Journal of Geotechnical and Geoenvironmental Engineering. Submitted June 14, 2012; accepted April 8, 2013; posted ahead of print April 10, 2013. doi:10.1061/(ASCE)GT.1943-5606.0000941
Evaluation of PCC Pile Method in Mitigating Embankment Vibrations from High-Speed Train Pham-Ngoc Thach 1 ; Han-Long Liu 2 ; Gang-Qiang Kong 3
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Abstract: Dynamic response of a railway embankment to a high-speed train is
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simulated for two cases: the soft ground is improved by cast-in-situ concrete pipe piles (PCC piles), and the soft ground is not improved. The obtained results are compared to evaluate the effectiveness of the ground improvement in mitigating the embankment vibration from high-speed train. The study shows that the ground improvement significantly reduces the embankment vibration at all considered train speeds (36-360 km/h). The possibility of vibrational resonance when the train speed approaches the critical speed governed by the soft soil is completely excluded. However, the vibrational resonance still happens when the train speed approaches the critical speed governed by the embankment material, and this suggests the following implication. Even the soft ground of a railway embankment system has been already improved, the vibrational resonance can still happen at high speeds of train. Furthermore, for a given site, each ground improvement scheme results in a different change in the natural vibration properties of the system and hence a different behavior of vibrational resonance. Therefore, besides design issues concerning stability and settlement of the embankment system under static loads, its vibrational resonance behavior is another issue of concern that should be carefully evaluated because it is associated with the operational safety of high-speed trains. CE Database subject headings: Pile; Embankment; Ground improvement; Highspeed train; Dynamic response. 1
Copyright 2013 by the American Society of Civil Engineers
J. Geotech. Geoenviron. Eng.
Journal of Geotechnical and Geoenvironmental Engineering. Submitted June 14, 2012; accepted April 8, 2013; posted ahead of print April 10, 2013. doi:10.1061/(ASCE)GT.1943-5606.0000941
------------------------------------------------------------------------------------------------------1
Researcher, Geotechnical Research Institute, Hohai Univ., Nanjing, 210098, China;
and Lecturer, Faculty of Transportation Engineering, Hochiminh Univ. of Transportation,
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Hochiminh
City,
Vietnam
(corresponding
author).
E-mail:
pnt.geo@https://www.doczj.com/doc/e51677216.html,
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Professor, Geotechnical Research Institute, Hohai Univ., Nanjing, 210098, China. Email: hliuhhu@https://www.doczj.com/doc/e51677216.html,
3
2
Associate Professor, Geotechnical Research Institute, Hohai Univ., Nanjing,
210098, China. E-mail: gqkong1@https://www.doczj.com/doc/e51677216.html,
2
Copyright 2013 by the American Society of Civil Engineers
J. Geotech. Geoenviron. Eng.
Journal of Geotechnical and Geoenvironmental Engineering. Submitted June 14, 2012; accepted April 8, 2013; posted ahead of print April 10, 2013. doi:10.1061/(ASCE)GT.1943-5606.0000941
Introduction Ground improvement using piles has been increasingly used as a rapid construction technique for highway and railway embankments over soft soil areas. A variety of design methods have been developed in the literature, ranging from simple methods
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(e.g., British Standards Institution 1995; Poulos 2007) to relatively sophisticated
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methods involving advanced numerical analysis (e.g., Russell and Pierpoint 1997; Han and Gabr 2002; Huang et al. 2009). However, most studies conducted so far have investigated the behavior of pile-supported embankments under static loads, and very limited attention has been paid to the behavior of this embankment system under dynamic loads. In particular, the effectiveness of the ground improvement in mitigating vehicle-induced vibrations is not well known, and therefore it deserves research attention. In recent years, a ground improvement method, using cast-in-situ concrete pipe piles (PCC piles), has been developed and applied for highway construction (Liu et al. 2007 and 2009). As an extension of the applicability to railway construction, the method has been used for ground improvement of Jing-Hu railway embankment, which is located in a suburb of Nanjing city and belongs to the high-speed line connecting Beijing and Shanghai. The design's performance was evaluated for two conditions: the staged construction loading and the high-speed train loading. The latter was done by means of numerical simulation, and it is reported herein. In this paper, a three-dimensional finite element simulation approach is first introduced and validated by comparison with an existing analytical solution. Based on this approach, train-induced dynamic response of the Jing-Hu embankment is 3
