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Speleology in Kazakhstan

Shakalov on 04 Jul, 2018
Hello everyone!   I pleased to invite you to the official site of Central Asian Karstic-Speleological commission ("Kaspeko")   There, we regularly publish reports about our expeditions, articles and reports on speleotopics, lecture course for instructors, photos etc. ...

New publications on hypogene speleogenesis

Klimchouk on 26 Mar, 2012
Dear Colleagues, This is to draw your attention to several recent publications added to KarstBase, relevant to hypogenic karst/speleogenesis: Corrosion of limestone tablets in sulfidic ground-water: measurements and speleogenetic implications Galdenzi,

The deepest terrestrial animal

Klimchouk on 23 Feb, 2012
A recent publication of Spanish researchers describes the biology of Krubera Cave, including the deepest terrestrial animal ever found: Jordana, Rafael; Baquero, Enrique; Reboleira, Sofía and Sendra, Alberto. ...

Caves - landscapes without light

akop on 05 Feb, 2012
Exhibition dedicated to caves is taking place in the Vienna Natural History Museum   The exhibition at the Natural History Museum presents the surprising variety of caves and cave formations such as stalactites and various crystals. ...

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That acclivity is ascending a slope [16].?

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Your search for equivalent porous media (Keyword) returned 14 results for the whole karstbase:
Structure et comportement hydraulique des aquifers karstiques, DSc thesis, 1996, Jeannin, P. Y.

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.


The problem of modeling limestone springs: The case of Bagnara (north Apennines, Italy), 1997, Angelini P, Dragoni W,
The Bagnara spring (Central Italy), fed by a fractured, carbonate, and, in some areas, karstic aquifer, was examined. The available information is derived from geological mapping and daily flows over a period of 20 consecutive years. There are no data on the hydrogeological parameters nor on the aquifer hydraulic head, which is known only at the elevation of the spring. The objective of the work was to construct an appropriate mathematical model for the spring despite the scarcity of available information. The MODFLOW code was used to simulate the system following the equivalent porous media approach. The hydraulic conductivity and the specific yield equivalents were estimated by calibrating the model on the master depletion curve and taking into consideration the topographic elevation of the system's surface. The size of the protection area around the spring was investigated on the basis of the isochrons constructed from the results of the model

Structure et comportement hydraulique des aquifers karstiques, DSc. Thesis, faculte des Sciences de l'Universite de Neuchatel., 1998, Jeannin Py.
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.

Regional groundwater flow model construction and wellfield site selection in a karst area, Lake City, Florida, 1999, Dufresne Dp, Drake Cw,
The city of Lake City is in the process of expanding their water supply facilities by 45 420 m(3) day(-1) (12 MGD) to meet future demands. One portion of wellfield site selection addressed here includes analysis of ambient groundwater quality and its potential for contamination. This study also addresses the potential impacts of groundwater withdrawals to existing legal users, wetlands, surface waters and spring flows. A regional groundwater flow model (MODFLOW) was constructed using existing hydrogeologic data from state and federal agencies in order to simulate the existing hydrologic conditions of this karst area and to predict withdrawal impacts. The model was calibrated by matching potentiometric surface maps and spring flows to within reasonable ranges. Drawdowns in the Floridan and surficial aquifers predicted by the model show minimal impacts to existing legal users and only a 5% reduction in the flow at Ichetucknee Springs ca 21 km (13 miles) away. Due to the karstic nature of the Floridan aquifer here, the equivalent-porous-medium flow model constructed would not be appropriate for contaminant transport modeling. The groundwater flow model is, however, appropriate to represent hydraulic heads and recharge/discharge relationships on a regional scale. (C) 1999 Elsevier Science B.V. All rights reserved

