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Processes of Speleogenesis: A Modeling Approach
Abstract
This book draws together the major recent advances in the modeling of karst systems. Based on the dissolution kinetics of limestone, and flow and transport processes in its fractures, it presents a hierarchy of cave genetic situations that range from the enlargement of a single fracture to the evolution of cavernous drainage patterns in confined and unconfined karst aquifers. These results are also applied to the evolution of leakage below dam sites in karst. The book offers a wealth of informations that help to understand the development of cave systems. It addresses geologists, hydrologists, geomorphologists, and geographers. It is also of interest to all scientists and engineers who have responsibilities for groundwater exploration and management in karst terrains.
... Therefore, the decision to use a 2D numerical modeling approach is justified. Details on the Karst2D numerical modeling tool and its applications can be found elsewhere (Romanov et al., 2003;Dreybrodt et al., 2005). Here we will present only the general framework and the implementations relevant to the current study. ...
... The time at which a certain evolution stage is reached is related to variations in parameters determining the karst evolution. Generally, the criteria used in other karst evolution sensitivity studies to describe the development is the breakthrough time or the time when the initial karstification is finished and there is a direct well developed channel connecting the in-and the outflow boundaries (Dreybrodt et al., 2005, for example). The sensitivity of the Breakthrough Time (BT) on the basic karstification factors is well studied, therefore, we will use the (BT) together with the activation time when 10% of the supports are dissolved (AT10), when 30% are dissolved (AT30) and when 50% are dissolved (AT50), as benchmarks describing the stage of karstification for the presented calculations. ...
... This is not the case with the fracture aperture widths. They develop during the whole time and because the influence of the fracture aperture widths on the evolution is generally very strong, a power law of higher magnitude in comparison with the dependence on the length of the fracture (directly related to the spacing) (see Dreybrodt, 1996;Dreybrodt et al., 2005). Obviously, the effect of the decreasing initial fracture aperture widths to compensate the spacing, reflects very strong on the evolution times. ...
Collapse sinkholes are closed depressions appearing at the surface as a consequence of a complex interplay between dissolution, erosion and mechanical stability in karst aquifers. Sinkholes are difficult to study and their locations are almost impossible to predict because of the multiple parameters involved and complex mechanisms controlling their evolution and collapse. With this work we present a systematic theoretical research focused on the processes responsible for the development of collapse sinkholes. Splitting the evolution time in different stages we propose a conceptual model allowing decoupling of the main processes and a sensitivity study on the controlling parameters. The conceptual framework is implemented with the help of a high resolution 2D karst evolution model and a simplified 3D DEM mechanical model.
Our results demonstrate that the development of a collapse sinkhole is controlled by dissolution throughout most of its evolution, while the mechanical collapses occur during short time intervals. The karstification is extremely sensitive to variations in the hydraulic conductivity or the amount of water flowing through the aquifer. Finally, we discuss the hydro-geological conditions, which allow or not for systematic sensitivity studies.
... The roles of early MC were quantified in theoretical models expanded from one-dimensional (1-D) networks (Dreybrodt (1981a;1981b;1988) to 2-D by Gabrovsek and Dreybrodt (2000) and Dreybrodt et al. (2005), in 2-D networks with the wider concept of mixing flow by Romanov et al. (2003) and Kaufmann (2003;2016), and in 3-D networks, as reviewed by Kaufmann and Romanov (2019). Dreybrodt and Gabrovsek (2019) studied 'wormhole' formation in limestones with many closely spaced fractures. ...
... The mathematics of dissolution along a single micro-conduit under constant head phreatic and initially laminar flow conditions were proposed in three classic papers by Palmer (1981), Dreybrodt (1990) and Palmer (1991), as presented subsequently by Dreybrodt (1996), Dreybrodt et al. (2005) and Palmer (2007). Dissolution begins under open conditions at the entry to the conduit, which might have C 0 >0 if the catchment is karstic. ...
