Intermediate Principal Stress Ratio Research Articles

Micromechanical modeling of hollow cylinder torsional shear test on sand using discrete element method

Previous studies on the hollow cylinder torsional shear test (HCTST) have mainly focused on the macroscopic behavior, while the micromechanical responses in soil specimens with shaped particles have rarely been investigated. This paper develops a numerical model of the HCTST using the discrete element method (DEM). The method of bonded spheres in a hexagonal arrangement is proposed to generate flexible boundaries that can achieve real-time adjustment of the internal and external cell pressures and capture the inhomogeneous deformation in the radial direction during shearing. Representative angular particles are selected from Toyoura sand and reproduced in this model to approximate real sand particles. The model is then validated by comparing numerical and experimental results of HCTSTs on Toyoura sand with different major principal stress directions. Next, a series of HCTSTs with different combinations of major principal stress direction (α) and intermediate principal stress ratio (b) is simulated to quantitatively characterize the sand behavior under different shear conditions. The results show that the shaped particles are horizontally distributed before shearing, and the initial anisotropic packing structure further results in different stress–strain curves in cases with different α and b values. The distribution of force chains is affected by both α and b during the shear process, together with the formation of the shear bands in different patterns. The contact normal anisotropy and contact force anisotropy show different evolution patterns when either α or b varies, resulting in the differences in the non-coaxiality and other macroscopic responses. This study improves the understanding of the macroscopic response of sand from a microscopic perspective and provides valuable insights for the constitutive modeling of sand.

Experimental study on strain accumulation characteristics of saturated remolded loess under pure rotation of the principal stress axis

The study conducted a pure rotation test of 720° for saturated remolded Q2 loess under principal stress axis (PSA) rotation when deviatoric stress and the intermediate principal stress ratio are different, also paying attention to examining the changes of strain accumulation and pore pressure of such loess. According to the test, as the PSA rotates continuously, the pore water pressure exhibited by saturated remolded loess presents a normal cyclic accumulation elevation, and under the same deviatoric stress conditions, the pore water pressure accumulation trend of different principal stress ratios is the same; however, the magnitude is different. The increment of pore water pressure becomes smaller as the number of cycles increases. When the deviatoric stress level is low, the material hardening is in a cyclic stable state, the strain component remains stable with the continuous rotation of the PSA, and the strain path area is reduced, together with a stable final size. In case of higher deviatoric stress, the material strength cycle becomes weaker and the strain component accumulates slowly as the PSA (the spiral line of the strain path) continuously rotates in the γzθ−(ϵz−ϵθ) plane, and gradually expands until failure. The increased intermediate principal stress is accompanied by accelerated strain development speed and advanced failure.

Influence of intermediate principal stress ratio on strength and deformation characteristics of frozen sandy soil under different moisture contents

Frozen ground often contain non-uniform moisture content and are under true triaxial stress state and their practical engineering application are still explored. The present study is carried out to investigate the strength and deformation characteristics of frozen soil with different moisture contents under true triaxial stress state conditions. A series of true triaxial tests were conducted on frozen soil specimens having constant minimum principal stress (σ3) and constant intermediate principal stress ratio (b). The experimental test results showed that the stress-strain curves represent the strain-hardening characteristics under different test conditions. The intermediate principal stress ratio (b) has a dual effect of strengthening and weakening on the strength of frozen sandy soil. When 0 ≤ b ≤ 0.5, the strengthening effect was found to be dominant in the frozen soil specimen, whereas, the weakening effect was dominant when 0.5 < b ≤ 1. The strength of frozen soil under true triaxial stress state is 8.18% to 36.33% higher under different water content conditions, compared to that under generalized triaxial compression stress state. The difference in deformation between the direction of the intermediate principal stress and the minimum principal stress increased with the increment in the intermediate principal stress ratio value. The volumetric strain in the soil sample initially exhibited the characteristics of shear contraction and then shear dilation.