Determining karst transmissivities with inverse modeling and an equivalent porous media, 1999, Larocque M. , Banton O. , Ackerer P. , Razack M. ,
Flow simulation is difficult to implement in heterogeneous media such as karst aquifers, primarily because the structure of the rock is extremely complex and usually unknown. The aim of this study was to verify the possibility of using inverse modeling and an equivalent porous media to identify transmissivities in a slightly karstified aquifer, the La Rochefoucauld karst (Charente, France), Different simulation scenarios were tested: using two spatial discretizations with different finite-element cell sizes and using measured or interpolated heads. The inverse modeling was performed with the downscaling parameterization procedure, using a finite-element representation of bidimensional ground water flow. The inverse modeling converged satisfactorily with all scenarios: head residuals were small and spring flow rates and the river/aquifer exchanges were adequately stimulated. The scenario using small cells and measured heads generated a highly heterogeneous transmissivity field, indicating an overparameterization of the problem. The calibrated transmissivities and simulated heads of this scenario proved less reliable overall than those of the other scenarios. The use of interpolated heads generated more uniform transmissivities as a result of the head smoothing. A rotation of the initial parameter mesh showed that the scenarios using interpolated heads generate the most stable and reliable results. The scenarios with interpolated heads could therefore be used when head measurements are limited or are unevenly distributed over the aquifer. Overall, the calibrated transmissivities reproduced the entire range of transmissivities measured in the field using different methods. The results indicate that inverse modeling and an equivalent porous media can be used to determine transmissivities in a moderately karstified aquifer

