Papers by Keyword: Granular Material

Abstract: This study investigates the assessment of stresses in a Thermoplastic Polyurethane (TPU) disk under diametral compression relying on full-field strain measurements by Localized Spectrum Analysis (LSA). A checkerboard pattern was first laser-engraved on the disk surface. The LSA processing of the checkerboard images captured in the undeformed (reference state) and deformed (at –8 kN) configurations allowed the determination of the two in-plane principal stretch ratios and the corresponding principal directions. An incompressible behavior was assumed to derive the out-of-plane stretch ratio. Using a neo-Hookean constitutive model, the maps of the Cauchy stress tensors and the First Piola-Kirchhoff stress tensors were deduced. This study demonstrates the potential of the LSA strain measurement technique for deriving stress maps in soft materials, which will be used in future work to feed into the Virtual Fields Method (VFM) for identifying interparticle contact forces in soft granular systems.

Abstract: A modified Mohr – Coulomb criterion is presented. This criterion, in addition to adhesion and the angle of internal friction, contains the third parameter of the material (d). Depending on the value of this parameter (d), the modified criterion can take the form of the original Mohr – Coulomb criterion (with d = 0.5) or the original Treska criterion (with d = 0). For all other values of the parameter (d), varying in the range of 0 <d <0.5, the tangential stresses by the modified criterion are larger than the Mohr – Coulomb criterion, but less than the Tresca criterion. The paper presents the methodology and results of determining this parameter (d) using experiments on the triaxial compression of soils. The technique contains recommendations for the appointment the value of the axial strain of the sample material when determining the value of the parameter d. The value of the ultimate deformation is advisable to take in the range from 8 to 12%. This range is due to the fact that with axial deformation of the sample of 8%, the formation of slip areas begins in it, and with axial deformation of the sample 12%, the slip area is completely formed. In this case, the parameter d varies in the range 0 <d <0.5, having a shear strength bigger than in the Tresca criterion, but less than in the original Mohr – Coulomb criterion. The tangential stresses according to the modified criterion, on the contrary, have a bigger value than according to the Mohr – Coulomb criterion, but the values of the tangential stresses are lower than in the Tresca criterion.

Abstract: The analysis of the models for calculating residual deformations accumulated by granular materials under the influence of repeated loads is performed. Determined the hereditary nature of the accumulation of deformation of granular materials. This allowed the use of integral calculus for the analytical solution of the problem of the dependence of residual deformation on the number of repeated loads, the value of the main stresses. The solution is obtained in the form of logarithmic and power-law functions that associate the accumulated deformation with the deformation arising from the first load application with the number of applied loads. The deformation from the first load application is represented by the sum of the two components, instantaneous irreversible and viscoplastic. The viscoplastic component of the deformation is a consequence of stress relaxation in a relatively short period of time equal to the duration of the impact of the load. The analysis of experimental data on the triaxial compression of various granular materials is carried out and the parameters obtained for the power and logarithmic functions are determined. The materials studied include: granite, gneissic, granodiorite and diorite crushed stone, sand and gravel and crushed stone and gravel mixtures with a mineral part from various rocks, fortified sands. The possibility of application of the obtained solutions for the calculation displacement of the surface of the pavement layers of granular materials is shown. The tasks of further research are formulated.

Abstract: The paper is devoted to the comparison results of experimental data and theoretical stress calculations (arising in pavement layers made from granular materials). The formulas of continuum mechanics and mechanics for granular materials and mathematical dependences, got in accordance with engineering calculation method, were taken as a calculation model. The experimental stress values, measured by Steven B.D. using ring stand (University of Canterbury), were applied as a standard. The ring stand ley us employ moving loads to the stand segments with pavement constructed over the ring stand. It was discovered that the best match of values of experimental and calculation data is got by stress computing based on formulas of mechanics for granular materials (M.E. Harr or I.I. Kandaurov) or continuum mechanics, but with O.C. Frohlich parameter added to С.R. Foster, R.G. Ahlvin and H.H. Ulery’s formula. This Frohlich parameter can be taken as a material parameter. In the conclusion the authors show the way of modification of the well-known approaches in mechanics for granular materials. This new way makes possible to calculate minimum principal stress σ3.The modified mathematical relationships of principal stress calculation can be used in models for elastic, plastic, elastic-plastic deformation calculations and in conditions of plasticity.

