PAPERS
A Simple Method for Predicting Track Settlement Caused by Culvert Pipe Damage
2025 Volume 66 Issue 2 Pages 78-83
Details
2025 Volume 66 Issue 2 Pages 78-83
In this study, we developed a nomogram to easily predict track settlement due to culvert pipe damage. First, a calculation method was developed to estimate the reduction ratio of the subgrade reaction coefficient under railway tracks. The accuracy of this method was verified by comparison with trap-door tests and field tests. Secondly, to produce the nomogram, we calculated track displacement under conditions of reduced subgrade reaction.
In railway embankments, small-diameter ceramic pipes are buried divert the water source around or under the track. If these culvert pipes are damaged (Fig. 1), the surrounding ground may become loose. There is a possibility that the subgrade reaction force under the track will decrease, leading to settlement of the track (Fig. 2).
To ensure safe train operation, railway operators regularly need to inspect and repair culvert pipes. However, this work is time-consuming because there are many culvert pipes in railway embankments, often hidden in the grass (Fig. 3).
In this study, we developed a nomogram to easily predict track settlement caused by culvert pipe damage (Fig. 4). By plotting the pipe diameter and depth on this nomogram, railway operators can understand the degree of track settlement. This information helps to determine more accurately the priority and frequency of inspections of the culvert pipes. First, we developed a calculation method to estimate the reduction ratio of the subgrade reaction coefficient under railway tracks when a culvert pipe is damaged. The accuracy of this method has been verified through laboratory tests and field tests. Secondly, we used this method to calculate track settlement under various conditions and prepared a nomogram by aligning these calculation results with track management values.
The calculation method created in this study is shown in Fig. 5, and the calculation steps are as follows:
Step 1: Divide the ground into two layers at the top of the loosened area (layer1 below the boundary and layer2 above the boundary). It is assumed that the height of the loosened area is equal to the diameter of the pipe.
Step 2: Assuming there is a ground surface beside the pipe, calculate the reduction ratio (λ) of the ground reaction coefficient on the top surface of Layer 1. The reduction ratio (λ) is calculated using a method for designing foundations near slopes, as described in the ‘Design Standards and Commentary for Railway Structures (Foundation Structures)’[1]. In this method, the ultimate bearing capacity near the slope and on level ground is calculated and their ratio is used as a reduction factor for the ground reaction coefficient (k). In this study, we calculated the ultimate bearing capacity of ground surfaces on level ground and used their ratio as the reduction ratio (λ).
Step 3: With stress propagating at an angle of 30 degrees from the edge of a sleeper in Layer 2, calculate the average reduction ratio (λ') on the top surface of Layer 2.
To verify the accuracy of the calculation method shown in Fig. 5, we conducted a model experiment known as a ‘trap-door test’ and carried out simulation analysis using the calculation method. The trap-door test is a geotechnical model test used to study the behavior of soil and structures under specific conditions. In this test, a model ground is constructed within a soil tank, and a portion of the tank floor, referred to as the ‘trap door,’ is gradually lowered. This test has been widely used to simulate ground loosening caused by tunnel excavation. In this study, we simulated ground conditions after culvert pipe damage, with a semi-circular culvert pipe fixed on top of the trap door that was gradually lowered.
The experimental apparatus is shown in Fig. 6, and the test procedure is detailed in Fig. 7. The ground material used was dry silica sand No. 7, compacted to achieve a target relative density of 70%. We carried out trap-door tests by varying the overburden.
Figure 8 shows the relationship between the horizontal distance from the center of the culvert pipe and the reduction ratio of the subgrade reaction coefficient. It can be seen that these results are generally in agreement with each other.
Field tests were carried out at three sites where culvert pipe collapses were observed using a borehole camera. The internal strength of the ground was measured using a surface wave exploration test, and a portable falling weight deflectometer (FWD) test was carried out to measure the distribution of the ground reaction coefficient on the ground surface.
At two of these sites with higher shear wave velocity, the ground reaction coefficient did not decrease above the culvert pipe. On the other hand, at the site with lower shear wave velocity compared to the other two sites, the ground reaction coefficient decreased above the culvert pipe. The detailed results of these investigations for one of the higher shear wave velocity sites (Site 1) and the lower shear wave velocity site (Site 2) are described in the next section.
2.3.1 Test results of site 1Figure 9 shows the results of the surface wave exploration test carried out along lines A-A' and B-B' (Fig. 10). The results indicate that a layer with high shear wave velocity is distributed near the ground surface. Table 1 shows the results of the portable FWD test, where significant differences were not observed above the culvert pipe. The K30 values were approximately 70 - 80 MN/m3, meeting the requirements specified in the ‘Design Standards for Railway Structures and Commentary (Earth Structures)'[2].
| ① | ② | ③ | ④ | ⑤ | |
| K30 (MN/m3) | 69.0 | 71.1 | 67.4 | 80.7 | 81.0 |
There are also two culvert pipes: Pipe A, which has a large soil cover, and Pipe B, which has a small soil cover (Fig. 11). Since this is an abandoned railway line, the track and facilities have been removed.
