Failure In Geomaterials Research Articles

2D Phase-Field Modelling of Hydraulic Fracturing Affected by Cemented Natural Fractures Embedded in Saturated Poroelastic Rocks

AbstractThe interaction between a propagating hydraulic fracture (HF) and a pre-existing natural fracture (NF) embedded in saturated poroelastic rock formations is studied numerically in 2D plane–strain configurations. In this study, the phase-field method is further developed to be employed for modelling the HF propagation and the evolution of tensile and shear failure in geo-materials as gradient-type diffusive damaged zones. The shear slippage and dilation mechanisms inside the cemented NF are modelled using a Mohr–Coulomb–Griffith failure criterion that fitted in the framework of the phase-field fracture using appropriate energy functionals. The most important factors controlling the HF–NF interaction outcome are the approaching angle, differential in-situ stress, and hydro-mechanical characteristics of the NF. It is found out that higher tensile and shear strengths of the cemented NF are in favour of the crossing outcome when the differential stress is high enough to mobilise the resisting shear stresses against the slippage. Small hydraulic aperture (low hydraulic conductivity) for the NF is also in favour of the crossing outcome which helps to restrict the pressurised region local to the HF tip, lowering the possibility of shear slippage in the NF and the HF’s diversion. It is also concluded that the injection rate and the viscosity of fracturing fluid are operative factors to be adjusted for increasing the chance of crossing, a critical element for successful operation of hydraulic fracturing for effective use of subsurface energy resources.

On the predictability of localization instabilities of quasibrittle materials from accelerating rates of acoustic emission

Forecasting quasibrittle failure in geomaterials is of paramount importance in the physics of fractures but rarely succeeds. To clarify the physics relating to the failure predictability in a quasibrittle regime, a combined AE (acoustic emission)-DIC (digital image correlation) technique is used in uniaxial compression experiments of flawed granite to trace its damage conditions in real time. The mechanistic correlations of the AE rate-process with the internal FPZ (fracture process zone) development are available. It is shown that the complete record of the AE activities does not meet a deterministic scaling law (e.g., typical time‐reversed Omori law), indicating a challenge in predicting ultimate failure via AE. Subsets of a power law acceleration registered much earlier than ultimate failure imply that the procedural sample-sized localization instability is predictable but still depends on the FPZ dynamic evolutions. More importantly, we find that the coexistence of FPZs and the intermittency of crack growth are the two main reasons for the difficulty of forecasting failure in flawed granite. This study sheds light on upcoming investigations in which the roles of FPZs, especially their spatiotemporal patterns, should be highlighted.

Non-associated Cosserat plasticity

Frictional plasticity models with a non-associated flow rule, ubiquitous for describing failure in geomaterials, can lead to a local loss of ellipticity for low hardening rates, i.e. before entering a strain-softening regime. This leads to an excessive dependence on the spatial discretisation and to an inability of Newton–Raphson methods to converge. Higher-order continuum models can remedy this. The Cosserat continuum is particularly suitable for granular media because the rotational degrees of freedom of this model can represent the rotation of (assemblies of) grains or blocks which form the microstructure of such materials. We illustrate this analytically by the example of an infinitely long shear layer and through a three-dimensional bifurcation analysis. Numerical simulations show the consequences, i.e. the anomalies of standard continuum models and the correct behaviour of non-associated plasticity models embedded in a Cosserat continuum. The motivation for using a Cosserat continuum for granular and blocky materials is further strengthened through shear band simulations of biaxial tests, where the inclination angle shows the same dependence on the internal length scale as that on the grain size in tests. This result is the first proper explanation for this dependence.

A thermodynamics- and mechanism-based framework for constitutive models with evolving thickness of localisation band

Localised failure in geomaterials invalidates the assumption of homogeneous deformation that constitutive models based on continuum mechanics rest on. In such cases, the deformation and nonlinear processes inside the localisation zone dominate the inelastic response of the material, while the material outside this zone usually undergoes negligible inelastic or even elastic deformation. As a consequence, internal variables representing micromechanical failure processes should better be defined inside the localisation zone, not averaged over the whole volume element containing it. In this study, we propose a thermodynamics-based framework for constitutive models that take into account the transition from homogenous to localised deformation. Two spatial scales involved in the mechanisms of localised failure, macro scale of the considered volume element and smaller scale of the localisation zone, are included in the formulation and derived constitutive models. This separation of spatial scales is combined with enrichments of the constitutive kinematics for the integration of three constitutive relationships describing the behaviour of the materials inside and outside the localisation zone, and the evolving size of this zone. As a result, the internal variables are associated with their own spatial zones, instead of being averaged over the whole volume element like in classical continuum approaches. The gradual transition from homogenous to localised deformation is represented by the onset and evolution of the thickness of the localisation band, both of which appear naturally in the proposed formulation. The obtained model therefore consists of both size and orientation of the localisation band, and three constitutive relationships connected through the equilibrium condition across the boundary of the localisation zone. They help provide a smooth transition from homogeneous to localised failure. Numerical examples show promising features of the proposed approach in connecting the macro behaviour with the underlying evolution of the localisation zone.