Mixing corrosion (MC) in limestone occurs where saturated and unaggressive streams with differing amounts of dissolved carbon dioxide and calcium carbonate mix and become aggressive. This arises from the non-linear relationship of calcite solubility with the CO 2 partial pressure (P CO2) in solution, whereas mixing is a linear process. Recent studies explore MC and speleogenetic inception within high matrix and/or fracture permeability karst, commonly restricted to mixing at equal temperatures, using two-or three-dimensional models. However, a one-dimensional approach remains important for karstification along long flow routes in indurated limestones with negligible primary porosity and low fracture density, where early MC might apply and be influenced by varying temperatures. Dissolution and any late MC after phreatic conduits reach maturity is also essentially a 1-D process, because other permeabilities are then insignificant. When MC occurs in phreatic conduits closed to resupply of CO 2 , there is a complex relationship between the P CO2 in solution and that in the upstream cave air. However, during speleogenetic inception, only the palaeo cave air P CO2 can be estimated directly. This paper derives the relationship between P CO2 in solution and that in the cave air and uses mixing equations to determine the chemistry of the mixed solution. The MC possibilities are scoped by applying graphical and mathematical methods to the four extremes of mixing two saturated streams that have different cave air P CO2 and temperature in completely open or completely closed conditions. These show that MC can cause either pre-or post-chemical breakthrough aggressivity, validating a previous conjecture that MC might cause fast dissolution rates and therefore could be key to speleogenesis. Post-breakthrough MC just occurs where the mixing line is tangential to the kinetic trigger concentration curve, at which point the calculated chemical and flow ratios are ultimately determined by the kinetic trigger fraction for the new mixed temperature. The conjecture is valid for wide ranges of conditions, especially at high but different temperatures where a closed conduit with the lower initial P CO2 has the greater flow rate. However, mixing two saturated waters cannot cause an ultra-fast rate law regime to be entered, which occurs in dilute solutions that are ≤20% saturated. These findings are discussed with estimates of the climatic conditions in karst environments in relevant geographical regions during the glacial, deglacial and interglacial stages of the Quaternary. One-dimensional epigenic speleogenesis in indurated limestones can be greatly accelerated by MC in many environments, especially in, but not limited to, warmer climates.
... To gain fundamental understanding of the effect of on wormholing, we use a 2-D numerical pore network model (PNM). PNMs are frequently used to represent dissolution in porous (e.g., Algive et al., 2010;Hoefner & Fogler, 1988;Nogues et al., 2013;Raoof et al., 2012) and fractured media (e.g., Dreybrodt et al., 2005;Perne et al., 2014). Despite their simplicity, PNMs capture the major characteristics of wormholing observed experimentally, including their structure and advancement rate, permeability evolution and the non-monotonic relationship between injection rate and fluid volume required for breakthrough (e.g., Budek & Szymczak, 2012;Fredd & Fogler, 1998;Wang et al., 2016). ...
... At pore surfaces, first-order dissolution reaction is considered. Such assumption is often applied to describe dissolution of limestone by acidic solutions (at pH ∼ 3 or lower; Peng et al., 2015) and under natural conditions (karst, with pH ∼ 6; Dreybrodt et al., 2005;Palmer, 1991), or of halite (Alkattan et al., 1997) and gypsum (Colombani, 2008) by water. ...
Plain Language Summary
The flow of corrosive fluids in an aquifer (e.g., acidic water in limestone) can become focused in conductive pathways leading to the formation of pronounced dissolution conduits—wormholes. Wormholes can form across a large range of scales, from microns to the extended systems of karst conduits. Wormholing patterns evolve by competitive dynamics: Longer wormholes drain more flow and hence grow faster, increasing their conductivity, in turn focusing even more flow. In the meantime, shorter wormholes become devoid of reactant and stop growing. This results in a hierarchical distribution of wormhole lengths, with many small and only a few long ones. Here, using a numerical model, we study wormholing in anisotropic media characterized by different permeabilities along different directions—a common feature of geological media. We find that anisotropy markedly affects wormhole dynamics and the evolution of overall medium permeability. Particularly, anisotropy affects wormhole competition and thus their number, shapes, and branching. Wormholing is further compared to other pattern‐forming processes in nature, and similarities and differences are analyzed. These findings contribute to the understanding of wormholing, with implications to subsurface flow‐related processes such as karst and contaminant migration. The results demonstrate how micro‐scale features control the large‐scale morphology.
