**Author details**

Teng Wang1,2\*, Yanmei Ding1,2, Wangchun Zhang1,2 and Yu Song1,2,3

\*Address all correspondence to: wangteng2035@163.com

1 Key Laboratory of Protected Horticulture, Shandong provincial Education Department, Weifang, China

2 Architectural and Civil Engineering Institute, Weifang University of Science and Technology, Weifang, China

3 Western Engineering Research Center of Disaster Mitigation in Civil Engineering of Ministry of Education, Lanzhou University of Technology, Lanzhou, China

## **References**

**6. Conclusions**

(b) dip 250 All values contrast.

98 New Trends in Structural Engineering

forcement design.

**Author details**

Weifang, China

Technology, Weifang, China

ductile failure of concrete in compression.

improves the beam's structural performance.

1. The load-deflection curve for a RC SSB can be divided into four portions, which correspond to the four deformation stages: elastic deformation, yielding, hardening, and failure. The RC beam specimens failed in two modes: brittle failure of external tendons and

**Figure 15.** Comparison of simulation value and test value of related specimens. (a) Dip 200 All values contrast and

**2.** The application of DWM external prestressing results in redistribution of stress at the cross-section of the RC beam, which allows the materials to make greater contribution and

**3.** The theoretical calculation method proposed can deliver reliable results for the stage of

**4.** Small tendon cross-sectional areas and high initial stress are not recommended for rein-

1 Key Laboratory of Protected Horticulture, Shandong provincial Education Department,

2 Architectural and Civil Engineering Institute, Weifang University of Science and

Ministry of Education, Lanzhou University of Technology, Lanzhou, China

3 Western Engineering Research Center of Disaster Mitigation in Civil Engineering of

elastic deformation and provide a basis for applications in practice.

Teng Wang1,2\*, Yanmei Ding1,2, Wangchun Zhang1,2 and Yu Song1,2,3

\*Address all correspondence to: wangteng2035@163.com


**Section 4**

**Vibration Control**

**Section 4**

**Vibration Control**

**Chapter 5**

**Provisional chapter**

**Vertical Natural Vibration Modes of Ballasted Railway**

Impact loads from running trains induce natural vibration within the ballast layer, which causes ballast deterioration over time. This study measured the natural vibration characteristics of the ballast layer using field measurements, full-scale impact loading experiments and large-scale finite element analysis. Experimental test results indicate that the vibration components in the high-frequency range are dominant in ballast responses under loading and that ballast motions during unloading are mainly induced by vibration components in the low-frequency range, causing large displacement over a long duration. Numerical results indicate that the normal frequency of the vertical elastic vibration mode is detected at approximately 310 Hz and that the rigid-body bounce mode of the ballast layer occurs at one-third of the elastic vibration mode frequency. They coincide substantially with values held by field measurements. Stress acting on the angular part of the ballast is more than 1000 times greater than the average loading stress under the sleeper bottom. The combined structure, which consists of the ballast layer and sleepers, vibrates easily in synchrony with resonance motions induced by the impulse waves. Improvement of the contact condition on the sleeper bottom is expected to decrease the

displacement amplitude of ballast gravel, thereby reducing ballast degradation.

**Keywords:** impact loads, natural vibration of granular layer, full-scale impact loading

A ballasted track is characterized by its structure, with a ballast layer sandwiched between sleepers and a roadbed, which greatly reduces impact loads generated by dynamic rolling contact interaction between the wheels and rails. However, this benefit has an adverse effect:

**Vertical Natural Vibration Modes of Ballasted** 

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

DOI: 10.5772/intechopen.79738

**Track**

Akira Aikawa

Akira Aikawa

**Railway Track**

**Abstract**

**1. Introduction**

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

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

experiments, tensionless analysis

#### **Vertical Natural Vibration Modes of Ballasted Railway Track Vertical Natural Vibration Modes of Ballasted Railway Track**

DOI: 10.5772/intechopen.79738

#### Akira Aikawa Akira Aikawa

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

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

#### **Abstract**

Impact loads from running trains induce natural vibration within the ballast layer, which causes ballast deterioration over time. This study measured the natural vibration characteristics of the ballast layer using field measurements, full-scale impact loading experiments and large-scale finite element analysis. Experimental test results indicate that the vibration components in the high-frequency range are dominant in ballast responses under loading and that ballast motions during unloading are mainly induced by vibration components in the low-frequency range, causing large displacement over a long duration. Numerical results indicate that the normal frequency of the vertical elastic vibration mode is detected at approximately 310 Hz and that the rigid-body bounce mode of the ballast layer occurs at one-third of the elastic vibration mode frequency. They coincide substantially with values held by field measurements. Stress acting on the angular part of the ballast is more than 1000 times greater than the average loading stress under the sleeper bottom. The combined structure, which consists of the ballast layer and sleepers, vibrates easily in synchrony with resonance motions induced by the impulse waves. Improvement of the contact condition on the sleeper bottom is expected to decrease the displacement amplitude of ballast gravel, thereby reducing ballast degradation.

