# Search in KarstBase

**equivalent porous media**(Keyword) returned

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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.

A long-duration pumping test performed in the conduit of a mixed flow karst system (MFKS) is analyzed and interpreted. It constitutes a unique experiment of catchment wide response of a karst system, with drawdowns measured both in the pumped conduit and in the matrix. A modeling approach is proposed for this interpretation. The developed double continuum model consists of two reservoirs - karst conduits and the surrounding carbonate rocks - between which flow exchange is modeled using the superposition principle and the hypothesis of Darcian flow in the matrix considered as an equivalent porous media. The karst conduits are assumed to have an infinite hydraulic conductivity. Model calibration results in a very good match (relative root mean square [rRMS] = 2.3 %) with drawdown measured at the pumping well (karst conduit). It shows that the matrix hydrodynamic parameters (hydraulic conductivity and storativity) have a greater influence on the drawdown than the storage capacity of the conduit network. The accuracy of the model relies mostly on a very good knowledge of both pumping rate and natural discharge at the spring (with and without pumping). This type of approach represents an advance in double continuum modeling of karst systems. It also provides a methodology for the management of water resources from karst aquifers.

Carbonate rocks present a particular challenge to hydrogeologists as the major groundwater flux is through an integrated network of dissolutionally enlarged channels that discharge via discrete springs. The channels span a very wide aperture range: the smallest are little more than micro-fractures or pathways through the rock matrix but at the other end of the spectrum (and commonly in the same rock mass) channels may grow to dimensions where they can be explored by humans and are called caves. Groundwater transmission through the smaller channels that are commonly intersected by boreholes is very slow and has often been analysed using equivalent porous media models although the limitations of such models are increasingly recognised. At the other end of the spectrum (and commonly in the same rock mass) flow through the larger conduits is analogous to ‘a surface stream with a roof’ and may be amenable to analysis by models devised for urban pipe networks. Regrettably, hydrogeologists have too often focussed on the extreme ends of the spectrum, with those carbonates possessing large and spectacular landforms regarded as “karst” whereas carbonates with little surface expression commonly, but incorrectly labelled as “non-karstic”. This can lead to failures in resource management. Britain is remarkable for the variety of carbonate rocks that crop out in a small geographical area. They range in age and type from Quaternary freshwater carbonates, through Cenozoic, Mesozoic and Paleozoic limestones and dolostones, to Proterozoic metacarbonates. All near surface British carbonates are soluble and groundwater is commonly discharged from them at springs fed by dissolutionally enlarged conduits, thereby meeting one internationally accepted definition of karst. Hence, it is very appropriate that Britain, and Birmingham as Britain's second largest city, hosts this International Conference on Groundwater in Karst. The meeting will consider the full range of carbonate groundwater systems and will also have an interdisciplinary approach to understanding karst in its fullest sense.

Hermeneutics is the theory of interpretation. One of its major components is recognizing prejudgments, or forestructures, that we bring to our objects of study. In this paper, we construct a historical narrative of the evolution of thinking about the role of caves in relation to groundwater flow in limestone, and we tabulate forestructures as they appear in the story. This account consists of three overlapping time periods: the before and after of an incident that repelled hydrogeologists and students of karst from each other in the middle of the 20th century; a period, up to around the turn of this century, when karst science and mainstream hydrogeology were on different tracks; and a period of convergence, now intertwining, beginning roughly in the last quarter of the 20th century. Two influential players in our story are M.K. Hubbert, whose introduction of the Eulerian perspective of flow was a force for divergence, and R.M. Garrels, whose founding of the field of sedimentary geochemistry was a force for convergence. Other key players include F.T. Mackenzie, J.E. Mylroie, V.T. Stringfield, the U.S. Geological Survey, the Bermuda Biological Station, and the Gerace Research Center in the Bahamas, along with the historical accounts of W.B. White. Our narrative ends with the broader acceptance of the concept of multiple-permeability karst aquifers. We flag in our construction a total of 43 forestructures distributed amongst the categories of hermeneutic theory: 14 in the category of preconceptions; 9 in goals; 14 in tools such as skills; and 6 in tools such as institutions. These counts are an example of the concept of social construction of statistics, and we discuss the implications in terms of the huge number of potential combinations of forestructures that could shape alternative historical narratives of this subject over this time frame.

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