Coastal karst springs in the Mediterranean basin : study of the mechanisms of saline pollution at the Almyros spring (Crete), observations and modelling, 2002, Arfib B, De Marsily G, Ganoulis J,
Variations in salinity and flow rate in the aerial, naturally salty spring of Almyros of Heraklion on Crete were monitored during two hydrological cycles. We describe the functioning of the coastal karstic system of the Almyros and show the influence of the duality of the flow in the karst (conduits and fractured matrix) on the quality of the water resource in the coastal area. A mechanism of saltwater intrusion into this highly heterogeneous system is proposed and validated with a hydraulic mathematical model, which describes the observations remarkably well. Introduction. - Fresh groundwater is a precious resource in many coastal regions, for drinking water supply, either to complement surface water resources, or when such resources are polluted or unavailable in the dry season. But coastal groundwater is fragile, and its exploitation must be made with care to prevent saltwater intrusion as a result of withdrawal, for any aquifer type, porous, fractured or karstic. In karstic zones, the problem is very complex because of the heterogeneous nature of the karst, which makes it difficult to use the concept of representative elementary volume developed for porous or densely fractured systems. The karstic conduits focus the major part of the flow in preferential paths, where the water velocity is high. In coastal systems, these conduits have also an effect on the distribution of the saline intrusion. As was shown e.g. by Moore et al. [1992] and Howard and Mullings [1996], both freshwater and salt-water flow along the fractures and conduits to reach the mixing zone, or the zone where these fluids are superposed in a dynamic equilibrium because of their differences in density ; but the dynamics of such a saltwater intrusion are generally unknown and not represented in models. Such coastal karstic systems are intensely studied at this moment in the Mediterranean region [Gilli, 1999], both as above sea-level or underwater springs, for potential use in areas where this resource would be of great value for economic development. This article discusses the freshwater-saltwater exchange mechanisms in the karstic aquifer of the Almyros of Heraklion aquifer (Crete) and explains the salinity variations observed in the spring. First, the general hydrogeology of the study site is described, then the functioning of the spring : a main conduit drains the freshwater over several kilometres and passes at depth through a zone where seawater is naturally present. The matrix-conduit exchanges are the result of pressure differences between the two media. These processes are represented in a mathematical model that confirms their relevance. General hydrogeology of the studied site. - The karstic coastal system of the Almyros of Heraklion (Crete) covers 300 km2 in the Ida massif whose borders are a main detachment fault, and the Sea of Crete in the north, the Psiloritis massif (highest summit at 2,456 m) in the south and west, and the collapsed basin of Heraklion filled in by mainly neo-geneous marl sediments in the east. The watershed basin consists of the two lower units of characteristic overthrust formations of Crete (fig. 1) : the Cretaceous Plattenkalk and the Cretaceous Tripolitza limestones. The two limestone formations are locally separated by interbedded flysch or phyllade units that form an impervious layer [Bonneau et al., 1977 ; Fassoulas, 1999] and may lead to different flow behaviour within the two karstic formations. Neo-tectonic activity has dissected these formations with large faults and fractures. The present-day climate in Crete is of Mediterranean mountain type, with heavy rain storms and snow on the summits in winter. Rainfall is unevenly distributed over the year, with 80 % of the annual total between October and March and a year-to-year average of 1,370 mm. The flow rate of the spring is high during the whole hydrologic cycle, with a minimum in summer on the order of 3 m3.s-1 and peak flow in winter reaching up to 40 m3.s -1. The water is brackish during low flow, up to a chloride content of 6 g.l-1, i.e. 23 % of seawater, but it is fresh during floods, when the flow rate exceeds 15 m3.s-1. During the 1999-2000 and 2000-2001 hydrologic cycles, the water was fresh during 14 and 31 days, respectively. The water temperature is high and varies very little during the year (see table I). In the areas of Keri and Tilissos (fig. 1), immediately south of the spring, the city of Heraklion extracts water from the karstic system through a series of 15 wells with depth reaching 50 to 100 m below sea level. Initially, when the wells were drilled, the water was fresh, but nowadays the salinity rises progressively, but unequally from well to well (fig. 2). The relatively constant temperatures and salinities of the wells, during the hydrological cycle, contrast with the large salinity variations at the spring (fig. 2 and table I). They show that the karstic system is complex and comprises different compartments, where each aquifer unit reacts to its individual pressures (pumping, rainfall) according to its own hydrodynamic characteristics [Arfib et al., 2000]. The Almyros spring seems disconnected from the surrounding aquifer and behaves differently from that which feeds the wells (upper Tripolitza limestone). It is recharged by fresh water from the mountains, which descends to depths where it probably acquires its salinity. The spring would thus be the largest resource of the area, if it was possible to prevent its pollution by seawater. A general functioning sketch is proposed (fig. 3), which includes the different geological units of interest. Identification of the functioning of the Almyros spring through monitoring of physical and chemical parameters. - The functioning of the aquifer system of the Almyros spring was analysed by monitoring, over two hydrological cycles, the level of the spring, the discharge, the electric conductivity and the temperature recorded at a 30 min time interval. In the centre of the watershed basin, a meteorological station at an altitude of 800 m measures and records at a 30 min time interval the air temperature, rainfall, relative humidity, wind velocity and direction ; moreover, an automatic rain gauge is installed in the northern part of the basin at an altitude of 500 m. The winter floods follow the rhythm of the rainfall with strong flow-rate variations. In contrast, the summer and autumn are long periods of drought (fig. 7). The flow rate increases a few hours after each rainfall event ; the water salinity decreases in inverse proportion to the flow rate a few hours to a few days later. Observations showed that the water volume discharged at the Almyros spring between the beginning of the flow rate increase and the beginning of the salinity decrease is quite constant, around 770,000 m3 (fig. 4) for any value of the flow rate, of the salinity and also of the initial or final rainfall rates. To determine this constant volume was of the upmost importance when analyzing the functioning of the Almyros spring. The lag illustrates the differences between the pressure wave that moves almost instantaneously through the karst conduit and causes an immediate flow rate increase after rainfall and the movement of the water molecules (transfer of matter) that arrives with a time lag proportionate to the length of the travel distance. The variation of the salinity with the flow rate acts as a tracer and gives a direct indication of the distance between the outlet and the seawater entrance point into the conduit. In the case of the Almyros, the constant volume of expelled water indicates that sea-water intrusion occurs in a portion of the conduit situated several kilometres away from the spring (table II), probably inland, with no subsequent sideways exchange in the part of the gallery leading up to the spring. As the lag between the flow rate and the salinity recorded at the spring is constant, one can correct the salinity value by taking, at each time step, with a given flow rate, the salinity value measured after the expulsion of 770,000 m3 at the spring, which transforms the output of the system so as to put the pressure waves and the matter transfer in phase [Arfib, 2001]. After this correction, the saline flux at the spring, equal to the flow rate multiplied by the corrected salinity, indicates the amount of sea-water in the total flow. This flux varies in inverse proportion to the total flow rate in the high-flow period and the beginning of the low-flow period, thereby demonstrating that the salinity decrease in the spring is not simply a dilution effect (fig. 5). The relationship that exists between flow rate and corrected salinity provides the additional information needed to build the conceptual model of the functioning of the part of the Almyros of Heraklion aquifer that communicates with the spring. Freshwater from the Psiloritis mountains feeds the Almyros spring. It circulates through a main karst conduit that descends deep into the aquifer and crosses a zone naturally invaded by seawater several kilometers from the spring. The seawater enters the conduit and the resulting brackish water is then transported to the spring without any further change in salinity. The conduit-matrix and matrix-conduit exchanges are governed by the head differences in the two media. Mathematical modelling of seawater intrusion into a karst conduit Method. - The functioning pattern exposed above shows that such a system cannot be treated as an equivalent porous medium and highlights the influence of heterogeneous structures such as karst conduits on the quantity and quality of water resources. Our model is called SWIKAC (Salt Water Intrusion in Karst Conduits), written in Matlab(R). It is a 1 D mixing-cell type model with an explicit finite-difference calculation. This numerical method has already been used to simulate flow and transport in porous [e.g. Bajracharya and Barry, 1994 ; Van Ommen, 1985] and karst media [e.g. Bauer et al., 1999 ; Liedl and Sauter, 1998 ; Tezcan, 1998]. It reduces the aquifer to a single circular conduit surrounded by a matrix equivalent to a homogeneous porous medium where pressure and salinity conditions are in relation with sea-water. The conduit is fed by freshwater at its upstream end and seawater penetrates through its walls over the length L (fig. 6) at a rate given by an equation based on the Dupuit-Forchheimer solution and the method of images. The model calculates, in each mesh of the conduit and at each time step, the head in conditions of turbulent flow with the Darcy-Weisbach equation. The head loss coefficient {lambda} is calculated by Louis' formula for turbulent flow of non-parallel liquid streams [Jeannin, 2001 ; Jeannin and Marechal, 1995]. The fitting of the model is intended to simulate the chloride concentration at the spring for a given matrix permeability (K), depth (P) and conduit diameter (D) while varying its length (L) and its relative roughness (kr). The spring flow rates are the measured ones ; at present, the model is not meant to predict the flow rate of the spring but only to explain its salinity variations. Results and discussion. - The simulations of chloride concentrations were made in the period from September 1999 to May 2001. The depth of the horizontal conduit where matrix-conduit exchanges occur was tested down to 800 m below sea level. The diameter of the conduit varied between 10 and 20 m, which is larger than that observed by divers close to the spring but plausible for the seawater intrusion zone. The average hydraulic conductivity of the equivalent continuous matrix was estimated at 10-4 m/s. A higher value (10-3 m/s) was tested and found to be possible since the fractured limestone in the intrusion zone may locally be more permeable but a smaller value (10-5 m/s) produces an unrealistic length (L) of the saline intrusion zone (over 15 km). For each combination of hydraulic conductivity, diameter and depth there is one set of L (length) and kr (relative roughness) calibration parameters. All combinations for a depth of 400 m or more produce practically equivalent results, close to the measured values. When the depth of the conduit is less than 400 m, the simulated salinity is always too high. Figure 7 shows results for a depth of 500 m, a diameter of 15 m and a hydraulic conductivity of 10-4 m/s. The length of the saltwater intrusion zone is then 1,320 m, 4,350 m away from the spring and the relative roughness coefficient is 1.1. All the simulations (table II) need a very high relative roughness coefficient which may be interpreted as an equivalent coefficient that takes into account the heavy head losses by friction and the variations of the conduit dimensions which, locally, cause great head losses. The model simulates very well the general shape of the salinity curve and the succession of high water levels in the Almyros spring but two periods are poorly described due to the simplicity of the model. They are (1) the period following strong freshwater floods, where the model does not account for the expulsion of freshwater outside the conduit and the return of this freshwater which dilutes the tail of the flood and (2) the end of the low-water period when the measured flux of chlorides falls unexpectedly (fig. 5), which might be explained by density stratification phenomena of freshwater-saltwater in the conduit (as observed in the karst gallery of Port-Miou near Cassis, France [Potie and Ricour, 1974]), an aspect that the model does not take into account. Conclusions. - The good results produced by the model confirm the proposed functioning pattern of the spring. The regulation of the saline intrusion occurs over a limited area at depth, through the action of the pressure differences between the fractured limestone continuous matrix with its natural saline intrusion and a karst conduit carrying water that is first fresh then brackish up to the Almyros spring. The depth of the horizontal conduit is more than 400 m. An attempt at raising the water level at the spring, with a concrete dam, made in 1987, which was also modelled, indicates that the real depth is around 500 m but the poor quality of these data requires new tests to be made before any firm conclusions on the exact depth of the conduit can be drawn. The Almyros spring is a particularly favorable for observing the exchanges in the conduit network for which it is the direct outlet but it is not representative of the surrounding area. To sustainably manage the water in this region, it is essential to change the present working of the wells in order to limit the irreversible saline intrusion into the terrain of the upper aquifers. It seems possible to exploit the spring directly if the level of its outlet is raised. This would reduce the salinity in the spring to almost zero in all seasons by increasing the head in the conduit. In its present state of calibration, the model calculates a height on the order of 15 m for obtaining freshwater at the spring throughout the year, but real tests with the existing dam are needed to quantify any flow-rate losses or functional changes when there is continual overpressure in the system. The cause of the development of this karstic conduit at such a great depth could be the lowering of the sea level during the Messinian [Clauzon et al., 1996], or recent tectonic movements

