*3.2. Experimental Analysis Method*

*3.2. Experimental Analysis Method*  Figure 8a shows the acceleration values that were measured in the experiment. They are the measurement results of the impact in the bridge axis direction when the surcharge load was 0 kN. In the case of the impact vibration test, it is possible to determine the natural frequency and vibration mode by analyzing the spectrum of the repetitive waveform that was obtained from multiple recorded waveforms. For the spectrum analysis, it is desirable to use the FFT technique, which is capable of dividing the signals by the frequency. The natural frequency of the pier can be derived from the frequency domain using the FFT technique as shown in Figure 8b. In addition, the phase of the measured position can be represented as shown in Figure 8c. Based on this, the phase difference between the measuring instruments can be obtained, and the overall behavior of the pier can be analyzed. For example, in the case of the first mode and the second mode, the natural frequency occurs when the phase of the attached measuring instrument is in the same direction, so when the phase difference is 0°, it can be determined as the natural frequency of the first and second mode. In addition, in the case of the third mode, the natural frequency of the pier can be derived when the Figure 8a shows the acceleration values that were measured in the experiment. They are the measurement results of the impact in the bridge axis direction when the surcharge load was 0 kN. In the case of the impact vibration test, it is possible to determine the natural frequency and vibration mode by analyzing the spectrum of the repetitive waveform that was obtained from multiple recorded waveforms. For the spectrum analysis, it is desirable to use the FFT technique, which is capable of dividing the signals by the frequency. The natural frequency of the pier can be derived from the frequency domain using the FFT technique as shown in Figure 8b. In addition, the phase of the measured position can be represented as shown in Figure 8c. Based on this, the phase difference between the measuring instruments can be obtained, and the overall behavior of the pier can be analyzed. For example, in the case of the first mode and the second mode, the natural frequency occurs when the phase of the attached measuring instrument is in the same direction, so when the phase difference is 0◦ , it can be determined as the natural frequency of the first and second mode. In addition, in the case of the third mode, the natural frequency of the pier can be derived when the phase difference occurs 180◦ because it has torsional behavior.

phase difference occurs 180° because it has torsional behavior.

*Appl. Sci.* **2020**, *10*, x FOR PEER REVIEW 8 of 17

**Figure 8.** Natural frequency analysis method. (**a**) Representative signal; (**b**) representative natural frequency; and (**c**) representative phase. **Figure 8.** Natural frequency analysis method. (**a**) Representative signal; (**b**) representative natural frequency; and (**c**) representative phase.

#### *3.3. Full-Scale Pier Test Results 3.3. Full-Scale Pier Test Results*

eigenvalue analysis.

Through a series of tests, the mode number of the pier was analyzed, and the natural frequency of the pier in each mode was derived. Figure 9a shows the natural frequency of the pier in case-2 where an impact was applied to the top of the pier in the bridge axis direction. The natural frequency was determined to be approximately 15.14 Hz. In addition, the phase was obtained for each height by using the measured values to analyze the behavior of the pier. Figure 9b shows the phase difference results that were obtained by using the phase for each position. It was determined that all of the phase differences where the natural frequency points occurred had a tendency to converge to 0°. This is because all the measuring instruments that were attached to each height were deformed in the same direction. In other words, the behavior of the pier occurred in the same direction. The behavior had a tendency to be similar to the first mode of the pier eigenvalue analysis. Through a series of tests, the mode number of the pier was analyzed, and the natural frequency of the pier in each mode was derived. Figure 9a shows the natural frequency of the pier in case-2 where an impact was applied to the top of the pier in the bridge axis direction. The natural frequency was determined to be approximately 15.14 Hz. In addition, the phase was obtained for each height by using the measured values to analyze the behavior of the pier. Figure 9b shows the phase difference results that were obtained by using the phase for each position. It was determined that all of the phase differences where the natural frequency points occurred had a tendency to converge to 0◦ . This is because all the measuring instruments that were attached to each height were deformed in the same direction. In other words, the behavior of the pier occurred in the same direction. The behavior had a tendency to be similar to the first mode of the pier eigenvalue analysis. *Appl. Sci.* **2020**, *10*, x FOR PEER REVIEW 9 of 17

