Avaliação da aplicabilidade e desempenho de métodos de aproximação e amostragem na simulação probabilística de hidrogramas de ruptura de barragens com leitos não erodíveis

Abstract

Hypothetical dam breach studies are characterized by a high degree of complexity and inherent uncertainties. Understanding the uncertainties to which hydrodynamic models are exposed is crucial for interpreting the obtained results. A probabilistic approach offers an alternative for assessing risks associated with flooding resulting from dam breaches. The most common method for this approach is the Monte Carlo Method (MCM) coupled with Simple Random Sampling (SRS). Nevertheless, this method demands numerous simulations, imposing substantial computational burdens that limit the number of random variables considered and the spatial resolution of computational grids. This research conducted an evaluation of the applicability and performance of four Point Estimate Methods (PEM), as well as the Latin Hypercubic Sampling (LHS) method for analyzing the impact of uncertainties related to breach parameters involved in the probabilistic simulation of rupture hydrographs. This evaluation considered breach geometries under the assumption of non-erodibility of the bed in the dam deployment section. Five breach parameters (Bottom Elevation, Left and Right Side Slopes, Bottom Width, and Formation Time) were treated as random variables. Two codes were developed, offering reusability and adaptability for future studies. Both codes automated hydrodynamic simulations within the HEC-RAS program, referencing the framework developed by Silva et al. (2021). The first code pertained to the application of SRS associated with MCM, while adhering to the restriction that breaches remain within the bounds defined by the natural terrain. The second code focused on the application of LHS under the same restrictive assumption. Applicability assessments considered theoretical aspects and the specific characteristics of the adopted hypothetical case study, proposed by Zenz and Goldgruber (2013). Results indicated that LHS, as well as two of evaluated PEMs, were unsuitable for the examined conditions. Furthermore, the hypothesis of non-erodibility of the natural terrain yielded results that were, on average, 37% lower than the peak flow quantiles found under the assumption of terrain erodibility. Additionally, the non-erodibility scenario demonstrated a substantial reduction in indications of numerical instability within the hydrodynamic model compared to the erodible terrain scenario. The application of the other two PEMs allowed for the derivation of statistical moments for peak flows, facilitating the fitting of probability distributions to the peak flows of rupture hydrographs estimated by these methods. Results indicated that Rosenblueth (1981) Method (RPEM) exhibited superior performance to Tsai and Franceschini (2005) method (TPEM). However, neither method approximated the results obtained by applying SRS with MCM, resulting in an underestimation of quantiles associated with lower exceedance probabilities and, therefore, a less conservative risk assessment perspective. This research underscores the importance of addressing uncertainties in dam breach simulations and offers insights into the suitability of various probabilistic methods. The findings are significant for enhancing the accuracy and reliability of flood risk assessments in the context of dam safety and emergency planning.