**Keywords:** impact loads, natural vibration of granular layer, full-scale impact loading experiments, tensionless analysis

### **1. Introduction**

A ballasted track is characterized by its structure, with a ballast layer sandwiched between sleepers and a roadbed, which greatly reduces impact loads generated by dynamic rolling contact interaction between the wheels and rails. However, this benefit has an adverse effect:

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The ballasted tracks are structurally prone to deteriorate over time. They absolutely require periodic maintenance work and repair. Recently, many attempts were made to improve the ballasted track structure. For example, many types of elastic and/or viscoelastic structural members, such as rail pads, under-sleeper pads and under-ballast mats, were attempted to reduce ballast degradation [1–3]. In one experimental investigation, the sleeper's vibration characteristics, including the dynamic effects of sleeper/ballast interactions, were investigated through a modal analysis to predict the railway track's dynamic response [4]. Dynamic wheel/ rail interactions, which significantly contribute to impact vibration and noise, were also investigated for rail and wheel surface defects in field measurements and numerical simulations [5–8]. When considering the future of the railway management, it is impossible to disregard the necessity for frequent maintenance that is dependent upon manual aid. Therefore, the need exists to improve maintenance methods for the ballasted track based on findings from empirical and numerical investigations of the dynamic response characteristics and deterioration factors of the ballast layer.

**2. Rigid-body bounce vibration mode and elastic natural vibration** 

In general, a dynamic load propagates as an elastic wave through the interior of an object, consequently inducing the natural vibration modes specific to the object, which can be applied to the ballasted track composed of the ballast aggregate. Although the ballast layer is a discontinuous structure, it presumably has natural vibration modes that are specific to the ballasted track. **Figure 1** shows some characteristics of the principal natural vibratory motions in the vertical direction of the ballast layer [20]. One characteristic is the rigid-body bounce natural vibration mode. Another is the elastic shrinkage natural vibration mode. The ballasted track structure represents a single degree of freedom system that includes sleepers, rails and other components which constitute the track structure mass, along with the ballast layer and roadbed which constitute the spring rigidity component. In the bounce natural vibration mode, this single degree of freedom system moves vertically and rigidly under a train's dynamic load. The ballast layer acts as an elastic one-directional spring in the vertical direction. Rigid-body natural vibration modes of six kinds exist: They are translational and rotational along each of the three axes. In both the dynamic loads applied to the ballast layer and in the responses of the ballast layer, the translational vibration components in the vertical

Therefore, this research specifically examines the translational bounce behaviour in the vertical direction. According to the dynamics, the natural frequency of the first-order rigid-body

ballast stiffness and overburden mass of the track structure. This mode reportedly exists at

The elastic vibration mode is the motion by which the whole ballast layer shrinks and stretches vertically as an elastic body. This natural vibration mode is considered not to occur in a normal-state ballast layer but to occur when the ballast layer is under high confining pressure generated by the train's weight applied to the layer. To date, no report of the relevant literature has described a study conducted to capture this mode, that is, ballast motion in the frequency domain related to this mode. Moreover, on a real track, natural vibration that

**Figure 1.** Principal vertical natural vibration motions of the ballast layer. (a) Rigid-body bounce mode, (b) elastic

*k*/*m*/(2*π*), where *k* and *m*, respectively, denote the

Vertical Natural Vibration Modes of Ballasted Railway Track

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

105

<sup>1</sup> = √ \_\_\_\_

**mode**

direction are predominant.

1

is given theoretically as *f*

bounce mode *f*

shrinkage mode.

approx. 100 Hz [21].

Running trains cause dynamic loads mainly through two mechanisms [9, 10]. One is the dynamic load from passing axle loads as a train passes. The related frequency characteristics, which depend on the number of axles passing per unit of time, are limited to low frequencies of only several Hertz to approximately 30 Hz. The other mechanism is the impact load that is generated dynamically by the rolling contact mechanism between the wheels and rails. The ballast layer transmits this sharp pulse-shaped impact load superimposed on the low-frequency loads from passing axles. This waveform, when transformed into a frequency domain, exhibits numerous vibration components with broadband characteristics that extend from low frequencies to several kilohertz. That is to say, dynamic response measurements of the ballasted track require high-precision measurements of vibration components ranging broadly from several Hertz to several kilohertz. Outputs of sensor would be degraded by noise of tens of millivolts deriving from the inductive currents of high-voltage overhead cables in conventional field measurements, which necessitated the use of a low-pass filter to alleviate that interference. Ensuring the measurement accuracy of high-frequency vibration components exceeding 50–100 Hz was impossible under such conditions. For that reason, no comprehensive discussion of these components has been reported in the literature to date.

This chapter gives accurate field measurements of the dynamic responses of the ballasted track with a train passage at a sampling frequency of 10 kHz without low-pass filters, using special sensing sleepers and sensing stones produced by the authors [11, 12]. Using the measurement effects, the analysis can be done with a focal point on propagation characteristics of dynamic loads inside the ballast layer and vertical natural modes of the ballast layer. Moreover, the author conducted a free fall-weight impact loading test on a full-scale mock-up of a ballasted track to ascertain the response motions of the ballast layer, with high rapidity and with high accuracy, in the high-frequency region immediately after the impact load was used [13]. Furthermore, using a direct solver MUMPS [14–17] corresponding to large-scale parallel computing of a distributed memory type, according to finite element transient response analysis FrontISTR [18] and Advance/FrontSTR [19] based on a fine ballast aggregate model, both the elastic natural vibration mode and the rigid-body bounce natural vibration mode of the granular ballasted layer are simulated numerically.
