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1、-目录目录一根本资料 1二荷载确定 1三衬砌几要素 23.1 衬砌几尺寸 23.2 半拱轴线长度 S 及分段轴长S33.3 割分块接缝重心几要素 3四计算位移 44.1 单位位移 44.2 载位移主动荷载在根本构造中引起的位移 74.3 载位移单位弹性抗力及相应的摩擦力引起的位移 104.4 墙低弹性地基上的刚性梁位移 12五解力法程 12六计算主动荷载和被动荷载h1分别产生的衬砌力 13七最大抗力值的求解 13八计算衬砌总力 14九衬砌截面强度检算检算几个控制截面159.1 拱顶截面 0159.2截面7179.3 墙低截面 8偏心检查 17.z.-十力图 17.z.-一 根本资料一级公路隧道
2、，设计时速 60km/h，构造断面如图 1 所示，围岩级别为 V 级，容重s18KN m3，围岩的弹性抗力系数K 1.5105KN/m3，衬砌材料 C25 混凝土，弹性模量Eh 2.85107kP，容重h 23KN / m3。图 1衬砌构造断面二 荷载确定2.1 深埋隧道围岩压力确定竖向均布压力：q 0.452s1式中：s围岩级别，此处s=5;s围岩容重，此处s=18kN/；跨度影响系数，=1+i(Bm-5)，毛洞跨度Bm=12.00m，Bm=515 时，i=0.1，此处:=1+0.112.00-5=1.7所以：q0.4525-1181.7220.32kPa考虑到初期之处承担大局部围岩压力，而
3、二次衬砌一般作为平安储藏，故对围压力进展折减，对于本隧道按照 40%折减，即 q=(140%)220.32=132.19 kPa围岩水平均布力：e =0.4q=0.4132.19=52.88kPa2.2 浅埋隧道围岩压力确定荷载等效高度hqqs=132.19 7.35m，18分界深度HP2.5hq2.57.35=18.38m.z.-1埋深H小于或等于等效荷载高度hq时竖向均布压力：在隧道埋深7m 处q s H 187.001- 40% 75.6kPae 12gs(H 2Ht)tan (45 -2)围岩水平均布力：18(7 13627.6)tan2(45-2)50.46kPa2埋深H大于hq、小
4、于或等于Hp时竖向均布压力：q浅浅QBH(1HtBtan)t式中：q浅作用在支护构造上的均布荷载；围岩的天然容重；H隧道埋深；侧压力系数；破裂面摩擦角，此处取 0.5g因此：围岩水平均布力：e1H1818.380.32 105.88kPae2h18 25.980.32 149.65kPa三 衬砌几要素3.1 衬砌几尺寸轮廓半径 r1=5.4m，r2=7.9m；径r1、r2所画圆曲线的终点截面与竖直轴的夹角1=90，二次衬砌厚度d=0.45m。.z.2=105；-此处墙底截面为自轮廓半径 r2的圆心向轮廓墙底做连线并延长至与外轮廓相交，其交点到轮廓墙底间的连线。外轮廓线半径：R1=5.4+0.4
5、5=5.85mR2=7.9+0.45=8.35m拱轴线半径：r1=5.4+0.50.45=5.625r2=7.9+0.50.45=8.125拱轴线各段圆弧中心角：1=902=153.2 半拱轴线长度 S 及分段轴长S905.6258.8357m分段轴线长度:S118018011半拱轴线长度为：S=S1+S2=8.8357+2.1271=10.9628m将半拱轴线等分为 8 段，每段轴长为：3.3 割分块接缝重心几要素1与竖直轴夹角i21 1 27.7175，32 1 41.8764,431 55.8351,54 1 69.7939 ,65 183.7527 ,71另一面，812 9015105
6、角度闭合差=0。各接缝中心点坐标可由图 1 中直接量出。S1218095.3389,.z.-四 计算位移图 2衬砌构造计算图4.1 单位位移用辛普生法近似计算，按计算列表进展。单位位移的计算见表1单位位移计算如下：计算精度校核为：闭合差 0。单位位移计算表表 1截面 sincos00.00113.96227.71341.88455.84569.79683.75795.340.001.000.240.970.470.890.670.740.830.560.940.350.990.11*m y(m)d(m)0.001.362.623.754.655.285.59I1/Iy/I0.0021.8684
7、.93.04324.49484.49659.59839.42y*y/I0.003.6354.83271.59800.221783.933306.475355.17(1+y)2/I131.58.92356.27781.251580.772884.484757.237165.5910144.830.000.450.01131.690.170.450.01131.690.650.450.01131.691.440.450.01131.692.470.450.01131.693.680.450.01131.695.010.450.01131.696.380.450.01131.697.780.450.
