**5. Drop-weight impact loading test**

The author repeatedly performed drop-weight impact loading tests using a full-scale mock-up of the ballasted track, dropping a steel weight from a given height and applying impact loads having a sharp pulse shape directly to the track structure. **Figure 8(a)** presents an overview of the test device. **Figure 8(b)** depicts the positions of sensors used for the measurements. The test setup consists of a 30 cm-thick ballast layer built with new andesite ballast gravel on a concrete roadbed. A track structure was built using three pieces of type 3 PC sleepers and two pieces of rails weighing 60 kg/m. The steel weight frame, positioned over the sleeper at the centre, was dropped repeatedly from the given height to apply impact loads to the track structure. Measured data for the magnitude of the impact loads, the vertical displacement of

**Figure 8.** Overview of impact loading test. (a) Drop-weight impact test device, (b) sensor positions.

ballasted track explained in the preceding paragraph. These curves identify the rigid-body resonance mode of the ballast layer around 100 Hz and indicate another large peak profile at around 300 Hz. From the full-scale experiment presented in **Figure 3**, the rigid-body natural

**Figure 7.** Distribution of vertical loading at the bottom of the sensing sleeper and normalized displacement at the top of

**Figure 7** shows the relation between the two-dimensional distribution of the vertical loading on the bottom surface of the sleeper and the normalized vertical displacement of the sleeper in cases of two frequencies (110 and 310 Hz), which give the peak profiles of the response curves. In the figures, *θ* denotes the relative phase angles with reference to vertical motion at the centre of the sleeper. In the distribution maps, red denotes the positive load (compression). Blue shows the negative load (tension). Regarding the sleeper motion, the downward direction indicates the downward behaviour of the sleeper. The upward direction indicates the upward behaviour of the sleeper. Panels (a) and (b) show that the sleeper repeats a vertical periodic movement at these frequencies, entailing bending deformation of the sleeper at high

The author repeatedly performed drop-weight impact loading tests using a full-scale mock-up of the ballasted track, dropping a steel weight from a given height and applying impact loads having a sharp pulse shape directly to the track structure. **Figure 8(a)** presents an overview of the test device. **Figure 8(b)** depicts the positions of sensors used for the measurements. The test setup consists of a 30 cm-thick ballast layer built with new andesite ballast gravel on a concrete roadbed. A track structure was built using three pieces of type 3 PC sleepers and two pieces of rails weighing 60 kg/m. The steel weight frame, positioned over the sleeper at the centre, was dropped repeatedly from the given height to apply impact loads to the track structure. Measured data for the magnitude of the impact loads, the vertical displacement of

vibration mode of the ballasted track appears at 98 Hz.

the sleeper (measured).

110 New Trends in Structural Engineering

frequencies, in synchronization with the phase angles.

**5. Drop-weight impact loading test**

the sleepers and the acceleration responses of sleepers and ballast were recorded by sampling the data at 10 kHz or 20 kHz. This chapter presents a discussion of the measurement results of the displacement responses of the sleepers [9, 13].

**Figure 9(a)** shows the time history response of the centre sleeper's vertical displacement after impact loading. This average curve shows results obtained from about 4000 loading tests, excluding initial loading of the first 1000 iterations. The downward displacement in the chart shows the ballast layer compression. The upward displacement represents extension of the ballast layer. **Figure 9(b)** especially depicts data obtained at the moment immediately after loading. The average value of the impact load on the ballast through the left and right rails was 217 kN. The figure shows that because of the compression applied by an impact load, the ballast layer instantaneously deforms elastically. The compression produces maximum downward displacement of 0.178 mm in 0.71 ms. Subsequently, it returns to the preloading

**Figure 9.** Vertical displacement of sleepers immediately after impact loading. (a) Sleeper displacement, (b) close-up of displacement.

position in 1.1 ms. Results show that only about 1 ms is necessary for the ballast layer compression and restoration. Displacement responses of the sleeper and load during that time include few vibration components at low frequencies.

mesh size of 1 cm was adopted to support the precise representation of natural frequencies of

**Figure 10.** Exemplary pictures of existing ballasts and the digitized models. (a) Ballast, (b) DEM model, (c) FEM model.

*E* = 30 (GPa), Poisson's ratio *ν* = 0.2 and structural damping parameter *η* = 0.01 are adopted. The ballast gravel density was the laboratory experimental value obtained from specific gravity tests. The Young's moduli and Poisson's ratio were referred or derived from previous reports of the literature. Regarding the structural damping coefficient, the author adopted

**Figure 11** presents a procedure for the creation of the ballast aggregate using both discrete element and finite element modeling. First, about 100 pieces of the ballast polyhedron discrete element models with different shapes and sizes were placed randomly in the air above rectangular box frames of 20 cm width and length. The gravel was then dropped freely with gravity and was compressed vertically with a loading plate using discrete element software. Next, all individual polyhedron discrete element models were converted into assemblages consisting of the small finite tetrahedron second-order elastic solid elements and split into 1 cm meshes with geometry and contact point information maintained. Each polyhedron discrete element model was divided into approximately 1000 tetrahedron finite elements. The finished rectangular block model has 20 cm width and length, with 17 cm height, and has more than 90,000 tetrahedron finite elements.

), Young's modulus

Vertical Natural Vibration Modes of Ballasted Railway Track

http://dx.doi.org/10.5772/intechopen.79738

113

Regarding the physical properties of the ballast, density *ρ* = 2700 (kg/m3

individual ballast gravel up to several 10 kHz.

**Figure 11.** Compaction and modeling of the ballast aggregate with MPCs.

general values of a concrete structure.

Following the compression and restoration motions of the ballast layer, sleeper-jumping occurs. The average jumping speed is approximately 1.71 times as high as the average of the compression speed. Their initial speed can be approximately 12.1 times faster than the average compression speed. The jumping height of the sleeper reaches 5.1 mm in 24.4 ms. The sleeper returns to the initial position within 46.7 ms after loading. The jumping behaviour during unloading includes no high-frequency vibration component. Most of the vibration comprises low-frequency components. The author posits that the cause of sleeper-jumping is the abrupt release of the strain energy stored in the ballast.

**Figure 9**, as described, presents the vertical displacement of the sleeper. Presumably, similar behaviour occurs in the upper part of the ballast layer immediately under the sleepers, which means that the motion under impact loading is extremely slight. The compression and restoration behaviours are high-frequency responses that last for a very short time: about 1 ms. Therefore, high-frequency vibration components are dominant in ballast responses under loading. However, ballast motions during unloading are induced mainly by low-frequency vibration components that cause large displacement and which last longer.
