[pt] Nos últimos anos, os materiais compósitos cimentícios vêm ganhando destaque na indústria da construção civil. Suas excelentes propriedades mecânicas e contribuição para o controle de propagação de fissuras são um atrativo para seu emprego como material de construção. No entanto, normas técnicas para projeto envolvendo estes materiais e estruturas ainda não são consagradas. Uma melhor compreensão do comportamento de materiais cimentícios com adição de fibras requer o estudo de suas fases e da interação entre elas. Análises em diferentes escalas possibilitam esta representação. Tensões e deformações, dano e iniciação de fissuras ocorrem na escala das heterogeneidades e ajudam a explicar e prever o comportamento do concreto em uma escala macroscópica. A modelagem e simulação do comportamento destes compósitos é complexa e desafiadora. Para tal, é necessário definir os principais mecanismos que descrevem o comportamento do material de modo a escolher a descrição matemática adequada. Esta dissertação propõe metodologias para a modelagem numérica multiescala de materiais compósitos cimentícios. A partir de informações obtidas na escala do material, busca-se compreender melhor o comportamento global do compósito. Para isto, serão desenvolvidos métodos numéricos e computacionais baseados no Método dos Elementos Finitos, em técnicas de Inteligência Artificial e nos conceitos da Mecânica do Dano Computacional. Na macroescala, um modelo contínuo equivalente é desenvolvido através de técnicas probabilísticas e de Inteligência Artificial. Na mesoescala, duas abordagens são propostas. A primeira inclui as fibras através de elementos de interface, e a segunda através de um novo elemento compósito fibra-matriz. Os modelos desenvolvidos permitem avaliar a evolução do dano, o processo de propagação de fissuras, e o comportamento global carga-deslocamento do compósito até a ruptura. Resultados experimentais da literatura suportam as conclusões do trabalho. / [en] In recent years, fiber reinforced cement-based materials have gained relevance in the civil engineering industry. Due to its excellent mechanical properties and contribution to crack propagation control, there is a great appeal to its usage as a construction material. However, technical standards for fiber reinforced concrete are still not established. A better understanding of the behavior of cement composite materials requires the representation of the material phases and their interfacial behavior. Stresses and strain distributions, damage evolution and fracture initiation develop at the observation scale of the heterogeneities and help to explain and predict the behavior of concrete at a macroscopic level. The numerical modeling of these composites emerge as challenging and complex problems. For this, it is necessary to define the main mechanisms that describe the material behavior in order to choose the proper mathematical formulation. This dissertation proposes methodologies for the numerical modeling of cement composite materials in a multiscale approach. From the information obtained at the material scale, this work aims at assessing the global behavior of the composite. Numerical and computational procedures will be developed based on the Finite Element Method, Artificial Intelligence techniques and concepts of Computational Damage Mechanics. At the macroscale, an equivalent continuum model is developed through probabilistic and Artificial Intelligence techniques. At the mesoscale, two approaches are proposed. The first includes the fibers through interface elements. The second adopts a new fiber-matrix composite element. With the models developed here, it is possible to evaluate damage evolution, fracture propagation patterns, load-displacement global behavior of the composite upto failure. Experimental results from the literature give support to the conclusions.

