PSI - Issue 54

Koji Uenishi et al. / Procedia Structural Integrity 54 (2024) 67–74 Uenishi / Structural Integrity Procedia 00 (2023) 000–000

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train network in the near field of the Niigata-ken (Niigata Prefecture) Chuetsu earthquake that occurred on October

j = 6.8. Thus, structural failures are highly possible even in the

23, 2004, with a shallow focal depth of 13 km and M

underground, if an earthquake occurs directly underneath (Uenishi, 2021).

3. Generation mechanisms of the dynamic structural failures

Now let us mechanically consider the generation mechanisms of the Daikai failure. Assume a column of a cross

sectional area A , height h , mass density  and elastic modulus E that is supporting the overburden M . Suppose that

the bottom of the column is under a harmonic vertical vibration given in terms of displacement, = / ,

and  are the displacement amplitude and the

which travels into the linear elastic column. Here, t is time and u 0

wavelength of the incident wave. The wave speed in the column is expressed as = / . Then, an elastodynamic

analysis can show that the load M plays a crucial role in the failure of the columns and if the condition

−

2

=0,

(1)

is satisfied, the column resonates, or vibrates severely and failure may occur. Together with A = 0.4 × 1.0 m 2 at the

Daikai station or 0.4 × 0.6 m 2

between the stations, h = 5.5 m,  = 2,200 kg/m 3

and c = 4,100 m/s, the above

condition (1) for resonance indicates that if the dominant frequency c /  is as high as about 17 Hz, the overburden M

that induces resonance is some 235 tons at the Daikai station or 140 tons between the stations, and with this

frequency only the columns at the limited sections such as shown in Fig. 3(b) vibrate significantly and can fail

(Uenishi and Sakurai, 2000). If the resonance is really the main cause of the failure, then the wavelength  with a

dominant frequency of 17 Hz is some 240 m in the column, which is about 43.6 times as large as the column height.

However, if the shear (S) wave speed and Poisson’s ratio of the linear elastic surrounding soil are 140 m/s and 0.333

(Kishi et al., 2020), then the speed of the incident P wave with vertical shaking is some 280 m/s and the wavelength

of the P wave of audible 17 Hz is 16.5 m in the surrounding soil, which is of the order of the structure and just three

times as large as the column height.

A similar discussion of the effect of higher-frequency vertical shaking or vertical shock applies for the flattened

middle floor (Fig. 3(a)). For instance, an analysis of eigenfrequencies and eigenmodes of a five-story RC structure

indicates that the structural vibrations are all horizontal only up to the fourth eigenmode, 11.6 Hz, and above the

14th mode, 49.3 Hz, the vibrations are all vertical. That is, for the incident waves of frequencies above 50 Hz,

vertical shaking dominates in the structure and collapse of the structure in the vertical direction without horizontal

movement is possible (Sakurai and Uenishi, 2005). Thus, the above photographs of the structural failures do point

out the existence of audible higher-frequency P waves with vertical shaking, and the obtained results may be

consistent with the verbal evidences of earthquake-related sounds on that day such as the abovementioned one and

another one “There was a thumping sound, like a door being slammed as hard as it could be”, reported in the daily

newspaper Asahi Shimbun on January 17, 2022. Note also that in Kobe, one or two vertical shocks, so-called

seaquakes, were experienced even on board floating bodies (e.g. ferry and fishing boats) at sea during the 1995

quake (Uenishi and Sakurai, 2014). However, as shown in Fig. 2, the higher-frequency shaking has not been

detected, and the existence of such higher frequencies, especially those of vertical ones, and their effect on structures

still remain “out of question” in engineering seismology (at least in Japan) even after the 1995 seismic event.

4. Detecting audible earthquakes just underneath

The photographs shown in Fig. 3 do suggest that higher-frequency vertical shaking or a vertical shock can cause

“unusual” structural failures that have been previously unrecognized. However, there is still a myth that structures

are more resilient against vertical shaking than against horizontal one, based on the belief that structures are built so

that they can withstand the vertical effect of gravity (multiplied by safety factors of three or so). Indeed, structures

are designed to resist the vertical but static downward forces and possibly the horizontal dynamic forces (like winds

for surface structures), but it does not mean that these structures are resilient against vertical but dynamic upward

forces from bottom. Moreover, we should note that historically seismology has been developed to detect the