Influences of loading direction and intermediate principal stress ratio on the initiation of strain localization in cross-anisotropic sand

Since cross-anisotropic sand behaves differently when the loading direction or the stress state changes, the influences of the loading direction and the intermediate principal stress ratio (b = (σ ₂ ? σ ₃)/(σ ₁ ? σ ₃)) on the initiation of strain localization need study. According to the loading angle (angle between the major principal stress direction and the normal of bedding plane), a 3D non-coaxial non-associated elasto-plasticity hardening model was proposed by modifying Lode angle formulation of the Mohr–Coulomb yield function and the stress–dilatancy function. By using bifurcation analysis, the model was used to predict the initiation of strain localization under plane strain and true triaxial conditions. The predictions of the plane strain tests show that the major principal strain at the bifurcation points increases with the loading angle, while the stress ratio decreases with the loading angle. According to the loading angle and the intermediate principal stress ratio, the true triaxial tests were analyzed in three sectors. The stress–strain behavior and the volumetric strain in each sector can be well captured by the proposed model. Strain localization occurs in most b value conditions in all three sectors except for those which are close to triaxial compression condition (b = 0). The difference between the peak shear strength corresponding to the strain localization and the ultimate shear strength corresponding to plastic limit becomes obvious when the b value is near 0.4. The influence of bifurcation on the shear strength becomes weak when the loading direction changes from perpendicular to the bedding plane to parallel. The bifurcation analysis based on the proposed model gives out major principal strain and peak shear strength at the initiation of strain localization; the given results are consistent with experiments.     

Calcite texture development in experimentally induced ductile shear zones

Specimens of fine grained micritic limestone were deformed in plane strain geometry in pure shear, a combination of simple and pure shear, and in simple shear. Temperatures were 400° C and 500° C, confining pressure was 100 MPa. In the experiments with a simple shear component strain is concentrated and approximately homogeneous in a 2–3 mm wide shear zone. Shear displacement is documented by marker lines and circles. Shear strain γ varies between 0.84 and 1.56. Strain is recorded by flattening of individual grains, defining a foliation normal to the axis of principal finite shortening ε ₁. No twinning is observed on a macroscopic scale. X-ray and neutron diffraction techniques were used to characterize texture before and after deformation. All specimens display strong preferred orientation as documented by 0006, 10¯14 and 11¯220 pole-figures, c axes pole-figures display three maxima in the ε₁–ε₃ plane. If the axes of the strain ellipsoids are used as a coordinate system textures in pure and simple shear are similar but there is considerable monoclinic distortion in simple shear which is attributed to the noncoaxial strain path.     

Shear strengths of sandstone fractures under true triaxial stresses

True triaxial shear tests have been performed to determine the peak shear strengths of tension-induced fractures in three Thai sandstones. A polyaxial load frame is used to apply mutually perpendicular lateral stresses (σ_p and σ_o) to the 76 × 76 × 126 mm rectangular block specimens. The normal to the fracture plane makes an angle of 59.1° with the axial (major principal) stress. Results indicate that the lateral stress that is parallel to the fracture plane (σ_p) can significantly reduce the peak shear strength of the fractures. Under the same normal stress (σ_n) the fractures under high σ_p dilate more than those under low σ_p. According to the Coulomb criterion, the friction angle decreases exponentially with increasing σ_p/σ_o ratio and the cohesion decreases with increasing σ_p. The lateral stress σ_p has insignificant effect on the basic friction angle of the smooth saw-cut surfaces. The fracture shear strengths under σ_p = 0 correlate well with those obtained from the direct shear tests. It is postulated that when the fractures are confined laterally by σ_p, their asperities are strained into the aperture, and are sheared off more easily compared to those under unconfined condition.     

