Application of Hagstrom-Warburton high-order truncation boundary condition on time harmonic analysis of concrete arch dam-reservoir systems

Abstract

Purpose

Subsequently, the response of idealized Morrow Point arch dam is studied due to stream, vertical and cross-stream ground motions for reservoir bottom/sidewalls conditions of both fully reflective and absorptive. For each combination, different orders of Hagstrom–Warburton (HW) condition are evaluated from accuracy point of view by comparing them against exact solutions. It should be emphasized that normalized length of reservoir near-field region is taken as a very low value of L/H = 0.2 during this process which makes it a very challenging test for any kind of truncation boundary condition.

Design/methodology/approach

In present study, dynamic analysis of concrete arch dam-reservoir systems is formulated by FE-(FE-TE) approach [i.e. finite element-(finite element-truncation element)]. In this technique, dam and reservoir are discretized by solid and fluid finite elements. Moreover, the HW high-order condition imposed at the reservoir truncation boundary. This task is formulated by employing a truncation element at that boundary. It is emphasized that reservoir far-field is excluded from the discretized model. The formulation is initially explained in details.

Findings

The trend in gaining accuracy with increase in order of HW condition were basically the same for all three types of excitations under both full reflective and absorptive reservoir bottom/sidewalls conditions. The only exception was for cross-stream excitation response which was showing less accurate results near the first major peak for moderate orders of HW (e.g. O3-2) in comparison to what was observed for responses due to symmetric excitations (stream and vertical). This is mainly attributed to the selection of evanescent-type parameters of HW condition which is based on the first symmetric mode of reservoir. However, it is noted that error diminishes even for cross-stream excitation as order increases. High orders of HW condition, such as O5-5 considered herein, generate highly accurate responses for all three possible excitations under both types of full reflective and absorptive reservoir bottom/sidewalls conditions. It is such that responses are hardly distinguishable from corresponding exact responses. This reveals that proposed FE-(FE-TE) analysis technique based on HW condition is quite successful, and one may fully rely on that for accurate and efficient analysis of concrete arch dam-reservoir systems.

Originality/value

Dynamic analysis of concrete arch dam-reservoir system is formulated by new method. HW high-order condition is applied for a very low and challenging reservoir length. Different orders are evaluated against exact solution with excellent agreement. Generalized matrices of truncation element are derived for FEM programmers. The method is discussed for all types of excitation and reservoir base conditions.

Citation

Lotfi, V. and Lotfi, A. (2021), "Application of Hagstrom-Warburton high-order truncation boundary condition on time harmonic analysis of concrete arch dam-reservoir systems", Engineering Computations, Vol. 38 No. 7, pp. 2996-3020. https://doi.org/10.1108/EC-08-2020-0441