Computational modeling of syntaxial overgrowth cementation and fracture propagation in sedimentary rocks

Die vorliegende Dissertation befasst sich mit der rechnerischen Modellierung des Phänomens a) syntaktischer Überwuchszementierung und b) spröder anisotroper Bruchausbreitung in Sedimentgesteinen, mithilfe des Phasenfeldansatzes. Im ersten Teil wurde ein Multiphasenfeldmodell (MPF-Modell) für die Zementierung angepasst, um die Rolle von Rissöffnungsraten und Zementwachstumsraten bei der Entwicklung verschiedener Calcitvenenmorphologien als Ergebnis des bitaxialen Wachstums in syntaxialen Venen in zwei Dimensionen (2-D) zu untersuchen. Ein geometrischer Verschiebungsalgorithmus wurde entwickelt, um die inkrementelle Öffnungsweite unter verschiedenen Randbedingungen zu simulieren. Die numerischen Ergebnisse erläutern den bergang von Venentexturen von faserigen zu länglichen blockartigen Formen und schließlich zu euhedrisch terminierten Kristallmorphologien im offenen Raum, zur Erhöhung der Rissöffnungsraten. Zum ersten Mal wurden die Bildungsmechanismen gleichmäßiger und ungleichmäßiger Faservenen in Abhängigkeit von der anfänglichen Rissöffnung verstanden. Die starke Ähnlichkeit der numerisch versiegelten Venenmikrostrukturen mit den natürlichen Venenproben zeigt die Fähigkeit des angepassten MPF-Modells, die Wachstumsdynamik von Calcitvenen zu erfassen. Als nächstes wurde das MPF-Modell angepasst, um die syntaktische Quarzzementierung in Sandsteinen in 3-D zu untersuchen. Während der fortschreitenden Quarzzementierung wurde der Einfluss der anfänglichen Korngröße von unikristallinen Quarzaggregaten auf die Entwicklung der wichtigsten petrophysikalischen Gesteinseigenschaften, d. h. Porosität, Permeabilität und Porengrößenverteilung, untersucht. Die dynamischen Zusammenhänge zwischen diesen Eigenschaften wurden weiter ermittelt und im Vergleich zur vorhandenen Literatur kritisch analysiert. Im weiteren Forschungsverlauf wurde das MPF-Modell erweitert, um die facettierungsabhängigen Wachstumstendenzen von Quarzzementen genauer zu berücksichtigen. Darüber hinaus wurde ein systematisches Verfahren entwickelt, um mehrere digitale Kornpackungen zu erzeugen, die, analog zu natürlichen Sandsteinen und mit Hinblick auf die Kornformen, Größen und Ablagerungsporositäten, aus unterschiedlichen Anteilen unikristalliner und polykristalliner Aggregate bestehen. Unter Verwendung dieser digitalen Packungen wurde während der fortschreitenden Quarzzementierung der Einfluss der Polykristallinität von Körnern auf das Zementvolumen, die Porosität und die Permeabilität von Sandsteinen untersucht. Die simulierten Wachstumsgeschwindigkeiten entlang verschiedener Facetten, unter ungestörten Wachstumsbedingungen, zeigen eine gute Übereinstimmung mit der analytischen Lösung sowie früheren Studien. Die numerisch zementierten Mikrostrukturen von unikristallinen und polykristallinen Packungen zeigen hinsichtlich der Kristallmorphologien und des verbleibenden Porenraums deutliche Ähnlichkeiten mit den entsprechenden natürlichen Proben. Die numerisch abgeleiteten Beziehungen zwischen den petrophysikalischen Eigenschaften und ihren Variationen in verschiedenen Sandsteinen, die auf der Grundlage der anfänglichen Korngröße und des Anteils der polykristallinen Quarzaggregate während der fortschreitenden Zementierung variieren, liefern im Einklang mit den vorherigen experimentellen Befunden und empirischen Gesetzen wertvolle Einblicke in die Dynamik des Quarzwachstums in Sandsteinen. Im letzten Teil wurde ein separates MPF-Bruchmodell angepasst, um das Phänomen der spröden Mikrofrakturierung in Quarzsandsteinen anzugehen. Zwei neue Aspekte dieses Modells sind die Formulierungen von I) anisotroper und II) reduzierter Grenzflächenrissbeständigkeit. Während im ersteren Fall die bevorzugten Spaltungsebenen in jedem Quarzkorn berücksichtigt werden, bietet der letztere Fall kontinuierlich und gleichmäßig eine reduzierbare Rissbeständigkeit entlang der Korngrenzen, wodurch das Modell das intergranulare Bruchwachstum simulieren kann. Mit diesen Bestandteilen kann die Konkurrenz zwischen trans- und intergranularen Rissausbreitungsmodi durch das Modell simuliert und dabei bevorzugte Bruchrichtungen innerhalb jedes Korns aufgezeigt werden. Das Modell kann als leistungsstarkes Werkzeug zur Untersuchung der komplizierten Bruchprozesse in heterogenen polykristallinen Gesteinen dienen, die aus Körnern mit unterschiedlichen elastischen Eigenschaften, Spaltungsebenen und Korngrenzattributen bestehen. Die Leistung und Fähigkeiten des Modells werden anhand der repräsentativen numerischen Beispiele verdeutlicht. Die Ergebnisse der vorliegenden Dissertation zeigen erfolgreich, dass die Phasenfeldmethode angewendet werden kann, um die wesentliche Physik dieser Prozesse effizient und elegant erfassen zu können