**Figure 9.** Results of the impact vibration load test in the bridge axis direction. (**a**) Natural frequency of the first mode and (**b**) phase difference of the first mode. **Figure 9.** Results of the impact vibration load test in the bridge axis direction. (**a**) Natural frequency of the first mode and (**b**) phase difference of the first mode.

pier length direction than in the bridge axis direction. This confirms that the difference in the stiffness affected the natural frequency. To examine the behavior of the pier in the pier length direction, the phase difference was analyzed as shown in Figure 10b. In this instance, the phase difference converged to 0° when the natural frequency occurred along with the behavior in the first mode mentioned above. This appears to be similar to the behavior in the second mode of the pier

**Figure 10.** Results of the impact vibration load test in the pier length direction. (**a**) Natural frequency

Figure 11a shows the natural frequency results in case-3 where the acceleration was measured by applying an impact to the upper outer point of the pier. Two clear natural frequencies were observed, and they were 15.14 and 54.19 Hz. The phase difference results in Figure 11b show that the phase difference converged to 0° at 15.14 Hz. This indicates that the first mode occurred, as the behavior and the natural frequency were the same as those of the first mode. Figure 11b, however, shows that the phase difference was 180° at 54.19 Hz. These results demonstrated that the outer part of the pier behaved in opposite directions; thus, indicating torsional behavior. This behavior was similar to the third mode, and it appeared that applying an impact to the outer point of the pier in the bridge axis direction led to the first mode and the third mode, which was the torsional behavior

of the second mode and (**b**) phase difference of the second mode.

Figure 10a shows the results in case-1 where the natural frequency for each height was derived

Figure 10a shows the results in case-1 where the natural frequency for each height was derived by applying an impact to the top of the pier in the pier length direction. The natural frequency of the pier was determined to be approximately 22.4 Hz, which is approximately 7 Hz higher in comparison to case-2 (bridge axis direction). This is because the stiffness of the pier was higher in the pier length direction than in the bridge axis direction. This confirms that the difference in the stiffness affected the natural frequency. To examine the behavior of the pier in the pier length direction, the phase difference was analyzed as shown in Figure 10b. In this instance, the phase difference converged to 0◦ when the natural frequency occurred along with the behavior in the first mode mentioned above. This appears to be similar to the behavior in the second mode of the pier eigenvalue analysis. by applying an impact to the top of the pier in the pier length direction. The natural frequency of the pier was determined to be approximately 22.4 Hz, which is approximately 7 Hz higher in comparison to case-2 (bridge axis direction). This is because the stiffness of the pier was higher in the pier length direction than in the bridge axis direction. This confirms that the difference in the stiffness affected the natural frequency. To examine the behavior of the pier in the pier length direction, the phase difference was analyzed as shown in Figure 10b. In this instance, the phase difference converged to 0° when the natural frequency occurred along with the behavior in the first mode mentioned above. This appears to be similar to the behavior in the second mode of the pier eigenvalue analysis.

**Figure 9.** Results of the impact vibration load test in the bridge axis direction. (**a**) Natural frequency

Figure 10a shows the results in case-1 where the natural frequency for each height was derived

of the first mode and (**b**) phase difference of the first mode.

*Appl. Sci.* **2020**, *10*, x FOR PEER REVIEW 9 of 17

**Figure 10.** Results of the impact vibration load test in the pier length direction. (**a**) Natural frequency of the second mode and (**b**) phase difference of the second mode. **Figure 10.** Results of the impact vibration load test in the pier length direction. (**a**) Natural frequency of the second mode and (**b**) phase difference of the second mode.

