Dynamic Performance of Pile-supported Bridge-embankment ... - Core

Procedia Engineering Volume 143, 2016, Pages 1059–1067 Advances in Transportation Geotechnics 3 . The 3rd International Conference on Transportation Geotechnics (ICTG 2016)

Dynamic Performance of Pile-Supported BridgeEmbankment Transition Zones Under High-Speed Train Moving Loads Wei Li1 and Xuecheng Bian1*

1

Zhejiang University, Hangzhou, China [email protected], [email protected]

Abstract Faster degradation of railway tracks can be observed in bridge-embankment transition zones. Degradation is triggered by abrupt variation in the track's vertical stiffness due to different support conditions. Developing efficient transition zone design strategies is imperative to minimize this problem. For slab track-embankment over soft soil areas, very limited consideration has been given to ground improvement when designing transition zones. In this study, cement fly-ash gravel piles were used to improve the soft ground near a bridge and two pile configurations were considered. The dynamic performance of the slab track-embankment-ground system under high-speed train moving loads was investigated using a finite/infinite-element simulation approach. The dynamic responses of the slab track-embankment-ground system change more smoothly near the bridge abutment in the case of varying-length piles, and are amplified in the vicinity of the bridge abutment when a train travels from the embankment to the bridge. Keywords: High-speed railway, Pile-supported embankment, Transition zone, Varying-length piles, soft ground

1 Introduction Vibrations in track structure and the underlying ground induced by high-speed trains have been increasingly studied for the purpose of ensuring the safety, reliability, and comfort of train operations (Bian et al., 2008; Bian et al., 2014). A smooth railway track can help reduce vibration intensity. However, a railway line consists of different sections, such as an embankment and a bridge. The performance of the track system at the bridge-embankment transition zone is characterized by track geometry degradation (Li and Davis, 2005; Li et al., 2010; Mishra et al., 2012), which gives rise to vertical rail irregularity. Dynamic responses of the track and the ground will be amplified, especially when the train travels on the irregular rail at a high speed (Bian et al., 2011). A stiff bridge abutment is usually supported by deep piles, but an embankment consisting of compressible fillers is usually constructed on natural ground. Thus, the abrupt change in the

Selection and peer-review under responsibility of the Scientiﬁc Programme Committee of ICTG 2016 c The Authors. Published by Elsevier B.V.

doi:10.1016/j.proeng.2016.06.101

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Bridge-Embankment Transition Zones under Train Moving Loads

Wei Li and Xuecheng Bian

supporting stiffness is reported to be the mechanism for track degradation at the transition zone (Hunt, 1997; Varandas et al., 2014; Steenbergen, 2013). The recent development of high speed railway in China has led to an increased use of slab tracks. Compared to traditional ballasted tracks, slab tracks have striker design requirements. The differential settlement between the embankment and the bridge abutment should be less than 5mm for slab track while for ballasted track, it is from 30mm to 50mm (TB-10020-2009). Effective remedies should be able to mitigate abrupt changes in track stiffness and eventually smooth the deformations of the track system close to the transitions. Two main remedies have been proposed: (a) improve the "soft side"; (b) reduce the vertical track stiffness on the bridge abutment (Li et al., 2010; Mishra et al., 2012; Li and Davis, 2005). A transition section is usually built between the bridge abutment and the ordinary embankment to smooth the changes in track stiffness. Shan et al. (2013) developed a coupled track-subgrade model based on the finite element method to compare the efficiency of various transition configurations in mitigating the dynamic responses of a track system close to a bridge abutment, and found that both a longer transition section and a two-part transition configuration can lead to better dynamic performance. An optimized solution to guide the design of the transition section between an embankment and the adjacent structures was proposed by Gallego Giner and Lopez Pita (2009) with the aid of the finite element method. Most studies have concentrated on optimizing the configurations and the fillers' properties of the transition section close to the stiff structures. No studies take the natural ground improvement into consideration when designing the bridge-embankment transitions. Finite element analysis carried out by Gallego et al. (2011) showed that vertical track stiffness is a function of the properties of the embankment fillers, the natural ground and the height of the embankment. In particular, when a railway embankment is constructed over a soft soil stratum characterized by high compressibility and low stiffness, the improvement of the soft ground is vital to determine the vertical track stiffness. Pile raft structures have been increasingly used to improve the soft ground because they have a short construction period, high bearing capacity and large stiffness, and they can significantly reduce total and uneven settlements. In this study, a multistage improvement strategy using varying-length piles is introduced to improve the soft ground in the vicinity of a bridge abutment. A coupled vehicletrack-embankment-ground model based on the finite/infinite-element method is developed to calculate the dynamic responses of the slab track-embankment-ground system under high-speed train moving loads. The dynamic performance was compared when the soft ground is improved by constant-length piles and varying-length piles. The effects of the train's travelling direction were also studied.

