Static Analysis of the Interaction Among Soil, Slab and Piles in Pile-Slab Structure

Transcription

1 Sensors & Transducers 203 by IFSA Static Analysis of the Interaction Among Soil, Slab and Piles in Pile-Slab Structure Xiao Hong, 2 Gong Xiaoping, 3 Yang Song BeiJing key Laboratory of Track Engineering, Bei Jing Jiao Tong University, 00044, Beijing, China 2 China Railway Fifth Survey and Design Institute Group Co, Ltd., 02600, Beijing, China 3 BeiJing key Laboratory of Track Engineering, BeiJing JiaoTong University, 00044, Beijing, China Tel.: xiaoh@bjtu.edu.cn Received: 28 April 203 /Accepted: 9 July 203 /Published: 3 July 203 Abstract: Pile-slab structure is a new subgrade construction with the development of high-speed railways in China. It is currently used in a number of high-speed railways. However, it is mainly designed by the empirical design method since the interaction mechanism among piles, slab and subgrade soil is not clear. The supporting effect on the slab and the lateral constraint effect on piles caused by subgrade soil is not considered using the empirical design method. A three-dimensional finite element model including train, track and pile-slab structure is established so as to make a systemic mechanical analysis of the slab, piles and subgrade soil in pile-slab structure. The conclusions is as follows:() When the supporting effect on the slab is not considered, the stress of the slab increases by.8 % ~ 3.4 %, the stress at the bottom of piles increases by 0.3 % ~.2 %, the deflection of the slab increases by.0 % ~ 2.0 %. (2) The vertical displacement of the slab increases by about 52.9 % that of piles increases by about 69.4 % after removing the soil of the embankment and the soft soil in the roadbed. This indicates that the embankment soil plays a significant role in the supporting effect on the slab and provides a positive frictional resistance on piles. (3)The lateral deformation of the pile-slab structure increases by approximately 25 % when slab and soil doesn't contact, indicating that the contact between slab and soil has a certain effect on the lateral deformation of the pile-slab structure. The lateral deformation of the pile-slab structure increases by about 2.5 times when removing the embankment layer, indicating that the lateral constraint effect on piles is very obvious. So the pile-slab structure has significant advantages compared with bridges. Copyright 203 IFSA. Keywords: Pile-slab structure, Pile-soil interaction, Slab-soil interaction, Coupling model, Mechanics characteristics analysis.. Introduction In order to meet the requirements of the post construction settlements in high-speed railways, some new forms of subgrade structure such as pile-slab and pile-net structures are used [2-3]. Pile-slab structure has outstanding advantages in solving problems such as deep soft ground, collapsed loess, short transition sections between bridges and tunnels, turnout district embankment, existing embankment reinforcement and geological environment problems such as carst, goaf, etc. Because of that it s widely used in highspeed railways in our country [4-5]. The typical structure is shown in Fig Article number 275

2 Fig.. Typical form of the pile-slab structure. Since the interaction mechanism among piles, slab and subgrade soil is not clear, the supporting effect on the slab and the lateral constraint effect on piles caused by subgrade soil is often not considered when the pile-slab structure is designed. This may result in the situation that the calculation results are usually conservative and the project cost is high. Moreover, the conservative design results can lead to a greater rigidity of the structure, making the structure more sensitive to the effect caused by the temperature stress. This can even become a potential safety danger sometimes [6-9]. To sum up, a three-dimensional finite element model including train, track and pile-slab structure is built to make a systemic mechanical analysis of the slab, piles and subgrade soil. The slab-soil and pilesoil interactions are the main part of the analysis so as to provide theoretical guidance for engineering designs. 2. Parameters and Judging Criteria ) According to Technical Code for Ground Treatment of Railway Engineering, the vertical deflection of the slab should not exceed the requirements shown in Table. 2) According to Code for Design of High Speed Railway [], the limit value of the vertical angle at the beam end under the ZK static load should meet the requirements shown in Table 2. 3) According to Code for Design of High Speed Railway and other criteria: The lateral deformation of the reinforced concrete slab and piles should meet the requirements of the lateral deformation in ballastless track: the lateral deformation of the bearing slab should be limited to 2 mm; the lateral deformation of the piles should be limited to 5 L ; the horizontal angle should less than /000. The vertical displacement of the reinforced concrete slab is influenced by the limit value of the rail longitudinal displacement. It should be limited to 5 mm when designed. 3. Calculation Parameters and Model ) Calculation parameters. The Calculation parameters of the vehicle, the track and the pile-slab structure are shown in Tables 3-5. Table. Limit value of the vertical deflection of the bearing slab. Target value of the speed (km/h) Limit value of the vertical deflection.l/300.l/400.l/600.l/700 Limit value for span of 7.5m on single track railway Attention: L is the longitudinal span of the bearing slab; The limit value of the vertical deflection for single track railway should be 0.6 times that of double track railway. Table 2. Limit value of the vertical angle at the beam end. Track style Position Limit value (rad) Side span between trimmer beam and bearing slab.0 Ballastless track Middle span between two adjacent bearing slabs Fig. 2. Diagram of the angle at the beam end. 235