Figure 11a shows the natural frequency results in case-3 where the acceleration was measured by applying an impact to the upper outer point of the pier. Two clear natural frequencies were observed, and they were 15.14 and 54.19 Hz. The phase difference results in Figure 11b show that the phase difference converged to 0° at 15.14 Hz. This indicates that the first mode occurred, as the behavior and the natural frequency were the same as those of the first mode. Figure 11b, however, shows that the phase difference was 180° at 54.19 Hz. These results demonstrated that the outer part of the pier behaved in opposite directions; thus, indicating torsional behavior. This behavior was similar to the third mode, and it appeared that applying an impact to the outer point of the pier in the bridge axis direction led to the first mode and the third mode, which was the torsional behavior Figure 11a shows the natural frequency results in case-3 where the acceleration was measured by applying an impact to the upper outer point of the pier. Two clear natural frequencies were observed, and they were 15.14 and 54.19 Hz. The phase difference results in Figure 11b show that the phase difference converged to 0◦ at 15.14 Hz. This indicates that the first mode occurred, as the behavior and the natural frequency were the same as those of the first mode. Figure 11b, however, shows that the phase difference was 180◦ at 54.19 Hz. These results demonstrated that the outer part of the pier behaved in opposite directions; thus, indicating torsional behavior. This behavior was similar to the third mode, and it appeared that applying an impact to the outer point of the pier in the bridge axis direction led to the first mode and the third mode, which was the torsional behavior of the pier. Table 2 summarizes the natural frequency of the pier by the mode number according to the surcharge load. *Appl. Sci.* **2020**, *10*, x FOR PEER REVIEW 10 of 17 of the pier. Table 2 summarizes the natural frequency of the pier by the mode number according to the surcharge load.

**Figure 11.** Results of the impact vibration load test in the bridge axis direction (outside). (**a**) Natural **Figure 11.** Results of the impact vibration load test in the bridge axis direction (outside). (**a**) Natural frequency of the third mode and (**b**) phase difference of the third mode.

frequency of the third mode and (**b**) phase difference of the third mode.

*3.4. Field Pier Test Results* 

frequency, which is affected by all of the variables.

25 23.40 14.65 55.66 50 24.40 13.67 56.12 75 22.95 12.70 56.61 100 22.40 12.20 57.12 125 23.90 11.23 54.20 150 24.40 10.74 55.18 175 23.50 10.25 55.66 200 N/A 9.766 N/A 225 N/A 9.765 N/A 250 N/A 8.3 N/A

The conditions in the field pier test were mainly divided into three cases: (1) the pier with a girder, (2) the pier without a girder (removed), and (3) the 1 m deep scour on the ground that is adjacent to the pier. The natural frequency of the field pier was analyzed in the same way as the analysis method of the full-scale pier model test. Figure 10 shows the first mode natural frequency under the three field conditions. The natural frequencies under the field conditions were 21, 13, and 9.5 Hz, respectively, as demonstrated in Figure 12a–c. In the first mode, the natural frequency had the most sensitive change according to the field conditions (surcharge load and scour). This indicates that there are limitations in accurately evaluating the stability of the pier using the first mode natural

**Table 2.** Natural frequency results of the full-scale model pier according to the surcharge load.


**Table 2.** Natural frequency results of the full-scale model pier according to the surcharge load.

#### *3.4. Field Pier Test Results*

The conditions in the field pier test were mainly divided into three cases: (1) the pier with a girder, (2) the pier without a girder (removed), and (3) the 1 m deep scour on the ground that is adjacent to the pier. The natural frequency of the field pier was analyzed in the same way as the analysis method of the full-scale pier model test. Figure 10 shows the first mode natural frequency under the three field conditions. The natural frequencies under the field conditions were 21, 13, and 9.5 Hz, respectively, as demonstrated in Figure 12a–c. In the first mode, the natural frequency had the most sensitive change according to the field conditions (surcharge load and scour). This indicates that there are limitations in accurately evaluating the stability of the pier using the first mode natural frequency, which is affected *Appl. Sci.* by all of the variables. **2020**, *10*, x FOR PEER REVIEW 11 of 17

**Figure 12.** First mode natural frequency for each field condition. (**a**) With a girder; (**b**) Without a **Figure 12.** First mode natural frequency for each field condition. (**a**) With a girder; (**b**) Without a girder; and (**c**) 1 m deep scour on the ground adjacent to the pier.

girder; and (**c**) 1 m deep scour on the ground adjacent to the pier.

presence of a girder, unlike the first mode. This was similar to the result that the natural frequency of the second mode was not affected by the surcharge load in the full-scale pier model test. Due to the occurrence of scour, the natural frequency was reduced by approximately 6 Hz. Therefore, it is determined that the second mode natural frequency can be used as an indicator that can predict the condition of the ground that is adjacent to the pier without being affected by the surcharge load.

