Granular Geomaterials Research Articles

Anisotropic Breakage Mechanics for cemented granular materials

The anisotropy of granular geomaterials is sensitive to their fabric, which exhibits anisotropic mechanical properties as a function of deposition history, microscopic fabric, and loading paths. Here, a new fabric-enriched continuum breakage model is proposed to examine the relation between elastic and inelastic anisotropy in granular materials and cemented granular materials. A microstructure model is first implemented in the framework of fabric-enriched continuum breakage mechanics (F-CBM), where the anisotropic behaviour prior to yielding is introduced through a symmetric second-order fabric tensor embedded in the expression of the elastic energy potential. The anisotropic strain energy storage prior to grain crushing leads to the rotation and distortion of the yield surface of cemented granular materials. Parametric analyses are performed to assess the overall capability of the model to characterize the anisotropic inelastic processes in cemented granular. It is shown that the proposed model can accurately predict the strong correlation between anisotropic elasticity and breakage-damage processes in cemented granular materials. When damage involving the skeleton is the dominant inelastic process, the size of the elastic domain contracts and the material exhibits augmented brittleness with the disintegration of cement. While breakage processes are predicted to dominate the response of lightly cemented granular materials resulting in hardening behaviour. This work can be further extended to dynamically capture the anisotropic response of cemented granular materials with water-sensitive mineral constituents by accounting for the evolution of microstructural anisotropy.

A theoretical model for estimating the thermal conductivity of granular geomaterials with low porosity

The thermal conductivity has an important influence on the geotechnical and geoenvironmental engineering. Most existing thermal conductivity models appear to estimate the thermal conductivity of soils samples with large porosity, few of them were proposed to model the thermal conductivity of soil samples with low porosity. In this study, a theoretical model was proposed to estimate the thermal conductivity of unsaturated granular geomaterials with low porosity. Two parameters (i.e., ζ and β) were introduced. The parameter ζ can be applied to control porosity and solid particle shape, while the parameter β can be used to control water content. Mathematical comparison showed that the proposed thermal conductivity model fell within the Wiener bounds. The new model and five thermal conductivity models were evaluated with experimental data, showing that the new model accurately estimates the relationship between thermal conductivity and saturation for granular geomaterials with low porosity.

A refined deviatoric hardening plastic model for sand

The classical deviatoric hardening models are capable of characterizing the mechanical response of granular materials for a broad range of degrees of compaction. This work finds that it has limitations in accurately predicting the volumetric deformation characteristics under a wide range of confining/consolidation pressures. The issue stems from the pressure independent hardening law in the classical deviatoric hardening model. To overcome this problem, we propose a refined deviatoric hardening model in which a pressure-dependent hardening law is developed based on experimental observations. Comparisons between numerical results and laboratory triaxial tests indicate that the improved model succeeds in capturing the volumetric deformation behavior under various confining/consolidation pressure conditions for both dense and loose sands. Furthermore, to examine the importance of the improved deviatoric hardening model, it is combined with the bounding surface plasticity theory to investigate the mechanical response of loose sand under complex cyclic loadings and different initial consolidation pressures. It is proved that the proposed pressure-dependent deviatoric hardening law is capable of predicting the volumetric deformation characteristics to a satisfactory degree and plays an important role in the simulation of complex deformations for granular geomaterials.

Calibration of Sliding Friction Coefficient in DEM between Different Particles by Experiment

Granular materials are widely prevalent in nature and industry, and the discrete element method (DEM) is the most effective method for the mechanical analysis of granular materials. Because of the difficulty inherent in friction coefficient determination, the friction behavior of granular geomaterials has always been a difficult problem in DEM. In order to study the variation rules of the sliding friction coefficients in DEM, an experiment designed to determine the sliding friction coefficient between particles with different shapes and different contact forms and an experiment designed to determine the sliding friction coefficient between particles and different boundaries were proposed, and the experimental results were fitted. In order to verify the reliability of the experiments, the fitting results were embedded into DEM software, and several packing experiments and simulation experiments were carried out and compared. The simulated results are detailed and discussed with reference to the experimental results as part of this paper. The results indicate that the simulation results are highly consistent with the experimental results, and the sliding friction coefficient obtained by the proposed experiment is in accordance with that determined theoretically. The sliding friction coefficient determined by fitting according to the experimental results can determine the sliding friction coefficient in DEM simulation and improve the accuracy of simulation results.