3 Table 3. Calculation parameters of the vehicle. Name Value Unit Mass of the vehicle kg Mass of the bogie 3200 kg Mass of the wheelset 2400 kg Rolling inertia of the vehicle.5e5 kg m 2 Nodding inertia of the vehicle 2.7e6 kg m 2 Yawing inertia of the vehicle 2.7e6 kg m 2 Rolling inertia of the bogie 3200 kg m 2 Nodding inertia of the bogie 7200 kg m 2 Yawing inertia of the bogie 6800 kg m 2 Rolling inertia of the wheelset 200 kg m 2 Yawing inertia of the wheelset 200 kg m 2 Longitudinal stiffness of the first series/axle box 9.0e3 kn/m Lateral stiffness of the first series / Axle box 3.0e3 kn/m Vertical stiffness of the first series / Axle box.04e3 kn/m Longitudinal stiffness of the second series /Bogie side 0.24e3 kn/m Lateral stiffness of the second series /Bogie side 0.24e3 kn/m Vertical stiffness of the second series /Bogie side 0.40e3 kn/m Longitudinal damping of the first series/axle box 0.0 kn s/m Lateral damping of the first series/axle box 0.0 kn s/m Vertical damping of the first series/axle box 5/0.-9/0.3 kn s/m Longitudinal damping of the second series /Bogie side 0/0.0-2/0. kn s/m Lateral damping of the second series /Bogie side 30.0 kn s/m Vertical damping of the second series /Bogie side 6/0.-0/0.3 kn s/m Half of the lateral distance of first series m Half of the lateral distance of second series m Nominal rolling radius of wheels 0.46 m Length between truck pivot centers m Wheelbase of the bogie 2.5 m Height from the mass center of the vehicle to rail surface.7 m Height from the mass center of the wheelset to rail surface 0.46 m Height from the mass center of the bogie to rail surface 0.6 m Table 4. Calculation parameters of the track slab, the supporting layer and the pile-slab structure. Name Strength grade Size (m) Density (kg/m 3 Modulus of Poisson ) of concrete elasticity ratio Track slab C Hydraulic supporting layer C Bearing slab C Piles C Soil type Thickness (m) Table 5. Calculation parameters of the roadbed. Unit weight (kn/m 3 ) Modulus of compressibility Cohesion Poisson ratio Internal friction angle (º) Packing of A and B groups Silty clay Mudstone with sandstone

4 Sensors & Transducers, Vol. 54, Issue 7, July 203, pp ) Calculation conditions. Taking the pile-slab structure whose span is 7.5 m for example, the analysis is done for three kinds of pile-slab structures with different curves. The three different curve radii are as follows: R=400 m; R2=2200 m; R3=, i.e. a straight line. For pile-slab structure, separation may appear between slab and soil because of the vibration of the slab under long-term train load. So two Calculation conditions are calculated: Slab and soil doesn t contact, not considering the supporting effect Slab2 and soil contacts, considering the supporting effect. 3) Calculation model Based on the existing research results, a threedimensional coupling dynamical model is established using ABAQUS finite analysis software including the vehicle, the contact of rail and wheels, the ballastless track and the pile-slab structure [0~]. The model is shown in Fig. 3 to Fig. 5. The slab-soil and pile-soil interaction are simulated by the contact, shown in Fig. 6. Fig. 3. Model of the vehicle. Fig. 4. Model of the contact between rail and wheels. Fig. 5. Model of the pile-slab embankment (partially sectioned). Fig. 6. Model of the contact among slab, soil and piles. Fig. 7. Vertical displacement of the pile-slab structure. Fig. 8. Longitudinal stress of the bearing slab. 4. Mechanical Behaviors Under the Vertical Load The results under the vertical load are shown in Table 6 and Figs

