Modelización de costas rocosas acantiladas

El retroceso de las costas acantiladas es un fenómeno muy extendido sobre los litorales rocosos expuestos a la incidencia combinada de los procesos marinos y meteorológicos que se dan en la franja costera. Este fenómeno se revela violentamente como movimientos gravitacionales del terreno esporádicos, pudiendo causar pérdidas materiales y/o humanas. Aunque el conocimiento de estos riesgos de erosión resulta de vital importancia para la correcta gestión de la costa, el desarrollo de modelos predictivos se encuentra limitado desde el punto de vista geomorfológico debido a la complejidad e interacción de los procesos de desarrollo espacio-temporal que tienen lugar en la zona costera. Los modelos de predicción publicados son escasos y con importantes inconvenientes: a) extrapolación, extienden la información de registros históricos; b) empíricos, sobre registros históricos estudian la respuesta al cambio de un parámetro; c) estocásticos, determinan la cadencia y magnitud de los eventos futuros extrapolando las distribuciones de probabilidad extraídas de catálogos históricos; d) proceso-respuesta, de estabilidad y propagación del error inexplorada; e) en Ecuaciones en Derivadas Parciales, computacionalmente costosos y poco exactos. La primera parte de esta tesis detalla las principales características de los modelos más recientes de cada tipo y, para los más habitualmente utilizados, se indican sus rangos de aplicación, ventajas e inconvenientes. Finalmente como síntesis de los procesos más relevantes que contemplan los modelos revisados, se presenta un diagrama conceptual de la recesión costera, donde se recogen los procesos más influyentes que deben ser tenidos en cuenta, a la hora de utilizar o crear un modelo de recesión costera con el objetivo de evaluar la peligrosidad (tiempo/frecuencia) del fenómeno a medio-corto plazo. En esta tesis se desarrolla un modelo de proceso-respuesta de retroceso de acantilados costeros que incorpora el comportamiento geomecánico de materiales cuya resistencia a compresión no supere los 5 MPa. El modelo simula la evolución espaciotemporal de un perfil-2D del acantilado que puede estar formado por materiales heterogéneos. Para ello, se acoplan la dinámica marina: nivel medio del mar, cambios en el nivel medio del lago, mareas y oleaje; con la evolución del terreno: erosión, desprendimiento rocoso y formación de talud de derrubios. El modelo en sus diferentes variantes es capaz de incluir el análisis de la estabilidad geomecánica de los materiales, el efecto de los derrubios presentes al pie del acantilado, el efecto del agua subterránea, la playa, el run-up, cambios en el nivel medio del mar o cambios (estacionales o interanuales) en el nivel medio de la masa de agua (lagos). Se ha estudiado el error de discretización del modelo y su propagación en el tiempo a partir de las soluciones exactas para los dos primeros periodos de marea para diferentes aproximaciones numéricas tanto en tiempo como en espacio. Los resultados obtenidos han permitido justificar las elecciones que minimizan el error y los métodos de aproximación más adecuados para su posterior uso en la modelización. El modelo ha sido validado frente a datos reales en la costa de Holderness, Yorkshire, Reino Unido; y en la costa norte del lago Erie, Ontario, Canadá. Los resultados obtenidos presentan un importante avance en los modelos de recesión costera, especialmente en su relación con las condiciones geomecánicas del medio, la influencia del agua subterránea, la verticalización de los perfiles rocosos y su respuesta ante condiciones variables producidas por el cambio climático (por ejemplo, nivel medio del mar, cambios en los niveles de lago, etc.). The recession of coastal cliffs is a widespread phenomenon on the rocky shores that are exposed to the combined incidence of marine and meteorological processes that occur in the shoreline. This phenomenon is revealed violently and occasionally, as gravitational movements of the ground and can cause material or human losses. Although knowledge of the risks of erosion is vital for the proper management of the coast, the development of cliff erosion predictive models is limited by the complex interactions between environmental processes and material properties over a range of temporal and spatial scales. Published prediction models are scarce and present important drawbacks: extrapolation, that extend historical records to the future; empirical, that based on historical records studies the system response against the change in one parameter; stochastic, that represent of cliff behaviour based on assumptions regarding the magnitude and frequency of events in a probabilistic framework based on historical records; process-response, stability and error propagation unexplored; PDE´s, highly computationally expensive and not very accurate. The first part of this thesis describes the main features of the latest models of each type and, for the most commonly used, their ranges of application, advantages and disadvantages are given. Finally as a synthesis of the most relevant processes that include the revised models, a conceptual diagram of coastal recession is presented. This conceptual model includes the most influential processes that must be taken into account when using or creating a model of coastal recession to evaluate the dangerousness (time/frequency) of the phenomenon to medium-short term. A new process-response coastal recession model developed in this thesis has been designed to incorporate the behavioural and mechanical characteristics of coastal cliffs which are composed of with materials whose compressive strength is less than 5 MPa. The model simulates the spatial and temporal evolution of a cliff-2D profile that can consist of heterogeneous materials. To do so, marine dynamics: mean sea level, waves, tides, lake seasonal changes; is coupled with the evolution of land recession: erosion, cliff face failure and associated protective colluvial wedge. The model in its different variants can include analysis of material geomechanical stability, the effect of debris present at the cliff foot, groundwater effects, beach and run-up effects, changes in the mean sea level or changes (seasonal or inter-annual) in the mean lake level. Computational implementation and study of different numerical resolution techniques, in both time and space approximations, and the produced errors are exposed and analysed for the first two tidal periods. The results obtained in the errors analysis allow us to operate the model with a configuration that minimizes the error of the approximation methods. The model is validated through profile evolution assessment at various locations of coastline retreat on the Holderness Coast, Yorkshire, UK and on the north coast of Lake Erie, Ontario, Canada. The results represent an important stepforward in linking material properties to the processes of cliff recession, in considering the effect of groundwater charge and the slope oversteeping and their response to changing conditions caused by climate change (i.e. sea level, changes in lakes levels, etc.).

