In this study oedometric compression tests of hydrocarbon coke, Fontainebleau sand and silica sand are simulated in three dimensions using breakable particles. The method adapts a rigorous breakage criterion for elasto-brittle spheres to represent failure of grains isolated between platens or within granular masses. The breakage criterion allows for the effect of particle bulk and contact properties to be treated separately. A discrete fragmentation multigenerational approach is applied as a spawning procedure. The number of particles quickly increases during the simulation, but is kept manageable by systematic fine exclusion and upscaling. Fine exclusion leads to mass losses between generations, but that loss is accounted for outside the mechanical model. Sensitivity analysis shows that it is enough to keep 53% of the crushed particle mass within the mechanical model to correctly reproduce experimental macroscopic behaviour. Practical upscaling rules are proposed for (a) contact stiffness, (b) breakage criteria and (c) grain size distribution, and validated simulating the same test, reducing by half the initial number of particles. The results are promising as both the mechanical and grading evolution are well captured with two orders of magnitude savings in computing efficiency.
A virtual calibration chamber was built using a threedimensional model based on the discrete-element method. The chamber was then filled with a scaled granular\ud
equivalent of Ticino sand, the material properties of which were selected by curve-fitting triaxial tests. Cone penetration tests were then performed under different\ud
initial densities and isotropic stresses. Penetration resistance in the virtual calibration chamber was affected by the same cone/chamber size effect that affects physical calibration chambers and was corrected accordingly. The corrected cone resistance obtained from the virtual calibration chamber cone penetration tests shows good quantitative agreement with correlations that summarise previous physical results.Peer ReviewedPostprint (published version
Bender elements are piezoelectric transducers frequently employed for the measurement of the small-strain shear modulus of soils. The measurement is based on transmission of a mechanical signal through a soil sample. A very common set-up involves transmission along the axis of a cylindrical sample, with source and receiver transducers mounted, for instance, in the end platens of a triaxial apparatus. Current test interpretation is generally based on the assumption of plane wave transmission between transducers. However, this model does not explain the heavily distorted transmission usually observed. The result is substantial measurement uncertainty. Although other phenomena do play a role, it is here proposed that a main culprit for signal distortions is sample-size effects due to lateral boundary reflections. To support this hypothesis, results from a series of numerical 3D simulations of the problem are analysed. Velocity estimates obtained from the simulated traces using plane-wave based time and frequency domain methods are compared with the known exact value. Errors in velocity determination are shown to be very important and directly related to lateral boundary influences. Comparison with some experimental data confirms the need to include sample-size effects in a renewed interpretative framework for bender tests.
This paper presents a computational framework for the numerical analysis of fluid-saturated porous media at large strains. The proposal relies, on one hand, on the Particle Finite Element Method (PFEM), known for its capability to tackle large deformations and rapid changing boundaries, and, on the other hand, on constitutive descriptions well-established in current geotechnical analyses (Darcy's law; Modified Cam Clay; Houlsby hyper-elasticity). An important feature of this kind of problem is that incompressibility may arise either from undrained conditions or as a consequence of material behavior; incompressibility may lead to volumetric locking of the low-order elements that are typically used in PFEM. In this work, two different three-field mixed formulations for the coupled hydro-mechanical problem are presented, in which either the effective pressure or the Jacobian are considered as nodal variables, in addition to the solid skeleton displacement and water pressure. Additionally, several mixed formulations are described for the simplified single-phase problem due to its formal similitude to the poromechanical case and its relevance in geotechnics, since it may approximate the saturated soil behavior under undrained conditions. In order to use equal order interpolants in displacements and scalar fields, stabilization techniques are used in the mass conservation equation of the biphasic medium and in the rest of scalar equations. Finally, all mixed formulations are assessed in some benchmark problems and their performances are compared. It is found that mixed formulations that have the Jacobian as a nodal variable perform better.
A three-dimensional discrete element model is used to investigate the effect of grain crushing on the tip resistance measured by cone penetration tests (CPT) in calibration chambers. To do that a discrete analogue of pumice sand, a very crushable microporous granular material, is created. The particles of the discrete model are endowed with size-dependent internal porosity and crushing resistance. A simplified Hertz-Mindlin elasto-frictional model is used for contact interaction. The model has 6 material parameters that are calibrated using one oedometer test and analogies with similar geomaterials. The calibration is validated reproducing other element tests. To fill a calibration chamber capable of containing a realistic sized CPT the discrete analogue is up-scaled by a factor of 25. CPT is then performed at two different densities and three different confinement pressures. Cone tip resistance in the crushable material is practically insensitive to initial density, as had been observed in previous physical experiments. The same CPT series is repeated but now particle crushing is disabled. The ratios of cone tip resistance between the two types of simulation are in good agreement with previous experimental comparisons of hard and crushable soils. Microscale exploration of the models indicates that crushing disrupts the buttressing effect of chamber walls on the cone. A three-dimensional discrete element model is used to investigate the effect of grain 6 crushing on the tip resistance measured by cone penetration tests (CPT) in calibration 7 chambers. To do that a discrete analogue of pumice sand, a very crushable microporous 8 granular material, is created. The particles of the discrete model are endowed with size-9 dependent internal porosity and crushing resistance. A simplified Hertz-Mindlin elasto-10 frictional model is used for contact interaction. The model has 6 material parameters that are 11 calibrated using one oedometer test and analogies with similar geomaterials. The calibration 12 is validated reproducing other element tests. To fill a calibration chamber capable of 13 containing a realistic sized CPT the discrete analogue is up-scaled by a factor of 25. CPT is 14 then performed at two different densities and three different confinement pressures. Cone tip 15 resistance in the crushable material is practically insensitive to initial density, as had been 16 observed in previous physical experiments. The same CPT series is repeated but now particle 17 crushing is disabled. The ratios of cone tip resistance between the two types of simulation are 18 in good agreement with previous experimental comparisons of hard and crushable soils. 19Microscale exploration of the models indicates that crushing disrupts the buttressing effect of 20 chamber walls on the cone. 21
KEY WORDS: 22Discrete element method, pumice sand, cone penetration, particle crushing, double porosity 23 *Manuscript Click here to view linked References 2 2
Granular materials reach critical states upon shearing. The position and shape of a critical state line (CSL) in the compression plane are important for constitutive models, interpretation of in situ tests and liquefaction analyses. It is not fully clear how grain crushing may affect the identification and uniqueness of the CSL in granular soils. Discrete-element simulations are used here to establish the relation between breakage-induced grading evolution and the CSL position in the compression plane. An efficient model of particle breakage is applied to perform a large number of tests, in which grading evolution is continuously tracked using a grading index. Using both previous and new experimental results, the discrete-element model is calibrated and validated to represent Fontainebleau sand, a quartz sand. The results obtained show that, when breakage is present, the inclusion of a grading index in the description of critical states is advantageous. This can be simply done using the critical state plane (CSP) concept. A CSP is obtained for Fontainebleau sand.
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