Abstract: The paper analyses the data on measuring the packaging density γ and porosity ω of the medium-loading of balls with d diameter and the loading tank of D diameter, as well as the compound of balls of diameters d₁ and d₂ ≤ d₁. The stabilization of γ and ω was observed with D/d≥4-5: γ=0.61-0.63, ω=0.37-0.39, which allows evaluating the medium-loading of the commensurable granules as a conditionally orderly structure with cells, on average close to square-rhombic ones. As to the compound of the granule-balls in the range of d₂/d₁=1-0.5, judging by the data on γ and ω variance with d₂/d₁<0.4-0.5 (up to γ=0.85-0.87 and ω=0.13-0.15 with d₂/d₁→0), the media-loadings of multi-dimensional granules with characteristic γ and ω values can be considered as provisionally ordered structures with corresponding cells. We provide the expression for defining averaged values of the coordination number of the granule.

Abstract: The deformation characteristic of granular material is important. It is important factor to analysis the bearing capacity and the thickness of granular material footings. There are many factors influence the deformation of granular material, such as material characteristic, content of water, degree of compaction, test method, etc. For analyzing size effect on the deformation characteristic of granular material, hypoplastic constitutive model considering void ratio is introduced. The influence of an initial void ratio, pressure and a mean grain diameter on the deformation is investigated by polar quantities: rotations, curvatures, couple stresses and a characteristic length. Thus, the influence of density and pressure on the initiation of shear bands can be investigated with a single set of constitutive constants.

Abstract: Modelling of large-scale deformation patterning in geomaterials is important for predicting instabilities and failures in the Earths crust. Shear band formation and the evolution of the bands is a predominant mechanism of deformation patterning. Independent rotations of separate grains/particles can affect the pattern formation by adding the effect of rotational degrees of freedom to the mechanism of instability. To model this mechanism we use a special experimental technique based on digital image correlation in order to recover both displacement and independent rotation fields in 2D physical models of granular material. In the physical model the particles are represented by smooth steel monodispersed disks with speckles painted on them to enable the rotation reconstruction. During the loading the deformation pattern undergoes stages of shear band formation followed by its dissolution due to re-compaction and particle rearrangement with the subsequent formation of multiple shear bands merging into a single one and the final dissolution. Also, patterns of rotations are observed at an intermediate scale between the scale of the particles and the scale of the shear band.

Abstract: A numerical triaxial apparatus based on discrete element method is developed on the platform of Yade using Python script. A DEM model with rolling resistance contact considered is proposed for dense granular materials, which is then applied in triaxial compression test of Chende sand. Stress-strain response and volume-axial strain response of the DEM model agree well with that of experiments, with a good prediction of dilatancy angle. Degradation of granular materials duo to particle erosion is also investigated using triaxial compression tests. It is indicated that peak friction angle decreases with the remove of particles if strong force network of granular materials is destroyed.

Abstract: The intrinsic complexity of granular materials stems from the fact that the characterizing variables at the micro-scale and the macro-scale are of different nature. Macroscopically, tensorial variables (stress tensor, strain tensor, fabric tensor) are commonly used based on Representative Volume Element (RVE), while vectorial variables (contact force, contact displacement, contact normal) are adopted at particle-scale. This paper mainly discusses some basic characterizations for these two scales, as well as their correlations. Numerical simulations using Discrete Element Method (DEM) are then conducted to show the evolutions of both microscopic and macroscopic variables during monotonic loading. It is indicated that the particle reorientations in the dense sample are much more pronounced than that in the loose one during shearing.

Abstract: Three different numerical tests, i.e. no rolling test, free rolling test and rolling resistance test, in the framework of discrete element method (DEM) are carried out to simulate the micro-structure development in shear bands. The rotational angles and effective strain in the specimen under different conditions are given out. By contrast, it can be concluded that the development of shear bands in granular material can be simulated well when the rolling resistance is taken into account in DEM.