Since its construction, the dam of a hydropower plant in Southeastern Europe has recorded a water leakage through the karst terrain, which during 20 years of exploitation has continuously risen, reaching water loses of about 25 Olympic swimming pools per hour. To reduce water and energy losses and to prevent further erosion or even collapse of the dam, an urgent remediation of the dam environment was required. In order to discover the unknown geometry of the karst conduits as the main pathways of water leakage, a number of various investigations and remediation actions were performed. Initial investigations, as well as continuous monitoring and directing of the remediation process, required usage of a sophisticated computational platform, capable of giving an in-silico perspective to the problem on top of the in-situ experimental investigations, but also of combining these two perspectives into an augmented and comprehensive picture of the problem.

Remediation of the dam

The main purpose of the computational platform for dam seepage investigation and remediation was to provide an automated and continuous estimation of the spatial distribution of karst faults, their geometric parameters, and hydraulic properties before and during the remediation process, based on the measurements obtained by the installed monitoring system, as well as deterministic and empirical physical laws. During the remediation, investigations over the computational model were performed with the aim of gathering the information necessary in making decisions about optimal granulate injection. The model was developed as an assemblage of components for simulating phenomena that can otherwise be only particularly observed using the system for continuous monitoring or measured through periodical experiments (sinking upstream the dam, velocity of the flow at the downstream springs, sodium fluorescein dye tracing, sodium chloride tracing, tomography, etc.).

Based on the geological structure of the terrain and the hypothesis that erosion and water flow were predisposed by the spatial distribution of fault structures, an initial model topology containing all the possible water conduits was proposed. The proposed topology was represented by a set of nodes interconnected by conduits, creating a hypothetical network of the underground flows. As a basis of the mathematical model of underground flow we formed a 1D hydraulic model of the flow under pressure, subjected to boundary conditions in the form of upstream and downstream elevations (potentials). The input parameters of the model were cross-section areas and frictions in all conducting elements of the system, while the results were potentials, velocities, and flow rates at all nodes and conduits. Furthermore, as an extension to the hydraulic model, we formed a mathematical model of solution transport, which strongly relies on the results of the hydraulic model (velocities and flow rates). The outputs from this model are concentrations of the dissolved substance at the model nodes. Finally, coupling the hydraulic model and the model of solution transport we obtained an integral computational model of underground flow. The results obtained by the integral model now can be compared with the variables measured at the certain elements of the system, such as sinking velocity at the largest sinkhole, velocities at the downstream springs, piezometric levels, as well as the traveling times and concentrations of the tracers.

The difference between measured and calculated values are strong indicators of how well the real system is described by the model. Varying the values of the conduit parameters (dimensions of karst cracks and frictions along the conduits), we obtain different model results, which less or more differ from measured ones. This way it is possible to search for the parameters that will give us a model that is a realistic picture of the underground network of fissures. Bearing in mind all the complexity of the considered models, it is clear that such a demanding iterative process cannot be effectively performed without the implementation of adequate algorithms. This problem can be considered as a mathematical optimization problem that searches for the dimensions and hydraulic properties of the conduits within the given network, that minimize the difference between calculated and measured values. Since the optimization problem is highly nonlinear and multi-objective, for the optimization purposes we employed genetic algorithm (GA), due to its inherent generality and robustness. The whole process of the simulation-based optimization using GA is implemented through a computational platform that automates the process of finding the most adequate model parameters using the principles and techniques of high-performance computing (HPC). Using the platform during the whole period of remediation, a series of simulations of granulate injection, transport, and deposition were ran periodically in an automated manner, giving the optimal parameters of the granulate mixture and speed of injection, regarding the sealing cracks in the most desirable way.

Conceptual view of a computational platform for dam seepage investigation and remediation

The core component of the platform is Hydraulic model created according to the investigation about karst fissures topology. As precise geometric and hydraulic characteristics of the conduits are not known, they are initially assumed within the expected realistic ranges. After the hydraulic simulation on the assumed model configuration, the calculated flow rates are further used to run the Tracer transport model that results with tracer dynamics over time. Calculated piezometric levels, flow rates, and tracer concentrations are compared to measured values and used as indicators of the assumed configuration quality. These indicators are further used within Genetic algorithm as a driving factor in the evolution of the assumed system states to the system state that best describes the real state under the dam. In an iterative procedure, the GA creates better and better configuration assumptions, runs simulations, evaluates their fitness, and selects the best for the next generation. To take into account the effects of the granulated material injection on the Hydraulic model, the amount of the deposited material is calculated in each iteration of GA based on the previously calculated flow rates. Once the most adequate system configuration is obtained it is provided to the Remediation operators through a specially designed user application, enabling near real-time monitoring of the remediation process and conducting the appropriate actions.

To provide continuous estimation of the system state within an acceptable timeframe, the platform is designed to run GA and all necessary calculations on high-performance computing infrastructure. The platform also incorporates a data management system with automated quality control, so data for calculations is reliable and provided in near real-time. The Application for remediation monitoring is designed as a comprehensive 3D graphical application that provides all the indicators important for decision making in numerical, tabular, and graphical form.

A 3D view of karst conduits visualized in application for analysis and planning

The platform fulfilled all the requirements defined before and during the remediation, and enabled monitoring the effects of granulated material injection in near real-time, but also the predictions of the hypothetic injection scenarios during the remediation planning. The reliability of the results was at the satisfactory level, which was proven by comparison of the predicted changes of key variables and their measured values.

Initial flows through conduits (left) and assessed flow after inert material deposition (right)​

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