Figure 13 shows the natural frequency of the second mode for each field condition. The natural

Figure 13 shows the natural frequency of the second mode for each field condition. The natural frequencies under the field conditions were determined to be 20, 20, and 14 Hz, respectively, as displayed in Figure 13a–c. In the second mode, the natural frequency was identical regardless of the presence of a girder, unlike the first mode. This was similar to the result that the natural frequency of the second mode was not affected by the surcharge load in the full-scale pier model test. Due to the occurrence of scour, the natural frequency was reduced by approximately 6 Hz. Therefore, it is determined that the second mode natural frequency can be used as an indicator that can predict the condition of the ground that is adjacent to the pier without being affected by the surcharge load. Figure 13 shows the natural frequency of the second mode for each field condition. The natural frequencies under the field conditions were determined to be 20, 20, and 14 Hz, respectively, as displayed in Figure 13a–c. In the second mode, the natural frequency was identical regardless of the presence of a girder, unlike the first mode. This was similar to the result that the natural frequency of the second mode was not affected by the surcharge load in the full-scale pier model test. Due to the occurrence of scour, the natural frequency was reduced by approximately 6 Hz. Therefore, it is determined that the second mode natural frequency can be used as an indicator that can predict the condition of the ground that is adjacent to the pier without being affected by the surcharge load.

**Figure 12.** First mode natural frequency for each field condition. (**a**) With a girder; (**b**) Without a

*Appl. Sci.* **2020**, *10*, x FOR PEER REVIEW 11 of 17

**Figure 13.** Second mode natural frequency for each field condition. (**a**) With a girder; (**b**) without a **Figure 13.** Second mode natural frequency for each field condition. (**a**) With a girder; (**b**) without a girder; and (**c**) 1 m deep scour on the ground adjacent to the pier.

girder; and (**c**) 1 m deep scour on the ground adjacent to the pier. Figure 14 shows the third mode natural frequency for each field condition when the torsional behavior of the pier occurred. The accelerometers were attached to the left and right of the top of the pier. The side that simulated scour was named left and the side that did not simulate scour was named right. There was no significant difference in the third mode natural frequency depending on the field conditions as in the first and second modes. Figure 14a shows the natural frequencies in the torsional behavior (third mode) before removing the girder. It was observed that very similar natural frequencies occur on both sides. In Figure 14b, however, a difference of approximately 2.5 Hz occurred between the natural frequencies that are measured on both sides after the girder removal. This is because the fixed end effect of the upper girder disappeared with the girder removal; thus, restraining the torsional behavior. Figure 14c shows the natural frequency results for the torsional behavior (third mode) when a 1 m deep scour was simulated on one side of the pier. The natural frequency values were determined to be similar to those in Figure 14b, but the acceleration of the side with a 1 m deep scour exhibited a sharp reduction in the amplitude. This indicates that it is possible to predict the location and degree of the scour. Table 3 summarizes the natural frequency results for each mode number of the pier according to the presence of scour. It was Figure 14 shows the third mode natural frequency for each field condition when the torsional behavior of the pier occurred. The accelerometers were attached to the left and right of the top of the pier. The side that simulated scour was named left and the side that did not simulate scour was named right. There was no significant difference in the third mode natural frequency depending on the field conditions as in the first and second modes. Figure 14a shows the natural frequencies in the torsional behavior (third mode) before removing the girder. It was observed that very similar natural frequencies occur on both sides. In Figure 14b, however, a difference of approximately 2.5 Hz occurred between the natural frequencies that are measured on both sides after the girder removal. This is because the fixed end effect of the upper girder disappeared with the girder removal; thus, restraining the torsional behavior. Figure 14c shows the natural frequency results for the torsional behavior (third mode) when a 1 m deep scour was simulated on one side of the pier. The natural frequency values were determined to be similar to those in Figure 14b, but the acceleration of the side with a 1 m deep scour exhibited a sharp reduction in the amplitude. This indicates that it is possible to predict the location and degree of the scour. Table 3 summarizes the natural frequency results for each mode number of the pier according to the presence of scour. It was confirmed that the presence of scour decreases the natural [29–31].

confirmed that the presence of scour decreases the natural [29–31].

