Numerical modelling of bit–rock fracture mechanisms in percussive drilling with a continuum approach

This paper presents a numerical method for continuum modelling of the dynamic bit–rock interaction process in percussive drilling. The method includes a constitutive model based on a combination of the recent viscoplastic consistency model, the isotropic damage concept and a parabolic compression cap. The interaction between the drill bit and rock is modelled using contact mechanics by treating the bit as a rigid body. As the bit–rock interaction in percussive drilling is a transient event, the method is implemented in explicit dynamics FEM. The rock strength heterogeneity is characterized at the mesoscopic level statistically using the Weibull distribution. The bit–rock interaction is simulated under axisymmetric conditions using cylindrical and hemispherical buttons. The choice of the quite complex constitutive model accounting, e.g. for plastic compaction, viscoplastic shear and tensile failure along with induced damage and rate dependency is justified by numerical simulations. Moreover, the quasi‐static and dynamic cases are compared in plane strain simulations. Finally, some results clarifying the discrepancy of opinions found in the literature concerning the side (lateral) crack formation are obtained. Copyright © 2010 John Wiley & Sons, Ltd.     

Granite rock fragmentation at percussive drilling – experimental and numerical investigation

The aim of this study is to numerically model the fracture system at percussive drilling. Because of the complex behavior of rock materials, a continuum approach is employed relying upon a plasticity model with yield surface locus as a quadratic function of the mean pressure in the principal stress space coupled with an anisotropic damage model. In particular, Bohus granite rock is investigated, and the material parameters are defined based on previous experiments. This includes different tests such as direct tension and compression, three‐point bending, and quasi‐oedometric tests to investigate the material behavior at both tension and confined compression stress states. The equation of motion is discretized using a finite element approach, and the explicit time integration method is employed. Edge‐on impact tests are performed, and the results are used to validate the numerical model. The percussive drilling problem is then modeled in 3D, and the bit‐rock interaction is considered using contact mechanics. The fracture mechanism in the rock and the bit penetration‐ resisting force response are realistically captured by the numerical model. Copyright © 2013 John Wiley & Sons, Ltd.     

A numerical study of the influence from pre‐existing cracks on granite rock fragmentation at percussive drilling

The aim of this study is to investigate the effect of pre‐existing, or structural, cracks on dynamic fragmentation of granite. Because of the complex behavior of rock materials, a continuum approach is employed relying upon a plasticity model with yield surface locus as a quadratic function of the mean pressure in the principal stress space coupled with an anisotropic damage model. In particular, Bohus granite rock is investigated, and the material parameters are chosen based on previous experiments. The equation of motion is discretized using a finite element approach, and the explicit time integration method is employed. The pre‐existing cracks are introduced in the model by considering sets of elements with negligible tensile strength that leads to their immediate failure when loaded in tension even though they still carry compressive loads as crack closure occurs because of compressive stresses. Previously performed edge‐on impact tests are reconsidered here to validate the numerical model. Percussive drilling is simulated, and the influence of the presence of pre‐existing cracks is studied. The results from the analysis with different crack lengths and orientations are compared in terms of penetration stiffness and fracture pattern. It is shown that pre‐existing cracks in all investigated cases facilitate the drilling process. Copyright © 2014 John Wiley & Sons, Ltd.     

3-D numerical modelling of radial-axial rock splitting

Radial–axial rock splitters are potential primary mechanical excavating tools for underground hard rock mines. In an effort to further guide the development of a working prototype, a series of laboratory, field, and numerical experiments were conducted. The results of a three-dimensional finite element analysis of a radial-axial splitter used to break intact granite blocks are presented. Numerical results are in good agreement with the physical modelling and field studies, thus validating the numerical formulation implemented. © Rapid Science Ltd. 1998     

Capturing the complete stress–strain behaviour of jointed rock using a numerical approach

