Principal Stress Ratio Research Articles

The flowability and aerodynamic dispersion of cohesive powders

Abstract The relationship between bulk powder cohesion and ease of powder dispersion is of interest for many applications including particle characterisation and drug delivery from dry powder inhalers. Quasi-static bulk powder testing is used to evaluate powder cohesion and its link with powder dispersion is explored. The flow function of a range of powders (defined as the ratio of major principal stress to unconfined yield strength) has been determined using a shear tester. The dispersion performance of the powders has been analysed using a proprietary dry powder disperser (Scirocco, manufactured by Malvern Instruments, UK). It is shown that as the flow function decreases the dispersion efficiency decreases. For cohesive powders, full dry dispersion is not easily achieved. A quantitative relationship has been established between the unconfined yield strength and the dispersion efficiency for the powders tested. In addition, it is possible to use this relationship to evaluate the performance of different dispersers. In this study, two other dispersers in addition to the Scirocco were evaluated; a right angle disperser, which performed the best, and a co-axial disperser, which had the lowest dispersion efficiency.

Study on Rockmass Deterioration Model Based on the Unified Strength Theory

Strain softening model;Unified strength theory;Rockmass deterioration model;FLAC3D Abstract:Aiming at the problem that traditional elasto-plastic constitutive models have not been successful in predicting the depth and extent of brittle failed of hard rocks under high geo-stress condition, a new rockmass deterioration model(RDM) based on the unified strength theory is put forward in the basis of strain softening model and cohesion weaking and friction strengthening (CWFS)model. In the new model, the influence of intermediatemain stress to characteristic of rockmechanics is considered. Based on the method of lagrangian finite difference, a finite difference format of unified strain- softening elastoplastic model with strength parameters of c and φ is established. The constitutive unified elastoplastic model is imported into FLAC3D using a dynamic-link library file developed by VC++.Based on the new model, the traditional triaxial tests (with different confining pressure) and true triaxial tests (with intermediate principal stress ratio) are simulated in FLAC3D, and the measured data are compared with the results that are are simulated by strain softening model and CWFS model. The analytic results suggest that the rockmass deterioration model based on the twin shear unified strength theory has more strong applicability

Numerical Simulation on Fracture Formation on Surfaces of Bi-Layered Columnar Materials

Parallel fracture formation on surfaces of bi-layered columnar materials like growing tree trunk has been previously studied numerically. In this paper, numerical results of a continuous transition from parallel to polygonal fracture patterns with principal stress ratio provides the clear convincing theoretical explanation for fracture spacing. We perform three-dimensional simulations of fracture growth in a bi-layered columnar model with an embedded heterogeneous layer under inner radial expansion and terminal tension by finite element approach. As a result of this expansion, the bark stretches until it reaches its limit of deformation and cracks. A novel numerical code, 3D Realistic Failure Process Analysis code (abbreviated as RFPA3D) is used to obtain numerical solutions. In this numerical code, the heterogeneity of materials is taken into account by assigning different properties to the individual elements according to statistical distribution function. Elastic-brittle constitutive relation with residual strength for elements and a Mohr-Coulomb criterion with a tensile cut-off are adopted so that the elements may fail either in shear or in tension. The discontinuity feature of the initiated crack is automatically induced by using degraded stiffness approach when the tensile strain of the failed elements reaching a certain value. Numerical results of a continuous transition from parallel to polygonal fracture patterns with principal stress ratio are obtained by varying simulation parameters, the thickness of the material layer. We find that, except for further opening of existing fractures after they are well-developed (saturation), new fractures may also initiate and propagate along the interface between layers, which may serve as another mechanism to accommodate additional strain for fracture saturated layers.

Measurement and the Distribution Law of <i>In Situ</i> Stresses at Deep Depth of Xingcun Coal Mine

