Robert Charlier

The deformation of the Egersund-Ogna anorthosite massif, south Norway: finite-element modelling of diapirism

Abstract This paper aims at testing the mechanical relevance of the petrological model of anorthosite massif diapiric emplacement. The Egersund–Ogna massif (S. Norway) is of particular interest because recent petrological and geochronological data constrain the initial geometry, emplacement conditions and timing (about 2 m.y.). The formation of this anorthosite massif is in agreement with the classical petrological model, in which accumulation of plagioclase takes place in a deep-seated magma chamber at the crust–mantle limit, from which masses of plagioclase separate and rise through the lower crust up to the final level of emplacement at mid-crustal depths. The Egersund–Ogna massif also displays a foliated inner margin, in which strain ellipsoids have been reconstructed by investigating at 51 sites the deformation of megacrysts of high-alumina orthopyroxene. Based on these petrological data, a model made up of one rigid layer (upper granitic crust) and three viscous layers (lower part of the granitic crust, noritic lower crust and anorthosite) has been built up. The upper crust behaviour is represented by an elastoplastic law and the viscous layers obey elastic-viscoplastic laws with Newtonian viscosity. An inverse density gradient is considered between the lower crust (d=3.00) and the anorthosite (d=2.75), the loading consisting only in gravity. The modelling is carried out under axisymmetrical conditions, using the LAGAMINE finite-element code coupled with an automatic re-meshing algorithm designed to deal with large strains in complex structures. The results show that, from a mechanical point of view, the diapirism model is a robust and consistent assumption for the emplacement of anorthosites, because realistic diapir and rim-syncline shapes are obtained. Moreover, the numerically obtained emplacement time (about 2.5 m.y.) is in agreement with the available geochronological data, and the computed strain field is coherent with field measurements, especially regarding the circumferential extension, which becomes the largest extension strain component in the expansion phase.

Development of an enzymatic assay for the determination of cellulose bioavailability in municipal solid waste

AbstractAs there is a constant need to assess the biodegradation potential of refuse disposed of in landfills, we have developed a method to evaluate the biodegradability of cellulosic compounds (cellulose and hemicellulose) in municipal solid waste. This test is based on the quantification of monosaccharides released after the hydrolysis of solid waste samples with an optimised enzyme preparation containing commercially available cellulases and hemicellulases. We show that the amounts of monosaccharides could be related to the biodegradability of the cellulosic material contained in the samples. This enzymatic cellulose degradation test was assayed on 37 samples originating from three Belgian landfills and collected at different depths. As results correlated well with those obtained with a classical biochemical methane potential assay, this new and rapid test is sufficiently reliable to evaluate cellulose bioavailability in waste samples.

Numerical modelling of coupled transient phenomena

ABSTRACT The basic phenomena involved in thermo-hydro-mechanical processes in geomaterials have been described in the 1st chapter. The equations describing these phenomena are non-linear differential equations. Their solution can generally only be approximated thanks to numerical methods. This is the main subject of the present chapter. First the type of problems and the set of equations to be solved will be shortly recalled. Emphasis will be given on the non-linear contributions. In a second section, the mostly developed numerical method, i.e. the finite difference and the finite element methods will be discussed under the light of the problems to be treated. The iterative techniques allowing the solution of non linear equations will be described. A third section will be dedicated to the coupling terms and to their modelling. The question that rises then is How to model efficiently problems, which may differ highly from, the point of view of the time and length scales?

Finite elements modelling of a large water table aquifer in transient conditions

Abstract A chalky aquifer located near Liege (Belgium), is recharged by infiltration through the overlying loess. Wells and collecting tunnels produce a daily flow of 60 000 m3 out of this aquifer when hydrogeological balances have shown that an average yield of 100 000 m3/day should be possible. Finite element modelling has been developed to foresee the evolution of the water table to get some additional information especially about the main drainage axis. The transient flow constitutive laws are recalled in confined and unconfined aquifers. A new law is proposed to model the water table surface in transient conditions and with a fixed meshing network. Using the local flow equilibrium and the virtual power principle, the FEM formulation is set up. The time integration and the iteration technique are shortly discussed. The 3D discretization and the modelling of the entire aquifer has been realized. The problem requires about 3600 DOF and 2670 8-nodes isoparametric brick finite elements. The modelling has been quite delicate because of the geometric complexity of the different geological layers. This complexity justifies fully the use of the finite element method; there is indeed a great diversity of geological characteristics and the range of the different permeabilities is very wide. Sensitivity of the model to permeabilities and storage coefficient variations has been studied and various numerical problems have been notified. The calibration procedure is described in its main steps, and the most significant results are presented.

