Observation of Seismic Ground Motion and Pore Water Pressure in Lineated Valley Fill of Wakayama, Southwest Japan

Abstract

We performed in-situ observations of seismic ground motion, pore-water pressure, and ground-water level at lineated valley fill (LVF) in Wakayama city, southwest Japan, from 2004 to 2008. In Wakayama city and its surrounding area, felt earthquakes often occur with epicenters in the northwestern part of the Kii Peninsula and the Nankai Trough off the coast of the Kii Peninsula. We obtained simultaneous observation records of surface ground motion and pore-water pressure from several small- to medium-sized earthquakes. The excess pore-water pressure was clearly observed during a medium-sized earthquake with magnitude Mj 4.5. From the detailed analysis of surface ground motion, we detected a long-period pulse, although it was usually hidden behind oscillating short-period components with large amplitudes. The strong shaking induced ground tilting motion, causing a step-like acceleration change in the seismometer pendulum. Although no ground deformation could be confirmed through visual observation during the earthquake, the in-situ instrumental observation revealed ground tilting motion. Theoretical long-period pulses were synthesized assuming models of ground tilting motion during an earthquake. From comparison of the theoretical model with the observed long-period pulse, the permanent tilt is of an order of 10⁻⁶ degree down nearly toward the direction of the valley line.

1 Introduction

In the process of expansion of large cities from alluvial plains to hilly areas, large-scale residential areas have been developed by filling valleys with soil. Such areas have often suffered damage from earthquake-induced landslides. To reduce damage, it is necessary to develop countermeasures based on damage prediction. To predict the damage by earthquake-induced landslide, it is necessary to understand the behavior of ground during moderate to strong earthquakes. For this purpose, in-situ continuous observation of seismic ground motion, pore-water pressure, etc. at landslide ground is necessary, but there are very few such observations (Ishihara et al. 1987, 1989; Iai and Kurata 1991; Kamai 2011).

We performed in-situ continuous observation of seismic ground motion, pore-water pressure, and ground water level at LVF in Wakayama city, southwest Japan. We obtained simultaneous observation records of surface ground motion and pore-water pressure during several small- to medium-sized earthquakes. In particular, excess pore-water pressure was clearly observed during the medium-sized earthquake with magnitude Mj 4.5.

In this paper, first we examine the relation between surface ground motion and pore-water pressure during earthquakes. Next, we detect minute signals caused by ground tilting motion from seismograms of surface ground motion when excess pore-water pressure occurs. We construct the model for ground tilting motion based on the detected signal. Based on this model, the inclination of ground during an earthquake is estimated by fitting the theoretically calculated waveform for ground tilting motion to the observed one.

2 Observations

We performed in-situ simultaneous and continuous observations of seismic motion, pore-water pressure and ground-water level at a LVF in Wakayama city, from 2004 to 2008. In Wakayama city and its surrounding area, many felt earthquakes occur annually with epicenters in the northwestern part of the Kii Peninsula and the Nankai Trough off the coast of the Kii Peninsula (Figs. 1 and 2). A seismometer and a pore-water pressure transducer with a high dynamic range and wide frequency band were used for the observations. The observation site OIK is shown in Fig. 3. From this figure, we can see large changes of topography and ground structure of the observation site due to the urban planning. That is, the valley was converted into LVF, and many houses were built there. Furthermore, it should be noted that the residential area on the LVF is adjacent to a large pond. The topography and ground environment of the observation site satisfy the conditions for landslide occurrence. The observation site OIK is considered a suitable test site for the observation of earthquake-induced landslides.