Figure 12 shows the results of the surface wave exploration test. These results indicate that a layer with low shear wave velocity is distributed near the ground surface, and that Pipe B is located within this layer. Table 2 shows the results of the portable FWD test. It can be seen that the K30 value is lower above Pipe B. The value at point 1 was approximately 70% lower than the value at point 3. This result indicates that the impact of the pipe B damage appeared on the ground surface due to the weak soil conditions.
| ① | ② | ③ | ④ | ⑤ | |
| K30 (MN/m3) | 30.3 | 84.6 | 104.5 | 167.1 | 176.7 |
Figure 13 shows the relationship between the field test results (Pipe B at Site 2, where a decrease in the ground reaction coefficient was observed) and the calculated values. It is apparent that the calculated values are about 10-20% smaller. For other field test results where the ground reaction coefficient did not decrease, the calculated values showed that the ground reaction coefficient ratio above the culvert pipe was also approximately 20% smaller.
The result was that the calculation method can safely estimate the reduction ratio of the ground reaction coefficient in the field.
Figure 14 shows the calculation conditions used to produce the nomogram. The train load was assumed to be in accordance with EA-17 and a crossing angle of 30° between the track and the culvert pipe was taken into account. Although actual culvert damage would be partial, it was assumed that the pipe was completely damaged.
The limit values for track settlement were set at two levels: Limit 1 is set at 6 mm, which is 0.4 times the standard track management value of 15 mm for conventional lines (Class 1, vertical displacement, static value). Limit 2 is set at 10 mm, which is 0.7 times the standard value.
The coefficient of subgrade reaction of the original ground is calculated using the K30 value (70 MN/m3) required for railway embankment Performance Rank II, which is commonly used for conventional lines. The types of soil used in the calculations are shown in Table 3. The cohesion and internal friction angle for the calculations were determined from triaxial compression test results using samples extracted from the existing embankment (Fig. 15).
| Types of soil | Category | γt (kN/m3) |
| Soil 3 (sand and gravel with poor particle size distribution, sandy soil, etc.) |
GF, GF-S, GFS SF, SF-G, SFG |
16 |
| Soil 4 (cohesive soil, etc.) |
ML, CL, MH, CH OL, OH, OV, Pt, Mk VL, VH1, VH2 |
14 |
Table 4 shows examples of the nomogram produced for different ground conditions. The nomogram categorizes the impact as small if it is below Limit 1, medium if it is between Limit 1 and Limit 2, and large if it is above Limit 2. In all cases, the larger the pipe diameter or the shallower the depth, the greater the impact on the track. It is also clear that a lower cohesion and internal friction angle will result in a larger area of high impact.
| φ=12° | φ=17° | |
| c=30 kPa |
;%0A%09%09%09newWindow.document.open();%0A%09%09%09newWindow.document.write('<img src=%22./Graphics/02-1016.png%22>');%0A%09%09%09newWindow.document.close();%0A%09%09)
|
;%0A%09%09%09newWindow.document.open();%0A%09%09%09newWindow.document.write('<img src=%22./Graphics/02-1017.png%22>');%0A%09%09%09newWindow.document.close();%0A%09%09)
|
| c=10 kPa |
;%0A%09%09%09newWindow.document.open();%0A%09%09%09newWindow.document.write('<img src=%22./Graphics/02-1018.png%22>');%0A%09%09%09newWindow.document.close();%0A%09%09)
|
;%0A%09%09%09newWindow.document.open();%0A%09%09%09newWindow.document.write('<img src=%22./Graphics/02-1019.png%22>');%0A%09%09%09newWindow.document.close();%0A%09%09)
|
Area A: Track settlement is large
Area B: Track settlement is moderate
Area C: Track settlement is small
Additionally, since the cohesion and internal friction angle of the embankment are often unknown in the field, a consolidated nomogram is produced (Fig. 3).
The results obtained from this study are summarized as follows:
(1)As a result of comparative verification with model experiments, it was confirmed that the calculation method developed in this study is applicable for calculating the distribution of the subgrade reaction coefficient under the track when a culvert pipe is damaged.
(2)Comparative verification with on-site portable FWD tests showed that the calculation method developed in this study can safely estimate the distribution of subgrade reaction coefficients under the track.
(3)A nomogram has been developed to easily evaluate the impact on the track by calculating the track settlement under various conditions. This nomogram helps to determine more accurately the priority and frequency of inspections of the culvert pipes.
The method for calculating the reduction ratio of subgrade reaction coefficients developed in this study tends to produce values that are approximately 20% on the safe side. Additionally, conservative conditions were used to produce the nomogram. It is therefore possible to estimate the impact with higher accuracy by further in-depth analysis. We are currently working on revising the chart through comparative verification with actual field conditions. Furthermore, this nomogram evaluates the impact immediately after the culvert pipe is damaged. If soil erosion into the pipe occurs due to prolonged rainfall after the damage, the impact may change. We are currently investigating this aspect and will report on new findings in due course.
|
Takashi NAKAYAMA, Dr.Eng. Senior Researcher, Tunnel Engineering Laboratory, Structures Technology Division Research Areas: Tunnel Engineering |
|
Yu OHARA
Researcher, Tunnel Engineering Laboratory, Structures Technology Division Research Areas: Tunnel Engineering |
|
Akihiko MIWA
Assistant Senior Researcher, Tunnel Engineering Laboratory, Structures Technology Division Research Areas: Tunnel Engineering |
|
Takaki MATSUMARU, Dr.Eng Senior Researcher, Foundation & Geotechnical Engineering Laboratory, Structures Technology Division Research Areas: Geotechnical Engineering |