DEM Analysis of Fabric Evolution and Behavior of Granular Geomaterials in True Triaxial Test with Flexible Boundary

The fabric of granular geomaterials used in roads and embankments is related to properties such as shear strength, permeability and liquefaction resistance. To evaluate the fabric evolution and behavior of geomaterials, a series of the true triaxial test simulations with flexible boundaries under general stress states in this study were performed using the three-dimensional discrete element method (DEM). First, the stress states at the axial strain of 20%, which indicates that the stress under the critical state conforms to the Matsuoka-Nakai criterion, were examined. Then the uniqueness of the coordination number and non-uniqueness of void ratio and invariant of anisotropic fabric tensor under the critical state were investigated based on the contact density, which indicates the relative number of contacts in different orientations. In particular, the contact density at the critical state under different mean effective principal stresses with its effects on the invariant of anisotropic fabric tensor were discussed. It was found that the contribution of the contact density to the fabric anisotropy decreased as the mean effective principal stress increased due to geometric limitations.

Variational Approach to Damage Induced by Drainage in Partially Saturated Granular Geomaterials

Within the context of immiscible biphasic flow in porous media, when the nonwetting fluid invades the pore spaces which are a priori saturated with the wetting fluid, capillary forces dominate if the pore network is formed by fine-grained soils. Owing to the cohesion-less frictional behavior of such soils, a capillary force–driven fracturing phenomenon has been put forward by some researchers. Unlike the purely mechanistic tensile force–driven mode-I fracturing that typically has been attributed to the formation of desiccation cracks in soils, attempts to model this alternate capillarity-driven mechanism have not yet been realized at a continuum scale. However, the macro-scale counterpart of the capillary energy associated with the various pore-scale menisci is well-established as the interfacial energy characterized by the soil-water retention curve. An investigation of the possible contribution of this interfacial energy in supplying the dissipation related to fracture initiation is the essence of this work, inspired by the vast literature on gradient damage modeling.

Comparative Study on Particle Size Effect of Crushable Granular Soils through DEM Simulations

Abstract The particle size plays an important role in the mechanical behavior of granular geomaterials. With respect to the crushable granular soils, the particle breakage under different pressures leads to the variation of the particle size distribution of soils. Therefore, it is essential to accurately model the particle fracture process to reproduce the key response of granular soils in the simulation. In this study, two simulated approaches, cluster method and replacement method, were performed to investigate the particle size effect for the crushable granular soils by three-dimensional (3D) discrete element method (DEM). DEM simulations were validated through the available results of diametric and oedometric compression tests with the help of the Weibull statistics. Based on the evaluation at particle and assemble-scale, it is found that both the cluster method and replacement method could simulate the particle strength and size dependence of sample failure with a good agreement with experimental results. The particle breakage phenomenon is also successfully modeled in DEM simulation and analyzed by the breakage index. Meanwhile, the computational efficiency was analyzed compared with two simulated methods. The findings in this study can provide a viable approach to investigate the particle breakage effect of the crushable geomaterials.

A Level Set-Discrete Element Method in YADE for numerical, micro-scale, geomechanics with refined grain shapes

A C++-Python package is proposed for 3D mechanical simulations of granular geomaterials, seen as a collection of particles being in contact interaction one with another while showing complex grain shapes. Following the so-called Level Set-Discrete Element Method (LS-DEM), the simulation workflow stems from a discrete field for the signed distance function to every particle, with its zero-level set corresponding to a particle’s surface. A Fast Marching Method is proposed to construct such a distance field for a wide class of surfaces. In connection with dedicated contact algorithms and Paraview visualization procedures, this shape description eventually extends the YADE platform for discrete simulations. Its versatility is illustrated on superquadric particles i.e. superellipsoids. On computational aspects, memory requirements possibly exceed one megabyte (MB) per particle when using a double numeric precision, and time costs, though also significant, appear to be lighter than the use of convex polyhedra and can be drastically reduced using a simple, OpenMP, parallel execution.

