高速公路隧道工程课程设计计算书

PAGE高速公路隧道工工程课程设设计计算书书目录HYPERLINK\l"_Toc282798273"一基本资料1HYPERLINK\l"_Toc282798274"二荷载确定1HYPERLINK\l"_Toc282798275"2.1围岩竖竖竖向均布布压力力1HYPERLINK\l"_Toc282798276"2.2围岩水水水平均布布力22HYPERLINK\l"_Toc282798277"三衬砌几何要素素素2HYPERLINK\l"_Toc282798278"3.1衬砌几何何何尺寸2HYPERLINK\l"_Toc282798279"3.2半拱轴轴轴线长度度S及分段轴轴长△S2HYPERLINK\l"_Toc282798280"3.3割分块块块接缝重重心几几何要素素3HYPERLINK\l"_Toc282798281"四计算位移3HYPERLINK\l"_Toc282798282"4.1单位位位位移4HYPERLINK\l"_Toc282798283"4.2载位移移移——主动荷荷载载在基本本结构构中引起起的位位移4HYPERLINK\l"_Toc282798284"4.3载位移移移——单位弹弹性性抗力及及相应应的摩擦擦力引引起的位位移88HYPERLINK\l"_Toc282798285"4.4墙低（弹弹性地基基上的的刚性梁梁）位位移12HYPERLINK\l"_Toc282798286"五解力法方程1113HYPERLINK\l"_Toc282798287"六计算主动荷载载载和被动动荷载载（）分别别产产生的衬衬砌内内力13HYPERLINK\l"_Toc282798288"七最大抗力值的的的求解155HYPERLINK\l"_Toc282798289"八计算衬砌总内内内力16HYPERLINK\l"_Toc282798290"九衬砌截面强度度度检算（检检算算几个控控制截截面）166HYPERLINK\l"_Toc282798291"9.1拱顶（截截面0）16HYPERLINK\l"_Toc282798292"9.2截面面面（7）18HYPERLINK\l"_Toc282798293"9.3墙低（截截面8）偏心检检查查18HYPERLINK\l"_Toc282798294"十内力图18PAGE5一基本资料高速公路隧道，结结构断面面如图图1所示，围围岩岩级别为V级，容重重，围围岩的弹弹性抗抗力系数数，衬衬砌材料C20混凝土，弹弹弹性模量量，容容重。图1衬砌砌结结构断面二荷载确定2.1围岩竖竖竖向均布布压力力：式中：s——围围围岩级别别，此此处s=5;;——围岩容重，此此此处=188kkN/㎡；——跨度影响系系数数，=1+ii((Bm-5)，毛毛洞洞跨度Bm=12..330m，Bm=5~1155时，i=0..1，此处:=1+00..1×（12.33--5）=1.7733所以，有：考虑到初期之处处处承担大大部分分围岩压压力，而而二次衬衬砌一一般作为为安全全储备，故故对对围岩压压力进进行折减减，对对于本隧隧道按按照50%折减，即即2.2围岩水水水平均布布力：：e=0...4×qq=00.4××1112.11044=444.884166kPPa三衬砌几何要要素素3.1衬砌几何何何尺寸内轮廓半径r111=5.77m，r2=8.22mm；内径r1、rrr2所画圆曲曲线线的终点点截面面与竖直直轴的的夹角=9900°，=1011..6°；截面厚度d=000.455m。此处墙底截面为为为自内轮轮廓半半径r2的圆心向向内内轮廓墙墙底做做连线并并延长长至与外外轮廓廓相交，其其交交点到内内轮廓廓墙底间间的连连线。外轮廓线半径：：：R1=5.77++0.445==6.115mmR2=8.2++00.45===8.665mm拱轴线半径：===5.77+00.5××0..45==5..9255=8.2+0...5×00.445=88.4425拱轴线各段圆弧弧弧中心角角：=90°=1111.6°°3.2半拱轴轴轴线长度S及分段轴轴长△S分段轴线长度:::半拱轴线长度为为为：S=S1+S2=9.33006966+11.7005771=111..0122688m将半拱轴线等分分分为8段，每段段轴轴长为：：3.3割分块块块接缝重重心几几何要素素（1）与竖直轴轴夹夹角另一方面，角度闭合差=000。各接缝中心点坐坐坐标可由由图1中直接量量出出。四计算位移图2衬砌结结结构计算图图4.1单位位位位移用辛普生法近似似似计算，按按计计算列表表进行行。单位位位移移的计算算见表表1单位位移计算如如如下：计算精度校核为为为：闭合差4.2载位移移移——主动荷载载在在基本结结构中中引起的的位移移（1）每一楔楔块上上的作用用力竖向力：式中：bi———衬砌外缘相相邻邻两截面之之之间的水水平投投影长度度，由由图2量得：PAGE6单位位移移计计算表表1截面Φ（°）sinΦcosΦx（m）y(m)d(m)0001000.450.0075999131.6877720.00000.0000131.687772113.31188810.23030.97311.36680.16080.450.0075999131.68777221.1753333.4050177.442228226.62366630.44810.8942.65320.63320.450.0075999131.68777283.38444452.799000351.254449339.93544440.64190.76683.79891.38690.450.0075999131.687772182.637770253.