... Stream hydrographs are commonly separated into a baseflow component, which varies little over time, and a stormflow or quickflow component, where there can be a substantial increase in flow during and immediately after rainfall or snowmelt events. Quickflow in turn can be divided into three components: overland flow, interflow, and groundwater flow (Beven, 2012;Klaus and McDonnell, 2013;Davie and Quinn, 2019). Rapid flow down hillslopes can be readily comprehended, making overland flow (i.e. on the surface) the most intuitively obvious component. ...
... Fractures are created by physical processes and then may be enlarged by weathering processes such as dissolution, which is especially important in carbonate aquifers. The most weathering occurs where there is the most flow, resulting in a feedback process that results in self-organized networks of enlarged fractures (Dreybrodt et al., 2005;Worthington and Ford, 2009). We refer to these as fissures, following Maurice et al. (2006). ...
Celerity (the speed of a pressure wave) in fracture networks in bedrock can result in large and rapid water level responses in both aquifers and streams, but has been little documented in detail. To examine the role played by preferential flow in fracture networks, groundwater and stream data were analysed in a headwater catchment in a chalk aquifer in the UK. Hourly data show that aquifer water levels and streamflow both respond promptly to rain and have a high correlation. The stream exhibits double peaks in flow during stormflow events. The initial peak hardly lags rainfall, is composed of dilute water, and is attributed to direct flow (i.e. overland flow and/or interflow). The second peak occurs several days after rainfall, has high solute concentrations and a high correlation with aquifer water levels, indicating that the second peak is composed of groundwater. Groundwater inputs provide 89% of quickflow in the stream. Calibration of a numerical model gave a fissure porosity (calculated as an equivalent specific yield) of 0.0015, with the low porosity being associated with high celerities and a fissure residence time of 0.14 years. Conversely, the low matrix permeability results in a residence time of 26 years. A review of a further 13 carbonate aquifers in six countries shows that similar dual-porosity behaviour is common. High celerities in fissure networks provide a potent process for the rapid transfer of groundwater to stormwater hydrographs in streams.
... Higher order kinetics, which can be caused by mixed insoluble materials from the host rock leaving a lag coating on the soluble surface, can also allow for aggressive solutions to eventually permeate the length of the fissure. These effects are observed in terrestrial karstic systems, as kinetic differences between pure and native (mixed) gypsum (Jeschke et al., 2001) and limestone (Eisenlohr et al., 1999) have been ascribed to surface lag impurities (for models of development of mixed karst systems, see: Dreybrodt, 1990;Eisenlohr et al., 1999;Dreybrodt et al., 2005). As flow and dissolution widening progresses, at some key point, laminar flow converts to turbulent flow and "kinetic breakthrough" occurs. ...
We propose that cycling hydrocarbon rains on Saturn's moon Titan are likely to create subsurface conduits through dissolution geology of the extensive organic and largely‐soluble substrate. In this work we inventory different terrains and locations on Titan that could host potential subsurface access points or caves. Using Cassini data, we identified and enumerated a cryovolcanic construct, filled and empty lake basins that may have formed through karstic processes, estimates of closed valleys in organic plateaux, and enigmatic equatorial pits. Our preliminary survey identified over 21,000 estimated locations for future exploration to identify potential caves and cave forming processes on that world. We speculate that the exploration of these caves could teach us about the cave forming processes, as well as the past climate history and perhaps even chemical deposition history on Titan.
