Purpose

The response of the Pine Flat dam–water–foundation rock system is studied by a new described approach (i.e. FE-(FE-TE)-FE). The initial part of study is focused on the time harmonic analysis. In this part, it is possible to compare the transfer functions against corresponding responses obtained by the FE-(FE-HE)-FE approach (referred to as exact method which employs a rigorous fluid hyper-element). Subsequently, the transient analysis is carried out. In that part, it is only possible to compare the results for low and high normalized reservoir length cases. Therefore, the sensitivity of results is controlled due to normalized reservoir length values.

Design/methodology/approach

In the present study, dynamic analysis of a typical concrete gravity dam–water–foundation rock system is formulated by the FE-(FE-TE)-FE approach. In this technique, dam and foundation rock are discretized by plane solid finite elements while, water domain near-field region is discretized by plane fluid finite elements. Moreover, the H-W (i.e. Hagstrom–Warburton) high-order condition is 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.

Findings

High orders of H-W condition, such as O5-5 considered herein, generate highly accurate responses for both possible excitations under both types of full reflective and absorptive reservoir bottom conditions. It is such that transfer functions are hardly distinguishable from corresponding exact responses obtained through the FE-(FE-HE)-FE approach in time harmonic analyses. This is controlled for both low and high normalized reservoir length cases (L/H = 1 and 3). Moreover, it can be claimed that transient analysis leads practically to exact results (in numerical sense) when one is employing high order H-W truncation element. In other words, the results are not sensitive to reservoir normalized length under these circumstances.

Originality/value

Dynamic analysis of concrete gravity dam–water–foundation rock systems is formulated by a new method. The salient aspect of the technique is that it utilizes H-W high-order condition at the truncation boundary. The method is discussed for all types of excitation and reservoir bottom conditions.

中文翻译：

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利用 HW 截断边界条件对 Pine Flat 坝-水-基岩系统进行动力分析

目的

通过一种新描述的方法（即 FE-(FE-TE)-FE）研究 Pine Flat 坝-水-基岩系统的响应。研究的最初部分集中于时间谐波分析。在这一部分中，可以将传递函数与 FE-(FE-HE)-FE 方法（称为采用严格流体超单元的精确方法）获得的相应响应进行比较。随后，进行瞬态分析。在该部分中，只能比较低标准化储层长度和高标准化储层长度情况的结果。因此，结果的敏感性由于归一化的储层长度值而受到控制。

设计/方法论/途径

在本研究中，典型混凝土重力坝-水-基岩系统的动力分析采用有限元-(FE-TE)-有限元方法进行。该技术中，大坝和基岩采用平面固体有限元离散，水域近场区域采用平面流体有限元离散。此外，在储层截断边界处施加HW（即Hagstrom-Warburton）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，离散模型中不包括油藏远场。

发现

高阶 HW 条件（例如本文考虑的 O5-5）在两种类型的全反射和吸收储层底部条件下为两种可能的激励生成高精度响应。因此，传递函数很难与时间谐波分析中通过 FE-(FE-HE)-FE 方法获得的相应精确响应区分开来。对于低标准化储层长度和高标准化储层长度情况（L/H = 1 和 3），这都是受控的。此外，可以说，当使用高阶 HW 截断元件时，瞬态分析实际上可以产生精确的结果（在数值意义上）。换句话说，在这些情况下，结果对储层归一化长度不敏感。

原创性/价值

采用新方法制定了混凝土重力坝-水-基岩系统的动力分析。该技术的显着特点是它在截断边界处利用了 HW 高阶条件。该方法针对所有类型的激励和储层底部条件进行了讨论。