Reduced-order models are frequently used in the simulation of complex flows to overcome the high computational cost of direct numerical simulations, especially for three-dimensional nonlinear problems. Proper orthogonal decomposition, as one of the most commonly used tools to generate reduced-order models, has been utilized in many engineering and scientific applications. Its original promise of computationally efficient, yet accurate approximation of coherent structures in high Reynolds number turbulent flows, however, still remains to be fulfilled. To balance the low computational cost required by reduced-order modeling and the complexity of the targeted flows, appropriate closure modeling strategies need to be employed. In this dissertation, we put forth two new closure models for the proper orthogonal decomposition reduced-order modeling of structurally dominated turbulent flows: the dynamic subgrid-scale model and the variational multiscale model. These models, which are considered state-of-the-art in large eddy simulation, are carefully derived and numerically investigated. Since modern closure models for turbulent flows generally have non-polynomial nonlinearities, their efficient numerical discretization within a proper orthogonal decomposition framework is challenging. This dissertation proposes a two-level method for an efficient and accurate numerical discretization of general nonlinear proper orthogonal decomposition closure models. This method computes the nonlinear terms of the reduced-order model on a coarse mesh. Compared with a brute force computational approach in which the nonlinear terms are evaluated on the fine mesh at each time step, the two-level method attains the same level of accuracy while dramatically reducing the computational cost. We numerically illustrate these improvements in the two-level method by using it in three settings: the one-dimensional Burgers equation with a small diffusion parameter, a two-dimensional flow past a cylinder at Reynolds number Re = 200, and a three-dimensional flow past a cylinder at Reynolds number Re = 1000. With the help of the two-level algorithm, the new nonlinear proper orthogonal decomposition closure models (i.e., the dynamic subgrid-scale model and the variational multiscale model), together with the mixing length and the Smagorinsky closure models, are tested in the numerical simulation of a three-dimensional turbulent flow past a cylinder at Re = 1000. Five criteria are used to judge the performance of the proper orthogonal decomposition reduced-order models: the kinetic energy spectrum, the mean velocity, the Reynolds stresses, the root mean square values of the velocity fluctuations, and the time evolution of the proper orthogonal decomposition basis coefficients. All the numerical results are benchmarked against a direct numerical simulation. Based on these numerical results, we conclude that the dynamic subgrid-scale and the variational multiscale models are the most accurate. We present a rigorous numerical analysis for the discretization of the new models. As a first step, we derive an error estimate for the time discretization of the Smagorinsky proper orthogonal decomposition reduced-order model for the Burgers equation with a small diffusion parameter. The theoretical analysis is numerically verified by two tests on problems displaying shock-like phenomena. We then present a thorough numerical analysis for the finite element discretization of the variational multiscale proper orthogonal decomposition reduced-order model for convection-dominated convection-diffusion-reaction equations. Numerical tests show the increased numerical accuracy over the standard reduced-order model and illustrate the theoretical convergence rates. We also discuss the use of the new reduced-order models in realistic applications such as airflow simulation in energy efficient building design and control problems as well as numerical simulation of large-scale ocean motions in climate modeling. Several research directions that we plan to pursue in the future are outlined. / Ph. D.

Multiple studies have documented declines of forest breeding birds in the eastern United States, but the temporal and spatial scales of most studies limit inference regarding large scale bird-habitat trends. A potential solution to this challenge is integrating existing long-term datasets such as the U.S. Forest Service Forest Inventory and Analysis (FIA) program and U.S. Geological Survey Breeding Bird Survey (BBS) that span large geographic regions. The purposes of this study were to determine if FIA metrics can be related to BBS population indices at multiple spatial and temporal scales and to develop predictive models from these relationships that identify forest conditions favorable to forest songbirds. I accumulated annual route-level BBS data for 4 species guilds (canopy nesting, ground and shrub nesting, cavity nesting, early successional), each containing a minimum of five bird species, from 1966-2004. I developed 41 forest variables describing forest structure at the county level using FIA data from for the 2000 inventory cycle within 5 physiographic regions in 14 states (AL, GA, IL, IN, KY, MD, NC, NY, OH, PA, SC, TN, VA, and WV). I examine spatial relationships between the BBS and FIA data at 3 hierarchical scales: 1) individual BBS routes, 2) FIA units, and 3) and physiographic sections. At the BBS route scale, I buffered each BBS route with a 100m, 1km, and 10km buffer, intersected these buffers with the county boundaries, and developed a weighted average for each forest variable within each buffer, with the weight being a function of the percent of area each county had within a given buffer. I calculated 28 variables describing landscape structure from 1992 NLCD imagery using Fragstats within each buffer size. I developed predictive models relating spatial variations in bird occupancy and abundance to changes in forest and landscape structure using logistic regression and classification and regression trees (CART). Models were developed for each of the 3 buffer sizes, and I pooled the variables selected for the individual models and used them to develop multiscale models with the BBS route still serving as the sample unit. At the FIA unit and physiographic