Response of granular material under combined principal stress value and orientation change in 3D space

Laboratory tests on soil adopt simplified stress paths compared to real world counterparts due to mechanical limitations. This study investigates the deformation of granular material under combined principal stress value and orientation change in full 3D space using the discrete element method. Such stress paths are achieved by applying a 3D force line boundary condition on spherical granular material samples. Continuous cyclic tests with stress paths restricted in a fixed plane and in full 3D space, simulating a bidirectional seismic stress path, are both conducted. The importance of taking both principal stress value and orientation change into consideration is highlighted. In the tests, the greatest deformation is observed under pure stress orientation change, while the smallest deformation is observed when the principal stress axes are fixed. The change of stress value and orientation in 3D is also shown to result in deformations different to those within a fixed plane. The origins of these differences are found to be associated with difference in shear modulus, dilatancy, and non-coaxiality at the macroscale, and particle contact and fabric anisotropy at the microscale.

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Enriching constitutive models with meso-scale behaviour: a thermodynamics-based formulation and examples

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 provides 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.

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The perpetual shearing of granular soils under low stresses using the stadium shear device

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.

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Effects of Particle Shape on the Shear Wave Velocity and Shear Modulus of 3D Printed Sand Analogs

Isolating the effects of individual particle properties (e.g. shape, size, mineralogy, surface roughness) on the mechanical behavior of naturally occurring coarse-grained 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.

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Removal of the membrane penetration error from triaxial data

Most triaxial tests are fraught with substantial membrane penetration errors. A simple correction procedure for data obtained from various tests is proposed. Correction formulas for the membrane penetration error have been derived for different types of tests including not perfectly saturated soils. In particular, a correction of the undrained cyclic stress paths is presented in detail. It is demonstrated that the correction for the membrane penetration error is indispensable for a realistic estimation of the cyclic resistance ratio in coarse- and medium-grained liquefiable soils. A Mathematica code for the correction of laboratory data is given. An analogous Matlab code is available from the authors. Without the correction many results could lie far on the unsafe side. This is the case especially for the undrained cyclic loading.

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Finite deformation hyperplasticity theory for crushable, cemented granular materials

The work is focused on the formulation of a thermodynamically–based constitutive theory for granular, cemented geomaterials, often characterized by a open structure with high porosity and voids of large diameter. Upon mechanical degradation processes such as bond rupture and grain crushing, these material undergo large volumetric and shear strains, and in some cases the deformations are so large that the usual assumption of linearized kinematics may be not applicable. In the first part of this work, the theory of hyperplasticity is extended to the finite deformation regime by adopting a multiplicative split of the deformation gradient into an elastic and a plastic part, under the assumption of material isotropy. Grain breakage and bond damage processes are accounted for through two micromechanically–inspired internal variables. A specific constitutive model for carbonatic cemented sands and calcarenites is proposed as a relevant example of application. In the second part, an implicit stress–point algorithm has been developed which is amenable to closed form linearization, for the implementation of the model into standard FE platforms. A series of numerical tests have demonstrated the accuracy and efficiency of the proposed algorithm. The simulation of plane strain biaxial tests, modeled as boundary–value problems, has highlighted the role played by geometric non–linearity in determining the evolution of the specimen deformation upon reaching a bifurcation condition.

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A simple method for the determination of sensitivity to density changes in sand liquefaction

Fully saturated loose coarse-grained soils are known to be prone to liquefaction. Conventional laboratory tests for soil liquefaction include usually cyclic testing in triaxial apparatus. However, such investigations are complicated and time-consuming. The objective of the outlined work is to evaluate the sensitivity of different sands to density change with respect to liquefaction using a relatively simple method. This method enables a fast setup of the tested specimen and a subsequent investigation of the pore water pressure build-up during cyclic shearing within a short time. The results have confirmed a good repeatability of the new method as well as an expected dependence of the pore pressure build-up on initial density. Validation of the method was performed using the results of cyclic triaxial tests. A good agreement between both methods was observed regarding the rate of the pore pressure increase with initial density. Furthermore, it was shown that the initial fabric of soil has a larger impact on the pore pressure build-up during cyclic loading than the relative density.

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Modeling acoustic emissions in heterogeneous rocks during tensile fracture with the Discrete Element Method

A computationally efficient and open sourced methodology designed for the investigation of rock matrix heterogeneities and their effect on pre- and post- fracture 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.

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Micro-macro mechanics of damage and healing in rocks

This paper presents the state of the art of the theory of rock damage and healing mechanics, with a particular emphasis on the strategies available to relate the micro-scale of crystals, cracks and pores to the scale of a Representative Elementary Volume (REV). We focus on mechanical degradation and recovery of stiffness and strength. Damage and healing models formulated in the author’s group are used as examples to illustrate and compare the reviewed micro-macro approaches, which include fabric enrichment, micromechanical formulations and homogenization schemes. This manuscript was written for doctoral students or researchers relatively new to the field of damage mechanics of geomaterials. Equations are provided to explain how to formulate a thermodynamically consistent model from scratch. Reviewing damage and healing modeling strategies led to the following conclusions: (i) The framework of hyperplasticity, which does not require any postulate on the existence or uniqueness of yield functions and which automatically ensures thermodynamic consistency, was never applied to Continuum Damage Mechanics (CDM). There may be an avenue to improve state-of-the-art damage and healing models in a similar framework of “hyper-damage mechanics”. (ii) In damage softening models, the mesh dependence of the width of the damage localization zone is currently alleviated by non-local regularization. Perhaps the next step is to couple micro-macro damage and healing models at the REV scale to discrete fracture mechanics at a larger scale to understand how damage and healing localization occurs. (iii) There may be an opportunity to use fabric-enriched models to capture the effect of microstructure organization on both mechanical properties and permeability. (iv) Coupling chemo-mechanical damage and healing processes across the scales would be useful to model the competition between damagre and healing whenever both can occur at the same temperature and pressure conditions. (v) Many challenges still exist to implement healing models in the Finite Element Method, especially in regards to the mapping of net damage.

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Comparative performance of some constitutive models in stress rotation

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 with each other and also with experimental results from the 1γ2ε and the hollow cylinder apparatuses.

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Frictional Plasticity in a Convex Analytical Setting

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.

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Proppant-Induced Opening of Hydraulically Created Fractures

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.

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Editorial

This Editorial is the first publication from the journal Open Geomechanics, a radically open-access scientific journal for Geomechanics Research, edited by Geomechanics researchers for Geomechanics researchers. We believe that the results of scientific research should be available to all. For this reason, this journal is committed to publishing high quality work within the remit of diamond open access — free to publish and read. Our aim is to become a recognised journal in the field of geomechanics, and a launchpad for new ideas for the dissemination of research in this field. Research manuscripts (in any geomechanics related topics such as analytical, numerical or experimental studies) or case studies, negative results, as well as replicability or reproducibility studies are welcome.

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