Copyright 2013 by the American Society of Civil Engineers
J. Geotech. Geoenviron. Eng.
Journal of Geotechnical and Geoenvironmental Engineering. Submitted June 14, 2012; accepted April 8, 2013; posted ahead of print April 10, 2013. doi:10.1061/(ASCE)GT.1943-5606.0000941
simulated for two cases: the soft ground is improved by PCC piles, and the soft ground is not improved, i.e. the natural ground. The obtained results are compared to evaluate the effectiveness of the ground improvement in mitigating the embankment vibration from high-speed train.
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Simulation approach and validation Finite element simulation approach Krylov (1995) proposed a frequency-domain analytical solution to train- induced ground vibration velocity for the case of a track resting on an elastic half space. The solution was based on two ideas. First, the loading of a moving train was represented approximately as a series of equivalent concentrated forces vertically acting on the half space. Second, the solution was obtained by the superposition of the velocity fields generated by each equivalent force. The simulation approach in this paper makes use of the first idea above to represent the train load as equivalent forces vertically acting on the ballast surface, and the finite element method is then used to analyze the ballast-embankment-ground system subjected to the equivalent forces. Infinite elements based on the work of Lysmer and Kuhlemeyer (1969) are used to represent the infinite boundary condition of the soil ground. The explicit central difference method (e.g., Belytschko et al. 2000) is used for time integration of the dynamic equilibrium equations. Note that (1) equations involved in the loading model can be found in the Krylov's study, and (2) program ABAQUS (Dassault Systemes 2007) is used for finite element simulation, in which both the Lysmer-Kuhlemeyer (LK) infinite element and the explicit solver are available integrated. Validation 4
Copyright 2013 by the American Society of Civil Engineers
J. Geotech. Geoenviron. Eng.
Journal of Geotechnical and Geoenvironmental Engineering. Submitted June 14, 2012; accepted April 8, 2013; posted ahead of print April 10, 2013. doi:10.1061/(ASCE)GT.1943-5606.0000941
A unit axle load moving on a track resting on an elastic half space is considered. The moving speed is 60m/s. Density, Poisson's ratio and shear wave speed of the half space are 1800kg/m3, 0.3 and 65.4m/s, respectively. Sleeper distance is 0.54m, and parameter E (Krylov 1995) is 1.25 m-1. The problem is solved by the finite element
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method and the Krylov's analytical method, and the obtained results are then
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compared to verify the proposed simulation approach. Finite element modeling of the half space is as follows. By taking the advantage of symmetry, only one half of the model is built as shown in Fig. 1. The interior domain of the model is uniformly meshed using 8-node cubic hexahedral elements with reduced integration and hourglass control. The element size is 0.18m. The symmetry boundary is restrained from the translation in Z-direction, and the LK infinite elements are used on the remaining boundaries to represent the infinite boundary condition. No material damping is considered. Fig. 2 shows the Fourier amplitude spectrum of vertical velocity at location A (Fig. 1) resulting from both methods. It can be observed from the figure that the finite element solution well represents the velocity amplitude at all important frequencies. Modeling of the pile-supported embankment The system is a two-lane ballasted embankment on a soft ground which is improved by PCC piles. Pile dimensions: total length is 15m; outer and inner diameters are 1m and 0.76m; cap diameter and thickness are 1.2m and 0.5m. Full description of the model geometry is shown in Fig. 3. Sleeper distance is 0.54m, and parameter E (Krylov 1995) is 1.25 m-1. Fig. 4 shows geometric and loading parameters of the selected train. The model is meshed using 8-node hexahedral elements with reduced integration and hourglass control, Fig. 5. The fixed boundary is used at the bottom to 5