Effect of principal stress direction on the instability of sand under the constant shear drained stress path

Results of torsional shear hollow cylinder (TSHC) tests carried out on a reconstituted sand maintaining a constant direction of major principal stress relative to the vertical axis (α) and intermediate principal stress ratio (b) during shearing are presented. Tests were undertaken following the constant shear drained (CSD) stress path, which simulates stress conditions under a rising phreatic surface. The test programme was complemented by undrained TSHC tests to provide further insight regarding the behaviour of the sand when sheared under a range of α values. Various reconstitution methods (i.e. moist tamped (MT), dry pluviated (DP) and wet pluviated (WP)) were included to examine the effects of fabric on CSD triggering. Only MT and DP specimens could be prepared loose enough to exhibit liquefaction behaviour; hence the focus of this study was on these preparation methods. The programme indicated that the instability stress ratio (ηIL) under the CSD stress paths decreases as α increases, suggesting that cross-anisotropy strongly influences the shearing behaviour of sands under this trigger mechanism. In addition, the DP sand showed a greater decrease of ηIL with increasing α compared to the MT sand, consistent with other studies examining the effect of fabric and preparation methods on inherent anisotropy. The results of this study suggest that ignoring the effect of cross-anisotropy on the CSD trigger mechanism will lead to unconservative slope stability assessments.

Experimental Study on Directional Shear of Q2 Remolded Loess Considering the Direction of Principal Stress

To investigate the strength and deformation characteristics of Q2 remodeled loess, soil samples from the Lishi area in Shanxi Province were adopted to examine the effects arising from the principal stress axis direction angle α and the medium principal stress ratio b on the shear and non-coaxial properties of remodeled loess based on the hollow cylindrical torsional shear system. As indicated by this study, when b was constant, the generalized shear stress ratio decreased with the increase in α at 0°–45°, while achieving the minimum value when α = 45°; α increased again with the increase in the principal stress axis direction angle at 45°–90°. When α was 0–45°, the generalized shear stress ratio tended to decrease with the increase in the intermediate principal stress ratio b. When α was 60°–90°, the shear strength ratios at different intermediate principal stress ratios were obtained as: strength at b = 0.5 &amp;gt; strength at b = 1 &amp;gt; strength at b = 0. Moreover, after the degree of strength volatility of this remodeled loess was defined to determine its breaking strain standard, it was found through a comparative analysis that when the generalized shear strain of this remodeled loess was 6.5%, the strength of this remodeled loess was over 90%. Thus, this study suggested the use of its generalized shear strain of 6.5% as its breaking strain standard. In addition, when α was at 0–45°, the direction angle of strain increment increased with the increase in the direction angle of the principal stress axis and reached the peak at 45°. When α was at 60°–90°, the direction angle of strain increment decreased with the increase in the direction angle of the principal stress axis, i.e., the non-coaxial characteristics of the remolded loess first increased, then decreased, and further tended to be coaxial.

A three-stage strength criterion for frozen soils

The strength criterion of frozen soil is necessary for the evaluation of failure problems of the engineering constructed in cold regions or by artificial ground freezing method. Due to the combining effect of stress conditions and temperature, the unique feature of the three-stage development in shear strength of frozen soils has been widely recognized. However, the existing theories are found hard to uniformly describe this characteristic for various frozen soils. In this work, we carried out an analysis of the shear strength characteristics of frozen soil based on the available test results. A novel strength criterion is proposed, in which the total shear strength consists of the basic strength qf and the special contribution strength qi. By combining the basic strength in the power function form and a newly proposed special contribution strength, the theoretical description of the three-stage shear strength variation is suggested. In addition, the expression of the generalized nonlinear strength theory (GNST) in the deviatoric plane is introduced to capture the effect of the intermediate principal stress ratio. Therefore, a three-stage strength criterion (3SSC) for frozen soil is established, whose characteristics are analyzed. Determination methods of parameters and their relationship with temperature are also given. The performance of the 3SSC and the comparison with test results show that the 3SSC is applicable to capture the salient behaviour of the shear response of frozen soil.