2 The Finite/Infinite-Element Simulation Approach and Its Validation In this study, train-induced vibrations were simulated using the software ABAQUS, which has adopted infinite elements (Lysmer and Kuhlemeyer, 1969). The semi-analytical results (Kausel, 1994) were used to validate the finite/infinite-element approach and determine model size. The geometry of this example as well as the soil properties are graphed in Figure 1(a), and the load has a magnitude of 1N. In Figure 1(b), the adopted finite element mesh has a width of 21.125m.

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2m


(a) (b) Figure 1: (a) A homogeneous soil layer on a rigid base and (b) its finite/infinite-element model

In Figure 2, the vertical displacement of point A is presented, for passage speeds below and above the shear wave propagation velocity in the ground. The numerical results provided by the finite\infinite element approach are very close to the semi-analytical solutions.

(a) (b) (c) Figure 2: Vertical displacements at point A for different speeds of passage: (a) c=100m/s; (b) c=200m/s; (c) c=300m/s

3 Case Studies 3.1 Modeling The Vehicle - Track System The considered vehicle is the Chinese CRH3 high-speed train shown in Figure 3. Only a set of reduced degrees of freedom is considered in the simulation: the vertical displacements of all parts and the pitch angle of the carriage and bogie. The parameters of the CRH3 train are summarized in Lei and Zhang (2011).

Figure 3: Geometry and axle loads of the CRH3 high-speed train's carriage

The CRTSII slab track, widely used in Chinese high-speed railway lines, was modeled. It is composed of a rail, slab, cement-asphalt mortar and concrete base. These four parts are meshed by 81061



node linear hexahedral elements with reduced integration. The continuous rail interacts with the slab through regularly spaced fasteners represented by springs and dashpots. The parameters of the CRTSII slab track are given in Lei and Zhang (2011). The link between the vehicle and the track is defined through the mechanical contact between the wheels and the rail. The normal contact force ft is determined according to Hertz's theory, but for the purpose of simplicity, it is linearized about the wheel/rail penetrations dp. f t kc d p (1) where kc is the normal contact stiffness and its value is 1325MN/m according to Lei and Zhang (2011).

3.2 Description of the Pile - Supported Bridge-Embankment Transition Zone Model The geometry of the embankment was determined according to the design code of high speed railways (TB-10020-2009). The height of the embankment is 4.55m; its side slope is 1:1.5 and its top width is 8.6m. The underlying foundation is improved by a cement fly-ash gravel pile raft structure. The diameter of the C20 piles is 0.4m; the piles are arranged in a rectangular pattern: the longitudinal spacing is 1.8m and the horizontal spacing ranges from 1.4m to 1.8m. The thickness of the C20 concrete raft is 0.5m. The ground consists of a 12m-thick layer of soft clay underlain by a 10m-thick layer of dense sand, and the bedrock is assumed to be below this sand layer. There is a fill layer of 1.7m on the top of the soft soil layer. Two pile configurations were compared in present study: Figure 4(a) shows the foundation improved by piles with a constant length of 15.7m; Figure 4(b) shows multistage improvement where the length of the piles decreases gradually from 23.7m to 15.7m as a function of the distance from abutment. Table 1 summarizes the material parameters in this model. Concrete slab Embankment

Bridge Abutment 1.7m 12m

d=2m

10m CFG Piles

(a) (b) Figure 4: Two pile configurations in the foundation: (a) 15.7m long piles; (b) piles of incrementally varying length Material Embankment Concrete slab Soil layer ķ Soil layer ĸ Soil layer Ĺ CFG pile

ȡ (kg/m3) 2000 2500 1800 1800 1900 2500

Table 1: Material properties

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E (MPa) 500 2.55×104 9.5 3.5 52.5 7×103

ȣ 0.3 0.2 0.3 0.3 0.3 0.2

Vp (m/s) 500 3193.7 72.3 44.1 166.2 1673.3

Vs (m/s) 310.1 2061.6 45.1 27.3 103.1 1080.1

VR (m/s) 287.2 1872.6 41.7 25.3 95.5 981.1



By taking advantage of symmetry, only half of the finite element model needs to be built (Figure 5(a),(b)). The model is meshed using 8-node linear hexahedral elements with reduced integration. As shown in Figure 5(c), three carriages with a total length of 75m were simulated in the present model, the bridge abutment was not included in present mode for simplicity and it is a restraint boundary in X direction at the joint between the embankment and the bridge abutment. The bottom of the track underlain by the bridge abutment was fixed assuming that no settlement takes place at the bridge abutment. There were 396497 8-node linear hexahedral elements with reduced integration and 3725 infinite elements in the finite/infinite-element model. The time step size used in the ABAQUS implicit analysis was 0.0015s, which is small enough to ensure solution accuracy and numerical stability.

