustic emission monitoring, deformations, and thermal measurements. The device can accommodate diverse research, from rock mass properties and geophysical fractured rock characterizations, to coupled hydro-chemo-thermo-mechanical processes, drilling, and grouting. Preliminary wave propagation data gathered under isotropic and anisotropic stress conditions for an assembly of 4,000 rock blocks demonstrate the system’s versatility and provide unprecedented information related to long-wavelength propagation in fractured rock under various stress anisotropies.

Explicit Procedure and Analytical Solution for the Ground Reaction Due to Advance Excavation of a Circular Tunnel in an Anisotropic Stress Field

The convergence–confinement method applied in boring a circular tunnel through a rock-mass assumed to be subject to a non-hydrostatic stress is investigated. The closed-form analytical solutions of the stresses/displacements in the elastic region and plastic region for the ground reaction due to excavation of the tunnel in an anisotropic stress state field are presented in a theoretically consistent way. The explicit procedure realized the analytical solution to an executable computation that can be estimated using a simple spreadsheet. The validity of the procedure for the analytical solution was examined by numerical analysis to investigate the influence of in situ stress ratio on the ground reaction curve, the stress path at the intrados of the tunnel, and the distribution of stresses/displacements on the cross-sections of a circular tunnel. The agreement between the finite element results and the proposed closed-form solutions with the explicit procedure was found to be excellent.

A state-of-the-art anisotropic rock deformation model incorporating the development of mobilised shear strength

Currently rock deformation is estimated using the relationship between the deformation modulus Em and the stress-strain curve. There have been many studies conducted to estimate the value of Em. This Em is basically derived from conducting unconfined compression test, UCS. However, the actual stress condition of the rock in the ground is anisotropic stress condition where the rock mass is subjected to different confining and vertical pressures. In addition, there is still no empirical or semi-empirical framework that has been developed for the prediction of rock stress-strain response under anisotropic stress condition. Arock triaxial machine GCTS Triaxial RTX-3000 has been deployed to obtain the anisotropic stress-strain relationship for weathered granite grade II from Rawang, Selangor sampled at depth of 20 m and subjected to confining pressure of 2 MPa, 7.5 MPa and 14 MPa. The developed mobilised shear strength envelope within the specimen of 50 mm diameter and 100 mm height during the application of the deviator stress is interpreted from the stress-strain curves. These mobilised shear strength envelopes at various axial strains are the intrinsic property and unique for the rock. Once this property has been established then it is being used to predict the stress-strain relationship at any confining pressure. The predicted stress-strain curves are compared against the curves obtained from the tests. A very close prediction is achieved to substantiate the applicability of this rock deformation model. This is a state-of-the art rock deformation theory which characterise the deformation base on the applied load and the developed mobilised shear strength within the rock body.

Estimating Tunnel Strain in the Weak and Schistose Rock Mass Influenced by Stress Anisotropy: An Evaluation Based on Three Tunnel Cases from Nepal

Total plastic deformation in tunnels passing through weak and schistose rock mass consists of both time-independent and time-dependent deformations. The extent of this total deformation is heavily influenced by the rock mass deformability properties and in situ stress condition prevailing in the area. If in situ stress is not isotropic, the deformation magnitude is not only different along the longitudinal alignment but also along the periphery of the tunnel wall. This manuscript first evaluates the long-term plastic deformation records of three tunnel projects from the Nepal Himalaya and identifies interlink between the time-independent and time-dependent deformations using the convergence law proposed by Sulem et al. (Int J Rock Mech Min Sci Geomech 24(3):145–154, 1987a, Int J Rock Mech Min Sci Geomech 24(3):155–164, 1987b). Secondly, the manuscript attempts to establish a correlation between plastic deformations (tunnel strain) and rock mass deformable properties, support pressure and in situ stress conditions. Finally, patterns of time-independent and time-dependent plastic deformations are also evaluated and discussed. The long-term plastic deformation records of 24 tunnel sections representing four different rock types of three different headrace tunnel cases from Nepal Himalaya are extensively used in this endeavor. The authors believe that the proposed findings will be a step further in analysis of plastic deformations in tunnels passing through weak and schistose rock mass and along the anisotropic stress conditions.