Many kinds of in situ stress measurement methods are used nowadays, two most common of which are the overcoring and the hydraulic fracturing methods. In order to study the distribution law of in situ stress field in the deep position of Xingcun coal mine, 4 points of in situ stress measurement were carried out in underground roadways at the -1200 m level adopting the overcoring method. The hollow included technique was used to measure the 4 points of in-situ stress. According to the analysis of the measurement data, the results indicated that: (1) Among the three principal stresses on all measurement points, two principal stresses were nearly horizontal and one was nearly vertical. Furthermore, the maximum horizontal principal stress was more than the vertical principal stress, and the magnitude of vertical stress was equal to the weight of overburden rock mass;(2)The value of the maximum horizontal principal stress reached 52.3 MPa , the directions mainly concentrated on the extension of N42°W – N85°W, and the obliquity mainly concentrated on the extension of -29° – 10°;(3)The ratio of maximum horizontal principal stress to vertical principal stress was 1.42 - 1.64 with an average value of 1.55. The result presented that the in situ stress field in Xingcun coalmine at the depth of -1200m was dominated by tectonic horizontal stress. According to the results above, we gained the in situ stress states and the distribution law in the measured region. At the same time, it can offer reasonable basic parameters for underground roadway layout and support design of Xingcun coalmine.

Dilatancy equation of rockfill material under the true triaxial stress condition

Rockfill material is widely used for construction of high rockfill dam due to its facility, economical cost, high strength and effective aseismatic property. It is provoked profoundly to propose a suitable constitutive model for a better application of this material. The dilatancy equation of rockfill material plays a significant role in the constitutive model. For the sake of simplicity, a dilatancy equation is established by the linear least square method on the basis of the rearranged data of rockfill material in the true triaxial tests. Based on the fact that the rearranged data at different initial confining pressures are aligned in a narrow band, the dilatancy behavior of rockfill material is independent of the initial confining pressure. However, different from the initial confining pressure, both the intermediate principal stress ratio and the specimen density exhibit a remarkable influence on the dilatancy behaviors of rockfill material. Furthermore, the predictions of the proposed dilatancy equation are in a good agreement with the rearranged test data of rockfill material at different specimen densities and stress paths.

The characteristic of in situ stress in outburst area of China

In order to obtain the characteristics of in situ stress field in outburst mining area, using the hollow inclusion (HI) technique to measure the in situ stress of coal and gas outburst mining area. The measurement sites located in northeast, middle and east of china, which include eight mining areas such as Fuxin, Pingdingshan, Hebi and Huainan. Base on the analysis of measurement data from outburst mining area, conclusions could be obtained as follow: (a) major principal stress and minor principal stress is horizontal stress and interim principal stress is vertical stress, and the type of outburst area’s stress field is dynamic stress field; (b) the major principal stress and minor principal stress are higher than other regions and the tectonic stress is outstanding; and (c) the ratio of major principal and vertical stress is decrease with the increase of depth and the type of stress field is likely transfer dynamic to static. Thus, in situ stress plays a key role during the occurring and development of coal and gas outburst, which is an important reason of severe outburst in China.

Experimentation of Steel Fiber Reinforced Concrete Tri-Axial Split Strength under Quasi-Static Loading and High Strain-Rate

A split tensile test methodology has been established for the concrete spheriform specimens with the principal stress ratio of σ1:σ2:σ3=0.24:0.24:-1 in order to study the tensile-tensile-compressive tri-axial strength. Using a Universal Material Testing Machine and Split Hopkinson Pressure Bar, the quasi-static and dynamic spliting tensile tests have been conducted for the concrete spheriform specimens consisting of 1% steel fiber. In the quasi-static test, the average strain rate of the steel fiber reinforced concrete specimens was 8.3×10-5s-1 and the split tensile strength was found to be 0.77MPa, which is consistent with the existing literature. In the high strain rate tests, the average strain rate was 170s-1 and the split tensile strength was found to be 1.01MPa. When compared with the quasi-static testing results, it is seen that the split tensile strength of the steel fiber reinforced concrete increases with increasing strain rate. The split tensile test methodology established in the present paper is simple and inexpensive, while the strength obtained located on the meridian plane of tension and compression, has practical significance.

The Onset of Strain Localization in Cross-Anisotropic Soils Under True Triaxial Condition

ABSTRACT The influences of inherent cross-anisotropy on soil strength on the homogeneous deformation and bifurcation characteristic of the stress-strain relationship are studied. By neglecting the cohesion term and employing an elliptical shape function in Mohr-Coulomb failure criterion, a 3D anisotropic failure criterion is proposed to describe the strength of cross-anisotropic sands under true triaxial conditions. Based on the proposed failure criterion, the influence of the anisotropic parameter on the failure curve on the deviatoric plane and the relationship between the peak friction angle and the intermediate principal stress ratio are obtained. The suitability of the criterion is justified by comparing with a series of true triaxial tests on sands without strain localization. The proposed failure criterion is adopted to build a three dimensional anisotropic elasto-plastic model, which allows the bifurcation analysis to be incorporated with the non-coaxial flow rule for the purpose of studying the onset of strain localization. Compared with the true triaxial tests under several intermediate principal stress ratios conditions in the literature, the proposed model and bifurcation analysis is shown to be capable of predicting the influence of inherent cross-anisotropy on the onset of strain localization.