Fig. 1

(a) Wakayama area in the northwest of the Kii Peninsula, southwestern Japan. (b) Epicentral distribution of earthquakes observed for the period from 1 January 2000 to 31 December 2002 by the Wakayama Seismological Observatory of the Earthquake Research Institute, University of Tokyo, using the telemetered network for microearthquake observation. (c) Vertical distribution of earthquakes in and around the Kii Peninsula, obtained by projecting hypocenters of earthquakes located within the area indicated in Fig. 1b on a vertical plane along the A-B line in Fig. 1b. Most of the earthquakes in the upper crust are located in and around the Wakayama plain in the northwest of the Kii Peninsula, where intense swarm activity occurs. The earthquake swarm region is indicated by A in Fig. 1c

Fig. 2

A series of seismic activities off the coast of the Kii Peninsula in 2004. Pore-water pressure clearly responds to seismic motion during the six largest earthquakes in seismic activity

Fig. 3

Location of observation site OIK. As cities expanded from alluvial plains to hilly areas, large-scale housing ground, such as LVF, have been developed. The observation site is located on the ground adjacent to the pond

We carried out surface wave exploration and boring survey at the site OIK. The results obtained are shown in Fig. 4. According to that, a sandy layer with an S-wave velocity (Vs) of 130–190 m/s and an N-value of 5 or less is deposited up to a depth of approximately 4 m. At a depth of 4 m or more, a gravel layer with Vs = 200 to ~260 m/s and N-value of 5 or more is deposited. This approximately 4 m-thick surface sandy layer corresponds to the artificially constructed soft ground. The groundwater level is approximately 2 m. It is thought to be saturated with water at depths of 2 m or deeper.

Fig. 4

Surface geological structure and S-wave velocity structure of OIK. This figure also shows the location of observation instruments

Figure 4 also shows the locations of seismometers, pore-water pressure transducer, ground-water level meter and GPS. The seismometers were installed on the ground surface. The pore-water pressure transducer was installed 2.9 m directly below the seismometer (GL-2.9 m). The groundwater level meter was installed at a depth of 2.9 m (GL-2.9 m) inside the well.

Figure 5a shows a photograph of the velocity-type seismometer used. Figure 5b shows a frequency characteristics of the servo-type velocity seismometer used here. The amplitude response is flat in the frequency range of 0.1–70 Hz. The resolution is nearly 100μcm/s, and the maximum measurement range is ±20 cm/s. The observed seismograms were recorded into a data logger with 100 Hz sampling. Figure 6 shows a frequency characteristics of pore-water pressure transducer used here. The amplitude and phase characteristics are flat to nearly 13 Hz. The observable range is from 0.024 kPa to 96 kPa. The observed pore-pressure is recorded into a data logger with 10 Hz sampling. Since the seismometer and pore-water pressure transducer have a flat characteristics in the wide frequency range, we can directly compare waveforms of pore-water pressure with those of surface velocity observed at the site OIK.

Fig. 5

(a) Servo-type velocity seismometer, (b) Frequency characteristics of servo-type velocity seismometer. Amplitude response is flat in the frequency range of 0.1–70 Hz

Fig. 6

Frequency characteristics of pore-water pressure transducer. Upper: amplitude. Lower: phase

3 Data and Analysis

Figure 7 shows the records of pore-water pressure and water-level meter observed during the foreshock (M6.9) and the main shock (M7.4) shown in Fig. 2. We can see the rapid changes in pore-water pressure induced by seismic ground motion. The three-component waveforms (Rd, Vt, and Tr) of surface ground velocity observed at OIK during the mainshock are shown in Fig. 8. Rd is the radial component, Tr is the transverse component, and Vt is the vertical component. The radial direction is the direction from the epicenter to the observation point, and the transverse direction is the direction perpendicular to the radial direction. The maximum surface velocity is 1.171 cm/s in the transverse component (Tr) of seismograms. The vertical component (Vt) is smaller than the other two horizontal components. This is due to the soft surface ground. Figure 9 shows the waveform of pore-water pressure along with those of surface ground velocity.

