1 Introduction

The rapidly developing track transportation system in the frozen regions of northern and western China has brought not only environmental problems, but also damage risk to frozen soils, particularly in permafrost. Frozen soil damage has become an important issue affecting traffic safety and its sustainable development in cold regions. Generally speaking, frozen soil subsidence and large deformations are typical hazards due to track vibration loads, especially for express track systems. Soil vibration characteristics and responses arefundamental problems in soil deformation and subsidence mechanisms trigged by traffic vibration. Although research on traffic vibration mechanism and its action on soil and structure have a long history, very few studies involve soil dynamic response of movingtraffic loads under railways(Sheng et al., 1999; Hall, 2003; Takemiya, 2003;Zhang, 2007). In order to explore the vibration characteristics of frozen soil and assess the potential hazard due to moving track load, the seismic observation array technique(SOA) and finite element analysis(FEA)are presented in this paper to provide vibration signals and simulate frozen soil dynamic response under moving traffic load. Based on SOA and FEA, the relationship betweensoil dynamic characteristic with traffic vibration frequency and moving velocity was analyzed. The vibration attenuation characteristics was also studied, which may be helpful for foundation design to resist traffic vibration damage and environmental protection in cold regions, particularly for the rapidly developing railway system in Qinghai Province, Tibet and Northern Heilongjiang Province.

2 Vibration characteristics based on seismic observation array

Seismic observation array technology(SOA)is a common tool in monitoring seismic waves and its propagation during earthquakes or micro tremors. In general, SOA consists of at least five sets of seismographs, installed according to signal capturing requirements. In this paper, a linear and rectangular SOA were set up to monitor vibration signals of frozen soil along the Daqing-Harbin Railway line, perpendicular and parallel to the track line, respectively(Figure 1). The linear array was used to study the relationship of vibration characteristics at a remote distance from the track line. The rectangular array was applied to explore the vibration field of frozen soil when the train entered and exited the array. Typical vibration signals are presented in Figures 2a, b. According to field observation tests, one can get a sense of how vibration characteristics and it spatial distribution in frozen soils operate.

Based on acceleration power spectrum analysis, the vibration frequency changes from 10 to 80 Hz, the predominant frequency is 15-60 Hz(Figure 2c), herein, the frozen soil temperature is −2 °C, and train velocity is about 60 km/h. In linear SOA, vibration characteristics are different in space, not only the amplitude, but also wave form, and the vibration has an obvious attenuation with increasing distance from the track line(Figure 2a). Based on the 20 time-history in the linear array, the maximum acceleration amplitudes in the three directions have obvious attenuation tendency(Table 1). However along the track line or perpendicular to track line, from track line to 20 m, the acceleration attenuation in the vertical direction is more rapid decreasing than that in the horizontal surface. From 20 to 50 m, the acceleration has a similar propagation attenuation rate, but from 50 to 60 m, the acceleration has a small increasing and the attenuation is much slower. The predominant frequency is 54 Hz(P1), 34 Hz(P2), 46 Hz(P3), 26 Hz(P4) and 22 Hz(P5), respectively. Thus, the number of high frequency vibrations increases closer to the track line. The SOA test has also detected that the weight of train has effect on the vibration due to the running track, including the acceleration and frequency of vibration in vertical and horizontal directions(Figure 3). Overall, train velocity, frozen soil temperature and water content, and stratum structure of the soil have a dramatic effect on vibration characteristics.

Based on 50 observation tests and 813 records, considering train velocity, unevenness of track and foundation, bump of the train, wheel weight, and referring to models of Volberg(1983), Pan(1994), and Yoshioka(2000), the train vibration load model can beconstructed:

$\begin{array}{l} F(t) = {k_1}{k_2}{F_0}(t)\\ = {k_1}{k_2}({P_0} + {P_1}\sin {\omega _1}t + {P_2}\sin {\omega _2}t + {P_3}\sin {\omega _3}t) \end{array}$

(1)

where, k₁ is the coefficient which reflect the superposition characteristics of every wheel dynamic loads produced by an entire train in the line direction, in general, the value of k₁ is 1.2-1.7, herein, k₁=1.538. k₂ is the coefficient of the dispersed value of one of every five sleepers to bear one wheel load, k₂=0.7(in general, k₂ ranges from 0.6to 0.9). P₀ is static loads of every wheel; P₁, P₂, P₃ are amplitude of vibration dynamic loads with respect to unevenness of track and foundation. Generally, if the mass is M₀, then P_i will be calculated by following equation:

${P_i} = {M_0}{a_i}\omega _i^2$

(2)

where, M₀is the total mass of track and train mass, a_i is the wave-amplitude of unevenness of track and foundation, which is used to describe the unevenness characteristics of track and foundation. ω_i is the vibration frequency of track and train, which is achieved by equation:

${\omega _i} = 2{\rm{\pi }}v/{L_i}$

(3)

where, v is train velocity, and L_i is the wavelength of unevenness of track and foundation. Generally speaking, if the track runs in a steady condition, L_i is 10 m, and a_i is 3.5 mm. If there is an added dynamic, L_i is 2 m, and a_i is 0.4 mm. If the track and foundation areuneven, L_i is 0.5 m, and a_i is 0.08 mm. This vibration dynamic loads formulation contains the following factors:(1)train weight, including axial weight and non-suspension systems, (2)uneven characteristics of track and foundation, including geometric and stochastic unevenness of track and foundation, (3)train speed and its vibration characteristic, and (4)movable characteristic of train dynamic loads and dispersed effect of track and sleepers.