section scales I calculated average abundance/route for each bird species within each FIA unit and physiographic section and extrapolated the plot-level FIA variables to the FIA unit and physiographic section levels. Landscape variables were recalculated within each unit and section using NCLD imagery resampled to a 400 m pixel size. I used regression trees (FIA unit scale) and general linear models (GLM, physiographic section scale) to relate spatial variations in bird abundance to the forest and landscape variables. I examined temporal relationships between the BBS and FIA data between 1966 and 2000. I developed 13 forest variables from statistical summary reports for 4 FIA inventory cycles (1965, 1975, 1989, and 2000) within NY, PA, MD, and WV. I used linear interpolation to estimate annual values of each FIA variable between successive inventory cycles and GLMs to relate annual variations in bird abundance to the forest variables. At the BBS route scale, the CART models accounted for > 50% of the variation in bird presence-absence and abundance. The logistic regression models had sensitivity and specificity rates > 0.50. By incorporating the variables selected for the models developed within each buffer (100m, 1km, and 10km) around the BBS routes into a multiscale model, I was able to further improve the performance of many of the models and gain additional insight regarding the contribution of multiscale influences on bird-habitat relationships. The majority of the best CART models tended to be the multiscale models, and many of the multiscale logistic models had greater sensitivity and specificity than their single-scale counter parts. The relatively fine resolution and extensive coverage of the BBS, FIA, and NLCD datasets coupled with the overlapping multiscale approach of these analyses allowed me to incorporate levels of variation in both habitat and bird occurrence and abundance into my models that likely represented a more comprehensive range of ecological variability in the bird-habitat relationships relative to studies conducted at smaller scales and/or using data at coarser resolutions. At the FIA unit and physiographic section scales, the regression trees accounted for an average of 54.1% of the variability in bird abundance among FIA units, and the GLMs accounted for an average of 66.3% of the variability among physiographic sections. However, increasing the observational and analytical scale to the FIA unit and physiographic section decreased the measurement resolution of the bird abundance and landscape variables. This limits the applicability and interpretive strength of the models developed at these scales, but they may serve as indices to those habitat components exerting the greatest influences on bird abundance at these broader scales. The GLMs relating average annual bird abundance to annual estimates of forest variables developed using statistical report data from the 1965, 1975, 1989, and 2000 FIA inventories explained an average of 62.0% of the variability in annual bird abundance estimates. However, these relationships were a function of both the general habitat characteristics and the trends in bird abundance specific to the 4-state region (MD, NY, PA, and WV) used for these analyses and may not be applicable to other states or regions. The small suite of variables available from the FIA statistical reports and multicollinearity among all forest variables further limited the applicability of these models. As with those developed at the FIA unit and physiographic sections scales, these models may serve as general indices to the habitat components exerting the greatest influences on bird abundance trends through time at regional scales. These results demonstrate that forest variables developed from the FIA, in conjunction with landscape variables, can explain variations in occupancy and abundance estimated from BBS data for forest bird species with a variety of habitat requirements across spatial and temporal scales. / Ph. D.

High dimensional space-time datasets are available nowadays in various aspects of life such as economy, agriculture, health, environment, etc. Meanwhile, it is challenging to reveal possible connections between climate change and weather extreme events such as hurricanes or tornadoes. In particular, the relationship between tornado occurrence and climate change has remained elusive. Moreover, modeling multivariate spatio-temporal data is computationally expensive. There is great need to computationally feasible models that account for temporal, spatial, and inter-variables dependence. Our research focuses on those areas in two ways. First, we investigate connections between changes in tornado risk and the increase in atmospheric instability over Oklahoma. Second, we propose two multiscale spatio-temporal models, one for multivariate Gaussian data, and the other for matrix-variate Gaussian data. Those frameworks are novel additions to the existing literature on Bayesian multiscale models. In addition, we have proposed parallelizable MCMC algorithms to sample from the posterior distributions of the model parameters with enhanced computations. / Doctor of Philosophy / Over 1000 tornadoes are reported every year in the United States causing massive losses in lives and possessions according to the National Oceanic and Atmospheric Administration. Therefore, it is worthy to investigate possible connections between climate change and tornado occurrence. However, there are massive environmental datasets in three or four dimensions (2 or 3 dimensional space, and time), and the relationship between tornado occurrence and climate change has remained elusive. Moreover, it is computationally expensive to analyze those high dimensional space-time datasets. In part of our research, we have found a significant relationship between occurrence of strong tornadoes over Oklahoma and meteorological variables. Some of those meteorological variables have been affected by ozone depletion and emissions of greenhouse gases. Additionally, we propose two Bayesian frameworks to analyze multivariate space-time datasets with fast and feasible computations. Finally, our analyses indicate different patterns of temperatures at atmospheric altitudes with distinctive rates over the United States.