A new method to calculate the equivalent Mohr–Coulomb friction angle for cohesive and frictional materials

AbstractIn this note, a new method to calculate the equivalent Mohr–Coulomb friction angle ϕ′mc for cohesive and frictional materials is presented. This method makes a transformation from the failure surface for cohesive materials to the failure surface for cohesionless materials and obtains ϕ′mc as well as the principal stress ratio σ′1/σ′3 for cohesionless materials in the transformed space first, then obtains ϕ′mc for cohesive materials by linking σ′1/σ′3 in the transformed space and in the original space. In the application example, an analytical solution of the invariant stress ratio L is derived from the failure function in the transformed space. The influence of the intermediate effective principal stress σ′2 is also demonstrated using the already calculated ϕ′mc. Copyright © 2010 John Wiley & Sons, Ltd.

Distribution Laws of in-Situ Stress in Deep Underground Coal Mines

Abstract With depth and intensity of coal mining increasing, effects of in-situ stress on deformation and failure of the surrounding rock are increasingly growing. Through data independently measured and collected within 600-1500m, this paper summaries distribution laws of in-situ stress in deep underground coal mines of our country, main existing types of in-situ stress and its directional characteristics. Maximum horizontal stress, minimum horizontal stress, vertical stress and lateral pressure ratio variation laws with depth are obtained by using regression analysis. Generally, in-situ stresses increase with depth. With increasing depth the rate of increase in horizontal stresses decreases. A considerable scatter in the in-situ stress test data may be due to distinct differences in both the strength and deformation moduli of strata located in varying geological environments and different coal districts. Two types of stress field distribution have been noted with σHvh (σHmax>σv>σhmin) and σvHh(σv>σHmax>σhmin) found mainly in deep coal mines. The ratio of the maximum horizontal principal stresses to vertical stress is usually between 0.63 and 2.42 in the deep coal districts.

Strength and deformation behaviour of coarse-grained soil by true triaxial tests

In order to investigate the influence of intermediate principal stress on the stress-strain and strength behaviour of a coarse-grained soil, a series of true triaxial tests were performed. The tests were conducted in a recently developed true triaxial apparatus with constant minor principal stress σ3 and constant value of intermediate principal stress ratio b=(σ2−σ3)/(σ1−σ3) (σ1 is the vertical stress, and σ2 is the horizontal stress). It is found that the intermediate principal strain, ɛ2, increases from negative to positive value with the increase of parameter b from zero to unity under a constant minor principal stress. The minor principal strain, ɛ3, is always negative. This implies that the specimen exhibits an evident anisotropy. The relationship between b and friction angle obtained from the tests is different from that predicted by LADE-DUNCAN and MATSUOKA-NAKAI criteria. Based on the test results, an empirical equation of g(b) that is the shape function of the failure surface on π-plane was presented. The proposed equation is verified to be reasonable by comparing the predicted results using the equation with true triaxial test results of soils, such as coarse-grained soils in this study, sands and gravels in other studies.

In-situ stress measurements and stress distribution characteristics in underground coal mines in China

The theory, equipment and method of hydraulic fracturing stress measurement used in underground coal mine roadways in China are presented. A quality assurance system and a quality ranking scheme were developed for hydraulic fracturing stress measurements under specific conditions encountered in Chinese underground coal mines. During the last 8 years, a total of 204 hydraulic fracturing stress measurement campaigns have been carried out in 49 coal mines within 13 Chinese coal districts. The test sites which are located in sub-horizontal, inclined and steeply dipping coal measures range in depth from 69.2 m to 1 283 m. Each stress data record was assigned a quality between A and E according to a proposed data quality ranking scheme. A total of 97 stress data records of A and B quality were used to investigate the distribution characteristics of in-situ stresses within the coal districts. Generally, in-situ stresses increase with depth. In shallow coal mines, the rate of increase in horizontal stresses with depth is greater than the rate of increase of vertical stress. With increasing depth the rate of increase in horizontal stresses decreases. A considerable scatter in the in-situ stress test data may be due to distinct differences in both the strength and deformation moduli of strata located in varying geological environments and different coal districts. In addition, large folds and faults often result in a change in orientation of the maximum horizontal stress, and in distinct changes in stress values. Three types of stress field distribution have been noted with σ H > σ h > σ v found mainly in relatively shallow coal mines (< 400 m), the σ H > σ v > σ h type in moderately deep coal mines (400–600 m), and the σ v > σ H > σ h type predominantly in moderately deep to deep coal mines. The ratio of the maximum horizontal principal stresses to vertical stress is usually between 0.5 and 2.0 in the coal districts.

