Inter-particle Friction Angle Research Articles

Arching development above active trapdoor: insight from multi-scale analysis using FEM–SPH

AbstractUnderground excavation is usually accompanied by complex soil-structure interaction problems in practical engineering. This paper develops a novel multi-scale approach for investigating the soil arching effect through trapdoor tests. This approach adopts the finite element method (FEM) and smoothed particle hydrodynamics (SPH) method to handle the particle-rigid body interaction in the trapdoor tests, incorporating a micromechanical 3D-H model to derive the nonlinear material response required by the SPH method. The variation of the earth pressure on the trapdoor in simulations exhibits good agreement with those of the experiments. Extensive parametric analyzes are performed to assess the effects of soil height and inter-particle friction angle on the evolution of load transfer and soil deformation. Three deformation patterns are observed under different buried conditions, including the trapezoid, the triangle, and the equal settlement pattern. Results indicate that the planes of equal settlement develop progressively with the trapdoor movement and then enter the range of experimentally observed values. Additionally, three failure mechanisms are identified that correspond to the three deformation patterns. Due to the advantages of the micromechanical model, mesoscale behavior is captured. The anisotropy of stress distribution in the plastic region is found during the arching process.

Cyclic modeling of unsaturated sands using a pore‐scale hydromechanical approach

AbstractDetermining proper strain‐dependent shear modulus and damping ratio for soils is of utmost importance when investigating their response to cyclic loads. Experimental studies on the effect of the degree of saturation and suction on the shear modulus at large strain amplitudes are scarce due to the complexities involved in testing such soils. Furthermore, the previously presented micromechanical models for the cyclic behavior of unsaturated soils lack some of the required features of soil pore skeleton essential to model unsaturated soils’ hydromechanical behavior. This paper is, thus, aimed at addressing this shortcoming by incorporating a pore‐scale numerical method that couples the discrete element simulation of the solid phase and the fluid pore network to capture the cyclic behavior of unsaturated sands. To this end, the model is first calibrated to determine the micro‐scale parameters using experimental results from static drained triaxial compression tests on dry and saturated sand samples. Next, the coupled model is employed to simulate the observed behavior during cyclic triaxial tests on unsaturated sands. A linear dependence of the plastic rolling coefficient and the interparticle friction angle on the degree of saturation is proposed from simulations of suction‐controlled cyclic triaxial tests. Variation of shear modulus with shear strain amplitude and degree of saturation indicates a continuous increase in the shear modulus with the decrease in saturation. In contrast, the trend for the damping ratio is the opposite. Finally, closed‐form relationships are proposed based on the simulation results for the shear modulus and damping ratio of unsaturated soils.

Modelling the impact of landslides on geosyntethics-reinforced barrier using DEM-FDM analyses

Geosynthetics-reinforced barriers can be used as protection structures for mitigating the risk posed by fast-moving flow-like landslides such as debris avalanches. In the design of such kind of barriers a crucial role is generally played by the correct analysis of the mutual interaction between the flowing mass and the barrier. This paper is focused on the evaluation of the impact forces and the deformation mechanisms of the barrier. An extensive numerical campaign of dynamic analyses has been performed by means of a coupled 3D Discrete Element Model (DEM) code, namely Particle Flow Code (PFC) and a continuum Finite Difference Method model, named Fast Lagrangian Analysis of Continua (FLAC3D code), both provided by Itasca software. The impacting flow with given initial height and velocity is here simply schematised as a dry granular mass, made of a random distribution of rigid spherical particles. The barrier is conceived as multilayered embankment reinforced by geogrids wrapped around the facing. The geometry of the barrier and the combinations of the materials have been varied to take in account a large variety of factors, also including the size of the impacting mass, the inter-particle friction angle and the initial velocity of the flowing mass. From the numerical results it was learned that the height of the flow may change significantly (or not) during the impact process depending on some of the previously mentioned factors. On the other hand, the global response of the deformable barrier depends on the combined behaviour of the granular soil and the geosynthetics reinforcements installed inside the barrier. Other novelty of the paper is that far from the semi-empirical formulations typically used for a safe design of such barriers, here the time-space dependent mutual interactions are accurately computed along the impact front also providing the chance to adequately take into account the mechanical features of the flowing mass and of the impacted barrier.