Modeling fracture cementation processes in calcite limestone: a phase-field study

The present work investigates the influence of crack opening rates on the development of four important calcite vein morphologies, namely fibrous, elongate-blocky, partially open, and euhedral, as a result of bitaxial growth in syntaxial veins using a multiphase-field model. The continued fracturing that occurs during synkinematic cementation in these veins is simulated using the geometric shift algorithm. The stark resemblance of the numerically sealed vein microstructures with the natural samples in terms of structural characteristics as well as remaining pore space signifies a dominant role of crack opening rates in the resulting morphological patterns. Further, simulation results of slow crack opening rates reveal that non-uniform fibers of variable lengths are formed when initial crack aperture is small, due to suppression of growth competition and vice versa

Seismic Anisotropy of Temperate Ice in Polar Ice Sheets

We present a series of simple shear numerical simulations of dynamic recrystallization of two‐phase nonlinear viscous materials that represent temperate ice. First, we investigate the effect of the presence of water on the resulting microstructures and, second, how water influences on P wave (Vp) and fast S wave (Vs) velocities. Regardless the water percentage, all simulations evolve from a random fabric to a vertical single maximum. For a purely solid aggregate, the highest Vp quickly aligns with the maximum c‐axis orientation. At the same time, the maximum c‐axis development reduces Vs in this orientation. When water is present, the developed maximum c‐axis orientation is less intense, which results in lower Vp and Vs. At high percentage of water, Vp does not align with the maximum c‐axis orientation. If the bulk modulus of ice is assumed for the water phase (i.e., implying that water is at high pressure), we find a remarkable decrease of Vs while Vp remains close to the value for purely solid ice. These results suggest that the decrease in Vs observed at the base of the ice sheets could be explained by the presence of water at elevated pressure, which would reside in isolated pockets at grain triple junctions. Under these conditions water would not favor sliding between ice grains. However, if we consider that deformation dominates over recrystallization, water pockets get continuously stretched, allowing water films to be located at grain boundaries. This configuration would modify and even overprint the maximum c‐axis‐dependent orientation and the magnitude of seismic anisotropy

Phase-field approach to polycrystalline solidification including heterogeneous and homogeneous nucleation

Advanced phase-field techniques have been applied to address various aspects of polycrystalline solidification including different modes of crystal nucleation. The height of the nucleation barrier has been determined by solving the appropriate Euler-Lagrange equations. The examples shown include the comparison of various models of homogeneous crystal nucleation with atomistic simulations for the single component hard-sphere fluid. Extending previous work for pure systems (Gránásy L, Pusztai T, Saylor D and Warren J A 2007 Phys. Rev. Lett. 98 art no 035703), heterogeneous nucleation in unary and binary systems is described via introducing boundary conditions that realize the desired contact angle. A quaternion representation of crystallographic orientation of the individual particles (outlined in Pusztai T, Bortel G and Gránásy L 2005 Europhys. Lett. 71 131) has been applied for modeling a broad variety of polycrystalline structures including crystal sheaves, spherulites and those built of crystals with dendritic, cubic, rhombododecahedral, truncated octahedral growth morphologies. Finally, we present illustrative results for dendritic polycrystalline solidification obtained using an atomistic phase-field model

Coupled DEM-LBM method for the free-surface simulation of heterogeneous suspensions

The complexity of the interactions between the constituent granular and liquid phases of a suspension requires an adequate treatment of the constituents themselves. A promising way for numerical simulations of such systems is given by hybrid computational frameworks. This is naturally done, when the Lagrangian description of particle dynamics of the granular phase finds a correspondence in the fluid description. In this work we employ extensions of the Lattice-Boltzmann Method for non-Newtonian rheology, free surfaces, and moving boundaries. The models allows for a full coupling of the phases, but in a simplified way. An experimental validation is given by an example of gravity driven flow of a particle suspension