Recycling of End-of-Life Tires (ELTs) for Sustainable Geotechnical Applications: A New Zealand Perspective

End-of-life tires (ELTs) are tires, unusable in their original form, which go into a waste management scheme (for recycling and energy recovery purposes), or otherwise are disposed. In New Zealand, the annual disposal of 3.5 million ELTs is posing critical environmental and socio-economic issues, and the reuse of ELTs through large-volume recycling engineering projects is a necessity. In this study, gravel and recycled granulated rubber were mixed to explore the possibility of obtaining synthetic granular geomaterials (with adequate geotechnical and environmental characteristics) that are suitable as structural fills for geotechnical applications including foundation systems for low-rise light-weight residential buildings. Moreover, an original framework with a set of geo-environmental criteria is proposed for the acceptance of gravel–rubber mixtures (GRMs) as structural fills. It is shown that when gravel-size like rubber particles are used, GRMs with volumetric rubber content of 40% or less have adequate strength (ϕ’ > 30°), low compressibility (εv ≤ 3%), excellent energy adsorption properties, and acceptable leachate metal concentration values (e.g., Zn < 1 mg/L), making them ideal synthetic structural fill materials for many sustainable geotechnical applications.

Operation of Vibrating Dryer with Elastic Transporter for Granular Geomaterials

Operation of Vibrating Dryer with Elastic Transporter for Granular Geomaterials

Key geomechanical properties of the historically liquefiable TP-Lisbon sand

The intrinsic properties of sands have a strong influence on the behaviour of these soils. Therefore, particle shape and granular packing can provide relevant insights into the mechanical properties of granular geomaterials. This study presents the characterisation of the key mechanical geomechanical properties controlling the behaviour of an alluvial fine sand, which composes the liquefiable layer of the geological profile at ‘Praça do Comercio’ square, located in the downtown of Lisbon (Portugal). For this purpose, a comprehensive experimental plan was conducted in the laboratory using accurate testing procedures. The experimental plan addressed: (i) the evaluation of the particle shape from a large number of particles using a computational geometry algorithm and statistical procedures; (ii) the estimation of the minimum and maximum void ratio through two standard methods; (iii) the assessment of the stress–strain behaviour by triaxial tests using lubricated end platens and an embedded connection piston, and void ratio measurements using end-of-test soil freezing; and (iv) the stress-dependency assessment of seismic wave velocities using bender elements. Results are interpreted within the critical state soil mechanics framework, highlighting the effects of the particle shape and granular package on the behaviour of this natural sand. In addition, critical state and small-strain parameters are compared and thoroughly discussed against selected data of other sands. Results provide experimental evidence about the influence of the particle shape and granular packing on the key geomechanical properties of TP-Lisbon sand.

Operation of Vibrating Dryer with Elastic Transporter for Granular Geomaterials

Operation of Vibrating Dryer with Elastic Transporter for Granular Geomaterials

Statistical analysis and comparative study of multi-scale 2D and 3D shape features for unbound granular geomaterials

Morphological analysis is a prerequisite step for studying the mechanical properties of unbound granular geomaterials through both laboratory experiments and numerical simulations. In this study, two typical geomaterials, e.g., ballast and cobble particles, were sampled for study. First, a systematic framework was established to acquire two-dimensional (2D) particle outline and three-dimensional (3D) morphology for statistical shape analysis. The photographic-based system was set up to acquire 2D images of particle projections from multiple surrounding directions, then the images obtained were used to reconstruct 3D particle morphology based on close-range photogrammetry. Second, in order to quantify particle shape at three different geometric scales, 6 well-acknowledged 2D and 3D geometry descriptors, i.e., aspect ratio, sphericity, convexity, roundness, regularity, and roughness were computed. Third, the probability distribution function (PDF) of shape descriptors were fitted with different functions. Finally, 2D and 3D shape descriptors were statistically compared and the relationships between them were revealed by analyzing their cumulative distribution functions (CDFs).

