隧道畢業(yè)設計之明洞計算示例

1、第4章明洞設計明洞長度確定進口端圍巖等級為IV級，坡度比較平緩，因此有很長的超淺埋段。為了施工上的 方便，考慮把超淺埋段設為明洞。坍落拱高度按下式計算h = 0.45 2s1 i B - 5 1-0.45 24-1 1 0.1 12.6-5 .1- 6.36mh。= h = 6.336m q當埋深H Ehq時，即為超淺埋隧道。洞口段Xm#埋7為hq；斜坡坡度為1025, 路面縱坡為1.2%。則有xtan200 - x2% =6.336得x=18.0m在考慮巖石巖性考慮取明洞長度為 50m明洞設置由于明洞圍巖級別很差，垂直壓力和側(cè)向壓力較大，故采用拱式明洞，并假設仰 拱，明洞內(nèi)輪廓線與暗洞內(nèi)輪廓

2、線一致。襯砌厚度為60m襯砌材料采用鋼筋混凝土結(jié)構(gòu)，C25級混凝土，直徑25mmHRB335鋼筋。明洞邊墻用5#漿砌石片回填，拱部用 挖土回填，最低回填土不小于1.5m,填土坡度設為70,以利于排水。明洞配筋圖如下： 4.3襯砌內(nèi)力計算基本資料回填土 y =18kN/m3重度r =22KN / m3 ,計算內(nèi)摩擦角中2 =500 ,混凝土彈性模713136量 Ec =2.95父10 kB , I= bh = 父1父0.6 = 0.018, Ec = 0.531 父 10。1212荷載確定hP =0.45 2sl 1 i B - 5 1= 0.45 24,1 0.1 12.6-5 1 =6.33

3、6H hp時屬于淺埋。 ph =50 tan 70 1.5 =7.639m2 q =rh =18 7.639 =137.502KN /m2e, =rh ta = tan2 7T 中2 )=tan2 5=0.36 TOC o 1-5 h z 42 J6.0013.2993r1二3.14: 2-11=13.299313.2993,=26.59861 3-2y=26.598613.2993,=39.8979二 4二31=39.897913.2993,=53.1972：-5-4y=53.197213.2993,=66.4965：6 二:5 二。1 =66.496513.2993 =79.7958S1

4、=7 S-S1 =7 1.392699 -9.4247778 =0.32411526 1807 y 二 90 -0.3241152 180二92.18488.503.14二。2S 180X 21.3926998.50180 x3.14= 9.3877 8 二:7 乜 =92.1848 - 9.3877, =101.5725另一方面 ：8 一 詢 2 =90 11.5 72 51 0.57 2 5角度閉合差：0接縫中心點坐標計算a =r2 -r1 = 8.20 - 5.70 = 2.50mxi = n sin ： i = 6.00 0.2300 = 1.3802m (x2 = ri sin 1

5、2 = 6.00 0.4477 = 2.6864m . x3 = r1 sin 1 3 = 6.00 0.6414 = 3.8485m (x4 = q sin ： 4 = 6.00 0.8007 = 4.8042m (x5 = r1 sin ： 5 = 6.00 0.9170 = 5.5022m . x6 = r1 sin ： 6 =6.00 0.9842 = 5.9051m . x7 =2 sin ： 7 - a = 8.50 0.9993 - 2.50 = 5.9938m (x8 = r2 sin ： 8 - a = 8.50 0.9797 - 2.50 = 5.8272m - y1 =

6、r1 1 -cos：=6.00 1 -0.9732 =0.1609m(y2 =r1 1 -cos： 2 =6.00 1 -0.8942 = 0.6350m (y3 = r1 1 - cos： 3 =6.00 1 -0.7672 =1.3969m 九X y4 =r1 1 -cos： 4 =6.00 1 -0.5991 = 2.4056m (y5 = r1 1 - cos： 5 ):=6.00 1 -0.3988 = 3.6072my61 -cos： 6 =6.00 1 -0.1772 = 4.9371m , y7-r2 cos： 7 -6.00-8.50 - 0.0381 )=6.3240m ,