A Micromechanics-based Multiscale Approach toward Continental Deformation, with Application to Ductile High-Strain Zones and Quartz Flow Laws

Earth’s lithosphere may be regarded as a composite material made of rheologically heterogeneous elements. The presence of these heterogeneous elements causes flow partitioning, making the deformation of Earth’s lithosphere heterogeneous on all observation scales. Understanding the multiscale heterogeneous deformation and the overall rheology of the lithosphere is very important in structural geology and tectonics. The overall rheology of Earth’s lithosphere on a given observation scale must be obtained from the properties of all constituents and may evolve during the deformation due to the fabric development. Both the problem of flow partitioning and characterization of the overall rheology are closely related and require a fully mechanical multiscale approach. This thesis refines a micromechanics-based multiscale modeling approach called the self-consistent MultiOrder Power Law Approach (MOPLA). MOPLA treats the heterogeneous rock mass as a continuum of rheologically distinct elements. The rheological properties and the mechanical fields of the constituent elements and those of the composite material are computed by solving partitioning and homogenization equations self-consistently. The algorithm of MOPLA has been refined and implemented in MATLAB for high-performance computing. The micromechanical approach is used to investigate the deformation of ductile high-strain zones, advancing previous work on this subject to a full mechanical level. This thesis considers a ductile high-strain zone as a flat heterogeneous inclusion embedded in the ductile lithosphere subjected to a tectonic deformation due to remote plate motion. The kinematic and the mechanical fields inside and outside the high-strain zone, including the finite strain accumulation in there, are solved by partitioning equations. The overall rheology of the high-strain zone is obtained by means of a self-consistent homogenization scheme. Understanding the continental rheology requires an accurate quartz dislocation creep flow law. Despite decades of experimental studies, there are considerable discrepancies in quartz flow law parameters. This thesis proposes that the discrepancies could be explained by considering both the pressure effect on the activation enthalpy and the slip system dependence of the stress exponent. Two distinct dislocation creep flow laws corresponding to two dominant slip systems are determined based on the current dataset of the creep experiments on quartz samples

Simulation of pore-scale flow using finite element-methods

I present a new finite element (FE) simulation method to simulate pore-scale flow. Within the pore-space, I solve a simplified form of the incompressible Navier-Stoke’s equation, yielding the velocity field in a two-step solution approach. First, Poisson’s equation is solved with homogeneous boundary conditions, and then the pore pressure is computed and the velocity field obtained for no slip conditions at the grain boundaries. From the computed velocity field I estimate the effective permeability of porous media samples characterized by thin section micrographs, micro-CT scans and synthetically generated grain packings. This two-step process is much simpler than solving the full Navier Stokes equation and therefore provides the opportunity to study pore geometries with hundreds of thousands of pores in a computationally more cost effective manner than solving the full Navier-Stoke’s equation. My numerical model is verified with an analytical solution and validated on samples whose permeabilities and porosities had been measured in laboratory experiments (Akanji and Matthai, 2010). Comparisons were also made with Stokes solver, published experimental, approximate and exact permeability data. Starting with a numerically constructed synthetic grain packings, I also investigated the extent to which the details of pore micro-structure affect the hydraulic permeability (Garcia et al., 2009). I then estimate the hydraulic anisotropy of unconsolidated granular packings. With the future aim to simulate multiphase flow within the pore-space, I also compute the radii and derive capillary pressure from the Young-Laplace equation (Akanji and Matthai,2010

A novel highly efficient Lagrangian model for massively multidomain simulations: parallel context

A new method for the simulation of evolving multi-domains problems has been introduced in a previous work (RealIMotion), Florez et al. (2020). In this article further developments of the model will be presented. The main focus here is a robust parallel implementation using a distributed-memory approach with the Message Passing Interface (MPI) library OpenMPI. The original 2D sequential methodology consists in a modified front-tracking approach where the main originality is that not only interfaces between domains are discretized but their interiors are also meshed. The interfaces are tracked based on the topological degree of each node on the mesh and the remeshing and topological changes of the domains are driven by selective local operations performed over an element patch. The accuracy and the performance of the sequential method has proven very promising in Florez et al. (2020). In this article a parallel implementation will be discussed and tested in context of motion by curvature flow for polycrystals, i.e. by considering Grain Growth (GG) mechanism. Results of the performance of the model are given and comparisons with other approaches in the literature are discussed