*Appl. Sci.* **2020**, *10*, x FOR PEER REVIEW 12 of 17

**Figure 13.** Second mode natural frequency for each field condition. (**a**) With a girder; (**b**) without a

Figure 14 shows the third mode natural frequency for each field condition when the torsional behavior of the pier occurred. The accelerometers were attached to the left and right of the top of the pier. The side that simulated scour was named left and the side that did not simulate scour was named right. There was no significant difference in the third mode natural frequency depending on the field conditions as in the first and second modes. Figure 14a shows the natural frequencies in the torsional behavior (third mode) before removing the girder. It was observed that very similar natural frequencies occur on both sides. In Figure 14b, however, a difference of approximately 2.5 Hz occurred between the natural frequencies that are measured on both sides after the girder removal. This is because the fixed end effect of the upper girder disappeared with the girder removal; thus, restraining the torsional behavior. Figure 14c shows the natural frequency results for the torsional behavior (third mode) when a 1 m deep scour was simulated on one side of the pier. The natural frequency values were determined to be similar to those in Figure 14b, but the acceleration of the side with a 1 m deep scour exhibited a sharp reduction in the amplitude. This indicates that it is possible to predict the location and degree of the scour. Table 3 summarizes the

girder; and (**c**) 1 m deep scour on the ground adjacent to the pier.

confirmed that the presence of scour decreases the natural [29–31].

**Figure 14.** Third mode natural frequency for each field condition. (**a**) With a girder; (**b**) without a **Figure 14.** Third mode natural frequency for each field condition. (**a**) With a girder; (**b**) without a girder; and (**c**) 1 m deep scour on the ground adjacent to the pier.


**Table 3.** Natural frequency results of the field pier according to the presence of a scour.

#### simulated 1 m deep scour 9.5 14 60 62.5 **4. Discussion**

Without a girder and

#### **4. Discussion**  *4.1. Analysis of the Influence of the Surcharge Load through the Full-Scale Pier Test*

girder; and (**c**) 1 m deep scour on the ground adjacent to the pier.

*4.1. Analysis of the Influence of the Surcharge Load through the Full-Scale Pier Test*  Figure 15 presents the normalized natural frequency results of the full-scale pier for each mode number according to the surcharge load. As described above, the surcharge load was increased from 0 to 250 kN by 25 kN, and normalization was performed by assuming that the natural frequency that occurred for a surcharge load of 0 kN was 1. In the case of the first mode, the natural frequency showed a tendency to slowly decrease from 1 at 0 kN to 0.55 at 250 kN as the surcharge load increased. In the case of the second and third modes, however, the natural frequency was determined to be 1 or higher regardless of the surcharge load. Hence, the natural frequency of the structural system decreased with increasing mass, therefore the first mode of natural frequency increased eliminating the girder. The natural frequencies of the second and third mode are not significantly affected by the mass because the transverse direction is still stiffer than the longitudinal direction. For these modes, when the surcharge load was 200 kN or higher, it was not possible to calculate the natural frequency because clear signals could not be obtained. These results indicate Figure 15 presents the normalized natural frequency results of the full-scale pier for each mode number according to the surcharge load. As described above, the surcharge load was increased from 0 to 250 kN by 25 kN, and normalization was performed by assuming that the natural frequency that occurred for a surcharge load of 0 kN was 1. In the case of the first mode, the natural frequency showed a tendency to slowly decrease from 1 at 0 kN to 0.55 at 250 kN as the surcharge load increased. In the case of the second and third modes, however, the natural frequency was determined to be 1 or higher regardless of the surcharge load. Hence, the natural frequency of the structural system decreased with increasing mass, therefore the first mode of natural frequency increased eliminating the girder. The natural frequencies of the second and third mode are not significantly affected by the mass because the transverse direction is still stiffer than the longitudinal direction. For these modes, when the surcharge load was 200 kN or higher, it was not possible to calculate the natural frequency because clear signals could not be obtained. These results indicate that the mode number that was most affected by the surcharge load was the first mode.

that the mode number that was most affected by the surcharge load was the first mode.

**5. Conclusions** 

field pier test.

through the third mode.

all authors contributed to the writing of the paper.

*Appl. Sci.* **2020**, *10*, x FOR PEER REVIEW 14 of 17

**Figure 15.** Normalized natural frequency according to the surcharge load (first, second, and third modes). **Figure 15.** Normalized natural frequency according to the surcharge load (first, second, and third modes).