Simple shear of isotropic elasto–plastic soil

The implications of assuming isotropic elasto–plasticity to model the behaviour of soil under simple shear conditions are considered. For small strains, use of such a model implies the following three consequences: (1) strains and strain increments at any stage of shearing may be expressed as the sum of elastic and plastic components; (2) principal directions of stress and of plastic strain increment are collinear; (3) principal directions of stress increment and of elastic strain increment are collinear. These consequences are used in order to establish relationships between the stresses, stress increments and strains which develop in a simple shear test. No additional assumptions with regards the form of the yield function, the flow rule or the hardening function are required for this development. By defining the ratio of the plastic to the total shear strain increment on the horizontal plane (the plane of zero extension) as λ, it is possible to define the horizontal normal stress σ_x in terms of λ and other stresses and strains which are normally known during simple shear loading. As a result, all components of the stress tensor in the simple shear plane may be defined. Results of some direct simple shear tests on soft clay have been interpreted using the model and found to be generally consistent with some of the observations reported in the literature from tests in which boundary stresses were measured.     

Evaluation of Shear Modulus and Damping Ratio of Granular Materials Using Discrete Element Approach

In this paper, an attempt has been made to highlight the influence of different parameters such as number of cycles, confining pressure, void ratio, gradation, initial anisotropy and stress path on the dynamic properties of granular materials using Discrete Element Method (DEM). A series of strain controlled cyclic triaxial numerical simulations using three dimensional DEM have been carried out on an assembly of spheres. Dynamic properties such shear modulus (G) and damping ratio (D) were determined from the typical hysteresis loop obtained during cyclic triaxial test simulation. It has been observed from the test results that the numerical simulation using DEM has captured the variation of dynamic properties over a wide range of shear strain values for different parameters considered for the current investigation. Maximum shear modulus (G _max) was found to be influenced by initial confining pressure, void ratio, gradation and initial anisotropy. Whereas, the damping ratio (D) was found to be influenced by number of cycles, initial confining pressure, gradation and stress path. Further it has been shown that the variation of shear modulus with shear strain can be divided into three distinct zones such as Isotropic Zone (IZ), Anisotropic Zone (AZ) and Stable Anisotropic Zone (SAZ). A drastic reduction of shear modulus with shear strain has been observed in the Anisotropic Zone (AZ). In addition, the results obtained using numerical simulations have been compared with the laboratory experimental values.     

Exploring the influence of loading geometry on the plastic flow properties of geological materials: Results from combined torsion + axial compression tests on calcite rocks

For technical reasons, virtually all plastic deformation experiments on geological materials have been performed in either pure shear or simple shear. These special case loading geometries are rather restrictive for those seeking insight into how microstructure evolves under the more general loading geometries that occur during natural deformation. Moreover, they are insufficient to establish how plastic flow properties might vary with the 3rd invariant of the deviatoric stress tensor (J₃) which describes the stress configuration, and so applications that use those flow properties (e.g. glaciological and geodynamical modelling) may be correspondingly compromised. We describe an inexpensive and relatively straightforward modification to the widely used Paterson rock deformation apparatus that allows torsion experiments to be performed under simultaneously applied axial loads. We illustrate the performance of this modification with the results of combined stress experiments performed on Carrara marble and Solnhofen limestone at 500°–600 °C and confining pressures of 300 MPa. The flow stresses are best described by the Drucker yield function which includes J₃-dependence. However, that J₃-dependence is small. Hence for these initially approximately isotropic calcite rocks, flow stresses are adequately described by the J₃-independent von Mises yield criterion that is widely used in deformation modelling. Loading geometry does, however, have a profound influence on the type and rate of development of crystallographic preferred orientation, and hence of mechanical anisotropy. The apparatus modification extends the range of loading geometries that can be used to investigate microstructural evolution, as well as providing greater scope for determining the shape of the yield surface in plastically anisotropic materials.     

Strain geometry,microstructure and metamorphism in the dextral transpressional Mubarak Shear Belt,Central Eastern Desert,Egypt

