五级围岩隧道二次衬砌计算书

第二章V级围岩二级衬砌计算书2.1基本资料建子沟二级公路隧道的衬砌结构断面如下图，围岩级别为V级，围岩容重片19.5kN/m3,围岩的弹性抗力系数K=0.2x106kN/m3,衬砌材料为C25混凝1.9x104kPa。附图1:衬砌结构断面图 (单位：米)2.2荷载确定2.2.1围岩竖向荷载压力围岩松散压力：g'=0.45x25-1yw式中：q'=0.45x2s-1yg0.45x25-1x19.5x(1+0.1x(11.4459-5))=230.9004kPa围岩竖向均布压力q按松散压力的40%计：q=0.4q'=92.3602kPa2.2.2围岩水平压力：e=0.4q=0.4x92.3602=36.9441kPa2.3衬砌几何要素内轮廓半径r1=5.273m,外轮廓半径r广5.723m,拱轴线半径r0=5.498m。终点截面与隧道中心线夹角甲0=113.1241。拱顶截面厚度do=0.45m墙底截面厚度d8=0.45m半拱轴线长度为S=10.86299m，将半拱轴线等分为8段，每段轴长为△S=1.35787m其它几何要素表. 附表1截面air0xy005.67500114.1385.6751.31966610.1555701228.27145.6752.56697960.6137511342.40035.6753.67355461.3494224456.52555.6754.57872162.3222499570.62065.6755.25144183.5237251684.76135.6755.60008654.7559483798.90525.6755.66028666.08338828905.6755.41015317.3884376表中ai为各分块接缝中心与竖直轴的夹角，x和y为接缝中心点的横、纵坐标。2.4计算位移2.4.1单位位移用辛普生法近似计算，按计算列表进行。单位位移的计算见附表2,单位位移值计算如下：5日0s也dsQ坚^-L35787x1053.498=48.4921x1011EhI Ehuo1= 2.95x107 *5=§ =f0sM12-d^Z^^My-=x—— 6.43&35742.988x10-612 21 Eh1s i=0I 2.95x107—2sM-2d^=xAS辜巴1542737833=710.137x10-6Eh1sEhi=0 2.95x107附表2附表2截面asinacosaxyd1Iy y2(I系数］1+y)积分I1/30001000.45131.68720 0 131.687241114.1380.2442580.9697101.34340.16470.45131.687221.688893.57216178.637184228.27140.4736490.8807142.60590.65250.45131.687285.9259356.066667359.605762342.40030.6743060.7384523.71091.43410.45131.6872188.8527270.83362780.226214456.52550.8341310.5515664.59152.46180.45131.6872324.1877798.085171578.14772570.62060.9433420.3318225.19433.67320.45131.6872483.71361776.77672875.89114684.76130.9958230.0913055.48294.9960.45131.6872657.90953286.91574734.42192798.90520.987946-0.1548005.43966.34870.45131.6872836.04285307.78497111.55784890105.06418.0650.45131.68721062.0588565.494710821.2971注：I为截面惯性矩,I=bd匕2，Z1053.4983106.43215427.83322(>94.195b取单位长度。计算精度校核为:811+2812+822=(48.4921+2x142.988+710.137)x10_6=1044.6051x106AV8(、顼)2135787竺 y+1)_顼x3578726984.195=1044.605x10-61 E=i 2.95)7闭合差=0。2.4.2载位移——主动荷载在基本结构中引起的位移附图3附图3楔块受力示意图ea1.ea1.每一楔块上的作用力竖向力：Q.=qb.式中：b——寸砌外缘相邻两截面之间的水平投影长度：.水平力：E.=eh.自重力：Gi=d0XASxyh=0.45x1.35787x23=14.05399KN8号块自重为楔块面积乘yh:G8=14.12706KN.外荷载计算表 附表3截面qebihiQGE092.360236.944100000192.360236.94411.39840.1715129.156514.053996.335913292.360236.94411.31410.5079121.370514.0539918.76391392.360236.94411.15020.8136106.232714.0539930.05772492.360236.94410.91661.069984.6573614.0539939.52649592.360236.94410.62741.261457.9467914.0539946.60129692.360236.94410.30031.376527.7357714.0539950.85355792.360236.94410.0451.40814.15620914.0539952.02099892.360236.944101.3544014.1270650.03709外荷载在基本结构中产生的内力计算公式为：Mp=Mj1p—△%£(Q^G)_Ay^E—Qa ~Gag—EacTOC\o"1-5"\h\z1 i^nN=N +乙(Q+G)-cosa乙Eip0 i0-1,p ii i计算过程和结果均列入附表3中。