Stress In Granular Materials Research Articles

Glass Beads Test with True Triaxial Stress Path Achieved by Conventional Triaxial Apparatus

The impact of fabric anisotropy, fractal dimension, and breakage on the strength and deformation of granular materials were diminished by uniform-size spherical glass beads. Triaxial drained and undrained tests were performed on glass beads based on a novel method to substitute true triaxial stress paths with conventional triaxial apparatus equivalents with varying intermediate principal stress coefficients (b-values). The result indicates that all specimens manifested a noticeable strain-softening phenomenon. The peak strength decreased with increasing b-value, and the specimens showed more pronounced dilatancy. This pattern is similar to the results of the true triaxial test in current research. Compared to the undrained test, the peak friction angle in the drained test displayed a greater variation with varying b-values, which indicated that the mechanical response of glass beads is sensitive to water. This difference provides experimental evidence for comprehending effective stress in granular materials with constant friction coefficients. The experiments reflect the effect of b-value changes on the p-q stress path, as well as on the peak stress ratio, the state transition stress ratio, and the critical state stress ratio. The specimens exhibited a distinct shear band at different b-values ranging from 0.2 to 0.6, which is different from observations in conventional triaxial tests for granular materials.

Particle shape transforms the driving of shear stress in granular materials

Particle shape transforms the driving of shear stress in granular materials

Mesoscale Investigation of Fine Grain Contribution to Contact Stress in Granular Materials

Mesoscale Investigation of Fine Grain Contribution to Contact Stress in Granular Materials

Machine learning approach to force reconstruction in photoelastic materials

Photoelastic techniques have a long tradition in both qualitative and quantitative analysis of the stresses in granular materials. Over the last two decades, computational methods for reconstructing forces between particles from their photoelastic response have been developed by many different experimental teams. Unfortunately, all of these methods are computationally expensive. This limits their use for processing extensive data sets that capture the time evolution of granular ensembles consisting of a large number of particles. In this paper, we present a novel approach to this problem that leverages the power of convolutional neural networks to recognize complex spatial patterns. The main drawback of using neural networks is that training them usually requires a large labeled data set which is hard to obtain experimentally. We show that this problem can be successfully circumvented by pretraining the networks on a large synthetic data set and then fine-tuning them on much smaller experimental data sets. Due to our current lack of experimental data, we demonstrate the potential of our method by changing the size of the considered particles which alters the exhibited photoelastic patterns more than typical experimental errors.

Comparison of Continuum Stresses in Granular Material Computed by Volume Average Approach and Boundary Average Approach Under Static and Quasi-Static Conditions

Averaging approaches have been widely used to estimate continuum stress in granular materials to facilitate the assimilation of granular materials’ behavior into a continuum mechanics framework. At present, selection criteria for the appropriate averaging approach are still poorly understood. This paper compares the stresses computed by two popular averaging approaches, i.e., volume average approach (VAA) and boundary average approach (BAA) in order to investigate relative errors between the two approaches under various conditions. The comparisons between VAA and BAA under a static condition were first carried out based on the rigid particle analytical framework proposed by Rothenburg, L. [1980] “Micromechanics of idealized granular systems,” Ph.D. thesis, Carleton University, Ottawa, followed by discrete element modelling (DEM) simulations using PFC3D under a quasi-static condition. The results of theoretical comparison suggested that the relative error in the computed stresses by VAA with an omission of overlap could be grossly estimated by the ratio of overlap to length of contact branch, while the relative error in the computed stresses by VAA with an omission of external contacts could be grossly estimated by the ratio of maximum particle diameter to specimen size. At the ratio of maximum particle diameter to specimen size of 5, which is usually taken as the minimum recommended ratio to minimize boundary effect, the relative error caused by omitting the external contacts was as high as 20%. Numerical comparisons suggested that the relative errors of the two approaches under a quasi-static condition were significantly influenced by the strain energy ratio defined in this study. The VAA was recommended as a preferred computation method over the BAA when the strain energy ratio was considerably lower than unity.

Analytical and DEM studies of thermal stress in granular materials

The ability to predict thermal-induced stresses in granular materials is of practical importance across a range of disciplines ranging from process engineering to geotechnical engineering. This study presents an analytical formula to predict thermal-induced stress increments in mono-disperse granular materials subject to an initial isotropic stress state. A complementary series of DEM simulations were carried out to explore the applicability of the proposed analytical formula. The comparative analysis showed that the proposed expression can accurately predict stress changes in packings where there are negligible particle displacements as a consequence of the thermal loading (e.g. regular packings and medium/dense random packings); however large errors were observed in loose samples with a random packing.