... While many speleogenic processes on Earth are well understood (Dreybrodt et al., 2004), extrapolating this information to planetary caves will require theoretical modeling and laboratory experiments to understand the key intrinsic properties (Cornet et al., 2015;Malaska & Hodyss, 2014;Raulin, 1987) (Q52). To illustrate, the putative karstic processes on Saturn's moon Titan involve liquid methane and ethane as the working fluid dissolving organic bedrock and/or other organic minerals (Malaska et al., 2011;Maynard-Casely et al., 2018). ...
Nearly half a century ago, two papers postulated the likelihood of lunar lava tube caves using mathematical models. Today, armed with an array of orbiting and fly-by satellites and survey instrumentation, we have now acquired cave data across our solar system—including the identification of potential cave entrances on the Moon, Mars, and at least nine other planetary bodies. These discoveries gave rise to the study of planetary caves. To help advance this field, we leveraged the expertise of an interdisciplinary group to identify a strategy to explore caves beyond Earth. Focusing primarily on astrobiology, the cave environment, geology, robotics, instrumentation, and human exploration, our goal was to produce a framework to guide this subdiscipline through at least the next decade. To do this, we first assembled a list of 198 science and engineering questions. Then, through a series of social surveys, 114 scientists and engineers winnowed down the list to the top 53 highest priority questions. This exercise resulted in identifying emerging and crucial research areas that require robust development to ultimately support a robotic mission to a planetary cave—principally the Moon and/or Mars. With the necessary financial investment and institutional support, the research and technological development required to achieve these necessary advancements over the next decade are attainable. Subsequently, we will be positioned to robotically examine lunar caves and search for evidence of life within martian caves; in turn, this will set the stage for human exploration and potential habitation of both the lunar and martian subsurface.
... Modelling has also shown that both recharge chemistry and whether recharge is focused or distributed have a major influence on whether caves form or whether there is a more distributed fissure network (Lauritzen et al. 1992;Liedl et al. 2003;Bloomfield et al. 2005;Dreybrodt et al. 2005;Hubinger and Birk 2011). These processes explain why caves are common in the British Carboniferous Limestone but rare in the English Chalk, and why the distributed flow along many fissures in chalk makes it more easily exploited by water-supply wells (Worthington and Ford 2009). ...
The Cretaceous Chalk in England forms dual-porosity aquifers, with low-permeability matrix and high-permeability networks of fissures, which are predominantly stress-relief fractures that have been enlarged by dissolution. This enlargement is a function of the volume of water that has passed along a fracture (the flowrate effect) and its degree of chemical undersaturation. Feedback effects result in the development of a distinctive permeability structure, with four particular characteristics: (i) troughs in the water table with high transmissivity and convergent groundwater flow; (ii) substantial increases in transmissivities in a downgradient direction; (iii) downgradient decreases in hydraulic gradient; and (iv) discharge from the high-transmissivity zones to the surface commonly at substantial springs. This distinctive self-organized permeability structure occurs throughout unconfined chalk aquifers. Early enlargement of fissures at a depth of 50–100 m below the water table is slow, but is much more rapid close to the water table and in the uppermost bedrock due to non-linear dissolution kinetics. A modelled dissolution profile shows that more than 95% of dissolution takes place in the top 1 m of bedrock, and that enlargement of fissures in the saturated zone results from progressive dissolution occurring over a period of a million years or more.
... O entendimento dos fatores que condicionam e controlam o desenvolvimento de um sistema cársico, sobretudo no que concerne à sua componente subterrânea, através da determinação e interpretação dos tempos da carsificação de um determinado maciço lítico, desde a situação de précarso (em que se definem as condições de suscetibilidade à carsificação) até, eventualmente, ao termo do processo de carsificação (e.g. com a perda da função hidrológica do sistema), é a principal preocupação dos estudos sobre a espeleogénese Dreybrodt et al., 2005;Palmer, 2007;Audra & Palmer, 2011, 2015Ford, 2014;Gabrovšek et al., 2014;entre outros). Uma das questões mais debatida no entendimento da espeleogénese reside mesmo na definição do 282 Controles estratigráficos da (paleo)carsificação nas unidades calco-dolomíticas da base do Jurássico Inferior em Coimbra (Portugal Central) "início" da carsificação ("inception") que, pelo menos em termos teóricos, pode acontecer logo durante as primeiras etapas de organização do maciço lítico potencialmente carsificável -ou mesmo antes da diagénese (Ford, 2002). ...
