**3.1 Bending test results**

**Figure 7** shows the load-displacement relationship at the rail seat, and **Table 5** shows applied loads of each state. In all cases, the cracking loads and ultimate loads were overdesign-proof and design-ultimate oriented. It can be confirmed that the bending of sleepers tends to soften gradually after the load exceeds cracking levels (i.e., around 110 kN). Both the cracking and ultimate loadings of Sleeper No. 9 in the posttension system are larger than those of Sleeper No. 1 in the pretension system. Although bending tests were performed at the right and left rail seats, explicit differences between the respective cases were not observed.

**Figure 7,** moreover, presents numerical calculation results. The results agree well with the experimental findings for pretension type Sleeper No. 1. A first crack occurred at the bottom of the rail seat as shown in **Figure 8**. The crack load is altogether depicted in **Table 5**, and the 112 kN cracking load agrees with the 111 kN

**Figure 7.** *Load-displacement envelope curve on bending test.*


**Figure 8.** *Contours of cracks at (a) 112 kN and (b) 184 kN applied loads.*

experimental result. For the ultimate state, three total cracks were found at the rail seat. This fracture mode is likewise consistent with the experimental one, as shown in **Figure 9**. Thus, it can be confirmed that the numerical model can accurately reproduce those realistically propagated in the damaged state.

**Figure 10** shows the crack-width at the bottom of the rail seat calculated by the numerical model. **Figure 10(a)** indicates the general trend of prestressed concrete and that the maximum width of the first crack, crack 2, becomes wider with increasing load. In contrast, **Figure 10(b)** shows the residual crack-width after unloading. Residual cracks first appeared after an approximate 170 kN loading, which is close to the ultimate load. This means that most opened cracks due to such a loading can ultimately close back together after unloading, due to residual prestresses.

#### **3.2 Modal identification results with bending tests**

**Figure 11** presents the time history and Fourier spectrum of measured accelerations at Sleeper No. 1 prior to the bending test. The vibrational measurements of Sleeper Nos. 1 and 9 (intact) were conducted based on TEST I, and the modal characteristics were identified by the ERA method.

**Figure 12** shows the identified and numerically calculated natural frequencies and modal shapes from the first to third modes of Sleeper No. 1. These numerical results were calculated using the calibrated numerical model. The model displayed a value of 1.3 times that of the nominal elastic modulus for concrete based on the core

**Figure 9.** *Photograph of cracking at ultimate condition.*

#### **Figure 10.**

*Relationship between maximum applied load and crack width: (a) maximum crack width under load and (b) residual crack width after unloading.*

**85**

**Figure 13.**

*bending mode.*

in **Figures 13** and **15**.

*Application of a Frequency-Based Detection Method for Evaluating Damaged Concrete Sleepers*

test result of Sleeper No. 1. The numerical and identified natural frequencies and

*Comparison of identified and calculated natural frequencies and mode shapes: (a)–(c) identified first-third* 

**Figures 13–15** show natural frequencies, modal damping ratios, and mode shapes of the first to third modes. These were identified by the ERA method using TEST I, which were conducted for each loading-unloading step. Numerical results, natural frequencies, and modal shapes, obtained by eigenvalue analysis, are shown

*Impact of applied load on natural frequency: (a) first bending mode; (b) second bending mode; and (c) third* 

modal shapes showed good agreement within each mode.

*bending mode; (d)–(f) calculated first-third bending mode of Sleeper No. 1.*

*Measured acceleration time history and spectrum on the midspan of Sleeper No. 1.*

**3.3 Impact of applied loads on modal characteristics**

*DOI: http://dx.doi.org/10.5772/intechopen.82711*

**Figure 11.**

**Figure 12.**

*Application of a Frequency-Based Detection Method for Evaluating Damaged Concrete Sleepers DOI: http://dx.doi.org/10.5772/intechopen.82711*

**Figure 11.**

*Advances in Structural Health Monitoring*

experimental result. For the ultimate state, three total cracks were found at the rail seat. This fracture mode is likewise consistent with the experimental one, as shown in **Figure 9**. Thus, it can be confirmed that the numerical model can accurately

**Figure 10** shows the crack-width at the bottom of the rail seat calculated by the numerical model. **Figure 10(a)** indicates the general trend of prestressed concrete and that the maximum width of the first crack, crack 2, becomes wider with increasing load. In contrast, **Figure 10(b)** shows the residual crack-width after unloading. Residual cracks first appeared after an approximate 170 kN loading, which is close to the ultimate load. This means that most opened cracks due to such a loading can

**Figure 11** presents the time history and Fourier spectrum of measured accelerations at Sleeper No. 1 prior to the bending test. The vibrational measurements of Sleeper Nos. 1 and 9 (intact) were conducted based on TEST I, and the modal

**Figure 12** shows the identified and numerically calculated natural frequencies and modal shapes from the first to third modes of Sleeper No. 1. These numerical results were calculated using the calibrated numerical model. The model displayed a value of 1.3 times that of the nominal elastic modulus for concrete based on the core

*Relationship between maximum applied load and crack width: (a) maximum crack width under load and* 

ultimately close back together after unloading, due to residual prestresses.

reproduce those realistically propagated in the damaged state.