On some uncertainties related to static liquefaction triggering assessments

Static liquefaction has been identified as the cause of several recent tailings storage facility (TSF) failures. Partially based on the investigations carried out, significant advances on the analysis of static liquefaction triggering (SLT) have been made. These include applications of critical-state-based models in a stress–deformation framework to identify if in situ conditions are approaching a level where SLT could occur. However, several important uncertainties remain. In this work, three of these uncertainties (geostatic stress ratio K0, intermediate principal stress ratio and principal stress angle from vertical) were investigated, along with their effects (both independently and in conjunction) on the identification of SLT and slope failure. These uncertainties were examined through a series of numerical analyses of an idealised TSF. Various values of K0 were used to examine their effect on SLT, while different approaches were taken to assess the potential effects of the intermediate principal stress ratio and the principal stress angle from vertical on instability. This work revealed that the current state of knowledge in these areas is such that significant uncertainty seems unavoidable in attempting to identify exactly when a particular slope may undergo SLT. Experimental and in situ test programmes that may be useful in reducing this uncertainty are outlined.

Strength and deformation properties of frozen sand under a true triaxial stress condition

In recent years, the mechanical properties of frozen soils under complex stress states have attracted significant attention; however, limited by the test apparatus, true triaxial tests on frozen soils have rarely been conducted. To study the strength and deformation properties of frozen sand under a true triaxial stress state, a novel frozen soil testing system, i.e., a true triaxial apparatus, was developed. The apparatus is mainly composed of a temperature control system, a servo host system, a hydraulic servo loading system, and a digital control system. Several true triaxial tests were conducted at a constant minor principal stress (σ3) and constant intermediate principal stress ratio (b) to study the effect of intermediate principal stress (σ2) on the mechanical properties of frozen sand. The test results showed that the stress–strain curve can be mainly divided into three stages, with evidence of strain hardening characteristics. The strength, elastic modulus, and friction angle increased with the increase in b from 0 to 0.6, but decreased when increasing b from 0.6 to 1, whereas the cohesion varied little with the variation in b. The deformation in the direction of σ2 changed from dilative to compressive and that in the direction of σ3 remained dilative throughout.

The Behavior of a Coarse Granular Material under Complex Stress Conditions

In recent years, dozens of high rockfill dams are under construction or planning for hydropower exploration in western China. In dam construction, the mechanical behavior of coarse granular material greatly affects the compatible deformation of dam body. In this article, an indirect in situ density prediction approach for coarse granular material is firstly proposed to solve the technical obstacle on prediction of the material density in thick overburden layer of a dam site in southwest China. Adopting a self-developed large-scale true triaxial apparatus with a special friction-reduction technique, four series of true triaxial tests were then performed to investigate the behavior of a coarse granular material with a maximum particle diameter of 60 mm. Test results show that the peak strength of the material increases together with the increasing confining stress and the increasing intermediate principal stress ratio. The material dilatancy is restricted by both the confining stress and the intermediate principal stress ratio. With the increase in intermediate principal stress ratio, the internal friction angle increases firstly and then decreases slightly, but the slope of stress path reduces gradually. The tested peak states were compared with several well-known strength criteria under the framework of generalized stress, showing a good fitness with the Lade–Duncan criterion and underestimation by the Mohr–Coulomb criterion and the Matsuoka–Nakai criterion. The strength envelope in the π plane shrinks with the increasing confining stress.

Strength Characteristics of Reinforced Granular Soils in Three-Dimensional Space

A series of true triaxial numerical tests were carried out on reinforced granular soils based on DEM method, effects of reinforcement layers and intermediate principal stress ratio on the strength characteristic of granular soils were conducted. The simulation results show that the shear strength of reinforced soils can be improved with the increase of reinforcement layers. However, the improvement effect becomes weak with increase of the intermediate principal stress ratio. Furthermore, the shear strength of granular soils will decrease with the increase of intermediate principal stress ratio b under constant P stress path, the maximum shear strength can be obtained in case of b=0 test, while the minimum shear strength appears under b=1.0 condition.