5 Fig. 9. Displacement nephogram of soil. Fig. 0. Displacement nephogram of piles, slab and soil (cross section). Table 6. Results under the vertical load. Pile-slab type R=2200 R=400 Straight line Condition One Two Three Four Five Six Seven Eight Nine Whether or not consider the supporting effect on the slab Y N N Y Y N Y Y N Whether or not allow the separation between soil and slab Y N Y Y N Y Y N Y Vertical displacement Bottom Outer tension stress of the bearing Middle tension stress slab Inner tension stress Inner compression stress Piles Outer compression stress Vertical displacement Compression stress under piles Compression stress under the outer slab Soil Compression stress under the middle slab Compression stress under the inner slab Vertical displacement Results can be drawn as follows from the calculations above: ) The deformations of the pile-slab structure are very small, much far from the limit value. The separation of piles and soil has little effect on the deformation and stress of piles, slab and soil, indicating that the pile-soil interface properties have little effect on the stresses and displacements of the pile-slab structure. 2) The vertical displacement of the slab, the stress at the bottom of piles, the mechanical behaviors of the slab can be influenced if the separation between slab and soil is allowed (i.e. the supporting effect on the slab is not considered). When the supporting effect on the slab is not considered, the stress of the slab increases by.8 % ~ 3.4 %, the stress at the bottom of piles increases by 0.3 % ~.2 %, the deflection of the slab increases by.0 % ~ 2.0 %. It can be seen from the above that the supporting effect on the slab caused by the soil should be considered when the pile-slab structure is designed. The results can be conservative when the supporting effect is not considered. 3) Compared to the pile-slab structure in straight lines, the stress of the slab of the pile-slab structure in curves is basically the same under the vertical load. The difference is less than.5 %. So as the piles. The difference is less than 3 %. It can be seen that the mechanical behaviors of the pileslab structures in curves and straight lines are almost the same when the lateral constraint effect on piles is considered. 238

6 -0.60 With contact between slab and soil Without contact between slab and soil Vertical displacement/mm Longitudinal coordinate of the first span of the bearing slab/mm Fig.. Vertical displacements of the bearing slab (the first and the third conditions). 0.0 soil pile -0. Vertical displacement/mm Depth of the pile/m Fig. 2. Settlements of the pile and soil. 5. Mechanical Behaviors under Vertical and Lateral Coupling Loads In this part a pile-slab model under vertical and lateral coupling load is established to put emphasis on the supporting effect on the slab and the lateral constraint effect on piles caused by the soil. To have a good analysis of the relationship between the mechanical behaviors of the pile-slab structure and the constraint conditions caused by the soil, the soil under the slab is removed step by step. Take the condition whose curve radius is 2200 m and span is 7.5 m for example. The design speed is taken as 200 km/h, the superelevation is 05 mm, parameters of the road bed are taken according to Table 5. Results after applying transverse rocking force, centrifugal force and ZK load to the surface of the rail are shown in Table 7 and Figs It is can be seen from the calculations above: ) The vertical deformation of the pile-slab structure becomes a little larger when slab and soil doesn t contact. That of the slab increases by about 52.9 % that of the pile increases by about 69.4 % after removing the soil of embankment and the clay in the roadbed. That indicates the embankment soil plays a significant role in the supporting of the slab and provides a positive frictional resistance on piles. 2) The lateral deformation of the pile-slab structure increases by approximately 25 % when the slab and soil doesn't contact, indicating that the contact between slab and soil has a certain effect on the lateral deformation of the pile-slab structure. The lateral deformation of the pile-slab structure increases by about 2.5 times when removing the embankment layer and that of the slab already exceeds the limit value by 2mm. The lateral displacement of the pileslab structure increases obscurely when the silty clay layer is removed, indicating that the constraint effect caused by the soil besides piles has a larger relationship with soil properties. Overall, the lateral constraint effect on the piles caused by the subgrade soil is very obvious. The pile-slab structure has significant advantages compared with bridges. 239

7 Fig. 3. Model of the pile-slab structure without embankment. Fig. 4. Model of the pile-slab structure only with the mudstone layer. Table 7. Results under different constraint conditions. Conditions Vertical displacement Bearing slab Piles Soil Lateral displacement Tension stress at the bottom of the slab Mise stress Vertical displacement Lateral displacement Lateral displacement Soil pressure besides the 3# pile Soil pressure besides the 4# pile Fully restricted Slab and soil is separated Separated by m Separated by 2 m Separated by 3 m Separated by 4 m Separated by 5 m Separated by 6 m Separated by 7 m Separated by 8 m Separated by 9 m separation appears fully restricted rem oving em bankm ent rem oving clay layer only with rock layer vertical displacement/m deep of separation/m Fig. 5. Relationship between the vertical displacement of the slab and subgrade soil 240

8 5 separation appears only with rock layer 4 fully restricted removing embankment removing clay layer lateral displacement/mm deep of separation/m Fig. 6. Relationship between the lateral displacement of the pile and subgrade soil 5 separation appears only with rock layer lateral displacement/mm fully restricted removing embankment removing clay layer deep of separation/m Fig. 7. Relationship between the lateral displacement of the slab and subgrade soil. a) only with the rock layer b) fully restricted Fig. 8. Comparison of the vertical displacement. 24

