Calculation and Analysis of Tunnel Longitudinal Structure under Effect of Uneven Settlement of Weak Layer

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1 Calculation and Analysis of Tunnel Longitudinal Structure under Effect of Uneven Settlement of Weak Layer 1,2 Li Zhong, 2Chen Si-yang, 3Yan Pei-wu, 1Zhu Yan-peng School of Civil Engineering, Lanzhou University of Technology, *2,Corresponding Author Western Engineering Research Center of Disaster Mitigation in Civil Engineering, 3 Western Zhongda Construction 1,First Author Abstract By analyzing many problems of the longitudinal design of tunnels in soft ground, using the theory of elastic foundation beam and finite element methods, the force and vertical settlement joint set of tunnel longitudinal structure were calculated and analyzed at the bottom of the tunnel where the soil characteristics mutations and the thickness of covered soil layer changes sharply. Considered the effect of uneven settlement of weak layer, a plane numerical model is established based on elastic foundation beam. Then, the force and deformation of tunnel longitudinal structure are calculated and analyzed. By calculating that, the model can make full consideration of all factors which affect the uneven settlement of the tunnel, and are suit for the calculations of the settlement of tunnel in complex conditions. The conclusions recommended reasonable data about the arrangement of settlement joint of the tunnel under the effect of uneven settlement of weak layer. Keywords: Tunnel Longitudinal Structure, Uneven Settlement, Weak Layer 1. Introduction For the large diameter weak layer tunnel, the affect of vertical uneven settlement can not be ignored, especially in the area where the soil characteristics mutations and the thickness of covered soil layer changes sharply. The schematic diagram of the different strata along the tunnel longitudinal structure is shown below in Figure 1. Figure 1. Schematic diagram of the different strata along the tunnel longitudinal At present, the theory models to analyze the tunnel structure generally assume the cross-section is like a quality circle, and use a spring to imitate the interaction between tunnel and soil. Tunnel is equivalent to a homogeneous beam rooted in the foundation. By calculating the elastic foundation beam, we can get some data of differential settlement and force distribution of tunnel vertical structure. Researchers has done many researches by site tests [1], theoretical analysis[2][3][4], numerical imitation[5][6]and other tools[7], to solve those problems such as why and how to eliminate the vertical differential settlement of tunnel[8], tunnel longitudinal stiffness, the model of interaction between tunnel and soil[9], and so on. Yu [10] proposed a reasonable method of dual elastic foundation beam and then deduced the internal force, deformation and ground reaction due to a concentrated force, concentrated couple, local uniformly distributed load, the local linear distribution load on elastic foundation beams. It is a more reasonable and comprehension analytical model which take the Advances in information Sciences and Service Sciences(AISS) Volume4, Number10, June 2012 doi: /AISS.vol4.issue

2 interaction of soil and earth into consideration. Though, there are still some differences between the theory model and the actual project. Therefore, considering the influence of tunnel uneven subsidence of various factors, and using the finite element method, based on the model of elastic foundation beam, the model is set up that can use to solve the calculation of the force and deformation of tunnel longitudinal structure in order to provide a exact theoretical basis for the longitudinal design and construction of weak layer tunnel. 2. Theory Model 2.1. Basic Assumptions (1) The soil and materials of lining structure are in elastic state, and double-sided spring is a non-linear model. (2) Interaction areas between the soil and tunnel do not occur sliding along the vertical beam. (3) Do not take the changes of the underground water and water pressure into consideration for the setting of the settlement joins. (4) Didn t consider soil arching unloading effect along the buried depth of the tunnel, and use the theory of soil column to calculate the earth pressure of the shield tunnel vault, and carries on some corresponding reduction Plane Calculaion Model The schematic diagram of plane FEM calculation model is shown below in Figure 2. FEM transition zone FEM transition zone Soil Equivalent continuous beam of tunnel structure Spring Soil Figure 2. Schematic diagram of FEM calculation model In Figure 2, the external loads mainly include water pressure and the change of the loads worked upon the tunnel at high tide and low tide. For boundary conditions, the displacement of the right side, left side and bottom of the model is limited to zero. The area of the 20 m range on both sides of the model is treated as a transitional zone to consider the boundary effect on the calculation results. The middle area is taken as the effective zone of calculating and analyzing. The spring of the model choose nonlinear spring. For the uneven subsidence of soil layer, it will be achieved by control calculation parameters and local boundary displacement Stiffness Calculation of Elastic Foundation Beam The actual structure of the tunnel is simplified to the elastic beam. Firstly, it is necessary to calculate the inertia and stiffness according to the cross-section and material of tunnel, and take into account the interaction between the tunnel and soil. When the tunnel is simplified to an elastic beam, its stiffness is a reduction. The calculation of the cross-section effective stiffness is shown below by formula (1). EI ηei' ηe π [D4 (D t)4] πηe[d4 (D t)4] The meaning of symbols: D diameter of tunnel; t the sickness of tunnel segment; E the elasticity modulus of concrete; η effective stiffness; I cross-section inertia. 85