Representation of stress and strain in granular materials using functions of direction

This paper proposes a new way of describing effective stress in granular materials, in which stress is represented by a continuous function of direction in physical space. The proposal provides a rigorous approach to the task of upscaling from particle mechanics to continuum mechanics, but is simplified compared to a full discrete element analysis. It leads to an alternative framework of stress–strain constitutive modelling of granular materials that in particular considers directional dependency. The continuous function also contains more information that the corresponding tensor, and thereby provides space for storing information about history and memory. A work-conjugate set of geometric rates representing strain-rates is calculated, and the fundamental principles of local action, determinism, frame indifference, and rigid transformation indifference are shown to apply. A new principle of freedom from tensor constraint is proposed. Existing thermo-mechanics of granular media is extended to apply for the proposed functions, and a new method is described by which strain-rate equations can be used in large-deformations modelling. The new features are illustrated and explored using simple linear elastic models, producing new results for Poisson’s ratio and elastic modulus. Ways of using the new framework to model elastoplasticity including critical states are also discussed.

A New Method of Calculating the State of Stress in Granular Materials under Plane Strain Conditions

The system of equations comprising the Mohr-Coulomb yield condition and the stress equilibrium equations may be studied independently of the flow law. This system of equations is hyperbolic. Accordingly, to solve the aforementioned system of equations, it is reasonable to apply the method of characteristics. In the special case of plasticity theory for materials whose yield criterion does not depend on the average stress, two methods are used to construct an orthogonal net of characteristics and to determine the stress field: the R-S method and Mikhlin’s coordinate method. In the case of the Mohr-Coulomb yield condition, the angle between the characteristic directions depends on the internal friction angle. Therefore, the above-mentioned methods should be generalised in accordance with this property of characteristics. Purpose. In the case of Plasticity theory for materials whose yield strength does not depend on the average stress, to calculate the stress filed, Mikhlin’s coordinate method is widely used. The purpose of this study is to generalise this method for the equation system consisting of the Mohr-Coulomb yield criterion and the pressure equilibrium equations. Methods. The geometrical properties of the characteristics of the equations’ system consisting of the Mohr-Coulomb yield condition and the equilibrium equations are used to introduce the generalised Mikhlin coordinates. Results. It’s been pointed out that solving equation system consisting of the MohrCoulomb yield condition and equilibrium equation comes to solving equation of telegraphy and to subsequent integration. Practical Significance. The developed method of system of equations’ solution, consisting of the Mohr-Coulomb yield condition and equilibrium equation enables obtaining high precision solutions at insignificant computer time expenditures.

Model Tests on Additional Stress Transmission between Different Granular Materials in Foundation Soils

To research and analyze the additional stress distribution and change of granular materials, the model tests are used to observe vertical additional stress in different position and depth in different foundations. And the comparison between observed values both in different soils and single soils is conducted to analyze the transmission and attenuation of additional stress in granular materials. The research results show that the existing of boundary surface can lead to different vertical additional stress transmit obviously. And with the increasing of loading, the vertical additional stress differences between that of different soils get larger, meanwhile, the ratio of stress differences to smaller additional stress increases slightly. With the increasing of depth, the attenuation rate of vertical additional stress of silty soil changes much fast than that of fine sand. Wherever in horizontal direction or vertical direction, the vertical additional stress of fine sand which has higher compression modulus in different soils is slightly larger than that in single soil and transfers additional stress (loading) more under the same loading. To granular materials, inner friction structure effect is evident influence to additional stress transfer.

Friction Structure Effect Analysis of Granular Materials in Foundation Soil

To research and analyze the additional stress distribution and change of granular materials, the model tests are used to observe vertical additional stress in different position and depth. And the comparison between observed values and theoretical values is conducted to analyze the transmission and attenuation of additional stress in granular materials. The research results show that calculated values are based on Boussinesq solution which ignores the property of soil layer (materials), the distribution of additional stress for fine sand which belongs to granular materials is largely deviated from theoretical value. For granular materials, inner friction structure effect is evident influence to additional stress transfer. And continue using calculation method which is based on continuum materials will have bigger difference and even wrong.

Stresses in granular materials

When circularly polarised light is passed through a granular material under boundary stresses patterns—‘light stripes’—are seen in the resulting images which have been traditionally associated with the directions of major principal stresses in the equivalent continuum. In this paper the passage of polarised light through a single spherical particle under stress is studied experimentally and analytically. The effect of placing the particle within a layer of particles, a layer of thickness 2–3 particles, and within a mass of particles is investigated experimentally. The appearance of light stripes is a visual reinforcement of effects seen at the particle level provided the level of stresses in individual particles is low. The implications for quantitative photoelastic interpretation of granular media are discussed.

A fibre Bragg grating stress cell for geotechnical engineering applications**South African Provisional Patent Application no 2005/06016.