Bayesian Calibration of GPU–based DEM meso-mechanics Part II: Calibration of the granular meso-structure

The spatial configuration is a significant contributing factor to dry granular materials' shear strength and dilative properties. This paper studies the effects of the particle size distribution (PSD) and the initial void ratio of a meso-structure through the drained triaxial compression using DEM. A novel multi-threaded two-level optimization is applied to the Force-Biased Generation (FGB) algorithm to enable the PSD and initial void ratio to be varied independently and studied systematically. The GPU-based Periodic Boundary Conditions (PBC) algorithm is developed in the CoSim-DEM framework and used to generate numerous statistical samples of triaxial responses in parallel. The optimized-FBG algorithm is used to study the effects of the initial void ratio and PSD of granular meso-structures for the DEM triaxial simulations. An increase in size polydispersity leads to an increase in shear strength at a constant initial void ratio. Sensitivity analysis of the parameters under DEM triaxial compression is performed. It is shown that dense samples are more sensitive to material parameters than loose samples. The interparticle friction angle monotonically increases in proportion to the volumetric strain for the dense sample, but interestingly, monotonically decreases for the loose sample. Next, Bayesian calibration is performed on synthesized DEM triaxial compressions. The macro responses are inverted, and the initial void ratio converged to the true value, other parameters are however difficult to recover due to the strong linear correlation between the material parameters and the mesostructure configuration. Finally, the micro-parameters are inferred for the drained triaxial condition of fordry graded sand for various confining pressures. The inverted macro responses are more accurate when including the PSD in the inversion process but may augment the values of the other parameters.

Measuring Interparticle Friction of Granules for Micromechanical Modeling

The aim of this paper is to develop an experimental procedure to measure contact friction between granular particles. The contact friction is a micro-property needed in the micromechanical modeling of a granular medium. The proposed method can measure the interparticle friction of idealized spherical particles using the conventional direct shear apparatus in soil testing. In preparation for the test, the test specimen is made of four steel balls embedded halfway in a sulfaset paste plate positioned in a statically determinant configuration to provide point contacts among the steel balls. The upper half of the shear box contains one steel ball, which is supported by three steel balls in the lower shear box, ensuring contact points at all times during the test. Shear force and shear displacement are measured under a specific normal force during the test. An analytical equation is developed based on the geometrical configuration of the balls to calculate the interparticle friction angle. The test is shown to be repeatable, and the calculated interparticle friction angle agrees well with experimental measurements with a high degree of accuracy and consistency.

Investigation on the Influencing Factors of K0 of Granular Materials Using Discrete Element Modelling

Earth pressure coefficient at rest K0 is commonly estimated by empirical equations, which to date has had insufficient accuracy and universality. For better prediction, the investigation on the factors influencing K0 is required. A series of discrete element method (DEM) simulations of oedometer tests are conducted to verify the key factors influencing K0 of granular materials. The influences of initial fabric anisotropy, particle shape, initial void ratio, inter-particle friction angle is investigated. The evolution of microstructure is monitored during the tests to reveal the relationship between the microstructure evolution and K0 values. The results show that the effect of fabric anisotropy exists but is limited. Particle shape, initial void ratio, and inter-particle friction angle all significantly affect the K0 values alone. According to the DEM results, an attempt is made to propose a more reasonable empirical equation in which K0 is a function of relative density, critical state friction angle, and “shape factor”. This new empirical equation has higher accuracy and can consider the effect of particle shape, inspiring the determination of K0 values in practical engineering.