Intraply fracture of fiber-reinforced composites: microscopic mechanisms and modeling

The fracture behavior parallel to the fibers of an E-glass/epoxy unidirectional laminate was studied by means of three-point tests on notched beams. Selected tests were carried out within a scanning electron microscope to ascertain the damage and fracture micromechanisms upon loading. The mechanical behavior of the notched beam was simulated within the framework of the embedded cell model, in which the actual composite microstructure was resolved in front of the notch tip. In addition, matrix and interface properties were independently measured in situ using a nanoindentor. The numerical simulations very accurately predicted the macroscopic response of the composite as well as the damage development and crack growth in front of the notch tip, demonstrating the ability of the embedded cell approach to simulate the fracture behavior of heterogeneous materials. Finally, this methodology was exploited to ascertain the influence of matrix and interface properties on the intraply toughness.

Three dimensional (3D) microstructure-based modeling of interfacial decohesion in particle reinforced metal matrix composites

Modeling and prediction of the overall elastic–plastic response and local damage mechanisms in heterogeneous materials, in particular particle reinforced composites, is a very complex problem. Microstructural complexities such as the inhomogeneous spatial distribution of particles, irregular morphology of the particles, and anisotropy in particle orientation after secondary processing, such as extrusion, significantly affect deformation behavior. We have studied the effect of particle/matrix interface debonding in SiC particle reinforced Al alloy matrix composites with (a) actual microstructure consisting of angular SiC particles and (b) idealized ellipsoidal SiC particles. Tensile deformation in SiC particle reinforced Al matrix composites was modeled using actual microstructures reconstructed from serial sectioning approach. Interfacial debonding was modeled using user-defined cohesive zone elements. Modeling with the actual microstructure (versus idealized ellipsoids) has a significant influence on: (a) localized stresses and strains in particle and matrix, and (b) far-field strain at which localized debonding takes place. The angular particles exhibited higher degree of load transfer and are more sensitive to interfacial debonding. Larger decreases in stress are observed in the angular particles, because of the flat surfaces, normal to the loading axis, which bear load. Furthermore, simplification of particle morphology may lead to erroneous results.

Potential theory

In this chapter we will introduce the reader to the techniques of the Boundary Element Method applied to simple Laplacian problems. Most classical applications refer to electrostatic and magnetic fields, but the Laplacian operator also governs problems such as Saint-Venant torsion, irrotational flow, fluid flow through porous media and the added fluid mass in fluidstructure interaction problems. This short list, to which it would be possible to add many other physical problems governed by the same equation, is an indication of the importance of the numerical treatment of the Laplacian operator. Potential theory has pioneered the use of BEM since the papers of Jaswon and Hess. An interesting introduction to the topic is given by Cruse. In the last five years a renaissance of integral methods has been detected. This can be followed in the books by Jaswon and Symm and by Brebbia or Brebbia and Walker.In this chapter we shall maintain an elementary level and follow a classical scheme in order to make the content accessible to the reader who has just started to study the technique. The whole emphasis has been put on the socalled "direct" method because it is the one which appears to offer more advantages. In this section we recall the classical concepts of potential theory and establish the basic equations of the method. Later on we discuss the discretization philosophy, the implementation of different kinds of elements and the advantages of substructuring which is unavoidable when dealing with heterogeneous materials.

Statistical mechanics approaches to granular media: between micromechanics and macromechanics

The mechanical behavior of granular materials has been traditionally approached through two theoretical and computational frameworks: macromechanics and micromechanics. Macromechanics focuses on continuum based models. In consequence it is assumed that the matter in the granular material is homogeneous and continuously distributed over its volume so that the smallest element cut from the body possesses the same physical properties as the body. In particular, it has some equivalent mechanical properties, represented by complex and non-linear constitutive relationships. Engineering problems are usually solved using computational methods such as FEM or FDM. On the other hand, micromechanics is the analysis of heterogeneous materials on the level of their individual constituents. In granular materials, if the properties of particles are known, a micromechanical approach can lead to a predictive response of the whole heterogeneous material. Two classes of numerical techniques can be differentiated: computational micromechanics, which consists on applying continuum mechanics on each of the phases of a representative volume element and then solving numerically the equations, and atomistic methods (DEM), which consist on applying rigid body dynamics together with interaction potentials to the particles. Statistical mechanics approaches arise between micro and macromechanics. It tries to state which the expected macroscopic properties of a granular system are, by starting from a micromechanical analysis of the features of the particles and the interactions. The main objective of this paper is to introduce this approach.

