A new formulation and error analysis for vibrating dam–reservoir systems with upstream transmitting boundary conditions

This paper proposes and validates a new formulation to investigate the dynamic response of dam–reservoir systems with upstream transmitting boundary conditions (TBCs). The mathematical derivations are provided for the new formulation as well as for exact and various approximate TBCs. The developed analytical equations can be solved numerically to assess the accuracy of a given TBC and determine the associated error independently of FEM or BEM modeling of the reservoir. The method is first validated in the case of semi-infinite reservoirs and an excellent agreement is obtained against classical techniques. The paper presents a fundamental understanding of the behavior of various TBCs and a systematic identification of their influence on the systemʹs dynamic response, considering: (i) dam flexibility, (ii) water compressibility, (iii) reservoir bottom wave absorption, (iv) reservoir truncation length, and (v) excitation frequency. The new method is used to obtain exact error estimators to evaluate the effects of various TBCs on the dam–reservoir first resonant frequency and hydrodynamic forces acting on the dam upstream face. The proposed formulation can be programmed easily and used efficiently for rigorous assessment of classical or newly developed TBCs for vibrating dam–reservoir systems or similar fluid–structure problems.