Critical cyclic stress ratio of undisturbed saturated soft clay in the yangtze estuary under complex stress conditions

There exists a critical cyclic stress ratio when sand or clay is subjected to cyclic loading. It is an index distinguishing stable state or failure state. The soil static and dynamic universal triaxial and torsional shear apparatus developed by Dalian University of Technology in China was employed to perform different types of tests on saturated soft marine clay in the Yangtze estuary. Undisturbed samples were subjected to undrained cyclic vertical and torsional coupling shear and cyclic torsional shear after three-directional anisotropic consolidation with different initial consolidation parameters. The effects of initial orientation angle of major principal stress, initial ratio of deviatoric stress, initial coefficient of intermediate principal stress and stress mode of cyclic shear on the critical cyclic stress ratio were investigated. It is found that the critical cyclic stress ratio decreases significantly with increasing initial orientation angle of major principal stress and initial ratio of deviatoric stress. Compared with the effects of the initial orientation angle of major principal stress and initial ratio of deviatoric stress, the effect of initial coefficient of intermediate principal stress is less evident. Under the same consolidation condition, the critical cyclic stress ratio from the cyclic coupling shear test is lower than that from the cyclic torsional shear test, indicating that the stress mode of cyclic shear has an obvious effect on the critical cyclic stress ratio. The main reason is that the continuous rotation in principal stress directions during cyclic coupling shear damages the original structure of soil more than the cyclic torsional shear does.

Aspects of sand behaviour by modified constant shear drained tests

Constant shear drained tests (CSD) are probably the most suitable to simulate the strength and deformation behaviour of soils in slopes under water infiltration conditions or lateral stress relief. This is significant because soil behaviour following a CSD stress path could differ from that of traditional compression triaxial tests. In this paper, CSD tests on sand following an alternative procedure are presented and discussed. The modified CSD tests were conducted by increasing the pore water pressure at a constant rate from one end of the specimen with water free to drain from the opposite end. Among the results from specimens consolidated at variable initial void ratios and principal stress ratios it was revealed that specimens showed a tendency to dilate even for loose sands; failure was reached at low axial strains; and a pre-failure type of instability could be identified. The modified procedure has the potential to provide new insights into the failure mechanisms of slopes under a water infiltration condition.

Permanent deformation behaviour and model of crushed rock base

This study aims to report on the permanent deformation behaviour of a crushed rock base (CRB) subjected to repeated cyclic loads from repeated load triaxial tests with different stress levels in order to gain more understanding of such materials for Western Australian roads based on mechanistic-empirical pavement design and analysis. As is well known, road surface rutting is generally considered one of the main types of damage in flexible pavements. One factor contributing to the rutting of an asphalt road surface is the excessive deformation of a base course layer. CRB is the commonly used base course material in the Western Australia metropolitan area. In recent times, CRB has not been fully characterised based on fundamental pavement analysis, therefore the behaviour of a plastic deformation response of CRB under service loads is not well understood. In this study, CRB was mechanically investigated and the shakedown concept was utilised to explain its behaviour under cyclic loading conditions, and the limited use of CRB subjected to various degrees of stress conditions was defined. While the plastic shakedown limit of an unbound granular material is known from macro-mechanical observations of its response following the shakedown concept, the limitations of the accumulated plastic deformation in an unbound granular layer causing deterioration in pavements is predictable. The investigation was designed such that compacted CRB samples, at a compaction condition of 100% maximum dry density and 100% optimum moisture content, were subjected to applied load conditions at various stress levels (the ratio of a vertical principal stress, σ1 and a horizontal principal stress, σ3). The limitations on the use of CRB as a base course material will be introduced, as well as its appropriate working stress ranges.