In this dissertation, we consider two different strategies for improving the projection-based reduced order model (ROM) accuracy: (I) adding closure terms to the standard ROM; (II) using Lagrangian data to improve the ROM basis. Following strategy (I), we propose a new data-driven reduced order model (ROM) framework that centers around the hierarchical structure of the variational multiscale (VMS) methodology and utilizes data to increase the ROM accuracy at a modest computational cost. The VMS methodology is a natural fit for the hierarchical structure of the ROM basis: In the first step, we use the ROM projection to separate the scales into three categories: (i) resolved large scales, (ii) resolved small scales, and (iii) unresolved scales. In the second step, we explicitly identify the VMS-ROM closure terms, i.e., the terms representing the interactions among the three types of scales. In the third step, we use available data to model the VMS-ROM closure terms. Thus, instead of phenomenological models used in VMS for standard numerical discretizations (e.g., eddy viscosity models), we utilize available data to construct new structural VMS-ROM closure models. Specifically, we build ROM operators (vectors, matrices, and tensors) that are closest to the true ROM closure terms evaluated with the available data. We test the new data-driven VMS-ROM in the numerical simulation of four test cases: (i) the 1D Burgers equation with viscosity coefficient $nu = 10^{-3}$; (ii) a 2D flow past a circular cylinder at Reynolds numbers $Re=100$, $Re=500$, and $Re=1000$; (iii) the quasi-geostrophic equations at Reynolds number $Re=450$ and Rossby number $Ro=0.0036$; and (iv) a 2D flow over a backward facing step at Reynolds number $Re=1000$. The numerical results show that the data-driven VMS-ROM is significantly more accurate than standard ROMs. Furthermore, we propose a new hybrid ROM framework for the numerical simulation of fluid flows. This hybrid framework incorporates two closure modeling strategies: (i) A structural closure modeling component that involves the recently proposed data-driven variational multiscale ROM approach, and (ii) A functional closure modeling component that introduces an artificial viscosity term. We also utilize physical constraints for the structural ROM operators in order to add robustness to the hybrid ROM. We perform a numerical investigation of the hybrid ROM for the three-dimensional turbulent channel flow at a Reynolds number $Re = 13,750$. In addition, we focus on the mathematical foundations of ROM closures. First, we extend the verifiability concept from large eddy simulation to the ROM setting. Specifically, we call a ROM closure model verifiable if a small ROM closure model error (i.e., a small difference between the true ROM closure and the modeled ROM closure) implies a small ROM error. Second, we prove that a data-driven ROM closure (i.e., the data-driven variational multiscale ROM) is verifiable. For strategy (II), we propose new Lagrangian inner products that we use together with Eulerian and Lagrangian data to construct new Lagrangian ROMs. We show that the new Lagrangian ROMs are orders of magnitude more accurate than the standard Eulerian ROMs, i.e., ROMs that use standard Eulerian inner product and data to construct the ROM basis. Specifically, for the quasi-geostrophic equations, we show that the new Lagrangian ROMs are more accurate than the standard Eulerian ROMs in approximating not only Lagrangian fields (e.g., the finite time Lyapunov exponent (FTLE)), but also Eulerian fields (e.g., the streamfunction). We emphasize that the new Lagrangian ROMs do not employ any closure modeling to model the effect of discarded modes (which is standard procedure for low-dimensional ROMs of complex nonlinear systems). Thus, the dramatic increase in the new Lagrangian ROMs' accuracy is entirely due to the novel Lagrangian inner products used to build the Lagrangian ROM basis. / Doctor of Philosophy / Reduced order models (ROMs) are popular in physical and engineering applications: for example, ROMs are widely used in aircraft designing as it can greatly reduce computational cost for the aircraft's aeroelastic predictions while retaining good accuracy. However, for high Reynolds number turbulent flows, such as blood flows in arteries, oil transport in pipelines, and ocean currents, the standard ROMs may yield inaccurate results. In this dissertation, to improve ROM's accuracy for turbulent flows, we investigate three different types of ROMs. In this dissertation, both numerical and theoretical results show that the proposed new ROMs yield more accurate results than the standard ROM and thus can be more useful.

