地铁线路平面曲线设计相关参数的确定

收稿日期:20030317作者简介:欧阳全裕(1938)),男,高级工程师,1963年毕业于长沙铁道学院铁道建筑专业。

地铁线路平面曲线设计相关参数的确定欧阳全裕(铁道第三勘察设计院 天津 300051)摘 要 针对地铁不同于一般铁路的特点和现有技术资料不完全适用的情况,对地铁线路平面曲线设计中如何合理确定相关参数问题作了较详细论述。

关键词 地铁 线路 曲线 设计 参数 确定地铁线路平面曲线设计涉及行车速度、圆曲线半径、缓和曲线长度、外轨超高、线间距加宽等多个参数,各参数相互关联制约。

1993年发布的现行5地下铁道设计规范6(GB5015792)(以下简称5设规6)中有关规定尚不尽完善,而地铁又有其不同于一般铁路的自身特点,既有的铁路设计手册等技术资料也不完全适用,因此,设计中常需自行计算合理确定这些参数,以期取得地铁线路较好的技术条件和节省部分工程投资。

1 曲线半径选择曲线半径应根据行车速度、沿线地形、地物等条件因地制宜由大到小合理选定。

地铁线路不同于野外一般铁路,它往往受城市道路和建筑物控制,曲线半径选择自由度小,常须设置较小半径曲线。

地铁5设规6规定:/最小曲线半径一般情况300m,困难情况250m 。

0在实际设计中,对250m 半径曲线,因其钢轨磨耗陡然加剧,除非因特殊条件控制不得已时方可采用,一般应控制在最小300m 。

例如,天津地铁1号线南段,因受津萍大厦桩基(地下线)和城市干道交叉口及地铁设站位置(高架线)控制,经多次研究比选,设计了3处300m 半径曲线,最终经市建委审批确定。

2 曲线超高与限速计算列车通过较小半径曲线地段,为保证行车安全和乘客舒适要求,列车必须限速运行。

列车通过曲线的最大允许速度(通常简称曲线限速),根据曲线外轨超高和旅客舒适度计算确定。

列车在曲线上运行时产生惯性离心力使乘客有不适感。

因此,通常以设置外轨超高产生向心力,以达到平衡离心力的目的。

从理论上分析,车体重力P 产生的离心力为:J =Pv 2/gR(1)由于设置外轨超高使车体向曲线内侧倾斜产生的车体重力P 和轨道对车辆的反力Q 的合力形成向心力(图1)为F n =P h/s(2)当F n =J 时,可得h =Sv 2/gR =11.8V 2/R(3)式中 g )))重力加速度,9.8m/s 2;r )))曲线半径,m ;s )))内外轨头中心距离,取1500mm ;v 、V )))行车速度,v 单位为m/s ,V 单位为km/h ;h )))所需外轨超高度,mm。

图1 超高与向心力关系图由式(3)可见,当曲线半径一定时,速度越高,要求设置的超高就越大。

为保证行车安全,又必须限制超高的最大值h max ,因此,当速度要求的超高超过h max 时,即产生了欠超高h q 和未被平衡的离心力而影响乘客舒适度,因而对欠超高值也必须有所限制。

我国客货混运铁路规定,一般情况下,曲线最大超高150mm ,允许欠超高75mm ,曲线限速为4.32R 。

地铁5设规6规定了曲线最大超高值120mm ,而对欠超高值未作条文规定,但从乘客舒适要求角度,根据国内外试验资料,规定/允许有不超过0.4m/s 2的未被平衡横向加速度0,据此可推算出地铁线路允许的最大欠超高值。

对某一实设曲线而言,超高h 是定值。

当列车以v max 通过时,将产生最大的欠超高h qma x 为#线路/路基#h q max=h-Sv2max/gR=Sv2/gR-Sv2max/gR=s(a-a max)/g=-153$a max(4)式中各参数含义同式(3)。

右边负号表示欠超高, $a max为未被平衡的离心加速度允许最大值。

以$a max =0.4m/s2代入式(4),即可得出地铁允许的最大欠超高值为h qmax=153$a max=61.2mm铁路外轨超高值通常按5mm取整,得60mm。

可见地铁允许的最大欠超高值60mm,小于客货混运铁路允许的最大欠超高值(75mm),即允许产生的未被平衡的离心力较小,从而保证了专运旅客的地铁具有较好的乘坐舒适度。

