Modelling of landslides propagation with SPH : effects of rheology and pore water pressure

El estudio desarrollado en este trabajo de tesis se centra en la modelización numérica de la fase de propagación de los deslizamientos rápidos de ladera a través del método sin malla Smoothed Particle Hydrodynamics (SPH). Este método tiene la gran ventaja de permitir el análisis de problemas de grandes deformaciones evitando operaciones costosas de remallado como en el caso de métodos numéricos con mallas tal como el método de los Elementos Finitos. En esta tesis, particular atención viene dada al rol que la reología y la presión de poros desempeñan durante estos eventos. El modelo matemático utilizado se basa en la formulación de Biot-Zienkiewicz v - pw, que representa el comportamiento, expresado en términos de velocidad del esqueleto sólido y presiones de poros, de la mezcla de partículas sólidas en un medio saturado. Las ecuaciones que gobiernan el problema son: • la ecuación de balance de masa de la fase del fluido intersticial, • la ecuación de balance de momento de la fase del fluido intersticial y de la mezcla, • la ecuación constitutiva y • una ecuación cinemática. Debido a sus propiedades geométricas, los deslizamientos de ladera se caracterizan por tener una profundidad muy pequeña frente a su longitud y a su anchura, y, consecuentemente, el modelo matemático mencionado anteriormente se puede simplificar integrando en profundidad las ecuaciones, pasando de un modelo 3D a 2D, el cual presenta una combinación excelente de precisión, sencillez y costes computacionales. El modelo propuesto en este trabajo se diferencia de los modelos integrados en profundidad existentes por incorporar un ulterior modelo capaz de proveer información sobre la presión del fluido intersticial a cada paso computacional de la propagación del deslizamiento. En una manera muy eficaz, la evolución de los perfiles de la presión de poros está numéricamente resuelta a través de un esquema explicito de Diferencias Finitas a cada nodo SPH. Este nuevo enfoque es capaz de tener en cuenta la variación de presión de poros debida a cambios de altura, de consolidación vertical o de cambios en las tensiones totales. Con respecto al comportamiento constitutivo, uno de los problemas principales al modelizar numéricamente deslizamientos rápidos de ladera está en la dificultad de simular con la misma ley constitutiva o reológica la transición de la fase de iniciación, donde el material se comporta como un sólido, a la fase de propagación donde el material se comporta como un fluido. En este trabajo de tesis, se propone un nuevo modelo reológico basado en el modelo viscoplástico de Perzyna, pensando a la viscoplasticidad como a la llave para poder simular tanto la fase de iniciación como la de propagación con el mismo modelo constitutivo. Con el fin de validar el modelo matemático y numérico se reproducen tanto ejemplos de referencia con solución analítica como experimentos de laboratorio. Finalmente, el modelo se aplica a casos reales, con especial atención al caso del deslizamiento de 1966 en Aberfan, mostrando como los resultados obtenidos simulan con éxito estos tipos de riesgos naturales. The study developed in this thesis focuses on the modelling of landslides propagation with the Smoothed Particle Hydrodynamics (SPH) meshless method which has the great advantage of allowing to deal with large deformation problems by avoiding expensive remeshing operations as happens for mesh methods such as, for example, the Finite Element Method. In this thesis, special attention is given to the role played by rheology and pore water pressure during these natural hazards. The mathematical framework used is based on the v - pw Biot-Zienkiewicz formulation, which represents the behaviour, formulated in terms of soil skeleton velocity and pore water pressure, of the mixture of solid particles and pore water in a saturated media. The governing equations are: • the mass balance equation for the pore water phase, • the momentum balance equation for the pore water phase and the mixture, • the constitutive equation and • a kinematic equation. Landslides, due to their shape and geometrical properties, have small depths in comparison with their length or width, therefore, the mathematical model aforementioned can then be simplified by depth integrating the equations, switching from a 3D to a 2D model, which presents an excellent combination of accuracy, computational costs and simplicity. The proposed model differs from previous depth integrated models by including a sub-model able to provide information on pore water pressure profiles at each computational step of the landslide's propagation. In an effective way, the evolution of the pore water pressure profiles is numerically solved through a set of 1D Finite Differences explicit scheme at each SPH node. This new approach is able to take into account the variation of the pore water pressure due to changes of height, vertical consolidation or changes of total stress. Concerning the constitutive behaviour, one of the main issues when modelling fast landslides is the difficulty to simulate with the same constitutive or rheological model the transition from the triggering phase, where the landslide behaves like a solid, to the propagation phase, where the landslide behaves in a fluid-like manner. In this work thesis, a new rheological model is proposed, based on the Perzyna viscoplastic model, thinking of viscoplasticity as the key to close the gap between the triggering and the propagation phase. In order to validate the mathematical model and the numerical approach, benchmarks and laboratory experiments are reproduced and compared to analytical solutions when possible. Finally, applications to real cases are studied, with particular attention paid to the Aberfan flowslide of 1966, showing how the mathematical model accurately and successfully simulate these kind of natural hazards.