8、01131.691.00-0.095.578105.000.97-0.265.321023.787965.701185.183627.5919541.5327980.93.z.-bd3取单位长度。.z.,b注：1. I截面惯性矩，I122.不考虑轴力的影响-4.2 载位移主动荷载在根本构造中引起的位移1每一楔块上的作用力竖向力：Qi qbi侧向力：i=ehi自重力：Gi=di-1+dish2式中：bi衬砌外缘相邻两截面之间的水平投影长度，由图 2 量得：hi衬砌外缘相邻两截面之间的竖直投影长度，由图 2 量得di接缝 i 的衬砌截面厚度。.z.-自重力：Gi diSh14.1836kN式中：d
9、i接缝 i 的衬砌截面厚度，本设计为等厚度衬砌；作用在各楔体上的力均列入表 2，各集中力均通过相应的图形的行心。2外荷载在根本构造中产生的力。楔体上各集中力对下一接缝的力臂由图 2 中量得，分别记为aq,ae,ag力按照下式计算见图 3 。0弯矩：Mip Mi01,pxi(QG)yiE QaqQagQaeXi1i10 sinai(QG)cosaiE轴力：Nipii式中：xi,yi相邻两接缝中心点的坐标增值0000计算图示、NipMip,Nip的计算见表2及表3.图 3力Mip0载位移Np计算表表 3截面sincosQ+G)0.0000251.3677484.1271695.4745865.76
10、70988.3457E0.000012.963549.7153110.3856.3051282.5261384.5479489.3219596.7330sinQ+G)0.000060.6299225.1191464.2292716.3356927.56241040.44651056.49301038.5734cosE0.000012.580744.012582.1920106.310097.584541.8465-45.5069-154.43450Np0.000048.0492.1066382.0372610.0257829.9779998.60001101.99991193.007900.0
11、0001.000010.24120.970520.46500.885330.66750.744640.82740.561650.93850.345460.99410.10881046.621670.9957-0.09301061.055580.9659-0.25881075.2391.z.-0载位移Mp的计算表表 2截集中力GE力臂aqagaeQaq面Q00.0000Gag0.00000.00000.00000.00000.65130.67340.55020.61530.44190.49470.28150.39450.11360.26550.00000.00000.00001237.18411
12、4.183612.96352218.575814.183636.75183197.163814.183660.67034.108914.183678.91950.1244154.47809.55120.2775120.26048.72720.395687.12670.514743.94470.608012.31370.66540.00000.68330.00000.70060.0000i17.01665.59543.76571.6113-0.7149-2.27085108.395114.183693.2210644.092370.250380.0000Eaei114.1836102.02180
13、.00000.113614.1836104.77400.0000-0.050414.1836107.41110.0000-0.1601(QG)Ei1*yx(Q G)yEi10Mp0.00000.00001.61270.000010.1986251.367724.0012484.127140.6199695.474556.6784865.767067.8853988.34570.00000.00000.00000.00000.00001.35690.16610.00000.00000.00000.0000-165.6419-627.615312.96351.25940.4794316.57256
14、.214749.71531.13850.7912551.178739.3347-1336.2732110.38560.89951.0294625.5793113.6309-2165.6434.30510.62451.2160540.6715230.1950-3009.2677282.52610.31281.3308309.1545375.9857-3763.9045525.5616-4342.132271.59211046.6216384.5479-0.01741.3667-18.211275.25221061.0555489.3219-0.25661.4011-272.2668685.588
15、9-4828.4356.z.-.z.-根本构造中，主动荷载产生弯矩的校核为：0M8q qBB11.700011.7000(x8) 166.8900(5.3176) 2355.9109KN / m2424e276.66200M8 H 7.78062 2320.4719KN / m ,M8eg Gi(x8 xi+agi) 152.372KN / m220000M8p M8q+M8e+M8g -4828.7548KN / m0另一面，从表 2 中得到M8p 4828.73564828.75484828.4356100% 0.0066%闭合差 4828.75483主动荷载位移计算过程见表 4 。主动荷
16、载位移计算表表 4截面012345678-165.6419-627.6153-1336.2732-2165.6434-3009.2677-3763.9045-4342.1322-4828.43560Mp1I131.6872131.6872131.6872131.6872131.6872131.6872131.6872131.6872131.6872yI0.000021.855384.9342.0395324.4868484.4868659.5921839.4211(1+y)1.00001.16611.64552.43673.46614.68216.01297.37960MpI0MpyI0Mp(
17、1 y)I0.0000-3620.1473-53306.0085-252608.3846-702722.7922-1457950.6067-2482641.7162-3644877.1440-4943238.06060.0000-21794.9868-82580.9582-175825.4226-284953.0807-395956.2768-495250.5967-571333.1783-635320.48020.0000-25415.1342-135886.9666-428433.8072-987675.8729-1853906.8834-2977892.3129-4216210.3223