据此可得出适用于地铁线路曲线限速V Qmax为V Qmax=(h ma x+h qmax)R/11.8=(120+60)R/11.8=3.90R(5)由式(5)便可简捷地计算出不同较小半径的曲线限速列于表1。

表1较小半径曲线限制速度km/h R/m250300350400450500550V Qm ax61.767.573.078.082.787.291.55设规6规定,我国地铁设计最高速度90km/h,国内现有地铁大多采用80km/h,由表1可见,当曲线半径分别为550m和450m及以上时,列车通过该曲线地段时已不限速,可按设计最高速度运行。

根据表1曲线限速,由式(3)可计算出较小半径曲线外轨设计超高理论值为170~179mm,按5设规6规定的最大超高值120mm实设,其差值即产生的欠超高为50~59 mm,均小于允许的最大值60mm,即均可满足未被平衡横向加速度小于0.4m/s2的要求。

3合理配置缓和曲线长度地铁5设规6列有各种曲线半径对应不同行车速度的缓和曲线表,表列缓和曲线长度均可保证行车安全和旅客舒适度的要求。

但应注意的是,设计中对某一半径圆曲线配置缓和曲线长度不可随意择取,无特殊理由,应严格按该曲线限速即表1所列行车速度(通常按5 km/h取整值)选取与之相匹配的或较长的缓和曲线长度,即使为满足曲线加宽要求配置左线的较短缓和曲线长度时,其长度也应当与曲线限速相匹配,以避免因缓和曲线长度的限制而降低了曲线地段行车速度。

4曲线线间距加宽地铁双线并行区间曲线地段为满足车辆、设备、建筑等限界要求,曲线地段线间距应在直线地段线间距基数上予以加宽。

其加宽值应根据车辆选型、曲线半径、外轨超高等计算确定,其计算式为曲线内侧加宽E内=L12+a28R+X4c os A+Y4sin A-X4(6)曲线外侧加宽E外=L02-(L12+a2)8R+X8cos A-Y8sin A-X8(7)式中R)))圆曲线半径,mm;A)))外轨超高角度,A=arcsin h/s;L0)))车体长度,mm;L1)))车辆定距,mm;a)))车辆固定轴距;(X4、Y4),(X8、Y8)分别为计算加宽的控制点座标值。

以地铁5设规6中的国内常用的国产B型车为例,式8、式9代入各参数后可简化为E内=20506250/R+1593cos A+3282sin A-1593(8) E外=24618750/R+1625cos A-432sin A-1625(9)根据式8、式9可计算出不同半径曲线线间距加宽值W=E内+E外,列于表2。

表2曲线线间距加宽值mm R/m2503003504004505006007008001000120015002000W399368347331318308293255230183147122875左线圆曲线半径的确定与一般铁路不同,地铁应为右侧行车的双线铁路,线路设计通常以右线为基准,其圆曲线半径一般设计为整数;左线按同心圆设计,其半径按下式计算确定R左=R右?D?W=R右?D?$G(10)式中R左、R右)))分别为左、右线圆曲线半径;D)))直线地段线间距;W)))曲线线间距加宽值,由表2查取;$G)))左、右线缓和曲线内移值的差值。