Impact of Ballast Fouling on the Mechanical Properties of Railway Ballast: Insights from Discrete Element Analysis

Ballast fouling is a major factor that contributes to the reduction of shear strength of railway ballast, which can further affect the stability of railway supporting structure. The major sources of ballast fouling include infiltration of foreign fines into the ballast material and ballast degradation induced by train movement on the supported tracks. In this paper, a discrete element model is developed and used to simulate the shear stress–strain response of fouled ballast assembly subjected to direct shear loading. A simplified computational approach is then proposed to model the induced ballast fouling and capture the mechanical response of the ballast at various levels of contamination. The approach is based on the assumption that fine particles comprising the fouling material will not only change the interparticle friction angle, but also the contact stiffness between the ballast particles. Therefore, both the interparticle friction coefficient and effective modulus are adjusted based on a fouled ballast model that is validated using experimental results. The effect of ballast degradation is also investigated by gradually changing the particle size distribution of the ballast assembly in the discrete element model to account for the increased range of particle sizes. Using the developed model, the effect of ballast degradation on the shear strength is then evaluated. Conclusions are made to highlight the suitability of these approximate approaches in efficiently modeling ballast assemblies under shear loading conditions.

Evolution of surface roughness of single sand grains with normal loading

The surfaces of soil grains are not perfectly smooth, especially examined at small scale. In geotechnical engineering, surface roughness has been found to be able to influence the inter-particle friction angle at micro scale and small-strain stiffness at macro scale. However, the quantity and quality of the studies on surface roughness of natural soils are still limited. In this study, the evolution of surface roughness of natural sand grains with increasing normal load was investigated by a single-particle compression apparatus. Thirty Leighton Buzzard sand (LBS) grains coarser than 2·36 mm were tested, and the surface roughness was measured before and after compression by an optical interferometer. The deformations of the asperities and of the bulk of the sand grains in the vicinity of the contact were mapped. Three stages were identified as the normal load increased: (a) plastic deformation of the asperities; (b) asperities and bulk plastic deformation; and (c) bulk only plastic deformation. At very small normal load, only the asperities were found to deform plastically, and the surface roughness of the sand grains decreases due to the flattening of the asperities. Within this regime, the load–displacement relationship of LBS grains under compression could be simulated by the modified Hertz model, which takes surface roughness into consideration. With increasing normal load, the bulk of the sand grains began to yield near the contact. The geometry of the surfaces of LBS grains in contact with the loading platen is the main factor that influences the plastic deformation of the bulk. Differently from the plastic deformation of the asperities, the plastic deformation of the bulk could both smoothen and roughen the surfaces. When plastic deformation of the bulk occurred, both Hertz and modified Hertz theory could not predict the load and displacement relationship of sand grains. Through analysing the cumulative distributions of surface roughness of 30 LBS grains at different normal loads by the Weibull function, the surface roughness was found to decrease dramatically with increasing normal load at first and then tended to be constant.

Characterization of additive manufactured particles for DEM validation studies

Discrete element method (DEM) simulations are often validated using physical laboratory tests on analogue soils to confirm the macro-scale response. These analogue soils have typically consisted of steel ball bearings or glass beads, thus limiting the shapes to spherical particles. Additive Manufacturing (AM) technologies can be used to create 3D objects of any shape layer-by-layer. Using these AM particles as analogue soils allows for DEM validations to be performed using a wide range of shapes, more realistically replicating natural sands and gravels. In order to use these AM particles, however, characterization of the AM material is essential to ensure its suitability for laboratory testing and to determine the intrinsic material properties input into the DEM models. This paper describes a study in which material properties and surface characteristics of two different additively manufactured materials are determined. A gypsum-epoxy composite material and a photopolymer material were tested to determine properties such as Young’s modulus, Poisson’s ratio, shape, surface roughness, and inter-particle friction angle. In comparison to the commonly used steel ball bearings and alkaline glass beads, the AM particles exhibited improved circularity. The hardness and Young’s modulus values were measured directly and then a fitting procedure was used to assess the Hertzian behavior of the spheres under uniaxial compression. While the inter-particle friction angle and the surface roughness were higher for the AM particles in comparison to the steel ball bearings and glass beads, the ability to control particle shape for the AM particles proves advantageous for manipulation of shape parameters for DEM validation.