Hollow Cylinder Tests on Boom Clay: Modelling of Strain Localization in the Anisotropic Excavation Damaged Zone

Boom Clay is extensively studied as a potential candidate to host underground nuclear waste disposal in Belgium. To guarantee the safety of such a disposal, the mechanical behaviour of the clay during gallery excavation must be properly predicted. In that purpose, a hollow cylinder experiment on Boom Clay has been designed to reproduce, in a small-scale test, the Excavation Damaged Zone (EDZ) as experienced during the excavation of a disposal gallery in the underground. In this article, the focus is made on the hydro-mechanical constitutive interpretation of the displacement (experimentally obtained by medium resolution X-ray tomography scanning). The coupled hydro-mechanical response of Boom Clay in this experiment is addressed through finite element computations with a constitutive model including strain hardening/softening, elastic and plastic cross-anisotropy and a regularization method for the modelling of strain localization processes. The obtained results evidence the directional dependency of the mechanical response of the clay. The softening behaviour induces transient strain localization processes, addressed through a hydro-mechanical second grade model. The shape of the obtained damaged zone is clearly affected by the anisotropy of the materials, evidencing an eye-shaped EDZ. The modelling results agree with experiments not only qualitatively (in terms of the shape of the induced damaged zone), but also quantitatively (for the obtained displacement in three particular radial directions).

Consequences of the Thermal Transient on the Evolution of the Damaged Zone Around a Repository for Heat-Emitting High-Level Radioactive Waste in a Clay Formation: a Performance Assessment Perspective

A proper evaluation of the perturbations of the host rock induced by the excavation and the emplacement of exothermic wastes is essential for the assessment of the long-term safety of high-level radioactive waste disposals in clay formations. The impact of the thermal transient on the evolution of the damaged zone (DZ) has been explored in the European Commission project TIMODAZ (thermal impact on the damaged zone around a radioactive waste disposal in clay host rocks, 2006–2010). This paper integrates the scientific results of the TIMODAZ project from a performance assessment (PA) point of view, showing how these results support and justify key PA assumptions and the values of PA model parameters. This paper also contextualises the significance of the thermal impact on the DZ from a safety case perspective, highlighting how the project outcomes result into an improved understanding of the thermo–hydro–mechanical behaviour of the clay host rocks. The results obtained in the TIMODAZ project strengthen the assessment basis of the safety evaluation of the current repository designs. There was no evidence throughout the TIMODAZ experimental observations of a temperature-induced additional opening of fractures nor of a significant permeability increase of the DZ. Instead, thermally induced plasticity, swelling and creep seem to be beneficial to the sealing of fractures and to the recovery of a very low permeability in the DZ, close to that of an undisturbed clay host rock. Results from the TIMODAZ project indicate that the favourable properties of the clay host rock, which guarantee the effectiveness of the safety functions of the repository system, are expected to be maintained after the heating–cooling cycle. Hence, the basic assumptions usually made in PA calculations so far are expected to remain valid, and the performance of the system should not be affected in a negative way by the thermal evolution of the DZ around a radioactive waste repository in clay host rock.

Finite element modelling of the competition between shear bands in the early stages of thrusting: Strain localization analysis and constitutive law influence

Abstract Finite element simulation of a sandbox model of thrusting is performed using large strain analysis and two different non-associated elastoplastic constitutive laws (namely Drücker-Prager and Van Eekelen criteria). The analysis of strain localization using the Rice bifurcation criterion coupled with a kinematic indicator shows that, in the early stages of imbricated thrusting, the development of major shear bands can be influenced by some competition with second order bands. The influence of the vertical/horizontal stress ratio is checked, as well as the influence of Lode angle in the constitutive law. Significant differences are found between a classical plasticity criterion (Drücker-Prager) and a more realistic one (Van Eekelen) regarding the resistance of the model and the stress paths. These differences may result in erroneous fault type prediction.

Water Influence on Bearing Capacity and Pavement Performance: Field Observations

This chapter presents a mechanical behaviour study, i.e. the bearing capacity as a function of the moisture degree. The field point of view is expressed and the chapter summarises a number of observations on road behaviour, in relation to variations of moisture. First, the road structure is recalled with respect to the mechanical analysis point of view. Then some observations on field under temperate climate, humid, are given. In a second step, the specific case of frost and thawing are discussed.

NUMERICAL MODELLISATION OF CONTACT WITH FRICTION PHENOMENA BY THE FINITE ELEMENT METHOD

Abstract Finite element modelling contact with friction in two-dimensional, axisymmetric and three-dimensional cases are proposed. They take in account large displacements and rotations between a strained body and a so-called tool or between two strained bodies. The interface behaviour is based on a penalty method and on the COULOMB dry friction law, and is developed using the elasto-plastic formalisms. Due to the algorithm modularity it seems to be easy to introduce other interface behaviours as instance including dilatancy. The time integration of the generalised contact stresses and the objectivity treatment are discussed. At the end an application is proposed which could serve as comparison test between algorithms modelling same problems.

Modelling Contamination of Clays

Abstract A constitutive model for the behaviour of clays in contact with organic liquids is presented. The model was originally proposed by Hueckel (1997) , based on experimental data reported by Fernandez and Quigley (1985 , 1991 ). It is recognized that the physico-chemical phenomena taking place at the scale of the clay particles are responsible for changes in permeability and deformation in the clay. Two types of chemical strains are identified: an elastic expansive strain at stress level lower than the plastic yield limit, and a plastic compaction strain at higher stress level. The plastic yield limit is assumed to decrease as the contaminant mass concentration increases. This is referred to as chemical softening. The chemo-plastic behaviour of a cylindrical clay layer subjected to vertical flow of contaminant is simulated.