Analysis of Water Pressure in Ballastless Track Crack
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(2) ,:. !1 ". 37. #$% & '()*+,-./01234567. ,. L0øù ÿ;1w Saouma )Øó2ª«J']. , ;. ^L34{]L5ZËm@Aµ¶ Z[\ [59] Tinawi ~ {']^L6ã7HI{8«*L y9¬{|:ª«ÚÛÜ8L0Z;\. ,. ]^L#$@A <Ec¬ª«òB{]^L [1011]. =>@Aì?2']^L èü¥ *. ,. {äK]^L@A@AÊBVWFG8Cª« * ¬c{_9.. 、. ,. ÎD2wK E cdª«VWFGXYZ[. ,. \K ] ^ L a ¢ b £ ¤ ¥ ¦ § a b ¨ © ANSYS w CFX abª«¬ ª«®¯ Z[°. ,. 、. 、. 、. ,. ± Z[²³U~K]^L{ ¶FK]^. ,. LòBJó E#ÉþabVWFGGH ½¿ØiIJKL.. (a)j). (b){w. c 2 FGquj)w{w Fig. 2 Slurry and hollowedout under the track slab. 1. 2 XYZ[ CRTS Ⅱ|q£VWFGñ}F ~`© FGq ()Xp8XUIq bc 3 d e. ÎDZ[p8XJ()X TÂ. 、. 、. ,. ( ), ( ); , , sy~`2{, uk Rs8F=, [ , ] . ; åÇbµ 1 de. 1. 1 ?@ABST\)]UV VWFGXYZ[M¸{»ÃJN²è. ,. ¿BO#`{P²JQ4. R«S ñZ[T{. , , Z^L, [·¸³CD¹º»¼,½¾*¯¿ \«S, ñZ[T{åU]N, BsZ[ÀÁÂ; WÓZ[÷]X^_Z[\, YSZ[\òB`^ L, [·¸³CD¹aR»¼,½¾¯¿Bs Z[ÀÁÂ, bc 1 de. åUVà WÓZ[\]Xx YSZ[\òB. . . . (a)CRTSII |q£VWFGHIT. . . . . . (b)ⅠⅠTc . . . . . . . . . . . . . . . . . . . . . . . (a)R«. . . . . . . . . c 3 | Fig. 3 Calculation model. . . . . . ^ 1 XY_` Tab. 1 Calculation parameters. (b)\« k©. c 1 VWFGZ[\]{fKw^La Fig. 1 Water flow and pressure distribution in crack of the ballastless track. ,. ( ·). -1 d± / km h ¡8 / kN ¡¢ / mm. sª« Z[\k{]6òBÉ. ,. ,. 67 K-|. ,. {^Lwd± [~Z[µT#$Êô{gh s Z[³Âiqj)Þk bc 2 a de lm. () ; , nØo#{ª«J]{34, p8XJF Gq Y ; r s t a *, Ï F G q u X v w,b c 2 (b)de; Y÷, òB{K]^LxyZ [µT, qEZ[{zKL, RdZ[{.. ,. ½ÙZ[°±E L 0. 2 ~ 1. 2 m ²³E h 1 ~ 5 mm Z[\] ]{^` ª« 3 1213. 1 6789:;<=>?@ABS TUVWXYZ[. 、. ù. FGq p8X CA (). CRH3 270 150 2 500. ~` / MPa. 36 000. £¤ ~` / MPa. 0. 20 25 500. £¤ ~` / MPa. 9 000. £¤. 0. 34. 0. 20.