7、 , y8 = q -r2 cos： 8 =6.00-8.50 - 0.2006 )=7.7052m計算位移1、單位位移-112暑ds單位位移值計算如下11.392699444.4448 =20.9823 10I 2.95 10SMM2-6%. y 1.39269912 =、21 =Mds -77 1289.1973 = 60.8632 100 hEhI 2.95 10SSW 1 y2EhI1.3926992.95 1079327.0785 = 440.3326 10”閉合差0用辛普生近似計算，按計算列表4.1進行表4,1單位位移計算表截面asin民cos民xydI1/Iy/iy2/I(1+y

8、)2/I積分系數(shù)1/300.00000.00001.00000.00000.00000.600.018055.5560.00000.000055.55561113.2930.23000.97321.38020.16090.600.018055.5568.93891.438374.87174226.5960.44770.89422.68640.63500.600.018055.55635.27722.401148.51262339.8990.64140.76723.84851.39690.600.018055.55677.606108.41319.17414453.1920.80070.5991

9、4.80422.40560.600.018055.556133.46321.50644.34002566.4950.91700.39885.50223.60720.600.018055.556200.40722.881179.23944679.7980.98420.17725.90514.93710.600.018055.556274.281354.21958.28802792.1880.9993-0.03815.99386.32400.600.018055.556351.332221.82980.05664890.0001.00000.00005.82727.70520.600.018055

10、.556428.063298.34210.03151444.481289.96304.29327.07852、載位移(主動荷載在基本結(jié)構(gòu)中引起的位移)豎向力Qj=qbj式中bj為襯砌外緣相鄰兩截面之間的水平投影長度b1 -1.4492m, b2 -1.3420m, b3 -1.2497m, b4 -1.0035m, bs -0.7329m, b6 = 0.4230m, =0.0996m B % b =6.30m = = 6.30m2水平壓力 Ej = eh式中hj為襯砌外緣相鄰兩截面之間的豎直投影長度h1 = 0.1690m, h2 = 0.4831m, h3 = 0.8146m, h4 =

11、1.0592m, h5=1.2616m, h6 =1.3964m, h7 =1.4516m, h8 =1.4299m 、hi =8.0654m : H =8.0655m自重力 G =d s rh =0.60 1.392699 25 = 20.8905kPa 式中d為接縫的襯砌截面厚度。作用在各楔塊上的力均列入表4.2 ,各集中力均通過相應圖形的形心。(1)外荷載在基本結(jié)構(gòu)中產(chǎn)生的內(nèi)力楔塊上各集中力對下一接縫的力臂由圖中量得，分別記為aq,ae,ag內(nèi)力按下式計q e g彎矩M ； = M 二 - ：xQ G - y- E-Qaq - Gag - Ea, , TOC o 1-5 h z ij(4

12、-1)軸力NP =sin1 Q G -cos E ij(4-2)式中Axi,Ayj為相鄰兩接縫中心點的坐標增值，按下式計算Xi = Xi -Xiyi =yi-yi，(4-3)第一截面的MiP，NiP的計算見表4.2及表4.3表4.2彎矩計算表截面集中力力臂-Qaq-Gag-EaeE(Q+G)EE x y-Ax匯(Q+G)-AyEEMp0QGEaqagae00.0 000.0000.0000.00000.00000.00000.0000.0000.0000.0000.0000.00000.00000.0000.0000.0001199.26820.89021.0320.65560.68640.3

13、764-130.640-14.339-7.9170.0000.0001.38020.1090.0000.000-152.8962184.52820.89060.1230.53810.62860.5105-99.294-13.131-30.693220.15821.0321.30620.4741-287.570-9.971-593.5563171.83620.890101.3790.43240.57700.6375-74.302-12.054-64.629425.57681.1551.16210.7619-494.562-61.832-1300.9344137.98320.890131.8200

14、.26150.45470.7093-36.083-9.499-93.500618.302182.5340.95571.0087-590.911-184.122-2215.0485100.77520.890157.0090.09130.32140.7505-9.201-6.714-117.835777.175314.3530.69801.2016-542.468-377.727-3268.993658.1 6320.890173.785-0.08370.17090.75134.868-3.570-130.564898.840471.3620.40291.3299-362.143-626.864-

15、4387.266713.6 9520.890180.655-0.25640.00900.71433.511-0.188-129.042977.894645.1470.08871.3869-86.739-894.754-5494.47780.0 0020.890177.9540.0000-0.10570.65480.0002.208-116.5241012.479825.801-0.16661.3812168.679-1140.597-6580.711表4.3軸力計算表截面sin acos aE(Q+G)EEsin a E (Q+G)COSa EENp000.00001.00000.0000.0