Copyright 2013 by the American Society of Civil Engineers
J. Geotech. Geoenviron. Eng.
Journal of Geotechnical and Geoenvironmental Engineering. Submitted June 14, 2012; accepted April 8, 2013; posted ahead of print April 10, 2013. doi:10.1061/(ASCE)GT.1943-5606.0000941
represent the bedrock. On the remaining boundaries, LK infinite elements are used to represent the infinite boundary condition. Kaynia et al. (2000), Correia (2001) and Mashus et al. (2004) have reported that the passage of high speed trains could produce considerable deformation in the ballast, embankment and ground, and the shear
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modulus in the materials nonlinearly decreases with increasing the amplitude of cyclic
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shear strain. This behavior is considered in the present study in an approximate manner through the equivalent linear approach (see, for example, Kaynia et al. 2000) using the modulus reduction curves given in Fig. 6, which are established based on the work of Ishibashi and Zhang (1993). Table 1 summarizes the equivalent-linear material parameters used in all simulations, which are obtained from a number of linear iterations for the case of train speed 60m/s. Lumped mass scheme is used for the finite elements. Rayleigh damping is used to represent energy-dissipating mechanisms in the system; the mass and stiffness proportional damping constants are 1.4226 and 0.00024, which provide slight damping ratios of 2-4% in the frequency range of 3-50Hz. Note that for the model case which the ground is not improved, the modeling procedure is similar to that of the pile-supported embankment. The only difference is that there are no piles, and therefore it is not detailed herein. In addition, for consistency of comparison, the same material parameters given in Table 1 are used for this model case. Results and discussion Fig. 7 shows the peak vertical displacement at location S (see Fig. 3) versus train speed. For the model case which the ground is not improved, the peak displacement is 6
Copyright 2013 by the American Society of Civil Engineers
J. Geotech. Geoenviron. Eng.
Journal of Geotechnical and Geoenvironmental Engineering. Submitted June 14, 2012; accepted April 8, 2013; posted ahead of print April 10, 2013. doi:10.1061/(ASCE)GT.1943-5606.0000941
large at all considered train speeds. The degree of response amplification does not increase monotonically with increasing the train speed, but rather, strongly depends on the relation between the train speed and the natural vibration properties of the system. It is noticeable that the peak displacement at 20m/s and 60m/s is particularly
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high. These observations can be interpreted as follows. Since the structure is a multi-
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layer system which inherently has a dispersive nature in material, the surface wave field generated by the train load is predominantly governed by two generalized modal waves whose characteristic propagation speeds are about 20m/s and 60m/s. When the train speed approaches these characteristic wave speeds, the embankment response is maximally amplified as a consequence of vibrational resonance phenomenon. Note that this interpretation is based on the well-known concept of 'critical speed' (e.g., Mashus et al. 2004). According to this concept, the train speeds 20m/s and 60m/s at which the vibrational resonance happens can be referred to as the critical speeds. On the other hand, it can be realized that these two speeds are very close to the Rayleigh wave speeds of the silty clay (19.9m/s) and the embankment (60.7m/s). This indicates that the critical speeds of the system are governed by the silty clay and the embankment. For the model case which the ground is improved by the piles, the squared marks in Fig. 7, the peak displacement is significantly reduced at all of the train speeds as compared with the case without ground improvement. In particular, the peak displacement is reduced 90.1% at 20m/s and 62.5% at 60m/s. These observations can be interpreted as follows. First, since the silty clay layer is soft and thick, it can be expected that the deformation of this layer is the significant contributor to the large displacement response observed in the case without ground improvement. After the 7
