This study examines the undrained cyclic behavior of granular assemblies under true triaxial loading, with a particular focus on the micromechanical effects of initial anisotropy and Lode angle. The Discrete Element Method (DEM) is coupled with the Coupled Fluid Method (CFM) to model fluid-solid interactions under undrained conditions. Three transversely isotropic specimens, composed of elongated particles, are generated with bedding plane orientations of 0 ∘ , 45 ∘ , and 90 ∘ to represent different initial fabric conditions. Simulations are performed under constant mean total stress with a fixed Lode angle. The results reveal that both initial fabric and Lode angle significantly influence liquefaction susceptibility and shear strength. Specifically, increasing the bedding plane angle from 0 ∘ to 90 ∘ increases the number of loading cycles required to reach liquefaction, primarily due to better alignment between the bedding plane and the major principal stress direction. Furthermore, the Lode angle affects the secant shear modulus and the rate of excess pore pressure generation, underscoring its role in preliquefaction behavior.
Instabilities and failure in ductile non associated materials have been widely investigated during last decades especially in the case of geomaterials. It has been shown experimentally that collapse of some specimens can occur strictly within the ultimate plasticity limit, which is experimentally characterized by the maximum shear stress in a drained triaxial test. From a theoretical point of view such instability problems are well described using the so called second order work criterion derived from the Hill’s stability analysis. Hence a question arises as to the experimental characterization of the ultimate plasticity limit with respect to the choice of stress paths. After a few reminders on Hill’s theory, we prove in a general framework that the drained triaxial paths allow to determine with certainty this ultimate plasticity limit without any risk of preliminary bifurcation whatever the elasto-plastic material considered. We conclude that the plasticity limit is only slightly sensitive to variation of the internal state of the material, which can be described by different micromechanical quantities such as the void ratio and the fabric tensor. Furthermore, we define the limit of the bifurcation domain as the surface drawn in the 6-dimensional stress space that delimits the unconditionally stable space from the one where instabilities and failures can occur within the plasticity limit. However, we show that this latter limit is itself very sensitive to the evolution of the internal state of the soil sample.
The interaction between particles in granular materials is largely determined by their shape and interparticle friction. Thus, understanding their combined effects is essential for modelling the mechanical behaviour at the bulk scale. Previous studies have focused on the link between the morphology of the particles and the bulk response of the specimen. The emergence of non destructive full-field techniques, such as x-ray tomography, present a novel opportunity for the detailed quantification of key particle-scale phenomena. This study investigates the impact of inter-particle friction and particle shape on the deformation processes of granular materials through in-operando x-ray tomography. Monodisperse specimens, comprising ellipsoidal particles with a given aspect ratio and interparticle friction coefficients, are here tested under triaxial compression conditions. Three values of aspect ratio and two friction coefficients are explored, yielding in total six specimens. Over 30 scans per test are acquired, every 0.5 % of axial shortening. Each of the more than 20000 individual particles are identified and tracked throughout a test. Strain localisation dominates post-peak stress ratio, forming compressive and dilative zones within the shear band. The results show that higher aspect ratios lead to an increase of volumetric strain, while lower interparticle friction makes the response less dilative. The study of the interplay between particles interlocking and rotation, reveals that particles with a mild degree of anisometry and high friction yield the highest degree of bulk dilatancy, due to a balancing between the interlocking and rotation.
Glaciation cycles are one aspect to be considered in assessing the safety of deep geological repository sites for long-term radioactive waste storage. This study examines the impact of time-dependent boundary conditions and thermo-hydro-mechanical (THM) couplings on geological formations under glaciation-induced stresses, pressures and temperature changes. Using OpenGeoSys, an open-source finite element simulator, we analyzed various process couplings to understand the underlying physical processes and numerical instabilities. We simulated vertical cross-sections of geological models relevant to nuclear waste repository sites, incorporating comprehensive geological data to capture the formations' heterogeneity and structural features. A viscoplastic material model was used for rock salt strata to account for dislocation creep and pressure-solution creep. The study benefited from rigorous automation of the entire simulation workflow, making the setup suitable for evaluating actual repository sites regarding integrity criteria. Although the modeled rock salt strata were hydraulically deactivated, results were highly dependent on hydraulic boundary conditions. Groundwater flow significantly altered the geological temperature profile via advective heat transport and influenced the temperature-dependent creep behavior. The rock salt creep law, applied over the extensive timescales at hand, approached the limits of the finite-element-method (FEM) with small-strain assumptions. Throughout the modeled glacial cycle, the salt strata exhibit low deviatoric stresses. Fluid pressure and dilatancy criteria are not violated in the repository during the modeled period.