Bifurcation analysis of shear band in sand under true triaxial conditions with hypoplasticity

AbstractPredicting the onset of shear band is of significance in understanding the failure of geomaterials. The prediction accuracy is dictated by the constitutive model used for the description of the pre‐bifurcation behaviour. In this study, we first modify a recently proposed hypoplastic constitutive model by incorporating a general strength criterion and a stiffness function. We proceed to consider the onset of shear band in sand under true triaxial conditions. We demonstrate that our analyses capture the pre‐bifurcation stress–strain relationship at different values of intermediate principal stress and predict fairly well the onset of shear band. The acoustic tensor criterion generally adopted in elastoplastic approaches is inadequate for hypoplastic approaches. No special non‐coaxial treatment is required for the present approach to yield a reasonable variation trend of bifurcation strain with intermediate principal stress ratio .

Discrete Element Modelling of the Mechanical Behavior of Sand-Rubber Mixtures under True Triaxial Tests.

Sand–rubber mixtures (SRMs) consisting of stiff sand particles and soft rubber particles are typical binary mixture materials that possess a variety of complicated properties. The complexity of the properties of sand–rubber mixtures is increased when complex stress path is involved. This study investigates the mechanical behavior of sand–rubber mixtures under generalized loading conditions using the discrete element method. A series of numerical true triaxial shear tests were conducted on pure sand and sand–rubber mixtures. The effect of rubber content and loading path on both of the macroscopic and microscopic performances of sand–rubber mixtures was investigated, and the associated microscale mechanism was also discussed. Numerical simulations show that the relationship between the peak friction angle and the intermediate principal stress ratio is influenced by the addition of rubber particles, and a suggested explanation of this phenomenon is that the rubber particles mainly affect the inherent stability of the strong network. Particle-scale observations, including the coordinate number, the proportion of strong contacts, and the fabric anisotropy, are also presented in this study. Microscopic results confirm the explanation above, and explore the force transmission characteristics of sand–rubber mixtures under generalized loading conditions. This research can provide a reference for the constitutive model development of sand–rubber mixtures.

DEM investigations of the effects of intermediate principal stress ratio and particle breakage on the critical state behaviors of granular soils

Three dimensional discrete element (DEM) analyses were performed in Particle Flow Code (PFC3D) to study the effects of intermediate principal stress ratio and particle breakage on the critical state behaviors of granular materials. The variation of intermediate principal stress ratio is achieved by increasing intermediate and major principal stresses at different ratios. The breakage of calcareous sand particles is simulated in DEM with clumped particles using the octahedral shear stress crushing criterion. The macroscopic behaviors of crushable and uncrushable particles during shearing and at the critical state are compared. It is found that intermediate principal stress ratio and particle breakage affect the dilation and peak strength but have different effects on the critical stress ratios of the assemblies. The evolutions of micromechanical parameters such as redundancy factor, fabric and force anisotropies are examined to explain the difference between the behaviors of crushable and uncrushable assemblies under different stress paths.

An evolution law for fabric anisotropy and its application in micromechanical modelling of granular materials