Existing technology used to measure stress in granular materials is susceptible to water ingress and resulting damage to the electrical components, which limits this technology's use in long-term monitoring of soil structures. The connections of these instruments to readout or recording devices are also fragile and easily damaged. In order to explore the efficacy of fibre optic technology not just as a replacement component, but rather as a material of robust elastic properties, a series of experiments was devised to test the possibility of applying a transverse lateral stress to the fibre and measuring its transformed longitudinal strain. The fibre was inscribed with a 5 mm long Bragg grating and encapsulated in a softer material of high Poisson's ratio in an attempt to enhance the longitudinal strain developed in the fibre. This encapsulated device was then subjected to one-dimensional stress in a standard sand, and the strain in the fibre measured. The experiment showed that satisfactory correlation exists between the measured strain output when converted to an applied stress and the mathematically (and numerically) derived stresses. The fibre/silicone bonding was also modelled and results showed that slippage on that interface could be considered insignificant. In both theoretical and practical applications, this experiment can be regarded as successfully validating the principle of deriving stress from a longitudinal elastic strain measured normal to the applied stress. Hence, development can move towards both miniaturization (for research) and more robust construction (to withstand field conditions). Further research will encompass investigating the response of the cell to water and saturated soil conditions, particularly the device sensitivity to transient stress conditions. In addition, development of the sensor to read the complete three-dimensional state of stress in a soil remains the ultimate goal.

GRANULAR MEDIA AS A PHYSICS PROBLEM

Although there is a vast engineering literature for granular materials, as a subject for physicists it has seen great growth in recent years. This is because, when stripped down to the fundamental problem, it is quite novel, and demands a rethink of the kind of laws familiar elsewhere in physics. We consider the transmission of stress in granular materials and investigate the simplest statically determinate problem.

Transmission of stress in granular materials as a problem of statistical mechanics

We consider the problem of stress transmission in granular materials. We formulate the simplest statically determinate problem of stress transmission through a static granular material. This is the case when grains are rigid and have an average coordination number of z ̄ =d+1 . Under this condition the system of Newton's equations of interparticle force and torque balance is complete. This means that there exists a complete set of equations for the macroscopic stress tensor σ ij( r ) i.e., the d (where d is the dimension of the problem) equations of force balance ∇ jσ ij( r )=g i( r ) have to be supported by d( d−1)/2 equations. These equations have their origin in Newton's laws of interparticle force and torque balance and incorporate tensorial geometrical characteristics of the packing. We conjecture that in order to have a coherent and self-consistent continuum theory of stress transmission in static granular media it is necessary to link the averaging procedure to the concept of compactivity. We emphasize that although real granular materials have many features ignored within the proposed framework it is essential for making progress to derive equations of stress transmission for the simplest model, as opposed to guessing and postulating.

Vector lattice model for stresses in granular materials

A vector lattice model for stresses in granular materials is proposed. A two-dimensional pile built by pouring from a point is constructed numerically according to this model. Remarkably, the pile violates the Mohr Coulomb stability criterion for granular matter, probably because of the inherent anisotropy of such poured piles. The numerical results are also compared to the earlier continuum fixed principal axes model and the (scalar) lattice q-model.

Compactivity and transmission of stress in granular materials.

We outline a statistical-mechanical theory of granular materials. Stress propagation and force fluctuations in static granular media are still poorly understood. We develop the statistical-mechanical theory that delivers the fundamental equations of stress equilibrium. The formalism is based on the assumptions that grains are rigid, cohesionless, and that friction is perfect. Since grains are assumed perfectly rigid, no strain or displacement field can enter the equations for static equilibrium of the stress field. The complete system of equations for the stress tensor is derived from the equations of intergranular force and torque balance, given the geometric specification of the material. These new constitutive equations are indeed fundamental and are based on relations between various components of the stress tensor within the material, and depend on the topology of the granular packing. The problem of incorporating into the formalism the "no tensile forces" constraint is considered. The compactivity concept is reviewed. We discuss the relation between the concept of compactivity and the problem of stress transmission. (c) 1999 American Institute of Physics.

Establishment of in-situ horizontal stress in granular materials using local friction (CPT) as governing parameter : Broug, N W A Proc 10th European Conference on Soil Mechanics and Foundation Engineering, Florence, 26–30 May 1991V1, P23–26. Publ Rotterdam: A A Balkema, 1991

Establishment of in-situ horizontal stress in granular materials using local friction (CPT) as governing parameter : Broug, N W A Proc 10th European Conference on Soil Mechanics and Foundation Engineering, Florence, 26–30 May 1991V1, P23–26. Publ Rotterdam: A A Balkema, 1991

Stresses in granular materials flowing in converging hopper sections

Pressure and velocity measurements have been made using a radio pill in flowing granular materials. The experiments were carried out in Perspex model hoppers. From the results the mean pressure at various points in the material during discharge can be obtained. The stress distributions from the results are compared with those predicted by the Jenike-Johanson and Walker theories. The experimental pressures are of the same order of magnitude as those predicted by the two theories.