On the 13th October at 2pm CET, Yves Frantz successfully defended his work entitled: "Stochastic Simulation of Karstic Systems".

Congratulations to Yves and thanks a lot for the PhD committee members (Anne Johannet, Nicolas Massei, Philippe Renard, Valérie Plagnes, Sophie Viseur) for their participation !


Despite intensive explorations by speleologists, karstic networks remain only partially described  as many conduits are not accessible to humans. The classical exploration techniques produce  sparse data subject to uncertainties concerning the conduit position and their dimensions,  which are essential parameters for flow simulations. Stochastic simulations make it possible  to better handle and assess these uncertainties by offering several equally probable karsticsystem representations. The ideal simulator should allow for the construction of tridimensional  karstic drain networks, respecting the field observations (karstification markers), the knowledge  brought by tracer tests, the information collected in the accessible parts of the network and  those obtained by the study of other networks. In this context, this PhD thesis offers 3 main contributions:
  • The first contribution is the statistical analysis of a database of 49 karstic networks. It  focuses on the study of conduit geometry, through the analysis of two metrics : the equivalent  radius and the width-height ratio. No generic statistical law describing the network geometry was found. Nonetheless, the spatial variability of the geometrical properties at different  scales was characterized, mostly through the development of 1D-curvilinear variograms. The widespread hypothesis of a hierarchical organization of the conduit geometries has also been  analysed and rejected.
  • The second contribution is the development of two methods allowing stochastic simulations  of properties along karstic networks and based on the results of the statistical analysis. The  first method focuses on the reproduction of the property variability at the network scale, while  the second  one focuses on the reproduction of the variability within and between the network  branches. Both are based on the Sequential Gaussian Simulation methods and are adapted to  1D-curvilinear objects.
  • The third contribution is the prototype of a method aiming to stochastically simulate discrete karstic networks as graphs (known as network skeletons). We hope that once completed,  it would allow the simulation of different network types, while taking directly into account  field data and geological information. It is divided in three main steps :
    • i) the generation of  a point cloud,
    • ii) the computation of the point connectivity and
    • iii) their connection to create  the skeleton of the karstic network.
These contributions open new prospects regarding the simulation of karstic drain networks  usable for flow simulation (e.g., SWMM, Epanet, Modflow-CFP), which should allow a better  characterization of the associated flows.
To learn more, you can read the recent Geomorphology paper.