式中,右偏角曲线取正号,左偏角曲线取负号。

设计中通常采用左、右线匹配不同缓和曲线长度的方法,利用其内移值的差值$G大于等于W值来满足曲线加宽的要求。

但应注意配置的缓和曲线最小长度,不应短于按表1曲线限速相匹配的缓和曲线长度。

参考文献1GB5015792地下铁道设计规范2西南交通大学主编.铁道工程.北京:中国铁道出版社,2000#线路/路基#RAILWAY STANDARD DESIGNNo.7,2003Abstracts and KeywordsA n A nalysis of the Selection of Desig n Parameters for Hig h-speed Ra ilway StructuresW ang Xingduo,Zhang Duan,Han QimengAbstract An anal ysis was made of research achievements on high-speed railway of China.A sum mary was gi ven of speed increase of Guangzhou-Shenzhen quasi high-speed rail way and existing rail ways. Tracks were made for the latest technological develop ment of hi gh-speed railway design and construction of foreign countries.Based on tes t opera-tion of Qinhuangdao-Shen yang Passenger Dedicated Rail way,an analy-si s was made of opti mization design of structures for higher speed passen-ger dedicated rail ways.Keyw ords high-speed rail way;railway line;bridge;design parame-ter;optimizationDetermination of Design Param eters for Horizontal C urve of Metro LinesO uyang Q uanyuAbstract Based on disti nct characteristics of metro,a detailed descrip-tion was given of determination of appropriate design parameters for hor-i zontal curve of metro lines.Keyw ords metro;railway line;cu rve;design;parameter;d etermi nation Strengthening of Soft Soil Subgrade by Vacuum Pre-com paction M ethodYuan GuanglongAbstract A descripti on was given of the principle and construction technology of vacuum pre-compaction method and its practical applica-tion.An analysis was made of the effect of this method i n strengthening soft soil subgrade.Keyw ords vacuu m pre-compacti on method;soft soil subgrade treat-ment;construction technologyA n Analysis o f Stable Bearing C apacity of Long Spa n Steel Tubular Co ncrete Arch BridgeY an Quansheng,Xu ShengqiaoAbstract A di scussion was presented of elastic s tability and ultimate bearin g capacity of l ong span steel tubular concrete arch bridge during construction and operation.In analysis and computation,the i mpact of the following factors was taken i nto consideration:rigidity variation of bridge structure at different s tages;successi ve formation of section;and ultimate beari ng capacity of s tructural members.Keyw ords Keywords steel tubular concrete;arch bridge;ultimate bearin g capacity;stability;non-linearTechnological Research ov er Medium and Small Span Long Con-nected C ontinuous Girder BridgeSong Shunchen,W ang Zhaohu,Niu Y uanzhiAbstract A brief descrip tion was given of research achievements on mediu m and small span long con tinuous gi rder brid ge,including longitud-i nal force tran smi ssion sys tem,longitudinal force of long welded rail,spe-cial requirements on design of gi rders,piers and abutments,longi tudinal force transmission device and expansion ins tallation,dyna mic analysis of car-bridge coupling,and econ omic and technical comparison,etc. Keyw ords hi gh-speed railway;medium and small span;long con-nected continuous girder;continuous girder brid ge;research Wind Resistance Design for Lizig ou Extra-large Bridge During its Co nstructionZhang Shi.anAbstract Wind resistance design was applied to the temporary struc-tures of Lizigou Extra-large Bri dge to increase its wind resistance.An analysis was made of dynamic property of main structure of the bridge un-der typical working condi tions,and wind load internal force was calculat-ed.Wind resistant measures were put forward at each construction stages.Keyw ords high way bridge;wind resistance design;dynamic property; buffeting;wind load internal force;measu reA pplication of Ground Surface Dynamic Well-point Dew atering M ethod to the Sand Stratum Section of Shenzhen MetroXue Momei,Deng DunyiAbstract Based on the application of ground surface dynamic well-point dewateri ng method to a section of Shenzhen metro,an analysis was made of the ground settlement caused by well-point dewaterin g for the purpose of effective control of over settlement.Keyw ords metro;dynamic well-point dewatering;ground settle-ment;anal ysi s of settlementA Comparative Study on Two A dvance Pre-support Technologies for Ground Settlement C ontrolG ao Chenglei,Zhu Y ongquanAbstract In the construction of urban pedestrian tunnel of Guangzhou, the measured ground settlement value exceeded the permi ssible value.To find out the reason and seek more appropriate construction program,a si mulation calculation was conducted to actual program and alternative program through three-di mensional fini te element parative calculation result i ndicated the disadvantage of the original program,and pointed out that strengthening the surrounding ground by chemical churn-ing pile may effectively control ground settlement.Keyw ords tunnel;advance pre-support;three-dimensi onal fini te element;ground settlementVentilation Technology for Portal Construction o f Jindong Tunnel Wu HongboAbstract Ventilati on and smoke discharge are key technologies for rapid construction of long tunnels.A description was given of ventilation and smoke di scharge technology for long tunnels with parallel heading. Keyw ords long tunnel;construction;stage;ventilation and smoke dischargeC hanging the Fixed Boom of a160t Railway C rane into Telescopic BoomLi ZhichengAbstract To meet the requiremen t of electrified rail way develop ment and rail way rescue assign ment,and to make full use of exi sting rescue e-quipmen t,the fi xed boom of the160t railway crane was changed in to telescopic boom,brin ging significant social and economic benefi ts. Keyw ords rail way crane;fixed boom;telescopic boom;rescue equip-ment。