Computer simulation of random parckings for self-similar particle size distributions in soil and granular materials: porosity and pore size distribution

A 2D computer simulation method of random packings is applied to sets of particles generated by a self-similar uniparametric model for particle size distributions (PSDs) in granular media. The parameter p which controls the model is the proportion of mass of particles corresponding to the left half of the normalized size interval [0,1]. First the influence on the total porosity of the parameter p is analyzed and interpreted. It is shown that such parameter, and the fractal exponent of the associated power scaling, are efficient packing parameters, but this last one is not in the way predicted in a former published work addressing an analogous research in artificial granular materials. The total porosity reaches the minimum value for p = 0.6. Limited information on the pore size distribution is obtained from the packing simulations and by means of morphological analysis methods. Results show that the range of pore sizes increases for decreasing values of p showing also different shape in the volume pore size distribution. Further research including simulations with a greater number of particles and image resolution are required to obtain finer results on the hierarchical structure of pore space.

In situ pore water oxygen microprofiles from the Polar Front, Southern South Atlantic Ocean

Without doubt, global climate change is directly linked to the anthropogenic release of greenhouse gases such as carbon dioxide (CO2) and methane (UN IPCC-Report 2007). Therefore, research efforts to comprehend the global carbon cycle have increased during the last years. In the context of the observed changes, it is of particular interest to decipher the role of the hydro-, bio- and atmospheres and how the different compartments of the earth system are affected by the increase of atmospheric CO2. Due to its huge carbon inventory, the marine carbon cycle represents the most important component in this respect. Numerous findings suggest that the Southern Ocean plays a key role in terms of oceanic CO2 uptake. However, an exact quantification of such fluxes of material is hard to achieve for large areas, not least on account of the inaccessibility of this remote region. In particular, there exist so far only few accurate data for benthic carbon fluxes. The latter can be derived from high resolution pore water oxygen profiles, as one possible method. However the ex situ flux determinations carried out on sediment cores, tend to suffer from temperature and pressure artefacts. Alternatively, oxygen microprofiles can be measured in situ, i.e. at the seafloor. Until now, no such data have been published for the Southern Ocean. During the Antarctic Expedition ANT-XXI/4, within the framework of this thesis, in situ and ex situ oxygen profiles were measured and used to derive benthic organic carbon fluxes. Having both types of measurements from the same locations, it was possible to establish a depth-related correction function which was applied subsequently to revise published and additional unpublished carbon fluxes to the seafloor. This resulted in a consistent data base of benthic carbon inputs covering many important sub-regions of the Southern Ocean including the Amundsen and Bellingshausen Seas (southern Pacific), Scotia and Weddell Seas (southern South Atlantic) as well as the Crozet Basin (southern Indian Ocean). Including additional locations on the Antarctic Shelf, there are now 134 new and revised measurement locations, covering almost 180° of the Southern Ocean, for which benthic organic carbon fluxes and sedimentary oxygen penetration depth values are available. Further, benthic carbon fluxes were empirically related to dominant diatom distributions in surface sediments as well as to long-term remotely sensed chlorophyll-a estimates. The comparison of these results with benthic carbon fluxes of the entire Atlantic Ocean reveals significantly higher export efficiencies for the Southern Ocean than have previously been assumed, especially for the area of the opal belt.