18、-5578558.54091023.77638.7807-2663014.9802-13540964.8601-16203979.8403计算精度校核：1p 2p 0.1279 0.6511 0.7791闭合差： 0.z.-4.3 载位移单位弹性抗力及相应的摩擦力引起的位移1各接缝处的抗力强度抗力上零点假定在接缝 3，3 41.8764 b最大抗力值假定在接缝 6，6 83.7527 h最大抗力值以上各截面抗力强度按下式计算：查表 1，算得3 0,4 0.4407h,5 0.8019h,6h;最大抗力值以下各截面抗力强度按下式计算：式中： 2.7678m;由图 2 中量得：y71.3667m,
19、y8则：7 (1yiy22h)h 0.7562h,8 0;按比例将所求得抗力绘于图 2 上。2各楔体上抗力集中力Ri按下式计算：Ri (i1i2)Si外式中：Si外表示楔体 i 外缘长度，可以通过量取夹角，用弧长公式求得，Ri的向垂直于衬砌外缘，并通过楔体上抗力图形的形心。3抗力集中力与摩擦力的合力Ri按下式计算：Ri Ri12式中：围岩于衬砌间的摩擦系数，此处取 0.2。则：Ri1.0198Ri其作用向与抗力集中力的夹角 arctan11.30990；由于摩擦力的向与衬砌位移向相反，其向向上。将Ri的向线延长，使之交于竖直轴，量取夹角，将Ri分解为水平和竖直两个分力：RH Risink,RV
20、 Ricosk;以上计算结果列入表 5 中。.z.-弹性抗力及摩擦力计算表表 5截1(i1i)2(h)S外R()h0.00000.31850.89821.30241.24340.5354ksinkcoskRH()hRV()h面(h)3456780.00000.00000.44070.22040.80190.62131.00000.90100.75620.87810.00000.37811.44561.44561.44561.44561.41601.41600.00000.00001.00000.00000.000063.12270.89200.45210.28410.144074.90860.
21、96550.26040.86720.233888.38640.99960.02821.30190.0367101.30990.9806-0.19611.2192-0.2438113.25480.9188-0.39480.4919-0.21144计算单位抗力及其相应的摩擦力在根本构造中产生的力0弯矩：Mi0 Rjrji轴力：Ni siniRvcosiRH式中：rji力Rj至接缝中心点ki的力臂，由图 2 量得。计算见表 6 及表 7.0计算表表 6MR4=0.3185R5=0.8982R6=1.3024R7=1.2434R8=0.53540-M(h)截R44i面4i(h)R55i5i(h)R66
22、i6i(h)R77i7i(h)R88i8i(h)-0.1498-1.2191-3.876340.47040.149851.83320.58390.71150.635263.16031.00662.07051.84850.78411.0212.z.-74.45631.41933.39883.03442.14382.79210.85881.0678-8.313785.77041.83794.76054.25023.54384.61542.27912.83381.10590.5921-14.12940计算表表 7N截( )sin cos RV(h)sinRVRH(h)cosRH(h)面455.835
23、1569.7939683.7527795.3389(h)N0( )0.82740.56160.14400.11920.28410.1596-0.03650.93850.34540.37780.35461.15130.3977-0.04790.99410.10880.41450.41212.45320.26700.10780.9957-0.09300.17070.16993.6724-0.34170.51528105.00000.9659-0.2588-0.0407-0.03934.1643-1.07781.0193.z.-.z.-5单位抗力及相应摩擦力产生的载位移。计算见表 8.单位抗力及相应
24、摩擦力产生的载位移计算表表 8截面45678校核为：闭合差： 0;0-M(h)h-0.1498-1.2191-3.8763-8.31371IyI(1 y)0MI131.6872324.48683.4661-19.72970MyI-48.61540M(1 y)I-68.3851-751.6646131.6872484.48684.6821-160.5400-590.6386131.6872659.59216.0129-510.4604-2556.7833-3069.3472131.6872839.42117.3796-1094.8075-6978.6925-8079.2415-3646.2019
25、-24640.0992-28306.5729-14.1294131.68721023.77638.7807-1860.6642-14465.3694-16337.93464.4 墙底弹性地基上的刚性梁位移单位弯矩作用下的转角：a主动荷载作用下的转角：单位抗力及相应摩擦力作用下的转角：1131.68724=8.7791106KI80.1510五解力法程衬砌矢高计算力法程的系数为：以上将单位抗力及相应摩擦力产生的位移乘以h， 即为被动荷载的载位移。 求解程为：式中：X1p 402.6846,X1 1.9463h式中：X2 p 572.0134，X2 2.0634以上解的X1, X2值应带入原程，校
26、核计算。.z.-六计算主动荷载和被动荷载h1分别产生的衬砌力计算公式为：计算过程列入表 9、10。.主、被动荷载作用下衬砌弯矩计算表表 9M0截p面0123456780.0000X1pX y2 pM poM(h)X1(h)X2 y(h)M(h)-1.9643-1.6216-0.63241.00022.97444.4142402.68460.0000402.68460.0000332.05410.0000-1.96430.0000-1.96430.3427-1.96431.3319-1.96432.9645-165.6419402.684695.0114-627.6153402.6846369.