This paper presents the results of a series of numerical experiments using the synthetic rock mass (SRM) approach to quantify the behaviour of jointed rock masses. Field data from a massive sulphide rock mass, at the Brunswick mine, were used to develop a discrete fracture network (DFN). The constructed DFN model was subsequently subjected to random sampling whereby 40 cubic samples, of height to width ratio of two, and of varying widths (0.05 to 10 m) were isolated. The discrete fracture samples were linked to 3D bonded particle models to generate representative SRM models for each sample size. This approach simulated the jointed rock mass as an assembly of fractures embedded into the rock matrix. The SRM samples were submitted to uniaxial loading, and the complete stress–strain behaviour of each specimen was recorded. This approach provided a way to determine the complex constitutive behaviour of large‐scale rock mass samples. This is often difficult or not possible to achieve in the laboratory. The numerical experiments suggested that higher post‐peak modulus values were obtained for smaller samples and lower values for larger sample sizes. Furthermore, the observed deviation of the recorded post‐peak modulus values decreased with sample size. The ratio of residual strength of rock mass samples per uniaxial compressive strength intact increases moderately with sample size. Consequently, for the investigated massive sulphide rock mass, the pre‐peak and post‐peak representative elemental volume size was found to be the same (7 × 7 × 14 m). Copyright © 2015 John Wiley & Sons, Ltd.     

Damage‐viscoplastic consistency model for rock fracture in heterogeneous rocks under dynamic loading

This paper presents a damage‐viscoplastic consistency model for numerical simulation of brittle fracture in heterogeneous rocks. The model is based on a combination of the recent viscoplastic consistency model by Wang and the isotropic damage concept with separate damage variables in tension and compression. This approach does not suffer from ill‐posedness, caused by strain softening, of the underlying boundary/initial value problem since viscoplasticity provides the regularization by introducing a length scale effect under dynamic loading conditions. The model uses the Mohr–Coulomb yield criterion with the Rankine criterion as a tensile cut‐off. The damage law in compression is calibrated via the degradation index concept of Fang and Harrison. Thereby, the model is able to capture the brittle‐to‐ductile transition occurring in confined compression at a certain level of confinement. The heterogeneity of rock is accounted for by the statistical approach based on the Weibull distribution. Numerical simulations of confined compression test in plane strain conditions demonstrate a good agreement with the experiments at both the material point and structural levels as the fracture modes are realistically predicted. Copyright © 2009 John Wiley & Sons, Ltd.     

A macro‐element for a circular foundation to simulate 3D soil–structure interaction

This paper presents a non‐linear interface element to compute soil–structure interaction (SSI) based on the macro‐element concept. The particularity of this approach lies in the fact that the foundation is supposed to be infinitely rigid and its movement is entirely described by a system of global variables (forces and displacements) defined in the foundation's centre. The non‐linear behaviour of the soil is reproduced using the classical theory of plasticity. Failure is described by the interaction diagram of the ultimate bearing capacity of the foundation under combined loads. The macro‐element is appropriate for modelling the cyclic or dynamic response of structures subjected to seismic action. More specifically, the element is able to simulate the behaviour of a circular rigid shallow foundation considering the plasticity of the soil under monotonic static or cyclic loading applied in three directions. It is implemented into FedeasLab, a finite element Matlab toolbox. Comparisons with experimental monotonic static and cyclic results show the good performance of the approach. Copyright © 2007 John Wiley & Sons, Ltd.     

Fluid–rock interactions during continuous diagenesis of sandstone reservoirs and their effects on reservoir porosity

The Cretaceous sandstone reservoir in the Kuche Depression, Tarim Basin, western China, was investigated with reference to its reservoir property evolution during diagenesis. Six general diagenetic stages were recognized through petrographic, mineralogical and geochemical analyses. Fluid–rock interaction experiments were conducted under these six continuous diagenetic conditions, that is with a simulation sequence of compaction → early diagenesis → organic acid incursion I → elevated temperature/pressure → organic acid incursion II → late diagenesis. Corresponding to these six experimental stages, a total of six models were constructed. Finally, an extended model of fluid–rock interaction during diagenesis at a geological timescale (from 30 Ma to present) was constructed after various parameters had been validated. Results demonstrate that the diagenetic stages from both the experimental and numerical simulations generally matched findings obtained from the petrographic and geochemical analyses: (i) With compaction becoming weakened, cementation by various minerals was gradually increased. (ii) Quartz overgrowth occurred because the contemporaneous sedimentary water was alkaline. (iii) Most minerals (for example, calcite and feldspar minerals) displayed dissolution owing to the first organic acid incursion, resulting in the visual porosity increasing to 29·26%. (iv) Increases in temperature and pressure caused a minor fluctuation of the porosity change. (v) The cement that formed during earlier stages largely dissolved with the second organic acid incursion. (vi) During the last stage, the reservoir fluid was diluted by sedimentary alkaline water and most minerals precipitated under an alkalic environment. The present porosity simulated is about 11·4%, comparable with the actually measured data. This study demonstrates that the combination of petrographic observations, laboratory experiments and numerical simulations can not only reconstruct the diagenetic process, but also provide a quantitative evaluation and prediction of reservoir petrophysical properties.     