In dieser Dissertation wird eine allgemeine zweiskalige Homogenisierungsmethode für große Deformationen entwickelt, welche die Trägheitskräfte der Mikroskala konsistent berücksichtigt. Die energetische Skalenkopplung der Methode basiert auf der erweiterten Hill-Mandel Bedingung für Makrohomogenität. Darüber hinaus wird die kinematische Skalenkopplung diskutiert und eine Volumenintegrals-Verschiebungsbedingung aufgezeigt, die eine allgemeine dynamische Betrachtung ermöglicht. Um einen effizienten Algorithmus zu gewährleisten, werden vier makroskopischen Tangenten-Module in geschlossener Form hergeleitet. Es werden zwei Rechenbeispiele genutzt, um allgemeine Eigenschaften der Methode zu analysieren. Dazu gehören das makroskopische Konvergenzverhalten und die Übereinstimmung mit einskaligen Referenzsimulationen. Des Weiteren wird der Einfluss der Verschiebungsbedingung und die Wahl der Einheitszelle als representatives Volumenelement auf die Antwort der Makroskale untersucht. Der Fokus der Arbeit wird im Anschluss auf die Modellierung hochduktiler Betone (Engl.: Strain-Hardening Cementitious Composites – SHCC) unter Stoßbelastung gelegt. Zunächst wird anhand von experimentellen Daten ein vereinfachtes Materialmodell kalibriert, welches das homogenisierte Faserauszugsverhalten repräsentiert. Danach wird dieses Faserauszugsmodell auf der Mikroskale eingesetzt und mit der vorgestellten Homogenisierungsmethode untersucht. Schließlich wird ein Split-Hopkinson-Bar Zugversuch numerisch repliziert. Dieser wird verwendet um die Funktionaltät der Methode aufzuzeigen, wie dynamische Effekte des Materials und der Struktur untersucht werden können. / A general numerical two-scale homogenization method for large strains is developed, which consistently takes into account inertia forces at the microscale. The energetic scale coupling of the framework is based on the extended Hill-Mandel condition of macro-homogeneity. Furthermore, kinematic scale links are discussed and a volume integral displacement constraint is proposed. To enable an efficient algorithm, closed form formulations of four macroscopic tangent moduli are derived. These consistently include the microscale inertia effects as well as the proposed displacement constraint. Two numerical examples are presented, a layered microstructure and a locally resonant material. These examples are used to analyze general properties of the presented framework, namely the macroscopic convergence behavior and the overall match with single-scale reference calculations. In addition, both the displacement constraint and the choice of unit cell as representative volume element are studied with respect to their influence on the macroscopic response. Subsequently, the thesis focuses on the modeling of strain-hardening cementitious composites under impact loading. First, a simplified material model representing the homogenized fiber pullout behavior is calibrated using experimental data. Then, this fiber pullout model is used at the microscale and studied using the proposed dynamic homogenization framework. Finally, a split Hopkinson bar tension test is numerically replicated and used to showcase the ability of the framework to thoroughly study the dynamic effects of the material and structure.