3 3. Modeling and Computations 3.1. Load and Conditions Consider all the factors that affect the vertical deformation of tunnel, the main loads in the calculation of the tunnel includes: (1) Its gravity. (2) The water pressure upon overlying soil. For the conditions of calculation, the uneven settlement at the connection area of work well and tunnel structure is mainly considered Model Parameters According to the geological data and structure design parameters, the parameters of structure material and spring stiffness of the tunnel is shown below in Table 1. Table 1. The design parameters of tunnel structure and spring stiffness Design parameters of tunnel structure Material Parameters E(Pa) Parameters of Tunnel Cross Section μ Outer Diameter(m) In Diameter(m) 3.8e Bending Spring Horizontal Spring Vertical Nonlinear Spring Parameters of Spring Stiffness 2.2e e+12 Spring stiffness (Pa) 5.00E E E E E E Displacement (m) 3.3 Build Model The model is build and shown in the figure3. Figure 3. Calculation model of tunnel longitudinal structure under effect of uneven settlement In the calculation model, the initial vertical displacement is 0.05m; the external load act upon the surface is set to 50KN/m. 86

4 Considering the uneven settlement of weak layer at the bottom of tunnel, the force and displacement of the tunnel is calculated on the differential conditions according to the spacing of settlement joint from 20m to 60m. By calculation, when the spacing of the settlement joint is 20m, the main results were as shown in figure4, figure 5, and figure 6. Figure 4. The contour image of displacement when the spacing of settlement joint is 20 m Figure 5. The bending moment diagram when the spacing of settlement joint is 20 m Figure 6. The shear diagram when the spacing of settlement joint is 20 m By calculation, when the spacing of the settlement joint is 30m, the main results were as shown in figure 7, figure 8, and figure 9. Figure 7. The contour image of displacement when the spacing of settlement joint is 30 m 87

5 Figure 8. The bending moment diagram when the spacing of settlement joint is 30 m Figure 9. The shear diagram when the spacing of settlement joint is 30 m By calculation, when the spacing of the settlement joint is 40m, the main results were as shown in figure 10, figure 11, and figure 12. Figure 10. The contour image of displacement when the spacing of settlement joint is 40 m Figure 11. The bending moment diagram when the spacing of settlement joint is 40 m Figure 12. The shear diagram when the spacing of settlement joint is 40 m By calculation, when the spacing of the settlement joint is 50m, the main results were as shown in figure13, figure 14, and figure15. 88

6 Figure 13. The contour image of displacement when the spacing of settlement joint is 50 m Figure 14. The bending moment diagram when the spacing of settlement joint is 50 m Figure 15. The shear diagram when the spacing of settlement joint is 50 m By calculation, when the spacing of the settlement joint is 60m, the main results were as shown in figure 16, figure 17, and figure 18. Figure 16. The contour image of displacement when the spacing of settlement joint is 60 m Figure 17. The bending moment diagram when the spacing of settlement joint is 60 m 89

7 Figure 18. The shear diagram when the spacing of settlement joint is 60 m 4. Calculation Results 4.1. Bending Moment of Tunnel Structure The comparison on variation curve of longitudinal bending moment of the tunnel structure for the different spacing of settlement joint is show in figure 19. The Value of bending moment ( N.m) Spacing 20m Spacing 30m Spacing 40m Spacing 50m Spacing 60m No spacing The range of 0~300m along the tunnel longitudinal Figure 19. The contrast diagram of bending moment of the tunnel longitudinal structure for the different spacing of settlement joint Bending moment (N.m) As show in the Figure 19, along with the increasing of the spacing of settlement joint, the longitudinal bending moment of tunnel structure has a significant reduction when the spacing of the settlement joint is 20 m. The variation curve of maximum longitudinal bending moment of tunnel structure in different spacing of settlement joint is shown in figure 20. Spacing of Settlement Joint Figure 20. The variation curve of maximum bending moment of tunnel longitudinal for the different spacing of settlement joint In figure 20, the maximum longitudinal bending moment of the tunnel structure grow quickly when the spacing of settlement joint is in 20m to 40m section. And when the spacing of settlement joint is in 40m~60m, the growth of maximum longitudinal bending moment is not big. 90

