40 6 ( ) Vol.40 No.6 2009 12 Journal of Central South University (Science and Technology) Dec. 2009 1 1 2 (1. 410075 2. 410082) D Alembert Lagrange 0.05~0.35 mm 3 10 5 15.5~19.5 kpa 5% U211.4 A 1672 7207(2009)05 1705 07 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 410075, China; 2. Department of Mechanical Engineering and Automobile, Hunan University, Changsha 410082, 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 3 10 5 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 2009 01 252009 04 09 (50678177 50778180) (1983 ) 13875997482 E-mail: hupingfly@yahoo.com.cn
1706 ( ) 40 Makoto [1] [2] [3] ( 140 km/h) [4] [5] [6] Galerkin Lagrange [7] [8] 1 1.1 [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 138.6 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 ) 10 8 1% 1ω a σ 3
6 1707 1 Table 1 Dynamic strengths of soft rock improved with cement χ/% K h w a /% σ 3 /kpa σ d, f /kpa 3 0.95 12.0 25.0 187.7 4 0.90 12.0 25.0 278.9 0.92 12.0 25.0 338.7 0.95 12.0 25.0 417.4 0.98 12.0 25.0 551.8 0.95 8.5 0 164.9 0.95 11.0 0 236.6 0.95 12.5 0 248.1 0.95 14.4 0 223.4 0.95 16.2 0 189.4 5 0.95 11.0 0 406.8 6 0.95 11.0 0 568.3 7 0.95 11.0 0 671.6 χ=3% σ 3 =25.0 kpa K h =0.95 187.71 kpa 2 2.1 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] 2.2 3.5 m v=350 km/h 2 4 11.46 m 3.0 m 21.29 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
1708 2 1 U X =0 U Y =0 0 2 Table 2 Calculational parameters E/ GPa ν ρ/ (kn m 3 ) 210.000 0.300 78 Φ/ ( ) ( ) 40 σ c / MPa 35.000 0.167 30 CA 0.095 0.400 18 24.000 0.200 27 +5% 1.980 0.240 24 45.8 1.326 0 +5% 0.470 0.300 19 28 0.046 5 CFG 0.534 0.240 23 E ν ρ Φ σ c 1 Fig.1 Calculation model 2.3 2 3 m 1 2 1 2 2 1 1 2 ( 0.652 587 m) 0.375 mm 0.014 m/s 11 m/s 2 50 kpa 2.7 10 5 ( 1.052 587 m) 0.34 mm 0.01 m/s 11 m/s 2 13 kpa 2.2 10 5 ( 7.5 m) 0.27 mm 0.007 5 m/s 2.5 m/s 2 9 kpa 0.2 10 5 0.035 mm 37 kpa 0.5 10 5 0.070 mm 4 kpa 2.0 10 5 10 24 4 2.4 3 0.05~0.35 mm 0.35 mm [14 15]
6 1709 (a) ; (b) ; (c) ; (d) ; (e) 123 2 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
1710 ( ) 40 2.5 4~5 Fig.3 (a) ; (b) ; (c) ; (d) v/(km h 1 ): 1 150; 2 200; 3 250; 4 300; 5 350 3 Relationships between longitudinal distance and dynamic response at different train speeds 1 234 4 Fig.4 Dynamic displacements changing at different depths below track 123 5 Fig.5 Dynamic stress changing at different depths below track
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