Dynamic performance of bridge approach subgrade with improved soil as base course

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1 40 6 ( ) Vol.40 No Journal of Central South University (Science and Technology) Dec ( ) D Alembert Lagrange 0.05~0.35 mm ~19.5 kpa 5% U211.4 A (2009) Dynamic performance of bridge approach subgrade with improved soil as base course HU Ping 1, WANG Yong-he 1, QING Qi-xiang 2 (1. School of Civil and Architectural Engineering, Central South University, Changsha , China; 2. Department of Mechanical Engineering and Automobile, Hunan University, Changsha , China) Abstract: Dynamic strength was calculated by dynamic triaxial test and parameter-fitted method, and improved soft rock can fill the bridge approach embankment using permitted dynamic strength as a standard to judge. Based on weak variational form of the equilibrium equations for the transitional section in D Alembert method and whole Lagrangian form, an analysis model of semi-infinite tri-dimensional spatial finite elements was founded for the bridge approach embankment system, the longitudinal dynamic and time varying characteristics of the system at different train speeds were further analyzed, and this results were close to actual measure results, which approves the correctness of the model. The results show that under the train load, the fluctuant range of vertical vibrating displacement is from 0.05 mm to 0.35 mm and less than the controlling value. The fluctuant range of vertical vibrating elastic strain is less than and the embankment is in the state of small deformation. The fluctuant range of vertical vibrating stress is from 15.5 kpa to 19.5 kpa, and it is far below the dynamic strength of improved soft rock. Based on a comprehensive analysis, it is more rational to adopt rigid transition in this section, and improved soft rock with 5% cement can fill the bridge approach embankment. Key words: bridge approach subgrade; soft rock improved with cement; dynamic characteristics; dynamic stress ( ) (1983 ) hupingfly@yahoo.com.cn

2 1706 ( ) 40 Makoto [1] [2] [3] ( 140 km/h) [4] [5] [6] Galerkin Lagrange [7] [8] [9] β σzl K σ bcu η R g cr h (1) σ bcu (28 d) kpa β β=1.2 σ zl kpa h [9] h=0.7 m σ zl 50 kpa h=2.5 m σ zl 22 kpa η g [9] K h ( ) R cr R cr 0.45 K h =0.95 σ zl 50 kpa (1) σ bcu 117.8η g η g =0.95 σ bcu 124 kpa η g =0.85 σ bcu kpa K h =0.90 σ zl 22 kpa (1) σ bcu 52.8/η g η g =0.95 σ bcu 55.6 kpa η g =0.85 σ bcu 62.2 kpa 1.2 1% 50% 1% θ σ d, f = kn (2) k θ N σ d, f 1% β 1 ε p = αn (3) 1 + N ε p α β α β 1% (10 8 ) % 1ω a σ 3

3 Table 1 Dynamic strengths of soft rock improved with cement χ/% K h w a /% σ 3 /kpa σ d, f /kpa χ=3% σ 3 =25.0 kpa K h = kpa CA 5% CFG ANSYS APDL Timoshenko CA Lagrange [6] t () t () t = () t + () t + () t + int ext kin () t + () t (4) dam coup () t int () t exp () t kin () t dam () t coup (4) δ () t = δ () t + δ () t + δ () t + int ext kin δ () t + δ () t (5) dam coup [10 12] δ () t coup Lagrange Lagrange Lagrange α Lagrange Lagrange α α Lagrange λ * * T 1 T ( u, α, λ) = ( u) + λ g( u) + αg ( u) g( u) (6) 2 g(u)=0 ( u) (1) () t coup u Newton-Raphson [13] m v=350 km/h m 3.0 m m 196 kn 125 kn 18.0 m 2.5 m 25.5 m 124 kn 78 kn 48.0 m 3 m 6 m 51.0 m