Sand type effect on the behaviour of sand-granulated rubber mixtures: Integrated study from micro- to macro-scales

The mechanical behaviour of rubber mixed with different types of host sands is investigated from micro- to macro-scales. The change of the mobilized friction angle because of rubber inclusion is associated to the change of inter-particle friction angle and the friction angle due to particle rearrangement. The mobilized friction angles at the peak and critical states were obtained from triaxial testing data, and the inter-particle friction angles at different sand and sand-rubber interfaces were measured by means of grain-scale experiments. It is found that: (i) The peak friction angle decreases after adding rubber particles for all host sands, which is more significant for dilative sands. (ii) For smooth and non-breakable sands, adding rubber increases the friction angle at the critical state, due to the increasing inter-particle friction from sand-rubber interfaces, but the reduction of sand-sand contacts weakens the interlocking, leading to easier particle rearrangement. For rough and breakable sands, adding rubber decreases the friction angle at the critical state, since the inter-particle friction of sand-rubber interfaces is lower than that of pure sand interfaces, but leads to less particle breakage and thus harder particle rearrangement. (iii) State parameter works well in assessing the effect of rubber inclusion on the peak strength.

Geotechnical shear behavior of Xanthan Gum biopolymer treated sand from direct shear testing

Conventional geotechnical engineering soil binders such as ordinary cement or lime have environmental issues in terms of sustainable development. Thus, environmentally friendly materials have attracted considerable interest in modern geotechnical engineering. Microbial biopolymers are being actively developed in order to improve geotechnical engineering properties such as aggregate stability, strength, and hydraulic conductivity of various soil types. This study evaluates the geotechnical engineering shear behavior of sand treated with xanthan gum biopolymer through laboratory direct shear testing. Xanthan gum-sand mixtures with various xanthan gum content (percent to the mass of sand) and gel phases (initial, dried, and re-submerged) were considered. Xanthan gum content of 1.0% sufficiently improves the inter-particle cohesion of cohesionless sands 3.8 times and more (up to 14 times for dried state) than in the untreated (natural) condition, regardless of the xanthan gum gel condition. In general, the strength of xanthan gum-treated sand shows dependency with the rheology and phase of xanthan gum gels in inter-granular pores, which decreases in order as dried (biofilm state), initial (uniform hydrogel), and re-submerged (swollen hydrogel after drying) states. As xanthan gum hydrogels are pseudo-plastic, both inter-particle friction angle and cohesion of xanthan gum-treated sand decrease with water adsorbed swelling at large strain levels. However, for 2% xanthan gum-treated sands, the re-submerged state shows a higher strength than the initial state due to the gradual and non-uniform swelling behavior of highly concentrated biofilms.

Discrete element simulation of railway ballast: modelling cell pressure effects in triaxial tests

The paper investigates reproducing the effects of confining pressure on the behaviour of scaled railway ballast in triaxial tests in discrete element models (DEM). Previous DEM work, using a standard Hertzian elastic contact law with an elastic–perfectly plastic tangential slip model, has been unable to replicate the behaviour observed in laboratory tests across a range of confining pressures without altering both the material stiffness and the inter-particle friction. A new contact law modelling damage at the contacts between particles is introduced. Particle contact is via spherically-capped conical asperities, which reduce in height if over-stressed. This introduces plasticity to the behaviour normal to the contact surface. In addition, the inter-particle friction angle is varied as a function of normalized contact normal force. At relatively low normal forces the friction angle must be increased for peak mobilized friction angles to match the laboratory data, an effect that is attributed to interlocking at the scale of surface roughness. Simulation results show close agreement with laboratory data.

DEM assessment of impact forces of dry granular masses on rigid barriers

In the design of sheltering structures/embankments for the mitigation of the risk due to rapid and long spreading landslides, a crucial role is generally played by the assessment of the impact force exerted by the flowing mass on the artificial obstacle. This paper is focused on this issue and in particular on the evaluation of the maximum impact force on the basis of the results obtained by performing an extensive numerical campaign by means of a 3D discrete element code, in which a dry granular mass is schematised as a random distribution of rigid spherical particles. The granular mass is generated just in front of the obstacle: its initial volume, velocity distribution, height, length and porosity are arbitrarily assigned, and the impact process is exclusively analysed. The initial conditions are varied to take a large variety of geometrical/mechanical factors, such as the initial front inclination, its height, the initial void ratio, the length of the impacting mass and the inter-particle friction angle, into consideration. A design formula is also proposed on the base of the obtained results and critically compared with the literature data.

