Academic literature on the topic 'Stress-Dilatancy Relation'

It is hypothesized that a normalized shear stress – strain curve for granular materials can be obtained by accounting fully for the effects of volume change. In this sense, volume change behavior is a factor that controls the shear stress – strain behavior of a granular material. This hypothesis is applied to Rowe's stress-dilatancy theory to include slip, rolling, rearrangement, and crushing strains, and a theoretical normalizing relation is obtained. The relation is demonstrated to be reasonably correct for the published test data utilized in this study. Differing fabrics of a granular material at the same void ratio can be corrected for by the normalizing relation. The hypothesis is also applied to simple shear behavior and an empirical normalizing relation is obtained.On the basis of the success of the normalizing relation, it is suggested that the volume change rate at 4% axial strain may be, in relation to shear behavior, a more appropriate characterizing parameter than void ratio. However, owing to the long-standing use and acceptance of void ratio, the concept of a reference void ratio, determined by specific sample preparation and testing procedures, is introduced as a characterizing parameter for granular materials. Key words: volume change, dilatancy, normalization, fabric, stress, strain, deformation, sand, granular material.

A new evaluation method for the dilatancy of fine-grained soils based on monotonic and cyclic undrained triaxial tests has been established using two elasticity approaches: isotropic and transverse isotropic hypoelasticity. The evaluation of two clays, Kaolin and Lower Rhine Clay, with the new method also shows that the dilatancy of fine-grained soils is dependent on the stress ratio, the void ratio, and the straining direction along with the intrinsic material parameters. Similar to sand, we can observe a Phase Transformation Line beyond which further shearing induces a volume increase. A generalization of the Taylor dilatancy rule from direct shear to multiaxial space is established, and an extension accounting for the behaviour of soft soils is proposed. We formulate a simple hypoplastic constitutive relation with a modified flow rule that reproduces the observed dilatant as well as contractant behaviour. Some simulations of monotonic as well as cyclic tests prove the accurate performance of the proposed dilatancy relation.

This paper presents a mathematical modelling of the effects of initial fabric on the mechanical behaviour of sand. A stress-dilatancy model that incorporates microstructural aspects of sand is hereby obtained while writing energy conservation for an ensemble of particles over a representative elementary volume at micro- and macro-scales. The resulting stress-dilatancy model, when used within an elastoplastic framework, successfully reproduces certain aspects of sand behaviour that are reflective of its microstructure under both drained and undrained conditions. The role of microstructure in relation to the characterization of steady, quasi-steady, and phase-transformation states is discussed within the framework of the model. Numerical simulations obtained from the proposed model are generally very consistent with experimental observations and provide insightful information.Key words: sand, liquefaction, fabric, dilatancy, constitutive laws, granular materials, plasticity.

To investigate mechanical characteristics of rocks under different unloading conditions, triaxial tests are carried out with initial confining pressures of 10, 20, and 30 MPa and unloading rates of 0.05~1 MPa/s in three stress paths. Results show that the increment of axial strain is far less than that of the lateral strain. The unloading rates of confining pressures have less influence on variation of strain and lateral increment in path I. The variation of axial increment strain in the same time is slightly larger than the variation of lateral increment; D-value is influenced by unloading rates of confining pressures in path II. The variation of axial strain increment decreases firstly and then increases with the variation of confining pressures. The relation decreases and then increases with unloading rates increases in path III. The dilatancy angle decreases with initial confining pressures increases. The vary rates of dilatancy angle from initial point of dilatancy angle to peak point of dilatancy angle increase with the unloading rates of confining pressures. In the same rates, the vary rates of dilatancy angle from the initial point of the dilatancy angle to peak point of the dilatancy angle in path I are greater than those in path II.

The strength of sand is usually characterized by the maximum value of the secant friction angle. The friction angle is a function of deformation mode, density, and stress level and is strongly correlated with dilatancy at failure. Most often, the friction angle is evaluated from results of conventional compression tests, and correlation between the friction angle of sand at triaxial compression and triaxial extension and plane strain conditions is a vital problem of soil mechanics. These correlations can be obtained from laboratory test results. The failure criteria for sand presented in literature also give the possibility of finding correlations between friction angles for different deformation modes. The general stress-dilatancy relationship obtained from the frictional state concept, with some additional assumptions, gives the possibility of finding theoretical relationships between the friction angle of sand at triaxial compression and triaxial extension and plane strain conditions. The theoretically obtained relationships presented in the paper are fully consistent with theoretical and experimental findings of soil mechanics.