Experimental study of the hydro-mechanical response of Opalinus Clay – Part 2: Influence of the stress path on the pore pressure response

Triaxial tests on back-saturated specimens using different controlled stress paths were conducted to study the influence of the stress path on the hydro-mechanical behavior of a clay shale. Opalinus Clay, a clay shale chosen for the disposal of high-level nuclear waste in Switzerland, was utilized. Three different stress paths approximating a tunnel excavation were applied: a two-dimensional stress path with isotropic initial stress conditions (i.e. pure shear compression), a two-dimensional stress path with anisotropic initial stress conditions, and a three-dimensional stress path. The influence of the stress path was investigated with respect to the specimens' geometry. Two end members were tested: specimens where the axial load was applied parallel to bedding (P-specimens) and specimens where the load was applied normal to bedding (S-specimens).Differences in the hydro-mechanical response were identified with respect to the specimens' geometry but also to the stress paths. When subjected to the two-dimensional stress paths, positive excess pore pressure was measured for S-specimens at low differential stresses whereas P-specimens showed negative excess pore pressure. The magnitudes of excess pore pressure were higher for the anisotropic two-dimensional stress path. Dilation associated with yielding was observed for all specimens. The application of the three-dimensional stress path revealed pore pressure responses that were conceptually comparable to the pore pressure response observed in situ. Pore pressure increase in front of the tunnel face can be related to poroelastic response of the rock mass to a change in differential and mean stress. Again, differences between P- and S-specimens were identified. Decrease in pore pressure before the tunnel face can be related to the dilation associated with yielding.No difference in peak strength between P- and S-specimens and the different stress paths was found. Nevertheless, it was shown that the state of failure is affected by the transversal isotropy as S-specimens fail at lower effective stresses compared to P-specimens.

Dynamic properties of calcareous and siliceous sands under isotropic and anisotropic stress conditions

The strain-dependent dynamic properties of sand are generally described by their relative density and mean effective stress, while the contribution of other factors, like soil origin, mineralogy, grain morphology, and initial stress anisotropy, have not been fully recognized. This paper presents the results of an experimental study on the shear modulus and damping ratio of calcareous and siliceous sands of different origins and their identical grain size distribution and stress-density states. Resonant column and cyclic triaxial tests were conducted on reconstituted samples of these two sands obtained from coastal areas. The significance of the initial effective confining pressure and stress anisotropy on the dynamic properties of the sands is evaluated and compared. It is demonstrated that the small-strain shear modulus of the calcareous sand is more affected by an increase in mean effective confining pressure than the siliceous sand. However, the effect of the initial shear on the secant shear modulus of the sands is unique. Based on the test data, a rigorous correction factor is proposed to account for the influence of the initial stress anisotropy on the small-strain shear modulus of the sands. A comparison between the strain-dependent dynamic properties of the calcareous and siliceous sands reveals that the calcareous sand has a higher secant shear modulus, lower damping ratio, and higher linear and volumetric threshold strain. Since the stress-density states and grain size distribution of the two sands were identical in the experiments, the discrepancy in the dynamic properties can be attributed to other factors, including sand origin, grain angularity, mineralogy, and formation processes, which are not commonly taken into account in the current practice.

Experimental Study on Geomechanical Dilation of Oil Sands During Cold–Water Injection

Summary Steam-assisted-gravity-drainage (SAGD) processes become effective only after thermal and hydraulic communication between an injection and production well has been established during the startup operation of the well pair. Conventional steam-circulation startup operations typically take 2 to 3 months to achieve interwell communication, but reductions in the startup time can have a favorable impact on project economics. Enhancement of interwell permeability using fluid-injection (water, or steam, or solvent) strategies to promote geomechanical dilation of the oil sands has been proposed as a startup technique. These fluid-injection processes will produce complex interactions of thermal, geomechanical, and multiple-phase flow behavior in the interwell formation region. Understanding better the role that these interactions play in establishing well-pair communication will provide opportunities to improve SAGD recovery performance. A triaxial experimental program has been designed and executed to explore whether cold-water injection would be sufficient to induce enhancements in effective permeability to water from geomechanical dilation mechanisms. Sample preparation techniques were modified to allow the preparation of reconstituted, very dense water-wet/bitumen sand specimens with different fluid saturations and almost identical porosities. Reclaimed/cleaned tailings sand from oil-sands mining operations was used to prepare artificial specimens, which are representative of McMurray Formation oil sands. A water-wet or bitumen sand core plug was then tested in an environmental chamber to simulate reservoir boundary conditions in terms of stress state, temperature, and pore pressure. A set of experiments was carried out in a triaxial cell under either initial isotropic or initial anisotropic stress state. Experimental results highlight the promising potential to dramatically enhance effective permeability to water and porosity in the dilated zone using cold-water injection at modest levels of stress anisotropy. The experimental results also provide support for the development of numerical models used in predicting SAGD startup performance and proactive utilization of the dilation as startup process for in-situ oil-sands development.