Fig. 7

Rapid changes of pore-water pressure induced by the foreshock and main shock

Fig. 8

Surface velocity seismograms observed at OIK during the main shock of M7.4

Fig. 9

Waveforms of pore-water pressure and surface velocity during the main shock of M7.4

According to Roeloffs (1996), the pore-water pressure Pw is proportional to the radial component (Rd) of surface ground velocity, that is, Pw ∝ Rd. This relationship holds true for both in case of P-wave arrivals and in case of S-wave arrivals. Figure 10 briefly summarizes the derivation process of Pw ∝ Rd. To confirm the relationship of Pw ∝ Rd., the pore-water pressure waveform (Pw) is superimposed on the three surface velocity waveforms (Rd, Vt, and Tr), in Fig. 11. From this figure, Pw appears to be similar to Rd. To examine this relationship in more detail, Pw and Rd. were passed through a bandpass filter with a center frequency (fc) and the two were compared. Figure 12 shows the case where fc is 1/2 Hz, and Fig. 13 shows the case where fc is 1/8 Hz. From these figures, it can be seen that the waveform of Pw matches that of Rd. very well in both P-wave and S-wave parts. Furthermore, the waveform of Pw matches that of Vt fairly well in both P-wave part and S-wave part. On the other hand, the waveform of Pw does not quite match the Tr component of the surface ground velocity. In this way, the relation of Pw ∝ Rd. was confirmed using observational data. We can also understand the relationship of Pw ∝ Rd. in that Pw depends not on shear strain, but on volumetric strain. Next, we investigate the case when excess pore-water pressure is generated during an earthquake.

Fig. 10

Derivation of the relationship between pore-water pressure and surface velocity. Upper: case of P-wave incidence. Lower: case of S-wave incidence

Fig. 11

Pore-water pressure waveform (Pw) superimposed on surface velocity waveform (Rd, Vt, and Tr)

Fig. 12

Pore-water pressure waveform (Pw) superimposed on surface velocity waveform (Rd, Vt, and Tr). Case of bandpass filtered waveforms (fc = 1/2 Hz)

Fig. 13

Pore-water pressure waveform (Pw) superimposed on surface velocity waveform (Rd, Vt, and Tr). Case of bandpass filtered waveforms (fc = 1/2 Hz)

On May 15, 2006, there was an earthquake with a maximum seismic intensity of 4, whose hypocenter was in the northern part of Wakayama city. The magnitude Mj of the earthquake was 4.5, and the depth of the hypocenter was approximately 3 km. Figure 14 shows surface velocity waveforms of Mj 4.5 earthquake observed at OIK. From this figure, it can be seen that Ts-p is smaller than 1.0 s, where Ts-p is the difference Ts-Tp between S-wave arrival time Ts and P-wave arrival time Tp. From this Ts-p, the hypocentral distance is estimated to be less than 10 km. Although the magnitude Mj was not so large, the intensity of the earthquake was high, probably because the depth of the hypocenter was shallow and the hypocentral distance was very short. As shown in Fig. 1, in the Wakayama Earthquake Swarm Region, most earthquakes occur at a depth of around 7 km. For this reason, felt earthquakes frequently occur in this area. Furthermore, what is characteristic of this observed waveform is that the vertical component Vt is significantly smaller than the two horizontal components Rd. and Tr. This is thought to be due to the soft surface ground of OIK.

Fig. 14

Surface velocity waveforms during the Mj 4.5 earthquake that occurred on May 15, 2006. The hypocenter is in the northern part of Wakayama city, at a depth of 3 km

Figure 15 shows pore-water pressure response (P) during the Mj 4.5 earthquake. As shown in Iai and Kurata (1991), it is also clear that P is composed of a step-like rising long-period component and a dominantly oscillating short-period component. In this paper, the former will be referred to as Pshear and the latter as Pcomp (P = Pshear + Pcomp). Pshear is obtained by filtering P. Pcomp is obtained by subtracting Pshear from P. The maximum value of Pshear is 0.128 kPa, and that of Pcomp is 0.992 kPa.

Fig. 15

Response of pore-water pressure (P) during the Mj 4.5 earthquake. P contains a step-like rising long-period component. P is decomposed as P = Pcomp + Pshear

In order to compare the pore-water pressure waveform (P) and surface ground velocity waveforms (Rd, Vt, and Tr), they were displayed together. From Fig. 16, it can be seen that the rise time of Pshear matches that of S waves in Rd., Vt, and Tr. Figure 17 shows the separation process from total P to Pshear component. It can be seen that Pshear composed of a step-like rising long-period component is clearly different from Pcomp composed of oscillating short-period component with large amplitudes. This suggests that the cause for the generation of Pshear is different from that of Pcomp. Pcomp is dynamic water pressure caused by vibration of pore-water pressure transducer exited by ground motion. Therefore, Pcomp depends on the installation direction of the pore-water pressure transducer.