Dynamic excitation of reservoir systems trapping hydrocarbons is a potentially promising solution for increasing the production. At the laboratory scale, it was found that a dynamic vibration of the fluid pressure could induce an increase in permeability of fractures and improve the flow in the drainage system. This phenomenon was also confirmed on sites by the rise in water and oil well production following seismic events. In both cases, it has been hypothesized that the fluid pressure oscillations could contribute to breaking clusters of fine particles located in fractures that clog drains in the reservoir. In order to confirm such an assumption, we developed in a previous study experiments aimed at reproducing clogging in propped fractures and unclogging due to dynamic loads applied perpendicularly to the fracture (Fawaz et al., 2021). This paper built on this experimental set-up and presents a study of the major parameters governing the unclogging of propped fractures by dynamic stimulation. The influences of the proppant distribution density, proppant size, amplitude, and of the frequency of the signal were studied. After applying the dynamic load, results showed a significant increase in permeability with a high recovery rate reaching 75%.
In 2023, we (the Open Geomechanics editors) decided to award an “Impact Paper of the Year” for the papers published in 2022. The idea is to allow some key players in the geomechanics domain to shine a spotlight on a particular paper in the form of a short editorial and a recorded interview between the lead author of the paper and the editor that handled it.
Coupled thermo-hydro-mechanical (THM) processes are ubiquitous in subsurface energy production and geological utilization and storage operations. Numerical simulation of strongly coupled THM processes is a non-trivial task, yet required to predict the performance of many applications in energy geomechanics. The majority of existing and open THM numerical codes are not user adaptable and do not include elastoplasticity coupled to mass and energy balance equations. This article presents an open source thermo-poroelastoplastic finite element numerical code with a fully-coupled monolithic solution strategy that is solved with Fenicsx computing platform. The formulation employs a mixed finite element scheme for pore pressure diffusivity equation, mean stress dependent yield surface, and non-associative plastic potential. The numerical solution is verified with small-scale conventional triaxial tests including drained and undrained compression and extension. We present example simulations reaching the yield surface induced by coupled hydromechanical and thermal loads. In addition, we present two example large-scale applications related to geothermal energy and carbon geological storage. Results show that the numerical solution accurately predicts changes of temperature, pore pressure, and stress for a wide range of model geometries and boundary conditions, including the plastic response. The code is freely available to the general community for use and modification.
Dynamic excitation of reservoir systems trapping hydrocarbons is a potentially promising solution for increasing the production. At the laboratory scale, it was found that a vibration of the fluid pressure could induce an increase in permeability of fractures. We developed in a previous study experiments aimed at reproducing clogging in propped fractures and unclogging due to dynamic loads applied perpendicularly to the fracture [Fawaz et al. 2021]. This paper built on this experimental set-up and presents first a study of the major parameters governing the unclogging of propped fractures by dynamic stimulation. The influences of the quantity of fine particles clogging the fracture, amplitude and frequency of the signal are investigated at constant proppant density. Then, a prototype computational model based on coupled DEM and finite volume method is developed. An original formulation of the evolution of apparent permeability of the fracture due to the presence and motion of solid particles in each finite volume cell is presented. Computations are consistent with experiments, although axial fluid flow is modelled instead of radial flow in the experiments. Results show that the increase of fracture conductivity is strongly related to the movement of proppant which helps at releasing and destabilizing fines clusters.
Drying induced shrinkage is often attributed to two major mechanisms- capillary pressure in the bulk pore solution and disjoining pressure in the liquid film separating the vapor phase from the pore wall or separating solid surfaces in nanometric pores. There is sufficient ambiguity in literature regarding the relative contribution of these two mechanisms, as well as the means to quantify their contributions. The objective of this manuscript is to evaluate the contribution of disjoining pressure in the drying shrinkage of cementitious materials. An unconventional approach to determining disjoining pressure within the framework of continuum mechanics is presented. This approach utilizes the conservation of linear momentum to derive a generalized expression of the disjoining pressure from the Lorentz force vector. The expression suggests that disjoining pressure is essentially an osmotic pressure at the contact surfaces that counters the electrostatic contribution to linear momentum. The proposed theory accurately predicts measurements of osmotic pressure found in the literature for the swelling of charged bilayers in a dilute salt solution. Applied to the shrinkage problem, the theory suggests that shrinkage stress is induced by the reduction in the potential gradient between the liquid film and bulk solution from the reference (fully saturated) state. The reduction in the potential gradient is caused by an increase in the concentration of the solutes in the pore solution when liquid water is removed as the relative humidity decreases.