299993750.260006453.24722260.80120.59844.74362.38190.450.0075999131.687772313.665558747.1200071506.133396566.55900070.91750.39785.43713.56780.450.0075999131.687772469.8333371676.2777282747.622276679.87088890.98440.17595.8294.88430.450.0075999131.687772643.2000003141.5888184559.666690792.23822280.9992-0.0391115.91956.25110.450.0075999131.687772823.1900015145.8444386923.9111138101.60.9796-0.2011115.74867.61790.450.0075999131.6877721003.1888027642.1222689780.177745∑0.06834441185.1888523540.26666718662.444491126928.1116766注：1.I——截截面惯性矩矩矩，2.不考虑轴力力的的影响PAGE19自重力：式中：di————接缝i的衬砌截截面面厚度，本本设设计为等等厚度度衬砌；作用在各楔体上上上的力均均列入入表2，各集中中力力均通过过相应应的图形形的行行心。（2）外荷载在在基基本结构中中中产生的的内力力。楔体上各集中力力力对下一一接缝缝的力臂臂由图图2中量得，分分分别记为为内力力按照下下式计计算（见见图3）。弯矩：轴力：式中：图3内力计算图图示示载位移计算算表表3截面sinΦcosΦΣ（Q+G)ΣEsina(Q+++G）cosaΣE00.00001.00000.00000.00000.00000.00000.000010.23030.9731173.2522277.210539.9001117.016632.88355520.44810.8940337.49222328.842111151.23000325.784999125.44555430.64190.7668485.95888863.993444311.93666949.070222262.86666840.80120.5984609.639991110.413335488.44222866.071444422.37111450.91750.3978704.026666165.846667645.94444465.973888579.97000660.98440.1759764.614448227.136662752.68666839.953222712.73333670.9992-0.039111788.018881290.681112787.387777-11.365556798.75333380.9796-0.201111803.540005353.324449787.148883-71.053336858.201119载位移的计算表表表表2截面集中力力臂△x△y-△x-△yQGE0000000000000000-1158.86222614.2477777.21050.65330.67340.3015-103.788849-9.594444-2.1740000.00000.00000.68340.04020.00000.0000-115.5555332149.84999414.24777721.6316660.57290.63320.4422-85.848887-9.021666-9.565555173.1100027.21051.28640.4724-222.688890-3.406333-446.0888443134.07666414.24777735.1513330.45230.55280.5628-60.642227-7.876111-19.783332337.20777328.8421111.14570.7538-386.333384-21.741112-942.4666604109.29000214.24777746.4200000.31160.44220.6533-34.054448-6.300333-30.326662485.53111363.9934440.94470.9950-458.688815-63.673335-1535.5550222579.99744414.24777755.4332220.15080.31160.7035-12.063336-4.439666-38.997772609.069992110.4133350.69351.1859-422.388895-130.933393-2144.3333155646.19811114.24777761.2895550.02010.16080.7236-0.928666-2.291000-44.349991703.314442165.8466670.39201.3166-275.699992-218.355537-2685.999531179.013214.24777763.545000-0.1809990.01010.70351.6305-0.143999-44.703339763.760000227.1366620.09041.3668-69.043339-310.444497-3108.666640081.132314.24777762.643777-0.221111-0.0603330.65330.25030.8591-40.925551787.020008290.681112-0.1608881.3668126.552229-397.300030-3419.2222988基本结构中，主主主动荷载载产生生弯矩的的校核核为：另一方面，从表表表2中得到闭合差（3）主动荷载载位位移（计算过程程见见表4）。