Mubarak shear belt provides an opportunity to investigate quantitative finite strain (Rs), proportions of pure shear and simple shear components, sense of shear indicators, subhorizontal to steeply plunging mineral lineations, in a dextral transpressional zone. The structural style of the Mubarak shear belt is consistent with dextral transpression within the Central Eastern Desert where dextral and reverse shear have developed simultaneously with the regional foliation. The high strain zone of the Mubarak shear belt is characterized by steeply dipping foliation with sub-horizontal stretching lineation (simple shear) surrounded by thrust imbrications with slightly plunging stretching lineations. Strain estimates from the Mubarak shear belt are used to determine how pure and simple shear components of deformation are partitioned. The axial ratios in XZ sections range from 1.16 to 2.33 with the maximum stretch, S _X , ranges from 1.06 to 1.48. The minimum stretch, S _Z , ranges from 0.65 to 0.92 indicating a moderate variation in vertical shortening. Volcaniclastic metasediments and metagabbros were subjected to prograde low-grade regional metamorphism in the range of greenschist to lower amphibolite facies (450–650°C at 2–4 kbar). Medium pressure (6–8 kbar at 530°C) was estimated from the high strain zone within the dextral strike-slip shear zones. Retrograde metamorphism occurred at a temperature range of 250–280°C. There is a trend towards decreasing the ratio of 100Mg/(Mg + Fe_tot + Mn) away from the high strain zone of the Mubarak shear belt. Integrated strain and temperature estimates indicate that the simple shear (non-coaxial) components of deformation played a significant role in formation and exhumation of the Mubarak shear belt during the accumulation of finite strain and consequently during progressive transpression and thrusting.     

Interpretation of strains in torsion shear tests

The normal and shear strains obtained in torsion shear tests may be interpreted in two different ways to gain insight into (1) the type of plastic potential to be employed in hardening plasticity stress–strain models, and (2) the coincidence in physical space of the plastic strain increment direction with the stress direction during principal stress rotation. Thirty-four drained torsion shear tests were performed on hollow cylinder specimens of Santa Monica Beach sand deposited by dry pluviation. Twenty-six tests were performed on tall specimens with height of 40 cm, and eight tests were performed on short specimens with height of 25 cm to investigate the effect of the specimen height on the soil behavior in hollow cylinder specimens. Each test was conducted with the same, constant inside and outside confining pressure, σ_r, thus tying the value of b = (σ₂–σ₃)/(σ₁– σ₃) to the inclination, β, of the major principal stress. The directions of strain increment vectors at failure are compared with the directions corresponding to associated and non-associated flow. The relation between the directions of major principal strain increment and major principal stress during rotation of principal stress axes in physical space are investigated.     

Experimental investigation of shear strength of sands with inherent fabric anisotropy

Loading direction-dependent strength of sand has been traditionally characterized in the principal stress space as a direct extension of the Mohr–Coulomb criterion. A recent study found that it is more appropriate to define anisotropic strength of sand on failure/shear planes, but this proposition has only been demonstrated with discrete element method (DEM) simulations. The present study experimentally investigates anisotropic shear strength of sands in this new framework. Three granular materials with distinct grain characteristics ranging from smooth and rounded particles to flaky and angular particles are tested with the bedding plane inclination angle ψ _b varying over the full range of 0°–180°. The main objective is to study how the peak friction angle ? _p of sand is affected by the ψ _b angle and how the ψ _b–? _p relationship evolves with the change of characteristics of constituent sand particles. We find that the general trend of ψ _b–? _p curves for real sands resembles what was predicted by DEM in a previous study, whereas rich anisotropic strength behavior is revealed by the laboratory data. The effects of normal stress and initial density, as well as shear dilation behavior at different shear directions, are also studied.     

Development of quartz c-axis crossed/single girdles under simple-pure shear deformation: Results of visco-plastic self-consistent modeling

Quartz c-axis fabrics are widely used to determine the shear plane in ductile shear zones, based upon an assumption that the shear plane is perpendicular to both the central segment of quartz c-axis crossed girdle and single girdle. In this paper the development of quartz c-axis fabric under simple-pure shear deformation is simulated using the visco-plastic self-consistent (VPSC) model so as to re-examine this assumption. In the case of no or weak dynamic recrystallization, the simulated crossed girdles have a central segment perpendicular or nearly perpendicular to the maximum principal finite strain direction (X) and the XY finite strain plane, and at a variable angle relative to the imposed kinematic framework that is dependent on the modeled flow vorticity and finite strain. These crossed girdles have a symmetrical skeleton with respect to the finite strain axes, regardless of the bulk strain and the kinematic vorticity, and rotate in a way similar to the shear sense with increasing bulk strain ratio. The larger the vorticity number the more asymmetrical their legs tend to be. In the case of strong dynamic recrystallization and large bulk strain, under simple shear the crossed girdle switches into single girdles, sub-perpendicular to the shear plane, by losing the weak legs. The numerical results in our models do not confirm the above-mentioned assumption.     

