A significant vibration mode of Tainter gates is the rigid-body vibration of the gate around the trunnion pin. Any such rigid-body vibration of a Tainter gate is accompanied by periodic changes in the flow rate through the gate opening which, in turn, results in fluctuating loads on the gate. The induced loads are then fed back to excite or damp the initiating rigid-body vibration. The placement of the center of the circular-arc skinplate eccentric to and beneath the trunnion pin center results in the gate behaving as a press-shut device, with a strong likelihood of susceptibility to an intense dynamic instability. In this chapter the theory behind this eccentricity instability is developed and its potential applicability to the Wachi Dam failure examined with the conclusion that eccentricity instability was most likely not the cause of the Wachi failure.
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Many Tainter gates have been installed and continue to operate safely without destructive dynamic instabilities. Figure 1 shows the massive Tainter gates at the Itaipu Dam in Brazil as an example of gates that serve their as-designed function without dynamic instabilities. As discussed in Chapter 1, however, Itaipu Dam did have one isolated incident, speculatively related to vibrations, resulting in the failure of a rod in a hydraulic cylinder (see Cassidy, 2000). Figure 2 shows a second example of apparently stable gates at the Benmore Dam in New Zealand. There have been few notable gate failures among the many successful installations. Gate accidents since 1960 are documented in Table 1 in Chapter 1. The lessons we need to learn are from the instances when large Tainter gates do experience destructive failure.
Among the reported accidents is the Wachi Dam gate failure in Japan on July 2, 1967, when a 37-ton Tainter gate failed during pre-discharge tests (Yano, 1968). Additional details and analysis of the Wachi Dam gate failure are presented in Chapter 12. After the Wachi Dam gate failure, one of the co-authors of this book (Professor N. Ishii) initiated an investigation of the flow-induced vibration of Tainter gates. He identified an intense self-excited vibration, which he called eccentricity instability, which occurs under certain conditions (Ishii & Imaichi, 1976; Imaichi & Ishii, 1977, Ishii & Imaichi, 1977; Ishii et al., 1980; Ishii & Imaichi, 1982; Ishii & Naudascher 1992; Ishii, 1995). This instability is restricted to Tainter gates in which the center of the circular-arc skinplate is offset relative to the trunnion pin center.
Figure 1. Massive gates (20 x 21.34 m, each gate weighing 3185 kN or 74 tons) at Itaipu Dam in Brazil exemplify the many Tainter gates installed worldwide that are apparently stable and have not experienced recurrent dynamic instabilities.
Figure 2. Tainter gates (10.6 x 11.9 m) at the Benmore Dam in New Zealand are another example of apparently stable gates with no reported vibration problems.