Fig. 16

Pore-water pressure along with surface velocity during the Mj4.5 earthquake

Fig. 17

Extraction of Pshear from P. Pshear is obtained by filtering P

In order to investigate the rising time of Pshear, its waveform is superimposed on those of surface ground motion. As seen in Fig. 18, the rising time of Pshear matches S-wave rising time in the three components, Rd., Vt, and Tr. The rising time of Pshear agrees well with that of Tr. Therefore, it is thought that shear S waves, that is, SH waves contribute to the generation of Pshear.

Fig. 18

Pshear superimposed on surface velocity waveform (Rd, Vt, and Tr). Case of bandpass filtered waveforms (fc = 1/2 Hz)

Next, to investigate the relationship between Pcomp and surface ground motion, Pcomp is superimposed on the three surface velocity waveforms (Rd, Vt, and Tr). To examine in more detail, Pcomp and the three velocity waveforms (Rd, Vt, and Tr) were passed through a bandpass filter with a center frequency (fc). Figure 19 shows the case where fc is 1/8 Hz. This figure shows that the waveform of Pcomp matches those of Rd. and Vt, and also its rise nearly matches those of Rd. and Vt. However, one phase at the time of rising of Pcomp is not consistent with that of Rd. This is because Pshear rose at that time and Pcomp was disturbed by Pshear. On the other hand, the waveform of Pcomp does not quite match that of the Tr component of the surface ground velocity. In this way, the relation of Pcomp ∝ Rd. was confirmed. Furthermore, it was found that Pcomp was generated by the incidence of P or SV waves on surface ground, and Pshear by the incidence of strong SH waves.

Fig. 19

Pcomp superimposed on surface velocity waveform (Rd, Vt, and Tr). Case of bandpass filtered waveforms (fc = 1/2 Hz)

In Fig. 20, the observed waveform of ground motion is displayed at the normal display magnification of 1x. If a very small long-period component is hidden behind a dominantly oscillating short-period component with a large amplitude, the long-period component cannot be confirmed visually at the usual display magnification of 1×. The black line of Fig. 21 shows the waveform of the ground motion magnified 500 times and the red line shows waveforms smoothed by a time window with a width of 3 s. Fig. 22 shows a transient long-period waveform extracted in this way. Thus, ground motion observed at OIK during the Mj 4.5 earthquake contains long-period pulses, although they are hidden behind short-period components with large amplitudes. Since the period of the pulse are clearly exceeding the flat characteristic frequency range of the seismometer, the observed ground motion is not different from true ground motion at OIK. We need correct from the observed ground motion to true ground motion to examine the cause of the long-period pulse generation. To do this, we need a transfer function of the seismometer.

Fig. 20

Waveforms of surface velocity observed

Fig. 21

Black line: waveforms magnified 50×. Red line: waveforms smoothed by time window with a width of 3 s

Fig. 22

Long-period component extracted by smoothing

Details of internal electronics of the seismometer were made public by the manufacturer for only the two horizontal components of the servo-type velocity seismometer. The seismometer has a flat amplitude response in the frequency range from 0.1 Hz to 70 Hz, as shown in the Fig. 5b. Using these data, the transfer function of the seismometer was calculated. When Xn is input to the seismometer, the output Yn from the seismometer is expressed as follows using the fifth-order recurrence formula.

$$ {Y}_n=\sum {B}_ix\;{X}_{n-i}-\sum {A}_ix\;{Y}_{n-i}\mathrm{Y} $$

(1)

Conversely, the input X_n can be calculated from the output Y_n using the following formula.

$$ {X}_n=\left[{Y}_n+\sum {A}_ix\;{Y}_{n-i}-\sum {B}_ix\;{X}_{n-i}\right] $$

(2)

A detailed explanation of the coefficients A and B is omitted in the present paper.

