Fluviokarst landscapes are dominated by both fluvial and karst features. Interpreting hydrologic pathways of fluviokarst can be confounded by the unknown connectivity of the various flow regimes. A combined discrete-continuum (CDC) hybrid numeric model for simulating the surface and subsurface hydrology and hydraulics in fluviokarst basins was formulated to investigate fluviokarst pathways. This model was applied to the Cane Run Royal Springs basin in Kentucky USA. A priori constraints on parameterization were avoided via multi-stage optimization utilizing Sobol sequencing and high performance computing. Modelling results provide evidence of hydrologic pathways dominated by fracture flow, epikarst transfer and runoff. Fractures in karst basins with high fracture-matrix permeability ratios may influence both springflow and streamflow. Swallet features can be as important as spring features as they are sink features in streamflow during hydrologic events. Inflections in spring hydrographs represent shifts in the surface-subsurface connectivity via the fractures, as opposed to shifts in dominant storage zones. Existing methods of dual- and triunal hydrograph separation of karst springflow may not be directly transferrable to fluviokarst springs. The numerical model herein has advantages of suggesting dominant pathways in complex terrane and highlighting unforeseen surface-subsurface connectivity. However, disadvantages include computational expense and previous site studies.

Un mur de soutènement en pierre sèche (MSPS) est un ouvrage vernaculaire construit par empilement de blocs rocheux sans liant. Ce type de mur a fortement sculpté les campagnes françaises mais a aussi été utilisé par le passé dans des ouvrages de soutènement que ce soit routier ou ferroviaire. Pourtant, l’utilisation de cette technologie a disparu au cours du 20e siècle au profit de solutions industrialisées comme le béton armé. Face à ce patrimoine vieillissant, il est très difficile de proposer des protocoles de réparation alors que la réglementation associée à ces ouvrages est inexistante. Pour les mêmes raisons, alors que cette technologie répond parfaitement aux questions soulevées par le développement durable, elle est rarement envisagée ou retenue par les prescripteurs. La rupture des MSPSs neufs peut apparaître à cause de : (1) une poussée excessive du remblai soutenu par le mur, (2) un effort concentré excessif présent sur la surface du remblai et proche de la tête du mur. Ces deux causes induisent deux types de rupture très différents, respectivement : (1) rupture en déformation plane, (2) rupture par apparition d’un ventre. Trois expériences récentes à l’échelle 1 des MSPSs chargés par : (1) une poussée hydrostatique, (2) un remblai, (3) un remblai avec une force concentrée sur la surface de ce dernier, ont permis d’identifier certains phénomènes mis en jeu dans ces ruptures. Ce travail de thèse contribuera alors au développement de nouveaux outils scientifiques mais aussi à valider des outils existants pour dimensionner les MSPSs. Les expériences réalisées à l’échelle 1 serviront alors de cadre à ce travail pour valider les outils développés. Nous avons choisi d’utiliser une approche aux éléments discrets (MED) où chaque bloc de pierre du mur est modélisé individuellement, respectant ainsi la nature-Même de l’ouvrage réel. Dans un premier temps, une rupture de type déformation plane est modélisée par une approche discrète pure et une approche discrète-Continue. Les atouts et inconvénients de chacune des méthodes sont mis en avant. Une validation quantitative des modèles numériques est faite en comparant la hauteur critique de chargement avec les expériences à l’échelle 1. Ensuite, on étudie la sensibilité de plusieurs paramètres géométriques et mécaniques sur la hauteur critique de chargement, tout comme l’influence de la cohésion du remblai. Enfin, une première modélisation 3D de type qualitative sur la rupture des MSPS par un chargement concentré en surface du remblai est présentée. Les problèmes de modélisation sont soulevés et l’influence de la forme des blocs dans le processus de rupture est étudiée. / A dry-Stone retaining wall (DSRW) is a vernacular structure constructed by stacking the stone blocks without using any binder. In the past, this wall has been extensively used, shaping the French countryside area, built either for road or railroad retaining wall. However, the use of this technology has disappeared during 20th century, due to the emergence of more industrialized materials such as reinforced concrete. Confronted by these ageing heritage structures, it is very difficult to propose a proper reparation procedure since the building codes associated with this structure are nonexistent. For the same reason, though this technology perfectly answers the questions raised by the concept of sustainable development, in practice this structure is rarely considered or used by the engineering advisors. The failure of the newly built DSRWs can be attributed to the following reasons: (1) an excessive pressure of backfill retained by the wall, (2) a presence of an excessive concentrated load on the backfill surface, close to the top part of the wall. These two types of loading lead to two very different types of failure, respectively: (1) plane strain failure, (2) bulging failure. Three recent experimental campaigns of DSRWs loaded with: (1) hydrostatic pressure, (2) backfill, (3) backfill with a concentrated on its surface, provided a better understanding of phenomena involved in these failures. The work presented in this PhD thesis contributes to the development of new scientific tools capable to help design the DSRWs, as well as validating existing tools. The recent full-Scale experimental campaign will serve as a basis to the validation of the developed numerical tools. We have chosen to use a discrete element method (DEM) where each stone block of the wall is modeled individually, complying with the nature of real DSRW. In the first place, the plane strain failure is modeled by a purely discrete approach and a discrete-Continuum approach. The advantage and inconvenient of each method will be presented in advance. A quantitative validation of numerical models is provided by comparing the critical height of loading with results derived from the full-Scale experimental campaign. Thereafter, a 3D qualitative model of DSRWs loaded with a concentrated load on the backfill surface is presented. The modeling problem is noted and the influence of the block form in regards of the related failure mechanism is studied.

Multiscale mathematical modelling is one of the major driving forces behind the systems biology revolution. The inherently interdisciplinary nature of its study and the multiple spatial and temporal scales which characterise its dynamics make cell migration an ideal candidate for a systems biology approach. Due to its ease of analysis and its compatibility with the type of data available, phenomenological continuum modelling has long been the default framework adopted by the cell migration modelling community. However, in recent years, with increased computational power, complex, discrete, cell-level models, able to capture the detailed dynamics of experimental systems, have become more prevalent. These two modelling paradigms have complementary advantages and disadvantages. The challenge now is to combine these two seemingly disparate modelling regimes in order to exploit the benefits offered by each in a comprehensive, multiscale equivalence framework for modelling cell migration. The main aim of this thesis is to begin with an on-lattice, individual-based model and derive a continuum, population-based model which is equivalent to it in certain limits. For simple models this is relatively easy to achieve: beginning with a one-dimensional, discrete model of cell migration on a regular lattice we derive a partial differential equation for the evolution of cell density on the same domain. We are also able to simply incorporate various signal sensing dynamics into our fledgling equivalence framework. However, as we begin to incorporate more complex model attributes such as cell proliferation/death, signalling dynamics and domain growth we find that deriving an equivalent continuum model requires some innovative mathematics. The same is true when considering a non-uniform domain discretisation in the one-dimensional model and when determining appropriate domain discretisations in higher dimensions. Higher-dimensional simulations of individual-based models bring with them their own computational challenges. Increased lattice sites in order to maintain spatial resolution and increased cell numbers in order to maintain consistent densities lead to dramatic reductions in simulation speeds. We consider a variety of methods to increase the efficiency of our simulations and derive novel acceleration techniques which can be applied to general reaction systems but are especially useful for our spatially extended cell migration algorithms. The incorporation of domain growth in higher dimensions is the final hurdle we clear on our way to constructing a complex discrete-continuum modelling framework capable of representing signal-mediated cell migration on growing (possibly non-standard) domains in multiple dimensions.

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