(3) 8 9 : ; < = = >. 38. (. a ^ 1 k©. 67. . fù-|. ¥}ù 998. 2. (· ) ( ·). -3 ¦± / kg m KL§¨È / mPa s. fù. fª . «K¬ V®«¯T. -|. °±f 34. . n)dL = 0 , (1) ∮ (u· L. yí^f{Kaµ²£E dM d =ρ udA + ρ u u n dL = ∑ F dt dt A L. ∮ (·). , (2) m E{;ρ E{¦±;A E £Ù: {T;L E ª ;u E d ± ³ ; n Eª {÷gCD;M E { K F Es={L³. ; sg~`´µ\, HI{«Jª«*qg [ ] LY, ¶·c 4 deZ[{=µT `ÇÈ ; « y Jª«*qg`ÇÈ, ¸ x Â{Z[²³ ω E (3) ω = h + Fβ(x), £Ù: β(x)E+iÈ. 14. x. . ω. . . ( ) (. . c 4 Z[+ie¹c º* Fig. 4 Deformation diagram of crack amplification. ,. 、. , (v ,)¹»¼gi,½¾4£¿ÀfK[ , ],¸: (2y - ω ) ] . (4) v , = v , [1 - ω ÁÂc 4 de{ 1 (0 ~ x Yfù ), ½Ù v , = 0 ,à £ (3 )、(4 )Ä Å £ (1 )Ù,[ , ÆÓ: 3F (5) v, =- β(x)dx. 2ω ∫ f § ` · Z [ \ ] { d ± a 10 15. x y. 2. x. x y. x max. 2 x. 0 y. x. x max. x. 0. 、. ;. ;. ,. ñÌÍ\ÎÏíÐ f{§¨Ñ¤L τ. ,:. [13] ½ Jd±Ò±qZ τ x,y = μ. :. dv x,y dy. ,. (6). £Ù μ EKL§¨È.. (). H4£ 4 ÓÓdC4L· x CD{ aLE. ∑ F x = p x ωx - p L ωL - 12 μF∫x ω2 ∫0 β(x)dx. L. dx. x. x. (7) (5)、(7)ÄÅÔ£(2)Ù,[,ÆÓ: ã(3 )、 6 ρF ρF¨ p = - A(x)+ B (x)+ 5ω ω 2. x. x. . x. pL ωL 12 μF C x + ωx ωx. (). ,. (8). : A(x) = ∫ dx∫ β(x)dx; [ ∫ β(x)] - [ ∫ β(x)] ; B (x) = x. 0. 2. 0. ). . c 5 Ù τ x,FSI Ef~ ª Â{ǤL p η p x EÈÉÊ η x Â{]^L p L EZ[³Â ]{Ë~^©.. L. . . c 5 CLe¹c Fig. 5 Forces acting on the control volume. x. . . . . . L. . τ. η. £Ù. . . . . x. . . . θ. . . 、. ,. . τ. . S yí^f{. . τ. . 0. 2 <=>?@ABXYb2cd. . η. . . 0. 1. ∫. η. 1. 002. 34SY / s. ∫. ),. η. . . 0. 001. [10]. ÁÂc 4 de{ 2 x ~ L Yfù ½CLe¹cbc 5 de. . å~^© / Pa SYþo / s. aµ²£ E dm d = ρ dA + ρ dt dt A. ! 51 ?. x. 2. 0. ωL. ωx. () = ∫ ωdx ∫ β(x)dx. £(8 )½Eª«VWFGXYZ L. C x. x. x. 2 x. 0. [\K]^La¢b£.. 3 ?@ABeF2f'ghEF 3. 1 b2+i ÕZ[=µT«]Z[²³S s £ 9 deZÖª« Z[\K]^L. () , £(8 )í,E£(10 )dei£:. ,.
