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Publication# Laminar ground water flow through stochastic channel networks in rock

EPFL thesis

Abstract

The flow through fractured rock is of great importance for many civil engineering projects, for example, when considering the safe storage of nuclear waste or the stability and profitability of dams, tunnels and slopes. How the fluid actually flows through a fractured rockmass is still a matter of vivid discussion within the hydrogeologic community. Various approaches to calculate the flow through a fractured rockmass exist. Which approach is best depends on the rockmass properties and the size of the rockmass under investigation. This study presents a new model which assumes that groundwater flow will take place preferably at the intersection of fractures. Study of the scientific literature showed that flow through intersections of fractures exists and can play a major role in flow through a fractured rockmass. Fieldwork has been conducted at outcrops close to Granada, Spain. At these outcrops fossilized flow paths have been observed at the intersections of fractures. During this fieldwork, fracture data have been gathered, which could be used to reconstruct the fracture geometry. As part of this research a mathematical model has been developed to simulate flow along the intersections of fractures, neglecting flow within the fractures or through the rock matrix. To this end a computer program, CPA, developed for a different purpose, has been modified and completed in order to generate a stochastic tubular network of fracture intersections and calculate flow rates through this network. The new version of the CPA code has been applied to a number of problems to test the correctness of the model and investigate the effects of the different input parameters. The application part of this study can be roughly divided into: network generation, sensitivity analysis, and the comparison with a model, Joint-OKY, that assumes flow to take place through the fractures. The field data gathered during fieldwork in Spain have been used to confirm the geometric modelling capabilities of the CPA program. A comparison between the network model generated by CPA and the observations in the field showed good agreement. The use of an eigenvec- tor approach to represent fracture orientation distribution has proven to be a good and simple method. To better understand the influence of various input parameters in the CPA model, sensitivity analyses were performed on the models generated by the CPA code. The following parameters have been investigated: fracture density, size of the model area, fracture size and anisotropy of conductivity. Finally a comparison between the CPA code and the Joint-OKY code, which assumes flow to take place within the plane of the fractures, has been made. This comparison showed that a model assuming flow within the fractures is more conductive. Further studies are needed to better include the transport of contaminants in the current CPA program.

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Simone Deparis, Adelmo Cristiano Innocenza Malossi

This work is focused on the development of a geometrical multiscale framework for modeling the human cardiovascular system. This approach is designed to deal with different geometrical and mathematical models at the same time, without any preliminary hypotheses on the layout of the general multiscale problem. This flexibility allows to set up a complete arterial tree model of the circulatory system, assembling first a network of one-dimensional models, described by non-linear hyperbolic equations, and then replacing some elements with more detailed (and expensive) three-dimensional models, where the Navier-Stokes equations are coupled with structural models through fluid-structure interaction algorithms. The coupling between models of different scale and type is addressed imposing the conservation equations in terms of averaged/integrated quantities (i.e., the flow rate and the normal component of the traction vector); in particular, three coupling strategies have been explored for the fluid problem. In all the cases, these strategies lead to small non-linear interface problems, which are solved using classical iterative algorithms.