3D finite element modeling of sand particle fracture based on in situ X‐Ray synchrotron imaging

Compressive loading of granular materials causes inter‐particle forces to develop and evolve into force chains that propagate through the granular body. At high‐applied compressive stresses, inter‐particle forces will be large enough to cause particle fracture, affecting the constitutive behavior of granular materials. The first step to modeling particle fracture within force chains in granular mass is to understand and model the fracture of a single particle using actual three‐dimensional (3D) particle shape. In this paper, the fracture mode of individual silica sand particles was captured using 3D x‐ray radiography and Synchrotron Micro‐computed Tomography (SMT) during in situ compression experiments. The SMT images were used to reconstruct particle surfaces through image processing techniques. Particle surface was then imported into Abaqus finite element (FE) software where the experimental loading setup was modeled using the extended finite element method (XFEM) where particle fracture was compared to experimental fracture mode viewed in radiograph images that were acquired during experimental loading. Load‐displacement relationships of the FE analysis were also compared with experimental measurements. 3D FE modeling of particle fracture offers an excellent tool to map stress distribution and monitors crack initiation and propagation within individual sand particles. Copyright © 2015 John Wiley & Sons, Ltd.     

Numerical modeling of dynamic rock fracture with a combined 3D continuum viscodamage‐embedded discontinuity model

This paper deals with numerical modeling of dynamic failure phenomena in rate‐sensitive quasi‐brittle materials, such as rocks, with initial microcrack populations. To this end, a continuum viscodamage‐embedded discontinuity model is developed and tested in full 3D setting. The model describes the pre‐peak nonlinear and rate‐sensitive hardening response of the material behavior, representing the fracture‐process zone creation, by a rate‐dependent continuum damage model. The post‐peak response, involving the macrocrack creation accompanied by exponential softening, is formulated by using an embedded displacement discontinuity model. The finite element implementation of this model relies upon the linear tetrahedral element, which seems appropriate for explicit dynamic analyses involving stress wave propagation. The problems of crack locking and spreading typical of embedded discontinuity models are addressed in this paper. A combination of two remedies, the inclusion of viscosity in the spirit of Wang's viscoplastic consistency approach and introduction of isotropic damaging into the embedded discontinuity model, is shown to be effective in the present explicit dynamics setting. The model performance is illustrated by several numerical simulations. In particular, the dynamic Brazilian disc test and the Kalthoff–Winkler experiment show that the present model provides realistic predictions with the correct failure modes and rate‐dependent tensile strengths of rock at different loading rates. The ability of initial embedded discontinuity populations to model the initial microcrack populations in rocks is also successfully tested. Copyright © 2016 John Wiley & Sons, Ltd.     

Influence of tectonic overpressure on P–T paths of HP–UHP rocks in continental collision zones: thermomechanical modelling

The principle of lithostatic pressure is habitually used in metamorphic geology to calculate burial/exhumation depth from pressure given by geobarometry. However, pressure deviation from lithostatic, i.e. tectonic overpressure/underpressure due to deviatoric stress and deformation, is an intrinsic property of flow and fracture in all materials, including rocks under geological conditions. In order to investigate the influences of tectonic overpressure on metamorphic P–T paths, 2D numerical simulations of continental subduction/collision zones were conducted with variable brittle and ductile rheologies of the crust and mantle. The experiments suggest that several regions of significant tectonic overpressure and underpressure may develop inside the slab, in the subduction channel and within the overriding plate during continental collision. The main overpressure region that may influence the P–T paths of HP–UHP rocks is located in the bottom corner of the wedge‐like confined channel with the characteristic magnitude of pressure deviation on the order of ～0.3 GPa and 10–20% from the lithostatic values. The degree of confinement of the subduction channel is the key factor controlling this magnitude. Our models also suggest that subducted crustal rocks, which may not necessarily be exhumed, can be classified into three different groups: (i) UHP‐rocks subjected to significant (≥0.3 GPa) overpressure at intermediate subduction depth (50–70 km, P = 1.5–2.5 GPa) then underpressured at depth ≥100 km (P ≥ 3 GPa); (ii) HP‐rocks subjected to ≥0.3 GPa overpressure at peak P–T conditions reached at 50–70 km depth in the bottom corner of the wedge‐like confined subduction channel (P = 1.5–2.5 GPa); (iii) lower‐pressure rocks formed at shallower depths (≤40 km depth, P ≤ 1 GPa), which are not subjected to significant overpressure and/or underpressure.     