截面(1+y)00.000131.687770.0001.0000.0000.0000.0001-115.55553131.6877721.1751.161-15216...8911-2446.88876-17663...76772-446.08884131.6877783.3841.633-58743...6199-37196...4599-95940...07883-942.46666131.68777182.637772.387-12411000.7445-17212999.1992-29623999.93364-1535.55502131.68777313.666663.382-202206666005-68384000.66615-2144.33331131.68777469.834444.568-28238111.1000-100747779.22888-128986660.338776-2685.99953131.68777643.200005.884-35370555.7552-172760005.00055-208131110.775777-3108.66664131.68777823.190007.251-40937111.3992-255902221.55066-296839992.889778-3419.22230131.687771003.188808.618-45026888.9442-343010003.77722-388037772.77133Σ-189600004.44966-941761116.77022-1131366621..1998主动荷载位移计计计算表表4计算精度校核：：：闭合差：4.3载位移移移——单位弹性性抗抗力及相相应的的摩擦力力引起起的位移移（1）各接缝处处的的抗力强度度度抗力上零点假定定定在接缝3，最大抗力值假定定定在接缝6，最大抗力值以上上上各截面面抗力力强度按按下式式计算：：查表1，算得最大抗力值以下下下各截面面抗力力强度按按下式式计算：：式中：由图2中量得：：则：按比例将所求得得得抗力绘绘于图图2上。（2）各楔体上上抗抗力集中力力力按下式计算算：：式中：—表示楔楔楔体i外缘长度度，可可以通过过量取取夹角，用用弧弧长公式式求得得，的方向向垂垂直于衬衬砌外外缘，并并通过过楔体上上抗力力图形的的形心心。（3）抗力集中中力力玉摩擦力力力的合力力按下式计算：式中：—围岩于于于衬砌间间的摩摩擦系数数，此此处取。则：其作作用用方向与与抗力力集中力力的夹夹角；由于于摩摩擦力的的方向向与衬砌砌位移移方向相相反，其其方向向向上。将得方向线延长长长，使之交交于于竖直轴轴，量量取夹角角，将将分解为水水平平和竖直直两个个分力：：以上计算结果列列列入表5中。弹性抗力及摩擦擦擦力计算算表表5截面R300.00000.00000.000000.00001.00000.00000.000040.41270.20641.42890.300760.2262220.86800.49660.26100.149350.77150.59211.42890.862871.9529990.95080.30980.82030.267361.00000.88571.42891.290784.8520000.99600.08971.28540.115870.74820.87411.35521.208097.4317770.9916-0.1293331.1979-0.15622280.00000.37411.41330.5392108.6311130.9476-0.3195550.5110-0.172333（4）计算单位位抗抗力及其相相相应的摩摩擦力力在基本本结构构中产生生的内内力弯矩：轴轴轴力：式中：—力至接接接缝中心心点的的力臂，由由图图2量得。计算见表6及表表表7.计算表表7截面453.2473330.80120.59840.14930.11960.26100.1562-0.036555566.5591110.91750.39780.41660.38221.08130.4302-0.047999679.8709990.98440.17590.53240.52412.36680.41630.1078792.2383330.9992-0.0391110.37620.37593.5646-0.1394440.51528101.6000000.9796-0.2011110.20390.19974.0756-0.8196661.0193计算表表6截面40.4824-0.1451110.14511151.8593-0.5591110.6533-0.5636661.12277763.1959-0.9610002.0201-1.7429990.6935-0.8951113.59899974.4321-1.3327773.3567-2.8961112.0603-2.6591110.7638-0.9227777.81066685.5376-1.6651114.6029-3.9712223.4070-4.3972222.1407-2.5860000.9749-0.525777-13.145553（5）单位抗力力及相相应摩擦擦力产生生的载载位移。