Three-dimensional smoothed-particle hydrodynamics simulation of deformation characteristics in slope failure

This paper presents the development, validation and application of a smoothed-particle hydrodynamics model for three-dimensional (3D) simulation of the evolution of large deformation failure in geo-materials. The Drucker–Prager model with non-associated plastic flow rules is implemented into the smoothed-particle hydrodynamics formulations to describe elasto-plastic soil behaviour. Two typical numerical examples – a two-dimensional (2D) analysis of cohesive slope instability and a 3D simulation for instant collapse of a granular slope – are shown to demonstrate the effectiveness of the method for modelling large deformation of slope failure. Good agreement with experimental observations and previous simulated results is obtained in terms of the profile and internal deformation, respectively. The method is then applied to two special 3D slopes with different geometric configurations, including a curving slope surface and a slope that turns corners. The results suggest that 3D effects should be considered for natural landslides. By influencing the stress status, slope geometries have a significant effect on the final profile, slip surface and distance. The results provide a more accurate and detailed reference for landslide evaluation and foundation ditch design.

Describing failure in geomaterials using second-order work approach

Geomaterials are known to be non-associated materials. Granular soils therefore exhibit a variety of failure modes, with diffuse or localized kinematical patterns. In fact, the notion of failure itself can be confusing with regard to granular soils, because it is not associated with an obvious phenomenology. In this study, we built a proper framework, using the second-order work theory, to describe some failure modes in geomaterials based on energy conservation. The occurrence of failure is defined by an abrupt increase in kinetic energy. The increase in kinetic energy from an equilibrium state, under incremental loading, is shown to be equal to the difference between the external second-order work, involving the external loading parameters, and the internal second-order work, involving the constitutive properties of the material. When a stress limit state is reached, a certain stress component passes through a maximum value and then may decrease. Under such a condition, if a certain additional external loading is applied, the system fails, sharply increasing the strain rate. The internal stress is no longer able to balance the external stress, leading to a dynamic response of the specimen. As an illustration, the theoretical framework was applied to the well-known undrained triaxial test for loose soils. The influence of the loading control mode was clearly highlighted. It is shown that the plastic limit theory appears to be a particular case of this more general second-order work theory. When the plastic limit condition is met, the internal second-order work is nil. A class of incremental external loadings causes the kinetic energy to increase dramatically, leading to the sudden collapse of the specimen, as observed in laboratory.

A new method to estimate location and slip of simulated rock failure events

At the laboratory scale, identifying and locating acoustic emissions (AEs) is a common method for short term prediction of failure in geomaterials. Above average AE typically precedes the failure process and is easily measured. At larger scales, increase in micro-seismic activity sometimes precedes large earthquakes (e.g. Tohoku, L'Aquilla, oceanic transforms), and can be used to assess seismic risk.The goal of this work is to develop a methodology and numerical algorithms for extracting a measurable quantity analogous to AE arising from the solution of equations governing rock deformation. Since there is no physical property to quantify AE derivable from the governing equations, an appropriate rock-mechanical analog needs to be found.In this work, we identify a general behavior of the AE generation process preceding rock failure. This behavior includes arbitrary localization of low magnitude events during pre-failure stage, followed by increase in number and amplitude, and finally localization around the incipient failure plane during macroscopic failure. We propose deviatoric strain rate as the numerical analog that mimics this behavior, and develop two different algorithms designed to detect rapid increases in deviatoric strain using moving averages.The numerical model solves a fully poro-elasto-plastic continuum model and is coupled to a two-phase flow model. We test our model by comparing simulation results with experimental data of drained compression and of fluid injection experiments. We find for both cases that occurrence and amplitude of our AE analog mimic the observed general behavior of the AE generation process.Our technique can be extended to modeling at the field scale, possibly providing a mechanistic basis for seismic hazard assessment from seismicity that occasionally precedes large earthquakes.