Analysis of soil–pile–structure interaction in a two‐layer ground during earthquakes considering liquefaction

This study is conducted with a numerical method to investigate the seismic behaviour among certain soils, single piles, and a structure. A series of numerical simulations of the seismic behaviour of a single‐pile foundation constructed in a two‐layer ground is carried out. Various sandy soils, namely, dense sand, medium dense sand, reclaimed soil, and loose sand, are employed for the upper layer, while one type of clayey soil is used for the lower layer. The results reveal that when a structure is built in a non‐liquefiable ground, an amplification of the seismic waves is seen on the ground surface and in the upper structure, and large bending moments are generated at the pile heads. When a structure is built in a liquefiable ground, a de‐amplification of the seismic waves is seen on the ground surface and in the upper structure, and large bending moments are generated firstly at the pile heads and then in the lower segment at the boundary between the soil layers when liquefaction takes place. Copyright © 2007 John Wiley & Sons, Ltd.     

Mesozoic to Cenozoic tectono‐metamorphic history of the South Pamir–Hindu Kush (Chitral,NW Pakistan): Insights from phase equilibria modelling,and garnet–monazite petrochronology

The Karakoram–Hindu Kush–Pamir and adjacent Tibetan plateau belt comprise a series of Gondwana‐derived crustal fragments that successively accreted to the Eurasian margin in the Mesozoic as the result of the progressive Tethys ocean closure. These domains provide unique insights into the thermal and structural history of the Mesozoic to Cenozoic Eurasian plate margin, which are critical to inform the initial boundary conditions (e.g. crustal thickness, structure and thermo‐mechanical properties) for the subsequent development of the large and hot Tibetan–Himalaya orogen, and the associated crustal deformation processes. Using a combination of microstructural analyses, thermobarometry modelling and U–Th–Pb monazite and Lu–Hf garnet geochronology, the study reappraises the metamorphic history of exposed mid‐crustal metapelites in the Chitral region of the South Pamir–Hindu Kush (NW Pakistan). This study also demonstrates that trace elements in monazite (especially Y and Dy), combined with thermodynamical modelling and Lu–Hf garnet dating, provides a powerful integrated toolbox for constraining long‐lived and polyphased tectono‐metamorphic histories in all their spatial and temporal complexity. Rocks from the Chitral region were progressively deformed and metamorphosed at sub‐ and supra‐solidus conditions through at least four distinct episodes from the Mesozoic to the Cenozoic. Rocks were first metamorphosed at ~400–500°C and ~0.3 GPa in the Late Triassic–Early Jurassic (210–185 Ma), likely in response to the accretion of the Karakoram during the Cimmerian orogeny. Pressure and temperature subsequently increased by ~0.3 GPa and 100°C in the Early‐ to Mid Cretaceous (140–80 Ma), coinciding with the intrusion of calcalkaline granitic plutons across the Karakoram and Pamir regions. This event is interpreted as the record of crustal thickening and the development of a proto‐plateau within the Eurasian margin due to a long‐lived episode of slab flattening in an Andean‐type margin. Peak metamorphism was reached in the Late Eocene–Early Oligocene (40–30 Ma) at conditions of 580–600°C and ~0.6 GPa and 700–750°C and 0.7–0.8 GPa for the investigated staurolite schists and sillimanite migmatites respectively. This crustal heating up to moderate anatexis likely resulted in the underthrusting of the Indian plate after a NeoTethyan slab‐break off or to the Tethyan Himalaya–Lhasa microcontinent collision and subsequent oceanic slab flattening. Near‐isothermal decompression/exhumation followed in the Late Oligocene (28–23 Ma) as marked by a pressure decrease in excess of ~0.1 GPa. This event was coeval with the intrusion of the 24 Ma Garam Chasma leucogranite. This rapid exhumation is interpreted to be related to the reactivation of the South Pamir–Karakoram suture zone during the ongoing collision with India. The findings of this study confirm that significant crustal shortening and thickening of the south Eurasian margin occurred during the Mesozoic in an accretionary‐type tectonic setting through successive episodes of terrane accretions and probably slab flattening, transiently increasing the coupling at the plate interface. Moreover, they indicate that the south Eurasian margin was already hot and thickened prior to Cenozoic collision with India, which has important implications for orogen‐scale strain‐accommodation mechanisms.     