(4) ,:. !1 ". ( ), F sin(2 πft) A(x)+. (9). F = F m + F o sin 2 πft o. h. . 、. ( ) () 24 πμfF cos(2 πft) A(x)+ p , . (10). o. L. . h3. C. :. 、. Ë© R«Èß ]^LâãäL/Èßå q. Ë©æçîc 7 ½Z[°±E 0. 25 m ²³ E 3 mm. ÚÛÜUèE C30 ~`E 30 GPa £. 24 π2 ρf 2 F2o cos 2 πft B x + 5h2 B. . 、. K]^LËmÈßÛêñ]à áZ[ÚÛÜ. A 2. . 4 ?@ABnoop. ;. ;. £Ù F m Eª«¯ F o Eª«®¯ f Eª« ¬. ½Ù A 6 ? ñ Y { å U × ^ è ò B { B 6ñZ[=µT{+i ϲ³+,èò B C 6?ñf§`èòB{. Õ y h S. , ,. ,. ,. ,. , R, ª«E 25 ± 10 kN,¬E5 Hz,ª«i£EZ Ö. Z[\{]^L)Øcñ±ò^Lâãä (PT1、PT2、PT3)Ì,âãä{Ìñ±E 1 Pa, óYôE 10 ms. )ØËmÌÍÓÓ {Z[\]^Laîc 8. . . . (). . E¡#Éþ@A£ 10 Ù A 6w C 6{ÛÆ ÇÈ R CA E C 6¾*¯J A 6¾*¯{. ,:. . . . . . . ,. ,. (11) Ü£(11 )íÐ,sf`Fy+S,R CÔª«¬wZ[²³{Ý9; M¸R« , ¬wZ[²³{aR §`{stã 20 、 30 Hz ª« 7. )Ø£(11 )aÕ 10 、 R MZ[²³{+,ÇÈ, bc 6 de. ñYí Ð, ~c¬ª«{VWFGXYZ [, ÕZ[²³* 2 mm S,f§`~K] ^L{?ÙÚ{, YSK]^LÛêñ¢b £{ A 6dÞ,½]^L*JR«¬¹Å ÆCÇÈ, JR«®¯¹g`ÇÈ,JZ[²³ 6μ = 2 . πρh f. . . qÉÆÊÇÈ.. ( :) ( : ). c 7 Ëmõö ¥ cm Fig. 7 Experimental setup unit cm. . . . . . . . . . . . . )Øc 8 Ù{lmÌËwÍH´. ,. . íÐ ]^LalmÌËH´wÍH´¥. . . . . . . . .
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(6). c 6 f§`{ Fig. 6 Effect of the fluid viscosity. , ,. Ù÷{ÉÏ` Y íA<EÎDE {K]^ Lø£2Î?ZF{.. . . . c 8 Z[\]^La Fig. 8 Distribution of water pressure in the crack. . . . . CA. CA. . . ¸. R CA. ,. ¤E 0. 2. ]àÙéÅ 20 ℃ {] ]êë^Lâ ãä. ª«ñ 250 kN ì*íÖî^ïðËmó. Z[+i ϲ³+,èØq{^L+, ?ÙÚ{ YS B 6~Z[\K]^L{ íy. 3. 2 jklDmgh. ,. . 4 π ρf. 2. . 2. px =. 39. #$% & '()*+,-./01234567. . 5 6789:;<=>?@ABC DEF 5. 1 qrsZ[ ùLöTI{| îc 3. (. ),¤ .
(7) 8 9 : ; < = = >. 40. ,. ,. ANSYS J CFX #$°±f 34ab abR«. 、. 、. 、. ! 51 ?. ,. de ½Ù]NZ[}ù{¥§æçE 10 mm Z [ûÃ}ùfù¥§æçE 0. 5 mm ü |{¥§E 66 002 ü ý9E 73 027 ü.. ¬ R«®¯ ²³ Z[°±U~K]^ L{. |{Júk¥¦§¬bc 9. ;. ,. (a)áZ[VWFG. (b)Z[\] c 9 ¥¦§| Fig. 9 Finite element model. 5. 2 tuWEF 5. 2. 1 ª«¬{. 、. ). ,. °E 1 m ²³E 3 mm {VWFGZ[ s. ,. . . . . . . . . . . . . .