载位移MpQ计算表 附表4截面QGEaqagae-Qaq000000001129.156514.053996.3359130.64420.66660.3039-83.20262121.370514.0539918.763910.55040.61620.4521-66.80233106.232714.0539930.057720.42330.52840.5729-44.9683484.6573614.0539939.526490.27050.40860.6589-22.8998557.9467914.0539946.601290.10140.26390.7051-5.8758627.7357714.0539950.85355-0.0740.10350.70852.05244774.15620914.0539952.02099-0.2454-0.06180.66921.0199348014.1270650.037090-0.22840.59610续上表-Gag-Eae£@G-1£Ei-1AxAy-£QG-1-Ay£Ei-1M0p000000000-9.36839-1.92548001.34340.164700-94.4965-8.66007-8.48316143.210496.33591321.26250.4878-180.8032-3.09066-362.336-7.42613-17.2201278.6350225.0998221.1050.7816-307.8917-19.618-759.46-5.74246-26.044398.9217155.1575410.88061.0277-351.2905-56.6854-1222.12-3.70885-32.8586497.6330694.6840340.60281.2114-299.9732-114.7-1679.24-1.45459-36.0297569.63384141.285320.28861.3228-164.3963-186.892-2065.960.868537-34.8124611.4236192.13888-0.04331.352726.474642-259.906-2332.323.226621-29.8271629.6338244.15986-0.37551.7163236.42749-419.052-2541.54载位移N0计算表 附表5截面E(Q+G)EesimEQ+GcosaEEN0p0i0 i 0i0i001143.2104946.33591334.980346.14428.836342278.63502325.09982131.975122.10576109.86933398.92171555.15754268.995440.73119228.26424497.63306494.68403415.091452.22448362.86695569.633843141.2853537.359546.88158490.4786611.423601192.1389608.869717.54328591.32647629.6338244.1599622.0441-37.796659.848643.76086294.197643.76090643.7609基本结构中，主动荷载产4k弯矩的校核:BB 11.4459 11.4459M0=-q2(孔—4=-92.3602xx2(5.0484- 4 )=-1164.2477e 1M80e=-§2=-36.9441xx2§6842=-1172.8902:eL :，一，、M=-G(x—x+a)=-G(x—x+a)-G(x—x+a)80g i'8igi， 1、8 1 g1 2、8 2g2/-G(x—x+a)-G(x—x+a)-G(x—x+a)-G(x—x+a)3、8 3 g3/ 4、8 4g4/ 5、8 5g5/ 6、8 6g6/-G7(x8-x7+ag7)-Gag8=-191.7704I*908-询*I=0.497%2541.54Msq=M80q+MI*908-询*I=0.497%2541.54从附表4中查得M08p=-2541.54所以，闭合差小=附表6主动荷载位移附表6截面,,0Mp1i yM0pI叔 0m积分孕M（；1)―U3-00131.6872 000 0 11-221.06575131.68720.1555701-12443.98267-2049.523946-14493.5066242-847.93994131.68720.6137511-47715.02569-31134.05426-78849.0799523-1787.6659131.68721.3494224-100011.2192-143426.0894-243437.308544-2904.8762131.68722.3222499-160937.9219-396196.9761-557134.89825-4079.0791131.68723.5237251-221134.3558-812270.7157-1033405.07246-5062.4762131.68724.7559483-272060.5036-1359214.276-1631274.77927-5859.6808131.68726.0833882-307136.1367-1949915.191-2257051.32848-6340.766131.68727.3884376-334688.3432-2699261.488-3033949.8311主动荷载位移计算表E-1286339.341-5967666.06-7254005.401

„M1Mp0 ASM0p 135787△布-\0 加一E——=—1286339.341 1.35787=-59209.709x10PT0Eh1电~Eh I 2.95x107 -6A2f^M2MP%竺£也0p—5967666.06X^35787=—274689.393x10A2P=J0EhI*Eh I 2.95x107 -6计算精度校核：Alp+A2p=—333899.102x10-6仍5仍5*-7254005-401X1.357872.95x107=—333899.102x106闭合差A=0。2.4.3载位移一一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设在接缝3,a3=42.4003°=ab;最大抗力值假定在接缝5,a5=70.6206°=ah；最大抗力值以上截面抗力强度按下式计算：°Fcoqa—coqa；°Fcos2a—cos2ah hcos242.4003°-cos256.5255。°4= 2 2 °h=0.5353778°cos&2.4003°-cos270.6206 h最大抗力值以下截面抗力强度按下式计算:y,2°=(1-X7^藉h由图量得：以=1.3025m,”=2.7102m,为=3.9839m具体计算参见附表7:

截面b0)截面b0)n1(+"21△S外R(口n)□ksin□kcos=k(□)rhn(□)RVn30傍01.4105500010040.5353780.2676891.410180.38496663.23860.8928890.4502760.343730.173341510.7676891.407181.10166975.63510.9687350.2480961.067230.2733260.893110.9465551.411731.36274488.83050.9997920.020411.362460.02781470.5372080.7151591.412051.029839102.48070.976369-0.216111.0055-0.22256800.2686041.419540.388845114.71510.908398-0.418110.35323-0.16258弹性抗力及摩擦力计算表附表72.各楔块上的抗力集中力1计算公式：R7寸-^^｛八S外方向垂直于衬砌外缘并通过楔块上抗力图形的形心。抗力集中力与摩擦力的合力Ri=R>1+77H为围岩和衬砌间的摩擦系数，取0.2。Ri的作用方向与A,,的方向夹角为0=arctg|7=11.3099。将Ri的方向线延长，使之交于竖直轴，量取夹角Wk，再将Ri分解为水平与竖直两个分力：Rh=sinwk，RV=cosWk以上计算列入附表7%。" *3.计算单位弹性抗力及其相应摩擦角在基本结构中产生的内力弯矩：MOq=-ERfji轴力：N=sina泛Rv-cosa弯矩：MOq=-ERfji式中rji为力Rj到接缝中心点九的力臂。计算见附表8和附表9：Ma0计算表 附表8截面气0384966bhR=1.101669%RQ1362744b人r4i-Rr(bh)r5i-R5r5i(bh)r6i-R6r6i(bh)40.4726-0.1819451.82564-0.702810.6414-0.7066163.13665-1.20751.99437-2.197130.73519-1.0018874.32529-1.665093.29439-3.629332.08709-2.8441785.32424-2.049654.46847-4.922773.38728-4.616续上表截面R=1.029839a,7 hS88845ah0Mar7i-R7r7i9h)r8i-R8r8i9h)4-0.181945-1.409426-4.4065170.77946-0.8027-8.941382.13728-2.20110.97021-0.37726-14.1667、计算表 附表9截面asinacosa&（气）456.52550.8341313840.551570.173341570.62060.9433420210.331820.446661684.76130.9958229540.091310.474475798.90520.987945821-0.15480.251916890100.089337续上表截面sina£R(av£R(a)Hh£cosa"Rh(ah)N(ah)40.1)445892180.343732180.189591-0.045001750.4213542491.410957520.468187-0.04683247860.472493152.773417510.2532280.21926564870.2488791993.77892001-0.584980.83385620680.0893373954.1321456600.089337395单位抗力及相应摩擦力产生得载位移计算见附表10:单位抗力及摩擦力产生的载位移计算表 附表100sMsMbd0sMsMbd电

EhsE0¥y)Mb=-x -2.95x10111763=一953.068x10-6截面0Mb积分1 v M血 M血迭 M°©(y+1)I J I I系数 b0I1/34-0.2458953131.68722.3222499-23.9585189-58.981082 -82.9396009 25-1.4560821131.68723.5237251-185.602617-681.75553 -867.358149 46-4.2613131131.68724.7559483-580.281762 -2899.0877 -3479.36944 27-8.5395018131.68726.0833882-1177.45562 -7475.3125 -8652.76811 48-13.195478131.68727.3884376-1865.5783 -15045.889 -16911.4672 10a=£0sM^lb EhA=b0sH2b EhE-2842.09727 -17863.433 -20705.53010■dwASE-Mb=-x 1-38i809727=—130.821x10-6sEI 2.95x10h700^dwASE-yM^^-x 1137873.433=一822.247x10-6sE[I 2.95x10h7TOC\o"1-5"\h\zA+A==(130.821+822.247)=—953.068x10-6lb 2b闭合差A=0。2.4.4墙底（弹性地基上的刚性梁）位移单位弯矩作用下的转角：一1 1KI80.2x106主动荷载作用下的转角:0 0pap=M8ppa=-2541.54x658.436x106=-1673441.716x10字单位抗力及相应摩擦力作用下的转角：=M80Pa=-14.1667x658.436x10=-9327.891x10ab Ob 66 662.5解力法方程衬砌矢高 f二%=8.065m计算力法方程的系数："11=：11+阪=(48.4921+658.436)x10_6=706.9281x10_6a12=82+fPa=(142.988+658.436x8.065)x10_6=5453.276x10』a2=8 +f20a=(710.137+658.436x8.056)x10尸43537.611x10_6220a=A+pa0+(A+aO )帘—(1732651.425+9458.712bh)x10_62—^A+fo0+(A+必O)xb^-a20zp"ap 25aa h=-(13770996.83+76051.692bh)x106求解方程为：a一aaaaa1-1a?2a20牛43537.611x(1732651.42头9458.712bh)-5453.276<(13770996.83b76051.692bh)x1065453.276-706.9281x43537.611——2—325.517—2.8095b 一h式中X1p225.517X1b=28095a—aa

aa—1a2aX=706：9281x(沮770996.83b76051.692bh)—5453.276<(1732651.425~9458.712bh)5453.276-706.9281x43537.611——2—275.529+2.0987b -h式中：X2p=275.529 X2b=2.0987将以上解得的X1、X2值代入原方程，经校核证明计算正确。2.6计算主动荷载和被动荷载（bh=1）分别产生的衬砌内力计算公式为：0M=X1p+yX2p+MP0N=X2pcosa+NpM广X1。中X2。y+M浏N=Xcosa+N