Eogenetic karst from the perspective of an equivalent porous medium, 2002, Vacher H. L. , Mylroie J. E. ,
The porosity of young limestones experiencing meteoric diagenesis in the vicinity of their deposition (eogenetic karst) is mainly a double porosity consisting of touching-vug channels and preferred passageways lacing through a matrix of interparticle porosity. In contrast, the porosity of limestones experiencing subaerial erosion following burial diagenesis and uplift (telogenetic karst) is mainly a double porosity consisting of conduits within a network of fractures. The stark contrast between these two kinds of karst is illustrated by their position on a graph showing the hydraulic characteristics of an equivalent porous medium consisting of straight, cylindrical tubes (n-D space, where n is porosity, D is the diameter of the tubes, and log n is plotted against log D). Studies of the hydrology of small carbonate islands show that large-scale, horizontal hydraulic conductivity (K) increases by orders of magnitude during the evolution of eogenetic karst. Earlier petrologic studies have shown there is little if any change in the total porosity of the limestone during eogenetic diagenesis. The limestone of eogenetic karst, therefore, tracks horizontally in n-D space. In contrast, the path from initial sedimentary material to telogenetic karst comprises a descent on the graph with reduction of n during burial diagenesis, then a sideways shift with increasing D due to opening of fractures during uplift and exposure, and finally an increase in D and n during development of the conduits along the fractures. Eogenetic caves are mainly limited to boundaries between geologic units and hydrologic zones: stream caves at the contact between carbonates and underlying impermeable rocks (and collapse-origin caves derived therefrom); vertical caves along platform-margin fractures; epikarst; phreatic pockets (banana holes) along the water table; and flank margin caves that form as mixing chambers at the coastal freshwater-saltwater 'interface'. In contrast, the caverns of telogenetic karst are part of a system of interconnected conduits that drain an entire region. The eogenetic caves of small carbonate islands are, for the most part, not significantly involved in the drainage of the island