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(12) . . . . . . . . . . . (、、、、、、. ®¯E 75 kN {y9¬ 10 15 20 25 30 35 40 Hz ª« Z[\]^La]^LÔ ¯Mª«¬{+,bc 10 de.. (b)]^La(¯þ). (c)]^LÔ¯. c 10 ª«¬~]^L{ Fig. 10 Effect of the loading frequency on water pressure. () ( ) , ¹º»¼, ½¾*¯¿BsZ[ÀÁÂ;]^L {aíÜwK{ÿ±!¢ "; ÕZ[T×^fS, ñfíÐ, · ¸Z[³CDfd±6staR, ½d±¹a R»¼; d±{aR¶µeK{aR,ù LK, dC4LCDJKaR{C DÉÏ, ñYíî,]^L·¸Z[³CD¹º. () , {aRèaR, #]^LJª«¬2Î¹ÅÆC. ñc 10 a wc 10 b íÐ ]^L·¸Z[. ,. (、、、. ,. . .
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(33). (b)]^La(¯þ). (c)]^LÔ¯. c 12 Z[²³~]^L{ Fig. 12 Effect of the crack opening on water pressure. () ( ) , ½¾*¯¿BsZ[ ]^L·¸Z[¹º»¼, ( ) , . 12 c ÀÁ ñc íÐ ¢bJ¯þ2 , ÎÉÏ ½]^LM¸Z[²³{aRèº; ñc 12 a wc 12 b íÐ VWFGZ[\. #K]^LJZ[²³¹ÉÆÊÇÈ.. 5. 2. 4 Z[°±{ ²³E 3 mm y9°± 0. 2 0. 4 0. 6 0. 8. ( 、 、 、 、 , ,. a]^LÔ¯MZ[°±{+,îc 13.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (a)]^La(¢b). . . . . . . . . . . . . . ,. 、 ) 、. 1. 0 1. 2 m { V W F G X Y Z [ s ® ¯ E 75 kN ¬E 30 Hz {ª« Z[\]^L. . . . . . . . . . . . . . . (b)]^La(¯þ). (c)]^LÔ¯. c 13 Z[°±~]^L{ Fig. 13 Effect of the crack length on water pressure. (). () , [\]^L·¸Z[¹º»¼, ½¾*¯¿Bs Z[ÀÁÂ. ñc 13 (c )íÐ,¢bJ¯ þ2ÎÉÏ,½]^LM¸Z[°±{aRèa R; ÕZ[°± 0. 4 m S,òB{]^L , YS]^L~HI{]L5Z2Îí y; ÕZ[°±* 0. 4 m m,]^LM¸Z[ °±{aRè$daR, òB{]^Lxy Z[µT, ÕÀÁ{¤L©±%&'({)Z *`S, ¿B]L5Z, WHI°Y+,. -4=>@A,~ª«,sZ[ ñc 13 a wc 13 b íÐ VWFGXYZ. ,. i./0y+S $d±w¡8?VW. , $d±J¡8{a*èaR, #J$d±2 Î¹ÅÆCÇÈ, J¡8¹g`ÇÈ.. FGZ[\]^L{Ðü8ê ]^LM¸. 6 t v. ,. 1~c¬ª« VWFGXYZ[. , 、 、 þ, ÓAHÍ: (1)f{§`,2wK ª«VWFG , \]^Laúû )ØÍab Ëm@A ¯.