3 Dynamic response simulation of frozen soil under movable track load

There are numerous studies that explored the dynamic response mechanism of soil under track loads. Volberg(1983) and the Japan Railway Technique Institute(Yoshioka, 2000)provided several formulations for non-frozen soil dynamic characteristics under train-induced ground vibration. Hall(2003)studied a method based on two- and three-dimensional calculations to analyze train-induced ground vibration. Hanazato et al.(1991)analyzed traffic-induced ground vibrations based on a 3D simulation. Krylov(1997)analyzed the spectra of low-frequency ground vibrations generated by high-speed trains on layered ground. Takemiya(1997)studied a formula for predicting ground vibration induced by high-speed train operation. Volberg(1983)studied the propagation characteristics of ground vibration near railway tracks. Xia et al.(2005)performed numerous experiments to study train-induced vibrations on the environment and nearby buildings. These studies have shown that soil vibration induced by moving track load was is mainly related to soil characteristics, train velocity and train weight etc.. To simulate the dynamic response of frozen soil, train velocity and its vibration frequency, temperatures were selected herein and a numerical analysis was performed based on the ABAQUS platform. The soil parameters are listed in Table 2, and the Mohr-Coulomb model was selected to describe the stress-strain relationship. The boundary was simulated by a viscos-elastic element.

The model based on ABAQUS is listed in Figure 4. Here, x is parallel to the track line, z is the vertical direction perpendicular to the surface, and y is the direction perpendicular to the track line in the horizon.

Numbers 1-6 are points below the sleeper with the distance from the surface of 0, 4, 8, 12, 16, 20 m, letters a-f are points along the surface perpendicular to and at a distance away from the sleeper of 5, 10, 20, 30, 40 m, train velocity is 40, 60, 80, 100, 120 km/h, temperature fields of subgrade and foundation is 0, −5, −7, −10, −12 °C, respectively. The acceleration time history in vertical and horizontal directions was calculated and the results are illustrated in Figure 5(temperature is −5 °C).

According to our simulation, the distinct vertical acceleration response in the z direction is strongly related to train velocity. However, for depth, vertical acceleration has a rapid attenuation, and was propagated only about 20 m. For horizontal direction, the attenuation of vertical acceleration and horizontal acceleration in the y direction was also rapid within 20 m, but their propagation lasted until 40 m distance from the track line. The frozen soil temperature is also a key factor which affects the dynamic response of frozen soils. Dynamic response of five frozen soils with temperatures of 0, −5, −7, −10, −12 °C were analyzed of which are illustrated in Figure 6(train velocity is 60 km/h).

These results show an obvious temperature relationship on dynamic response of frozen soil in a limited spatial range. For horizontal direction, vertical acceleration within only 10 m had a strong relation to frozen temperature, but horizontal acceleration was more dependent on temperature. For depth, the more shallow the depth, the larger the vertical acceleration within 8 m, however the temperature changed. Over 8 m, the temperature had minimal effect on the dynamic response of frozen soil.

For train vibration source frequency relationship on dynamic response of soil and frozen soil, some studies have provided valuable conclusions that this source frequency had a great effect on the soil dynamic response(Cui, 2009; Gu, 2009; Zhu, 2009; Wang, 2011; Wei, 2011). This paper analyzed the dynamic response of frozen soil under train vibration source with different frequencies based on the aforementioned conclusions, inversion of SOA experiment, and in-situ test. Because the train vibration source frequency varied with the change of unevenness characteristics of track and foundation, the frozen soil temperature, train velocity and weight, and track-sleeper-subgrade structure, the range of vibration source frequency was widely distributed. Compared with non-frozen soil, the range of vibration source frequency in frozen soil was relatively narrow, its main frequency was 40-80 Hz when the frozen soil temperature was below −3 °C and −5 °C, the lower the temperature, the higher the frequency, and nearly 80% energy was concentered in 60-80 Hz(Figure 7). The natural frequency of subgrade was 30-50 Hz in winter and 30-40 Hz in summer, respectively(Figure 8). Thus, the dynamic response of frozen soil in winter is smaller than in summer, because the resonance of train vibration source and subgrade is easily transmitted in summer.

4 Conclusions

Vibration response characteristics of frozen soil under moving train loads was analyzed in this paper. The vibration signal in a frozen soil field can be successfully captured by use of the seismic observation array(SOA), which is a powerful tool in exploring the vibration of frozen soil. Based on SOA, a train vibration load model was constructed, considering train velocity, unevenness of track and foundation, bump of the train, and wheel weight.

The numerical simulation aimed at the parameter analysis for controlling the dynamic response characteristics of frozen soil. Our simulation shows that the vertical acceleration amplitude is the main vibration component and has the main energy, which means that vertical acceleration is the main factor for frozen soil damage. The train velocity, train vibration source frequency and temperature of frozen soil are three important factors that control the dynamic response of frozen soil under moving track loads, but only in a limited spatial range with an obvious temperature relationship on dynamic response of frozen soil.

Acknowledgments:

This research is supported by the National High Technology Research and Development Program of China(863, 2008AA11Z104). Many thanks for colleague comments on this manuscript, kind and careful jobs from the editors of this journal, which make this paper perfect.