Functional coatings produced using scalable and cost-effective processes such as electrodeposition and etching lead to the creation of random roughness at multiple length scales on the surface. The first part of thesis work aims at developing a fundamental mathematical understanding of multiscale coatings by presenting a fractal model to describe wettability on such surfaces. These surfaces are described with a fractal asperity model based on the Weierstrass-Mandelbrot function. Using this description, a model is presented to evaluate the apparent contact angle in different wetting regimes. Experimental validation of the model predictions is presented on various hydrophobic and superhydrophobic surfaces generated on several materials under different processing conditions. Superhydrophobic surfaces have myriad industrial applications, yet their practical utilization has been severely limited by their poor mechanical durability and longevity. Toward addressing this gap, the second and third parts of this thesis work present low cost, facile processes to fabricate superhydrophobic copper and zinc-based coatings via electrodeposition. Additionally, systematic studies are presented on coatings fabricated under different processing conditions to demonstrate excellent durability, mechanical and underwater stability, and corrosion resistance. The presented processes can be scaled to larger, durable coatings with controllable wettability for diverse applications. Apart from their use as superhydrophobic surfaces, the application of multiscale coatings in photo-thermal conversion systems as solar selective coatings is explored in the final part of this thesis. The effects of scale-independent fractal parameters of the coating surfaces and heat treatment are systematically explored with respect to their optical properties of absorptance, emittance, and figure of merit (FOM). / Master of Science / Coatings are extensively used through various industries and serve a range of purposes such as providing protection, changing the physical and chemical properties, decoration, and adding other new properties to the base surface. Coatings produced using scalable and cost-effective processes such as electrodeposition and etching are inherently rough and have features ranging from micro- to nano-scale, leading to their multiscale nature. The first part of thesis work aims at developing a fundamental mathematical understanding of these rough coatings by presenting a model to describe and predict the wettability on such surfaces. Wettability of a surface is its ability to maintain contact with a liquid, resulting from intermolecular interactions when the two are brought together. Wettability for a solid surface is generally quantified by the contact angle, measured through the liquid, where a liquid-vapor interface meets the solid surface. A mathematical model is presented to evaluate the apparent contact angle on such multiscale rough surfaces. Experimental validation of the model predictions is presented on various hydrophobic and superhydrophobic surfaces generated on several materials under different processing conditions. Superhydrophobic surfaces do not get wet by water and water droplet contact angle on these surfaces exceed 150°. Such surfaces have extensive industrial applications, yet their practical utilization has been severely limited by their poor mechanical durability and longevity. Toward addressing this gap, the second and third parts of this thesis work present low cost, facile processes to fabricate superhydrophobic copper and zinc-based coatings via electrodeposition. Additionally, systematic studies are presented on coatings fabricated under different processing conditions to demonstrate excellent durability, mechanical and underwater stability, and corrosion resistance. The presented processes can be scaled to larger, durable coatings with controllable wettability for diverse applications. Apart from their use as superhydrophobic surfaces, the application of multiscale coatings in photo-thermal conversion systems as solar selective coatings is explored in the final part of this iv thesis. Solar selective coatings aim to improve photo-thermal conversion efficiency by providing a high solar absorptance and low thermal emittance. Solar selective coatings ensure that maximum incoming solar radiation is absorbed into the surface and radiative losses due to emissions at high temperatures are minimized. The effects of scale-independent mathematical parameters of the coating surfaces and heat treatment are systematically explored with respect to their optical properties of absorptance, emittance, and figure of merit (FOM).

Over the past century, great strides have been made in the advancement of mine fire knowledge since the 1909 Cherry Mine Fire Disaster, one of the worst in U.S. history. However, fire hazards remain omnipresent in underground coal mines in the U.S. and around the world. A precise fire numerical analysis (simulation) before any fire events can give a broad view of the emergency scenarios, leading to improved emergency response, and better health and safety outcomes. However, the simulation cost of precise large complex dynamical systems such as fire in underground mines makes practical and even theoretical application challenging. This work details a novel methodology to reduce fire and airflow simulation costs in order to make simulation of complex systems around fire and mine ventilation systems viable. This study will examine the development of a Reduced Order Model (ROM) to predict the flow field of an underground mine geometry using proper orthogonal decomposition (POD) to reduce the airflow simulation cost in a nonlinear model. ROM proves to be an effective tool for approximating several possible solutions near a known solution, resulting in significant time savings over calculating full solutions and suitable for ensemble calculations. In addition, a novel iterative methodology was developed based on the physics of the fluid structure, turbulent kinetic energy (TKE) of the dynamical system, and the vortex dynamics to determine the interface boundary in multiscale (3D-1D) fire simulations of underground space environments. The proposed