4 U X =0 U Y =0 0 2 Table 2 Calculational parameters E/ GPa ν ρ/ (kn m 3 ) Φ/ ( ) ( ) 40 σ c / MPa CA % % CFG E ν ρ Φ σ c 1 Fig.1 Calculation model m ( m) mm m/s 11 m/s 2 50 kpa ( m) 0.34 mm 0.01 m/s 11 m/s 2 13 kpa ( 7.5 m) 0.27 mm m/s 2.5 m/s 2 9 kpa mm 37 kpa mm 4 kpa ~0.35 mm 0.35 mm [14 15]

5 (a) ; (b) ; (c) ; (d) ; (e) Fig.2 Relationships between time and dynamic response in some cross section 15.5~19.5 kpa [11] 0.002~0.013 m/s 2~9 m/s 2

6 1710 ( ) ~5 Fig.3 (a) ; (b) ; (c) ; (d) v/(km h 1 ): 1 150; 2 200; 3 250; 4 300; Relationships between longitudinal distance and dynamic response at different train speeds Fig.4 Dynamic displacements changing at different depths below track Fig.5 Dynamic stress changing at different depths below track

7 a. b. c. d. 5% [1] Makoto S. Vibration behavior of roadbed on soft grounds under trainload[j]. Quarterly Report of RTRI, 1990(31): [2],,. [J]., 2005(5): LIU Lin-ya, LEI Xiao-yan, LIAN Song-liang. Analysis of dynamic response by transition zone of speed-raise railway[j]. Journal of Railway Engineering Society, 2005(5): [3],. [J]., 1963, 9(2): YANG Can-wen, GONG Ya-li. Dynamic strength and vibration for subgrade due to running train[j]. China Civil Engineering Journal, 1963, 9(2): [4],. [J]., 1996, 31(1): CAO Xin-wen, CAI Ying. A model test study of the dynamic performance of subgrades[j]. Journal of Southwest Jiaotong University, 1996, 31(1): [5],. [J]., 1995, 17(1): LI Jun-shi, LI Ke-chuan. Finite element analysis for dynamic response of roadbed of high speed railway[j]. Journal of The China Railway Society, 1995, 17(1): [6]. [D]. :, QING Qi-xiang. Study on dynamical characteristics in soft zone for ballastless tracks on high speed railway[d]. Changsha: School of Civil and Architectural Engineering, Central South University, [7],,,. [J]., 2001, 1(1): CAI Cheng-biao, ZHAI Wan-ming, ZHAO Tie-jun, et al. Research on dynamic interaction of train and track on roadbed-bridge transition section[j]. Journal of Traffic and Transportation Engineering, 2004, 1(1): [8],,. [J]., 1999, 16(5): LUO Qiang, CAI Ying, ZHAI Wan-ming. Dynamic performance analyses on high speed railway bridge-subgrade transition[j]. Engineering Mechanics, 1999, 16(5): [9]. [R]. :, Ministry of Railway of People s Republic of China. Optimization of structure type and improving stuffings on Beijing Shanghai high-speed railway subgrade[r]. Beijing: Ministry of Railway of People s Republic of China, [10]. [M]. :, 2002: ZHAI Wan-ming. Vehicle-track coupling dynamics[m]. Beijing: China Railway Press, 2002: [11]. [M]. :, 1997: FU Yi-ming. Nonlinear dynamic analysis of structures[m]. Guangzhou:Jinan University Press, 1997: [12] Belytschko T, Liu W K, Moran B. Nonlinear finite elements for continua and structures[m]. London: John Wiley & Sons Ltd, 1998: [13] Wills J R. Hertz contact of anisotropic bodies[j]. Journal of Mechanics and Physics of Solids, 1966, 14(2): [14] Chung L, Hulbert G. A time integration algorithm for structural dynamics with improved numerical dissipation:the generalized α-method[j]. J Appl Mech, 1993, 60(4): [15],,,. - [J]. :, 2008, 39(3): XIANG Jun, WANG Yang, HE Dan, et al. Model of vertical vibration of train and floating slab track system in urban rail transit system e[j]. Journal of Central South University: Science and Technology, 2008, 39(3):

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