(Table 1) Deuterium ratios, chloride content and hydrate volume of pore water and hydrate meltwater from ODP Site 164-996

Site 996 is located above the Blake Diapir where numerous indications of vertical fluid migration and the presence of hydrate existed prior to Ocean Drilling Program (ODP) Leg 164. Direct sampling of hydrates and visual observations of hydrate-filled veins that could be traced 30-40 cm along cores suggest a connection between fluid migration and hydrate formation. The composition of pore water squeezed from sediment cores showed large variations due to melting of hydrate during core recovery and influence of saline water from the evaporitic diapir below. Analysis of water released during hydrate decomposition experiments showed that the recovered hydrates contained significant amounts of pore water. Solutions of the transport equations for deuterium (d2H) and chloride (Cl-) were used to determine maximum (d2H) and minimum (Cl-) in situ concentrations of these species. Minimum in situ concentrations of hydrate were estimated by combining these results with Cl- and d2H values measured on hydrate meltwaters and pore waters obtained by squeezing of sediments, by the means of a method based on analysis of distances in the two-dimensional Cl- d2H space. The computed Cl- and d2H distribution indicates that the minimum hydrate amount solutions are representative of the actual hydrate amount. The highest and mean hydrate concentrations estimates from our model are 31% and 10% of the pore space, respectively. These concentrations agree well with visual core observations, supporting the validity of the model assumptions. The minimum in situ Cl- concentrations were used to constrain the rates of upward fluid migration. Simulation of all available data gave a mean flow rate of 0.35 m/k.y. (range: 0.125-0.5 m/k.y.).

Refined method of potential enhancement in the equilibria characterization of activated carbon. Comparison with GCMC and DFT

In this paper, we present a technique for equilibria characterization of activated carbon having slit-shaped pores. This method was first developed by Do (Do, D. D. A new method for the characterisation of micro-mesoporous materials. Presented at the International Symposium on New Trends in Colloid and Interface Science, September 24-26, 1998 Chiba, Japan) and applied by his group and other groups for characterization of pore size distribution (PSD) as well as adsorption equilibria determination of a wide range of hydrocarbons. It is refined in this paper and compared with the grand canonical Monte Carlo (GCMG) simulation and density functional theory (DFT). The refined theory results in a good agreement between the pore filling pressure versus pore width and those obtained by GCMG and DFT. Furthermore, our local isotherms are qualitatively in good agreement with those obtained by the GCMC simulations. The main advantage of this method is that it is about 4 orders of magnitude faster than the GCMC simulations, making it suitable for optimization studies and design purposes. Finally, we apply our method and the GCMG in the derivation of the PSD of a commercial activated carbon. It was found that the PSD derived from our method is comparable to that derived from the GCMG simulations.

Parameters affecting the performance of wetting and drying in a two-dimensional finite element long wave hydrodynamic model

The marsh porosity method, a type of thin slot wetting and drying algorithm in a two-dimensional finite element long wave hydrodynamic model, is discussed and analyzed to assess model performance. Tests, including comparisons to simple examples and theoretical calculations, examine the effects of varying the marsh porosity parameters. The findings demonstrate that the wetting and drying concept of marsh porosity, often used in finite element hydrodynamic modeling, can behave in a more complex manner than initially expected.

A novel method to prepare mesoporous nano-zirconia

A novel method to prepare mesoporous zirconia was developed. The synthesis was carried out in the presence of PEO surfactants via solid-state reaction. The materials exhibit strong diffraction peak at low 2-theta angle and their nitrogen adsorption/desorption isotherms are typical of IV type with H3 hysteresis loops. The pore structure examined by TEM can be described as wormhole domains. The tetragonal zirconia nanocrystals are uniform in size (around 1.5nm) and their pores center at around 4.6nm. The zirconia nanocrystal growth is mainly via an aggregation mechanism. This study also reveals that the PEO surfactants can interact with the Zr-O-Zr framework to reinforce the thermal stability of zirconia. The ratio of NaOH to ZrOCl2, crystallization and calcination temperature play an important role in the synthesis of mesoporous zirconia.