**3.2 Modal identification results with bending tests**

characteristics were identified by the ERA method.

**84**

**Figure 10.**

**Figure 9.**

*Photograph of cracking at ultimate condition.*

*(b) residual crack width after unloading.*

*Measured acceleration time history and spectrum on the midspan of Sleeper No. 1.*

**Figure 12.**

*Comparison of identified and calculated natural frequencies and mode shapes: (a)–(c) identified first-third bending mode; (d)–(f) calculated first-third bending mode of Sleeper No. 1.*

test result of Sleeper No. 1. The numerical and identified natural frequencies and modal shapes showed good agreement within each mode.

#### **3.3 Impact of applied loads on modal characteristics**

**Figures 13–15** show natural frequencies, modal damping ratios, and mode shapes of the first to third modes. These were identified by the ERA method using TEST I, which were conducted for each loading-unloading step. Numerical results, natural frequencies, and modal shapes, obtained by eigenvalue analysis, are shown in **Figures 13** and **15**.

#### **Figure 13.**

*Impact of applied load on natural frequency: (a) first bending mode; (b) second bending mode; and (c) third bending mode.*

**Figure 14.**

*Impact of applied load on modal damping ratio: (a) first bending mode; (b) second bending mode; and (c) third bending mode.*

**Figure 15.**

*The impact of applied load on right rail seat (−0.45 m position in each figure) and modal shape: (a) first bending mode; (b) second bending mode; and (c) third bending mode.*

**Figure 13** indicates that the natural frequency decreases rapidly when the applied load reaches a value of 1.2 times the cracking load (about 130 kN) or greater. This tendency is consistent with the numerical model when a concrete crack remains open even after unloading. Thus, it is perceived that a reduction in bending rigidity due to an open crack has a greater impact on a decrease in natural frequency than other bending-damage modes such as the plasticizing of steel rods or stranded wires, or reduction of introduced pretension. As shown in **Figure 13**, the natural frequency of the third mode in the ultimate state drops by approximately 150 Hz (17%) in all samples. It can therefore be asserted that the agreement of location between a crack generation and a higher modal amplitude might cause these large decreases in natural frequency within the third mode.

**Figure 14** represents well-known large variations in mode-damping ratios. Some increasing tendencies of damping ratios due to increased applied loads can be seen in the first and second modes of Sleeper No. 9. Modal damping ratios are, however, difficult to apply as damage detection indicators due to a lack of certainty.

**Figure 15** shows the modal shapes of Sleeper No. 1 from bending tests conducted at the left rail seat. It is typically difficult to find the impact of loading influences on modal shapes. If a modal shape is ultimately adapted as a detection indicator, another challenge would be at hand in which the use of numerous sensors would be required for carrying out multipoint measurements.

**Figure 16** shows identified natural frequencies of concrete sleepers, in which damage has been generated during actual service. Vibration measurements were performed via TEST I on Sleeper Nos. 1–6 and 9–15 as shown in **Table 1**. Results of Sleeper Nos. 1 and 9 are representative of intact states prior to bending tests.

For the first mode frequency, some of the sleepers (e.g., Nos. 6 and 9) differ with the overall trend of decreasing frequency due to damage. The bending-tested Sleeper No. 6 and the intact Sleeper No. 9 have relatively high and low frequencies, respectively. Accordingly, it is not easy to detect damaged sleepers using first mode frequencies. With respect to the second mode, the frequencies of damaged sleepers

**87**

**Figure 16.**

*bending mode; and (c) third bending mode.*

*Application of a Frequency-Based Detection Method for Evaluating Damaged Concrete Sleepers*

are low in comparison to those of intact ones. The natural frequencies of Sleeper No. 14 with a steel rod fracture and Sleeper Nos. 6 and 15 after postloading are significantly reduced. For the third mode, frequencies of damaged sleepers are clearly less compared with those of intact ones. In essence, the overall tendency seems to point to the notion that severity of damage typically corresponds to a proportional decrease in frequency. An inconsistency in this trend can be seen only in Sleeper No. 5 which has cracks in nearly all areas and yet exhibits a slightly higher frequency than that of less-damaged Sleeper No. 2. Sleeper Nos. 2 and 5, however, show sufficient declines in frequency to be able to clearly identify their relative levels of damage. Thus, there were no hindrances to detect damaged sleepers when third bending frequencies were adopted as a detection index. Frequency-based damage detection is a well-known method based on simple concepts carried out through numerical analysis and laboratory tests; there are however, only limited examples of such application achievements within the civil structural domain. In response to this notion, this subject study strives to empirically validate the feasibility of a detection method using third bending mode frequency via experimental evaluation of actual damaged sleepers.