Development and Testing of a Fiber Bragg Grating Strain Sensor for Uniaxial Compression of Rock Specimens

Los sensores de fibra óptica son una tecnología que ha madurado en los últimos años, sin embargo, se requiere un mayor desarrollo de aplicaciones para materiales naturales como las rocas, que por ser agregados complejos pueden contener partículas minerales y fracturas de tamaño mucho mayor que las galgas eléctricas usadas tradicionalmente para medir deformaciones en las pruebas de laboratorio, ocasionando que los resultados obtenidos puedan ser no representativos. En este trabajo fueron diseñados, fabricados y probados sensores de deformación de gran área y forma curvada, usando redes de Bragg en fibra óptica (FBG) con el objetivo de obtener registros representativos en rocas que contienen minerales y estructuras de diversas composiciones, tamaños y direcciones. Se presenta el proceso de elaboración del transductor, su caracterización mecánica, su calibración y su evaluación en pruebas de compresión uniaxial en muestras de roca. Para verificar la eficiencia en la transmisión de la deformación de la roca al sensor una vez pegado, también fue realizado el análisis de la transferencia incluyendo los efectos del adhesivo, de la muestra y del transductor. Los resultados experimentales indican que el sensor desarrollado permite registro y transferencia de la deformación fiables, avance necesario para uso en rocas y otros materiales heterogénos, señalando una interesante perspectiva para aplicaciones sobre superficies irregulares, pues permite aumentar a voluntad el tamaño y forma del área de registro, posibilita también obtener mayor fiabilidad de resultados en muestras de pequeño tamaño y sugiere su conveniencia en obras, en las cuales los sistemas eléctricos tradicionales tienen limitaciones. ABSTRACT Optical fiber sensors are a technology that has matured in recent years, however, further development for rock applications is needed. Rocks contain mineral particles and features larger than electrical strain gauges traditionally used in laboratory tests, causing the results to be unrepresentative. In this work were designed, manufactured, and tested large area and curved shape strain gages, using fiber Bragg gratings in optical fiber (FBG) in order to obtain representative measurement on surface rocks samples containing minerals and structures of different compositions, sizes and directions. This reports presents the processes of manufacturing, mechanical characterization, calibration and evaluation under uniaxial compression tests on rock samples. To verify the efficiency of rock deformation transmitted to attached sensor, it was also performed the analysis of the strain transfer including the effects of the bonding, the sample and the transducer. The experimental results indicate that the developed sensor enables reliable measurements of the strain and its transmission from rock to sensor, appropriate for use in heterogeneous materials, pointing an interesting perspective for applications on irregular surfaces, allowing increasing at will the size and shape of the measurement area. This research suggests suitability of the optical strain gauge for real scale, where traditional electrical systems have demonstrated some limitations.

Fractal Behaviour and Irregularity of Wetting Fronts in Heterogeneous Porous Media

The wetting front is the zone where water invades and advances into an initially dry porous material and it plays a crucial role in solute transport through the unsaturated zone. Water is an essential part of the physiological process of all plants. Through water, necessary minerals are moved from the roots to the parts of the plants that require them. Water moves chemicals from one part of the plant to another. It is also required for photosynthesis, for metabolism and for transpiration. The leaching of chemicals by wetting fronts is influenced by two major factors, namely: the irregularity of the fronts and heterogeneity in the distribution of chemicals, both of which have been described by using fractal techniques. Soil structure can significantly modify infiltration rates and flow pathways in soils. Relations between features of soil structure and features of infiltration could be elucidated from the velocities and the structure of wetting fronts. When rainwater falls onto soil, it doesn?t just pool on surfaces. Water ?or another fluid- acts differently on porous surfaces. If the surface is permeable (porous) it seeps down through layers of soil, filling that layer to capacity. Once that layer is filled, it moves down into the next layer. In sandy soil, water moves quickly, while it moves much slower through clay soil. The movement of water through soil layers is called the the wetting front. Our research concerns the motion of a liquid into an initially dry porous medium. Our work presents a theoretical framework for studying the physical interplay between a stationary wetting front of fractal dimension D with different porous materials. The aim was to model the mass geometry interplay by using the fractal dimension D of a stationary wetting front. The plane corresponding to the image is divided in several squares (the minimum correspond to the pixel size) of size length ". We acknowledge the help of Prof. M. García Velarde and the facilities offered by the Pluri-Disciplinary Institute of the Complutense University of Madrid. We also acknowledge the help of European Community under project Multi-scale complex fluid flows and interfacial phenomena (PITN-GA-2008-214919). Thanks are also due to ERCOFTAC (PELNoT, SIG 14)