Micromechanics of vortices in granular media: connection to shear bands and implications for continuum modelling of failure in geomaterials

SUMMARYRecent analysis of data from triaxial tests on sand and discrete element simulations indicate the final pattern of failure is encoded in grain motions during the nascent stages of loading. We study vortices that are evident from grain displacements at the start of loading and bear a direct mathematical connection to boundary conditions, uniform continuum strain and shear bands. Motions of three grains in mutual contact, that is, 3‐cycles, manifest vortices. In the initial stages of loading, 3‐cycles initiate a rotation around a region Ω* where the shear band ultimately develops. This bias sets a course in 3‐cycle evolution, determining where they will more likely collapse. A multiscale spatial analysis of 3‐cycle temporal evolution provides quantitative evidence that the most stable, persistent 3‐cycles degrade preferentially in Ω*, until essentially depleted when the shear band is fully formed. The transition towards a clustered distribution of persistent 3‐cycles occurs early in the loading history—and coincides with the persistent localisation of vortices in Ω*. In 3D samples, no evidence of spatial clustering in persistent 3‐cycle deaths is found in samples undergoing diffuse failure, while early clustering manifests in a sample that ultimately failed by strain localisation. This study not only delivered insights into the possible structural origins of vortices in dense granular systems but also a tool for the early detection of the mode of failure—localised versus diffuse—a sample will ultimately undergo. Copyright © 2014 John Wiley & Sons, Ltd.

A constitutive modelling framework featuring two scales of behaviour: Fundamentals and applications to quasi-brittle failure

We propose a constitutive modelling framework with enhanced kinematics to capture localised mode of deformation. The total strain is decomposed into two components to reflect an inelastic localisation band embedded in an elastic bulk. This is the usual case in numerical analysis of localised failure in geomaterials, when the size of the localisation band is very small compared to an element of the discretised domain under consideration. The proposed framework takes into account the sizes and corresponding behaviours of the two inelastic and elastic zones and hence gives derived constitutive models a length scale. This is an essential feature in dealing with size effect issues as a consequence of localised failure in geomaterials. The proposed framework is applied to a constitutive model for the failure analysis of quasi-brittle materials. The implementation algorithms are developed and novel features are illustrated through numerical examples.

Failure and size effect for notched and unnotched concrete beams

SUMMARYModelling failure in geomaterials, concrete or other quasi‐brittle materials and proper accounting for size effect, geometry and boundary effects are still pending issues. Regularised failure models are capable of describing size effect on specimens with a specific geometry, but extrapolations to other geometries are rare, mostly because experimental data presenting size effect for different geometries and for the same material are lacking. Three‐point bending fracture tests of geometrically similar notched and unnotched specimens are presented. The experimental results are compared with numerical simulations performed with an integral‐type non‐local model. Comparisons illustrate the shortcomings of this classical formulation, which fails to describe size effect over the investigated range of geometries and sizes. Finally, experimental results are also compared with the universal size effect law. Copyright © 2013 John Wiley & Sons, Ltd.

Frequency signatures of damage localisation

Failure in geomaterials is often preceded by strain localisation and the related localisation of acoustic/microseismic/seismic events. Given that the localisation zone does not appear simultaneously – it is formed in a certain location and then propagates in a crack-like manner – the arrival times of the microseismic or acoustic pulses are synchronised. The aim of the study is to develop an indicator of the localisation based on the temporal synchronisation of the events. We found that the spectra of events generated by two- (2D) and three-dimensional (3D) localisation zones are shifted towards higher frequencies (‘blue shift’) as compared to the spectrum of randomly generated events. The indicator curve we propose is the relative difference between the frequency dependence of the energy of the power spectrum of arrival times of the recorded and pure random sequences of arrival times. The indicator curve for the 3D (cloud-like) localisation is always above the curve for the 2D (crack-like) localisation. The curves for these two localisation modes are above the indicator curve for one-dimensional localisation and for the randomly generated arrival times. When the pulses are recorded from a considerable distance and a number of recording stations are utilised, the comparison of the localisation indicator curves from all stations gives the information of the direction of propagation of the localisation zone provided that the length of the recording array is large enough.

Inertia effects as a possible missing link between micro and macro second-order work in granular media

This paper is concerned with a theoretical question as to the definition of instabilities in a granular assembly and its proper formulation at the microscopic level. Recently, this question has taken up much prominence with the emergence of intriguing failure modes such as diffuse failure associated to unstable plasticity of granular materials and microstructural instabilities. An analysis of the second-order work as a general and necessary criterion to detect instabilities is conducted both at the macroscopic and microscopic levels including large deformations. On the basis of a micromechanical analysis of a body consisting of arbitrary interacting particles in a representative element volume (REV), a general formula is derived to quantify the microscopic second-order work involving local variables on the grain scale. The latter emerges as a sum of a configurational term that involves contact forces between neighboring grains, plus a kinetic part consisting of the mechanical unbalance of intergranular forces under dynamics at incipient failure. The present analysis is thought to serve as a clarification of the question of failure in geomaterials typified by a transition from static to a dynamic regime with release of kinetic energy originating from microstructural interactions.