16、000.0000.0000.00010.23000.9732220.15821.03250.63620.46930.16820.44770.8942425.57681.155190.53072.569117.96130.64140.7672618.302182.534396.579140.040256.53940.80070.5991777.175314.353622.284188.329433.95550.91700.3988898.840471.362824.237187.979636.25860.98420.1772977.894645.147962.443114.320848.1237

17、0.9993-0.03811012.479825.8011011.770-31.4631043.23381.00000.00001033.3691003.7551033.3690.0001033.369基本結(jié)構(gòu)中，主動荷載產(chǎn)生彎矩的校核為0 B B、12.60 12.60、M；q = -q X8 -尸-137.502父父 5.8272 尸2319.2280 TOC o 1-5 h z q 2 4 J24 )0 e 2124.4522M 8e - - - H 2 = 8.06542 - -4047.356822M0g =，Gi X8 - Xiagi = -280.1897M*=M0m8-M4=-

18、2319.2280-4047.3568-280.1897=-6646.7745pqg6646.7745-6580.7110100% =1.0039%閉合差另一方面，從表12中得到M8P =-6580.71106580.7110(2)主動荷載位移計算過程見表4.4 。表4.4主動荷載位移計算表截面Mp01/Iy/I1+yMp0/IMp0y/IMp0(1+y)/I積分系數(shù)1/300.00055.55560.00001.00000.0000.0000.00011-152.89655.55568.93891.1609-8494.206-1366.718-9860.92442-593.55655.555

19、635.27781.6350-32975.354-20939.350-53914.70323-1300.93455.555677.60562.3969-72274.163-100959.778-173233.94044-2215.04855.5556133.64463.4056-123058.307-296029.063-419087.37025-3268.99355.5556200.40024.6072-181610.855-655106.677-836717.53246-4387.26655.5556274.28365.9371-243737.204-1203354.950-1447092

20、.15427-5494.47755.5556351.33367.3240-305248.990-1930394.610-2235643.59948-6580.71155.5556428.06708.7052-365595.362-2816985.385-3182580.7471E-1145216.648-5536314.413-6681531.061截面，一 0人s M1m0ASk M p1.392699常4P =1-ETds fc 2 =-7*1145216.64 8 = -54065.8332 M 100 hEhI2.95黑107sM2m!AS_ yM p 1,3926996 2-ds7

21、5536314.413 =-261370.1541 10一2p 0 EhIEh I 2.95 107計算精度校核:1P :2P =754065.8332 261370.1541 106 =-315435.9873 10-6S(1 + y M P 1.392699_6.：sp=p = -7 6681531.061 二315435.9874 10EhI2.95 10閉合差. ; ： 03、載位移(單位彈性抗力及相應的摩擦力引起的位移)(1)各接縫處的抗力強度 TOC o 1-5 h z 抗力上零點假定在接縫3處， =39.8979；最大抗力值假定在接縫5處，a5 M66.49650 =uh ;最大

22、抗力值以上各截面抗力強度按下式計算2 2 .cos b - cos iG.=。.22hcos 二 b - cos 二 h(4-4)查表算得仃3 = 0仃4 =0.5347仃 h仃5 = 3最大抗力值以下各截面抗力強度按下式計算(,2、9=1一% yh)(4-5)式中 yi為所考察截面外緣點到h點的垂直距離;yh為墻腳外緣點到h點的垂直距離。由圖中量得 . y6 = 1.2787m, y7 = 2.7283m, y8 =4.1582m1 127872 1則 仃6 = 1 -25h = 0.9057。h4.15822 J= 0.5695ch(2.7283212 *4.15822二 8 二0按比例將

23、所求得的抗力繪于圖上。(2)各楔塊上抗力集中力R；按下式近似計算一，1R = l&Si 外、2)(4-6)式中AS外為楔塊i的外緣長度，可通過量取夾角，用弧長公式求得，R；的方向垂直于襯砌外緣，并通過楔塊上抗力圖形的形心。(3)抗力集中力與摩擦力的合力 R按下式計算Ri = R；. 12(4-7)式中N為圍巖于襯砌間的摩擦系數(shù)，此處 卜=0.3則 Ri = R； 1 0.32 =1.0440 R；其作用方向與抗力集中力 R，的夾角P =arctanN = arctan0.3 = 16.6992。由于 摩擦阻力的方向與襯砌位移的方向相反， 其方向向上，畫圖時也可取 切向/徑向 =3/10的比例求