2011Significant progress has been made these last decades in the development of hydrogeological numerical flow modelling for describing the hydrodynamic behaviour of landslides. However, these new sophisticated methods are still very seldom used in the problems of slope instability in particular because of the hydrogeological complexity which characterizes them; thin aquifers, discontinuous media, succession of saturated and unsaturated zones, low permeabilities, high hydraulic gradients, lithological heterogeneity, strong contrasts of permeabilities and heterogeneous infiltration. Predictive models of flow in the subsurface, which are often based on homogeneous porous media types of representation, are badly adapted to natural systems that are characterized by highly heterogeneous media such as landslides. These models are good and reliable on a landslide scale (regional scale), but their quality may be affected on a local scale by strong geological heterogeneities. Geological heterogeneities of the subsurface take part in determining the hydrodynamical and geomechanical behaviour of landslides. However, their spatial distribution is partially unknown. Thus, the principal objectives of this PhD thesis are: (i) To carry out an integrated multidisciplinary characterization study on the internal structure of landslides in flysch and Quaternary environments, in order to clarify the organisation of the geological heterogeneities and to identify the hydrodynamic implications. (ii) To propose a conceptual model representing the geological architecture and the hydrogeological functioning. (iii) To examine the effects of heterogeneity and anisotropy on flow systems. (iv) To better understand the influence of geological heterogeneities on the mechanical behaviour of large landslides by performing numerical sensitivity analyses, by means of different heterogeneity scenarios on the field parameters. (v) Finally, to test the incidences on slope stabilization techniques; evaluation of the efficiency of a drainage gallery work. The main test site of la Frasse landslide (VD, Switzerland) was chosen, and completed with additional landslide cases. The main results are the following: In most of the case studies, the landslide mass is composed of an old prehistoric stabilized mass, pinched between the active sliding mass and the bedrock, and playing an important hydrologic role. The stabilized mass and the bedrock form the substratum of the landslide. Landslides occurring in these types of media are defined by an organized heterogeneous environment with "fracture" flows and discontinuity porosity. The overall hydraulic conductivity is low, and locally high permeable zones exist. Regional groundwater circulations are limited and form local interconnected aquicludes organised in thin aquifers, and presenting saturated and unsaturated zones. The hydrogeological analyses showed that the system presents a bimodal permeability; (i) Low hydraulic conductivities characterizing the global matrix and defining the capacitive fraction, and (ii) high permeable features, with high hydraulic conductivities defining the conductive fraction, and favouring strong channelling effects. Besides, the observation shows that the aquifer system is generally very reactive with important magnitudes. Often, there is a straight correlation between water level variation and climatic conditions (rainy events). Landslides are characterized by two important inflows namely effective infiltration from the surface and lateral inflows from the neighbouring units. Water transfer between the stabilized mass and the active mass may be important and thus have to be considered. The existence of water transfer between the bedrock and the landslide mass (stabilized and active) is not well established. The bedrock and the landslide mass present a hydrological behavioural independence. Theoretical two- and three-dimensional flow models are used to investigate the effects of the spatial variability of the hydraulic conductivity on the underground flows. The role of the connectivity in generating flow channelling is examined thanks to the observation of close relations between the permeability and the hydraulic pressures. The sensitivity analysis shows clearly that the relation between local permeability and hydraulic pressures is not straight, and that the organization of the flows depends on the heterogeneity of the hydraulic properties and their spatial correlation. Strong channelling effects are observed in highly heterogeneous porous media. The development of flow channelling as a function of the variance of the natural log permeability values and the correlation lengths is demonstrated. The integrated multi-disciplinary geological characterization at the La Frasse test site combined with the hydrogeological and lithological data of several additional case studies led to the proposal of a global conceptual model. The following assumptions are considered to enable a subsequent quantification of flow components: The flow occurs under confined to leaky conditions, with leakage varying in space; The flow framework is controlled by a complex multi-layer system, isolated lenses or perched aquifer; The aquifer system is divided into interconnected hydrological zones presenting various degrees of saturation; Each hydrological zone may function individually from the others; Horizontally and vertically, the flow direction in the porous matrix is affected by prevailing structural patterns generating channeling effects; The flow is multidirectional, free and channelized, and is affected by temporal and spatial changes; The aquifer is under an unsteady flow regime due to seasonal variation of natural gradients; A conceptual model based on a simple reservoir approach is proposed. It allows the representation of most of the field observations and the main characteristics, namely the organized heterogeneity and the duality of the aquifers. The system is represented by various reservoirs more or less connected and saturated. Complex storage capacities and plug-flow effects may record past events and reactive sliding processes several months after the last important rainy event. The analysis shows that function of the capacity and the degree of saturation of the system, an important hydrological event is not necessarily associated to a reactivation. And, according to the degree of complexity of the system (saturation, connectivity...) a localized geological modification (variation of permeability, reservoir burst...) may produce a chain reaction, and generate failures in unexpected places. The conductive fraction favours the drainage of the system, whereas the capacitive fraction controls the distribution of the hydraulic heads. The role of the phreatic nappe, through the conductive fraction, is to drain and control the hydrologic equilibrium of the system. Therefore landslide remediation with the help of a deep drainage gallery is obviously the most valuable method for this type of landslide. It supports and enhances the natural effects of the conductive fraction in draining the system. Finally, in this context the efficiency of civil engineering works was evaluated according to the heterogeneity of the medium. This study describes transient hydrogeological and geomechanical models realized jointly in 2006 by the EPFL and GeoMod SA within the framework of the stabilization work of the La Frasse landslide. These models evaluate the impact of a deep drainage gallery with subvertical pipes towards the surface in terms of reduction of the deformation velocities and increase of the factor of safety of the landslide. Three variants consisting of different inter pipe spacings are tested. Considering the local heterogeneities, the results show that a mean spacing between the pipes of the order of 10 m is able to control the temporal head fluctuations between the wells within a range of some meters. Moreover, this solution induces a strong diminution of the predicted displacements during a specific crisis, from 101cm for the model without drainage to around 14 cm for the drained model, and a significant gain of security (from 1.05 to 1.30).

