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This thesis aims to provide a better knowledge of karst flow systems, from a functional point of view (behaviour with time), as well as from a structural one (behaviour in space). The first part of the thesis deals with the hydrodynamic behaviour of karst systems, and the second part with the geometry of karstic networks, which is a strong conditioning factor for the hydrodynamic behaviour.

Many models have been developed in the past for describing the hydrodynamic behaviour of karst hydrogeological systems. They usually aim to provide a tool to extrapolate, in time and/or space, some characteristics of the flow fields, which can only be measured at a few points. Such models often provide a new understanding of the systems, beyond what can be observed directly in the field. Only special field measurements can verify such hypotheses based on numerical models. This is an significant part of this work. For this purpose, two experimental sites have been equipped and measured: Bure site or Milandrine, Ajoie, Switzerland, and Holloch site, Muotathal, Schwyz, Switzerland. These sites gave us this opportunity of simultaneously observe hydrodynamic parameters within the conduit network and, in drillholes, the "low permeability volumes" (LPV) surrounding the conduits.

These observations clearly show the existence of a flow circulation across the low permeability volumes. This flow may represent about 50% of the infiltrated water in the Bure test-field. The epikarst appears to play an important role into the allotment of the infiltrated waters: Part of the infiltrated water is stored at the bottom of the epikarst and slowly flows through the low permeability volumes (LPV) contributing to base flow. When infiltration is significant enough the other part of the water exceeds the storage capacity and flows quickly into the conduit network (quick flow).

For the phreatic zone, observations and models show that the following scheme is adequate to describe the flow behaviour: a network of high permeability conduits, of tow volume, leading to the spring, is surrounded by a large volume of low permeability fissured rock (LPV), which is hydraulically connected to the conduits. Due to the strong difference in hydraulic conductivity between conduits and LPV, hydraulic heads and their variations in time and space are strongly heterogeneous. This makes the use of piezometric maps in karst very questionable.

Flow in LPV can be considered as similar to flow in fractured rocks (laminar flow within joints and joints intersections). At a catchment scale, they can be effectively considered as an equivalent porous media with a hydraulic conductivity of about 10-6 to 10-7 m/s.

Flow in conduits is turbulent and loss of head has to be calculated with appropriate formulas, if wanting any quantitative results. Our observations permitted us to determine the turbulent hydraulic conductivity of some simple karst conduits (k', turbulent flow), which ranges from 0.2 to 11 m/s. Examples also show that the structure of the conduit network plays a significant role on the spatial distribution of hydraulic heads. Particularity hydraulic transmissivity of the aquifer varies with respect to hydrological conditions, because of the presence of overflow conduits located within the epiphreatic zone. This makes the relation between head and discharge not quadratic as would be expected from a (too) simple model (with only one single conduit). The model applied to the downstream part of Holloch is a good illustration of this phenomena.

The flow velocity strongly varies along the length of karst conduits, as shown by tracer experiments. Also, changes in the conduit cross-section produce changes in the (tow velocity profile. Such heterogeneous flow-field plays a significant role in the shape of the breakthrough curves of tracer experiments. It is empirically demonstrated that conduit enlargements induce retardation of the breakthrough curve. If there are several enlargements one after the other, an increase of the apparent dispersivity will result, although no diffusion with the rock matrix or immobile water is present. This produces a scale effect (increase of the apparent dispersivity with observation scale). Such observations can easily be simulated by deterministic and/or black box models.

The structure of karst conduit networks, especially within the phreatic zone, plays an important role not only on the spatial distribution of the hydraulic heads in the conduits themselves, but in the LPV as well. Study of the network geometry is therefore useful for assessing the shape of the flow systems. We further suggest that any hydrogeological study aiming to assess the major characteristics of a flow system should start with a preliminary estimation of the conduit network geometry. Theories and examples presented show that the geometry of karst conduits mainly depends on boundary conditions and the permeability field at the initial stage of the karst genesis. The most significant boundary conditions are: the geometry of the impervious boundaries, infiltration and exfiltration conditions (spring). The initial permeability field is mainly determined by discontinuities (fractures and bedding planes). Today's knowledge allows us to approximate the geometry of a karst network by studying these parameters (impervious boundaries, infiltration, exfiltration, discontinuity field). Analogs and recently developed numerical models help to qualitatively evaluate the sensitivity of the geometry to these parameters. Within the near future, new numerical tools will be developed and will help more closely to address this difficult problem. This development will only be possible if speleological networks can be sufficiently explored and used to calibrate models. Images provided by speleologists to date are and will for a long time be the only data which can adequately portray the conduit networks in karst systems. This is helpful to hydrogeologists. The reason that we present the example of the Lake Thun karst system is that it illustrates the geometry of such conduits networks. Unfortunately, these networks are three-dimensional and their visualisation on paper (2 dimensions) is very restrictive, when compared to more effective 3-D views we can create with computers. As an alternative to deterministic models of speleogenesis, fractal and/or random walk models could be employed.

Numerous quantitative relationships have been formulated to describe the nature of surface-drainage networks. These parameters have been used in various studies of geomorphology and surface-water hydrology, such as flood characteristics, sediment yield, and evolution of basin morphology. Little progress has been made in applying these quantitative descriptors to karst flow systems due to the lack of sufficiently complete data and inadequate technology for processing the large, complex data sets. However, as a result of four decades of investigation, an abundance of data now exists for the Mammoth Cave Watershed providing the opportunity for broader quantitative research in the organization of a large, highly-developed, karst-drainage network. Developing Geographic Information System (GIS) technology has provided tools to 1) book-keep the karst system's large, complex spatial data sets, 2) analyze and quantitatively model karst processes, and 3) visualize spatially and temporally complex data. []Karst aquifers display drainage characteristics that in many ways appear similar to surface networks. The purpose of my research was to explore techniques by which quantitative methods of drainage-network analysis can be applied to the organization and flow patterns in the Turnhole Bend Groundwater Basin of the Mammoth Cave Watershed. []Morphometric analysis of mapped active base-flow, stream-drainage density within the Turnhole Bend Groundwater Basin resulted in values ranging from 0.24 km/km2 to 1.13 km/km2. A nearby, climatologically similar, nonkarst surface drainage system yielded a drainage density value of 1.36 km/km2. Since the mapped cave streams necessarily represent only a fraction of the total of underground streams within the study area, the actual subsurface values are likely to be much higher. A potential upper limit on perennial drainage density for the Turnhole Bend Groundwater Basin was calculated by making the assumption that each sinkhole drains at least one first-order stream. Using Anhert and Williams’ (1998) average of 74 sinkholes per km2 for the Turnhole Bend Groundwater Basin, the minimum flow-length draining one km2 is 6.25-7.22 km (stated as drainage density, 6.25-7.22 km/km2). []Stream ordering of cave streams and their catchments generally follow Hortonian relationships observed for surface-stream networks. Subsurface streams within the Mammoth Cave Watershed generally exhibit a converging, dendritic pattern and possess drainage basins proportionately large for their order. However, even at base-flow conditions, the Turnhole Bend drainage system continues to possess confounding characteristics. These include at least one leakage to an adjacent groundwater basin (Meiman et al., 2001), diverging streams sharing the same surface catchment (Glennon and Groves, 1997), and highly complex, three-dimensional basin boundaries (Meiman et al., 2001). In spite of the incomplete data set available for the Mammoth Cave Watershed, study of initial values suggests an orderly subsurface flow network with numerical results that allow for comparison of the karst-flow network to surface fluvial systems.

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