Diffuse failure in geomaterials: Experiments, theory and modelling

AbstractThis paper presents a synthesis of the works performed by various teams from France, Italy and Canada around the question of second‐order work criterion. Because of the non‐associative character of geomaterials plastic strains, it is now recognized that a whole bifurcation domain exists in the stress space with various possible modes of failure. In a first part these failure modes are observed in lab experimental tests and in discrete element modelling. Then a theoretical study of second‐order work allows to establish a link with the kinetic energy, giving a basis to explain the transition from a prefailure (quasi)static regime to a postfailure dynamic regime. Eventually the main features of geomaterials failure are obtained by applying second‐order work criterion to five different constitutive rate‐independent models—three being phenomenological and two micromechanical. As a whole this paper tries to gather together all the elements for a proper understanding and use of second‐order work criterion in geomechanics. Copyright © 2010 John Wiley & Sons, Ltd.

Thermally and chemically induced failure in geomaterials

ABSTRACT Failure conditions in soils occurring during or as a result of heating or by altering their chemical environment appear to be strongly dependent on the history of the application of stress and temperature and or the chemical change. Several cases of such history leading to various modes of failure are identified and interpreted in terms of Thermal and Chemical Cam-Clay models. Particular attention is given to the influence of thermal variability on the coefficient of the critical state, M, or the angle of internal friction. A detailed analysis of the material history offers an explanation of an apparent confusion about whether the soil strength is decreased or increased by temperature. Dependence of failure conditions of clay on the ion concentration in pore water and on its acidity in the context of a landslide trigger mechanism are also discussed.

Thermally and chemically induced failure in geomaterials

Thermally and chemically induced failure in geomaterials

Thermally and chemically induced failure in geomaterials

Thermally and chemically induced failure in geomaterials

Granular material response with respect to loading direction and material instability

ABSTRACT The paper examines the emerging roles of instabilities towards characterizing various modes of failure in geomaterials. We show that conventional analysis of failure through a failure criterion is no longer sufficient and it is also important to study the causes leading to failure. Micromechanical in character, these causes relate to local instabilities such as inter-granular slippage, overriding, buckling, grain crushing, among others. We briefly investigate the phenomenon of instability using an elasto-plastic model. Hill's stability criterion, based on the second-order work, is employed to capture the existence of material instability inside classical plastic limit surface. The postulate of flow rule is another subject matter discussed here. Through discrete element analysis, we show that this postulate fails under general three-dimensional conditions and the plastic response is a function of loading direction.

3D bifurcation analysis in geomaterials

ABSTRACT In this paper, a study of failure in geomaterials is proposed using the second order work criterion and a phenomenological approach. In a first part, an analytical investigation of this criterion is proposed. General 3D equation of instability cones as well as of the 3D bifurcation domain limit are given for every incrementally piece-wise linear constitutive model. In the second part, these instability cones and bifurcation domain are displayed for constitutive models of Darve. Then a physical interpretation of these results is proposed. Noticeably, it is proved that, when the second order work vanishes along a given loading path, an extension a generalized flow rule can be defined for proper conjugated variables. Finally we conclude that this approach constitutes a good starting point when investigating bifurcation in geomaterials, and opens new horizons in experimental testing.

Large Deformation Dynamic Meshfree Simulation of Damage and Failure in Geomaterials

An explicit dynamic Galerkin meshfree formulation under the updated Lagrangian framework is presented to simulate large deformation damage and failure process in geomaterials. The failure initiation and development are characterized by the pressure sensitive Drucker-Prager plasticity coupled with the isotropic energy-based damage theory. A stabilized conforming nodal integration based on non-local gradient smoothing is employed to improve the computational efficiency and to regularize the material instability arising from strain localization. The capability of the proposed methodology to model the evolution of dynamic failure in geomaterials is demonstrated through a numerical example.

Diffuse failure in geomaterials: Experiments and modelling

While localized failure has been extensively studied, diffuse failure modes are still not characterized from an experimental point of view and not described by proper criteria from a theoretical point of view. The purpose of this paper is to tackle both these questions by considering, in a first part, undrained triaxial loading on very loose sands and the failure mode occurring at q-peak, and, in a second part, the bifurcation domain of sands in plane strain conditions through strain proportional paths and incrementally piece-wise linear and non-linear constitutive relations.