Shear strength characterization of coarse granular materials often requires modifying the original material in order to fit samples in standard testing devices. This is done, however, at the expense of changing the particle size distribution (psd), employing scaling-down techniques such as parallel grading or scalping methods. Such procedures hide, nevertheless, another challenge. As a given particle size can present a characteristic grain shape, altering the grain size distribution can strongly modify the distribution of grain shapes. While the effects of grain shape on shear strength have been vastly covered in the literature, the effect of having different shapes along grain sizes has yet to be systematically assessed and understood. This article explores the critical shear strength of samples composed of particles with size-shape correlations using 2D discrete element simulations. Two cases of particle shape variability across grain sizes are studied: (1) the sharpness of grains' corners - modeled via the number of sides of regular polygons - and (2) the geometric irregularity of grains - where the corners of a polygon are not necessarily evenly spaced. The effects of these geometrical properties on the shear strength are assessed through a series of numerical simple shearing tests up to large levels of deformation. We find that granular materials presenting different number of sides across grain sizes can strongly modify their mechanical response depending on the grain-size correlation. On the contrary, grain shape irregularity turns out not to have a major effect on the critical shear strength. Microstructural analyses allow us to identify how each correlation affects load transmission mechanisms between grains, and the contribution of each grain shape class to the macroscopic shear strength. This work shows that particle sizes are not the only sample descriptor to consider when applying scaling-down techniques. It is equally key to characterize particle shapes across grain sizes to capture the material's mechanical response adequately.
Unintended and unwanted high frequency oscillation motion is commonly observed in small-scale experiments and in numerical simulations when soil is subjected to harmonic input motions. This high frequency motion has been often attributed to the drawbacks of actuating systems in experimental setups and to numerical noise in computational analyses. This work presents introductory consideration supporting the hypothetical idea that the recorded and the computed high frequency oscillation motion can possibly be the consequence of an unrecognized before physical phenomenon of soil elastic waves released upon unloading due to soil inherent hysteretic stress-strain behaviour and affecting the steady state response to harmonic excitation. To this aim, simplified numerical studies representative of the most basic soil mechanical properties are carried out. The results reveal the presence and the potential importance of soil-released unloading elastic waves when understanding soil free field response and structural response in numerical simulations of small-scale experimental setups. Chosen numerical cases are compared with available examples of experimental works on dry sand from the literature. The discussion provides further comments, including the potential importance of the soil-released elastic waves in real earthquakes of large magnitudes.
. A generic approach to encapsulating meso scale details and their associated dissipative mechanisms in constitutive models for geomaterials is presented. The focus is the explicit meso-macro link as the basis for developments of constitutive models. These links are usually missing in constitutive modelling of geomaterials, leading to incorrect description of post-localisation behaviour at the constitutive (material) level. In other words, the classical definition of material behaviour associated with a unit volume element, based on conditions of homogenous deformation, ceases to exist once localised failure occurs. Such localisation issues can and should also be dealt with at the constitutive level. The proposed generic thermodynamics-based formulation to integrate meso scale behaviour of localisation band in constitutive models pro-vides a way to connect meso and macro scales so that post-localisation behaviour can be correctly described at the constitutive level. Examples on onset of localisation and post-localisation behaviour are used to demonstrate key features and benefits of the proposed approach.
. The water retention curve (WRC) represents a key function in unsaturated soil mechanics as it can be applied for the modeling of the hydro-mechanical behaviour of unsaturated soils. The macroscopic WRC is characterised by different phenomena, such as hysteresis upon cyclic drainage and imbibition. With the help of modern X-ray computed tomography and hydraulic experiments that can be performed in a CT scanning environment, so-called in situ CT experiments, we image cyclic drainage and imbibition in a sand on the pore scale in order to quantitatively measure and study the change of microstructure and capillary state variables , characterising capillary effects in unsaturated granular soils. The measured pore scale data can then be related to the macroscopic WRC. To our knowledge, for the first time very different capillary state variables , such as interfacial areas, contact lines and contact angles, could be extensively measured in high detail for various hydraulic cycles in our experiment. Besides the experimental procedure, the wealth of measured data will be comprehensively presented and discussed and finally shared with the research community.
The constitutive response of granular soils under indefinitely large shear deformation and low stress controls the dynamics of shallow landslides and offshore pipelines. Current testing devices, however, are either limited to small shear deformation or involve a non-uniform stress distribution across the sample being tested. This paper presents the development of an original stadium shear device (SSD) that is free from those issues. In the SSD, soil samples can deform perpetually within a closed stadium shaped container that is sheared continuously by a belt. The stress uniformity across the width of the device is validated using Discrete Element Method (DEM) simulations, which give insight into the relationships between the normal stresses acting on the material. The performance of the SSD is validated using experimental data obtained from tests on glass beads, which further disclose stress and void ratio relationship in soils. When applied to sub-angular natural sands with different degrees of polydispersity, the SSD reveals a weak rate hardening of friction coefficient and sample dilatancy that reaches the loosest possible density at critical state, regardless of the initial packing conditions.