Neotectonic fault analysis by 2D finite element modeling for studying the Himalayan fold-and-thrust belt in Nepal

This paper examines the neotectonic stress field and faulting in the fold-and-thrust belt of the Nepal Himalaya using the 2D finite element technique, incorporating elastic material behavior under plane strain conditions. Three structural cross-sections (eastern, central and western Nepal), where the Main Himalayan Thrust (MHT) has different geometries, are used for the simulation, because each profile is characterized by different seismicity and neotectonic deformation. A series of numerical models are presented in order to understand the influence of a mid-crustal ramp on the stress field and on neotectonic faulting. Results show that compressive and tensional stress fields are induced to the north and south of the mid-crustal ramp, and consequently normal faults are developed in the thrust sheets moving on the mid-crustal ramp. Since the shear stress accumulation along the northern flat of the MHT is entirely caused by the mid-crustal ramp, this suggests that, as in the past, the MHT will be reactivated in a future large (M_w > 8) earthquake. The simulated fault pattern explains the occurrence of several active faults in the Nepal Himalaya. In all models, the distribution of the horizontal σ₁ (maximum principal stress) is consistent with the sequence of thrusting observed in the fold-and-thrust belt of the Himalaya. Failure elements around the flat–ramp–flat coincide with the microseismic events in the area, which are believed to release elastic stress partly during interseismic periods.     

二维粒状材料双轴压缩试验研究

为了研究粒状材料的各向异性力学行为与细观组构演化之间的关系,采用自主研发的双轴压缩试验系统,以圆形和椭圆形截面的金属棒状材料组成的二维堆积体为试验对象,对不同大主应力方向角?（沉积面与大主应力作用面的夹角）的试样进行了各向等压、常侧向压力、等p剪切3种应力路径试验,并通过分析试样在不同变形阶段的数字照片得到了其细观组构演化规律。发现对于椭圆形截面的试样存在一个卓越剪切方向,随剪应变增大,颗粒长轴呈现出向该方向偏转的趋势,并且在大变形条件下沿该方向形成剪切带;卓越剪切方向与沉积面方向关系不大,而与大主应力作用面方向夹角约为45°+ /2, 为残余内摩擦角;随卓越剪切方向与沉降方向夹角的不同,颗粒偏转程度的不同是导致剪胀特性和峰值强度各向异性的主要原因     

A laboratory study of anisotropic geomaterials incorporating recent micromechanical understanding

This paper presents an experimental investigation revisiting the anisotropic stress–strain–strength behaviour of geomaterials in drained monotonic shear using hollow cylinder apparatus. The test programme has been designed to cover the effect of material anisotropy, preshearing, material density and intermediate principal stress on the behaviour of Leighton Buzzard sand. Experiments have also been performed on glass beads to understand the effect of particle shape. This paper explains phenomenological observations based on recently acquired understanding in micromechanics, with attention focused on strength anisotropy and deformation non-coaxiality, i.e. non-coincidence between the principal stress direction and the principal strain rate direction. The test results demonstrate that the effects of initial anisotropy produced during sample preparation are significant. The stress–strain–strength behaviour of the specimen shows strong dependence on the principal stress direction. Preloading history, material density and particle shape are also found to be influential. In particular, it was found that non-coaxiality is more significant in presheared specimens. The observations on the strength anisotropy and deformation non-coaxiality were explained based on the stress–force–fabric relationship. It was observed that intermediate principal stress parameter b(b = (σ ₂ ? σ ₃)/(σ ₁ ? σ ₃)) has a significant effect on the non-coaxiality of sand. The lower the b-value, the higher the degree of non-coaxiality is induced. Visual inspection of shear band formed at the end of HCA testing has also been presented. The inclinations of the shear bands at different loading directions can be predicted well by taking account of the relative direction of the mobilized planes to the bedding plane.     