Metamorphic petrology of a high‐T/low‐P granulite terrane (Damara belt,Namibia) – Constraints from pseudosection modelling and high‐precision Lu–Hf garnet‐whole rock dating

Migmatites comprise a minor volume of the high‐grade part of the Damara orogen of Namibia that is dominated by granite complexes and intercalated metasedimentary units. Migmatites of the Southern Central Zone of the Damara orogen consist of melanosomes with garnet+cordierite+biotite+K‐feldspar, and leucosomes, which are sometimes garnet‐ and cordierite‐bearing. Field evidence, petrographic observations, and pseudosection modelling suggest that, in contrast to other areas where intrusion of granitic magmas is more important, in situ partial melting of metasedimentary units was the main migmatite generation processes. Pseudosection modelling and thermobarometric calculations consistently indicate that the peak‐metamorphic grade throughout the area is in the granulite facies (~5 kbar at ~800°C). Cordierite coronas around garnet suggest some decompression from peak‐metamorphic conditions and rare andalusite records late, near‐isobaric cooling to <650°C at low pressures of ~3 kbar. The inferred clockwise P–T path is consistent with minor crustal thickening through continent–continent collision followed by limited post‐collisional exhumation and suggests that the granulite facies terrane of the Southern Central Zone of the Damara orogen formed initially in a metamorphic field gradient of ~35–40°C/km at medium pressures. New high‐precision Lu–Hf garnet‐whole rock dates are 530 ± 13 Ma, 522.0 ± 0.8 Ma, 520.8 ± 3.6 Ma, and 500.3 ± 4.3 Ma for the migmatites that record temperatures of ~800°C. This indicates that high‐grade metamorphism lasted for c. 20–30 Ma, which is compatible with previous estimates using Sm–Nd garnet‐whole rock systematics. In previous studies on Damara orogen migmatites where both Sm–Nd and Lu–Hf chronometers have been applied, the dates (c. 520–510 Ma) agree within their small uncertainties (0.6–0.8% for Sm–Nd and 0.1–0.2% for Lu–Hf). This implies rapid cooling after high‐grade conditions and, by implication, rapid exhumation at that time. The cause of the high geothermal gradient inferred from the metamorphic conditions is unknown but likely requires some extra heat that was probably added by intrusion of magmas from the lithospheric mantle, i.e., syenites that have been recently re‐dated at c. 545 Ma. Some granites derived from the lower crust at c. 545 Ma are the outcome rather than the cause of high‐T metamorphism. In addition, high contents of heat‐producing elements K, Th, and U may have raised peak temperatures by 150–200°C at the base of the crust, resulting in the widespread melting of fertile crustal rocks. The continuous gradation from centimetre‐scale leucosomes to decametre‐scale leucogranite sheets within the high‐grade metamorphic zone suggests that leucosome lenses coalesced to form larger bodies of anatectic leucogranites, thereby documenting a link between high‐grade regional metamorphism and Pan‐African magmatism. In view of the close association of the studied high‐T migmatites with hundreds of synmetamorphic high‐T granites that invaded the terrane as metre‐ to decametre‐wide sills and dykes, we postulate that crystallization of felsic lower crustal magma is, at least partly, responsible for heat supply. Late‐stage isobaric cooling of these granites may explain the occurrence of andalusite in some samples.     