#### *4.2. Analyzing the Influence of the Scour through the Field Pier Test 4.2. Analyzing the Influence of the Scour through the Field Pier Test*

Figure 16 shows the normalized natural frequency results for each mode number according to the presence of a scour. Step 0 represents the test results with a girder and step 1 represents the test results after the girder removal. Step 2 represents the test results when the 1 m deep scour was simulated on one side of the ground that is adjacent to the pier. In the case of step 1, the natural frequency of the first mode decreased, but those of the second and third modes were similar. This is in agreement with the result of the full-scale model pier test that the second mode was not affected by the surcharge load. In the case of step 2, the natural frequencies of the first and second modes decreased, but the third mode remained similar. These findings indicate that the mode number that is most affected by the structural condition of the pier and the ground condition is the first mode. If the stability of a pier is evaluated using the first mode, it will be difficult to identify accurate problems. Therefore, it is reasonable to determine the boundary state of the ground that is adjacent to the pier using the second mode, which is affected by the scour in the ground, even though it is not affected by the surcharge load. In addition, the third mode is considered to be an effective method for determining the scour direction in the ground as described above in relation to Figure 12. Figure 16 shows the normalized natural frequency results for each mode number according to the presence of a scour. Step 0 represents the test results with a girder and step 1 represents the test results after the girder removal. Step 2 represents the test results when the 1 m deep scour was simulated on one side of the ground that is adjacent to the pier. In the case of step 1, the natural frequency of the first mode decreased, but those of the second and third modes were similar. This is in agreement with the result of the full-scale model pier test that the second mode was not affected by the surcharge load. In the case of step 2, the natural frequencies of the first and second modes decreased, but the third mode remained similar. These findings indicate that the mode number that is most affected by the structural condition of the pier and the ground condition is the first mode. If the stability of a pier is evaluated using the first mode, it will be difficult to identify accurate problems. Therefore, it is reasonable to determine the boundary state of the ground that is adjacent to the pier using the second mode, which is affected by the scour in the ground, even though it is not affected by the surcharge load. In addition, the third mode is considered to be an effective method for determining the scour direction in the ground as described above in relation to Figure 12. *Appl. Sci.* **2020**, *10*, x FOR PEER REVIEW 15 of 17

**Figure 16.** Normalized natural frequency according to the presence of the scour (first, second, and third modes). **Figure 16.** Normalized natural frequency according to the presence of the scour (first, second, and third modes).

frequencies and phase differences were calculated by measuring the acceleration, and the modal

1. Using the numerical analysis, the eigenvalue and mode number of the pier were derived according to the direction of impact. Based on this, the test method for the piers that can derive the first, second, and third modes was established through the full-scale model pier test and the

2. Through the full-scale model pier, the natural frequencies of the first, second, and third modes were derived when the surcharge load on the pier increased. It was determined that the natural frequency of the first mode decreased as the surcharge load increased, and the second and third

3. Through the field pier test, scour was simulated on the ground that was adjacent to the side of the pier to measure the natural frequency when the scour occurred. Due to the influence of the scour, the first mode exhibited the largest decrease in the natural frequency, followed by the second and third modes. In the case of the third mode, the amplitude of the acceleration was significantly small on the side that simulated the scour even though the natural frequency change was the smallest. This indicates that the direction of the scour can be determined

4. The results of the full-scale model pier test and the field pier test showed that the mode number that is most affected by the surcharge load and the scour is the first mode. If the stability of a pier is evaluated with the first mode, there are limitations in identifying accurate problems. Therefore, it is reasonable to determine the boundary state of the ground that is adjacent to the

5. These research results have a limitation for applying to other types of bridge piers and can be applicable to the deteriorated bridge with a shallow foundation and a plate girder. For further study, additional field tests and analysis will be performed and an indicator will be suggested

**Author Contributions:** M.L. organized the paperwork, made a test plan, performed the impact load test; M.Y. and H.-S.J. helped the data analysis; K.H.K. performs numerical analysis; I.-W.L. supported making a test plan;

pier by using the second mode, which is not affected by the surcharge load.

for applying other type foundations, such as pile foundation.

number of piers was analyzed. The results of the study are summarized as follows.

modes were not significantly affected by the surcharge load.

In this study, the dynamic response analysis was performed on a shallow foundation used as a