A Constitutive Model for Shear Behavior of Rock Joints Based on Three-Dimensional Quantification of Joint Roughness

A new constitutive model to describe the shear behavior of rock joints under constant normal stiffness (CNS) and constant normal load (CNL) conditions is proposed. The model was developed using an empirical approach based on the results of a total of 362 direct shear tests on tensile fractured rock joints and replicas of tensile joints and on a new quantitative roughness parameter. This parameter, the active roughness coefficient C _r, is derived from the features of the effective roughness mobilized at the contact areas during shearing. The model involves a shear strength criterion and the relations between stresses and displacements in the normal and shear directions, where the effects of the boundary conditions and joint properties are considered by the shape indices C _d and C _f. The model can be used to predict the shear behavior under CNS as well as CNL conditions. The shear behavior obtained from the experimental results is generally in good agreement with that estimated by the proposed model, and the effects of joint roughness, initial normal stress, and normal stiffness are reasonably reflected in the model.     

Undrained behaviour of Changi sand in triaxial and plane-strain compression

The results of an experimental study of the undrained behaviour of Changi sand under axisymmetric and plane-strain conditions are presented. K₀ consolidated undrained plane-strain tests and K₀ or isotropically consolidated triaxial tests on very loose and medium dense specimens were conducted. The undrained behaviour of sand at very loose and medium dense states under plane-strain conditions was characterised and compared with that under axisymmetric conditions. It was observed that the undrained behaviour of very loose and medium dense sand under plane strain is similar to that under axisymmetric conditions. However, because of the formation of shear bands in plane-strain tests, the post-peak behaviour of medium dense sand in plane strain is different from that in triaxial tests. It was also established that an instability line for plane-strain conditions can be defined in a way similar to that for axisymmetric conditions. Using the state parameter, a unified relationship between the normalised slope of instability line and the state parameters can be established for both axisymmetric and plane-strain conditions. Using this relationship, the instability conditions established under axisymmetric conditions can be used for plane-strain conditions.     

Load–Deflection response of transversely isotropic piles under lateral loads

In general, pile materials are assumed to be isotropic during the analysis of the load–deflection response of piles under lateral loads. However, commonly used materials such as reinforced concrete and timber as well as potentially promising new pile materials such as fiber reinforced polymers are typically transversely isotropic materials. Experimental studies have shown that transversely isotropic materials have a high ratio of section longitudinal modulus to the section in‐plane shear modulus (E_zz/G_xz) compared to the value for isotropic materials. The high modulus ratio leads to a more significant shear deformation effect in beam bending. To account for the shear deformation effect, the Timoshenko Beam Theory has been adopted in deriving the solutions for the load–deflection response of transversely isotropic piles under lateral loads instead of the Classical (Euler–Bernoulli) Beam Theory. The load–deflection responses depend on the shear effect coefficient, the lateral soil resistance, the embedment ratio, and the boundary conditions. The deflection of the pile, if the shear deformation effect is considered, is always larger than if it is neglected. Copyright © 2000 John Wiley & Sons, Ltd.     

Deformation mechanisms in experimentally deformed single crystals of pyrrhotite,Fe1−xS

Single crystals of hexagonal and monoclinic pyrrhotite, Fe_1?xS, have been experimentally deformed by uniaxial compression at 300 MPa confining pressure, and at a strain rate of 1 × 10^?5 s^?1 in the temperature range from 200° C to 400° C. Very high anisotropy characterizes the mechanical behaviour of the crystal structure. During compression parallel to thec-axis, when no slip system may be activated, the maximum strength is observed. One or two degrees of non-parallelism between [c] and σ₁ results in slip on the basal plane, illustrating the very low resistance of the lattice against shear in this plane. At σ₁ Λ(0001)=45°, i.e. when maximum resolved shear stress is attained on the basal plane, the strength reaches a minimum. Thecritical resolved shear stress (CRSS) increases from less than 4.7 MPa at 400° C to 52 MPa at 200° C. A new slip system, \((10\overline 1 0)\parallel \left\langle {1\overline 2 10} \right\rangle \) prism slip, is described. It is activated only at high angles (>70°) between σ₁ and [c]. The CRSS of the prism slip ranges from 7 MPa (400° C) to 115 MPa (200° C). Twinning on \((10\overline 1 2)[(10\overline 1 2):(1\overline 2 10)]\) , earlier reported by several authors, has been produced only at the highest temperature either as secondary feature during pressure release (compression ‖[c]) or in heterogeneously strained areas (compression ⊥[c]). As twinning and prism slip attain their maximum values of the Schmidt factor under nearly equal stress conditions it is postulated that the former of the two deformation modes has the higher shear resistance.     

