Dynamic elastic modulus for frozen soil from the embankment on Beiluhe Basin along the Qinghai–Tibet Railway
Introduction
The Qinghai–Tibet Railway is currently the highest and longest plateau railway in the world, with a total length of 1925 km. The Golmud to Lhasa section of the Qinghai–Tibet Railway in China is 1118 km long, of which 550 km is over continuous permafrost and 82 km lies in discontinuous permafrost regions as shown in Fig. 1 (Ma et al., 2008). The key problem for the Qinghai–Tibet Railway is therefore permafrost and permafrost-related deformation (Wu et al., 2002). The thermal status of permafrost is sensitive to the change of ground surface temperature. Global warming and human infrastructures can increase the ground surface temperature, which will lead to extensive degradation of permafrost (Yu et al., 2005). Frost heave and thaw settlement in cold regions have attracted the interests of many geotechnical engineers; however, many problems concerning the stability of the embankments, induced by global warming and anthropogenic activities, have not been solved. Some researchers have paid more attention to the global warming-related frozen soil deformation; however, very few literatures have investigated the frozen soil deformation induced by passing train (Yu, 2004, Jin et al., 2008, Wang et al., 2003, Wang et al., 2004b, Ma et al., 2006, Cheng et al., 2008). Passing train-induced kinetic energy can raise the frozen soil temperature, leading to the frozen soil deformation; therefore, the dynamic stability of the embankment in the permafrost areas, induced by passing train, has caused significant attention from Chinese government, scholars and engineering professionals. The dynamic stability of the embankments in permafrost areas largely depends on the ground temperature, which is due to the close relationship between the ground temperature and the mechanical behavior of the frozen soil (Cheng, 2005a). Accordingly, the research on dynamic performance and stability of soil in permafrost areas is becoming a hot and key project in recent years. The dynamic elastic modulus is one of the most important dynamic parameters of the soil and the important research object of the soil dynamics; however, few investigations on it have been reported (Wang et al., 2007, Shi et al., 2006, Vinson et al., 1983, He et al., 1993, Zhao et al., 2003).
This paper investigates the dynamic elastic modulus and the main influential factors of frozen soil from the embankment on Beiluhe Basin along the Qinghai–Tibet Railway, based on the dynamic tri-axial test of the soil and the equivalent linearization model. Moreover, the effects of the temperature, water content and confining pressure on the dynamic elastic modulus ratio and the backbone curves are discussed.
For the sake of clarity, in this paper, the term “reference line strain amplitude” means the minimum line strain amplitude, which is the ratio of the ultimate dynamic stress amplitude to the maximum dynamic elastic modulus. The term “equivalent linearization model”, named as the equivalent nonlinear viscoelastic model, depicts the relationship between the dynamic stress and the soil damping ratio with the dynamic axial strain. The term “backbone line” is the curve of the variation of dynamic stress with the dynamic strain for the equivalent nonlinear viscoelastic model. The term “maximum dynamic elastic modulus” is the initial dynamic elastic modulus.
Section snippets
Experimental equipment and material
The tests were conducted in the State Key Laboratory of Soil Engineering of Chinese Academy of Science. The tri-axial Material Test Machine of MTS-810 made in the USA, is equipped with an automatic numerical control system and a data collection system, illustrated in Fig. 2.
The indexes of the tri-axial material test machine are as follows: the confining pressure ranging from 0 to 20 MPa, the experimental temperature ranging from the room temperature to − 30 °C, the frequency ranging from 0 to
The calculation method of the dynamic elastic modulus
The hysteretic curve of dynamic deformation for the soil is drawn according to an equivalent linearization model, based on the test data. The hysteretic curve shows the relationship between the dynamic axial stress σd and the dynamic axial strain εd, shown in Fig. 3. The mean slope of the hysteretic curve is defined as the dynamic elastic modulus Ed. The hyperbolic model expressed by Eq. (1) is adopted to depict the backbone line (Zhang et al., 1989, Seed and Idriss, 1970, Jin et al., 2008).
Conclusions
- (1)
Experimental expressions of the following parameters for frozen soil are obtained based on the dynamic tri-axial tests and the equivalent linearization model, including the maximum dynamic elastic modulus, the dynamic elastic modulus ratio and the reference line strain amplitude; experimental results of the three parameters show that the equivalent linearization model can well express the dynamic constitutive relations of the frozen soil; Polynomials can be adopted to well fit the relationships
Acknowledgments
The authors sincerely thank the following agents for their supports: National Natural Science Foundation of China (No.50678055), the Research Fund for the Doctoral Program of Higher Education of China (No.20070213076), and the Open Research Fund Program of State Key Laboratory of Permafrost Engineering of China (No.SKLFSE200402).
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