We corrected the observed ground motion (Fig. 23) to the true ground motion (black line of Fig. 24) using Eq. (2). As seen in Fig. 24, after oscillating short-period components, the corrected velocity waveform increases linearly in the negative direction for the NS component, and in the positive direction for the EW component. Such a monotonous increase (or decrease) of ground velocity is puzzling. However, since the seismometer is a velocity type, such a phenomenon occurs when a certain acceleration is applied to the seismometer. It is thought that a constant acceleration is applied to the seismometer.

Fig. 23

Surface velocity waveform output from seismometer

Fig. 24

Black line: waveform of actual surface velocity corrected by Eq. 2. Green line: straight line that best fits the black line (corrected waveform)

We investigate the observed and corrected ground velocity when a certain acceleration is applied to the velocity-type seismometer. The most likely cause of the constant acceleration added to the seismometer is ground tilting motion. As shown in Fig. 25a, here, it is assumed that the tilting motion is represented by a step function with a rise time. The height of the step function is an acceleration applied to the seismometer by ground tilting motion. It is assumed that the ground tilting progresses gradually, and the progress velocity is taken into consideration by the rise time. From examination for cases where the rise time was 1, 2, 4, 8 and 16 s, it was found that the case of 1 s showed good agreement. Therefore, the rise time of 1 s was used in this study.

Fig. 25

Generation process of long-period pulse waves observed. (a) Step-like acceleration applied to seismometer. (b) Velocity obtained by integrating acceleration (a). (c) Output signal from seismometer. It is obtained by inputting (b) into Eq. (1)

Figure 25a shows a step-like acceleration applied to the seismometer when the ground tilts. Figure 25b shows velocity waveform calculated from the acceleration applied to the seismometer. This velocity waveform is input into the seismometer. Figure 25c shows velocity waveform observed (output) by seismometer. As seen in this figure, the waveform is a smooth long-period pulse as in Fig. 22. This indicates that the narrowband frequency characteristic of the seismometer transforms a linearly increasing or decreasing velocity wave into a pulse wave consisting of smooth long-period component.

Next, we estimated the acceleration applied to the seismometer using long-period pulse waves. Figure 26 shows the observed long-period pulse waves (black line) and the theoretically calculated waves (green line). The observed pulse wave is obtained by smoothing the originally observed wave using a time window with a width of 3 s. The theoretical wave is obtained as follows. As shown in Fig. 24, first, the acceleration (Acc) applied to the seismometer by ground tilting is determined from the slope of a green straight line fitted to a corrected velocity waveform monotonically increasing (or decreasing) with time (black line in Fig. 24). Next, a step function (height Acc, rise time 1 second) representing the acceleration applied to the seismometer is created. A theoretical velocity waveform input into the seismometer is obtained by integrating this acceleration step function. By inputting this theoretical waveform into Eq. (1), we obtain a theoretical long-period pulse wave (green line in Fig. 26). The theoretical waves agree very well with the observed waves.

Fig. 26

Comparison of observed waves and theoretically calculated waves. Black line: by smoothing output wave from seismometer. Green line: by theoretical calculation based on ground tilting motion. The two are in good agreement

We calculated the amount of ground inclination from the inclination of the horizontal two components of seismometers. The ground tilting motion was assumed to be a step-like function with a rise time. We considered cases where the rise time was 1, 2, 4, 8, and 16 s. The case of 1 s showed a good agreement between the observed and theoretical long-period pulse waveforms. Table 1 lists accelerations applied to the two horizontal components of seismometer, the permanent tilt of tilting motion, and its direction.

