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# Search in KarstBase

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Three conceptual models are proposed for the integration of the large systems of conduits responsible for groundwater flow in soluble rocks. These models are supported by laboratory experiments with scaled solution models, flow-field analogues, and evidence from existing caves.

The three models reflect different boundary conditions imposed by geologic structure and stratigraphy. They have three characteristics in common. First, the smaller elements of the larger systems propagate separately from points of groundwater input toward points of discharge as distributary networks. Second, the integration of the smaller networks proceeds headward from the resurgence, in a stepwise fashion. Third, the result of the integration process in each case is a tributary system with many inputs discharging through a single discharge point.

The potential for growth of each of the smaller networks, within a common pressure field, is related to its distance from the discharge boundary and the distribution of other inputs. The first input to establish a low-resistance link to the discharge boundary will effect a localized depression within the potential field, thus attracting the flow and redirecting the growth of nearby networks until they eventually link with it. As additional orders of links develop, the system takes on a tributary pattern.

The first model applies to steeply dipping rocks. Inputs occur where bedding planes are truncated by erosion, and discharge takes place to the strike. Conduits in this case evolve as a roughly rectangular grid of strike and dip oriented elements. Dip elements are the initial form, with subsequent integration along the strike. The type example is the Holloch in Switzerland.

The second model applies to flat-lying rocks. Inputs occur over a broad area, and discharge takes place along a linear boundary. Conduits in this case evolve in a trellised array with elements normal to the discharge boundary predating those parallel to it. These latter conduits integrate the flow. The type example is the Mammoth Cave Region, Kentucky.

The third model applies to simple systems which occur beneath an impermeable cap rock. Inputs occur where erosion has breached the capping beds. The type example is Cave Creek, Kentucky.

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.

Kaltbach cave is developed within the Eocene Hohgant sandstone in the Siebenhengste area in Switzerland. A remapping project of the cave resulted in a huge increase in length. It also produced a complete, updated map and longitudinal section. The cave's morphology does not fit with the "normal" speleogenesis: it is a so-called phantom cave. Phantoms are created by differential weathering of impure limestone under a preferably warm climate and a very low hydrologic gradient. Once the gradient steepens, the undissolved residual sediments are piped out; the "cave" manifests itself. The paper discusses the geomorphological features that permit to recognize the phantom caves.

Climatic trends connected with short- and long-period variations of the solar activity occur as a reaction even in such conservative media as the air volumes of karst caves. The yearly mean air temperatures in the zone of constant temperatures of four show caves in Bulgaria were studied for a period of 36 years (1968–2003). The examination was made by everyday noon measurements in Ledenika, Saeva dupka, Snezhanka and Uhlovitsa cave. The caves are situated at different altitudes and geographic latitude. Seasonal fluctuations of the yearly mean air temperature in the ZCT of the explored caves have been identified by Fourier analysis. The same analysis has been applied for the Sunspot number and Apmax indices, which are representatives of the solar and geomagnetic activity, for the same period of data available. Autocorrelograms have been used for examination of the seasonal patterns of the air temperatures in the ZCT in every cave and in Sunspot number and Apmax indices. Cross-spectrum analysis has been applied for retrieving the correlations between air ZCT temperatures in the caves and solar and geomagnetic activity. It has been found that the correlation between ZCT temperature time series and sunspot number is better than that between the cave air temperature and Apmax indices. It has been found that View the MathML source is rather connected with the first peak in geomagnetic activity, which is associated with transient solar activity, i.e., coronal mass ejections (CMEs) than with the second one, which is higher and connected with the recurrent high speed streams from coronal holes (Webb, D.F., 2002. CMEs and the solar cycle variation in their geoeffectiveness. In: Wilson, A. (Ed.), Proceedings of the SOHO 11 Symposium on From Solar Min to Max: Half a Solar Cycle with SOHO, 11–15 March 2002, Davos, Switzerland. ESA Publications Division, Noordwijk, 2002, ISBN 92-9092-818-2, pp. 409–419). This work can contribute to studying the mechanisms of atmospheric circulation changes and calibration of long-period climatic data read from cave speleothems and deposits.

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