计计算算见表8.单位抗力及相应应应摩擦力力产生生的载位位移计计算表表8截面4-0.145111131.687772313.6655583.3819-19.102220-45.499990-64.6011105-1.122777131.687772469.8333374.5678-147.844492-527.499964-675.3444566-3.598999131.687772643.2000005.8843-473.933342-2314.8883677-2788.77770887-7.810666131.687772823.1900017.2511-1028.5555200-6429.5558155-7458.11133558-13.145553131.6877721003.1888028.6179-1731.0006322-13187...06665-14918...12997Σ-3400.5550066-22504...48001-25904...98007校核为：闭合差：4.4墙低（弹弹性地基基上的的刚性梁梁）位位移单位弯矩作用用用下的转角角：：主动荷载作用下下下的转角角：单位抗力及相应应应摩擦力力作用用下的转转角：：五解力法方程程衬砌矢高计算力法方程程程的系数为为：：以上将单位抗力力力及相应应摩擦擦力产生生的位位移乘以以，即即为被动动荷载载的载位位移。求求解方程程为：：式中：式中：，以上解的值应带带带入原方方程，校校核计算算。六计算主动荷荷载载和被动荷荷荷载（）分分别别产生的的衬砌砌内力计算公式为：计算过程列入表表表9、10。.主、被动荷载作作作用下衬衬砌弯弯矩计算算表表9截面00.0000294.2077730.0000294.2077730-2.4743330.0000-2.4743331-115.644492294.20777366.108000244.6666610-2.4743330.3287-2.1456662-446.455538294.207773260.320009108.0744440-2.4743331.2943-1.1800003-943.244406294.207773570.181117-78.8511160-2.4743332.83490.36064-1536.7774377294.207773979.245557-263.299907-0.145111-2.4743334.86882.24945-2146.0001266294.2077731466.799924-385.011128-1.122777-2.4743337.29283.69586-2687.9993633294.2077732008.033314-385.699977-3.598999-2.4743339.98393.91067-3110.7772600294.2077732569.944496-246.566691-7.810666-2.47433312.7777772.49288-3421.1112288294.2077733131.8666794.9524-13.145553-2.47433315.571555-0.048000主、被被被动荷载载作用用下衬砌砌轴力力计算表表10截面00.0000411.119996411.11999602.04412.0441132.883555400.060005432.94444001.98911.98912125.445554367.540009492.98666301.82741.82743262.866668315.246665578.11333301.56741.56744422.371114246.014440668.385554-0.0365551.22321.18665579.970006163.543334743.514440-0.0479990.81310.76526712.73333672.315999785.0499950.10780.35960.46737798.753333-16.074448782.6788860.5152-0.0799990.43538858.201119-82.676661775.5255581.0193-0.4111110.6083七最大抗力值值的的求解首先求出最大抗抗抗力方向向内的的位移。考考考虑到接接缝5的径向位位移移与水平平方向向有一定定的偏偏离，因因此修修正后有有：计算过程列入表表表11，位移值值为为：最大抗力值为：：：最大抗力位移修修修正计算算表表11截面038743.3334644-325.8333284.8843189234...12669-1591.4446499132219.4440488-282.5444894.7235152188...35887-1334.6661999214232.0002100-155.3888924.251160501.7774455-660.5777513-10383...7500547.4903333.4974-36316...12991166.0922254-34672...02449296.2200052.5024-86763...27552741.2622215-50701...27994486.6911151.3165-66748...23443640.7299936-50791...46007514.979994000Σ212096...59114-2038.5557600八计算衬砌总总内内力按下式计算衬砌砌砌总内力力：计计算过程程列入入表12.计算精度的校核核核为以下下内容