Can we simulate regional groundwater flow in a karst system using equivalent porous media models? Case study, Barton Springs Edwards aquifer, USA, 2003, Scanlon B. R. , Mace R. E. , Barrett M. E. , Smith B. ,
Various approaches can be used to simulate groundwater flow in karst systems, including equivalent porous media distributed parameter, lumped parameter, and dual porosity approaches, as well as discrete fracture or conduit approaches. The purpose of this study was to evaluate two different equivalent porous media approaches: lumped and distributed parameter, for simulating regional groundwater flow in a karst aquifer and to evaluate the adequacy of these approaches. The models were applied to the Barton Springs Edwards aquifer, Texas. Unique aspects of this study include availability of detailed information on recharge from stream-loss studies and on synoptic water levels, long-term continuous water level monitoring in wells throughout the aquifer, and spring discharge data to compare with simulation results. The MODFLOW code was used for the distributed parameter model. Estimation of hydraulic conductivity distribution was optimized by using a combination of trial and error and automated inverse methods. The lumped parameter model consists of five cells representing each of the watersheds contributing recharge to the aquifer. Transient simulations were conducted using both distributed and lumped parameter models for a 10-yr period (1989-1998). Both distributed and lumped parameter models fairly accurately simulated the temporal variability in spring discharge; therefore, if the objective of the model is to simulate spring discharge, either distributed or lumped parameter approaches can be used. The distributed parameter model generally reproduced the potentiometric surface at different times. The impact of the amount of pumping on a regional scale on spring discharge can be evaluated using a lumped parameter model; however, more detailed evaluation of the effect of pumping on groundwater levels and spring discharge requires a distributed parameter modeling approach. Sensitivity analyses indicated that spring discharge was much more sensitive to variations in recharge than pumpage, indicating that aquifer management should consider enhanced recharge, in addition to conservation measures, to maintain spring flow. This study shows the ability of equivalent porous media models to simulate regional groundwater flow in a highly karstified aquifer, which is important for water resources and groundwater management. (C) 2003 Elsevier Science B.V. All rights reserved