*Impact of actual damage and actual environment on natural frequency: (a) first bending mode; (b) second* 

For operational railway tracks, concrete sleepers are laid on supporting ballast, along with two rails and pads. In particular, ballast-supporting stiffness has been

**3.4 Impact of the actual environment on natural frequency**

*DOI: http://dx.doi.org/10.5772/intechopen.82711*

*Application of a Frequency-Based Detection Method for Evaluating Damaged Concrete Sleepers DOI: http://dx.doi.org/10.5772/intechopen.82711*

**Figure 16.**

*Advances in Structural Health Monitoring*

**Figure 14.**

**Figure 15.**

*bending mode.*

**Figure 13** indicates that the natural frequency decreases rapidly when the applied load reaches a value of 1.2 times the cracking load (about 130 kN) or

*The impact of applied load on right rail seat (−0.45 m position in each figure) and modal shape: (a) first* 

decreases in natural frequency within the third mode.

*bending mode; (b) second bending mode; and (c) third bending mode.*

required for carrying out multipoint measurements.

greater. This tendency is consistent with the numerical model when a concrete crack remains open even after unloading. Thus, it is perceived that a reduction in bending rigidity due to an open crack has a greater impact on a decrease in natural frequency than other bending-damage modes such as the plasticizing of steel rods or stranded wires, or reduction of introduced pretension. As shown in **Figure 13**, the natural frequency of the third mode in the ultimate state drops by approximately 150 Hz (17%) in all samples. It can therefore be asserted that the agreement of location between a crack generation and a higher modal amplitude might cause these large

*Impact of applied load on modal damping ratio: (a) first bending mode; (b) second bending mode; and (c) third* 

**Figure 14** represents well-known large variations in mode-damping ratios. Some increasing tendencies of damping ratios due to increased applied loads can be seen in the first and second modes of Sleeper No. 9. Modal damping ratios are, however,

**Figure 15** shows the modal shapes of Sleeper No. 1 from bending tests conducted at the left rail seat. It is typically difficult to find the impact of loading influences on modal shapes. If a modal shape is ultimately adapted as a detection indicator, another challenge would be at hand in which the use of numerous sensors would be

**Figure 16** shows identified natural frequencies of concrete sleepers, in which damage has been generated during actual service. Vibration measurements were performed via TEST I on Sleeper Nos. 1–6 and 9–15 as shown in **Table 1**. Results of Sleeper Nos. 1 and 9 are representative of intact states prior to bending tests. For the first mode frequency, some of the sleepers (e.g., Nos. 6 and 9) differ with the overall trend of decreasing frequency due to damage. The bending-tested Sleeper No. 6 and the intact Sleeper No. 9 have relatively high and low frequencies, respectively. Accordingly, it is not easy to detect damaged sleepers using first mode frequencies. With respect to the second mode, the frequencies of damaged sleepers

difficult to apply as damage detection indicators due to a lack of certainty.

**86**

*Impact of actual damage and actual environment on natural frequency: (a) first bending mode; (b) second bending mode; and (c) third bending mode.*

are low in comparison to those of intact ones. The natural frequencies of Sleeper No. 14 with a steel rod fracture and Sleeper Nos. 6 and 15 after postloading are significantly reduced. For the third mode, frequencies of damaged sleepers are clearly less compared with those of intact ones. In essence, the overall tendency seems to point to the notion that severity of damage typically corresponds to a proportional decrease in frequency. An inconsistency in this trend can be seen only in Sleeper No. 5 which has cracks in nearly all areas and yet exhibits a slightly higher frequency than that of less-damaged Sleeper No. 2. Sleeper Nos. 2 and 5, however, show sufficient declines in frequency to be able to clearly identify their relative levels of damage.

Thus, there were no hindrances to detect damaged sleepers when third bending frequencies were adopted as a detection index. Frequency-based damage detection is a well-known method based on simple concepts carried out through numerical analysis and laboratory tests; there are however, only limited examples of such application achievements within the civil structural domain. In response to this notion, this subject study strives to empirically validate the feasibility of a detection method using third bending mode frequency via experimental evaluation of actual damaged sleepers.

#### **3.4 Impact of the actual environment on natural frequency**

For operational railway tracks, concrete sleepers are laid on supporting ballast, along with two rails and pads. In particular, ballast-supporting stiffness has been

historically measured in large variations [33]. Thus, a superior detection indicator should not only be sensitive to damage but also "insensitive" to the states of other track members such as ballast and pads. In order to validate the feasibility of frequency-based damaged-sleeper detection in the actual field, potential impacts from the external environment were investigated. Vibration measurement TEST II and modal identification were hence conducted on intact concrete Sleeper Nos. 17–22, which were on a test line within Railway Technical Research Institute premises.

**Figure 16** presents the identified natural frequencies of Sleeper Nos. 17–22. A large variation could be confirmed in the first and second bending modes. It can thus be asserted that the variation of specifications in other track members causes this large variation because completely intact concrete sleepers themselves all display the same properties. On the other hand, the variations in the third bending mode are small. These empirical results are consistent with the trends pointed out in the existing literature [22], in which the variation of ballast-supporting stiffness mainly affects low-order modes, such as first and second bending. These results therefore imply that the third bending mode frequency is a suitable detection indicator, which consistently exhibits desirable characteristics for efficient damaged-sleeper detection, as described above.