Discrete Element Method Simulations of the Critical State of a Granular Material

The critical state of a granular material was investigated by performing cubical triaxial simulations using the discrete element method. These samples, assemblages of ellipsoids of two kinds, were prepared either by settling the randomly generated particles under gravity or by compressing these particles without gravity. Gravity was set to zero and the samples were further consolidated isotropically. Then, numerical drained tests were carried out until the critical state was reached. Macroscopic and microscopic data in the critical state were examined. The result shows a unique critical state line in the void ratio-mean stress space regardless of the initial conditions. The obliquity (ratio of major and minor principal stresses) as a function of strain is very similar for these samples at different confining pressures. The most interesting result is the linear critical state line in the void ratio-mean stress space. Three microscopic parameters including particle orientation, branch vector, and contact no...

Non‐coaxial elasto‐plasticity model and bifurcation prediction of shear banding in sands

AbstractNumerous constitutive models built on coaxial theory and validated under axi‐symmetric condition often describe the stress–stain relationships and predict the inceptions of shear banding in sands inaccurately under true triaxial condition. By adopting an elaborated Mohr–Coulomb yield function and using non‐coaxial non‐associated flow rule, a 3D non‐coaxial elasto‐plasticity model is proposed and validated by a series of true triaxial tests on loose sands. The bifurcation analysis of true triaxial tests on dense sands predicts the influence of the intermediate principal stress ratio on the onset of shear band accurately. The failure of soils is shown to be related to the formation of shear band under most intermediate principal stress ratio conditions except for those which are close to the axi‐symmetric compression condition. Copyright © 2009 John Wiley &amp; Sons, Ltd.

Experimental Research on Biaxial Compressive Strength of Grouted Concrete Block Masonry

Grouted concrete block masonry (GCBM) exhibits distinct directional properties. In total, 66 tests on 5 kinds of macro-elements were conducted for different principal stress ratios under biaxial compression. The surface of peak strength has been obtained in terms of heterogeneity index and stress ratio. The surface can express the anisotropic nature of GCMB. Comparisons of 5 kinds of macro-element failure curves were made and it has been found that the biaxial compressive strength when the applied stress direction and the material axis coincide is much greater than that of applied stress inclined to material axis. On term of heterogeneity index and stress ratio, the law of strength varying with orientation has been obtained. It shows that the degree of anisotropy is affected by the stress state. Strong behaviour occurs only when one principal stress predominates, that is, the stress ratio value is low, and gradually becomes weaken as the difference between the two principal compression stresses decreases, namely the stress ratio is increasing. Under equal biaxial compression, the different macro-element strengths are nearly equivalent and the masonry seems to be isotropic. The work conducted in this paper provides a basis for further theoretical study on the behaviour of GCBM under biaxial compressive stress.

Creep rupture life and damage evaluation under multiaxial stress state for type 304 stainless steel

The biaxial creep damage of type 304 stainless steel is studied at 973 K. Biaxial tension creep tests were carried out using cruciform specimens under the principal stress ratio ( λ) of 0 ≦ λ ≦ 1, where the principal stress ratio is the ratio of y-directional principal stress to x-directional stress in the gage part of the specimen ( λ = σ y / σ x ). Creep rupture times under biaxial stress conditions were shorter than those in uniaxial conditions at the same von Mises equivalent stress. Earlier void nucleation and faster void growth were observed in creep tests at larger principal stress ratio tests. Creep rupture times in biaxial stress states were discussed in relation to the void observations.

Particle shape effect on macro‐ and micro‐behaviors of monodisperse ellipsoids

AbstractThe microscopic and macroscopic behaviors of assemblages of monodisperse ellipsoids with different particle shapes were studied using the discrete element method. Four samples were created with 1170 identical prolate ellipsoids. The samples were compressed isotropically to 100 kPa. Then triaxial compression tests were carried out to very large strains until the ultimate state was reached. This paper presents typical macroscopic result including stress–strain relationship and volumetric behavior. In addition, the fabric of the samples was examined at the initial state, at the peak shear strength state, and at the ultimate state. We studied the evolution of three vector‐typed micromechanical arguments with strain including the particle orientation, branch vector, and normal contact force. The normal contact force (micromechanical argument) was found to have a direct relationship with the principal stress ratio (macroscopic parameter). The angles between these vectors were also investigated. The maximum angle between vectors is related to particle shape. The results indicate that the distributions and the maximum values of these angles do not change with loading. Copyright © 2008 John Wiley &amp; Sons, Ltd.