9 a) only with the rock layer b) fully restricted Fig. 9. Comparison of the lateral displacement. radinal displacement/mm along the deep of piles /m only with the rock layer embankment removed fully restricted no contact between slab and soil Fig. 20. Comparisons of the lateral displacements of piles under different conditions. 3) It can be seen from Fig. 20 that whether the roadbed fillings are present or not can have a large effect on the lateral deformation of the piles. Moreover, whether or not considering the contact between slab and soil causes little effect on the lateral deformation of the piles. This proves the roadbed filling is the main factor that controls the lateral deformation of the pile-slab structure. 6. Conclusions ) A three-dimensional refined model of the pileslab structure is established and its mechanical properties under the vertical load are analyzed. Results show that the vertical displacement of the bearing slab, the stress at the bottom of piles, the mechanical behaviors of the slab can be influenced if the supporting effect on the slab is not considered. When the supporting effect is not considered, the stress of the slab increases by.8 % ~ 3.4 %, the stress at the bottom of piles increases by 0.3 % ~.2 %, the deflection of the slab increases by.0 % ~ 2.0 %. It is suggested that the supporting effect on the slab caused by the soil should be considered when the pile-slab structure is designed. The results can be conservative if the supporting effect is not considered. 2) The vertical displacement of the slab increases by about 52.9 % (including the settlement of the pileslab structure as a whole), that of the pile increases by about 69.4 % after removing the soil of embankment and the clay in the roadbed, indicating that the embankment soil plays a significant role in the supporting of the slab and provides a positive frictional resistance on piles. 3) The lateral deformation of the pile-slab structure increases by approximately 25 % when slab and soil doesn't contact, indicating that the contact between the slab and the soil has a certain effect on the lateral deformation of the pile-slab structure. The lateral deformation of the pile-slab structure increases by about 2.5 times when removing the embankment layer, indicating that the lateral constraint effect on piles caused by the roadbed soil is very obvious. The 242

10 pile-slab structure has significant advantages compared with bridges. 4) Whether the roadbed fillings are present or not can have a large effect on the lateral deformation of the piles. In contrast, whether or not considering the contact between slab and soil causes little effect on the lateral deformation of the piles. This proves the roadbed filling is the main factor that controls the lateral deformation of the pile-slab structure. Acknowledgements This work was financially supported by National Natural Science Foundation of China Financing Projects (No ), and Beijing Nova Program (Z ). References []. The Ministry of Railways of The People's Republic of China, Code for Design of High Speed Railway (TB ), China Railway Publishing House, 200,. [2]. Zhan Yongxiang, Jiang Guanlu, Hu Anhua, Wei Yong-Xing, Study of dynamic response of pile-plank embankment of ballastless track based on field test in Suining-Chongqing High-speed Railway, Rock and Soil Mechanics, 2009, 30, 3, pp [3]. Hong Xiao, Guanlu Jiang, Yongxing Wei, Study of flexible arch of model test in column-net structure, Rock and Soil Mechanics, 2008, 29,, pp [4]. Qian Su, Anhong Li, Zhaofeng Ding, Weixiu Cui. Design and Analysis on Pile-Board Structure of Deep Collapsible Loess Ground along Zhengzhou-Xi an Passenger Dedicated Railway Line, Railway Construction Technology, 2007, 2, pp. -4. [5]. Yongxiang Zhan, Guanlu Jiang, Theoretical Exploration on Design of Pile-plate Structure Subgrade in Steep Slope Section of High Side Slope on Wuchang-Guangzhou Railway Passenger Dedicated Line, Journal of Railway Engineering Society, 2007, pp , 0. [6]. Hong Xiao, Xiaoping Gong, Huiting Yue, Research on Analytic Method for Mid-span Slab of Pile-slab Structure, Journal of Railway Engineering Society, 20, 7, pp [7]. Hong Xiao, Research on analytic calculation method for Pile-Slab Structure Design, The st International Conference on Railway Engineering, 200, 8, pp [8]. Hong Xiao, Weiwei Liu, Chengcheng Song. Statics Analysis to Pile-Slab Structure, in Proceedings of the 2 nd International Conference on Railway Engineering, 202, 7. [9]. Huiting Yue, Hong Xiao, Mechanical Analysis to Piled Slab Structure Subgrade of Different Pile Space, in Proceedings of the st International Conference on Railway Engineering, 200, 8, pp [0]. Daphne Lopez, S. V. Kasmir Raja, A Dynamic Error Based Fair Scheduling Algorithm for a Computational Grid, Journal of Theoretical and Applied Information Technology, 2009, 9, 2, pp []. M. Z. Shaikh, Dr. S. F. Kodad, Dr. B. C. Jinaga, Modeling and Simulation of MEMS Characteristics: A Numerical Integration Approach, Journal of Theoretical and Applied Information Technology, 2008, 4, 5, pp Copyright, International Frequency Sensor Association (IFSA). All rights reserved. ( 243