Modeling the salinity of an inland coastal brackish karstic spring with a conduit-matrix model, 2004, Arfib B, De Marsily G,
[1] The salinity of an inland coastal brackish karstic spring is modeled on the basis of a simple concept of fluid exchange through head differences between a continuous porous matrix and a karst conduit. The coastal aquifer is reduced to an equivalent porous medium ( matrix) naturally invaded by seawater, crossed by a single karst conduit where fresh water and brackish water mix in variable proportions and flow up into the spring. A new numerical model with an upwind explicit finite difference scheme, called salt-water intrusion in karst conduits (SWIKAC), was developed and successfully applied to the Almyros spring of Heraklio ( Crete, Greece). The good fit of the model to the observed salinity in the spring validates the proposed conceptual model of salinization. It provides a quantitative description of the seawater intrusion inside the karst conduit. The results open up new perspectives for managing the fragile and precious fresh water resources in karstic coastal zones

A quantitative method for the characterisation of karst aquifers based on spring hydrograph analysis, 2005, Kovacs A. , Perrochet P. , Kiraly L. , Jeannin P. Y. ,
This paper presents a method for characterizing flow systems in karst aquifers by acquiring quantitative information about the geometric and hydraulic aquifer parameters from spring hydrograph analysis. Numerical sensitivity analyses identified two fundamentally different flow domains, depending on the overall configuration of aquifer parameters. These two domains have been quantitatively characterized by deducing analytical solutions for the global hydraulic response of simple two-dimensional model geometries. During the baseflow recession of mature karst systems, the hydraulic parameters of karst conduits do not influence the drainage of the low-permeability matrix. In this case the drainage process is influenced by the size and hydraulic parameters of the low-permeability blocks alone. This flow condition has been defined as matrix-restrained flow regime (MRFR). During the baseflow recession of early karst systems and fissured systems, as well as the flood recession of mature systems, the recession process depends on the hydraulic parameters and the size of the low-permeability blocks, conduit conductivity and the total extent of the aquifer. This flow condition has been defined as conduit-influenced flow regime (CIFR). Analytical formulae demonstrated the limitations of equivalent models. While equivalent discrete-continuum models of early karst systems may reflect their real hydraulic response, there is only one adequate parameter configuration for mature systems that yields appropriate recession coefficient. Consequently, equivalent discrete-continuum models are inadequate for simulating global response of mature karst systems. The recession coefficient of equivalent porous medium models corresponds to the transition between matrix-restrained and conduit-influenced flow. Consequently, equivalent porous medium models yield corrupted hydrographs both in mature and early systems, and this approach is basically inadequate for modelling global response of karst aquifers. (c) 2004 Elsevier B.V. All rights reserved

Contributory area definition for groundwater source protection and hazard mitigation in carbonate aquifers, 2007, Gunn J. ,
Carbonate aquifers provide important sources of potable water but are known to be particularly prone to pollution owing to rapid transfer of pollutants from the surface to springs or boreholes. Source protection zones and groundwater vulnerability maps are commonly used to mitigate against the pollution hazard but cannot be applied simplistically to carbonate aquifers, which are usually highly heterogeneous with overlapping groundwater divides that may vary with water levels. Divergent flow and disjunct contributory areas provide further complexity. Under these conditions, water-tracing experiments, repeated under different flow conditions, are the only tool capable of identifying those areas that contribute recharge to a particular source. Examples of water pollution affecting disjunct and overlapping source contributory areas are presented from the Waitomo area (New Zealand), Cuilcagh Mountain (Ireland) and the Peak District (UK). Source protection zones (SPZ), that have been defined by the Environment Agency in the Buxton area of the Peak District using equivalent porous medium models, are shown to be deficient. Further water-tracing experiments are essential if carbonate aquifers are to be adequately protected from pollution

Interpretation of pumping tests in a mixed flow karst system, 2008, Maré, Chal J. C. Ladouche B. Dö, Rfliger N. & Lachassagne P.

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.


International Conference on Groundwater in Karst, Programme and Abstracts, 2015, University of Birmingham, Birmingham, 2015,

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.


Quantitative hermeneutics: Counting forestructures on a path from W. M. Davis to the concept of multiple-permeability karst aquifers., 2015,

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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