Evaluating the overconsolidation ratios and peak friction angles of granular soil deposits using noninvasive seismic surveying

The main objective of this study was to propose an approach to estimate the peak friction angles of over-consolidated granular soil deposits by using the P-wave velocity and the SV- and SH-wave velocities. To this end, seventeen pairs of P- and S-wave seismic refraction profiles were carried out at three different granular sites in Iran using noninvasive seismic wave methods. To estimate the overconsolidation ratio (OCR) in granular geomaterials in terms of SH/SV velocity ratios, a general regression analysis was performed on the obtained data from this study combined with those reported in the literature. In addition, by assuming cross-anisotropy of the soils, the P- and S-wave velocities were utilized to develop an equation for calculating the coefficient of lateral earth pressure at rest (K0). The Mayne and Kulhawy formula was finally employed to evaluate $$\varphi^{\prime}$$ in granular soil deposits by combining the calculated K0 values and the estimated OCR values. The findings of this study may be used as the appropriate approaches for economic and noninvasive determination of in-situ peak friction angle in granular soil deposits using the surface seismic surveying.

A microscale-based model for small-strain stiffness in unsaturated granular geomaterials

Stiffness at very small strains G0 is commonly assessed by way of laboratory and field methods, and used to design a wide range of infrastructure. When stiffness is inferred from field measurements, its value depends on the soil suction and state of saturation at the time of the measurement, and models are needed to infer G0 at varying suction and degree of saturation. When stiffness is measured on saturated specimens in the laboratory, models are needed to extrapolate the laboratory ‘saturated’ stiffness to the field ‘unsaturated’ stiffness. This paper presents an experimental investigation of G0 of unsaturated sand using the hanging water column method and the bender element technique. Experimental results revealed that wave propagation velocity and, hence, stiffness is not controlled by the product ‘suction times the degree of saturation’. A microscale-based model was formulated to interpret the experimental results, and to elucidate the mechanisms underlying different patterns of G0 in unsaturated materials observed in the literature. According to the proposed model, the evolution of G0 is controlled by the evolution of the suction/degree of saturation-induced intergranular stress during drying–wetting cycles. The breadth of the water retention curve and the magnitude of the intergranular stress due to the presence of the menisci were found to be responsible for the different patterns of G0.

Grain size and time effect on the deformation of rockfill dams: a case study on the Shuibuya CFRD

The mechanical behaviour of coarse, granular geomaterials critically depends on their grain size distributions. In the settlement analysis of rockfill dams, however, the stress–strain curves obtained from specimens with reduced gradations are often used to approximate the behaviour of prototype rockfills. Accumulated evidence has shown that such practice can underestimate the settlement of concrete face rockfill dams (CFRDs), leading to unexpected damage of the concrete slabs and excessive leakage of the dam. In this paper, the recently developed rate-dependent breakage mechanics theory and breakage-energy scaling law is applied for the settlement analysis of the Shuibuya CFRD. The model is first calibrated using triaxial data from reduced specimens and then the parameters are extrapolated to represent prototype rockfills. The constitutive equations are implemented in a finite-element package and later applied to full-scale simulations of the dam, covering its construction, impoundment and operation phases. The predicted settlement profiles agree reasonably well with the data measured from the internal displacement gauges, thus corroborating the predictive capability of the new methodology. Finally, it is shown that neglecting the scaling and creep effect in the constitutive behaviour of rockfills will underestimate the maximum settlement of the dam by 14% and 18%, respectively.