a 2a a0主、被动荷载作用下衬砌弯矩计算表 附表111111i截面M0pX1px2”Mp111100325.51744970325.5174497111111-94.49649341325.517449745.37957359276.4005299111112-362.3359763325.5174497179.7824637142.9639371111:3-759.4601954325.5174497395.1356799-38.807065811114-1222.122344325.5174497678.2965043-218.30839装:5-1679.239014325.51744971012.071947-341.6496171116-2065.959449325.51744971376.541285-363.90071411117-2332.315038325.51744971749.24893-257.5486581118-2541.539606325.51744972222.1388046.116647354订续上表:11111!截面M:（气）X(a)1a'h7X2ay(ah)Ma(ah)■00-2.80945580-2.8094558■10-2.80945580.345656065-2.46379974线120-2.80945581.369402444-1.4400533611130-2.80945583.0097471940.20029139411114-0.181935003-2.80945585.1665822772.1751914731115-1.409419871-2.80945587.7089487443.4900730731111i6-4.406514627-2.809455810.485110513.26914008311117-8.941303612-2.809455813.324023441.57326402611118-14.16673518-2.809455816.92602407-0.05016691主被动荷载作用下衬砌轴力计算表 附表12截面N0pXcosa2pNpNa(ah)Xcosa2aNa00275.5286799275.528679902.0987010632.09870106128.83634267.1829797296.019317602.0351318912.035131892109.8693242.661936352.53127601.8483551811.848355183228.2642203.4646524431.728873201.5497895991.54978964362.8669151.9721974514.8390786-0.04500171.1575717361.112570045490.47891.42647383581.9044391-0.0468324780.6963951550.649562686591.326425.1572073616.48358170.2192656480.1916223670.410888017659.84-42.65185345617.18818710.833856206-0.324879030.508977188643.76090643.76086040.08933739500.089337392.7最大抗力值的求解考虑到接缝5的径向位移与水平方向有一定的偏移，因此修正后有:TOC\o"1-5"\h\z国 Mp> (y5—yi)sina5Eh_ _ASM-he5bE—I 5i5h计算过程列入附表3中：最大抗力位移修正计算表 附表13截面MiMIe(eh)y5—yiMp(y5—yi)/IM(y5—y.)/1(eh)积分系数1/3042866.4954-369.96953.6732157457.211-1358.9719241136398.4237-324.4513.5085127703.8695-1138.3363124218826.5267-189.63673.020756869.28919-572.835446923-5110.395526.3758212.2391 -11442.6865559.0581017444-28748.43286.444971.2114 -34825.84812346.999433825-44990.896459.59810004£222196.275-2042.585597位移值为:TOC\o"1-5"\h\z8= 技5787x222196.275x0.96334=9648.134x10hp 2.95<10 —671.357878=— x2042.585597x0.96334=—88.6925x10h 2.95x107 —6最大抗力值为：e=—== h 1-8e=—== h 1-8Kh201——+88.6925x106 -62.8计算衬砌总内力按下式计算衬砌内力:M=Mp+b村厂N=N+bhN-衬砌总内力计算表 附表14截面MpMb[M]NpNb0325.5174497-289.308236.20922659275.5286799216.11711251276.4005299-253.713722.6867952296.0193176209.5709752142.9639371-148.2918-5.327870114352.531276190.33734323-38.8070657820.625328-187288732159.59207294-218.3083904223.993845.68544498514.8390786114.56868625-341.6496175359.3958817.74626239581.904439166.889759946-363.9007142336.64495-27.25576374616.483581742.311853227-257.5486578162.00939-95.53926802617.188187152.4127421686.116647354-5.1660180.9506292643.76086049.199661704续上表截面[N]MIMyI=M/N积分系数1/30491.6457924768.29321300.07364911505.5902932987.561508492.05138040.04487242542.868619-701.6125253-457.8021727-0.0098123591.320946-2394.302923-3433.669822-0.0307544629.407765748.70057351843.1510720.00903325648.7941992336.9563658584.1081190.02735346658.795435-3589.236377-17931.82494-0.0413727669.600929-12581.30278-79874.