8 4.2. Shear Force of Tunnel Structure The comparison on variation curves of shear force of tunnel longitudinal structure under various condition of the spacing of settlement joint is shown in figure 21. As show in the figure 21, The curve of shear force fluctuates along longitudinal direction where setting settlement joint. It is mainly caused by shear mutations in the settlement joints. When the spacing of settlement joint is 20m, tunnel structure longitudinal shear changes is the most significant, and maximum shear makes larger reductions relative to there is no settlement joint. The variation curve of maximum longitudinal shear force is shown in figure 22 with the various spacing of settlement joint. In figure 22, from the trend of the curve, when the spacing of settlement joint is more than 40m, maximum longitudinal shear force of the tunnel structure growing quickly. And when the spacing of settlement joint in 40m~60m section of tunnel structure, the growth of maximum longitudinal shear force is not big and the gap of maximum longitudinal shear force is relatively small when there is no settlement joint. The value of Shear( N) Spacing 20m Spacing 30m Spacing 40m Spacing 50m Spacing 60m No spacing The range of 0~300m along the tunnel longitudinal Figure 21. The shear contrast diagram for the different spacing of settlement joint Shear (N) S pacing of settlem ent joint (m ) Figure 22. The variation curve of maximumshear of tunnel longitudinal for the different spacing of settlement joint 4.3. Longitudinal Deformation of Tunnel Structure The vertical displacement diagram of tunnel structure for the different spacing of settlement joint is shown in figure

9 Vertical displacement( m) Spacing 20m Spacing 30m Spacing 40m Spacing 50m Spacing 60m No Spacing The range of 0~300m along the tunnel longitudinal Figure 23. The vertical displacement contrast diagram for the different spacing of settlement joint As the figure 23 shows, the structure vertical displacement will slightly larger than that there is no settlement joint. The vertical displacement of the tunnel structure is close to that there is no settlement joint. From the whole structure, the vertical displacement diagrams of longitudinal tunnel structure are similar no matter setting settlement joint or not. That s to say, it has little effect on vertical deformation if setting the settlement joint. 5. Conclusions (1) Based on elastic foundation beam, Numerical computation model of tunnel longitudinal structure is suitable for vertical settlement calculation of the tunnel. The calculation results are showed to be correct and reasonable. (2) For the arrangement of longitudinal settlement joint of tunnel longitudinal structure, It is recommended that according the geological survey data to choose uneven spacing of settlement joint in the whole longitudinal tunnel. In order to eliminate the uneven settlement, it is the best choice when the spacing of settlement joint is 20m, but if the spacing of settlement joint is bigger than 60m, it is unnecessary to set settlement joints. (3) If the interaction between structure and soil and the properties of soft soil are considered at the same time, the obtained results will be more accurate. Deeper research will be needed to do in the future. 6. Acknowledgment This work was financially supported by the Gansu Natural Science Foundation (1107RJYA276); Lan Zhou University of Technology Doctor Foundation (No: ). 7. References [1] Dong-Mei Zhang, Hong-Wei Huang and Jian-Ming Wang, Numerical Study on the Effect of Grouting on Long-Term Settlement of Tunnels in Clay, Computational Science ICCS 2007, Lecture Notes in Computer Science, Volume 4489/2007, , [2] WU Mengjun, ZHANG Yongxing, LIU Xinrong, "Routing Selection Method for Tunnel Design Using Dynamic Search", JCIT: Journal of Convergence Information Technology, Vol. 6, No. 7, pp. 179 ~ 184, [3] Hehua Zhu, Qianwei Xu, Qizhen Zheng and Shaoming Liao, Experimental study on working parameters of earth pressure balance shield machine tunneling in soft ground Frontiers of Architecture and Civil Engineering in China, Volume 2, Number 4, Pages , [4] Jun-sheng Chen and Hai-hong Mo, Mechanical behavior of segment rebar of shield tunnel in construction stage, Journal of Zhejiang University - Science A, Volume 9, Number 7, Pages , [5] Cheng Liu. "Study on Percolation Mechanism and Water Curtain Control of Underground Water Seal Oil Cavern". Computational Structural Engineering, Part 10, ,

10 [6] Yingbo Ji, "Analysis and Optimization Schedule for Tunnel Engineering Based on Information Management and Visual Simulation", JCIT, Vol. 6, No. 5, pp. 175 ~ 182, [7] Zichang Shangguan, Shouju Li, Wei Sun, Maotian Luan, "Model Reference Control for Bulkhead Pressure of EPB Shield in Tunneling", JCIT, Vol. 5, No. 1, pp. 111 ~ 115, [8] Huaina Wu, Yeshuang Xu, Shui-long Shen and Jin-chun Chai, Long-term settlement behavior of ground around shield tunnel due to leakage of water in soft deposit of Shanghai, Frontiers of Architecture and Civil Engineering in China,Volume 5, Number 2, Pages , [9] WU Mengjun, ZHANG Yongxing, LIU Xinrong, LI Xintong, "Forecasting Algorithm for Cracked Surrounding Rock Stability in Large Span Multi-arch Tunnel", JDCTA, Vol. 5, No. 12, pp. 104 ~ 110, [10] Yu Zhankui Huang Hongwei LiuYu, Structural Analysis of Shield Tunnel in Soft Soil Under Locally Even Load, Special Structures,vol.23,No4:75-77,

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