A supplementary analytical model for the stagnant effective thermal conductivity of low porosity granular geomaterials

A cylindrical unit cell model for predicting stagnant effective thermal conductivity of two-phase or three-phase low porosity granular geomaterials was proposed in this paper. In the present model, the cylindrical unit cell is made of a quasi-hemispherical/cylindrical solid particle, and the solid grain is surrounded by water or air or the mixtures of two phases. In addition to the thermal conductivity of each phase, the effects of porosity and saturation degree on the stagnant effective thermal conductivity of geomaterials were investigated by introducing the coefficients α and β that control the porosity and saturation degree, respectively. The stagnant effective thermal conductivity of cylindrical unit cell was obtained via lumped parameter method and a further spatial correction was then conducted. Comparisons with some empirical models and experimental data for three types of selected geomaterials indicate that this theoretical model successfully captures the stagnant effective thermal conductivity with variation of saturation degree and thus provides the stagnant effective thermal conductivity of granular geomaterials with acceptable accuracy in the porosity range [0, 0.33] at most degrees of saturation.

Compressive behaviour of very dense structured granular geo-materials

The isotropic compression behaviour of dense structured geo-materials and the associated degradation at failure is addressed in a non-qualitative manner. To this end, the general behaviour of fully de-structured geo-materials, e.g. sands, as an accepted reference is thoroughly investigated. The parameters affecting the behaviour of de-structured materials such as mineralogy, gradation and fines content, and relative density are discussed. The isotropic compression behaviour of a weathered weak sandstone, representative of a structured granular geo-material, is then investigated along the isotropic compression stress path under a range of pressures from nil to 100 MPa. Both structured and fully de-structured states of the material are tested implementing the proposed quantification method. The effect of structure on the compressibility of the material is found to be tangible. By plotting the specific volume versus natural log of the mean effective stress, the onset of structure collapse and the successive degradation of the structure are captured. By increasing the pressure, compaction bands throughout the sample increasingly develop and the compression curve asymptotically approaches to that of the fully degraded state of the material. At elevated pressures, the rate of compressibility will increase significantly due to particle crushing.

Reconstructing granular particles from X-ray computed tomography using the TWS machine learning tool and the level set method

X-ray computed tomography (CT) has emerged as the most prevalent technique to obtain three-dimensional morphological information of granular geomaterials. A key challenge in using the X-ray CT technique is to faithfully reconstruct particle morphology based on the discretized pixel information of CT images. In this work, a novel framework based on the machine learning technique and the level set method is proposed to segment CT images and reconstruct particles of granular geomaterials. Within this framework, a feature-based machine learning technique termed Trainable Weka Segmentation is utilized for CT image segmentation, i.e., to classify material phases and to segregate particles in contact. This is a fundamentally different approach in that it predicts segmentation results based on a trained classifier model that implicitly includes image features and regression functions. Subsequently, an edge-based level set method is applied to approach an accurate characterization of the particle shape. The proposed framework is applied to reconstruct three-dimensional realistic particle shapes of the Mojave Mars Simulant. Quantitative accuracy analysis shows that the proposed framework exhibits superior performance over the conventional watershed-based method in terms of both the pixel-based classification accuracy and the particle-based segmentation accuracy. Using the reconstructed realistic particles, the particle-size distribution is obtained and validated against experiment sieve analysis. Quantitative morphology analysis is also performed, showing promising potentials of the proposed framework in characterizing granular geomaterials.

Predictive potential of Perzyna viscoplastic modelling for granular geomaterials

SummaryThis paper reappraises Perzyna‐type viscoplasticity for the constitutive modelling of granular geomaterials, with emphasis on the simulation of rate/time effects of different magnitude. An existing elasto‐plastic model for sands is first recast into a Perzyna viscoplastic formulation and then calibrated/validated against laboratory test results on Hostun sand from the literature. Notable model features include (1) enhanced definition of the viscous nucleus function and (2) void ratio dependence of stiffness and viscous parameters, to model the pycnotropic behaviour of granular materials with a single set of parameters, uniquely identified against standard creep and triaxial test results. The comparison between experimental data and numerical simulations points out the predicative capability of the developed model and the complexity of defining a unique viscous nucleus function to capture sand behaviour under different loading/initial/boundary and drainage conditions. It is concluded that the unified viscoplastic simulation of both drained and undrained response is particularly challenging within Perzyna's framework and opens to future research in the area. The discussion presented is relevant, for instance, to the simulation of multiphase strain localisation phenomena, such as those associated to slope stability problems in variably saturated soils.