Copyright 2013 by the American Society of Civil Engineers
J. Geotech. Geoenviron. Eng.
Journal of Geotechnical and Geoenvironmental Engineering. Submitted June 14, 2012; accepted April 8, 2013; posted ahead of print April 10, 2013. doi:10.1061/(ASCE)GT.1943-5606.0000941
silty clay layer is strengthened by the piles, the large deformation of this layer would not exist, thus resulting in a significant reduction of the displacement response at all of the train speeds. Second, since the ground improvement has resulted in a change in the natural vibration properties of the system, the vibrational resonance behavior of
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the system is changed accordingly. Specifically, the possibility of vibrational
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resonance at 20m/s is completely excluded, thus resulting in 90.1% reduction of the peak displacement. However, the vibrational resonance still happens at 60m/s, though the peak displacement is reduced 62.5%. To further understand the behavior of vibration reduction at 60m/s, the vertical displacement history at location S is presented in Fig. 8, and the following observations are made: x For the case without ground improvement, the displacement response can be understood as a combination of two components. (1) The dynamic component, which is caused by the vibrational resonance. (2) The quasi-static component, which is caused by the self-weight of the train. This component is primarily associated with the deformation of the thick silty clay layer and manifests itself through the fact that the whole displacement pattern is significantly directed downward. x The ground improvement almost eliminates the quasi-static component from the response but does not seem to have effect on the dynamic component. In other words, the degree of response amplification caused by the vibrational resonance is almost not affected by the ground improvement. 8
Copyright 2013 by the American Society of Civil Engineers
J. Geotech. Geoenviron. Eng.
Journal of Geotechnical and Geoenvironmental Engineering. Submitted June 14, 2012; accepted April 8, 2013; posted ahead of print April 10, 2013. doi:10.1061/(ASCE)GT.1943-5606.0000941
Conclusions If the soft ground is not improved, the peak displacement on the ballast surface is
CLAY and large at all considered train speeds, and there exist two critical speeds VCR EMB VCR governed by the silty clay and embankment materials, respectively. When the
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train speed approaches these critical speeds, the peak displacement is maximally
Ac N ce ot p C ted op M ye a di nu te s d cr ip t
amplified as a consequence of vibrational resonance phenomenon. The ground improvement using PCC piles significantly reduces the peak displacement at all of the train speeds. The possibility of vibrational resonance when the train speed approaches
CLAY VCR is completely excluded. However, the vibrational resonance still happens when EMB , and this suggests the following implication. the train speed approaches VCR
Even the soft ground of a railway embankment system has been already improved, the vibrational resonance can still happen at high speeds of train. Furthermore, for a given site, each ground improvement scheme results in a different change in the natural
vibration properties of the system and hence a different behavior of vibrational
resonance. Therefore, besides design issues concerning stability and settlement of the
embankment system under static loads, its vibrational resonance behavior is another issue of concern that should be carefully evaluated because it is associated with the operational safety of high-speed trains.
Acknowledgements
The work described in this paper was supported by the National Science Joint High Speed Railway Foundation of China (No.U1134207) and the National Natural Science Foundation of China (No.51008116; 51278170).
9
Copyright 2013 by the American Society of Civil Engineers
J. Geotech. Geoenviron. Eng.
Journal of Geotechnical and Geoenvironmental Engineering. Submitted June 14, 2012; accepted April 8, 2013; posted ahead of print April 10, 2013. doi:10.1061/(ASCE)GT.1943-5606.0000941
References Belytschko, T., Liu, W.K., and Moran, B. (2000). Nonlinear finite elements for continua and structures. John Wiley & Son. British Standards Institution (1995). “British standards code of practice for
Downloaded from https://www.doczj.com/doc/e51677216.html, by ZHEJIANG UNIVERSITY OF on 05/27/13. Copyright ASCE. For personal use only; all rights reserved.
improved/reinforced soil.” BS 8006.
Ac N ce ot p C ted op M ye a di nu te s d cr ip t
Correia, A.G. (2001). "Soil mechanics in routine and advanced pavement and rail track rational design." Geotechnics for roads, rail tracks and earth structures, A.G. Correia and H. Brandl, Eds.; Balkema, Rotterdam, 165-187. Dassault Systemes (2007). ABAQUS theory manuals. Han, J., and Gabr, M. A. (2002). "Numerical analysis of geosynthetic-reinforced and pile-supported earth platforms over soft soil." J. Geotech. Geoenviron. Eng., 128(1), 44-53. Huang, J., Han, J., and Oztoprak, S. (2009). "Coupled mechanical and hydraulic modeling of geosynthetic-reinforced column-supported embankments." J. Geotech. Geoenviron. Eng., 135(8), 1011–1021. Kaynia, A. M., Madshus, C., and Zackrisson, P. (2000). “Ground vibration from high speed trains: Prediction and countermeasures.” J. Geotech. Geoenviron. Eng., 126(6), 531–537. Krylov, V. (1995). "Generation of ground vibrations by superfast trains." Appl. Acoust., 44, 149-164. Liu, H. L., Ng, C. W. W., and Fei, K. (2007). "Performance of a geogrid-reinforced and pile-supported highway embankment over soft clay: case study." J. Geotech. Geoenviron. Eng., 133(12), 1483-1493. Liu, H. L., Chu, J., and Deng, A. (2009). "Use of large-diameter cast-in-situ concrete pipe piles for embankment over soft clay." Can. Geotech. J., 46(7), 915-927. 10
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J. Geotech. Geoenviron. Eng.