The impact of vegetation on fractionation of rare earth elements (REE) during water–rock interaction

Previous studies on waters of a streamlet in the Vosges mountains (eastern France) have shown that Sr and rare earth elements (REE) principally originate from apatite dissolution during weathering. However, stream water REE patterns normalized to apatite are still depleted in light REE (LREE, La–Sm) pointing to the presence of an additional LREE depleting process. Speciation calculations indicate that complexation cannot explain this additional LREE depletion. In contrast, vegetation samples are strongly enriched in LREE compared to water and their Sr and Nd isotopic compositions are comparable with those of apatite and waters. Thus, the preferential LREE uptake by the plants at the root–water–soil (apatite) interface might lead to an additional LREE depletion of the waters in the forested catchment. Mass balance calculations indicate that the yearly LREE uptake by vegetation is comparable with the LREE export by the streamlet and, therefore, might be an important factor controlling the LREE depletion in river waters.     

Formation of bed‐scale spatial patterns in dolomite abundance during early dolomitization: Part I. Mechanisms and feedbacks revealed by reaction–transport modelling

Dolomites of varied ages exhibit metre‐scale nested patterns of lateral periodic variation in permeability and porosity and, by inference, dolomite abundance as most examples are 100% dolomite. Two‐dimensional reaction–transport modelling simulations of bed‐scale dolomitization were used to assess whether those patterns in dolomite abundance could form during near‐surface replacement dolomitization. Simulations used a 2 m high and 18 m long model domain, a low‐Mg calcite grainstone precursor and an evaporated Mississippian seawater brine (430 parts per thousand salinity) as the dolomitizing fluid. The domain was initially populated with random variations in porosity and/or grain size. Results reveal that spatial patterns in dolomite abundance emerge when there is as little as 1% dolomite formed, with similarities between the modelled patterns and outcrop‐documented patterns. The nested patterns include a near‐random component that constitutes ≤40% of the total variance, short‐range correlation ranging from 1·5 to 3·3 m and a longer‐range periodic trend with a wavelength up to 6·5 m. The emergence of pattern in dolomite abundance is the result of an autogenic self‐organizing phenomenon. It is triggered by variation in initial calcite reactive surface area that occurs due to the random heterogeneities in initial porosity and/or grain sizes. The pattern develops due to a combination of kinetic disequilibrium reactions (dolomite precipitation and calcite dissolution) and positive feedbacks between dolomite growth, calcite dissolution and fluid flow. Flow is around loci of higher dolomite, lower porosity and higher reactive surface areas, but through loci of lower dolomite, higher porosity and lower reactive surface areas. The resulting less porous/more dolomite and more porous/less dolomite structures at the metre‐scale arise from those localized interactions. This self‐organizing mechanism for pattern formation constitutes a new model for geochemical self‐organization during dolomitization and is the only self‐organization model that is proven applicable to the formation of metre‐scale patterns during early, near‐surface dolomitization.     

The 2D hydro‐mechanically coupled response of a rock mass with fractures via a mixed BEM–FEM technique

This paper describes the essential features of a numerical technique for the simulation of the coupled fluid flow and deformation in a 2D assembly of poroelastic blocks and transmissive fractures. The boundary element method (BEM) is applied to each block to reduce Navier and diffusion equations to a set of integral equations involving block boundary terms, whereas a Galerkin weighted‐residuals finite element method (FEM) is applied to the fracture diffusion equations. In addition, fracture local equilibrium is rendered through spring‐like equations relating the stresses to the relative displacements of the fracture walls. A time‐marching process is implemented leading to an algebraic system where the right‐hand side vector is built based on the collected solutions of the previous time steps. The technique requires the meshing of the fracture network only. The accuracy of the results is adequate even with relatively coarse meshes without the resort to small time steps at the beginning of the simulation. It furnishes outputs that focus only on the salient features of the response. The efficiency of the technique is demonstrated through the illustration of the results of three examples. Copyright © 2007 John Wiley & Sons, Ltd.     