Table 1 Accelerations applied to seismometers, tilt of ground, and direction estimated

4 Discussion

Iai and Kurata (1991) observed in-situ excess pore-water pressures and ground motions during the 1987 Chiba-Toho-Oki Earthquake of magnitude 6.7. The observed excess pore-water pressure record contained a smoothly rising long-period component with an amplitude of about 40 cm in water head and a dominantly oscillating short-period component. From a comparison of the short-period component waveform and the acceleration waveform observed in the ground, it was determined that this short-period component was dynamic water pressure caused by the vibration of the pore-water pressure transducer and the short-period component was separated by smoothing. Using these extracted long-period components, they conducted an earthquake response analysis that considered the rise in excess pore-water pressure and the nonlinearity of the ground.

Kamai (2011) conducted observations of seismic ground motion and pore-water pressure in valley fill in the southwestern Tokyo region from 2005 to 2011. The non-linear response of excess pore-water pressure in valley hill was observed during the 2005 Chibaken-Hokuseibu Earthquake of magnitude 6.0. After the arrival of the S-wave main motion, an asymmetrical rapid increase of about 0.75 kPa was observed. During the 2005 Miyagi Earthquake of magnitude 7.2, no nonlinear response of the pore-water pressure was observed. However, it has been reported that while the seismic ground motion ended in about 30 s, the pore-water pressure oscillations continued for 280 s, which is about 10 times longer. This kind of long-lasting pore-water pressure response has not been previously reported, even in the observations by Iai and Kurata (1991) and could not be confirmed in our observations, so this is an interesting report.

Although those observations succeeded in observing the nonlinear response of excess pore-water pressure, which is indicative of ground deformation during earthquakes, they did not precisely analyze ground acceleration records. Since seismic ground motion is also affected by ground deformation, it is necessary to perform a more precise analysis of observed ground motion. Our observation detected the very weak long-period pulse-like wave with an amplitude of 0.003 cm/s from surface ground motion record. Assuming that the long-period pulse was generated by ground tilting motion, the tilt of ground and its direction were estimated. An interesting result is that the direction of the estimated ground tilting motion closely corresponds to valley axis. However, ground deformation could not be confirmed through visual observation.

5 Conclusions

The principal conclusions of this study can be summarized as follows.

• 1. In-situ continuous observation of seismic ground motion, pore-water pressure, and ground-water level was performed at LVF in Wakayama city, southwest Japan. Simultaneous observation records during several small- to medium-sized earthquakes were obtained. Excess pore-water pressure was clearly observed during the medium-sized earthquake with magnitude Mj 4.5.

• 2. From comparison of Rd. (radial component of surface velocity) and pore-water pressure (Pw or Pcomp) during earthquakes, the waveform of Pw well agrees with that of Rd. (Pw ∝ Rd), indicating that Pw is generated by the incidence of P or SV waves on ground surface.

• 3. The observed excess pore-water pressure (P) can be decomposed into a step-like rising long-period component (Pshear) and a dominantly oscillating short-period component (Pcomp). Pcomp is the same as Pw in 1 mentioned above. The rising time of Pshear nearly agrees with that of Tr (transverse component of surface velocity), suggesting that shear S waves, that is, SH waves contribute to the generation of Pshear.

• 4. Seismograms of surface velocity observed at OIK during the Mj 4.5 earthquake contained long-period pulses, although they were hidden behind dominantly oscillating short-period components with large amplitudes.

• 5. The process of generating a long-period pulse-like signal is as follows. When the ground tilts with generation of excess pore-water pressure, the acceleration change due to the ground tilting motion is added to the seismometer. The wave converted (integrated) from the added step-like acceleration to linear velocity with a constant slope is input to the seismometer. The seismometer outputs the wave filtered by its own transfer function. The long-period pulse-like wave is observed in this way.

• 6. Based on the generation model of a long-period pulse wave, accelerations applied to the two horizontal components of seismometer, the direction of ground tilting motion, the permanent tilt of ground tilting motion, and its direction are estimated as 1.4 × 10⁻⁷ (m/s/s), −1.0 × 10⁻⁶ (m/s/s), −8 (degree), 5.9 × 10⁻⁶ (degree), respectively

• 7. An interesting result is that the direction of the estimated ground tilting motion approximately corresponds to the line of the valley, although visual observation could not confirm ground deformation.