Dry Granular Flows Impacts on Rigid Obstacles: DEM Evaluation of a Design Formula for the Impact Force

In the design of sheltering structures or embankments for the mitigation of the risk due to rapid and long spreading landslides, a crucial role is played by the evaluation of the impact force exerted by the flowing mass on the artificial obstacle. This paper is focused on this issue and in particular on the evaluation of the maximum impact force on the basis of the results obtained by performing an extensive numerical campaign by means of a 3D discrete element code (PFC3D), in which a dry granular mass is represented as a random distribution of rigid spherical particles. The analyses regard the impact process only, while triggering and the propagation phase of the flow are not considered. For this reason, in the model the granular mass is generated just in front of the obstacle; its initial volume, velocity distribution, height, length and porosity are assigned as initial conditions. The initial conditions are varied to take into consideration a large variety of geometrical/mechanical factors, such as the initial front inclination, its height, the initial void ratio, the length of the impacting mass and the inter-particle friction angle. A design formula is also proposed on the base of the obtained results and critically compared with the literature data and previous formulations based on hydrodynamic models.

Micromechanical Modeling of Yield in Isotropic Non-Cohesive Particulate Materials

We perform a micromechanical analysis of general isotropic non-cohesive particulate materials idealized as three-dimensional random assemblies of uniform spheres with a simple linear elastic inter-particle contact force law and inter-particle Coulomb friction law. We obtain analytical relationships between the inter-particle friction coefficient $$\mu$$ (or inter-particle friction angle $$\phi _\mu = \tan ^{-1} \mu$$ ) on the microscale and the material friction angle $$\phi$$ on the macroscale. Our micromechanical analysis directly employs force and moment equilibrium (together with compatibility and the contact constitutive assumptions noted) rather than energy methods, and thus can account for the effects of particle rotation, and in particular the effects of mechanisms or zero-energy modes due to particle rotation. To explore the effects of particle rotation, we perform analyses with particle rotation either allowed or prohibited. To validate the analytical results obtained here, we compare the $$\phi$$ versus $$\phi _\mu$$ curves determined theoretically to those obtained by the discrete element method (DEM) for six randomly packed specimens of 3430–29, 660 uniform spherical elements with uniform inter-element Coulomb friction in Fleischmann et al. in Geotech Geol Eng 32(4):1081–1100, (2014). The $$\phi$$ versus $$\phi _\mu$$ curves derived here show remarkable agreement with those obtained via DEM simulations in Fleischmann et al. in Geotech Geol Eng 32(4):1081–1100, (2014), especially for the case in which particle rotation is not artificially restrained.

Relationship between void- and contact normal-based fabric tensors for 2D idealized granular materials

Fabric tensors are commonly used in the study of granular materials as internal variables to quantify anisotropic fabrics. Fabric tensors can be constructed based on different microstructural entities in the material, such as particle long axis orientations, inter-particle contact normal directions, and orientations of void shapes. The current study explores the relationship between these different fabric tensors. Using two-dimensional discrete element method (DEM) simulations, we discover a simple and strong linear correlation between contact normal- and void vector-based fabric tensors for granular materials composed of non-elongated particles. This correlation holds true independent of the variations of all parameters and conditions exhaustively considered in this study, including the material’s packing density, stress state, inter-particle friction angle, particle size distribution, and particle shape. We also perform a preliminary and exploratory study of materials consisting of significantly elongated particles. The limited results show that the change of void vector-based fabric tensor appears to be affected by the corresponding components of the particle orientation-based fabric tensor and contact normal-based fabric tensor. Meanwhile, the normal component of the particle orientation-based fabric tensor and the corresponding component of contact normal-based fabric tensor are negatively correlated.