Damage–viscoplastic consistency model with a parabolic cap for rocks with brittle and ductile behavior under low‐velocity impact loading

This paper presents a damage–viscoplastic cap model for rocks with brittle and ductile behavior under low‐velocity impact loading, which occurs, e.g. in percussive drilling. The model is based on a combination of the recent viscoplastic consistency model by Wang and the isotropic damage concept. This approach does not suffer from ill posedness—caused by strain softening—of the underlying boundary/initial‐value problem since viscoplasticity provides a regularization under dynamic loading by introducing an internal length scale. The model uses the Drucker–Prager (DP) yield function with the modified Rankine criterion as a tension cut‐off and a parabolic cap surface as a compression cut‐off. The parabolic cap is smoothly fitted to the DP cone. The strain softening law in compression is calibrated with the degradation index concept of Fang and Harrison. Thereby, the model is able to capture the brittle‐to‐ductile transition and hardening behavior of geomaterials under highly confined compression, which is the prevailing stress state under a bit‐button in percussive drilling. Rock strength heterogeneity is characterized statistically at the structural level using the Weibull distribution. An explicit time integrator is chosen for solving the FE‐discretized equations of motion. The contact constraints due to the impact of an indenter are imposed with the forward increment Lagrange multiplier method that is compatible with explicit time integrators. The model is tested at the material point level with various uniaxial and triaxial tests. At the structural level confined compression, uniaxial tension tests and a rock sample under low‐velocity impact are simulated. Copyright © 2009 John Wiley & Sons, Ltd.     

Fluid–rock interaction in autoliths of agpaitic nepheline syenites in the Ilímaussaq intrusion, South Greenland

Within the 1.16 Ga old Ilímaussaq intrusion, up to 700 m large autoliths occur in one stratigraphic unit of the layered floor series of agpaitic nepheline syenites (kakortokites). These autoliths consist of two different rock types: augite syenite and naujaite (agpaitic nepheline syenite). All three rock types show a number of alteration features related to the entrapment of the autoliths in the kakortokite magma caused by the interaction with a fluid phase.

In the kakortokites, the oxidation of primary arfvedsonite to aegirine and fluorite is restricted to the close proximity to the autoliths. Close to the surrounding kakortokite, the primary mafic phases of the augite syenites (augite, fayalite, Fe–Ti oxides) are completely replaced by arfvedsonite, aenigmatite, biotite, aegirine and fluorite. The decomposition of primary hastingsite to spectacular aegirine–augite–nepheline–aenigmatite symplectites can be observed up to several meters inside the autoliths. Additionally, fluorite formed at grain boundaries of primary nepheline. In the naujaite autoliths, primary arfvedsonite is replaced by aegirine–biotite intergrowths and abundant aenigmatite is occasionally replaced by Ti-rich aegirine and Fe–Ti oxides.

The mineral reactions in the autoliths are used to decipher details of the late to post-magmatic processes in a peralkaline syenitic intrusion. Mineral equilibria record an evolution governed by falling temperature (620 to ca. 500 °C) and increasing relative oxygen fugacity from FMQ + 1 to above FMQ + 4. Quantification of the observed mineral reactions reveals the infiltration of the autoliths with an oxidizing fluid phase rich in Na and F and minor addition of K. Volatiles (H and F) and in some cases also Fe, Ti and Ca (± Mg) released from primary autolith phases were mainly just relocated within the autoliths.     

Study of the soil–atmosphere moisture exchanges through convective drying tests in non‐isothermal conditions

This paper deals with the moisture exchanges occurring between soils and the surrounding atmosphere. Convective drying tests are performed on Awans silts at different drying temperatures and air relative humidities in order to reproduce the natural drying conditions. The experiments improve the understanding of the vapour transfers kinetics between the soil samples and the atmosphere. The experimental results are analysed assuming that the transfers take place in a boundary layer existing at the surface of the porous medium. The influence of the thermal conditions on the evaporation is also taken into account. In our model, coupled vapour and energy exchanges are controlled by mass and heat transfer coefficients characterizing the boundary layer. These coefficients are determined from the drying experiments. The modelling of the drying tests in non‐isothermal conditions is performed in order to validate the formulation of the vapour and heat exchanges. The numerical results present a good agreement with the kinetic of the materials desaturation determined during the tests. The analysis of the moisture transport mechanisms into the sample and at the boundary shows that at the beginning of the test, the drying is first achieved by the transport of moisture in its liquid form and its evaporation at the sample outer boundary in contact with the atmosphere. In a second step, vapour diffusion becomes predominant into the sample and it corresponds to the most important decrease of relative humidity. Copyright © 2009 John Wiley & Sons, Ltd.