27、2346144.30400.0000-1336.2732402.6846821.8117-111.77700.0000-2165.6434402.68461410.6422-352.3166-0.1498-1.96435.0886-3009.2677402.68462106.2105-500.3726-1.2191-1.96437.5976-3763.9045402.68462867.4460-493.7740-3.8763-1.964310.34364.5030-4342.1322402.68463649.2167-290.2309-8.3137-1.964313.16372.8857-48
28、28.4356402.68464450.664724.9136-14.1294-1.964316.0547-0.0390主、被动荷载作用下衬砌轴力计算表表 10截面0123456780Np0.000048.0492.1066X2 pcosNp0N(h)X2cos)(hN(h)572.0134572.01340.0000555.1215603.17070.0000506.3990687.50560.00002.06342.06342.00252.00251.82671.82671.53641.5364382.0372425.9135807.95070.0000610.0257321.229393
29、1.2550-0.03651.15881.1223829.9779197.57231027.5503-0.04790.71270.6648998.600062.24651060.84650.10780.22450.3323-0.19200.3232-0.53400.48531101.9999-53.22391048.77600.51521193.0079-148.04801044.95991.0193七最大抗力值的求解首先求出最大抗力向的位移。.z.-考虑到接缝 5 的径向位移与水平向有一定的偏离，因此修正后有：计算过程列入表 11，位移值为：最大抗力值为：最大抗力位移修正计算表表 11Mp截
30、I面MI(h)Mp y )(y6iI(y6 yi)MI(h)(y6 yi)053028.4075-258.67325.0129265826.1037-1296.7027143727.2781-213.53994.8468211937.3714-1034.9853219002.9855-83.27574.367482993.6387-363.69843-14719.5949131.71183.5762-52640.2151471.02774-46395.5823391.69412.5468-118160.2689997.56665-65892.6618581.29941.3308-87689.9
31、543773.59326-65023.7105592.98850.00000.00000.0000302266.6754-453.1988八计算衬砌总力M MphM按下式计算衬砌总力：计算过程列入表 12.N NphN计算精度的校核为以下容：根据拱顶切开点的相对转角和相对水平位移应为零的条件来检查：式中：SM 4.8084108(2499.99) 0.0419EhI闭合差： 0SMy 4.8084108 （-37993. 07） -0.1672I式中： Ehfa 7.78070.0433 0.1791闭合差： 0衬砌总力计算表表 12截面MpMMNpNNeM/IMy/I.z.-0402.68-
32、1005.38-602.69572.011056.101628.11-0.37-79366.960.001332.05-829.96-497.91603.171024.911628.08-0.31-65567.77-10881.852144.30-323.67-179.36687.51934.961622.46-0.11-23619.61-15233.923-111.78511.92400.14807.95786.361594.310.2552693.7875642.924-352.321520.861168.54931.25574.401505.650.78153882.06379176.5
33、95-500.371698.761198.391027.55340.261367.810.88157812.34580603.146-493.77671.54824.91177.771060.85.101230.950.1423409.47117252.877-290.23-688.73-978.961048.78165.431214.20-0.81-128915.96-821756.19-691.85-666.941044.96248.361293.32-0.52-87827.37-682796.632499.99-377993.07九 衬砌截面强度检算检算几个控制截面9.1 拱顶截面 0e
34、=0.0370m0.45d=0.2025m可又有：e=0.0370m0.2d=0.09me0.0370 0.0822,可得d0.45式中：R混凝土极限抗压强度，取1.9104kPa9.2截面7e=0.081m0.2d=0.09m9.3 墙低截面 8偏心检查其他各截面偏心距均小于 0.45d .十 力图将力计算结果按比例绘制成弯矩图 M 与轴力图 N，如图 4 所示。图 4衬砌构造力图.z.-.z.-9.2截面7e=0.081m0.2d=0.09m9.3 墙低截面 8偏心检查其他各截面偏心距均小于 0.45d .十力图将力计算结果按比例绘制成弯矩图 M 与轴力图 N，如图 4 所示。图 4衬砌构造力图.z.