This work aims to outline a synthetic picture of the stratigraphic evidence that, directly or indirectly, controlled and conditioned the karstification in the Lowermost Jurassic carbonate units cropping out in the urban and peri-urban area of Coimbra city (Central Portugal). Several types of karrens, dolines, dissolution shafts and few caves, filled or already released by post-Jurassic siliciclastic deposits (autochthonous and/or allochthonous), were identified, implying a palaeokarst nature. The formal lithostratigraphic framework of the carbonate units shows a dolomitic-limestone succession (ca. 110-m-thick) with important sandy-argillaceous/shale and marly interbeds, temporarily attributed to the Early Sinemurian-base of Pliensbachian (Coimbra Formation + S. Miguel Formation). The recognized faciological and stratonomic patterns suggest a marginal to open-marine shallow-water carbonate succession with great facies variability. The lithostratigraphic characterization, the definition of facies architecture and depositional model previously established, as well as some fracture stratigraphy tests allow, as a whole, and in a preliminary way, to infer the type of interaction existing between carbonate depositional facies, diagenesis, discontinuities and local karstification. The high facies heterogeneity and the contrasts in porosity, associated to the contribution of the hydraulic connections established in the dependence of sin- and post-depositional discontinuities (bedding planes and fractures), influenced and controlled the earliest karst-forming processes (“inception”), as well as the subsequent speleogenesis and degree of karstification.
Bedrock aquifers are often characterized using porous medium concepts, but it is unclear to what extent these aquifers comply with the additional assumptions inherent in porous medium models. The core assumption is that aquifers can be treated as continuous single-porosity porous media, with Darcy’s law describing the flow. The auxiliary assumptions include that the aquifer framework is insoluble, and that permeability varies randomly in space. The combination of these assumptions is referred to here as the single-porosity archetype. The applicability of the major assumptions to transport in bedrock aquifers was examined by considering substantial data sets for each assumption. It is shown that weathering often substantially increases the permeability in both carbonate and silicate rocks. Nonrandom spatial organization of permeability frequently occurs during deposition and diagenesis of rocks, as bedding planes, fractures zones, and interflow zones. Subsequently, self-organization occurs due to feedbacks between flow and weathering. Bedrock aquifers thus deviate substantially from the assumptions of the single-porosity archetype. The common presence of continuous preferential flow paths shows that bedrock aquifers often behave as dual-porosity aquifers when considering transport.
The conceptualisations of matrix, fracture and fissure porosity are important for understanding relative controls on storage and flow of groundwater, and the transport of solutes (and non-aqueous phase liquids) within chalk aquifers. However, these different types of porosity, rather than being entirely distinct, represent elements in a continuum of void sizes contributing to the total porosity of the aquifer. Here we define such a continuum and critically examine the selection of appropriate values of effective porosity, a widely-used parameter for mass transport modelling in aquifers. Effective porosity is a transient phenomenon, related to the porosity continuum by the timescales under which mass transport occurs. An analysis of 55 tracer tests and 20 well inflow tests in English chalk aquifers identifies spatial scaling in groundwater velocity and groundwater flow respectively, which are interpreted within the context of the wider literature on carbonate aquifers globally. We advance transport modelling in the Chalk by developing a fissure aperture velocity mapping method using transmissivity data from existing regional groundwater models, together with the identified transient and spatial scaling phenomena. The results show that chalk aquifers exhibit widespread rapid groundwater flow which may transport contaminants rapidly in almost any setting.
Supplementary material at https://doi.org/10.6084/m9.figshare.c.5403807
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