Variations in shear behavior among specimens with different packing patterns

This paper describes variations in shear behavior among specimens with the same packing fraction but different coordination number (different packing patterns). The multi-sphere models to express grain shapes of Toyoura sand were employed in discrete-element method (DEM) simulation. Specimens with different packing patterns were produced by two methods: changing interparticle friction angle (FC method) and applying cyclic simple shear (CC method). A series of simple shear DEM simulation was carried out using the FC and CC specimens. The shear response in small strain range (secant shear modulus) of FC was larger than CC specimens, while difference in peak shear stress (bulk shear friction) between FC and CC specimens were insignificant. Strong correlation was found in the relation between secant shear modulus and coordination number of the system, as well as between the bulk shear friction and packing fraction. The initial coordination number rapidly decreases with increasing shear strain, and thereafter it reaches an isostatic value. On the other hand, the packing density required large shear strain for reaching the critical state. It was found that the initial difference in coordination number between FC and CC specimens disappeared before reaching their bulk shear frictions. Therefore, the bulk shear friction strongly correlates with the packing density.

Simulation of triaxial response of granular materials by modified DEM

A modified discrete element method (DEM) with rolling effect taken into consideration is developed to examine macroscopic behavior of granular materials in this study. Dimensional analysis is firstly performed to establish the relationship between macroscopic mechanical behavior, mesoscale contact parameters at particle level and external loading rate. It is found that only four dimensionless parameters may govern the macroscopic mechanical behavior in bulk. The numerical triaxial apparatus was used to study their influence on the mechanical behavior of granular materials. The parametric study indicates that Poisson’s ratio only varies with stiffness ratio, while Young’s modulus is proportional to contact modulus and grows with stiffness ratio, both of which agree with the micromechanical model. The peak friction angle is dependent on both inter-particle friction angle and rolling resistance. The dilatancy angle relies on inter-particle friction angle if rolling stiffness coefficient is sufficiently large. Finally, we have recommended a calibration procedure for cohesionless soil, which was at once applied to the simulation of Chende sand using a series of triaxial compression tests. The responses of DEM model are shown in quantitative agreement with experiments. In addition, stress-strain response of triaxial extension was also obtained by numerical triaxial extension tests.

Virtual Soil Tests for Determination of Particle Properties for Use in DEM Models from Measurable Bulk Properties

<abstract> <bold><sc>Abstract.</sc></bold> Distinct element modeling (DEM) is a powerful technique for describing the soil-machine interaction process. The technique is well suited for dealing with large deformations and topology compared to techniques such as the finite element method (FEM). Unfortunately, selecting interparticle properties (normal and tangential spring constants at the contact point, interparticle cohesion and friction angle) that can adequately represent the soil-machine interaction process has been one of the major bottlenecks in the widespread application of DEM. In this article, we describe novel approaches to determine key DEM interparticle parameters for use in soil-machine interaction studies. A series of virtual triaxial tests was carried out to relate interparticle cohesion and friction angle values to Mohr-Coulomb parameters of bulk soil. A virtual uniaxial consolidation test was conducted to determine the normal spring constant at the contact point. The results indicate high coefficient of multiple determination (R²) values between 0.85 and 0.95 for a range of realistic soils, indicating potential utility of the proposed techniques.

Determination of Yield Surfaces for Isotropic Non-Cohesive Particulate Materials by the Discrete Element Method

We perform numerical simulations using the discrete element method (DEM) to determine yield surfaces for large samples of randomly packed uniform spheres with constant normal and tangential contact stiffnesses (linear spring model) and uniform inter-particle friction coefficient μ, for a large range of values of the inter-particle friction coefficient μ. The beauty of DEM is that the micromechanical properties of the spheres, especially the inter-particle friction coefficient μ, are known exactly. Further, simulations can be performed with particle rotation either prohibited or unrestrained, which provides an effective means for evaluating analytical models that employ these assumptions. We compare the resulting yield surfaces to the Mohr–Coulomb, Matsuoka–Nakai, Lade–Duncan, and Drucker–Prager yield surfaces, and determine the relationship between the resulting material friction angle ϕ on the macroscale and the inter-particle friction coefficient μ (or the inter-particle friction angle ϕμ) on the microscale. We find the Lade–Duncan yield surface provides the best agreement, by far, with the simulations in all cases. We also monitor inter-particle friction work and particle rotation within each specimen during the DEM simulations, both globally and on a particle-by-particle basis, and we compare the results obtained from DEM simulations in which the spheres were allowed full three-dimensional translational and rotational freedom of motion and DEM simulations in which particle rotation was prohibited.