Effect of water and stress on the lattice-preferred orientation of olivine

The influence of water and stress on the lattice-preferred orientation (LPO) of olivine aggregates was investigated through large strain, shear deformation experiments at high pressures and temperatures (P = 0.5–2.1 GPa, T = 1470–1570 K) under both water-poor and water-rich conditions. The specimens are hot-pressed synthetic olivine aggregates or single crystals of olivine. Water was supplied to the sample by decomposition of a mixture of talc and brucite. Deformation experiments were conducted up to γ (shear strain)  6 using the Griggs apparatus where water fugacity was up to  13 GPa at the pressure of 2 GPa. The water content in olivine saturated with water increases with increasing pressure and the solubility of water in olivine at P = 0.5–2 GPa was  400–1200 ppm H/Si. Several new types of LPO in olivine are found depending on water content and stress. Samples deformed in water-poor conditions show a conventional LPO of olivine where the olivine [100] axis is subparallel to the shear direction, the (010) plane subparallel to the shear plane (type-A). However, we identified three new types (type-B, C, and E) of LPO of olivine depending on the water content and stress. The type-B LPO of olivine which was found at relatively high stress and/or under moderate to high water content conditions is characterized by the olivine [001] axis subparallel to the shear direction, the (010) plane subparallel to the shear plane. The type-C LPO which was found at low stress and under water-rich conditions is characterized by the olivine [001] axis subparallel to the shear direction, the (100) plane subparallel to the shear plane. The type-E LPO which was found under low stress and moderate water content is characterized by the olivine [100] axis subparallel to the shear direction, the (001) plane subparallel to the shear plane. Observations by transmission electron microscopy (TEM) and scanning electron microscopy (SEM) show that the dislocations in water-poor samples (type-A) are curved and both b =  [100] and b = [001] dislocations have a similar population. Numerous subgrains are seen in water-poor samples in backscattered electron images. In contrast, water-rich samples (both type-B and type-C) contain mostly b = [001] dislocations and dislocations are straight and sub-grain boundaries are rare compared to those in water-poor samples. These observations suggest that (1) dominant slip systems in olivine change with water fugacity (and stress) and (2) grain boundary migration is enhanced in the presence of water. Seismic anisotropy corresponding to the fabrics under water-rich condition is significantly different from that under water-poor condition. Consequently, the relationship between seismic anisotropy and flow geometry in water-rich regions is expected to be different from that in water-poor regions in which type-A fabric dominates (i.e., the lithosphere). A few cases are discussed including anisotropy in the subduction zone and in the deep upper mantle.     

结构性黄土的剪切带及强度特性的真三轴试验研究

采用西安理工大学自主研发的真三轴仪,对西安白鹿原黄土进行了不同中主应力比值、不同固结围压的试验研究,探讨了黄土剪切带形成与峰值强度、中主应变与大主应变关系曲线、体应变与大主应变关系曲线特征点之间的联系以及子午平面、 平面上的强度变化规律。分析了真三轴应力条件下黄土强度变形规律和试样剪切带破坏模式和黄土在复杂应力状态下剪切带形成的判断依据和原因,研究表明,真三轴压缩原状黄土具有明显的剪切带,围压和中主应力比值较小时表现为软化,围压和中主应力比值较大时则表现为硬化;中主应变、体应变与大主应变关系曲线较为一致的转折点反映了土变形性状发生变化;与中主应变方向一致的剪切带两侧土结构块体产生相对滑移,剪切带开始形成和发展;土应变曲线的转折点可以作为土固结结构内剪切带形成的判断依据;子午平面上强度线呈线性变化规律, 平面上呈曲边三角形非线性变化规律,并且与 -SMP强度准则较为接近。不同应力条件下剪切带变化复杂的破坏模式与黄土原生的结构特征和加载共同作用的变化有密切联系。