methodology was demonstrated to be a useful technique for the determination of near and far fire fields, and could be applied across a broad range of flow simulations and mine geometries. Moreover, this research develops a methodology to analyze the tenable limits in a methane fire event in an underground coal mine for bare-faced miners, mine rescue teams, and fire brigade teams in order to improve safety and training of personnel trained to fight fires. The outcomes of this research are specific to mining although the methods outlined might have broader impacts on the other fields such as tunneling and underground spaces technology, HVAC, and fire protection engineering industries. / Ph. D. / With the rapid advancement of technology, the mine fire knowledge has progressed significantly. Atmospheric monitoring and early sensing of heating has improved; the numerical analysis has been expedited with the usage of supercomputers, and more regulations and standards have been set to increase health and safety of miners. In spite of advancements in these areas, fire hazards remain a critical hazard in underground mines. Developing an emergency plan for the safe escape and for fighting the fire is one of the most important issues during a fire event in underground space environments such as mines. A precise fire numerical analysis (simulation) before any fire events can give a broad view of the emergency situation that leads to improving the health and safety issues in the mining industry. Unfortunately, the precise simulation of the large complex dynamical system such as a fire in underground spaces is costly. This work details a cutting edge approach to reduce the fire and airflow simulation costs in order to make simulation of complex systems around fire and mine ventilation systems viable. The main focus of this proposal is to develop novel methodologies to decrease the time of the fire and airflow simulations. The developed methodologies prove to be useful techniques for the reduction of fire simulation and airflow simulation costs. In addition, this study will examine the development of a comprehensive methodology to analyze the tenable limits in a fire event in an underground coal mine in order to improve safety and training of personnel trained to fight fires. These simulations, applied to training, will result in more efficient evacuations (e.g., the decision to leave can be made quickly and with less delay), as well as safe and effective firefighting under certain situations. The target of this research is specific to mining industry although the methods outlined might have broader impacts on the other fields such as tunneling and underground spaces technology, HVAC, and fire protection engineering industries. Therefore, this research may have an immense contribution on the improvement of health and safety associated with firefighting.

This study introduces numerical frameworks for simulating the interactions within soil systems subjected to freezing and thawing processes, crucial for addressing geotechnical challenges in cold regions. By integrating robust thermo-hydro-mechanical (THM), this research offers a general understanding and specific insights into the deformation, thermal, and moisture transport behaviors of freezing-thawing soils. The first part of this study presents a soil freezing characteristic curve (SFCC) adaptable to various computational frameworks, including THM models. The SFCC, enhanced by an automatic regression scheme and a smoothing algorithm, accommodates the dynamic changes in soil properties due to phase transitions. This model effectively captures the unique behaviors of different soil types under freezing conditions, addressing key factors such as freezing temperature, compaction, and mechanical loading. Building on this foundation, the second framework employs the phase-field method (PFM) coupled with THM to model the behavior of ice-rich saturated porous media. This approach advances the field by enabling distinct representations of the mechanical behaviors of ice and soil through a diffused interface, introducing anisotropic responses as the soil undergoes freezing. By integrating a transversely isotropic plastic constitutive model for ice, this method provides a tool for capturing the phase transition processes and the resulting mechanical responses of frozen soil. The third part extends these methodologies to model thaw consolidation in permafrost regions using a THM framework combined with phase field methods. This model incorporates internal energy functions and a multiscale modified Cam-Clay model within a damage phase field framework, adept at capturing the simultaneous effects of phase change and particle rearrangement. Through validation against experimental scenarios, this model demonstrates its effectiveness in understanding the microstructural evolution and plastic softening in thaw-sensitive soils, which is vital for enhancing infrastructure resilience under thaw conditions. Together, these integrated approaches represent a leap in the modeling and simulation of geotechnical behaviors in cold regions, offering potential applications in predicting and mitigating the impacts of climate change on permafrost and other freeze-thaw affected terrains. / Thesis / Doctor of Science (PhD)

This thesis presents the development of a new multiscale stochastic fracture mechanics modelling framework informed by in-situ X-ray Computed Tomography (X-ray CT) tests, which can be used to enhance the quality of new designs and prognosis practices for fibre reinforced composites. To reduce the empiricism and conservatism of existing methods, this PhD research systematically has tackled several challenging tasks including: (i) extension of the cohesive interface crack model to multi-phase composites in both 2D and 3D, (ii) development of a new in-house loading rig to support in-situ X-ray CT tests, (iii) reconstruction of low phase-contrast X-ray CT datasets of carbon fibre composites, (iv) integration of X-ray CT image-based models into detailed crack propagation FE modelling and (v) validation of a partially informed multiscale stochastic modelling method by direct comparison with in-situ X-ray CT tensile test results.