(a) (b) (c) Figure 5: Finite element model of the pile-supported embankment: (a) full mesh; (b) a cross section;(c) A plane view of the vehicle-track-embankment-ground system

4 Results 4.1 Characteristics of Dynamic Responses of the Bridge-Embankment Transition Zone at Critical Speed When the train speed approaches the characteristic wave speeds of the medium, the vibrations are maximally amplified (Ju and Lin, 2004). In most cases, the lowest critical speed is largely controlled by layers with small characteristic wave speeds. Since the soft ground has been improved by piles, the embankment has smaller characteristic wave speeds. The critical speed of this system is primarily controlled by the embankment's Rayleigh wave speed, 287.2m/s. In this study, to quantify the substructure's deformability, the vertical track stiffness K is used according to Esveld (2001) and Gallego et al. (2011). The value of the vertical track stiffness K can be obtained as follows: Q K (3) z where Q is the Chinese CRH3 high-speed train wheel load, which has a value of 74kN, and z is the amplitude of the rail's vertical displacement time history. Figure 6 shows the variations in vertical track stiffness as a function of the distance to the abutment. The maximum value found at the bridge abutment is about 80kN/mm, and the minimum is 57.5kN/mm on the embankment supported by 15.7m long piles. The installation of longer piles near the abutment leads to a smaller gap in the support stiffness. The results show that multistage reinforcement of the ground could make the transition of the vertical track stiffness much smoother. Consequently, a bridge-embankment transition zone supported by varying-length piles has better dynamic properties.

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(a) (b) Figure 6: Vertical track stiffness as a function of the distance to the abutment for two different pile configurations: the train travels (a) from the embankment to the bridge abutment and (b) from the bridge abutment to the embankment

Figure 6 shows that the vertical track stiffness fluctuates on the bridge when the train travels from the embankment to the bridge. The vertical deformations of the rail near the bridge experience more abrupt changes when the train travels from the "soft side" to the "stiff side". Changes in longitudinal stresses are more prone to activate slab cracking. Figure 7 shows the variations in slab stresses in the X direction as a function of the distance to the abutment. Negative values represent compressive stresses, and positive values represent tensile stresses. They are the minimum and maximum amplitudes of the longitudinal slab stress time history. The maximum compressive slab stresses occur 2.5m from the abutment, and a concentration of slab tensile stress can be observed at the junction of the embankment and the bridge abutment. Noted the slab's longitudinal stresses show more dramatic variation and have larger values near the bridge when the train travels from the embankment to the bridge.

(a) (b) Figure 7: Stress in the X direction of slab as a function of distance to the abutment for two different pile configurations: the train travels (a) from the embankment to the bridge abutment and (b) from the bridge abutment to the embankment

Figure 8 summarizes the distributions of the pile top stresses as a function of the distance to the abutment. When the train travels from the embankment to the bridge (Figure 8(a)), the vertical stress of the pile top increases from 64.7kPa at x=4.5m to 74.6kPa at x=0.9m in the case of varying-length piles and from 58.1kPa at x=4.5m to 74.6kPa at x=0.9m in the case of constant-length piles. This result shows that dynamic loading increases in the vicinity of the bridge abutment due to the abrupt variation in the supporting conditions. When the train travels from the bridge to the embankment (Figure 8(b)), the vertical stress increases from 36.8kPa at x=0.9m to about 60kPa on the top of 15.7m long piles in the case of varying-length piles and from 25.2kPa at x=0.9m to about 60kPa on the top of 15.7m long piles in the case of constant-length piles. Noted that the dynamic stress levels are higher in

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the case of varying-length piles, and the longer piles will bear much more dynamic loading. The results show that in the vicinity of the bridge abutment the stress levels of the pile top are higher when the train travels from the embankment to the bridge.

(a) (b) Figure 8: Vertical dynamic stress of the pile top as a function of the distance from the abutment for two different pile configurations: the train travels (a) from the embankment to the bridge abutment and (b) from the bridge abutment to the embankment

5 Conclusions The dynamic performance of the pile-supported bridge-embankment transition zone underlain by soft ground under high-speed train moving loads were studied using the validated finite/infiniteelement model. Two ground improvement strategies: varying-length piles and constant-length piles were compared, and the travelling direction of the train was also considered. It can be concluded that: (1) The dynamic responses of the track-subgrade system changed abruptly in the vicinity of the bridge abutment due to variation in the support conditions; a multistage improvement strategy using varyinglength piles can effectively smooth the transition of the vertical track stiffness, thus giving rise to smoother transitions of the dynamic responses of the track-subgrade system. (2) Both the tensile stress and compressive stress of the slab increased abruptly in the vicinity of the bridge abutment due to the sharp change in the supporting stiffness. Extra reinforcement should be used during slab precasting to avoid cracking. (3) When the underlying ground of the transition zone was improved by varyinglength piles, the piles near the bridge bore much greater dynamic loading. In the vicinity of the abutment, the vertical stress of the pile top increased when the train moved from the embankment to the bridge. The bridge-embankment transition zone had better dynamic properties when the soft ground was improved using varying-length piles. Furthermore, other design parameters, such the spacing, elastic modulus and diameter of the pile, can also be optimized. Investigation of such optimization issues would be a useful objective for further research.

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Acknowledgments Financial supports from the National Natural Science Foundation of China (Grant No. 515611130159) and Zhejiang Provincial Natural Science Foundation of China (Grant No LR16E080002) are gratefully acknowledged.

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