(34) 42. 8 9 : ; < = = >. ;. XYZ[\]^La¢b£ )ØËmm2µ ¶ ÍJËmÌËH´2ÎÉÏ.. ! 51 ?. [5] ÿ;1,3DE. ']^LÚÛÜF K )Z 2007 , 38 (7 ):792798. ËmÌ[J]. ]G+,, Jianmin. Experimental XU Shilang, WANG. , (2)ª«,VWFGXYZ[\K determination of doubleK fracture parameters of ]^L?ñf§`、Z;²³、ª«¬wª concrete under water pressure[J]. Journal of Hydraulic «® ¯ U - 4 Þ {;Õ Z [ ² ³ * Engineering,2007 ,38 (7 ):792798. 2 mm S, f§`{2Îíy, YS] [6] BRHWILER E, SAOUMA V. Water Fracture ^L*Jª«¬¹ÅÆCÇÈ, Jª«®¯¹ interaction in concrete,part Ⅰ:racture properties[J]. JZ[²³¹ÉÆÊÇÈ;¯ g`ÇÈ, ACI Materials Journal,1995 ,92 (3 ):296303. þJÍab2ÎÉÏ. [7] BRHWILER E, SAOUMA V. Water Fracture interaction in concrete,part Ⅱ:hydrostatic pressure in (3)Z[\]^L·¸Z[³CD¹º cracks[J]. ACI Materials Journal,1995 ,92 (3 ):383 »¼, ¾*¯¿BsZ[ÀÁÂ. 390. _w0O: [8] SLOWIK V, SAOUMA V. Water pressure in. [] Engineering,2000 ,126 (2 ):235242. [9] SHINMURA A,SAOUMA V. Fluid fracture interaction 929934. in pressurized reinforced concrete vessels[J]. Materials WANG Ping,XU Hao,CHEN Rong,et al. Effects and Structures,1997 ,30 (2 ):7280. analysis of cracking of CRTS Ⅱ slab track on 10 ] TINAWI R,GUIZANI L. Formulation of hydrodynamic [ subgrade[J]. Journal of Southwest Jiaotong University, pressure in cracks due to earthquakes in concrete 2012 ,47 (6 ):929934. dams[J]. Earthquake Engineering and Structural [2] 788,9:;,ÿ<=,U. u>q{w~q£VW Dynamics,1994 ,23 (7 ):699715. FG$KL_`{ [J ]. &'()*++,, 11 ] JAVANMARD F, LEGER P, TINAWI R. Seismic [ 2014 , 49 (6 ):951966. structural stability of concrete gravity dams considering REN Juanjuan, YAN Xiaobo, XU Guanghui, et al. transient uplift pressures in cracks[J]. Engineering Effect of contact loss underneath concrete roaded on Structures,2005 ,27 :616628. dynamic performances of slab Tracksubgrade [12] Ù&HIÝw-eGk. eD·[2005]754 JKL system[J]. Journal of Southwest Jiaotong University, gVWFG·M'[S]. NO:Ù-eGPQ, 2014 ,49 (6 ):951966. 2005. [3] ÿ!",MNO,S+T. ª«®¯~VWFGHI [ 13 ] 5oR. hifL+ [M ]. ST:&Ù1B*+ 2015 (1 ):32 Z[]^L [J ]. eGhi+,, 2008 :104105. PQ, 37. [14] U.V. ~`L+ [M]. NO,cUQjPQ, XU Guihong,YANG Rongshan,LIU Xueyi. Impact of 2001 :109114. load amplitude on the water pressure of nonballasted [15] WXG,7YD,3Z[. \]JÚÛÜ]L5Z; track structure[J]. Journal of Railway Engineering 2005 , 36 (6 ): \]^La{[J ]. ]G+,, Society,2015 (1 ):3237. 656661. [4] %&,?&@,A:=,U. ']q£VWFG LI Zongli,REN Qingwen,WANG Yahong. Formula CA ()L + ` * + , [J ]. c d e f B C,2014 , for water pressure distribution in rock or concrete 5 (4 ):1014. fractures formed by hydraulic fracturing[J]. Journal of YAN Hua,HU Huafeng,ZENG Xiaohui,et al. Studies Hydraulic Engineering,2005 ,36 (6 ):656661. on mechanical changes of CA mortar for slab track under hydrostatic effect[J]. High Speed Railway Technology, (@ABC:D E FABC:G H) 2014 ,5 (4 ):1014. [1] 3,ÿ4,56,U. f2= CRTSⅡ|q£FGZ 2012 , 47 (6 ): [ab [J ]. &'()*++,,. propagation concrete cracks J . Journal of Structural.
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