# Refined mathematical model for the breaching of concrete-face sand-gravel dams due to overtopping failure

Vol20 No.3: 670-687

Title】Refined mathematical model for the breaching of concrete-face sand-gravel dams due to overtopping failure

Author】QIU Wen; LI Yan-long*; WEN Li-feng; WANG Jing; YIN Qiao-gang

Addresses】State Key Laboratory of Eco-hydraulics in Northwest Arid Region, Xi'an University of Technology, Xi'an 710048, China

Corresponding author】LI Yan-long

Citation】Qiu W, Li YL, Wen LF, et al. (2023) Refined mathematical model for the breaching of concrete-face sand-gravel dams due to overtopping failure. Journal of Mountain Science 20(3). https://doi.org/10.1007/s11629-022-7490-7

DOI】https://doi.org/10.1007/s11629-022-7490-7

Abstract】Overtopping is one of the main reasons for the breaching of concrete-face sand-gravel dams (CFSGDs). In this study, a refined mathematical model was established based on the characteristics of the overtopping breaching of CFSGDs. The model characteristics were as follows: (1) Based on the Renormailzation Group (RNG) k-ε turbulence theory and volume of fluid (VOF) method, the turbulent characteristics of the dam-break flow were simulated, and the erosion surface of the water and soil was tracked; (2) In consideration of the influence of the change in the sediment content on the dam-break flow, the dam material transport equation, which could reflect the characteristics of particle settlement and entrainment motion, was used to simulate the erosion process of the sand gravels; (3) Based on the bending moment balance method, a failure equation of the concrete face slab under dead weight and water load was established. The proposed model was verified through a case study on the failure of the Gouhou CFSGD. The results showed that the proposed model could well simulate the erosion mode of the special vortex flow of the CFSGD scouring the support body of the concrete face slab inward and reflect the mutual coupling relationship between the dam-break flow, sand gravels, and concrete face slabs. Compared with the measured values, the relative errors of the peak discharge, final breach average width, dam breaching duration, and maximum failure length of the face slab calculated using the proposed model were all less than 12%, thus verifying the rationality of the model. The proposed model was demonstrated to perform better and provide more detailed results than three selected parametric models and three simplified mathematical models. The study results can aid in establishing the risk level and devising early warning strategies for CFSGDs.

Keywords】Concrete-face sand-gravel dam; Overtopping; Dam-break flow; Concrete face slab failure; Refined mathematical model