Statistical analysis and simulation of conduit dimensions within karstic systems

Abstract : Despite intensive explorations by speleologists, karstic systems remain only partially described as many conduits are not accessible to humans. Paleokarsts are buried karstic systems with a significant reservoir potential but they are not easily identifiable on seismic images, which leads to a huge uncertainty on the corresponding underground flow simulations. Stochastic simulations of karstic networks allow to better assess that uncertainty but only if the simulated networks are comparable to those observed in the field. One way to ensure some realism is to reproduce the topologies and geometries of explored networks, as proposed in various recent works. The height and width of the conduits are directly measured by speleologists. The general width-height ratio of different networks was already studied (Pardo-Iguzquiza et al., 2011; Jouves et al., 2017), but no generic study seems to have be done on their spatial repartition. It leads to a lack of constraints when simulating conduit dimensions (sections or volumes) during modeling, which is, however, a crucial parameter for further flow simulations. In this study, we analyze a set of different explored karstic systems to check if there are typical distributions of height, width and section of conduits within the networks. For the analysis, the karstic network is considered as a graph, whose nodes are the measurement stations while the edges correspond to lines-of-sight. Instead of directly working on the height and width, we chose to work on the average radius of the conduits. The distributions tend to be close to log-normal and the range of variation is rather similar from a network to another, both for the width-height ratio and the average radius. A direct correlation between these metrics and the degree of the nodes (i.e., the number of neighbors) also seems to exist. Besides, we propose a new method to spatially hierarchize the networks and check the consistency of usual approximations made when performing flow simulations. Even so, no relation between the point location inside the network and the studied metrics was observed. The spatial continuity of the conduit geometrical properties was also characterized by the use of 1-dimensional curvilinear variograms inside the whole network and its different branches. This method is more adapted to the case of karstic networks than the use of variogramms based on Cartesian coordinates. Based on these results, we propose a method to stochastically simulate the average radius and width-heigth ratio of karstic conduits. These simulated average radiuses can be directly taken into account when running flow simulations on explicit conduit networks (SWMM, Epanet…), while the WH ratios allow keeping information about the form of the conduits.
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https://hal.univ-lorraine.fr/hal-02186230
Contributor : Guillaume Caumon <>
Submitted on : Wednesday, July 17, 2019 - 11:02:28 AM
Last modification on : Friday, July 19, 2019 - 1:06:54 AM

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  • HAL Id : hal-02186230, version 1

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Yves Frantz, Pauline Collon, Philippe Renard, Sophie Viseur. Statistical analysis and simulation of conduit dimensions within karstic systems. IAMG 2019, International Association of Mathematical Geosciences, Aug 2019, State College, PA, United States. ⟨hal-02186230⟩

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