Micromechanical studies of granular materials have demonstrated the importance of their microstructure to their behaviour. This microstructure is often characterized by fabric tensors. Experimental and computational studies have shown that the fabric can change significantly during deformation. Therefore, the evolution of fabric is important to constitutive modelling. Current fabric evolution laws for granular materials have generally been developed for continuum-mechanical models, and use a loading index multiplier associated with a yield surface. Such evolution laws can not be employed with micromechanical models that do not involve an explicit macro-scale yield surface.This study develops an evolution law for fabric anisotropy, based on observations from experiments and Discrete Element Method simulations from literature. The proposed evolution law considers the effects of inherent anisotropy, void ratio, stress ratio, loading direction and intermediate principal stress ratio. In the critical state, the value of the fabric anisotropy depends only on the Lode angle. The predicted evolution of fabric anisotropy is in good agreement with results of Discrete Element Method simulations, showing both hardening and softening behaviour and describing the influence of the initial void ratio.The proposed evolution law can be embedded into micromechanics-based constitutive relations as well as conventional continuum-mechanical models. As an example, a well-established micromechanical model (in which the fabric is considered as constant) has been extended by accounting for the variations in fabric, in combination with the proposed fabric evolution law. The performance of this enhanced micromechanical model has been demonstrated by a comparison between the predicted behaviour and experimental results from literature for Toyoura sand under various loading conditions.

Effect of grain size on undrained anisotropic behaviour of sand–fibre composite

Abstract This study investigates the dependency of steady states on anisotropy in unreinforced uniform angular silica sands and those reinforced with micro-synthetic fibres. In doing so, the principal stress orientation varies from 15° to 60° for an intermediate principal stress ratio of 0.5 and 1.0 and the initial effective consolidation stress of 200 kPa. Twenty-four undrained torsional shear tests are conducted using a hollow cylindrical torsional shear apparatus. On randomly mixing sands with fibres, dilative and strain-hardening behaviour attains prominence, and the undrained strength generally improves. Anisotropy in the samples decreases and distortion of the deviatoric strength envelope is produced by the addition of fibres to the host sand. The results show that fibre reinforcement contribution growth by the increase of the major principal stress direction. This phenomenon is attributed to the change in the loading combination of the sample from compression to torsion. The contribution of the fibre to the strength in all principal stress directions is higher in the sand with smaller median grain size (D50). Furthermore, increasing the median grain size caused the stress-strain curves to be adjacent to one another and increased specimen anisotropy. The flow potential decreases and begins to follow an inverse relationship with the principal stress direction.

Numerical Investigation and Analysis of Intermediate Principal Stress Effects on Rock Failure Behaviors

A series of numerical experiments have been conducted to investigate the intermediate principal stress effects on rock failure behaviors. The numerical results show that the strength and deformation of the rock samples are significantly affected by the intermediate principal stress. The effects are inconsistent in different intervals. As intermediate principal stress ratio b increases, the rock strength increases initially and finally decreases. When b is approximately equal to 0.5, the strength of the rock sample reaches the maximum. In the microlevel, the intermediate principal stress affects the number and distribution of microcracks. The increase of the intermediate principal stress makes the projection of the microcracks on the loading plane change from uniform to uneven. On the one hand, the intermediate principal stress restricts the propagation of microcracks in the normal direction along the intermediate principal stress (or with a component in this direction), which will lead to an increase in the strength of the rock samples. On the other hand, the propagation of microcracks along the normal direction with small principal stress (or with a component in this direction) is promoted, which leads to a decrease in the strength of the rock sample. End friction can make the intermediate principal stress effect more significant because the friction of the loading end to the rock sample can result in stress deviation between the actual value and experimental value. Inhomogeneity of stress field induced by the change of stress states or end friction forces is the external factor of the intermediate principal stress effect. Also, the inhomogeneity of rock material itself is the internal factor. Intermediate principal stress will promote or restrict the failure of certain directions, thus affecting the overall strength of the rock samples. The numerical results can be very meaningful for stability analysis of rock masses in practical engineering.

The suction,yield and strength characteristics of unsaturated intact loess based on true tri-axial tests

To simulate the failure of loess under undrained condition in the actual engineering,a series of isotropic consolidation and shear tests with different intermediate principal stress ratio b under constant water content were performed on intact loess with various initial suctions using the true tri-axial apparatus for unsaturated soil. The relationship between the saturations and initial suctions,the characteristics of yield,suction and strength of unsaturated intact loess were studied. The results show that the initial suctions and the suctions after the isotropic consolidation decrease with the increase of saturations. The suctions increase with the increase of the intermediate principal stress ratio b at the true triaxial shear failure. The net mean yield stress increase with the increase of the initial suction. The yield suction is a constant,but not always equal to the maximum suction that the soil specimen experienced in the history. The strength of soil increase with the increase of the net confining pressure,initial suction and the intermediate principal stress ratio b.