Journal of Geotechnical and Geoenvironmental Engineering. Submitted June 14, 2012; accepted April 8, 2013; posted ahead of print April 10, 2013. doi:10.1061/(ASCE)GT.1943-5606.0000941
Lysmer, J., and Kuhlemeyer, R. L. (1969). "Finite dynamic model for infinite media". J. Eng. Mech. Div., ASCE 95, EM4, 859-877. Mashus, C., Lacasse, S., Kaynia, A.M., and Harvik, L. (2004). "Geodynamic challenges in high speed railway projects". Proc. Geotech. Eng. Transp. Projects,
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GSP-126, ASCE, 192-215.
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Poulos, H. G. (2007). "Design charts for piles supporting embankments on soft clay". J. Geotech. Geoenviron. Eng., 133(5), 493-501. Russell, D., and Pierpoint, N. (1997). "An assessment of design methods for piled embankments". Ground Eng., 30(11), 39-44. 11
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J. Geotech. Geoenviron. Eng.
Journal of Geotechnical and Geoenvironmental Engineering. Submitted June 14, 2012; accepted April 8, 2013; posted ahead of print April 10, 2013. doi:10.1061/(ASCE)GT.1943-5606.0000941
Table 1. Equivalent-linear material parameters Material Ballast Embankment
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U (kg/m3)
2200 1800 2000 1800 1800 1900 2400
v 0.3 0.3 0.3 0.3 0.35 0.3 0.2
VS (m/s) 72.4 65.4 69.3 38.7 21.3 88.9 1863.4
VR (m/s) 67.2 60.7 64.3 35.9 19.9 82.4 1698.8
Cushion Coarse-grained fill Silty clay Sand PCC pile
Note: U is density; v is Poisson's ratio; VS and VR are shear and Rayleigh wave speeds, respectively.
Accepted Manuscript Not Copyedited
12
Copyright 2013 by the American Society of Civil Engineers
J. Geotech. Geoenviron. Eng.
Journal of Geotechnical and Geoenvironmental Engineering. Submitted June 14, 2012; accepted April 8, 2013; posted ahead of print April 10, 2013. doi:10.1061/(ASCE)GT.1943-5606.0000941
List of figure captions Fig. 1. Finite element mesh of the half space Fig. 2. Fourier amplitude spectrum of the vertical velocity at location A Fig. 3. Geometry of the PCC pile-supported embankment
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Fig. 4. Geometry and axle loads of the five-carriage train
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Fig. 5. Finite element mesh of the PCC pile-supported embankment: (a) full mesh; (b) a cross-sectional slice Fig. 6. Modulus reduction curves for materials Fig. 7. Peak vertical displacement versus train speed (at location S) Fig. 8. Vertical displacement history at location S for the case of train speed 60m/s 13
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J. Geotech. Geoenviron. Eng.
)LJ Journal of Geotechnical and Geoenvironmental Engineering. Submitted June 14, 2012; accepted April 8, 2013; posted ahead of print April 10, 2013. doi:10.1061/(ASCE)GT.1943-5606.0000941
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Accepted Manuscript Not Copyedited
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J. Geotech. Geoenviron. Eng.
)LJ Journal of Geotechnical and Geoenvironmental Engineering. Submitted June 14, 2012; accepted April 8, 2013; posted ahead of print April 10, 2013. doi:10.1061/(ASCE)GT.1943-5606.0000941
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