Uncontrolled overtopping during flood events can endanger embankment dams. Erosion of the downstream slope and scouring of its base caused by the high velocity and energy of the overflow can indeed lead to breach formation until complete failure. In this context and faced with the important number of overtopped embankment dams to be rehabilitated, since the early eighties, researchers have investigated surface protection solutions for downstream slope. Overlays against erosion such as seeded goetextile or cable-tied cellular concrete blocks, are not sufficient. In fact, they can resist only short events with low discharge and velocity. Solution to overcome more severe overflow lies in overlays which dissipate flow energy along the downstream embankment slope. Conventional steps resulting from Roller Compacted Concrete (RCC) techniques fulfill efficiently this challenge. However, flows over steep stepped chutes are quite complex, characterizing by great aeration, high turbulence and confused wavy free surface. Then, most of hydraulic studies of such flows are performed on physical model. Yet, understanding and definition of flow behaviour and accurate approach to estimate energy dissipation are still lacking. General guidelines of hydraulics of aerated flows over stepped macro-roughness chutes and for optimal design of protection overlay remain confusing. To contribute to reduce these uncertainties, experimental study of flow over stepped chutes equipped with macro-roughness elements is performed in a laboratory gated flume for mild (~ 1:7H : 1V ) and weak (~ 3H : 1V ) chutes. Thus, they are representative of the range of embankment dams and spillways slopes. Three types of stepped macro-roughness overlays are assessed, namely rectangular conventional steps, steps equipped with endsills fixed on their nose over all the flume width and steps equipped with rectangular spaced blocks. Endsills overlays were characterized with different longitudinal distributions whereas blocks overlays consisted in different transverse patterns. Tests were conducted for the three nappe, transition and skimming flow regimes. Results can be extrapolated to 1/5 to 1/15 scaled prototypes using the Froude similarity with negligible scale effects. Flow depth, local air concentration and longitudinal velocities are measured with a double fiber-optical probe. Pressures at macro-roughness faces are taken with piezo-resistive sensors. Sequent depths of the hydraulic jump forced in the stilling basin at the flume base are measured with ultrasound sensors. Thus, this experimental phase of the thesis has allowed: to define flow parameters (regimes, depths, velocity and air concentration distributions, hydrodynamic forces) for tested overlays, to highlight that air-water flow depth is divided into: a rough boundary layer influenced by shear stress and by drag form (macro-turbulence) caused by macro-roughness, a homogeneous aerated layer which represents the main portion of flow involved in energy dissipation mechanism, a free surface layer which must be considered in the side walls design, to stress that energy dissipation is mainly a question of drag losses, to validate indirect method of hydraulic jump for energy dissipation estimation, to estimate relative energy loss for several stepped macro-roughness overlays. Tests finally show that an optimal alternative to dissipate the overflow energy during an overtopping event consists in spaced blocks, with transverse space larger than the width of block and fixed alternately on conventional steps. However, experimental results remain related and limited to their tested domains. Then, in order to provide more general governing equations of aerated flows over macro-roughness stepped chutes, a numerical modeling of two phase flows over conventional stepped flume was performed in collaboration with the Laboratory of Applied Hydrodynamics and Hydraulic Constructions at University of Liège. A quasi-2D numerical model based on the finite volume method was developed. It consists in applying the classical depth-averaged simplified Navier-Stokes equations (viscosity and Coriolis terms neglected) to a 1D incompressible air-water mixture flow over mild and steep slopes with a stepped topography. Self-aeration process is modeled by a transport equation of depth-averaged air concentration whereas turbulent structures are indirectly implemented through the Boussinesq coefficient. This first 1D-approach of semi-theoretical description of aerated flow over steps is tested for a 30o gated stepped flume and a 52° crested spillway laboratory model. This numerical model leads to realistic results regarding mixture depth, mean flow velocity, air concentration and wave amplitudes of the flow free surface. Finally, on the basis of existing protections of embankment dams and previous studies, the present experimental and numerical results contribute to extend the knowledge of high velocity aerated flows over macro-roughness and to provide elements of guidelines to optimize stepped macro-roughness overlays for embankment dams safety.