Cemented granular systems are encountered at various scales in nature and artificially. We present an experimental study carried out on the structure and mechanical behaviour of weakly cemented granular materials. We study the cemented granular materials at two scales -- micro (particle-bond-particle) scale and macro (ensemble) scale. At the micro-scale studies, a set of x-ray computed tomography experiments are performed. We characterize the structure of initial configuration of weakly cemented granular materials. We discuss, in detail, quantification of fabric and structure such as coordination number, fabric tensor, directional distribution of contact normal and particles, and grain size distribution. An alternative approach to arrive at the fabric tensor is also discussed. To obtain these characteristics, the scanned volume from XCT is segmented into particles and contacts (bonds - for a contact bound structure). For the segmentation, watershed along with h-minima or h-maxima transform are used. The algorithm is presented in detail for a two dimensional example image. From the segmentation results, it is observed that the particles of cemented granular materials orient themselves away from the direction of the gravity or body force whereas the contact normals have a tendency to orient along the direction of gravity. Further, we perform a set of uni-axial compression tests inside the X-ray computed tomograph. It is observed that the initial structure of cemented granular material does not changes significantly before the peak load is reached. The average coordination number increases at lower strains due to contraction of the specimen however at larger strains, continuous reduction in coordination number is observed. The evolution of average porosity field has similar trend to the volumetric strain. Further, the particle and contact align themselves along the direction of load at lower strains whereas at higher strains, they orient themselves away from the loading direction. At macro-scale, we perform a set of triaxial and hollow cylinder shear tests to understand the effect of confining pressure, intermediate principal stress ratio, and density on weakly cemented sands. These results are analyzed in the framework of plasticity theory. We present the extraction of gross yield points of bonds, plastic work contours or yield curves, plastic strain increments, and failure. Further, we calibrate and validate the Lade's single hardening elastic-plastic model. The details of model parameter calibration and integration algorithms for prediction of behaviour are provided. The Lade's model uses stress transformation for accommodation of cementation in the model. Stress transformation implies the translation of elastic-plastic surface along the hydrostatic axis in the stress-space by bond strength of cemented sands. With this stress transformation, the stress-strain response is predicted satisfactorily however, the volumetric predictions only show contraction. In contrast, the experimental volumetric behaviour is initially contractive followed by a dilative response (in the range of confining pressure tested). To validate the applicability of stress transformation, we perform a set of experiments with cemented sands and sands (equivalent sand) subjected to elevated confining pressure (increased by the bond strength). The response suggest that the stress transformation is satisfactory at small strain however due to bond breakage, a deviation in the cemented sands and equivalent sand is observed. This behaviour suggest that the inclusion of bond degradation with stress transformation should work successfully. To verify this, we include the bond degradation in the stress-dilatancy relation for prediction of stress-dilatancy behaviour of cemented sands. With inclusion of bond degradation, the Rowe's and Zhang-Salgado's stress dilatancy relation successfully predict the stress-dilatancy behaviour of cemented sands. We provide microstructural insights from our tomography experiments to the macro level response observed under various stress conditios. Further, a set of scaling studies are also performed on unconfined compressive strength with varying particle sizes (particle size effect), specimen sizes (specimen size effect), and controlled study (scaling specimen and particle sizes proportionally to keep number of particles fixed). With increase in the specimen size, the peak compressive strength of weakly cemented granular material increases. The peak compressive strength decreases with increase in the size of particle. In controlled study, the strength is insensitive to proportional scaling of specimen and particles. The scaling in these contact bound granular materials is significantly different from brittle and quasi-brittle solids such as rocks and concrete. To understand the emergence of the scaling, we use microstructural characteristics obtained from XCT. In particular, we obtain the geometric clusters which are akin to force chains i.e. geometric clusters are able to predict the force distribution in a granular material from its structure. Using the percolation probability of these geometric cluster and normalized cluster size, similar trends as strength are obtained. The primary source of these scaling is results of entanglement of force chains which is presented here by entanglement of geometric cluster.
Department of Science and Technology

DEM triaxial tests were run in a 3D periodic boundary cell containing 5000 spherical particles employing the open source code YADE to replicate the behavior of some typical seabed sands (i.e. Leighton Buzzard and North Australian shelf). The contact law adopted was the Hertz-Mindlin no-slip solution together with a linear moment – relative rotation law meant to account for the non-sphericity of the real sand grains. The chosen contact law is based on 5 independent micromechanical (i.e. at the level of contacts) parameters: two elastic parameters for the Hertz-Mindlin law, intergranular friction and two parameters for the moment - relative rotation law. The values for the elastic constants and the intergranular friction adopted in the simulations were taken from the elastic and frictional properties of the minerals of the sand grains (mainly quartz). Simulations were run for different values of the two parameters of the moment - relative rotation law. Tests were carried out on samples generated at various initial relative densities (from loose to very dense). The obtained results were very encouraging since the stress-strain behavior exhibited by the numerical samples well matched the experimentally measured values of critical state friction angle and dilatancy angle. However, dense samples showed a less good agreement regarding the peak friction angle. The tests were carried out as part of a larger research program on the lateral soil-structure interaction for pipelines lying on sandy seabeds. An extensive program of 3D plain strain tests involving a plane strain section of the pipeline is currently underway.

Drained triaxial monotonic test is one of the most frequently used experiments in geotechnical engineering, mostly because its results are starting points for many research topics. This paper presents triaxial drained monotonic experiments on natural sand borrowed from the terraces of river Vardar, that passes through Skopje. This Skopje sand is highly uniform sand with only 2% fines, and a uniformity coefficient Cu = 2 with mean grain size of d50 = 0.17mm. It can be found at multiple places along the riverbank of Vardar River at different depths. Since this is an urban area, such sandy layers can be exposed to different sources of dynamic loads (traffic from roads, railways, factories, etc.) Knowing the fact that cyclic preloading has effects on the soil strength characteristics, these effects were investigated in the case of prior cyclic loading on consolidated drained triaxial compression monotonic test. The specimens were prepared using wet-tamping method at high range of different initial relative densities, then confined at three levels of initial effective stress p0 = 50, 100 and 200kPa before shearing. The effect of the number of cycles and their amplitudes are also investigated not only on the curves of deviatoric stress q and volumetric strain ev versus axial strain e1 but additionally on the dependency curves that display the influence of the initial density IDO and initial effective pressure p0 on the peak friction angle fp, Young’s modulus E50, axial strain at peak ep and dilatancy angle y. The results indicate interesting outcomes concerning the physical behaviour of the investigated sand.