TMR forecasts 5% per annum growth in world iron oxide pigments market

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.

Numerical Simulation of Hydraulic Fracturing in Low-/High-Permeability, Quasi-Brittle and Heterogeneous Rocks

In this study, an elastic-brittle-damage constitutive model was incorporated into the coupled fluid/solid analysis of ABAQUS to iteratively calculate the equilibrium effective stress of Biot’s theory of consolidation. The Young’s modulus, strength and permeability parameter of the material were randomly assigned to the representative volume elements of finite element models following the Weibull distribution function. The hydraulic conductivity of elements was associated with their hydrostatic effective stress and damage level. The steady-state permeability test results for sandstone specimens under different triaxial loading conditions were reproduced by employing the same set of material parameters in coupled transient flow/stress analyses of plane-strain models, thereby indicating the reliability of the numerical model. The influence of heterogeneity on the failure response and the absolute permeability was investigated, and the post-peak permeability was found to decrease with the heterogeneity level in the coupled analysis with transient flow. The proposed model was applied to the plane-strain simulation of the fluid pressurization of a cavity within a large-scale block under different conditions. Regardless of the heterogeneity level, the hydraulically driven fractures propagated perpendicular to the minimum principal far-field stress direction for high-permeability models under anisotropic far-field stress conditions. Scattered damage elements appeared in the models with higher degrees of heterogeneity. The partially saturated areas around propagating fractures were simulated by relating the saturation degree to the negative pore pressure in low-permeability blocks under high pressure. By replicating previously reported trends in the fracture initiation and breakdown pressure for different pressurization rates and hydraulic conductivities, the results showed that the proposed model for hydraulic fracture problems is reliable for a wide range of pressurization rates and permeability conditions.

Effect of Water Imbibition on Fracture Generation in Mancos Shale under Isotropic and Anisotropic Stress Conditions

AbstractDuring hydraulic fracturing in shale oil and gas reservoirs, hydration swelling due to shale water imbibition is believed to create secondary fractures that improve permeability, as observe...

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%.

Onset of suffusion in upward seepage under isotropic and anisotropic stress conditions

Suffusion is one of the mechanisms initiating internal erosion in levees and dams. To estimate the risks of seepage erosion, understanding the mechanism of suffusion under different stress conditions is crucial. With a stress-controlled apparatus, experiments are conduced, in which suffusion is induced by step-wise increasing hydraulic gradients under the isotropic and the anisotropic stress conditions. Based on the results, a low critical hydraulic gradient (LCHG) and a high critical hydraulic gradient (HCHG) are defined, corresponding to the local and the global mobilisations of fine particles, respectively. It is found that the critical hydraulic gradients under isotropic and anisotropic stress conditions are remarkably different. Under the isotropic stresses, the critical hydraulic gradients increase monotonously with the confining stress. Whereas, under the anisotropic stress conditions, the critical hydraulic gradients increase at first and then decrease after reaching a maximum value. A microscopic scale conceptual model attributes this difference to the shear stress, created by the deviatoric stresses. In the end, a formula is proposed to estimate the critical hydraulic gradients, considering the effects of the stress conditions. The accuracy of the formula is verified by comparing the experiment results and the prediction by the formula.

The influence of the anisotropic stress state on the intermediate strain properties of granular material

This paper shows the effect of anisotropic stress state on intermediate strain properties of cylindrical samples containing spherical glass particles. Tests were carried out with the modified resonant column device available at Ruhr-Universität Bochum. Dry samples were subjected to two anisotropic stress states: (a) cell pressure, σ′h, constant and vertical stress, σ′v, increased (stress state GB-I) and (b) σ′v/σ′h equal to 2 (stress state GB-II). The experimental results revealed that the effect of stress state GB-II on the modulus and damping ratio was more significant and obvious than stress state GB-I. The effect of the anisotropic stress state was explained through the impact of confining pressure and anisotropic stress components on the stiffness and damping ratio. The results showed that: (a) G(γ) increased, η(γ) decreased and their strain non-linearity decreased with an increase in the confining pressure component σ′vσ′h; (b) G(γ) decreased, η(γ) increased and their strain non-linearity increased with an increase in the anisotropic stress component, σ′v/σ′h. The analysis of results revealed that reference shear strain was also affected by anisotropic stress state. Therefore, an empirical relationship was developed to predict the reference shear strain, as a function of confining pressure and anisotropic stress components. Additionally, the damping ratio was written as a function of the minimum damping ratio and the reference shear strain.