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.

中文翻译：

---

Hagstrom-Warburton高阶截断边界条件在混凝土拱坝-水库系统时谐分析中的应用

目的

随后，研究了理想化的 Morrow Point 拱坝在全反射和吸收的水库底部/侧壁条件下由于溪流、垂直和横流地震动引起的响应。对于每种组合，通过将它们与精确解进行比较，从准确度的角度评估不同阶的 Hagstrom-Warburton (HW) 条件。需要强调的是，在此过程中，油藏近场区域的归一化长度取为非常低的 L/H = 0.2 值，这对于任何类型的截断边界条件都是非常具有挑战性的测试。

设计/方法/方法

在目前的研究中，混凝土拱坝-水库系统的动力分析是通过FE-(FE-TE) 方法[即有限元-(finite element-truncation element)] 来制定的。在该技术中，大坝和水库由固体和流体有限元离散化。此外，在储层截断边界处强加了 HW 高阶条件。该任务是通过在该边界处使用截断元素来制定的。需要强调的是，储层远场被排除在离散化模型之外。最初详细解释了该配方。

发现

在全反射和吸收储层底部/侧壁条件下，所有三种类型的激发随着硬件条件顺序的增加而获得精度的趋势基本相同。唯一的例外是横流激励响应，与观察到的由于对称激励（流和垂直）引起的响应相比，对于中等数量级的 HW（例如 O3-2）在第一个主峰附近显示出不太准确的结果。这主要归因于基于储层第一对称模式的HW条件的渐逝型参数的选择。然而，值得注意的是，即使对于交叉流激励，随着阶数的增加，误差也会减小。高阶 HW 条件，例如此处考虑的 O5-5，在两种类型的全反射和吸收储层底部/侧壁条件下，对所有三种可能的激发产生高度准确的响应。正是这样，反应很难与相应的确切反应区分开来。这表明提出的基于 HW 条件的 FE-(FE-TE) 分析技术是相当成功的，完全可以依靠它来准确有效地分析混凝土拱坝-水库系统。

原创性/价值

采用新方法对混凝土拱坝-水库系统进行动力分析。HW 高阶条件适用于非常低且具有挑战性的储层长度。针对精确解评估不同的阶次，且具有极佳的一致性。截断元素的广义矩阵是为 FEM 程序员导出的。该方法针对所有类型的激发和储层基础条件进行了讨论。