A Two-Step Sol–Gel Method for Synthesis of Nanoporous TiO2

This article reports a study of the effects of synthesis parameters on the preparation and formation of mesoporous titania nanopowders by employing a two-step sol-gel method. These materials displayed crystalline domains characteristic of anatase. The first step of the process involved the hydrolysis of titanium isopropoxide in a basic aqueous solution mediated by neutral surfactant. The solid product obtained from step 1 was then treated in an acidified ethanol solution containing the same titanium precursor to thicken the pore walls. Low pH and higher loading of the Ti precursor in step 2 produced better mesoporosity and crystallinity of titanium dioxide polymorphs. The resultant powder exhibited a high surface area (73.8 m(2)/g) and large pore volume (0.17 cm(3)/g) with uniform mesopores. These materials are envisaged to be used as precursors for mesoporous titania films as a wide band gap semiconductor in dye-sensitized nanocrystalline TiO2 solar cells.

Application of density functional theory to analysis of energetic heterogeneity and pore size distribution of activated carbons

A new approach based on the nonlocal density functional theory to determine pore size distribution (PSD) of activated carbons and energetic heterogeneity of the pore wall is proposed. The energetic heterogeneity is modeled with an energy distribution function (EDF), describing the distribution of solid-fluid potential well depth (this distribution is a Dirac delta function for an energetic homogeneous surface). The approach allows simultaneous determining of the PSD (assuming slit shape) and EDF from nitrogen or argon isotherms at their respective boiling points by using a set of local isotherms calculated for a range of pore widths and solid-fluid potential well depths. It is found that the structure of the pore wall surface significantly differs from that of graphitized carbon black. This could be attributed to defects in the crystalline structure of the surface, active oxide centers, finite size of the pore walls (in either wall thickness or pore length), and so forth. Those factors depend on the precursor and the process of carbonization and activation and hence provide a fingerprint for each adsorbent. The approach allows very accurate correlation of the experimental adsorption isotherm and leads to PSDs that are simpler and more realistic than those obtained with the original nonlocal density functional theory.

Improvement of the Derjaguin-Broekhoff-de Boer theory for capillary condensation/evaporation of nitrogen in mesoporous systems and its implications for pore size analysis of MCM-41 silicas and related materials

In this work, we propose an improvement of the classical Derjaguin-Broekhoff-de Boer (DBdB) theory for capillary condensation/evaporation in mesoporous systems. The primary idea of this improvement is to employ the Gibbs-Tolman-Koenig-Buff equation to predict the surface tension changes in mesopores. In addition, the statistical film thickness (so-called t-curve) evaluated accurately on the basis of the adsorption isotherms measured for the MCM-41 materials is used instead of the originally proposed t-curve (to take into account the excess of the chemical potential due to the surface forces). It is shown that the aforementioned modifications of the original DBdB theory have significant implications for the pore size analysis of mesoporous solids. To verify our improvement of the DBdB pore size analysis method (IDBdB), a series of the calcined MCM-41 samples, which are well-defined materials with hexagonally ordered cylindrical mesopores, were used for the evaluation of the pore size distributions. The correlation of the IDBdB method with the empirically calibrated Kruk-Jaroniec-Sayari (KJS) relationship is very good in the range of small mesopores. So, a major advantage of the IDBdB method is its applicability for small mesopores as well as for the mesopore range beyond that established by the KJS calibration, i.e., for mesopore radii greater than similar to4.5 nm. The comparison of the IDBdB results with experimental data reported by Kruk and Jaroniec for capillary condensation/evaporation as well as with the results from nonlocal density functional theory developed by Neimark et al. clearly justifies our approach. Note that the proposed improvement of the classical DBdB method preserves its original simplicity and simultaneously ensures a significant improvement of the pore size analysis, which is confirmed by the independent estimation of the mean pore size by the powder X-ray diffraction method.