Isolating the effects of individual particle properties (e.g. shape, size, mineralogy, surface roughness) on the mechanical behavior of naturally occurring coarsegrained soils is a significant challenge in experimental studies. This challenge can be addressed by recent advances in 3D printing technology which enable generation of artificial sand-sized particles with independent control over particle size and shape. In this study, bender element tests are conducted to examine the isolated effects of particle shape on the shear wave velocity and shear modulus of 3D printed sand analogs. The experimental results show that the shear wave velocity and shear modulus of the 3D printed sand specimens exhibit a relationship with mean effective stress that is in agreement to that reported for natural sands. The specimens composed of 3D printed sands with greater particle roundness and sphericity exhibit greater shear wave velocity and shear modulus for a given void ratio, relative density, and mean effective stress. The changes in shear wave velocity can be captured in terms of differences in individual particle shape parameters such as roundness and sphericity as well as combined particle shape parameters such as regularity. Regression analysis is used to develop relationships between shear wave velocity and particle shape parameters and void ratio, which are shown to be in agreement with previously-published relationships and to reliably predict the shear wave velocity of natural sands. The results presented herein highlight the usefulness of testing 3D printed soils to identify functional trends and dependencies between soil response parameters and intrinsic properties. However, this requires verification of the results against published trends and assessment of the possible effects of the differences in constituent material between the 3D printed and the natural soils.
Most triaxial tests are fraught with substantial membrane penetration errors. A simple correction procedure for data obtained from various tests is proposed. In particular, a correction of the undrained cyclic stress paths is presented in detail. It is demonstrated that the correction of the membrane penetration error is indispensable for a realistic estimation of the cyclic resistance ratio in coarse- and medium-grained liquefiable soils.
The paper examines the problem of the open configuration created when a hydraulic fracture fluid containing a granular proppant is introduced into the fracture. The mathematical modelling examines the problem of an extended cracked region that is wedged open by a granular material present over a finite region of the crack. The combination of the geostatic stress state and the contact stress created between the granular proppant and the elastic rock mass is used to develop a consistency relationship for estimating the dimension of the region of the fracture that will remain open when the pressures applied to create the fracture are released. The interactive mechanics of the fracture and the proppant has an influence on the geometry of the open region that provides the pathway for extraction of the resource.
The dilatancy/contractancy of soil is of particular importance for compaction, consolidation, liquefaction, etc. Interestingly, constitutive relations are often unsatisfactory in modelling volume changes in the sense that their predictions deviate considerably from each other. This scatter is pronounced in problems with stress rotation. Therefore, in this paper some selected constitutive relations are investigated with respect to their performance at stress rotation. The obtained numerical simulations are compared to each other and also with experimental results from the 1γ2ε and the hollow cylinder apparatuses.
A computationally efficient and open sourced methodology designed for the investigation of rock matrix heterogeneities and their effect on preand postfracture Acoustic Emission (AE) distributions is presented. First, an image analysis method is proposed for building a statistical model representing rock heterogeneity. The statistical model is generalized and implemented into a discrete element contact model where it efficiently simulates the presence of defects and locally tough regions. The coupling of the heterogeneity model, discrete element model, and acoustic emission model is demonstrated using a numerical three point bending test. The shape parameter of the statistical model, which controls heterogeneity magnitude, is found to control the spatial width of the acoustic emission distribution generated during failure. The same acoustic emission distribution trend is observed in literature for rocks containing various magnitudes of heterogeneity. Further analysis of the numerical AE activity reveals that larger AE events are located directly along the fracture and they are linearly related to their number of constituent interactions. As such, an AE interaction count threshold is identified to distinguish between fracture and damage AE activity. These results demonstrate the ability of the presented methodology to investigate the location and energy release associated with large fracture events for various levels of heterogeneity.
A very simple frictional plasticity model for a granular material is presented, including the effects of dilation. The novelty lies in the fact that this is described within the hyperplasticity framework, expressed using the terminology of convex analysis. This allows a consistent mathematical treatment of the dilation constraint. The Fenchel Dual is used to link the force and flow potentials. The resulting model accommodates non-associated flow within a rigorous mathematical framework that ensures compliance with the Laws of Thermodynamics.