24、出合力R的方向.R的作用點即為R；與襯砌外緣的交點。將Ri的方向線延長，使之交于豎直軸，量取夾角 中將R分解為水平與豎 直兩個分力。Rh = R sin甲 kRV = R cos k(4-8)以上計算列入表4.5中表4.5 R分解為水平與豎直兩個分力計算表截面6 ( 6 h)R( b h)小ksin。kcos。kRH( bh)Rv( 6 h)30.00000.00000.00000.00000.00000.00000.00000.00000.000040.53470.26741.46230.408265.86610.91260.40890.37250.166951.00000.76741.46

25、231.171577.32790.97560.21941.14290.257060.90570.95291.46231.454789.71600.99990.00501.45460.007370.56950.73761.45761.1224106.52500.9587-0.28441.0760-0.319280.00000.28481.44180.4106111.82480.9283-0.37180.3812-0.1527(4)計算單位抗力及其相應的摩擦力在基本結(jié)構(gòu)中產(chǎn)生的內(nèi)力彎矩M后=-Z 0 r /(4-9)軸力N： =sinoii RV 一 cosi RH(4-10)式中r為力Rj至接縫

26、中心點ki的力臂，有圖上量得計算見表4.6及表4.7 。表4.6單位抗力及其相應的摩擦力在基本結(jié)構(gòu)中產(chǎn)生彎矩計算表截面R4=0.4082 hR5=1.1715 bhR6=1.4547 bhR7=1.1224 bhR8=0.4106 hM(r0r4i-R4r4i(/)r5i-R5r5i(/)r6i-R6r6i(bh)r7i-R7r7i(bh)r8i-R8r8i(bh)(bh)40.4944-0.2018-0.201851.8763-0.76590.6829-0.8000-1.565963.2547-1.32862.0686-2.42340.7766-1.1297-4.881774.5567-1.

27、86003.4413-4.03152.1640-3.14800.8268-0.9280-9.967585.7490-2.34674.7522-5.56723.5443-5.15592.2112-2.48191.0158-0.4171-15.9688表4.7單位抗力及其相應的摩擦力在基本結(jié)構(gòu)中產(chǎn)生軸力計算表截面asin acos a2 Rv( a h)sin a 2 Rv( o-h)NRH(bh)cos a 2 RH(ah)Na0( ah)453.19720.80070.59910.16690.13360.37250.2232-0.0895566.49650.91700.39880.42390.

28、38881.51540.6044-0.2156679.79580.98420.17720.43120.42442.97000.5263-0.1019792.18480.9993-0.03810.11200.11194.0460-0.15420.2661890.00001.00000.0000-0.0407-0.04074.42720.0000-0.0407(5)單位抗力及相應摩擦力產(chǎn)生的載位移計算見表4.8。表4.8載位移計算表截面Ma0( ah)1/Iy/I1+yM(r0/IM(r0y/IMb 0(1+y)/I積分系數(shù)1/34-0.201855.5556133.64463.4056-11.2

29、119-26.9714-38.183325-1.565955.5556200.40024.6072-86.9958-313.8112-400.807046-4.881755.5556274.28365.9371-271.2032-1338.9573-1610.160427-9.967555.5556351.33367.3240-553.7504-3501.9175-4055.667848-15.968855.5556428.06708.7052-887.1549-6835.7060-7722.86101E-1338.3233-8276.8260-9615.1493S M 1M 0M 0_ 瓦=313.6mm且 2as =80mm為小偏心受壓構(gòu)件所以k=2截面符合驗算如下_2KNe 0.5Rwbh0 +RgAg(h0 -as )_ _ _ 9 _2914 277 0.518.51000 560_.KNe e ,as = as故上式顯然湎足。在垂直于彎矩作用平面內(nèi)的強度驗算長細比1 J1.5147 =19.19, =0.89h 0.6Nu =0.9 Q A f sd Asd =0.9 0.89 60000 18.5 268 1946二 8472