A Novel Calculation Method of Hydrodynamic Pressure Based on Polyhedron SBFEM and Its Application in Nonlinear Cross-Scale CFRD-Reservoir Systems

Abstract

Hydrodynamic pressure is an important factor that cannot be ignored in the seismic safety evaluation of dams. However, when the polyhedron-scaled boundary finite element method is used to simulate dams in a cross-scale dynamic analysis, polygonal surfaces often appear on the upstream face of dams, which is difficult to deal with for conventional methods of hydrodynamic pressure. In this paper, a three-dimensional calculation method of hydrodynamic pressure based on the polyhedron-scaled boundary finite element method is proposed, in which polygon (triangle, quadrilateral, pentagon, hexagon, heptagon, octagon, etc.) semi-infinite prismatic fluid elements are constructed using the mean-value shape function. The proposed method, with a high efficiency, overcomes the limitation of conventional methods in which only quadrangle or triangle boundary faces of elements are permitted. The accuracy of the proposed method is proved to be high when considering various factors. Furthermore, combined with the polyhedron-scaled boundary finite element method for a solid dam, the proposed method for reservoir water is used to develop a nonlinear dynamic coupling method for cross-scale concrete-faced rockfill dam-reservoir systems based on the polyhedron SBFEM. The results of the numerical analysis show that when the hydrodynamic pressure is not considered, the error of rockfill dynamic acceleration and displacement could reach 15.4% and 12.7%, respectively, and the error of dynamic face slabs’ stresses could be 24.9%, which is not conducive to a reasonable seismic safety evaluation of dams.

Three-Dimensional Static and Dynamic Analyses of an Embedded Concrete-Face Rockfill Dam

“…Concrete-face rockfill dams have gradually become the preferred dam type in the engineering community owing to their safety, affordability, and applicability in complex terrain and climatic conditions [1][2][3]. The construction height of concrete-face rockfill dams has exceeded 240 m and is increasing towards 300 m [4][5][6].…”

An Efficient Dynamic Coupling Calculation Method for Dam–Reservoir Systems Based on FEM-SBFEM

“…Lin and Du [19] spearheaded research efforts in the computation of hydrodynamic pressure in front of dams based on the SBFEM. Until now, the SBFEM has made great progress and has been widely used in studying fluid-structure coupling analysis methods [2][3][4][5][6][7][8][9].…”

“…For the dynamic interactions between dams and reservoirs, the SBFEM possesses a unique advantage in that semi-infinite reservoir water can be simulated by discretizing only the interface between fluids and solids. Two main methods to model a semi-infinite reservoir water in front of the dam are as follows: (1) With the help of the SBFEM, the upstream surface of the dam body is directly discretized, and a prism-shaped, semiinfinite reservoir water is simulated in front of the dam [2,[19][20][21][22][23]. The discretization of the fluid-solid interface not only reduces the dimension of the solution by one, but it also automatically meets the radiation condition at infinite distance in the fluid domain.…”

“…The discretization of the fluid-solid interface not only reduces the dimension of the solution by one, but it also automatically meets the radiation condition at infinite distance in the fluid domain. (2) The finite element method (FEM) is used to discretize the near-field reservoir in front of the dam, and the SBFEM is used to simulate the prismatic semi-infinite reservoir to provide a truncated boundary condition for the reservoir tail, which can thusly exhibit characteristics of wave-free reflection [24,25]. Among the above two reservoir water simulation methods, the first method directly uses the SBFEM to calculate hydrodynamic pressure, while the second method uses the SBFEM to construct a truncated boundary at the end of the reservoir.…”

“…In the dynamic response analysis of dams under earthquake conditions, hydrodynamic pressure is one of the important factors that must be considered in order to reasonably evaluate the seismic safety of dams, so many researchers have done a lot of research work in this area. At present, the FEM [26][27][28][29][30][31][32][33][34][35][36][37], the boundary element method (BEM) [38][39][40][41][42][43], and the SBFEM [2,[19][20][21][22][23] are the three commonly used methods to calculate the hydrodynamic pressure of reservoir water in front of a dam. In the BEM and SBFEM, the reservoir model is established based on the Eulerian approach [21,31], while both Eulerian and Lagrangian [31,33,35] approaches could be used to model the reservoir with the FEM.…”