Anisotropy in Sand–Fibre Composites and Undrained Stress–Strain Implications

Among the plethora of studies on anisotropy in fibre-reinforced sands, there exist conflicting views on effects on the steady-state deformations of initial packing. These conflicting views are further confused by strictly limited experimental evidence on flow in complex loading environments where the principal stresses rotate whereby shearing and torsional stresses combine, and when extension in soil relieves the compressive stresses. In the heuristic of intrinsically anisotropic nature of the soil and in recognition of the inability of placement methods to overcome such anisotropy, this paper aims to use the orientation of principal stress and soil initial packing state combined as proxy parameters to further the knowledge of plastic behaviour in fibre-reinforced sands. This study furthers the knowledge of the dependency of steady states on anisotropy in composite geomaterials. In doing so, the direction of principal stress orientation is varied from 15° to 60° (from vertical axis), taking an intermediate principal stress ratio of 0.5 and 1.0 and two initial confining pressures. Twenty-four undrained torsional shear tests are conducted using a hollow cylindrical torsional shear apparatus. Under compression and plain strain conditions, torsional stresses limit the improvements in soils’ undrained shear strength upon fibre reinforcement. Extension in soil remarkably increases fibres’ contribution to betterment of undrained strength. Fibres are least effective under low isotropic confining pressures and also for certain ranges of torsional stresses.

Anisotropic Strength Characteristics of Loess under Three-Dimensional Stress Conditions

Abstract To study the failure conditions of anisotropic loess in the principal stress space, a series of true triaxial tests were performed on loess sampled in the Bailu Plateau of Xi’an, as loess deposits have a strong cross-anisotropic structure. The cuboid specimens of the prepared samples were cut along the vertical and horizontal directions to enable testing in any sector of the three-dimensional principal stress space. The shear strength laws of the p–q planes with different intermediate principal stress ratios corresponding to different principal stress spaces were revealed. The failure surface was assumed to be symmetric with respect to the vertical axis of the principal stress space octahedral plane, which varies as a function of the Lode angle. On the same octahedral plane, the shear strength of a specimen, as the major stress, is applied along the vertical direction and is larger than that along the horizontal direction. Failure surfaces in all sectors are ellipses, which are symmetric with respect to the vertical axis, and the loess structure is not damaged under the stress conditions of true triaxial compression. Once the structure was damaged, the failure surface of the cross-anisotropic loess on the octahedral planes presented as a circle or a curved triangle as the average principal stress increased.

A Stress-Dilatancy Relationship for Rockfill Incorporating Particle Breakage and Intermediate Principal-Stress Ratio

Rockfill material is widely used for construction of high rockfill dam, which undergoes significant particle breakage and three-dimensional stress path induced by the water pressure, earthquake, etc. The dilatancy equation, defined as the function of the dilatancy dg and the stress ratio η, is regarded as the foundation of elastoplastic constitutive model. Therefore, a dilatancy equation considering the influence of particle breakage and intermediate principal stress ratio b was proposed in this paper. A series of test data from rockfill materials including conventional triaxial test, constant-b test and plane strain test were used to verified the applicability of the equation. It was found that the proposed dilatancy equation considering two important factors (i.e., particle breakage and b-value) agree well with the rearranged test data of the rockfill material in terms of dg-η. While the other dilatancy equations showed significant poorer predictions when ignoring one or two of the factors. That is, the proposed dilatancy equation can well describe the dilatancy behavior of rockfill material when considering the combined influences of the particle breakage and b-value.