Edinburgh Napier University

  Soil is a particulate material. Therefore, any behaviours that a soil exhibits must be implicitly linked to its particle size distribution (PSD). Commonly, PSD is implemented into models/methods via gradation descriptors such as the coefficient of uniformity (Cu) or the average grain size (d50). However, these descriptors do not account for the full range of grain sizes in a PSD. Crucially, fines and gravel content are excluded by said descriptors entirely. This can have consequences on PSD criteria which determine liquefaction susceptibility or even particle breakage. Proposed by Lőrincz (1986), grading entropy not only accounts for all the information within a gradation curve, but also displays the entirety of a PSD as a single point on an entropy diagram, represented by two highly informative coordinates. Whilst the benefits of grading entropy over typical PSD descriptors is clear, the method has garnered little attention, particularly at the microscale.

The analysis of particulate behaviours from a microscale perspective has been enhanced by the discrete element method (DEM), which enables the analysis of individual particle behaviours and, uniquely, the orientation/concentration of particle contacts in a granular material. One clear benefit of DEM is the ability to obtain repeatable and reliable results in any simulated physical test. Soil, however, is random in nature. In DEM, to maintain a degree of randomness within a soils distribution, particles may be randomly generated between specified size ranges within a specified area/volume/cell. This implies that any number of DEM simulations with the same specimen generation procedures may have variable initial specimen properties. This suggests that parameters such as the initial void ratio and soil fabric, which is highly influential in the transfer of stresses in a soil, may also show a degree of inherent variability.

This thesis explores the effect of PSD on soil behaviour and inherent variability in DEM. Simulations of spherical particles using periodic boundaries were performed in order to assess the effect of variability on the macro and microscale results. DEM specimens of spheres with varied PSDs were randomly generated (1 mm – 2 mm and 0.5 mm – 2 mm), and isotopically compressed prior to triaxial shearing under undrained conditions. DEM specimens were also created with variable numbers of spheres between 500 and 10000. For each of the given particle counts, at least 200 simulations were performed under identical conditions (e.g., differing only in terms of the initial, random positions of individual particles). It has been found that variability is dependent on the parameter being assessed; and ultimately decreases as both the number of simulations, particles and PSD broadness increased. Whilst some parameters in the simulations experience more variability than others, all parameters experience significant variability amongst the first 40-60 repeated simulations.

This study also undertook laboratory tests of samples consisting of different PSDs of glass spheres(ballotini) consisting of two sizes: 0.5 mm – 0.75 mm (small) and 1 mm – 1.4 mm (large). The PSDs in this work consisted of 0% (100% large), 20% (80% large 20% small) and 40% (60% large and 40% small) mixtures. The PSDs were subjected to both drained and undrained triaxial (monotonic) loading at confinements of 100 kPa, 200 kPa and 300 kPa. All tests were recreated in DEM to investigate microscale behaviours. Grading entropy coordinates are used to describe the PSD behaviours seen in the physical tests and simulations. It was seen throughout this thesis, that PSDs which had larger normalised base entropy coordinates were found to be the most stable (in terms of peak stress, qmax and secant stiffness, G). These PSDs also presented the greatest alignment of contacts in the major principal fabric direction, suggesting that the A-coordinate may indicate the presence of strong force chains in a granular system.
Moreover, the normalised entropy increment (B) was seen to be related to the presence of contacts in the minor principal direction, providing an indication of weak force chains. The coordinates were further investigated with an analysis 14 PSDs chosen based on their location on a normalised grading entropy diagram to assess soil fabric effects, contact evolution, etc. The results provide further indication that the A and B coordinates possess the ability to indicate the magnitude of strong and weak force chains and may even be used to predict phase changes within a soil.

Finally, the internal stability criterion set out by Lőrincz (1986) is extended to provide insight into the effect of fines content (Fc) and liquefaction susceptibility. It is suggested that increasing the Fc works to (overall) increase its liquefaction susceptibility. This seemed to be significantly affected by the proportion of inter-particle contacts between coarser particles and the ability of fine particles to disrupt strong force chains. Moreover, previously established fabric relationships are applied to propose a new expression to determine the equivalent intergranular void ratio (e*). It is also suggested that the stability line present in the normalised entropy diagram may also indicate the fines content threshold, the point at which a material changes from a fines-in-sand to a sand-in-fines mixture.